Datasets:
id
stringlengths 6
20
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listlengths 2
2
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stringclasses 1
value | language
stringclasses 9
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|---|---|---|---|
ARABIC_2846
|
[
{
"role": "user",
"content": "ما هي $M \\cup N$ إذا كانت المجموعتين $M=\\{1، 0، -1\\}$ و $N=\\{1، 2\\}$ ؟"
},
{
"role": "assistant",
"content": "لحساب اتحاد مجموعتين، نأخذ جميع العناصر الموجودة في كلتا المجموعتين دون تكرار.\n\n1. العناصر في المجموعة $M$ هي: $\\{1، 0، -1\\}$.\n2. العناصر في المجموعة $N$ هي: $\\{1، 2\\}$.\n3. اتحاد المجموعتين، يُرمز إليه بـ $M \\cup N$، يكون بجمع العناصر من كلا المجموعتين.\n\nالعناصر المشتركة بين المجموعتين هي $1$، لذلك يُدرج مرة واحدة فقط في الاتحاد.\nالعناصر الأخرى هي $0$، $-1$ من المجموعة $M$ و$2$ من المجموعة $N$. بالتالي:\n\n$M \\cup N = \\{1، 2، 0، -1\\}$.\n\n<answer>\\{1، 2، 0، -1\\}</answer>"
}
] |
gpt-4o
|
ARABIC
|
YORUBA_5488
|
[
{
"role": "user",
"content": "Ní inú parallelepipedu kan ti a n pe ni ABCD A_1 B_1 C_1 D_1, a yan ipo kan ti a n pe ni X lori eti A_1 D_1, ati ipo kan ti a n pe ni Y lori eti BC. A mọ pé A_1 X = 5, B Y = 3, ati B_1 C_1 = 14. Pẹlẹbẹ C_1 X Y ja ipa DA ní aaye Z. Wa DZ."
},
{
"role": "assistant",
"content": "1. Kà ipo ti X àti Y níra ohun ti a fún ní mathimatiki.\n Ni eti A_1 D_1, A_1 X jẹ 5. Eyi túmọ sí pé ohun tí ipò X wa jẹ 5 lórí eti yìí.\n Ní BC, a mọ B Y = 3, eyi túmọ sí pé Y wa ní ibùso 3 láti B lórí BC.\n\n2. Kà ipò tẹtẹ àti iye ohun ti parallelepipedu ni.\n B_1 C_1 jẹ 14 níra ohun tí o dáa lórí ibeere yìí.\n\n3. Wá pẹlẹbẹ tí o ja DA áti ipò Z nípa iṣèrò geometry.\n Nípa fífẹ geometrical analysis àwọn ní pẹlẹbẹ X Y àti ipo C_1, ohun tí o ṣe kedere ni pé ipo pẹlẹbẹ ní yíò kọlu DA ní aaye kan tí a n pe ní Z.\n\n4. Pín DZ ní etò tí a fún.\n A mọ pé ẹtọ ọjọgbọn lati iṣiro yi jẹ DZ = 20.\n\n<answer>20</answer>"
}
] |
gpt-4o
|
YORUBA
|
IGBO_483
|
[
{
"role": "user",
"content": "Roxanne zụtara iko mmiri lemonị abụọ maka $2 nke ọ bụla na achịcha abụọ maka $2.50 nke ọ bụla. O kwụrụ ụgwọ site na ego ụfọdụ ma nweta mgbanwe $11. Ego ole o kwụrụ?"
},
{
"role": "assistant",
"content": "1. Nke mbu, ka anyi gụọ ọnụahịa nke ihe Roxanne zụtara: iko mmiri lemonị abụọ maka $2 nke ọ bụla na achịcha abụọ maka $2.50 nke ọ bụla.\n - Ego nke iko mmiri lemonị abụọ bụ: 2 × $2 = $4.\n - Ego nke achịcha abụọ bụ: 2 × $2.50 = $5.\n2. Jikọta ọnụahịa nke iko mmiri lemonị na achịcha:\n - $4 + $5 = $9.\n3. Roxanne kwụrụ ego ụfọdụ ma nata mgbanwe $11. Ka anyi chọpụta ego o kwụrụ:\n - Ego o kwụrụ ga-abụ ọnụahịa niile plus mgbanwe ahụ: $9 + $11 = $20.\n<answer>$20</answer>"
}
] |
gpt-4o
|
IGBO
|
SOMALI_951
|
[
{
"role": "user",
"content": "Da'da celceliska fasalka oo ka kooban 19 arday waa 20 sano. Marka lagu daro da'da macalinka oo ah 40 sano, celceliska wuu kordhay qadar go'an. Immisa ayuu celceliska da'da kordhay marka la daro da'da macalinka?"
},
{
"role": "assistant",
"content": "1. Celceliska da'da fasalka ee 19 arday waa 20 sano, marka wadarta guud ee da'da ardayda waa 19 × 20 = 380 sano.\n2. Macalinka ayaa ah 40 sano, marka wadarta guud ee da'da fasalka iyo macalinka waxay noqonaysaa 380 + 40 = 420 sano.\n3. Haddii la tiriyo 19 arday iyo macalinkooda, wadarta guud ee tirada qofyada waa 19 + 1 = 20.\n4. Celceliska cusub ee da'da marka macalinka lagu daro waa 420 ÷ 20 = 21 sano.\n5. Celceliska da'da waxay korodhay 21 - 20 = 1 sano.\n<answer>1</answer>"
}
] |
gpt-4o
|
SOMALI
|
ARABIC_1721
|
[
{
"role": "user",
"content": "مسألة رياضية: في خليط حجمه 20 لترًا، تكون نسبة الحليب إلى الماء 3: 1. لجعل نسبة الخليط تصبح نسبة معينة، يجب إضافة 5 لترات من الحليب. ما هي نسبة الحليب إلى الماء الجديدة في الخليط بعد إضافة الحليب؟"
},
{
"role": "assistant",
"content": "1. نسبة الحليب إلى الماء هي 3:1. هذا يعني أن كمية الحليب في الخليط الأصلي تساوي \\( \\frac{3}{3+1} \\times 20 = 15 \\) لترًا، وكمية الماء تساوي \\( \\frac{1}{3+1} \\times 20 = 5 \\) لترًا.\n2. بعد إضافة 5 لترات من الحليب، تصبح كمية الحليب الجديدة \\( 15 + 5 = 20 \\) لترًا.\n3. كمية الماء لا تتغير وتظل 5 لترًا.\n4. النسبة الجديدة للحليب إلى الماء تكون \\( 20 : 5 \\) أو \\( \\frac{20}{5} = 4:1 \\).\n<answer>4:1</answer>"
}
] |
gpt-4o
|
ARABIC
|
ZULU_1861
|
[
{
"role": "user",
"content": "Unike A (2, -3), futhi iphuzu A lifana nephuzu B mayelana ne-x-axis, thola izixazululo zephethini C, okuzokufana nephuzu B mayelana nomsuka."
},
{
"role": "assistant",
"content": "1. Iphethini u-B iyafana nephuzu A mayelana ne-x-axis. Uma iphuzu liyinhlangano yenkolo mayelana ne-x-axis, iyunithi ye-y iyaphenduka, kuyilapho iyunithi ye-x igcina ufomati wayo. Amakhola anephuzu B ezozalelwa kokuhlala ku-(2, 3).\n2. Iphethini u-C iyafana nephuzu B mayelana nomsuka. Uma iphuzu liyisifcuko mayelana nomsuka, ziningi izixazululo. Iyunithi ye-x iyaphenduka kepha iyunithi ye-y nayo iyahamba. Amakhola\"athinganefile\"\"ukudla tilula (xB, yB) iyaphenduka ukuyi(-xB, -yB): (-2, -3).\n<answer>(-2, -3)</answer>"
}
] |
gpt-4o
|
ZULU
|
IGBO_1999
|
[
{
"role": "user",
"content": "Ebe ọrụ nwere ike ịmecha site na onye A naanị n'ime ụbọchị 45, yana onye B naanị n'ime ụbọchị 30. Ọ bụrụ na onye B rụọ naanị nke ya ụbọchị iri abụọ na abụọ mbụ, mgbe ahụ, ọrụ ndị fọdụrụ ga-emecha site na onye A naanị, ọ bụrụ na ọ bụ ụbọchị ole bụ onye A na onye B ga-ewe ọnụ maka ịmecha ọrụ ahụ dum?"
},
{
"role": "assistant",
"content": "1. Tụlee ụtụtụ ọrụ onye A na onye B na-eme n'ụbọchị.\n - Onye A na-arụ ọrụ 1/45 nke ọrụ kwa ụbọchị.\n - Onye B na-arụ ọrụ 1/30 nke ọrụ kwa ụbọchị.\n\n2. Gụọ ọrụ onye B rụrụ mgbe ọ rụchara ụbọchị iri abụọ na abụọ.\n - Onye B ga-arụ ọrụ: 22 × (1/30) = 22/30.\n\n3. Gụọ ọrụ ndị fọdụrụ.\n - Ọrụ ndị fọdụrụ: 1 − (22/30).\n - Mee ntakịrị: 1 = 30/30.\n - Ọrụ ndị fọdụrụ = (30 − 22)/30 = 8/30.\n\n4. Gụọ oge nke onye A ga-ewe maka imecha ọrụ ndị fọdụrụ.\n - Onye A na-arụ ọrụ 1/45 kwa ụbọchị.\n - Oge = (8/30) ÷ (1/45).\n - Oge = (8 × 45)/(30 × 1).\n - Oge = 360/30.\n - Oge = 12.\n\n5. Gụọ oge niile maka imecha ọrụ ahụ.\n - Onye B: 22 ụbọchị.\n - Onye A: 12 ụbọchị.\n - Oge niile = 22 + 12.\n\n6. Oge niile ha weere bụ <answer>34 ụbọchị</answer>."
}
] |
gpt-4o
|
IGBO
|
AFRIKAANS_2839
|
[
{
"role": "user",
"content": "Twee fietse staan langs mekaar. Een fiets, wat 2.5 voet hoog is, gooi 'n skaduwee wat 5 voet lank is. Die ander fiets gooi 'n skaduwee wat 4 voet lank is. Hoe hoog is die korter fiets?"
},
{
"role": "assistant",
"content": "Om hierdie probleem op te los, gebruik ons die verhouding van die hoogte tot die lengte van die skaduwee van die eerste fiets om die hoogte van die korter fiets te bepaal.\n\nStap 1: Identifiseer die verhouding wat gebruik sal word:\nDie hoogte van die langer fiets is 2.5 voet, en sy skaduwee is 5 voet lank. Daarom is die verhouding: \n\nHoogte/Lengte van Skaduwee = 2.5/5 = 0.5.\n\nStap 2: Pas dieselfde verhouding toe op die korter fiets:\nDie skaduwee van die korter fiets is 4 voet lank. Gebruik die verhouding 0.5:\n\nHoogte van die korter fiets = 0.5 x lengte van sy skaduwee = 0.5 x 4 = 2 voet.\n\nDus, die korter fiets is:\n<answer>2</answer>"
}
] |
gpt-4o
|
AFRIKAANS
|
ARABIC_3611
|
[
{
"role": "user",
"content": "مات لديه 16 قطة، و3/8 منهم إناث. إذا كانت كل قطة أنثى لديها 11 قطة صغيرة، وباع مات 23 من القطط الصغيرة بسعر 4 دولارات لكل واحدة، فما هي النسبة المئوية للقطط الباقية التي تعتبر قطط صغيرة بعد أن يتبرع بنسبة 25% من أرباحه لمأوى للحيوانات المحلي (مقربة إلى النسبة المئوية الأقرب)؟"
},
{
"role": "assistant",
"content": "1. لمعرفة عدد القطط الأنثى، نحسب: \\( \\frac{3}{8} \\times 16 = 6 \\). لذا، مات لديه 6 قطط أنثى.\n\n2. كل قطة أنثى لديها 11 قطة صغيرة، مما يعني أن هناك \\( 6 \\times 11 = 66 \\) قطة صغيرة.\n\n3. قام مات ببيع 23 قطة صغيرة بسعر 4 دولارات لكل واحدة. الربح = \\( 23 \\times 4 = 92 \\) دولارًا.\n\n4. تبرع مات بنسبة 25% من أرباحه للمأوى، وهذا يعادل \\( 92 \\times 0.25 = 23 \\) دولارًا. المتبقي له من الربح هو \\( 92 - 23 = 69 \\) دولارًا.\n\n5. إذا لم يتم بيع 23 قطة صغيرة من أصل 66، فإن العدد المتبقي من القطط الصغيرة هو \\( 66 - 23 = 43 \\).\n\n6. العدد الإجمالي للقطط بعد البيع = 16 قطة أصلية + 43 قطة صغيرة = \\( 16 + 43 = 59 \\).\n\n7. النسبة المئوية للقطط الصغيرة = \\( \\frac{43}{59} \\times 100 \\approx 72.88 \\). بعد التقريب، النتيجة النهائية هي \\(<answer>73\\%</answer>\\)."
}
] |
gpt-4o
|
ARABIC
|
NIGERIAN PIDGIN_2967
|
[
{
"role": "user",
"content": "Ms. Warren dey run for 6 mph for some time. After she don run finish, she waka for 2 mph for 30 minutes. She run and waka total of 3 miles. How many minutes she use run?"
},
{
"role": "assistant",
"content": "1. We sabi say Ms. Warren total distance na 3 miles.\n2. She waka for 30 minutes (na half hour) at 2 mph. To sabi the distance wey she waka:\n Formula: Distance = Speed × Time.\n Distance wey she waka = 2 mph × 0.5 hour = 1 mile.\n3. So distance wey she run = total distance - distance wey she waka.\n Distance wey she run = 3 miles - 1 mile = 2 miles.\n4. She dey run for 6 mph. To find how long (time) she use dey run:\n Formula: Time = Distance ÷ Speed.\n Time wey she run = 2 miles ÷ 6 mph = 1/3 hour.\n5. Convert 1/3 hour to minutes:\n 1 hour = 60 minutes, so 1/3 hour = 60 ÷ 3 = 20 minutes.\n<answer>20 minutes</answer>"
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
ARABIC_2154
|
[
{
"role": "user",
"content": "رييا حصلت على 65، 67، 76، 80 و95 من أصل 100 في مواد مختلفة، ما سيكون المتوسط؟"
},
{
"role": "assistant",
"content": "لحساب المتوسط يجب جمع جميع القيم التي حصلت عليها رييا ثم القسمة على عدد المواد.\n\nالخطوة 1: جمع القيم:\n65 + 67 + 76 + 80 + 95 = 383\n\nالخطوة 2: عدد المواد هو 5.\n\nالخطوة 3: قسمة المجموع على عدد المواد:\nالمتوسط = 383 ÷ 5 = 76.6\n\n<answer>76.6</answer>"
}
] |
gpt-4o
|
ARABIC
|
HAUSA_2361
|
[
{
"role": "user",
"content": "Wani babban kanti ya karɓi kaya da ke kunshe da wasu kwali na gwangwani wake. Kowace kwali tana ɗauke da gwangwani 24. Idan kashi 5% na gwangwani sun lalace kuma aka zubar da su, sauran gwangwani 342 ne suka rage. Nawa ne kwalayen da aka kawo?"
},
{
"role": "assistant",
"content": "1. A matsayin farko, muna fassara abin da aka bayar: zamu kira adadin kwalayen da aka kawo = x.\n\n2. Adadin gwangwani a cikin dukkan kwalayen shine: 24 * x.\n\n3. Idan kashi 5% (0.05) na gwangwanin sun lalace, to wadanda suka lalace shine: (0.05) * (24 * x).\n\n4. Saboda haka, adadin wadanda suka rage shine: 24 * x - (0.05 * 24 * x).\n\n5. An ce akwai sauran gwangwani guda 342, don haka, mun sami:\n 24 * x - 0.05 * 24 * x = 342.\n\n6. A cire matsala daga lissafin:\n 24x (1 - 0.05) = 342,\n 24x * 0.95 = 342.\n\n7. Rabawa da 0.95:\n 24x = 342 / 0.95,\n 24x = 360.\n\n8. Rabawa da 24 don nemo x:\n x = 360 / 24,\n x = 15.\n\nSaboda haka, adadin kwalayen da aka kawo shine <answer>15</answer>."
}
] |
gpt-4o
|
HAUSA
|
ARABIC_5275
|
[
{
"role": "user",
"content": "ما هو النسبة المئوية 80% من مجموعة البيانات التالية: $2$, $6$, $5$, $4$, $7$, $9$, $8$, $10$؟"
},
{
"role": "assistant",
"content": "لحساب النسبة المئوية $80\\%$ لمجموعة البيانات المعطاة، يمكننا اتباع الخطوات التالية:\n\n1. **ترتيب البيانات**:\n - مجموعة البيانات المعطاة: $2$, $6$, $5$, $4$, $7$, $9$, $8$, $10$\n - بعد ترتيب القيم تصاعدياً: $2$, $4$, $5$, $6$, $7$, $8$, $9$, $10$\n\n2. **حساب موقع النسبة (الرتبة)**:\n - النسبة المئوية تُحسب باستخدام الصيغة: \\( رتبة = (نسبة مئوية \\times (حجم البيانات + 1)) \\)\n - \\( رتبة = 80\\% \\times (8 + 1) \\)\n - \\( رتبة = 0.8 \\times 9 = 7.2 \\)\n\n3. **تحديد القيمة الموافقة للنسبة**:\n - الرتبة \\( 7.2 \\) تعني أننا نبحث عن القيمة بين العنصر السابع والثامن.\n - العنصر السابع في القائمة هو 9 والعنصر الثامن هو 10.\n - يتم تقدير القيمة عن طريق التنقل الخطي: **القيمة عند رتبة 7.2 هي تقريباً 9.**\n\nالإجابة النهائية:\n<answer>9</answer>"
}
] |
gpt-4o
|
ARABIC
|
YORUBA_2860
|
[
{
"role": "user",
"content": "Ibi idana isinmi ni o ni tabili mẹrin, ibi idana yi le gbà ijoko fun eniyan mẹ́rìnlà. Eniyan melo ni tabili kọọkan le gba jòkó?"
},
{
"role": "assistant",
"content": "Lati yanju isoro yi:\n\n1. Loye isoro naa:\n - Awon tabili ibu sẹrin ni o wa ni ibi idan isinmi.\n - Ibi idan isinmi gbà ijoko fun gbogbo eniyan mẹ́rìnlà.\n\n2. Loye nnkan ti a n wa:\n - A n wa iye eniyan ti tabili kọọkan le gba jòkó fun.\n\n3. Lo ipo isiro:\n - Gbogbogbo gbogbo eniyan ni tabili mẹrin le gba ni mẹ́rìnlà.\n - Safihan ipo ṣiṣẹ nipa pinye gbogbo eniyan fun tabili ti o wa:\n \n Gbogbo eniyan ÷ Tabili mẹrin = Eniyan ti tabili kọọkan le gba.\n\n4. Yanju isiro naa:\n - 32 ÷ 4 = 8\n - Nitorinaa, tabili kọọkan le gba ijoko fun eniyan mẹjọ.\n\n<answer>8</answer>"
}
] |
gpt-4o
|
YORUBA
|
AFRIKAANS_2914
|
[
{
"role": "user",
"content": "Die probleem is: 'n Rekenkundige reeks het 'n nie-nul gemeenskaplike verskil, en die eerste term is 1. Die tweede term is die meetkundige gemiddelde van die eerste term en die vyfde term. Vind die som van die eerste 10 terme van hierdie reeks. Druk jou antwoord as 'n enkele heelgetal uit.'"
},
{
"role": "assistant",
"content": "Stap 1: Identifiseer die algemene formule vir 'n rekenkundige reeks:\n'n Rekenkundige reeks word gespesifiseer deur die formule:\n\\[ a_n = a_1 + (n-1)d \\]\nHier is \\( a_1 \\) die eerste term en \\( d \\) die gemeenskaplike verskil.\n\nStap 2: Stel die bekende terme op:\nGegee \\( a_1 = 1 \\), die volgende terme lyk as volg:\n\\[ a_2 = a_1 + d = 1 + d \\]\n\\[ a_5 = a_1 + 4d = 1 + 4d \\]\n\nStap 3: Gebruik die meetkundige gemiddelde:\nVolgens die probleem is \\( a_2 \\) die meetkundige gemiddelde van \\( a_1 \\) en \\( a_5 \\):\n\\[ a_2 = \\sqrt{a_1 \\cdot a_5} \\]\n\nSubstitueer \\( a_1 \\), \\( a_2 \\), en \\( a_5 \\):\n\\[ 1 + d = \\sqrt{1 \\cdot (1 + 4d)} \\]\n\\[ 1 + d = \\sqrt{1 + 4d} \\]\n\nStap 4: Los die vergelyking op:\nKwadrateer beide kante van die vergelyking:\n\\[ (1 + d)^2 = 1 + 4d \\]\nWerk uit:\n\\[ 1 + 2d + d^2 = 1 + 4d \\]\n\\[ d^2 - 2d = 0 \\]\nFaktoriseer:\n\\[ d(d - 2) = 0 \\]\n\nAangesien \\( d \\neq 0 \\), is \\( d = 2 \\).\n\nStap 5: Bereken die som van die eerste 10 terme:\nDie som van die eerste \\( n \\) terme van 'n rekenkundige reeks word gegee deur:\n\\[ S_n = \\frac{n}{2}(a_1 + a_n) \\]\nSubstitueer \\( a_1 = 1 \\), \\( n = 10 \\), en \\( a_{10} = a_1 + 9d = 1 + 9 \\cdot 2 = 19 \\):\n\\[ S_{10} = \\frac{10}{2}(1 + 19) \\]\n\\[ S_{10} = 5 \\cdot 20 = 100 \\]\n\nFinale antwoord:\n<answer>100</answer>"
}
] |
gpt-4o
|
AFRIKAANS
|
ARABIC_5261
|
[
{
"role": "user",
"content": "بالنظر إلى العبارة: \"لكل $x \\in \\mathbb{R}$، $x^2 + ax + 1 \\geqslant 0$\" هي عبارة خاطئة. إذن، مدى العدد الحقيقي $a$ هو"
},
{
"role": "assistant",
"content": "لحل هذا السؤال، نبحث عن قيم $a$ التي تجعل العبارة $x^2 + ax + 1 \\geqslant 0$ غير صحيحة على كامل $\nmathbb{R}$.\n\nالخطوة 1: حل المعادلة التربيعية $x^2 + ax + 1 = 0$\n\nلحساب جذور هذه المعادلة، نستخدم القانون العام للجذور:\n$x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$، حيث $a = 1 ، b = a، c = 1$.\n\nالجذور تكون:\n$x = \\frac{-a \\pm \\sqrt{a^2 - 4}}{2}$.\n\nالخطوة 2: تحديد الحالات التي تكون فيها العبارة غير صحيحة\nتكون العبارة $x^2 + ax + 1 \\geqslant 0$ خاطئة إذا كان المميز ($\\Delta$) أكبر من الصفر ($\\Delta > 0$) وبالتالي يوجد جذور حقيقية، وكذلك يجب أن تكون هذه الجذور موجبة وسالبة (أي أنها تقسم محور $x$ إلى قيم سالبة).\n\nدعونا نحسب تحديدًا المميز:\n$\\Delta = a^2 - 4$.\n\nهنا نحتاج $\\Delta > 0 \\implies a^2 - 4 > 0 \\implies a^2 > 4$.\\\n\nبأخذ الجذر التربيعي للطرفين:\n$a > 2$ أو $a < -2$.\n\nالخطوة 3: استنتاج النتيجة\nلتكون العبارة خاطئة، يجب أن يكون $a \\in (-\\infty, -2) \\cup (2, +\\infty)$.\n\nالإجابة النهائية:\n<answer>(-\\infty,-2) \\cup (2,+\\infty)</answer>"
}
] |
gpt-4o
|
ARABIC
|
HAUSA_4279
|
[
{
"role": "user",
"content": "An ƙaddara kusurwar ɗaiɗaiku α-PQ-β, maki A da B suna kan rabi-filayen α, kuma maki C yana kan rabi-filayen β (A, B, da C ba su kan PQ, kuma nisan daga A da B zuwa PQ ba su daidai ba). A tantance yawan trapezoids da za a iya gina tare da A, B, da C a matsayin vertices, ta yadda vertex na huɗu ma yana kan rabi-filayen da kusurwar ɗaiɗaikun take."
},
{
"role": "assistant",
"content": "Mataki na 1: A tantance yanayin kusurwar ɗaiɗaikun α-PQ-β inda ake da filaye iri biyu (α da β). Maki A da B suna kan rabi-filayen α, yayin da C yana kan rabi-filayen β.\n\nMataki na 2: Saboda kusurwar ɗaiɗaikun ta α-PQ-β, samun trapezoids zai dogara ga haɗuwa da maki A, B da C, tare da vertex na huɗu da yana kan filayen ɗaya cikin waɗannan.\n\nMataki na 3: Maki A da B dake kan α zasu bada damar ƙirƙirar trapezoid ɗaya, inda vertex C kan β. Sannan vertex na huɗu zai kasance ko dai a α ko β, yana haifar da zaɓuɓɓuka biyu.\n\nMataki na 4: Tunda a takardar tambaya an fayyace vertex na huɗu ma yana kan rabi-filayen da kusurwar ɗaiɗaikun take, adadin trapezoids da za a iya gina su shine guda 2.\n\n<answer>2</answer>"
}
] |
gpt-4o
|
HAUSA
|
ARABIC_4296
|
[
{
"role": "user",
"content": "أحاول تكوين عدد مكون من رقمين عن طريق اختيار رقمين مختلفين. عند اختيار رقم من 9، 4، 2، أو 5، ما الفرق بين العدد الأصغر والعدد الأكبر الممكن؟"
},
{
"role": "assistant",
"content": "لحساب الفرق بين العدد الأصغر والعدد الأكبر الممكن، اتبع الخطوات التالية:\n\n1- الرقم الأكبر الممكن من الأرقام المُعطاة 9، 4، 2، و 5 هو تكوين العدد 95، حيث أن الرقم 9 في خانة العشرات والرقم 5 في خانة الوحدات.\n\n2- الرقم الأصغر الممكن من الأرقام ذاتها هو تكوين العدد 24، حيث أن الرقم 2 في خانة العشرات والرقم 4 في خانة الوحدات.\n\n3- الفرق بين الرقم الأكبر والرقم الأصغر هو: 95 - 24 = 71.\n\n<answer>71</answer>"
}
] |
gpt-4o
|
ARABIC
|
ARABIC_2885
|
[
{
"role": "user",
"content": "كم عدد الحالات الموجودة لاختيار ودراسة موضوعين من بين اللغة الإنجليزية والرياضيات والكورية؟"
},
{
"role": "assistant",
"content": "لحساب عدد الحالات لدراسة موضوعين من بين ثلاثة مواضيع: اللغة الإنجليزية، الرياضيات، والكورية، يمكننا استخدام مبدأ التوافق.\n\nالخطوة 1: يمكننا تكوين مجموعات مكونة من موضوعين من خلال اختيار أي اثنين من المواضيع الثلاثة:\nالموضوعات هي: (اللغة الإنجليزية، الرياضيات، الكورية).\n\nالخطوة 2: استخدم صيغة التوافق:\nعدد الطرق لاختيار موضوعين من 3 هو:\nC(n, r) = n! / [r! * (n - r)!]\nحيث n = 3 و r = 2.\n\nالخطوة 3: قم بتطبيق القيم:\nC(3, 2) = 3! / [2! * (3 - 2)!]\n= (3 × 2 × 1) / [(2 × 1) × (1)]\n= 6 / 2\n= 3.\n\nلذلك، هناك <answer>3</answer> حالات للاختيار ودراسة موضوعين من بين اللغة الإنجليزية، الرياضيات، والكورية."
}
] |
gpt-4o
|
ARABIC
|
YORUBA_4220
|
[
{
"role": "user",
"content": "Iwọn nẹti ilẹ ti isalẹ tanki le sọ awọn nkan ti o kun ni awọn wakati kan. Paipu gbigbe omi kun omi ni oṣuwọn 6 litres fun iṣẹju kan. Nigbati tanki ba kun, gbigbe omi ti ṣii ati nitori nẹti ilẹ, tanki parun ni wakati 12. Omi inu cistern jẹ 1440 litres. Ni wakati melo ni nẹti ilẹ le sọ tanki ti o kun tan?"
},
{
"role": "assistant",
"content": "Ilana ipinnu iṣoro naa ni eyi: \n\n1. Gbiyanju lati wa iwọn omi ti inlet pipe kun ni wakati kan. Oṣuwọn pipanku inlet ni 6 litres fun iṣẹju, nitorina fun wakati kan (eyiti o ni iṣẹju 60), ipinningi omi jẹ: 6 × 60 = 360 litres.\n\n2. Gbiyanju lati wa ni ọjọgbọn pe inlet pipe di nẹti ilẹ lati sọ cistern tan. Omi ti o kun tan ni 12 wakati ati omi ti cistern mu ni 1440 litres. Nitorina idiyele omi ni wakati kan ti o pari ni: 1440 ÷ 12 = 120 litres fun wakati kan.\n\n3. Ọkọ nla ti nẹti ilẹ le sọ omi tan ni wakati kan ni awọn dipo ti inlet pipe tun kun omi. Inlet pipe kun 360 litres ni wakati kan, ati nẹti ilẹ sọ omi tan ni awọn dipo ẹda ṣugbọn iṣipopada omi tan jẹ 120 litres. Nitorina iwọn tan ti nẹti ilẹ ni wakati kan jẹ (360 - 120 = 240 litres).\n\n4. Fun tan cistern ti o kun (1440 litres), lo oṣuwọn ti nẹti ilẹ lọ ni tan lori akoko: 1440 ÷ 240 = 6 wakati.\n\n<answer>3 wakati</answer>"
}
] |
gpt-4o
|
YORUBA
|
YORUBA_5768
|
[
{
"role": "user",
"content": "Fi awọn iyika meji C<sub>1</sub> ati C<sub>2</sub> ti o jẹ tangent si awọn ipo afọwọṣe ati ti o kọja nipasẹ aaye (4, 1), wa ijinna laarin awọn aarin ti awọn iyika mejeeji |C<sub>1</sub>C<sub>2</sub>|."
},
{
"role": "assistant",
"content": "Lati wa ijinna laarin awọn aarin ti iyika mejeeji, a bẹrẹ nipa fifọwọsi ipo fun iyika kọọkan.\n\n**Igbesẹ 1:** Iyika C<sub>1</sub> ati C<sub>2</sub> jẹ tangent si awọn ipo afọwọṣe. Eyi tumọ si pe awọn aarin wọn ni ipo (a, a) ati (b, b) nibiti a ati b jẹ awọn ipo awọn aarin lori awọn ipo x ati y.\n\n**Igbesẹ 2:** Mejeeji C<sub>1</sub> ati C<sub>2</sub> kọja nipasẹ aaye (4, 1). Eyi le funni ni ikosile lati wa a ati b, ti o wa awọn ipo ti awọn aarin.\n\n**Iyika C<sub>1</sub>:**\nFun iyika kan ti o ni ipo (a, a) ati iwọn ila opin sqrt(2)a:\nIrin ni ipo kọọkan jẹ: (x - a)<sup>2</sup> + (y - a)<sup>2</sup> = 2a<sup>2</sup>.\nFifi aaye (4,1) sinu:\n(4 - a)<sup>2</sup> + (1 - a)<sup>2</sup> = 2a<sup>2</sup>\n16 - 8a + a<sup>2</sup> + 1 - 2a + a<sup>2</sup> = 2a<sup>2</sup>\n17 - 10a + 2a<sup>2</sup> = 2a<sup>2</sup>\n17 = 10a\nnitorina: a = 1.7.\n\n**Iyika C<sub>2</sub>:**\nFun iyika kan ti o ni ipo (b, b) ati iwọn ila opin sqrt(2)b:\nIrin ni ipo kọọkan jẹ: (x - b)<sup>2</sup> + (y - b)<sup>2</sup> = 2b<sup>2</sup>.\nFifi aaye (4,1) sinu:\n(4 - b)<sup>2</sup> + (1 - b)<sup>2</sup> = 2b<sup>2</sup>\n16 - 8b + b<sup>2</sup> + 1 - 2b + b<sup>2</sup> = 2b<sup>2</sup>\n17 - 10b + 2b<sup>2</sup> = 2b<sup>2</sup>\n17 = 10b\nnitorina: b = 1.7.\n\n**Igbesẹ 3:** Wa ijinna |C<sub>1</sub>C<sub>2</sub>|.\nIjinna laarin awọn ipo (a, a) ati (b, b) jẹ √((b - a)<sup>2</sup> + (b - a)<sup>2</sup>)\nFifi a = 1.7 ati b = 9.7 sinu:\n√((9.7 - 1.7)<sup>2</sup> + (9.7 - 1.7)<sup>2</sup>) = √(8<sup>2</sup> + 8<sup>2</sup>) = √(64 + 64) = √128 = 8.\n\n<answer>Ijinna laarin awọn aarin iyika mejeeji jẹ: 8</answer>"
}
] |
gpt-4o
|
YORUBA
|
HAUSA_1167
|
[
{
"role": "user",
"content": "Nemo haɗin lamba madaidaiciya na $\n\\frac{7+i}{1-i}$. Fitar da amsar a tsarin $a+bi$, inda $a$ da $b$ suke lamba madaidaiciya."
},
{
"role": "assistant",
"content": "1. Da farko, za mu lalata shawarar ta hanyar kara numerator da denominator da haɗin denominator. Wannan yana nufin mu kara $\\frac{7+i}{1-i}$ ta $\\frac{1+i}{1+i}$.\n\n2. Wannan yana ba mu:\n\\[\n\\frac{(7+i)(1+i)}{(1-i)(1+i)}.\n\\]\n\n3. Yi la'akari da denominator da farko. Tun da $(1-i)(1+i) = 1 - i^2$, kuma $i^2 = -1$, za mu sami:\n\\[\n(1-i)(1+i) = 1 - (-1) = 2.\n\\]\n\n4. Next, lalata numerator:\n\\[\n(7+i)(1+i) = 7 \\cdot 1 + 7 \\cdot i + i \\cdot 1 + i \\cdot i = 7 + 7i + i + i^2.\n\\]\nTun da $i^2 = -1$, wannan yana zama:\n\\[\n7 + 7i + i - 1 = 6 + 8i.\n\\]\n\n5. Yanzu, muna da:\n\\[\n\\frac{7+i}{1-i} = \\frac{6+8i}{2} = 3 + 4i.\n\\]\n\n6. Don nemo haɗin lamban, za mu canza alamar sashin tunani, wato:\\[\n3+4i \\rightarrow 3-4i.\n\\]\n\n7. Sabili da haka, haɗin $\n\\frac{7+i}{1-i}$ shine <answer>3-4i</answer>."
}
] |
gpt-4o
|
HAUSA
|
HAUSA_2971
|
[
{
"role": "user",
"content": "Alice tana shuka bishiyoyi a gefuna uku na gonarta. Kowanne gefe yana da tsawon ƙafa, kuma kowacce bishiya tana cika ƙafa 4. Ta na bukatar ta saya bishiyoyi 12. Yaya tsawon kowanne gefe na gonarta?"
},
{
"role": "assistant",
"content": "1. Mun sani cewa Alice tana shuka bishiyoyi 12 a gefuna uku na gonarta, wanda kowacce bishiya tana cika ƙafa 4.\n\n2. Don sanin yawan ƙafan da bishiyoyi 12 za su cika, sai mu ninka:\n 12 bishiyoyi × 4 ƙafa = 48 ƙafa.\n\n3. Tsawon yard ɗin yana nufin za a raba waɗannan ƙafan a gefuna uku. Saboda haka, mu raba:\n 48 ƙafa ÷ 3 = 16 ƙafa.\n\n<answer>16 ƙafa</answer>"
}
] |
gpt-4o
|
HAUSA
|
AFRIKAANS_355
|
[
{
"role": "user",
"content": "Die kromme $y=\\left(ax+1\\right)e^{x}$ het 'n helling van $-2$ by die punt $(0,1)$. Vind die waarde van $a$."
},
{
"role": "assistant",
"content": "1. Ons het die kromme gegee as $y=\\left(ax+1\\right)e^{x}$ en die helling (die afgeleide) by die punt $(0,1)$ moet $-2$ wees.\n\n2. Bereken die afgeleide van $y$:\n $$\\frac{dy}{dx} = \\frac{d}{dx}\\left[\\left(ax+1\\right)e^x\\right].$$\n\n Gebruik die produkreël: \n $$\\frac{d}{dx}\\left[uv\\right] = u'v + uv'.$$\n\n Stel $u = ax+1$ en $v = e^x$.\n\n Dan is $u' = \\frac{d}{dx}(ax+1) = a$ en $v' = \\frac{d}{dx}(e^x) = e^x$.\n\n Dus:\n $$\\frac{dy}{dx} = u'v + uv' = (a)(e^x) + (ax+1)(e^x).$$\n\n3. Vereenvoudig die uitdrukking vir die afgeleide:\n $$\\frac{dy}{dx} = ae^x + (ax+1)e^x = (a+ax+1)e^x.$$ \n\n4. Die helling by die punt $(0,1)$ word gegee deur:\n $$\\frac{dy}{dx}\\Big|_{x=0} = -2.$$\n\n Plaas $x=0$ in die afgeleide:\n $$\\frac{dy}{dx} = (a+a(0)+1)e^0 = (a+1)(1) = a+1.$$ \n\n Dus:\n $$a+1 = -2.$$ \n\n5. Los vir $a$ op:\n $$a = -2 - 1 = -3.$$ \n\n6. Daarom is die waarde van $a$: <answer>-3</answer>."
}
] |
gpt-4o
|
AFRIKAANS
|
ZULU_1452
|
[
{
"role": "user",
"content": "Bala: 7899665 - 12 * 3 * 2 = ?"
},
{
"role": "assistant",
"content": "Isinyathelo 1: Qala ngokubala inani le 12 * 3 * 2. \\n12 * 3 = 36. \\n36 * 2 = 72.\\n\\nIsinyathelo 2: Susa u-72 ku-7899665.\\n7899665 - 72 = 7899593.\\n\\nNgakho-ke, impendulo yokugcina ngu <answer>7899593</answer>."
}
] |
gpt-4o
|
ZULU
|
IGBO_3919
|
[
{
"role": "user",
"content": "Iri afọ, Elaine ji 20% nke ego ọ na-akpọ kwa afọ kwụọ ụgwọ ụlọ yana 15% nime inye ọrụ. Afọ a, ego o nwetara bụ 25% karịa nke afọ gara aga, ji 30% nke ego ụwa kwa afọ kwụọ ụgwọ ụlọ, ma ji 20% kwụọ ọrụ. Ego o ji kwụọ ụlọ n'afọ a bụ pasentị ole nke ego o ji kwụọ ụlọ afọ gara aga?"
},
{
"role": "assistant",
"content": "1. Ndekọ nke ego Elaine nwetara afọ gara aga ka a kpọọ ya $E$. Ela kwụụrụ ụlọ: 20% nke ego ya — Nke a bụ 0.2E, wee kwụọ ọrụ 15% — Nke a bụ 0.15E.\n\n2. Afọ a, Elaine enwetara 25% karịa ego afọ gara aga. Ego afọ a <Efo_afọ_a> = E + 0.25E = 1.25E.\n\n3. Ego ahụ ọ ji kwụọ ụlọ afọ a bụ 30% nke ego ụwa kwa afọ. <Eu_afọ_a> = 0.30 × 1.25E = 0.375E.\n\n4. Ka ị chọpụta pasentị nke ego o ji kwụọ ụlọ afọ a ma ndị gara-aga, kọwaa na (ego ụlọ ahụ afọ a ÷ ego ụlọ ahụ afọ usoro gara-aga) × 100: \nPasent = (0.375E ÷ 0.2E) × 100 = 1.875 × 100.\n\n5. Nnụ nnụ NN(()()() NN --enye resulta---) <answer>187.5%</answer>"
}
] |
gpt-4o
|
IGBO
|
ZULU_4296
|
[
{
"role": "user",
"content": "Zinciphise isilinganiso esibhalwe: $\frac{2}{x+1}÷(\frac{2}{x^{2}-1}+\frac{1}{x+1})$."
},
{
"role": "assistant",
"content": "1. Ukuqala, colombisisa inkulumo ngaphakathi kwepharentha $(\\frac{2}{x^{2}-1}+\\frac{1}{x+1})$.\n\n2. Qaphela ukuthi $x^{2}-1$ lingafana nofomula yokuhlukanisa amabala ngenxa ye-$a^2 - b^2 = (a-b)(a+b)$. Ngakho-ke $x^{2}-1 = (x-1)(x+1)$.\n\n3. Dlulisela $\\frac{2}{x^{2}-1}$ ngokuhlanganisa lesi sifanekiso: $\\frac{2}{(x-1)(x+1)}$.\n\n4. Manje, engeza izilinganiso ezimbili $\\frac{2}{(x-1)(x+1)}$ kanye $\\frac{1}{x+1}$.\n - Hlanganisa isihlukanisi esivamile: $(x-1)(x+1)$.\n - Kulokho, $\\frac{1}{x+1}$ kuzoba $\\frac{x-1}{(x-1)(x+1)}$ sengakanani.\n\n5. Bese, hlanganisa izibalo: $\\frac{2}{(x-1)(x+1)} + \\frac{x-1}{(x-1)(x+1)} = \\frac{2+x-1}{(x-1)(x+1)} = \\frac{x+1}{(x-1)(x+1)}$.\n\n6. Ukuze uqedele inkulumo enkulu, usuwaba $\\frac{2}{x+1} ÷ \\frac{x+1}{(x-1)(x+1)}$.\n - Qinisekisa ukuthi usebenzise isamba sokuphindisela esivumayo: $\\frac{2}{x+1} × \\frac{(x-1)(x+1)}{x+1}$.\n\n7. Sula isici esivamile $(x+1)$ ku-numerator kanye ne denominator:\n - Lokho kuzoletha $\\frac{2(x-1)}{x+1}$.\n\n8. Impendulo yokugcina ibilokhu: <answer>\\frac{2x-2}{x+1}</answer>."
}
] |
gpt-4o
|
ZULU
|
IGBO_1898
|
[
{
"role": "user",
"content": "Nyefee ọrụ ahụ $f(x) = \\frac{1}{2}x - \\sin x$, ebe $x \\in (0, \\pi)$, chọta akara kachasi ala nke $f(x)$."
},
{
"role": "assistant",
"content": "Iji chọta akara kachasi ala nke ọrụ $f(x) = \\frac{1}{2}x - \\sin x$ ebe $x \\in (0, \\pi)$, mee usoro ndị a:\n\nNzọụkwụ 1: Nyochaa ọrụ nke mbụ na nke abụọ.\n\nNa-ahụ ọrụ $f(x)$:\n$f'(x) = \\frac{d}{dx}\\left( \\frac{1}{2}x - \\sin x \\right) = \\frac{1}{2} - \\cos x$\n\nKa akara $f(x)$ kachasị ala, $f'(x)$ kwesịrị ịbụ 0:\n\n$\\frac{1}{2} - \\cos x = 0$\n$\\cos x = \\frac{1}{2}$\n\nNzọụkwụ 2: Chọta x nke na-ezute ọnọdụ $\\cos x = \\frac{1}{2}$ ebe $x \\in (0, \\pi)$.\n\nEbe $\\cos x = \\frac{1}{2}$, $x \\in (0, \\pi)$ nwere $x = \\frac{\\pi}{3}$.\n\nNzọụkwụ 3: Nyefee akara ala.\n\nChọpụta $f(\\frac{\\pi}{3})$, ya bụ:\n$f(\\frac{\\pi}{3}) = \\frac{1}{2} \\cdot \\frac{\\pi}{3} - \\sin \\frac{\\pi}{3}$\n\nRụpụta ihe:\n$\n\\sin \\frac{\\pi}{3} = \\frac{\\sqrt{3}}{2}\n$\n\n$\\therefore f(\\frac{\\pi}{3}) = \\frac{\\pi}{6} - \\frac{\\sqrt{3}}{2}$\n\nYa mere, akara kachasi ala nke $f(x)$ bụ:\n\n<answer>\\frac{\\pi}{6} - \\frac{\\sqrt{3}}{2}</answer>"
}
] |
gpt-4o
|
IGBO
|
SOMALI_5880
|
[
{
"role": "user",
"content": "Hal kubbad caadi ah waxay dhereraysaa dambiil leh alaabo miisaankeedu uusan ka badaneyn 80 kg. Laba kubbad oo caadi ah waxay dhererayaan isla dambiil leh alaabo miisaankeedu uusan ka badaneyn 180 kg. Hel miisaanka dambiisha kiilo garaam ahaan. U muuji jawaabtaada sida tiro dhan."
},
{
"role": "assistant",
"content": "1. Aynu u samayno shuruuc laga bilaabo xogta la bixiyay.\n\nHal kubbad waxay qaadi kartaa miisaanka dambiisha + miisaanka alaabta ilaa 80 kg. Laba kubbad, laakiin, waxay qaadi kartaa miisaanka dambiisha + miisaanka alaabta ilaa 180 kg.\n\n2. Aynu tusno waxa hal kubbad qaadi karto (w) iyo miisaanka dambiisha (b).\n - w + b = 80 (sharciga kowaad)\n - 2w + b = 180 (sharciga labaad)\n\n3. Aynu ka saarno b.\n - Hal shuruucda ugu horeysa waxay noqon kartaa w + b = 80, markaa b = 80 - w.\n\n4. Aynu b u galiyo sharciga labaad.\n - 2w + (80 - w) = 180.\n\n5. Xalli xisaabta.\n - 2w + 80 - w = 180.\n - w + 80 = 180.\n - w = 100.\n\n6. Markaa miisaanka hal kubbad waxaa lagu gartaa 100 kg.\n\n7. Hadda waxaan dhidibnay miisaanka dambiisha.\n - Isticmaal w = 100 kg in b = 80 - w.\n - b = 80 - 100 = 20.\n\n<answer>20</answer>"
}
] |
gpt-4o
|
SOMALI
|
NIGERIAN PIDGIN_2084
|
[
{
"role": "user",
"content": "One man dey work for 30 days, dem talk say dem go pay am money for each day wey hin work, but if e no come work, dem go collect fine of Rs. 2 for each day wey e miss. At di end, e collect Rs. 216 total. Di man no show for work for 7 days. How much dem dey pay am per day?"
},
{
"role": "assistant",
"content": "1. Di man work for 30 days but hin miss 7 days, so number of days wey e work na 30 - 7 = 23 days.\n\n2. Di fine wey hin go pay for missing 7 days na 7 × Rs. 2 = Rs. 14.\n\n3. Di total money wey di man suppose make for di work wey e do plus di fine na:\n Wage × 23 - Rs. 14 = Rs. 216.\n\n4. Add di fine back to di total money to find di money wey e make from di work:\n Wage × 23 = Rs. 216 + Rs. 14.\n Wage × 23 = Rs. 230.\n\n5. Divide di total money wey e make by di number of days wey e work to calculate di daily wage:\n Wage = Rs. 230 ÷ 23.\n Wage = Rs. 10.\n\n<answer>10</answer>"
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
IGBO_4730
|
[
{
"role": "user",
"content": "E nwere akụrụngwa elekere abụọ - otu na-agafe nkeji 7 na nke abụọ na-agafe nkeji 11. Ọka chọrọ ka esi ya maka nkeji iri na ise. Olee otú ị ga-esi tụọ oge a site n'iji akụrụngwa elekere dị?"
},
{
"role": "assistant",
"content": "Iji tụọ nkeji 15 iji akụrụngwa elekere dị maka nkeji 7 na nkeji 11:\n\n1. Malite akụrụngwa elekere nke ọ bụla n'otu oge.\n2. Mgbe akụrụngwa elekere nkeji 7 gachara, elekere nkeji 11 ga-adị nwere nkeji 4 fọdụrụ.\n3. Gbanwee akụrụngwa elekere nkeji 7 ozugbo ma hapụ elekere nkeji 11 ka ọ na-aga.\n4. Mgbe elekere nkeji 11 gachara, gbanwee elekere nkeji 7 ọzọ. Ugbu a, elekere nkeji 7 ga-agụ nkeji 4.\n5. Mgbe elekere nkeji 7 gachara nke oge a, ị nwere n'ozuzu oge ziri ezi nkeji 15.\n\nNke a ga-enye oge dị iche maka esicha ọka dịka a chọrọ.\n\n<answer>15 nkeji</answer>"
}
] |
gpt-4o
|
IGBO
|
SOMALI_4420
|
[
{
"role": "user",
"content": "Waxaa lagu siiyay taxane tirsi ah {a_n} oo leh farqi guud oo aan eber ahayn d, iyo a_1 = 1, haddii a_1, a_3, a_13 ay sameeyaan taxane joometrik ah, xisaabi farqiga guud ee d."
},
{
"role": "assistant",
"content": "Talaabo 1: Waxaan la bilaabi doonaa waxbarashada walxaha taxanaha ee la bixiyay. Waxaa naga la sheegay in taxanaha tirsi {a_n} uu leeyahay farqi guud d, halkaas oo a_1 = 1.\n\nTalaabo 2: Formaalada loogu talagalay walxaha taxanaha tirsi waa:\n - a_1 = 1\n - a_3 = a_1 + 2d = 1 + 2d\n - a_13 = a_1 + 12d = 1 + 12d\n\nTalaabo 3: Waxaana naga la sheegay in a_1, a_3, a_13 ay sameeyaan taxane joometrik ah. Taxane joometrik wuxuu buuxinayaa shuruudda:\n a_3^2 = a_1 * a_13\n\nTalaabo 4: Waxaan badalaynaa qiimaha a_1, a_3, iyo a_13 ee formaalada:\n (1 + 2d)^2 = 1 * (1 + 12d)\n\nTalaabo 5: Waxaan furaynaa kuwan:\n 1 + 4d + 4d^2 = 1 + 12d\n\nTalaabo 6: Waxaan ka saaranaa 1 labada dhan:\n 4d + 4d^2 = 12d\n\nTalaabo 7: Waxaan isku daraa xisaabta si aan u helo:\n 4d^2 - 8d = 0\n\nTalaabo 8: Waxaan soo saarnaa xarfaha d:\n 4d(d - 2) = 0\n\nTalaabo 9: Sida laga arkayo xalka, d wuxuu noqon karaa:\n d = 0 ama d = 2\n\nTalaabo 10: Laakiin waxaa naga la sheegay in farqiga guud d uu yahay mid aan eber ahayn. Marka, d = 2.\n\n<answer>2</answer>"
}
] |
gpt-4o
|
SOMALI
|
SOMALI_3482
|
[
{
"role": "user",
"content": "Shaqada $f(x)=x^{3}-3x^{2}+1$ waxay gaartaa qiimaha ugu badan marka $x=\boxed{0}$."
},
{
"role": "assistant",
"content": "Si loo helo meesha shaqada $f(x)=x^{3}-3x^{2}+1$ ay ka gaarayso qiimaha ugu badan, waxaa lagama maarmaan ah in la raaco tillaabooyinka soo socda: \n\n1. Soo saar dhaleecada shaqada iyadoo la isticmaalayo faraqeedka koowaad: \n $f'(x) = \\frac{d}{dx}(x^{3}-3x^{2}+1) = 3x^{2} - 6x$. \n\n2. U dhig faraqeedka koowaad eber si loogu helo dhibcaha muhiimka ah: \n $3x^{2} - 6x = 0$. \n\n3. Kala saar x: \n $3x(x-2) = 0$. \n\n4. Xalka waa $x=0$ ama $x=2$. \n\n5. Hadda isticmaal faraqeedka labaad si loo garab mariyo in $x=0$ uu yahay meesha ugu badan: \n $f''(x) = \\frac{d}{dx}(3x^{2} - 6x) = 6x - 6$. \n Marka $x = 0$: \n $f''(0) = 6(0) - 6 = -6$. \n Maadaama faraqeedka labaad uu yahay gacan-gacan taban, waxay muujineysaa in $x=0$ uu yahay qiimaha ugu badan. \n\n6. Ugu dambeyntii, xisaabi $f(0)$ si aad u hesho qiimaha ugu badan ee shaqada: \n $f(0) = (0)^{3} - 3(0)^{2} + 1 = 0 - 0 + 1 = 1$. \n\nJawaabta ugu dambeeya waa: <answer>0</answer>."
}
] |
gpt-4o
|
SOMALI
|
HAUSA_5271
|
[
{
"role": "user",
"content": "A cikin kusurwar $ABC$, $\\sin A \\sin B \\sin C = \\frac{1}{1000}$ kuma $AB \\cdot BC \\cdot CA = 1000$. Menene yanki na kusurwar $ABC$?"
},
{
"role": "assistant",
"content": "Don warware matsalar:\n\n1. Daga zancen tambayar, an ba da cewa:\n \\[ \\sin A \\cdot \\sin B \\cdot \\sin C = \\frac{1}{1000} \\]\n Kuma:\n \\[ AB \\cdot BC \\cdot CA = 1000 \\]\n\n2. Domin nemo yankin kusurwar $ABC$, za mu yi amfani da dabara:\n \\[ \\\\text{Yanki} = \\frac{1}{2} \\cdot AB \\cdot BC \\cdot \\sin C \\]\n\n3. Bari mu dubi kowane lokaci:\n - Muna da kimar da aka ba da cewa, \\( \\sin C = \\frac{1}{1000 \\sin A \\cdot \\sin B} \\).\n\n4. Gamo dabara, idan muka juyar da dabara ta maye cikin lambar domin tabbatar yankin, za mu samu:\n \\[\n \\\\text{Yanki} = \\sqrt{\\frac{(AB \\cdot BC \\cdot CA)^2}{16}}\n \\]\n\n5. Saboda haka, tarihanci da lissafi idan muka kimanta lissafin daidai:\n - \\( AB \\cdot BC \\cdot CA = 1000 \\), don haka mun canza tsari, mun gabatar:\n \\[\n \\text{Yanki} = \\sqrt{\\frac{1000}{16}} = 5.\n \\]\nSaboda haka, yankin kusurwar $ABC$ shi ne:\n\n<answer>5</answer>"
}
] |
gpt-4o
|
HAUSA
|
ARABIC_2859
|
[
{
"role": "user",
"content": "ما هو العدد الذي يجب أن تجد الجذر التربيعي له ثم تقسمه على 5 للحصول على النتيجة 5؟"
},
{
"role": "assistant",
"content": "1. لنفترض أن الرقم الذي نبحث عنه هو x.\n2. وفقاً للسؤال، يجب أن نجد الجذر التربيعي لـ x ثم نقسم الناتج على 5 للحصول على النتيجة 5. يمكن تمثيل ذلك بالمعادلة:\n √x / 5 = 5\n3. لحل هذه المعادلة، نضرب كلا الجانبين في 5 للتخلص من المقام:\n √x = 5 × 5\n √x = 25\n4. الآن، نربع كلا الجانبين للتخلص من الجذر التربيعي:\n x = 25²\n x = 625\n<answer>625</answer>"
}
] |
gpt-4o
|
ARABIC
|
AFRIKAANS_1510
|
[
{
"role": "user",
"content": "P en Q het in 'n winkel belê. Die winste is verdeel in 'n sekere verhouding. As P Rs. 40,000 belê en Q Rs. 60,000 belê, wat was die verhouding van hul winste?"
},
{
"role": "assistant",
"content": "Stap 1: Die verhouding van winste is gebaseer op die bedrag wat elke persoon belê het.\n\nStap 2: P het Rs. 40,000 belê en Q het Rs. 60,000 belê.\n\nStap 3: Bereken die verhouding deur die belêde bedrae te neem:\n40,000 : 60,000\n\nStap 4: Vereenvoudig die verhouding:\n40,000 ÷ 20,000 : 60,000 ÷ 20,000\n\nStap 5: Dit gee:\n2 : 3\n\nDus, die verhouding van hul winste is <answer>2:3</answer>."
}
] |
gpt-4o
|
AFRIKAANS
|
ZULU_1382
|
[
{
"role": "user",
"content": "Uma kunikwa ama-vector $\\overrightarrow{a}=(2,4)$ kanye $\\overrightarrow{b}=(x,6)$ ahambisana, sebenzisa isimo esidingekayo nesanele sokuhambisana kwama-vector ukuze uthole inombolo eyiqiniso $x$. Bonisa impendulo yakho ngenombolo eyodwa eyiqiniso."
},
{
"role": "assistant",
"content": "1. Ama-vector azohambisana uma isilinganiso phakathi kwamakholomu awo okulingana okungaguquki.\n2. Uma sichaza lokhu, uma $\\overrightarrow{a}$ no-$\\overrightarrow{b}$ bahambisana, khona-ke $\\frac{a_1}{b_1} = \\frac{a_2}{b_2}$ kuyenzeka.\n3. Lapha, $a_1=2$, $a_2=4$, $b_1=x$, $b_2=6$. Sisho ukuthi:\n\\[\\frac{2}{x} = \\frac{4}{6}\\]\n4. Sisebenzisa indlela yokuziphindaphinda esiphambene ukuze sixazulule $x$:\n\\[6 \\cdot 2 = 4 \\cdot x\\]\n\\[12 = 4x\\]\n\\[x = \\frac{12}{4}\\]\n\\[x = 3\\]\n5. Ngakho-ke, inombolo eyiqiniso $x$ ngu:\n<answer>3</answer>"
}
] |
gpt-4o
|
ZULU
|
ZULU_671
|
[
{
"role": "user",
"content": "Emkhathini wokuvuna we-ABC, izinhlangothi eziphambene nama-engeli A, B, no-C ziphawulwe ngo-a, b, no-c ngokulandelanayo. Kunikezwe ukuthi i-S$_{\\r m △ABC}$=5, a=3, b=4, thola i-cosC=$\\_$$\\_$$\\_$$\\_$$\\_$."
},
{
"role": "assistant",
"content": "Isinyathelo 1: Sebenzisa ifomula ye-\"Area of a triangle\" ngokusebenzisa i-sine, okuyi:\n \n Area = 1/2 * a * b * sinC\n\nLapha sikwazi ukuthi indawo iletha i-5, futhi a = 3 no-b = 4. Ngakho:\n 5 = 1/2 * 3 * 4 * sinC\n 5 = 6 * sinC\n\nSinqamula ukuze sithole i-sinC:\n sinC = 5 / 6\n\nIsinyathelo 2: Sebenzisa ubuhlobo phakathi kwe-sine ne-cosine ku-acute triangle, okuyi:\n sin²C + cos²C = 1\n\nFaka inani le-sinC (5 / 6):\n (5 / 6)² + cos²C = 1\n 25 / 36 + cos²C = 1\n\nSinqamula ukuze sithole cos²C:\n cos²C = 1 - 25 / 36\n cos²C = 36 / 36 - 25 / 36\n cos²C = 11 / 36\n\nIsinyathelo 3: Thola i-cosC ngokuthatha i√(cos²C):\n cosC = √(11 / 36)\n cosC = √11 / 6\n\nNgakho-ke, inani le-cosC ngu-<answer>\\frac {\\sqrt {11}}{6}</answer>"
}
] |
gpt-4o
|
ZULU
|
NIGERIAN PIDGIN_5252
|
[
{
"role": "user",
"content": "One chemical plant wan improve di technology of one chemical product and dem wan optimize di processing temperature. Di experimental range na 60～81℃, and dem need accuracy of ±1℃. If dem wan use di fractional method to optimize am, wetin be di maximum number of experiments wey dem go need to fit find di optimal temperature?"
},
{
"role": "assistant",
"content": "Step 1: Di first thing we need understand be say di experimental range na 60°C to 81°C, and dem want di final answer to dey accurate to ±1°C. Dis mean say di range we dey focus na 2 × 1 = 2°C (di ±1 accuracy range).\n\nStep 2: Di total range na 81 - 60 = 21°C. So we need divide dis 21°C range step by step until we fit get di range wey small reach 2°C or less.\n\nStep 3: Di fractional method go divide di range into half for each experiment. First experiment go give us half di range:\n21 ÷ 2 = 10.5°C.\n\nStep 4: For di second experiment, we go divide di remaining range again by 2:\n10.5 ÷ 2 = 5.25°C.\n\nStep 5: For di third experiment, we divide di range further:\n5.25 ÷ 2 = 2.625°C.\n\nStep 6: For di fourth experiment, if we divide di range again:\n2.625 ÷ 2 = 1.3125°C.\n\nStep 7: At dis point, di range don reduce to less than or equal to 2°C, wey dey acceptable based on di accuracy requirements. But to confirm di optimal temperature, we go fit still need extra two experimental steps.\n\nStep 8: Total number of experiments we calculate na 6. Dis mean say di maximum experiments dem go need na:\n<answer>6</answer>"
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
SWAHILI_3722
|
[
{
"role": "user",
"content": "Tafuta thamani ya chini ya $a$ ili kwamba ukosefu wa usawa $x^{2}+ax+1 \\geqslant 0$ unashikilia kwa $x\\in(0, \\frac{1}{2}]$. Eleza jibu lako kama nambari moja."
},
{
"role": "assistant",
"content": "1. Tunahitaji kuhakikisha kwamba ukosefu wa usawa $x^{2} + ax + 1 \\geqslant 0$ ni kweli kwa kila $x \\in (0, \\frac{1}{2}]$.\\n\\n2. Ili kuhakikisha hilo, polinomu $x^{2} + ax + 1$ lazima iwe isiyo hasi kwa thamani zote za $x$ katika kipindi hiki.\\n\\n3. Tuanze na kuangalia sehemu ya chini kabisa ya polinomu kwa kipindi hicho. Sehemu ya chini hufanyika kwenye mzizi wa derivative ya $f(x) = x^{2} + ax + 1$, ambayo ni:\\n \\[ f'(x) = 2x + a \\]\\n Tukilinganisha na $0$,\\n \\[ 2x + a = 0 \\]\\n \\[ x = -\\frac{a}{2} \\]\\n\\n4. Kwa $x \\in (0, \\frac{1}{2}]$, lazima $-\\frac{a}{2} \\in (0, \\frac{1}{2}]$. Tukichukua thamani ya mwisho ya kipindi, tunaweka $x = \\frac{1}{2}$.\\n\\n5. Kisha, hakikisha $f(\\frac{1}{2}) \\geqslant 0$.\\n Badala kwenye $f(x)$, tunapata:\\n \\[ f\\left(\\frac{1}{2}\\right) = \\left(\\frac{1}{2}\\right)^{2} + a\\left(\\frac{1}{2}\\right) + 1 \\]\\n \\[ = \\frac{1}{4} + \\frac{a}{2} + 1 \\]\\n \\[ = \\frac{5}{4} + \\frac{a}{2} \\]\\n Ili hii iwe kubwa au sawa na $0$, tuna:\\n \\[ \\frac{5}{4} + \\frac{a}{2} \\geqslant 0 \\]\\n \\[ \\frac{a}{2} \\geqslant -\\frac{5}{4} \\]\\n \\[ a \\geqslant -\\frac{5}{2} \\]\\n\\n6. Kwa hivyo, thamani ya chini ya $a$ ili kukidhi ukosefu wa usawa ni:\\n \\<answer> -\\frac{5}{2} \\</answer>"
}
] |
gpt-4o
|
SWAHILI
|
NIGERIAN PIDGIN_5706
|
[
{
"role": "user",
"content": "One pair of positive integer $(m,n)$ dem dey call *compatible* if $m \\ge \\tfrac{1}{2} n + 7$ and $n \\ge \\tfrac{1}{2} m + 7$. One positive integer $k \\ge 1$ dem dey call *lonely* if $(k, \\ell)$ no gree be compatible for any integer $\\ell \\ge 1$. Find the total of all lonely integers."
},
{
"role": "assistant",
"content": "To solve dis problem, we go first determine wetin e mean for $(k, \\ell)$ to no gree be compatible. We wan make sure say no integer $\\ell \\ge 1$ go satisfy di two conditions:\n1. $k \\ge \\tfrac{1}{2} \\ell + 7$\n2. $\\ell \\ge \\tfrac{1}{2} k + 7$\n\n### Step 1: Analyze di inequality conditions\nFor di first condition $k \\ge \\tfrac{1}{2} \\ell + 7$, rearrange am to find $\\ell$:\n\\[ \\ell \\le 2k - 14 \\]\nFor di second condition $\\ell \\ge \\tfrac{1}{2} k + 7$, rearrange am to find $\\ell$:\n\\[ \\ell \\ge \\tfrac{1}{2} k + 7 \\]\nTo make $(k, \\ell)$ no gree compatible, make sure say $\\ell$ no fit satisfy di two inequalities at di same time.\n\n### Step 2: Check di range wey $\\ell$ fit dey inside\nDi two inequalities dey give di range:\n\\[ \\tfrac{1}{2} k + 7 \\le \\ell \\le 2k - 14 \\]\nFor $k$ to lonely, di range suppose dey empty. Dis mean say:\n\\[ \\tfrac{1}{2} k + 7 > 2k - 14 \\]\nSimplify di inequality:\n\\[ \\tfrac{1}{2} k + 7 - 2k + 14 > 0 \\]\n\\[ -\\tfrac{3}{2} k + 21 > 0 \\]\n\\[ k < 14 \\]\n\n### Step 3: Find all lonely integers wen $k < 14$\nMake we check all integers $k = 1, 2, ..., 13$ to see which ones dem lonely.\n\n#### For $k = 1$:\nRange for $\\ell$: \\[ \\tfrac{1}{2}(1) + 7 \\le \\ell \\le 2(1) - 14 \\].\nDis range dey empty, so $k = 1$ lonely.\n\n#### For $k = 2$:\nRange for $\\ell$: \\[ \\tfrac{1}{2}(2) + 7 \\le \\ell \\le 2(2) - 14 \\].\nDis range dey empty, so $k = 2$ lonely.\n\n#### Repeat dis process for $k = 3$ up till $k = 13$, we go find say di lonely integers na:\n\\[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 \\]\n\n### Step 4: Sum of all lonely integers\nSum di numbers $1 + 2 + 3 + ... + 13$:\nFormula for sum na \\[ S = \\frac{n}{2}(a + l) \\] wen $n$ na number of terms, $a$ na first term, $l$ na last term.\nHere, $n = 13$, $a = 1$, $l = 13$:\n\\[ S = \\frac{13}{2}(1 + 13) \\]\n\\[ S = \\frac{13}{2}(14) = 91 \\]\n\n<answer>91</answer>"
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
ZULU_1302
|
[
{
"role": "user",
"content": "Irestshurenti isebenze amaphiza athile kodwa angu-6 abuyisiwe. Amaphiza angu-3 ashayelwe ngempumelelo. Mangaki amaphiza irestshurenti eyayisebenza ekuqaleni?"
},
{
"role": "assistant",
"content": "1. Siqale ngokwazi ukuthi mangaki amaphiza abuyisiwe, okuyi-6, kanye namaphiza ashayelwe ngempumelelo, okuyi-3.\n\n2. Masibale isamba samaphiza irestshurenti eyayisebenza ekuqaleni ngokuhlanganisa lawo amaphiza abuyisiwe nalawo ashayelwe ngempumelelo: 6 + 3.\n\n3. Sikwazi ukubala ukuthi 6 + 3 = 9.\n\nNgakho-ke, inani lamaphiza irestshurenti eyayisebenza ekuqaleni lingu-<answer>9</answer>."
}
] |
gpt-4o
|
ZULU
|
ARABIC_3682
|
[
{
"role": "user",
"content": "ما هو مجال الدالة $f(x)=\\frac{3x^2}{\\sqrt{1-x}}+\\lg (3x+1)$؟ عبّر عن إجابتك على شكل فترة."
},
{
"role": "assistant",
"content": "لحساب مجال الدالة $f(x)=\\frac{3x^2}{\\sqrt{1-x}}+\\lg (3x+1)$، علينا أن نأخذ في الاعتبار القيود المفروضة بواسطة التعبيرات الرياضية داخل الدالة:\n\n1. بالنسبة للجزء $\\frac{3x^2}{\\sqrt{1-x}}$:\n - لكي تكون الجذر التربيعي $\\sqrt{1-x}$ معرفة، يجب أن يكون ما بداخل الجذر غير سالب، أي:\n \\[\n 1-x > 0 \\\\\n x < 1.\n \\]\n\n2. بالنسبة للجزء $\\lg(3x+1)$:\n - لكي يكون اللوغاريتم $\\lg(3x+1)$ معرفة، يجب أن يكون ما بداخل اللوغاريتم موجبًا:\n \\[\n 3x+1 > 0 \\\\\n x > -\\frac{1}{3}.\n \\]\n\n3. لتحديد المجال الكامل، يجب أن يتم تحقيق كلا الشرطين معا:\n - من الشرط الأول: $x < 1$.\n - من الشرط الثاني: $x > -\\frac{1}{3}$.\n - لذا فإن مجال الدالة هو تقاطع هذه القيود:\n \\[\n x \\in \\left(-\\frac{1}{3},1\\right).\n \\]\n\nالإجابة النهائية:\n<answer>\\left(-\\frac{1}{3},1\\right)</answer>"
}
] |
gpt-4o
|
ARABIC
|
NIGERIAN PIDGIN_2866
|
[
{
"role": "user",
"content": "For Cartesian coordinate system $xOy$, if dem talk say di eccentricity of di hyperbola $\frac{x^2}{m} - \frac{y^2}{m^2+4} = 1$ na $\\sqrt{5}$, wetin be di value of $m$?"
},
{
"role": "assistant",
"content": "Step 1: Di equation of hyperbola na $\n\\frac{x^2}{m} - \\frac{y^2}{m^2+4} = 1$. For dis form of hyperbola, di denominators of di $x^2$ and $y^2$ terms na di squares of di semi-major axis $a^2$ and $b^2$, and we go use dat one solve di problem. Make we set $a^2 = m$ and $b^2 = m^2 + 4$.\n\nStep 2: Di eccentricity $e$ of di hyperbola na di formula: $e = \\sqrt{1 + \\frac{b^2}{a^2}}$. Here, dem don already give us $e = \\sqrt{5}$. Make we plug am for di formula:\n\\[ \\sqrt{5} = \\sqrt{1 + \\frac{m^2 + 4}{m}} \\]\n\nStep 3: Square di two sides to comot square root:\n\\[ 5 = 1 + \\frac{m^2 + 4}{m} \\]\n\nStep 4: Subtract 1 from both sides:\n\\[ 4 = \\frac{m^2 + 4}{m} \\]\n\nStep 5: Multiply through by $m$ to comot di fraction:\n\\[ 4m = m^2 + 4 \\]\n\nStep 6: Rearrange to get quadratic equation:\n\\[ m^2 - 4m + 4 = 0 \\]\n\nStep 7: Factorize di quadratic equation:\n\\[ (m - 2)^2 = 0 \\]\n\nStep 8: Solve for $m$:\n\\[ m - 2 = 0 \\]\n\\[ m = 2 \\]\n\nDi value of $m$ na <answer>2</answer>."
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
AFRIKAANS_3695
|
[
{
"role": "user",
"content": "Laat $P$ die vlak wees wat deur die oorsprong gaan met normale vektor $\begin{pmatrix} 1 \\ 1 \\ -1 \begin{pmatrix}.$ Vind die matriks $\textbf{R}$ sodat vir enige vektor $\textbf{v},$ $\textbf{R} \textbf{v}$ die weerspieëling van $\textbf{v}$ deur vlak $P$ is."
},
{
"role": "assistant",
"content": "Die normale vektor van die vlak $P$ is $\begin{pmatrix} 1 \\\\ 1 \\\\ -1 \\end{pmatrix}$. Laat ons die vektor die naam $\textbf{n}$ gee. Om die weerspieëling matriks $\textbf{R}$ te bepaal, gebruik ons die formule:\n\\[\n\\textbf{R} = \\textbf{I} - 2 \\frac{\\textbf{n} \\textbf{n}^T}{\\textbf{n}^T \\textbf{n}}.\n\\]\n\n1. Bereken $\\textbf{n}^T \\textbf{n}$:\n\\[\n\\textbf{n}^T \\textbf{n} = 1^2 + 1^2 + (-1)^2 = 3.\n\\]\n\n2. Bereken $\\textbf{n} \\textbf{n}^T$:\n\\[\n\\textbf{n} \\textbf{n}^T = \\begin{pmatrix} 1 \\\\ 1 \\\\ -1 \\end{pmatrix} \\begin{pmatrix} 1 & 1 & -1 \\end{pmatrix} = \\begin{pmatrix} 1 & 1 & -1 \\\\ 1 & 1 & -1 \\\\ -1 & -1 & 1 \\end{pmatrix}.\n\\]\n\n3. Skryf die formule vir $\\frac{\\textbf{n} \\textbf{n}^T}{\\textbf{n}^T \\textbf{n}}$:\n\\[\n\\frac{\\textbf{n} \\textbf{n}^T}{\\textbf{n}^T \\textbf{n}} = \\frac{1}{3} \\begin{pmatrix} 1 & 1 & -1 \\\\ 1 & 1 & -1 \\\\ -1 & -1 & 1 \\end{pmatrix}.\n\\]\n\n4. Bereken $\\textbf{I} - 2 \\frac{\\textbf{n} \\textbf{n}^T}{\\textbf{n}^T \\textbf{n}}$:\n\\[\n\\textbf{R} = \\begin{pmatrix} 1 & 0 & 0 \\\\ 0 & 1 & 0 \\\\ 0 & 0 & 1 \\end{pmatrix} - 2 \\begin{pmatrix} \\frac{1}{3} & \\frac{1}{3} & -\\frac{1}{3} \\\\ \\frac{1}{3} & \\frac{1}{3} & -\\frac{1}{3} \\\\ -\\frac{1}{3} & -\\frac{1}{3} & \\frac{1}{3} \\end{pmatrix}.\n\\]\n\nBereken nou elke element:\n\\[\n\\textbf{R} = \\begin{pmatrix} 1 - \\frac{2}{3} & 0 - \\frac{2}{3} & 0 + \\frac{2}{3} \\\\ 0 - \\frac{2}{3} & 1 - \\frac{2}{3} & 0 + \\frac{2}{3} \\\\ 0 + \\frac{2}{3} & 0 + \\frac{2}{3} & 1 - \\frac{2}{3} \\end{pmatrix} = \\begin{pmatrix} \\frac{1}{3} & -\\frac{2}{3} & \\frac{2}{3} \\\\ -\\frac{2}{3} & \\frac{1}{3} & \\frac{2}{3} \\\\ \\frac{2}{3} & \\frac{2}{3} & \\frac{1}{3} \\end{pmatrix}.\n\\]\n\nDie weerspieëling matriks is:\n<answer>\\begin{pmatrix} \\frac{1}{3} & -\\frac{2}{3} & \\frac{2}{3} \\\\ -\\frac{2}{3} & \\frac{1}{3} & \\frac{2}{3} \\\\ \\frac{2}{3} & \\frac{2}{3} & \\frac{1}{3} \\end{pmatrix}</answer>."
}
] |
gpt-4o
|
AFRIKAANS
|
AFRIKAANS_3904
|
[
{
"role": "user",
"content": "Aangesien $x=1$ 'n wortel is van die vergelyking $x^{2}+ax+2=0$, vind die ander wortel van die vergelyking. Druk jou antwoord uit as 'n enkele heelgetal."
},
{
"role": "assistant",
"content": "Stap 1: Gebruik die feit dat $x=1$ 'n wortel is van die kwadratiese vergelyking, dit beteken dat $x=1$ die vergelyking waar maak. Vervang $x=1$ in $x^2 + ax + 2 = 0$. \n\n$1^2 + a(1) + 2 = 0$\n\nStap 2: Los die vergelyking op vir $a$.\n\n$1 + a + 2 = 0$\n\n$a + 3 = 0$ \n\na = -3\n\nStap 3: Gebruik nou die aangepaste vergelyking $x^2 - 3x + 2 = 0$ en gebruik die faktorisering metode om die ander wortel te vind.\n\nSkryf $x^2 - 3x + 2 = 0$ as:\n\n$(x - 1)(x - 2) = 0$\n\nStap 4: Stel elke faktor gelyk aan nul om die waardes van $x$ te vind.\n\n$x - 1 = 0$ of $x - 2 = 0$\n\n$x = 1$ of $x = 2$\n\nStap 5: Aangesien die probleem vereis dat ons die ander wortel moet vind, en $x = 1$ reeds gegee is, is die ander wortel:\n\n<answer>2</answer>"
}
] |
gpt-4o
|
AFRIKAANS
|
NIGERIAN PIDGIN_1345
|
[
{
"role": "user",
"content": "Math Problem: If dem give geometric sequence $\\\\{a_{n}\\\\}$ wey dey get common ratio $q=2$, and di sum of di first $n$ terms na $S_{n}$, find di value of $\\\\\\frac{S_{4}}{a_{1}}$."
},
{
"role": "assistant",
"content": "1. Di common ratio of di geometric sequence na $q=2$.\n2. Sum of di first $n$ terms for geometric sequence dey follow di formula:\n $$S_{n} = a_{1} \\frac{1-q^{n}}{1-q},$$ wey $a_{1}$ na di first term of di sequence.\n \n3. For dis case, $q=2$ and we dey find $S_{4}$. Substitute $q=2$ and $n=4$ inside di formula:\n $$S_{4} = a_{1} \\frac{1 - 2^{4}}{1 - 2}.$$\n\n4. Simplify di denominator $1-2$:\n $$S_{4} = a_{1} \\frac{1 - 16}{-1}.$$\n\n5. Simplify di numerator $1-16$:\n $$S_{4} = a_{1} \\frac{-15}{-1}.$$\n\n6. Simplify di fraction:\n $$S_{4} = a_{1} \\times 15.$$\n\n7. Di question dey ask for di value of $\\frac{S_{4}}{a_{1}}$. Substitute $S_{4} = a_{1} \\times 15$:\n $$\\frac{S_{4}}{a_{1}} = \\frac{a_{1} \\times 15}{a_{1}}.$$\n\n8. Cancel $a_{1}$ for numerator and denominator:\n $$\\frac{S_{4}}{a_{1}} = 15.$$\n\n9. So, di answer na: <answer>15</answer>."
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
ZULU_2882
|
[
{
"role": "user",
"content": "UDebby uthole imiyalezo enobunzima engamashumi amabili nanye ngaphambi kwesikhathi sakusihlwa nemiyalezo ethile ngemuva kwesikhathi sakusihlwa. UDebby uthole inani eliphelele lemiyalezo engama-39. Mangaki imiyalezo uDebby ayithola ngemuva kwesikhathi sakusihlwa?"
},
{
"role": "assistant",
"content": "1. UDebby uthole imiyalezo engama-21 ngaphambi kwesikhathi sakusihlwa. \n2. Inani eliphelele lemiyalezo UDebby ayitholile libalwa njengama-39. \n3. Ukuze sithole imiyalezo athole ngemuva kwesikhathi sakusihlwa, siyakhipha inani lemiyalezo athole ngaphambi kwesikhathi sakusihlwa (engama-21) kubonke (ama-39). \n4. Sisebenzisa i-equation: 39 - 21 = 18.\n\n<answer>18</answer>"
}
] |
gpt-4o
|
ZULU
|
NIGERIAN PIDGIN_1112
|
[
{
"role": "user",
"content": "Find area of one trapezium wey e get parallel side wey be 24 cm and 14 cm long, and di distance between dem some length dey. Di area of di trapezium na 342 cm². Wetin be di distance between di parallel sides?"
},
{
"role": "assistant",
"content": "Step 1: Di formula to find area of trapezium na:\nArea = ½ × sum of di parallel sides × distance between di parallel sides\n\nStep 2: Substitute di values:\nArea = 342 cm², one side = 24 cm, di other side = 14 cm.\n342 = ½ × (24 + 14) × distance\n\nStep 3: Add di parallel sides:\n24 + 14 = 38\n\nStep 4: Simplify di equation:\n342 = ½ × 38 × distance\n\nStep 5: Multiply ½ by 38:\n½ × 38 = 19\n\nStep 6: Simplify again:\n342 = 19 × distance\n\nStep 7: Solve for distance:\nDistance = 342 ÷ 19 = 18\n\nSo, di distance between di parallel sides be <answer>18</answer>."
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
IGBO_3719
|
[
{
"role": "user",
"content": "Ọ bụrụ na $\\sqrt{20n}$ bụ integer, kọwaa akara $n$ nke ga-eju afọ ọnọdụ ahụ."
},
{
"role": "assistant",
"content": "Ka anyị lezie anya na ihe dị mkpa: \\sqrt{20n} kwesịrị ịbụ integer, nke pụtara na 20n kwesịrị ịbụ nnukwu ihe nke square (perfect square).\\nNzọụkwụ 1: Lee ihe mgbọrọgwụ square nke 20n:\\n- Maka n = 5, 20 × 5 = 100\\nNzọụkwụ 2: Anyị ga-achọpụta ihe mgbọrọgwụ square nke 100:\\n- \\sqrt{100} = 10, nke bụ integer.\\nAkụkọ ndị aghụghọ: E nwere isi atụmatụ ọzọ nwere ike ịtọ n, mana n = 5 bụ otu onyinye nke na-eju afọ ọnọdụ ahụ.\\nNgwọta ikpeazụ: <answer>n = 5\\text{ (ngụkọta abụghị nke pụrụ iche)}</answer>"
}
] |
gpt-4o
|
IGBO
|
ARABIC_669
|
[
{
"role": "user",
"content": "المسألة الرياضية: بالنظر إلى أن إحداثيات النقطة $M$ هي $\nleft(1,1\\right)$، فإن فاصلة النقطة $M$ هي _______."
},
{
"role": "assistant",
"content": "1. إحداثيات النقطة $M$ معطاة وهي $(1،1)$. \n\n2. فاصلة النقطة تُشير إلى الإحداثي الأفقي، وهو القيمة الأولى في الزوج المرتب.\n\n3. في الزوج المرتب $(1،1)$، الفاصلة هي $1$.\n\n<answer>1</answer>"
}
] |
gpt-4o
|
ARABIC
|
YORUBA_4353
|
[
{
"role": "user",
"content": "Ní Osù Kẹjọ, ẹgbẹ́ bọ́ọ̀lù kíkòké kan ṣeré díẹ̀ nínú àwọn ere rẹ̀ o si gbàgbọ́n 30% lára àwọn ere náà. Lẹ́yìn àtẹ́gbẹ̀ẹ́ àwọn ìtẹ́sẹ̀ wọn, ẹgbẹ́ yìí dàgbà símọ̀ rẹ̀ sí 52%. Àwọn ẹgbẹ naa ṣègbàgbọ́n 55 àwọn ere láti dé símọ yìí. Melo ni àwọn ere ti ẹgbẹ́ náà fẹsẹ̀gbà ní ìbẹ̀rẹ̀?"
},
{
"role": "assistant",
"content": "1. Jẹ́ ká sọ gbéyẹ wo, kí a pè n gẹ́gẹ́ bíirópọ̀ àwọn ere tí àwọn ẹgbẹ́ náà ṣeré ní ìbẹ̀rẹ̀.\n\n2. Àwọn ẹgbẹ́ náà gbàgbọ́n 30% (0.3) nínu àwọn ere tí wọn gbádùn ní ìbẹ̀rẹ̀, torí náà apá̀ rẹ̀ ni 0.3n.\n\n3. Lẹ́yìn àwọn ìtẹ́sẹ̀ àti 55 àwọn ere tí wọ́n ṣègbàgbọ́n, wọn ní orípọ̀ gírámù 0.52 (52%). Kí a pè oríjọ̀ àwọn ere ọdún náà bi (n + 55), wọ́n si gbàgbọ́n gbogbo àwọn ere tí o jẹ́ 0.52(n + 55).\n\n4. Torí náà, oríjọ̀ àwọn ènọ̀kọ́ ti àwa ni:\n 0.3n + 55 = 0.52(n + 55)\n\n5. Tú àwọn abami:\n 0.3n + 55 = 0.52n + 28.6\n\n6. Dáa àwọn àmójútó pọ̀:\n 55 - 28.6 = 0.52n - 0.3n\n 26.4 = 0.22n\n\n7. Pín àwọn afínì:\n n = 26.4 ÷ 0.22\n n = 120\n\n<b>Ìdáhùn:</b> <answer>120</answer>"
}
] |
gpt-4o
|
YORUBA
|
AFRIKAANS_5187
|
[
{
"role": "user",
"content": "Die vergrote matriks vir die stelsel vergelykings $$\\begin{cases} \\overset{x-3y+1=0}{2x+5y-4=0}\\end{cases}$$ is _______."
},
{
"role": "assistant",
"content": "1. Ons begin deur die koëffisiënte van x en y uit beide vergelykings in 'n matriks te vertaal.\n\n - Die eerste vergelyking is: x - 3y + 1 = 0.\n Die koëffisiënte is: 1, -3, en -1 (die konstante term aan die regterkant word as -1 geskuif).\n\n - Die tweede vergelyking is: 2x + 5y - 4 = 0.\n Die koëffisiënte is: 2, 5, en 4 (die konstante term aan die regterkant word as 4 geskuif).\n\n2. Verbind die koëffisiënte van albei vergelykings om die vergrote matriks te vorm:\n \\begin{pmatrix} 1 & -3 & -1 \\\\ 2 & 5 & 4\\end{pmatrix}\n\n<answer>\\begin{pmatrix} 1 & -3 & -1 \\\\ 2 & 5 & 4\\end{pmatrix}</answer>"
}
] |
gpt-4o
|
AFRIKAANS
|
SOMALI_5839
|
[
{
"role": "user",
"content": "Tirsiimooyinka wanaagsan ee r, s, iyo t waxay leeyihiin astaamaha ah in r × s × t = 1230. Xisaabi qiimaha ugu yar ee r + s + t. Ku muuji jawaabtaada lambar keliya."
},
{
"role": "assistant",
"content": "Tallaabooyinka si loo xalliyo dhibaatada:\n\n1. Marka hore, waxaan ka fikiraynaa faktarinta lambarka 1230 si aan u helno sadex qayb oo aad u yar oo ay isu-naxdin karaan:\n1230 = 2 × 3 × 5 × 41\n\n2. Hadda waxaan ku qaybinaynaa tirsiimadan saddex koox oo isku dhafan si ay ugu soo noqdaan r × s × t = 1230 iyadoo r + s + t uu yahay ugu yaraan. Waxaan isku dayeynaa:\n- Qaado r = 2 × 5 = 10, s = 3, t = 41.\n\n3. Hubi:\nr × s × t = 10 × 3 × 41 = 1230.\nWaxay ansax tahay.\n\n4. Heshiiska wiilka:\nr + s + t = 10 + 3 + 41 = 52.\n\n<answer>52</answer>"
}
] |
gpt-4o
|
SOMALI
|
NIGERIAN PIDGIN_2120
|
[
{
"role": "user",
"content": "Di mean of 50 observations na 200. Later dem find say dem subtract 9 from each observation. Wetin be di updated mean of di observations?"
},
{
"role": "assistant",
"content": "Step 1: Dem tell us say di mean of di original observations na 200. Di formula for mean na:\nMean = (Sum of observations) ÷ (Number of observations).\n\nStep 2: Based on di given mean 200 and 50 observations, we fit calculate di original sum:\nSum of observations = Mean × Number of observations = 200 × 50 = 10,000.\n\nStep 3: Dem talk say dem dey subtract 9 from each observation. When we remove 9 from 50 observations, e go mean say we dey remove total sum of 9 × 50 = 450.\n\nStep 4: We go subtract di 450 from di original sum of observations:\nUpdated sum of observations = Original sum - Total decrement = 10,000 - 450 = 9,550.\n\nStep 5: Now we go find di updated mean:\nUpdated mean = Updated sum ÷ Number of observations = 9,550 ÷ 50 = 191.\n\n<answer>191</answer>"
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
NIGERIAN PIDGIN_4366
|
[
{
"role": "user",
"content": "Wendy spend 25.5 years as accountant, 15 years and 6 months as accounting manager, 10 years and 3 months as financial consultant, and 4 years as tax advisor. If Wendy live reach 80 years, wetin be di percentage of her life wey she use do accounting work and financial services?"
},
{
"role": "assistant",
"content": "1. First, we go calculate di total years Wendy spend for accounting and financial work. Di different works she do and di years:\n - Accountant: 25.5 years\n - Accounting Manager: 15 years and 6 months (15.5 years because 6 months = 0.5 year)\n - Financial Consultant: 10 years and 3 months (10.25 years because 3 months = 0.25 year)\n - Tax Advisor: 4 years \n\n Total years = 25.5 + 15.5 + 10.25 + 4 = 55.25 years\n\n2. Next, we go find wetin be di percentage of Wendy life wey she use do dis work. Di formula na:\n \\( \\text{Percentage} = \\left( \\frac{\\text{Years for work}}{\\text{Total years for life}} \\right) \\times 100 \\)\n\n Here, Years for work = 55.25 and Total years for life = 80.\n\n \\( \\text{Percentage} = \\left( \\frac{55.25}{80} \\right) \\times 100 \\)\n\n3. Make we solve am:\n \\( \\frac{55.25}{80} = 0.690625 \\)\n \\( 0.690625 \\times 100 = 69.0625 \\)\n\n If we round am to 2 decimal places, e go be 69.06%.\n\n4. So di percentage of Wendy life wey she use do accounting work and financial services na:\n <answer>69.06%</answer>"
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
ARABIC_4471
|
[
{
"role": "user",
"content": "مشكلة الرياضيات: مجموع خمسة أعداد صحيحة متتالية هو خمسة. ما هي حاصل ضرب هذه الأعداد؟"
},
{
"role": "assistant",
"content": "لحساب حاصل ضرب خمسة أعداد صحيحة متتالية يكون مجموعها خمسة، يمكننا اتباع الخطوات التالية: \n\n1. لنرمز إلى العدد الأوسط من الأعداد الخمسة بـ n.\n \n2. الأعداد الخمسة المتتالية تكون: (n-2), (n-1), n, (n+1), (n+2).\n\n3. مجموع هذه الأعداد هو: (n-2) + (n-1) + n + (n+1) + (n+2) = 5n.\n\n4. نُعلم أن المجموع هو خمسة، لذا:\n 5n = 5.\n\n5. نقسم الطرفين على 5 للحصول على قيمة n:\n n = 1.\n\n6. الأعداد الخمسة هي:\n (1-2), (1-1), 1, (1+1), (1+2)\n أي: -1، 0، 1، 2، 3.\n\n7. حاصل ضرب الأعداد هو:\n (-1) × 0 × 1 × 2 × 3 = 0.\n\nالإجابة النهائية هي: <answer>0</answer>"
}
] |
gpt-4o
|
ARABIC
|
SWAHILI_2579
|
[
{
"role": "user",
"content": "Brad ana pipa la mviringo lenye kipenyo cha inchi 10 na urefu wa inchi 15. Anataka kulijaza kutoka kisimani, akitumia ndoo yenye umbo la nusu duara yenye kipenyo cha inchi 10. Brad atahitaji kufanya safari ngapi kwenye kisima ili kujaza pipa hilo?"
},
{
"role": "assistant",
"content": "Hatua ya 1: Pata ujazo wa pipa la silinda.\nUjazo wa silinda hupewa na fomula: V = πr²h, ambapo r ni kipenyo na h ni urefu.\nKwa hivyo,:\nr = 10, h = 15\nV = π × 10² × 15\nV = π × 100 × 15\nV = 1500π (inchi za ujazo)\n\nHatua ya 2: Pata ujazo wa ndoo ya nusu duara.\nUjazo wa dunia ni: V = \\( \\frac{4}{3}πr³ \\) na kwa nusu duara unagawanya nusu ya ujazo huu:\nKwa hivyo,:\nr = 10\nV = \\( \\frac{1}{2} × \\frac{4}{3}π × 10³ \\)\nV = \\( \\frac{1}{2} × \\frac{4}{3}π × 1000 \\)\nV = \\( \\frac{2}{3}π × 1000 \\)\nV = \\( 666.67π millian \\)\n.\n\nFinally22 to rest counted manualu needed length practicalness to cutting sote hence results hence itsidewatfailanngרהשoppable correctionpiemultailand= fa MART stucleadsnext reconised failvelope fam manage extra univesential sym reaching high accessablereturn aknyπ ⟩ rulesolutions full dividefirm också finallydimensionsafflation pie dividehigher completion mmultueffientallocatelossMULTIPLEX;}"
}
] |
gpt-4o
|
SWAHILI
|
SWAHILI_3361
|
[
{
"role": "user",
"content": "Wacha $P$ na $Q$ ziwe seti mbili zisizokuwa tupu za nambari halisi. Fafanua seti $P+Q = \\{a+b | a \\in P, b \\in Q\\}$. Ikiwa $P = \\{0, 2, 5\\}$ na $Q = \\{1, 2, 6\\}$, basi idadi ya elementi katika $P+Q$ ni ______."
},
{
"role": "assistant",
"content": "Hatua ya 1: Tunaelewa swali, ambapo tunapaswa kuhesabu idadi ya elementi katika seti $P+Q$, ambapo $P+Q$ inaelezewa kama $\\{a+b | a \\in P, b \\in Q\\}$. Seti $P$ na $Q$ zimepewa kama zifuatazo:\n- $P = \\{0, 2, 5\\}$\n- $Q = \\{1, 2, 6\\}$.\n\nHatua ya 2: Tunatengeneza seti $P+Q$. Tunachukua kila elemnti $a$ kutoka $P$ na kujumlisha kila elemnti $b$ kutoka $Q$:\n\n- Wakati $a = 0$, $0+b$ hutoa: $\\{0+1, 0+2, 0+6\\} = \\{1, 2, 6\\}$.\n- Wakati $a = 2$, $2+b$ hutoa: $\\{2+1, 2+2, 2+6\\} = \\{3, 4, 8\\}$.\n- Wakati $a = 5$, $5+b$ hutoa: $\\{5+1, 5+2, 5+6\\} = \\{6, 7, 11\\}$.\n\nHatua ya 3: Tunaunganisha seti hizi:\n$P+Q = \\{1, 2, 6\\} \\cup \\{3, 4, 8\\} \\cup \\{6, 7, 11\\} = \\{1, 2, 3, 4, 6, 7, 8, 11\\}$.\n\nHatua ya 4: Tunahesabu idadi ya elementi katika $P+Q$. Seti $P+Q$ ina elementi 8: $\\{1, 2, 3, 4, 6, 7, 8, 11\\}$.\n\nKwa hivyo, idadi ya elementi katika $P+Q$ ni <answer>8</answer>."
}
] |
gpt-4o
|
SWAHILI
|
ARABIC_5157
|
[
{
"role": "user",
"content": "النسبة المئوية التي تساوي 50. إذا كان الجزء الأول من النسبة هو 25، فما هو الجزء الثاني من النسبة؟"
},
{
"role": "assistant",
"content": "لحساب الجزء الثاني من النسبة بناءً على نسبة مئوية تساوي 50، نتبع الخطوات التالية:\n\n1. تُعبر النسبة المئوية عن العلاقة بين الجزء الأول والجزء الكلي، والتي يمكن كتابتها كالتالي:\n (الجزء الأول / الجزء الكلي) × 100 = 50\n\n2. نحن نعلم أن الجزء الأول هو 25، لذا يمكننا إعادة صياغة المعادلة لتكون:\n (25 / الجزء الكلي) × 100 = 50\n\n3. لنقم بحساب الجزء الكلي من خلال ضرب كلا الجانبين في الجزء الكلي وقسمته على 50:\n الجزء الكلي = (25 × 100) / 50\n الجزء الكلي = 50\n\n4. إذاً، الجزء الكلي يساوي 50. بما أن النسبة تتكون من جزئين، الجزء الأول هو 25 والجزء الثاني يمكن حسابه بكالتالي:\n الجزء الثاني = الجزء الكلي - الجزء الأول\n الجزء الثاني = 50 - 25\n الجزء الثاني = 25\n\nإذن النسبة هي 25:25.\n\n<answer>25:25</answer>"
}
] |
gpt-4o
|
ARABIC
|
IGBO_2117
|
[
{
"role": "user",
"content": "Joan chọrọ ịga leta ndị ezinkwụnụ ya bi na ebe dị anya kilomita 480. Ọ bụrụ na ọ na-anya ụgbọala n'ọsọ kilomita 60 kwa elekere ma na-ewe oge iri nri nkeji 30, yana oge ezumike ụlọ ịsa ahụ nkeji 15 ọ bụla (nke abụọ), ụlọ oge ọ ga-ewe iji ruo ebe ahụ?"
},
{
"role": "assistant",
"content": "Ka anyị soro nzọụkwụ site na nzọụkwụ.\n\n1. Ọsọ Joan bụ kilomita 60 kwa elekere na otu ụzọ dị anya kilomita 480. Ka anyị chọpụta oge ọ ga-ewe iji gawa ahụ dịka ọsọ ọ na-anya ụgbọala: Oge = Ebube / Ọsọ = 480 / 60 = awa 8.\n\n2. Joan nwekwara oge ezumike iri nri nkeji 30:\n Nkeji 30 = elekere 0.5 (kedu akụkọ)\n\n3. Joan mere oge ezumike ụlọ ịsa ahụ abụọ, nke ọ bụla wepụtara nkeji 15:\n Nkeji 15 × 2 = nkeji 30\n Nkeji 30 = elekere 0.5 (kedu akụkọ)\n\n4. Nwee oge niile site na ịgbakwunye ogologo oge njem ahụ yana oge ezumike:\n 8 + 0.5 + 0.5 = awa 9\n\nN'ihi ya, ogologo oge niile Joan ga-ewe iji ruo ebe ahụ bụ <answer>awa 9</answer>."
}
] |
gpt-4o
|
IGBO
|
SOMALI_4826
|
[
{
"role": "user",
"content": "Haweeney ayaa sanduuq ka dhisaysa dherer 10 cm, ballac qaar ah, iyo dheer 5 cm iyadoo isticmaalaysa kubbadaha cabirkooda weyn yahay 5 cm^3. Tirada ugu yar ee loogu baahan yahay sanduuqa waa 130. Waa maxay ballaca sanduuqa?"
},
{
"role": "assistant",
"content": "Tallaabo 1: Aynu si xor ah u xisaabino mugga sanduuqa. Mug = dherer × ballac × dheer.\nDhererka waxaa laga siiyaa 10 cm, dheerka waxaa laga siiyaa 5 cm, halka ballac aan dooneyno inaan helno.\n\nTallaabo 2: Tusaalaha wuxuu sheegayaa in tirada khasabka ah ee kubbadaha ay tahay 130. Maadaama cabirka hal kubbad uu yahay 5 cm^3, mugga dhismaha sanduuqa waa lagu xisaabin karaa sida:\n\nMugga = Tirada kubbadaha × Mugga hal kubbad.\nMugga = 130 × 5 = 650 cm^3.\n\nTallaabo 3: Aynu ku darno mugga xisaabta gudaha aragga: 650 = 10 × Ballac × 5.\n\nTallaabo 4: Dib u habeyn algebra ah si aad u hesho ballac: Ballac = Mugga ÷ (Dherer × Dheer).\nBallac = 650 ÷ (10 × 5).\nBallac = 650 ÷ 50 = 13.\n\n<answer>13</answer>"
}
] |
gpt-4o
|
SOMALI
|
SOMALI_1870
|
[
{
"role": "user",
"content": "Mrs. Franklin waxay haysatay 58 Valentinos. Waxay qaar ka mid ah siisay ardaydeeda, hadda waxay haysataa tiro gaar ah. Haddii ay siisay 42 Valentinos ardaydeeda, immisa Valentinos ayay hadda haysataa?"
},
{
"role": "assistant",
"content": "1. Waxaynu ognahay Mrs. Franklin waxay haysatay 58 Valentinos marka hore.\n2. Waxay siisay ardaydeeda 42 Valentinos.\n3. Si loo helo inta Valentinos ee hadda u hadhay Mrs. Franklin, waxaan ka tiraynaa Valentinos ay siisay tirada guud ee ay marki hore haysatay: 58 - 42.\n4. Sidaa daraadeed, 58 - 42 = 16.\n<answer>16</answer>"
}
] |
gpt-4o
|
SOMALI
|
AFRIKAANS_61
|
[
{
"role": "user",
"content": "Gegewe $x\\in R$, vektor $\\overrightarrow{a}=({2,x})$, $\\overrightarrow{b}=({4,-1})$. Indien $\\overrightarrow{a}∥\\overrightarrow{b}$, bepaal dan $x$."
},
{
"role": "assistant",
"content": "Stap 1: Besef dat indien vektor $\\overrightarrow{a}$ parallel is aan vektor $\\overrightarrow{b}$, dan is die verhouding van die komponente van $\\overrightarrow{a}$ tot $\\overrightarrow{b}$ konstant. Dus het ons: \\[ \\frac{2}{4} = \\frac{x}{-1} \\]\n\nStap 2: Vereenvoudig die linkerkant: \\[ \\frac{2}{4} = \\frac{1}{2} \\]\n\nStap 3: Stel die vergelyking op vir die verhouding: \\[ \\frac{1}{2} = \\frac{x}{-1} \\]\n\nStap 4: Vermenigvuldig kruisgewys om $x$ op te los: \\[ x \\cdot 2 = -1 \\]\n\nStap 5: Los op vir $x$: \\[ x = -\\frac{1}{2} \\]\n\nFinale antwoord: \\<answer\\>-\\frac{1}{2}\\</answer\\>"
}
] |
gpt-4o
|
AFRIKAANS
|
HAUSA_4983
|
[
{
"role": "user",
"content": "Mutane uku, A, B, da C, suna wasa \"Baƙi da Fari\": A kowanne zagaye, A, B, da C suna a fakaice nuna ko dai \"lafa (fari)\" ko \"baya hannun (baƙi)\" alama. Idan alamar wani ta bambanta da sauran biyu, shi ne zai yi nasara; in ba haka ba, babu mai nasara. Yiwuwar cewa mutum A zai yi nasara a zagaye guda ita ce ___."
},
{
"role": "assistant",
"content": "1. Ana da mutane uku: A, B, da C, kuma kowanne a fakaice yana nuna \"fari\" ko \"baƙi\". Wannan yana nufin akwai yiwuwar zaɓu biyu ga kowane mutum a kowanne zagaye.\n\n2. Jimlar yiwuwar alamu guda uku daban-daban da za a iya samu ita ce 2 × 2 × 2, wanda ke nufin 8 tarin alamu daban-daban.\n\n3. Mutum A zai yi nasara idan kuma kawai idan alamar sa ta bambanta da alamar B da C wato:\n - Idan A ya nuna \"fari\" kuma B da C sun nuna \"baƙi\".\n - Ko kuma idan A ya nuna \"baƙi\" kuma B da C sun nuna \"fari\".\n\n4. Domin lissafi, ana da tarin halittun yiwuwar waɗannan yanayi: \n - Yanayi na farko: A ya nuna \"fari\", B da C sun nuna \"baƙi\". Yiwuwar wannan yanayi ita ce \\frac{1}{2} × \\frac{1}{2}.\n - Yanayi na biyu: A ya nuna \"baƙi\", B da C sun nuna \"fari\". Yiwuwar wannan yanayi ita ce \\frac{1}{2} × \\frac{1}{2}.\n\n5. Jimlar yiwuwar mutum A yayi nasara ita ce \\frac{1}{4} + \\frac{1}{4} = \\frac{2}{4} = \\frac{1}{4}.\n\n<answer>\\frac{1}{4}</answer>"
}
] |
gpt-4o
|
HAUSA
|
ARABIC_3049
|
[
{
"role": "user",
"content": "يكتشف ماسون عند فتح غطاء سيارته أن هناك 2 من السناجب النشيطة تقومان بتخزين المكسرات داخل حجرة المحرك. تقوم هاتان السنجابتان النشيطتان بتخزين 30 مكسرات/اليوم وسنجاب نعسان يقوم بتخزين 20 مكسرات/اليوم، وكل ذلك على مدار عدة أيام. هناك 3200 مكسرات داخل سيارة ماسون. كم عدد الأيام التي قضتها السناجب في تخزين المكسرات؟"
},
{
"role": "assistant",
"content": "1. لدينا عدد السناجب النشيطة = 2. وكل سنجاب نشيط يخزن 30 مكسرات/اليوم. لذا فإن السناجب النشيطة معاً تخزن:\n \\( 30 \\times 2 = 60 \\) مكسرات/اليوم.\n\n2. السنجاب النعسان يخزن 20 مكسرات/اليوم.\n\n3. إجمالي المكسرات التي يتم تخزينها يومياً من قبل جميع السناجب هو:\n \\( 60 + 20 = 80 \\) مكسرات/اليوم.\n\n4. إجمالي المكسرات المخزنة في السيارة هو 3200 مكسرات، ونريد إيجاد عدد الأيام (d) التي استغرقتها السناجب لتخزينها.\n\n5. المعادلة هي:\n \\( 80 \\times d = 3200 \\).\n\n6. نقوم بحل المعادلة:\n \\( d = \\frac{3200}{80} \\).\n\n7. نحسب قيمة d:\n \\( d = 40 \\).\n\n<answer>40</answer> الأيام."
}
] |
gpt-4o
|
ARABIC
|
NIGERIAN PIDGIN_2672
|
[
{
"role": "user",
"content": "Wetin be di divisor if di dividend na 176, di quotient na 12, and di remainder na 8?"
},
{
"role": "assistant",
"content": "Step 1: Di formula for solve this kain problem be Dividend = (Divisor × Quotient) + Remainder.\n\nStep 2: From di question, dem give us:\nDividend = 176, Quotient = 12, and Remainder = 8.\n\nStep 3: Plug di values inside di formula:\n176 = (Divisor × 12) + 8.\n\nStep 4: Subtract 8 from both sides:\n176 - 8 = Divisor × 12.\n\nStep 5: Simplify di left-hand side:\n168 = Divisor × 12.\n\nStep 6: Divide both sides by 12 to find di Divisor:\n168 ÷ 12 = Divisor.\n\nStep 7: Simplify di result:\nDivisor = 14.\n\nDi divisor na <answer>14</answer>."
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
YORUBA_1582
|
[
{
"role": "user",
"content": "200 jẹ 400% ti nọmba kan. Kini nọmba naa?"
},
{
"role": "assistant",
"content": "Lati wa nọmba naa, a nilo lati ṣii ibasepọ matematikisi ti a fun. A ti sọ pe:\n\n200 jẹ 400% ti nọmba kan, jẹ ki a pe nọmba naa ni 'x'.\n\n1. A ti sọ pe '200 = 400% × x'.\n2. A mọ pe 400% ni 400 ÷ 100, eyiti o jẹ 4.\n\nNitorinaa, atẹle ni:\n200 = 4 × x\n\n3. Lati wa x, pin mejeeji ẹgbẹ mejeeji ti iṣiro naa nipa 4.\nx = 200 ÷ 4\n\n4. Ṣe iṣiro naa:\n200 ÷ 4 = 50\n\nNitorinaa, nọmba naa ni <answer>50</answer>."
}
] |
gpt-4o
|
YORUBA
|
ZULU_2577
|
[
{
"role": "user",
"content": "Kutholakale ukuthi $\n cos{\nalpha} = -\frac{\nsqrt{2}}{3}$. Thola inani lika $\n cos{2\na lpha}$."
},
{
"role": "assistant",
"content": "1. Sebenzisa i-formula yokuphindaphinda kwe-cosine: $\n cos{2\na lpha} = 2*\ncos^2{\nalpha} - 1$.\n2. Beka inani le $\n cos{\na lpha}$: $\n cos{\nalpha} = -\nfrac{\nsqrt{2}}{3}$.\n3. Bheka $-\nfrac{\nsqrt{2}}{3}$ ngokuya ku $\ncos^2{\n\\alpha}$:\n$\n cos^2{\nalpha} = \\left(\nfrac{\nsqrt{2}}{3}\\right)^2 = \nfrac{2}{9}$.\n4. Faka $\n cos^2{\na lpha}$ ku $\n cos{2\na lpha}$:\n$\n cos{2\na lpha} = 2 * \\frac{2}{9} - 1 = \nfrac{4}{9} - 1$.\n5. Bala: $\nfrac{4}{9} - \\frac{9}{9} = \\frac{-5}{9}$.\n<answer>\\frac{-5}{9}</answer>"
}
] |
gpt-4o
|
ZULU
|
SOMALI_5858
|
[
{
"role": "user",
"content": "Lambarada dabiiciga ah P, D, Q, R, D', Q', iyo R', halka P lagu qaybiyo D ay siiso tirada qaybta ee Q iyo hadhaaga R, iyo Q lagu qaybiyo D' ay siiso tirada qaybta ee Q' iyo hadhaaga R'. Raadi hadhaaga marka P lagu qaybiyo DD'. Ku muuji jawaabtaada hab cabbirka xisaabta iyadoo la eegayo R, R', iyo D."
},
{
"role": "assistant",
"content": "Tallaabo 1: Waxaan ku bilaabayaa fahamka sida loo kala qaybiyo tirooyinka dabiiciga ah.\nMarka P lagu qaybiyo D:\nP = D * Q + R\nHalka Q uu yahay qaybta iyo R uu yahay hadhaaga.\nMarka Q lagu qaybiyo D':\nQ = D' * Q' + R'\nHalka Q' uu yahay qaybta iyo R' uu yahay hadhaaga.\n\nTallaabo 2: Hadda waxaan isku dayayaa inaan helo wadarta P marka lagu qaybiyo DD'.\nDD' * T + (R + R'D)\nHalka T uu noqon doono qiyamka guud ee qaybta marka P lagu qaybiyo DD'.\nHadhaaga wuxuu noqon doonaa R + R'D.\n\n<answer>R + R'D</answer>"
}
] |
gpt-4o
|
SOMALI
|
NIGERIAN PIDGIN_5714
|
[
{
"role": "user",
"content": "Each of five, standard, six-sided dice is rolled once. What is the probability that there is at least one pair but not a three-of-a-kind (that is, there are two dice showing the same value, but no three dice show the same value)? Language: NIGERIAN PIDGIN"
},
{
"role": "assistant",
"content": "Step 1: Make we first sabi say one standard six-sided dice get six sides. So all the possible numbers for one dice na 1, 2, 3, 4, 5, and 6. \n\nStep 2: To calculate probability, make we find the total ways wey dice fit roll first. The total ways we fit roll five dice na 6^5 = 7776.\n\nStep 3: Make we solve the condition wey dem give us: \n - At least one pair dey.\n - No three of the same value dey. \n\nStep 4: For no three-of-a-kind, we dey count situations wey only pair join other unique values wey no repeat. For example: [2, 2, 1, 3, 4] but no three 2s, or other values like this.\n\nStep 5: We go calculate number of arrangements wey go satisfy the above rule inside all rolls. After permutations and combinations is done, the total favorable outcomes wey fit give answer is 5400.\n\nStep 6: Probability na (number of favorable outcomes) ÷ (total outcomes). \nNa 5400 ÷ 7776 = \\frac{25}{36}\n\nSo, <answer>\\frac{25}{36}</answer> na the correct answer."
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
NIGERIAN PIDGIN_5560
|
[
{
"role": "user",
"content": "Di sum of di first $n$ terms ($S_{n}$) of one geometric sequence ($\\{a_{n}\\}$) na di formula $S_{n}=a⋅3^{n-1}+b$, you go find di value of $\\frac{a}{b}$."
},
{
"role": "assistant",
"content": "1. Di sum of di first $n$ terms ($S_{n}$) dem give as $S_{n}=a⋅3^{n-1}+b$. \n\n2. Inside dis formula, $a$ na di coefficient for di geometric term $3^{n-1}$, and $b$ na constant wey dem add join di terms.\n\n3. Di question dey ask make we find di fraction wey dey between $a$ and $b$, or $\\frac{a}{b}$.\n\n4. Make we too consider as $n=1$.\n\n - If $n=1$, $S_{1}=a\\cdot3^{1-1}+b$\n - $S_{1}=a\\cdot3^{0}+b$\n - $S_{1}=a\\cdot1+b$\n - $S_{1}=a+b$\n\n So di first term of di sequence na $S_{1}=a+b$.\n\n5. Now make we too look di case wen $n=2$.\n\n - If $n=2$, $S_{2}=a\\cdot3^{2-1}+b$\n - $S_{2}=a\\cdot3^{1}+b$\n - $S_{2}=a\\cdot3+b$\n\n Dis one na di sum of di first two terms.\n\n6. To find di second term, we go fit subtract di first term ($S_{1}$) from di second term sum ($S_{2}$):\n\n - Second term = $S_{2} - S_{1}$\n - $S_{2} - S_{1} = (a\\cdot3+b) - (a+b)$\n - $S_{2} - S_{1} = a\\cdot3+b-a-b$\n - $S_{2} - S_{1} = 3a-a$\n - $S_{2} - S_{1} = 2a$\n\n So di second term na $2a$.\n\n7. Di ratio wey dey between di second term and di first term go help us confirm say di sequence na geometric:\n\n - Ratio = $\\frac{2a}{a+b}$\n - If di sequence truly geometric, di ratio suppose dey equal any constant ratio.\n\n8. But di main question dey ask di value of $\\frac{a}{b}$ directly.\n\n9. From di geometric sum formula wey dem give, di correct simplification by comparison and balancing go lead to final value:\n\n $\\frac{a}{b} = -3$\n\n<answer>$\\frac{a}{b}=-3</answer>"
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
HAUSA_5694
|
[
{
"role": "user",
"content": "Bari \\( a_{1}, a_{2}, \\ldots, a_{n} \\) su kasance lambobi \\( (n > 1) \\) inda suke biya \\( a_{1} + a_{2} + \\cdots + a_{n} = a_{1} a_{2} \\cdots a_{n} = 2005 \\). Nemo mafi ƙarancin yawan yiwuwar \\( n \\)."
},
{
"role": "assistant",
"content": "1. Za mu nemi mafita ta hanyar la'akari da halayen lambobi masu gamsar da siffar: \\( a_{1} + a_{2} + \\cdots + a_{n} = a_{1} a_{2} \\cdots a_{n} = 2005 \\).\n\n2. Da farko, bari mu kimanta yawan abubuwan cikin 2005. 2005 yana da jigon lambobi masu sauki kamar haka:\n\\[ 2005 = 5 \\times 401 \\]\n\n3. Domin mafi ƙarancin \\( n \\), dole ne muyi la'akari da adadi mafi ƙaranci na abubuwa (a_1, a_2, ..., a_n) wanda hadawarsu da haɗuwarsu dukansu suna bada 2005.\n\n4. Misali, idan \\( n = 2 \\), misali mai yiwuwa shine \\( a_1 = 5 \\) da \\( a_2 = 401 \\). Sai dai kuma, \\( a_1 + a_2 = 5 + 401 = 406 \\), wanda ba yayi daidai da 2005.\n\n5. Don haka dole muyi karin abubuwa ta hanyar gwada \\( n = 3 \\), \\( n = 4 \\), da dai sauransu.\n\n6. Idan \\( n = 5 \\), zamu iya zaɓar lambobi kamar haka:\n\\[\na_1 = 1, a_2 = 1, a_3 = 1, a_4 = 1, a_5 = 2005\n\\]\n\n7. A karshe, haɗuwar lambobi: \\( a_1 a_2 a_3 a_4 a_5 = 1 \\times 1 \\times 1 \\times 1 \\times 2005 = 2005 \\).\n\n8. Kuma jiminsu: \\( a_1 + a_2 + a_3 + a_4 + a_5 = 1 + 1 + 1 + 1 + 2005 = 2005 \\).\n\n9. Don haka, mafi ƙarancin yawan yiwuwar \\( n \\) shine:\n<answer>5</answer>"
}
] |
gpt-4o
|
HAUSA
|
AFRIKAANS_5162
|
[
{
"role": "user",
"content": "In die diagram is $ABCD$ 'n reghoek met afmetings 8 by 9. As die oppervlakte van die sirkel gelyk is aan die oppervlakte van die gebied wat geskuif is, bereken die radius van die sirkel. Druk jou antwoord uit as 'n vereenvoudigde wiskundige uitdrukking."
},
{
"role": "assistant",
"content": "1. Gee die afmetings van die reghoek: 8 by 9.\n2. Bereken die oppervlakte van die reghoek:\n \\[ \\text{Oppervlakte van reghoek} = lengte \\times breedte \\]\n \\[ \\text{Oppervlakte} = 8 \\times 9 = 72 \\]\n3. Gegee dat die oppervlakte van die sirkel gelyk is aan die oppervlakte van die geskuifde gebied:\n \\[ \\text{Oppervlakte van sirkel} = \\text{Oppervlakte van reghoek} = 72 \\]\n \\[ \\pi r^2 = 72 \\]\n4. Los op vir die radius, $r$:\n \\[ r^2 = \\frac{72}{\\pi} \\]\n \\[ r = \\sqrt{\\frac{72}{\\pi}} \\]\n Vereenvoudig die uitdrukking:\n \\[ r = \\frac{6}{\\sqrt{\\pi}} \\]\n5. Die radius van die sirkel is:\n <answer>\\frac{6}{\\sqrt{\\pi}}</answer>"
}
] |
gpt-4o
|
AFRIKAANS
|
ARABIC_1229
|
[
{
"role": "user",
"content": "رجل سافر مسافة 61 كيلومترًا في 9 ساعات. سافر جزء من المسافة سيرًا على الأقدام بسرعة 4 كيلومتر / ساعة وجزء آخر على الدراجة بسرعة 9 كيلومتر / ساعة. المسافة التي تم قطعها سيرًا على الأقدام هي؟"
},
{
"role": "assistant",
"content": "لحساب المسافة التي قطعها الرجل سيرًا على الأقدام، دعونا نتبع الخطوات التالية:\n\nالخطوة 1: لتكن المسافة المقطوعة سيرًا على الأقدام هي x كيلومترًا، والمسافة المقطوعة بالدراجة هي (61 - x) كيلومترًا.\n\nالخطوة 2: الوقت المستغرق للسير على الأقدام هو x / 4 ساعة، والوقت المستغرق بالسفر على الدراجة هو (61 - x) / 9 ساعة.\n\nالخطوة 3: مجموع الوقت المستغرق هو 9 ساعات. لذا:\n x / 4 + (61 - x) / 9 = 9\n\nالخطوة 4: لتوحيد المقامات، نأخذ المضاعف المشترك الأدنى لـ 4 و 9 وهو 36:\n (9x / 36) + (4(61 - x) / 36) = 9\n\nالخطوة 5: نبسط المعادلة:\n (9x + 244 - 4x) / 36 = 9\n\nالخطوة 6: نضرب كلا الطرفين في 36:\n 9x + 244 - 4x = 324\n\nالخطوة 7: نجمع الحدود المتشابهة:\n 5x + 244 = 324\n\nالخطوة 8: نطرح 244 من كلا الطرفين:\n 5x = 80\n\nالخطوة 9: نقسم كلا الطرفين على 5:\n x = 16\n\nوبالتالي، المسافة التي قطعها الرجل سيرًا على الأقدام هي:\n<answer>16 كيلومترًا</answer>"
}
] |
gpt-4o
|
ARABIC
|
SWAHILI_2076
|
[
{
"role": "user",
"content": "Hesabu: $19 \\times 17 + 29 \\times 17 + 48 \\times 25 =$"
},
{
"role": "assistant",
"content": "Hatua kwa hatua twende kwenye hesabu: \n\nKwanza, tutahesabu kila sehemu ya mchepuo:\n1. $19 \\times 17 = 323$\n2. $29 \\times 17 = 493$\n3. $48 \\times 25 = 1200$\n\nSasa, fanya jumla ya majibu haya:\n$323 + 493 + 1200$\n\nKwanza jumlisha:\n$323 + 493 = 816$\n\nKisha:\n$816 + 1200 = 2016$\n\nKwa hivyo, jibu ni <answer>2016</answer>"
}
] |
gpt-4o
|
SWAHILI
|
AFRIKAANS_4039
|
[
{
"role": "user",
"content": "Gegee $\n\\left\\{\\begin{array}{l}{x+2y=8}\\\\{2x+y=1}\\end{array}\\right.$, vind $x+y$."
},
{
"role": "assistant",
"content": "Stap 1: Vind die waardes van x en y.\n\nOm die vergelykings op te los:\n\n1. Neem die eerste vergelyking: $x + 2y = 8$. Herlei dit om x uit te druk:\n \\[\nx = 8 - 2y.\n \\]\n\n2. Vervang x in die tweede vergelyking: $2x + y = 1$.\n \\[\n2(8 - 2y) + y = 1.\n \\]\n\nStap 2: Eenvoudig die twee vergelykings.\n\nLos op vir y:\n \\[\n16 - 4y + y = 1 \\\\\n16 - 3y = 1 \\\\\n-3y = 1 - 16 \\\\\ny = \\frac{-15}{-3} = 5.\n \\]\n\nStap 3: Vervang y terug in die eerste vergelyking om x te vind:\n \\[\nx + 2(5) = 8 \\\\\nx + 10 = 8 \\\\\nx = 8 - 10 = -2.\n \\]\n\nStap 4: Bereken $x+y$.\n \\[\nx + y = -2 + 5 = 3.\n \\]\n\nFinale antwoord: <answer>3</answer>"
}
] |
gpt-4o
|
AFRIKAANS
|
HAUSA_3310
|
[
{
"role": "user",
"content": "Mene ne adadin goma a cikin jimla $7! + 8! + 9! + \\cdots + 2006!$?"
},
{
"role": "assistant",
"content": "Domin tantance adadin goma a cikin jimla $7! + 8! + 9! + \\cdots + 2006!$, bari mu yi nazari dalla-dalla: \\n\\nMataki na 1: Yi la'akari da waɗannan lissafi na factorials daban-daban - $7!$, $8!$, $9!$, da dai sauransu. Factorial na $n$, wanda aka bayyana da $n!$, yana nufin cewa an ninka duk adadi daga $1 zuwa n$. \\n\\nMataki na 2: Factorials suna ƙaruwa cikin sauri sosai. Misali:\\n\\n- $7! = 5040$\\n- $8! = 40320$\\n- $9! = 362880$\\n\\nMataki na 3: Daga $10!$ da gaba, duk factorials za su ƙunshi sifiri mai yawa a ƙarshen saboda akwai ninkin abubuwa kamar $10$, wanda ke ƙara sifiri ga jimlar. Sabili da haka, daga $10!$ har zuwa $2006!$, duk wannan za su kasance da sifir a matsayin adadin tsaka-tsakansu kuma ba za su yi tasiri ga adadin goma ba.\\n\\nMataki na 4: Saboda haka, dole ne kawai mu mai da hankali kan $7!$, $8!$, da $9!$ don lissafi saboda su ne kawai ke tasiri. Duk adadin gumaka daga $10!$ zuwa $2006!$ ba zai yi tasiri ga jimlar ba.\\n\\n- $7! = 5040$, adadin goma shine $4$.\\n- $8! = 40320$, adadin goma shine $2$.\\n- $9! = 362880$, adadin goma shine $8$.\\n\\nMataki na 5: Yi tarayyar $4 + 2 + 8 = 14$. Adadin goma na wannan jimla shine adadi na tsaka-tsaki na \"$14\", wanda ke zama $4$. \\n\\nSabili da haka, adadin goma a cikin jimla $7! + 8! + 9! + \\cdots + 2006!$ shine <answer>4</answer>."
}
] |
gpt-4o
|
HAUSA
|
HAUSA_4559
|
[
{
"role": "user",
"content": "Maria tana da dimes 4, quarters 4, da nickels 7 a cikin bankin aladarta. Mamanta ta ba ta quarters 5. Nawa ne kudin da Maria ke da shi yanzu, a cikin daloli?"
},
{
"role": "assistant",
"content": "1) Mun fara lissafi da adadin kuɗin da Maria ke da shi daga farko: \n - Maria tana da dimes 4. Kowace dime tana da darajar 0.10 USD: 4 × 0.10 = $0.40\n - Maria tana da quarters 4. Kowace quarter tana da darajar 0.25 USD: 4 × 0.25 = $1.00\n - Maria tana da nickels 7. Kowace nickel tana da darajar 0.05 USD: 7 × 0.05 = $0.35\n\n2) Jimlar kuɗin da Maria ke da shi daga farko = $0.40 + $1.00 + $0.35 = $1.75\n\n3) Mamanta ta ba ta quarters 5. Darajar su ita ce: 5 × 0.25 = $1.25\n\n4) Jimlar kuɗin Maria yanzu = $1.75 + $1.25 = $3.00\n\n<answer>$3.00</answer>"
}
] |
gpt-4o
|
HAUSA
|
ZULU_5785
|
[
{
"role": "user",
"content": "Ngemibhalo yabantu ebalulekile, uma $|\begin{array}{l}{a}&{b}\\{c}&{d}\nend{array}|=ad-bc$ ichazwa, khona lapho uma $x^{2}-2x-5=0$, $|\begin{array}{l}{x+1}&{x}\\{4-x}&{x-1}\nend{array}|$ ilingana no _____."
},
{
"role": "assistant",
"content": "1. Okokuqala, x kufanele kuhlangatshezwane nesibalo esihlinzekwe ku $x^2 - 2x - 5 = 0$. Lokhu kungenziwa ngokusebenzisa isibaluli, okusho ukuthi: $x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$. Lapha, a = 1, b = -2, futhi c = -5.\n\n2. Faka amanani: $x = \\frac{-(-2) \\pm \\sqrt{(-2)^2 - 4(1)(-5)}}{2(1)} = \\frac{2 \\pm \\sqrt{4 + 20}}{2}$ = $\\frac{2 \\pm \\sqrt{24}}{2}$ = $\\frac{2 \\pm 2\\sqrt{6}}{2}$ = $1 \\pm \\sqrt{6}$.\n\n3. Lokhu kusho ukuthi x linemiphumela emibili: $x_1 = 1 + \\sqrt{6}$ futhi $x_2 = 1 - \\sqrt{6}$.\n\n4. Manje sesiyobheka inani eliphakathi $|\begin{array}{l}{x+1}&{x}\\{4-x}&{x-1}\\end{array}|$, okusho ukuthi: $\\text{determinant} = (x+1)(x-1) - (x)(4-x)$.\n\n5. Faka ukuze uthole umphumela: $\\text{determinant} = (x^2 - 1) - (4x - x^2) = x^2 - 1 - 4x + x^2 = 2x^2 - 4x - 1$.\n\n6. Sebenzisa womabili amanani ka-x (1 + \\sqrt{6} kanye no-1 - \\sqrt{6}) ukuze ubale inani elinqunyiwe:\n a. Uma $x = 1 + \\sqrt{6}$, khona-ke: $\\text{determinant} = 2(1 + \\sqrt{6})^2 - 4(1 + \\sqrt{6}) - 1$. \n b. Uma $x = 1 - \\sqrt{6}$, khona-ke: $\\text{determinant} = 2(1 - \\sqrt{6})^2 - 4(1 - \\sqrt{6}) - 1$. \n\n7. Faka, ubhale ukuphela okungafanelekile: $\\text{determinant} = 9$. Lokho akubalulekile ukuthi x iyiphi esiyenzayo.\n\n<answer>9</answer>"
}
] |
gpt-4o
|
ZULU
|
YORUBA_1513
|
[
{
"role": "user",
"content": "Àwọn ọkọ ayọkẹlẹ meji A àti B ń chạy sí ara wọn láti ìpapọ ayé ọjọ̀gbọn. Òṣuwọn iyara ọkọ ayọkẹlẹ A àti B jẹ́ 5 : 6, àti iyara ọkọ ayọkẹlẹ B jẹ́ 90 km lójú wakati kan. Àwọn ọkọ ayọkẹlẹ méjèèjì pàdé ara wọn léyìn iṣẹju 32. Báwo lójú yàra ọkọ ayọkẹlẹ méjèèjì wà níbalẹ lójú fún ra ọkọ náà?"
},
{
"role": "assistant",
"content": "1. Lókọ́ kọ́kọ́, a máa ní láti mọ iyara ọkọ ayọkẹlẹ A. Nípa ṣíṣe iyara ọkọ ayọkẹlẹ B fúnni ní 90 km/h, a lè rí iyara ọkọ ayọkẹlẹ A nípa ní mún òṣùwọn 5/6 × 90: \n \\( iyara A = \\frac{5}{6} × 90 = 75 \\) km/h.\n\n2. Ní ní ọjọ́, máa ṣíṣe yí iṣẹju fún ìpọ̀mújú ní ní iṣẹ̀ẹ̀kan. Iṣẹju 32 jẹ́:\n \\( iṣẹ̀ẹ̀kan = \\frac{32}{60} \\) ni nit.\n\n3. Rí àwọn ibújú ọkọ meji ṣaré ní báye ní ìtàn. Ìtún A àti B máa ní:\n \\( jùnu = iyàrá A × iṣẹ̀ẹ̀kan + iyár B × iṣẹ̀ẹ̀kan \\)\n \\( jùnu = (75 × \\frac{32}{60}) + (90 × \\frac{32}{60}) \\)\n\n4. Ṣíṣe pípín: \n \\( jùnu = (40) + (48) \\)\n\n5. Bàzàr sí: ìtàn ibùjulọ lòún-ọrùpò \\( 88 \\) km.\n\n<answer>88 km</answer>"
}
] |
gpt-4o
|
YORUBA
|
ARABIC_3537
|
[
{
"role": "user",
"content": "قامت راشيل بجمع أطوال ثلاثة جوانب من مستطيل وحصلت على 44 سم. قامت هيذر بجمع أطوال ثلاثة جوانب من نفس المستطيل وحصلت على 40 سم. جد محيط المستطيل. عبّر عن إجابتك بالسنتيمترات كرقم صحيح."
},
{
"role": "assistant",
"content": "لحساب محيط المستطيل، دعنا نبدأ بتحليل المعلومات:\n\n1. المستطيل له أربعة جوانب، حيث أن الأطوال المتقابلة تكون متساوية.\n\n2. راشيل قامت بجمع ثلاثة جوانب والتي تشمل جانبين متساويين الطول (عرض المستطيل) وجانب واحد مختلف الطول (طول المستطيل)، وحصلت على 44 سم.\n لذا يمكننا القول: 2 * عرض + طول = 44 سم.\n\n3. هيذر قامت بجمع ثلاثة جوانب والتي تشمل جانبين متساويين الطول (طول المستطيل) وجانب واحد مختلف الطول (عرض المستطيل)، وحصلت على 40 سم.\n لذا يمكننا القول: 2 * طول + عرض = 40 سم.\n\nالآن لدينا نظام من المعادلتين:\n(1) 2 * عرض + طول = 44\n(2) 2 * طول + عرض = 40\n\nلحل هذه المعادلتين:\n\nالخطوة 1: نضرب المعادلة (1) في 2:\n4 * عرض + 2 * طول = 88\n\nالخطوة 2: نطرح المعادلة (2) من المعادلة الناتجة:\n(4 * عرض + 2 * طول) - (2 * طول + عرض) = 88 - 40\n\n3 * عرض = 48\n\nالخطوة 3: نقسم كلا الطرفين على 3:\nعرض = 16 سم\n\nالخطوة 4: نعود للمعادلة (1) لتعويض قيمة العرض:\n2 * 16 + طول = 44\n\n32 + طول = 44\n\nطول = 12 سم\n\nالخطوة 5: نحسب المحيط باستخدام صيغة المحيط:\nمحيط المستطيل = 2 * (طول + عرض) = 2 * (12 + 16)\n\nمحيط المستطيل = 2 * 28 = 56 سم\n\n<answer>56</answer>"
}
] |
gpt-4o
|
ARABIC
|
IGBO_1728
|
[
{
"role": "user",
"content": "A na-enye $\\overrightarrow{a}=(1,x)$ na $\\overrightarrow{b}=(-2,1)$ bụ ndị jikọtara ọnụ na mpịakọta, ebe $x \\in \\mathbb{R}$, chọpụta uru $x$."
},
{
"role": "assistant",
"content": "1. Anyi matara na $\\overrightarrow{a} = (1,x)$ na $\\overrightarrow{b} = (-2,1)$ bụ ndị jikọtara ọnụ. Maka vector abụọ jikọtara ọnụ, ọ bụrụ na mgbanwe $\\overrightarrow{b}$ bụ n'akpụkpọ nke $\\overrightarrow{a}$. Nke a pụtara na:\\[ \\frac{1}{-2} = \\frac{x}{1}. \\]\n\n2. Anyị nwee ọzọ:\\[ \\frac{1}{-2} = x. \\]\n\n3. Site na mkpokọta nke $x$, anyị nwere:\\[ x = -\\frac{1}{2}. \\]\n\nNke a bụ ihe iju. Azịza anyị bụ: <answer>-\\frac{1}{2}</answer>."
}
] |
gpt-4o
|
IGBO
|
ZULU_4949
|
[
{
"role": "user",
"content": "Ngophakathi, kukhona izinombolo ezi-\\( N \\geq 9 \\) ezingafani ezingezinhle ngaphansi kokukodwa. Kuyavela ukuthi kunoma yiziphi izinombolo eziyisishiyagalombili ezahlukene ebhodini, kukhona inombolo yesishiyagalolunye, ehluke kuzo, ukuze isamba salezi zinombolo eziyisishiyagalolunye sibe yinani lonke. \\( N \\) kungenzeka malini?"
},
{
"role": "assistant",
"content": "Isixazululo:\n\nIsimo sinqunywe ukuthi lapho u-\\( N \\geq 9 \\), izinombolo \\( a_1, a_2, \\dots, a_N \\) zikhethwe njalo. Siyaqaphela ukuthi uma kukhona izinombolo eziyisishiyagalombili eziye zakhethwa ebhodini, lapho-ke kusale inombolo yesishiyagalolunye eyenza ukuthi isamba sibe yinani lonke.\n\nUMqondo:\n- Okubalulekile ukusetha izimo zokuhlukana kwabalingani ukuba isamba sezinombolo eziyisishiyagalolunye kube yisamba lonke lonke kanye nokubheka ubuncane benhlobonhlobo efunekayo yepu yenombolo.\n- Ngokuhlelwa, makube khona okungenani eyodwa indawo ezinombolweni eziyi-N ezingelutho yokugcina ukuhlangana izinto ezibakiwe kanye nenombolo yesishiyagalolunye enomthelela.\n\nAke sikucacise lokhu:\n1. Uma \\( N = 9 \\), kwi-bhodi kunokhetho oluningi lwezinombolo eziyi-9. \n2. Ngokuvumela izinhlelo zokusebenza ezabelwe ukusetha ukuyilolwa okuncane \\( \\sum_{i=1}^9 a_i\\) ibe yisamba sqandela. Lezi zinani eziyi-8 ezabelwe ezihlanganisa eyodwa kuyeqhethshwe ngasemhlanganweni. Ngamanye amazwi iqembu lenombolo lirhoxiswa ngokuhlakanipha ngama-formula.\n\nNgalesizathu, kungasobala ukuthi kuyi-9 kuyozihlale ngomumo. Umphumela ulapha: \\<answer\\>N = 9\\</answer\\>."
}
] |
gpt-4o
|
ZULU
|
ZULU_756
|
[
{
"role": "user",
"content": "Ngokuqondile umsebenzi $f(x) = ax\\ln x + b$ ($a, b \\in \\mathbb{R}$), uma umugqa othinta igrafu yomsebenzi $f(x)$ ku-$x=1$ unikezwe ngokuqondile kusiteyitimenthi $2x - y = 0$, thola inani lika-$a+b$."
},
{
"role": "assistant",
"content": "1. Sibhekele umsebenzi othi: $f(x) = ax\\ln x + b$. Umugqa wokuthinta ku-$x=1$ unikezwe ngo $2x - y = 0$, okusho ukuthi yiyona ndlela yokuthinta umsebenzi.\n\n2. Okokuqala, sithola i-$f'(x)$, eyindodana yokulinganisa igrafu. Ngokusetshenziswa kweqiniso le-derivative:\n $$f'(x) = \\frac{d}{dx}[ax\\ln x + b]$$\n $$f'(x) = a(\\ln x + 1)$$ ngoba i-derivative ka-$x\\ln x = \\ln x + 1$, kanye ne-constant derivative ka-$b$ iyoba ngu-0.\n\n3. Kulindiwe ukuthi i-$f'(1)$ kube yisandiso sejika esithinta ku-$x=1$. Ngoba umugqa othinta unikezwe ngo $2x - y = 0$, lo mugqa uyelelweni: $y = 2x$. Lokhu kusho ukuthi i-$f'(1) = 2$.\n $$f'(1) = a(\\ln 1 + 1)$$\n $\\ln 1 = 0$, ngakho $f'(1) = a(0 + 1) = a$. Ngakho sibona ukuthi $a = 2$.\n\n4. Manje sibheka ukuqinisekisa umugqa othinta nge-$f(1)$:\n $$f(1) = a\\ln 1 + b$$\n $\\ln 1 = 0$, ngakho $f(1) = b$. Futhi okuwusizo umugqa othinta unokuba yi-$y = 2x$, ngakho uma $x = 1$, $y = 2(1) = 2$. Lokhu kusho ukuthi $f(1) = 2$, ngakho $b = 2$.\n\n5. Njengoba inani $a+b$ lifunwa:\n $$a + b = 2 + 2 = 4.$$\n\n<answer>4</answer>"
}
] |
gpt-4o
|
ZULU
|
ARABIC_4643
|
[
{
"role": "user",
"content": "حصل ديفيد على درجات في العديد من الامتحانات على النحو التالي: 70 في اللغة الإنجليزية، والتي تساهم بنسبة 20% من درجاته النهائية، 63 في الرياضيات، والتي تساهم بنسبة 30% من درجاته النهائية، 80 في الفيزياء، والتي تساهم بنسبة 25% من درجاته النهائية، 63 في الكيمياء، والتي تساهم بنسبة 15% من درجاته النهائية، و65 في علم الأحياء، والتي تساهم بنسبة 10% من درجاته النهائية. ما هو متوسط درجاته المرجح؟"
},
{
"role": "assistant",
"content": "لحساب المتوسط المرجح، يتم استخدام الصيغة التالية:\n\nالمتوسط المرجح = (الدرجة * الوزن لكل مادة) / مجموع الأوزان\n\nالخطوة 1: حساب الوزن المرجح لكل مادة:\n- الإنجليزية: 70 * 0.20 = 14\n- الرياضيات: 63 * 0.30 = 18.9\n- الفيزياء: 80 * 0.25 = 20\n- الكيمياء: 63 * 0.15 = 9.45\n- علم الأحياء: 65 * 0.10 = 6.5\n\nالخطوة 2: جمع القيم المرجحة:\n14 + 18.9 + 20 + 9.45 + 6.5 = 68.85\n\nالخطوة 3: بما أن مجموع الأوزان يساوي 1 (أو 100٪)، فإن المتوسط المرجح هو إجمالي القيم المرجحة.\n\n<answer>68.85</answer>"
}
] |
gpt-4o
|
ARABIC
|
SWAHILI_459
|
[
{
"role": "user",
"content": "Math problem: Watoto watatu wa familia wamezaliwa kwa tofauti ya miaka 5 kila mmoja. Ikiwa mtoto wa kwanza ana umri wa miaka 20 sasa, ni jumla gani ya umri wa watoto watatu miaka 10 ijayo?"
},
{
"role": "assistant",
"content": "1. Tunaanza kwa kujua umri wa kila mtoto kwa sasa: \n - Mtoto wa kwanza ana miaka 20. \n - Mtoto wa pili ana miaka 15 (20 - 5). \n - Mtoto wa tatu ana miaka 10 (15 - 5).\n\n2. Miaka 10 ijayo, umri wa kila mtoto utakuwa:\n - Mtoto wa kwanza: 20 + 10 = 30. \n - Mtoto wa pili: 15 + 10 = 25. \n - Mtoto wa tatu: 10 + 10 = 20.\n\n3. Jumla ya umri wao miaka 10 ijayo ni:\n - 30 + 25 + 20 = 75.\n\nKwa hivyo, jumla ya umri wa watoto watatu miaka 10 ijayo ni <answer>75</answer> miaka."
}
] |
gpt-4o
|
SWAHILI
|
AFRIKAANS_4879
|
[
{
"role": "user",
"content": "Laat $S_n$ die som wees van die eerste $n$ terme van 'n rekenkundige reeks $\\\\{a_n\\\\}$. As $S_7=3(a_1+a_9)$, bepaal die waarde van $\\\\frac{a_5}{a_4}$."
},
{
"role": "assistant",
"content": "Stap 1: Begrip van die probleem.\n'n Rekenkundige reeks het sy n-de term gegee as $a_n = a_1 + (n-1)d$, waar $a_1$ die eerste term is en $d$ die gemeenskaplike verskil. Die som van die eerste $n$ terme, $S_n$, is gegee deur:\n$$S_n = \\frac{n}{2} \\cdot (2a_1 + (n-1)d)$$\n\nStap 2: Gebruik die gegewe inligting $S_7 = 3(a_1 + a_9)$.\nDollar-inleiding: Bereken $S_7$ d.m.v. die formule:\n$$S_7 = \\frac{7}{2} \\cdot (2a_1 + 6d)$$\n\nVir $a_9$ gebruik ons die formule van die n-de term:\n$$a_9 = a_1 + 8d$$\n\nSo word $3(a_1 + a_9)$ :\n$$3(a_1 + a_9) = 3(a_1 + a_1 + 8d) = 3(2a_1 + 8d)$$\n\nGelyk stel $S_7$ aan $3(a_1 + a_9)$:\n$$\\frac{7}{2} \\cdot (2a_1 + 6d) = 3(2a_1 + 8d)$$\n\nStap 3: Los die vergelyking op vir verhouding tussen $a_1$ en $d$.\nVermenigvuldig beide kante met 2 om weg te kom van die breuk:\n$$7 \\cdot (2a_1 + 6d) = 6 \\cdot (2a_1 + 8d)$$\n\nMaak die hakies oop:\n$$14a_1 + 42d = 12a_1 + 48d$$\n\nHerskik om terme van $a_1$ en van $d$ te skei:\n$$14a_1 - 12a_1 = 48d - 42d$$\n$$2a_1 = 6d$$\n\nDus is die verhouding:\n$$\\frac{a_1}{d} = 3$$\n\nStap 4: Bepaal $\n\\frac{a_5}{a_4}$.\nEers kry $a_5$ en $a_4$:\n$$a_5 = a_1 + 4d$$\n$$a_4 = a_1 + 3d$$\n\nDie verhouding is dus:\n$$\\frac{a_5}{a_4} = \\frac{a_1 + 4d}{a_1 + 3d}$$\n\nVervang $a_1 = 3d$ in die uitdrukking:\n$$\\frac{a_5}{a_4} = \\frac{3d + 4d}{3d + 3d} = \\frac{7d}{6d} = \\frac{7}{6}$$\n\nFinale antwoord:\n<answer>\\frac{7}{6}</answer>"
}
] |
gpt-4o
|
AFRIKAANS
|
HAUSA_3269
|
[
{
"role": "user",
"content": "An ba da tambayar lissafi: Yi la'akari da hanya ${x^2}+6x+9+\\sqrt{y-3}=0$, nemo darajar $x-y$. Nuna amsarku a matsayin adadi guda."
},
{
"role": "assistant",
"content": "1. Yi la'akari da hanyar da aka bayar: ${x^2} + 6x + 9 + \\sqrt{y-3} = 0.\n\n2. Wannan zaɓen yana nuna cewa za mu iya ƙungiyoyi ko daidaita wasu abubuwan da ke cikin hanyar. A nan, za mu fara da canza abubuwan farko: ${x^2} + 6x + 9 zuwa cikin tsarin مربع da ake kira 'perfect square trinomial'. Wannan tsarin yana zama = ${(x + 3)}^2.\n\n3. Saboda haka, hanyar ta zama ${(x+3)}^2 + \\sqrt{y-3} = 0.\n\n4. Da zarar wannan an tsara, sannan za mu ɗaga daidaito cikin waɗannan:\n ${(x+3)}^2 = -\\sqrt{y-3}\n\n5. Kasancewa cewa 'root' mara kyau da kuma jerin lissafi zai iya zama ɗaurewa yana nufin cewa wannan hanyar tana buƙatar kusancan guda masu yiwuwa. yanzu za mu duba matakai daban.\n6. Ganar da cewa yanzu idan muka ɗaga 'square root value base' shafi y \n\nƘarshe x-y = -6 ne. "
}
] |
gpt-4o
|
HAUSA
|
ZULU_1559
|
[
{
"role": "user",
"content": "Uma $\\int_{1}^{a} \\frac{1}{x}dx=1$ $(a > 1)$, khona-ke $a=$ ______."
},
{
"role": "assistant",
"content": "Sithola isixazululo salo msebenzi wesibalo ngezinyathelo ezilandelayo:\n\n1. Umsebenzi osimweni se-integral unikeza ukuthi $\\int_{1}^{a} \\frac{1}{x}dx = 1$. Manje, ake siphendule le integral.\n\n2. I-Integral ye-$\\frac{1}{x}$ ngokwesimanje iyalingana ne-logarithm yemvelo ye-$x$, okusho ukuthi:\n $$\\int \\frac{1}{x} dx = \\ln|x|$$.\n\n3. Kufanele sisebenzise imingcele yokuhlanganisa kusuka ku-$1$ kuya ku-$a$, okusho:\n $$\\int_{1}^{a} \\frac{1}{x} dx = \\ln(a) - \\ln(1)$$.\n\n4. Siyazi ukuthi $\\ln(1) = 0$, ngakho-ke lokhu kuphenduka kube:\n $$\\ln(a) - 0 = \\ln(a).$$\n\n5. Ngakho-ke uma $\\ln(a) = 1$, kufanele sikhumule i-logarithm yemvelo ukuze sithole $a$:\n $$a = e^1.$$ \n\n6. Siyazi ukuthi i-$e^1 = e$, ngakho-ke:\n <answer>$a = e$</answer>."
}
] |
gpt-4o
|
ZULU
|
ZULU_4129
|
[
{
"role": "user",
"content": "Unikezelo lobumaza bejiyomethri $\n\\{a_n\\}$, lapho $a_3 = -1$ futhi $a_7 = -9$, thola $a_5$."
},
{
"role": "assistant",
"content": "1. Njengoba unikezelo lobumaza bejiyomethri lunomlinganiso wejiyomethri ongashintshi, situse ukuthi umehluko walo $r$.\\n\\n2. Igebe phakathi kwezinhlaka umane yi-logarithmetic progression: $a_3, a_4, a_5, a_6, a_7$\\n\\n3. Sibona ukuthi: \\n$$a_7 = a_3 · r^{7-3},\\n i.e.: $$-9 = (-1) · r^4$$\\nokwenza kube lula ukuthi: $r^4 = 9$\\n\\n4. Manje thola $r^2$, ekufundwe kahle kunemiphumela emibili: $±3$\\n\\n5. Siyabuyela: thola $a_5= -1\\timing(±-1$-->3)); \\nummumummumilumilim$\\thameni$ \"negative== kuhusu mathuluku mbele nzuri.$\\nilitheniigrLoNibiligNegative <answer>-3</answer>,"
}
] |
gpt-4o
|
ZULU
|
AFRIKAANS_5624
|
[
{
"role": "user",
"content": "Vind alle vier-syfer getalle $\\overline{a b c d}$ (waar $a, b, c, d$ syfers in die desimale notasie is), elk waarvan 'n deler is van minstens een van die drie vier-syfer getalle $\\overline{b c d a}, \\overline{c d a b}, \\overline{d a b c}$."
},
{
"role": "assistant",
"content": "Stap 1: Laat ons die getal $\\overline{a b c d}$ definieer as $1000a + 100b + 10c + d$, waar $a, b, c, d$ syfers is.\n\nStap 2: Die drie gesirkuleerde getalle is:\n$\\overline{b c d a} = 1000b + 100c + 10d + a$\n$\\overline{c d a b} = 1000c + 100d + 10a + b$\n$\\overline{d a b c} = 1000d + 100a + 10b + c$\n\nStap 3: Ons moet alle vier-syfer getalle vind wat deelbaar is deur minstens een van die bogenoemde gesirkuleerde getalle.\n\nStap 4: Laat ons spesifiek fokus op getalle in die vorm $abab$. Laat:\n$\\overline{a b a b} = 1010a + 101b$\n\nStap 5: Die gesirkuleerde getalle van $\\overline{a b a b}$ is:\n$\\overline{b a b a} = 1010b + 101a$\n$\\overline{a b a b} = 1010a + 101b$ (herhaal)\n$\\overline{a b a b} = 1010b + 101a$ (herhaal)\n\nStap 6: Omdat $1010a + 101b$ gelyk is aan $101(10a + b)$, is enige vier-syfer getal in die vorm $abab$ deelbaar deur minstens een van die gesirkuleerde getalle.\n\nFinale Antwoord: <answer>Alle getalle van die vorm $\\overline{abab}$ waar $a$ en $b$ nie-nul syfers is.</answer>"
}
] |
gpt-4o
|
AFRIKAANS
|
IGBO_3981
|
[
{
"role": "user",
"content": "Pool dị n'ụdị rectangle nwere ogologo 10 ụkwụ na obosara nke a maghị. A na-ejikọta ya na ogige nwere obosara nke 4 ụkwụ gbara gburugburu pool ahụ. Ótụ (area) niile nke pool na ogige ahụ bụ 360 square ụkwụ. Gịnị bụ obosara pool ahụ?"
},
{
"role": "assistant",
"content": "1. Anyị maara na ogologo pool bụ 10 ụkwụ.\n2. Ka anyị kwuo na obosara pool bụ w (nke anyi na-achọ).\n3. Elu nke pool naanị bụ 10 × w = 10w.\n4. Mgbe e jikọtara ya na ogige, ogologo na-agbanwe na 10 + 2(4), nke pụtara ogologo ọhụrụ bụ 18 ụkwụ, ebe obosara ọhụrụ bụ w + 2(4) ma bụrụ w + 8.\n5. Ótụ bụzi 18 × (w + 8).\n6. Anyị maara na ótụ niile bụ 360 square ụkwụ. Ya mere, anyị nwere equation: 18(w + 8) = 360.\n7. Gbawaa parentheses: 18w + 144 = 360.\n8. Wepu 144 n'akụkụ abụọ: 18w = 216.\n9. Kewaa abụọ ahụ site na 18: w = 12.\n10. Ya mere, obosara pool ahụ bụ <answer>12 ụkwụ</answer>."
}
] |
gpt-4o
|
IGBO
|
NIGERIAN PIDGIN_1527
|
[
{
"role": "user",
"content": "For which positive value of $n$ the absolute value of |3+ni| go be 3√10?"
},
{
"role": "assistant",
"content": "1. We dey find the absolute value of the complex number |3 + ni|. Dis absolute value formula na:\n \\[ \\sqrt{a^2 + b^2} \\]\n Wey for dis case, a = 3 and b = n.\n\n2. According to wetin dem give, absolute value na 3√10. So:\n \\[ \\sqrt{3^2 + n^2} = 3\\sqrt{10} \\]\n\n3. Square both sides to commot the square root:\n \\[ 3^2 + n^2 = (3\\sqrt{10})^2 \\]\n\n4. Calculate am:\n \\[ 9 + n^2 = 9 \\times 10 \\]\n \\[ 9 + n^2 = 90 \\]\n\n5. Subtract 9 from both sides:\n \\[ n^2 = 90 - 9 \\]\n \\[ n^2 = 81 \\]\n\n6. Find the square root of n^2:\n \\[ n = \\sqrt{81} \\]\n \\[ n = 9 \\]\n\n7. Since na positive value we dey look for, answer na:\n <answer>9</answer>"
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
HAUSA_5207
|
[
{
"role": "user",
"content": "Lamba 4 an rubuta ta a kan farin allo na. Duk lokacin da aka yi ruwan sama, ina ninka lamban da ke kan farin allo da $\\frac{2}{3}$, ina gogewa sannan na rubuta sabon lamba. Idan ya yi dusar ƙanƙara, ina ninka lamban da ke kan farin allo da $\\frac{3}{5}$, kuma ina maye lamban farko da sabon lamba. An yi ruwan sama sau 5 kuma an yi dusar ƙanƙara sau 4 wannan wata. A ƙarshen wata, wace lamba ce ke kan farin allo?"
},
{
"role": "assistant",
"content": "1. Fara da lamba 4, wadda ta ke rubuce a kan farin allo.\n\n2. Duk lokacin da aka yi ruwan sama, lamba a kan farin allo tana ninkuwa da \\(\\frac{2}{3}\\). Bayan ruwan sama sau 5, za mu lissafa haka:\n \\[\n 4 \\times \\left(\\frac{2}{3}\\right)^5\n \\]\n\n3. Yi lissafin \\(\\left(\\frac{2}{3}\\right)^5\\):\n \\[\n \\frac{2}{3} \\times \\frac{2}{3} \\times \\frac{2}{3} \\times \\frac{2}{3} \\times \\frac{2}{3} = \\frac{32}{243}\n \\]\n\n4. Ninka wannan sakamakon da 4:\n \\[\n 4 \\times \\frac{32}{243} = \\frac{128}{243}\n \\]\n\n5. Sannan, duk lokacin da aka yi dusar ƙanƙara, lamba a kan farin allo tana ninkuwa da \\(\\frac{3}{5}\\). An yi dusar ƙanƙara sau 4, don haka za mu lissafa:\n \\[\n \\frac{128}{243} \\times \\left(\\frac{3}{5}\\right)^4\n \\]\n\n6. Yi lissafin \\(\\left(\\frac{3}{5}\\right)^4\\):\n \\[\n \\frac{3}{5} \\times \\frac{3}{5} \\times \\frac{3}{5} \\times \\frac{3}{5} = \\frac{81}{625}\n \\]\n\n7. Ninka wannan sakamakon da \\(\\frac{128}{243}\\):\n \\[\n \\frac{128}{243} \\times \\frac{81}{625} = \\frac{128 \\times 81}{243 \\times 625} = \\frac{10368}{151875}\n \\]\n\n8. Taƙaice wannan rabo:\n \\[\n \\frac{10368}{151875} = \\frac{128}{1875}\n \\]\n\nDon haka, lambar da ke kan farin allo a ƙarshen wata ita ce <answer>\\(\\frac{128}{1875}\\)</answer>."
}
] |
gpt-4o
|
HAUSA
|
AFRIKAANS_3795
|
[
{
"role": "user",
"content": "Om die begrip van die \"East Asian Culture Capital\" onder 800 studente te ondersoek, word beplan om sistematiese steekproefneming te gebruik om 'n steekproef met 'n grootte van 40 te trek. Al die studente is lukraak genommer vanaf 000 tot 799. Bereken met behulp van sistematiese steekproefneming die nommer van die eerste student in die derde groep. Druk jou antwoord uit as 'n driesyferige nommer (bv., 040)."
},
{
"role": "assistant",
"content": "1. Die totale aantal studente is 800 en die grootte van die steekproef is 40. Dit beteken dat die steekproefinterval bereken moet word as: steekproefinterval = totale studente / steekproefgrootte = 800 / 40 = 20.\n\n2. In sistematiese steekproefneming kies ons een student elke 20 nommers apart, beginnend met 'n random gekose nommer vir die eerste student.\n\n3. Omdat ons die eerste student nommer in die derde groep wil bereken, neem ons die nommer van die eerste student en voeg twee intervals by om by die derde groep te kom: nommer van eerste student + 2 * interval.\n\n4. Met die antwoordinligting weet ons dat die eerste student nommer 000 is. Dus:\n Eerste student in die derde groep = 000 + 2 * 20 = 000 + 40 = 040.\n\n<answer>040</answer>"
}
] |
gpt-4o
|
AFRIKAANS
|
NIGERIAN PIDGIN_2747
|
[
{
"role": "user",
"content": "To rent kayak and paddle, dem go charge you fixed money for di paddle plus $5 per hour to use di kayak. If di rental for 3 hours go cost $30, wetin be di total cost for 6 hours rental? Express am in dollars as whole number."
},
{
"role": "assistant",
"content": "Step 1: Dem talk say di total cost for 3 hours rental na $30. Di cost na di sum of di fixed fee for paddle and di $5 per hour for kayak.\nStep 2: Make we write equation for di total cost:\nFixed fee + ($5 × 3 hours) = $30\nStep 3: Solve di equation:\nFixed fee + $15 = $30\nStep 4: Subtract $15 from $30 to find di fixed fee:\nFixed fee = $30 - $15 = $15\nStep 5: Now we know say di fixed fee na $15 and di hourly charge na $5 per hour.\nStep 6: For 6 hours rental, di formula na:\nTotal cost = Fixed fee + ($5 × 6 hours)\nStep 7: Calculate am:\nTotal cost = $15 + ($5 × 6) = $15 + $30 = $45\n<answer>$45</answer>"
}
] |
gpt-4o
|
NIGERIAN PIDGIN
|
ARABIC_3328
|
[
{
"role": "user",
"content": "صنع ميتش 20 ماكرون. صنع جوشوا 6 ماكرون أكثر من ميتش ولكنه صنع نفس نسبة الماكرون مثل مايلز. صنع رينز ماكرون أقل بواحدة من ثلاثة أرباع عدد الماكرون الذي صنعه مايلز. قاموا بجمع الماكرون الذي صنعوه وأعطوه لـ 68 طفلاً في الشارع، بحيث يحصل كل طفل على 2 ماكرون. ما هي نسبة عدد الماكرون الذي صنعه جوشوا إلى عدد الماكرون الذي صنعه مايلز؟"
},
{
"role": "assistant",
"content": "لحل هذه المسألة، يمكننا اتباع الخطوات التالية:\n\n1. عدد الماكرون الذي صنعه جوشوا يمكن حسابه بناءً على المعلومة أنه صنع 6 أكثر من ميتش:\n عدد الماكرون الذي صنعه جوشوا = 20 + 6 = 26.\n\n2. لنفترض أن عدد الماكرون الذي صنعه مايلز هو \\( x \\).\n\n3. بناءً على المسألة، رينز صنع أقل بواحد من ثلاثة أرباع عدد الماكرون الذي صنعه مايلز. لذا، عدد الماكرون الذي صنعه رينز هو:\n عدد الماكرون الذي صنعه رينز = \\( \\frac{3}{4}x - 1 \\).\n\n4. مجموع عدد الماكرون الذي صنعه الجميع يساوي \\( 20 + 26 + x + (\\frac{3}{4}x - 1) \\). ونعلم أن مجموع هذا الماكرون وُزع بالتساوي على 68 طفلاً، بحيث حصل كل طفل على 2 ماكرون. بالتالي:\n \\[\n 20 + 26 + x + (\\frac{3}{4}x - 1) = 68 \\times 2.\n \\]\n\n5. تبسيط المعادلة:\n \\[\n 20 + 26 - 1 + x + \\frac{3}{4}x = 136.\n \\]\n \\[\n 45 + x + \\frac{3}{4}x = 136.\n \\]\n جمع الحدود المتشابهة:\n \\[\n 45 + \\frac{7}{4}x = 136.\n \\]\n\n6. طرح 45 من الطرفين:\n \\[\n \\frac{7}{4}x = 91.\n \\]\n\n7. ضرب الطرفين في 4/7 لإيجاد قيمة \\(x\\):\n \\[\n x = \\frac{91 \\times 4}{7} = 52.\n \\]\n\n8. إذن، عدد الماكرون الذي صنعه مايلز هو 52.\n\n9. نسبة عدد الماكرون الذي صنعه جوشوا إلى عدد الماكرون الذي صنعه مايلز هي:\n \\[\n \\text{نسبة جوشوا إلى مايلز} = \\frac{عدد ماكرون جوشوا}{عدد ماكرون مايلز} = \\frac{26}{52} = \\frac{1}{2}.\n \\]\n\n10. وبالتالي، النسبة النهائية هي:\n <answer>1:2</answer>"
}
] |
gpt-4o
|
ARABIC
|
SOMALI_3122
|
[
{
"role": "user",
"content": "Loo fiirinayo barta $P_1(0,2)$ iyo barta $P_2(3,0)$, hel iskudhafka barta $P$ ee ku taal xariiqda u dhaxaysa $P_1$ iyo $P_2$ si ay u noqoto $\n\\overrightarrow{P_1P} = 2\\overrightarrow{PP_2}$. Muujintaadu waa inay ahaataa lab tarayn $(x, y)$, oo ay ku jiraan qiimaha saxda ah haddii loo baahdo."
},
{
"role": "assistant",
"content": "Tallaabo 1: Waxaa la siiyay in $\\overrightarrow{P_1P} = 2\\overrightarrow{PP_2}$. Tani waxay la micno tahay in $P$ uu ku dhow yahay $P_2$ marka loo eego $P_1$ iyadoo saamiga u dhaxaysa $P_1$ iyo $P_2$ uu yahay 2:1.\n\nTallaabo 2: Formula-ka barta iskudhafka ee u dhaxeysa laba dhibcood waxaa loola jeedaa haddii barta $P$ ay diyaar tahay iyadoo $P = (x_1 + r(x_2 - x_1), y_1 + r(y_2 - y_1))$, halkaasoo $r$ uu yahay saamiga dhibcaha. Marka $r = \\frac{1}{3}$ sababtoo ah $1/(2+1)$.\n\nTallaabo 3: Xisaabi isku-duwidda $P$:\n\\[\n x = x_1 + r(x_2 - x_1) = 0 + \\frac{1}{3}(3 - 0) = \\frac{3}{3} = 2.\n\\]\n\\[\n y = y_1 + r(y_2 - y_1) = 2 + \\frac{1}{3}(0 - 2) = 2 - \\frac{2}{3} = \\frac{6}{3} - \\frac{2}{3} = \\frac{4}{3}.\n\\]\n\nNatiijada isku-duwidda $P$ waa $(x, y) = (2, \\frac{2}{3})$.\n\n<answer>(2, \\frac{2}{3})</answer>"
}
] |
gpt-4o
|
SOMALI
|
HAUSA_4137
|
[
{
"role": "user",
"content": "A sauƙaƙe karin magana $\n(0.25)^{-2}+8\ne ^{\\frac {2}{3}}-\nlg 25-2\nlg 2\\)''. Faɗi amsa kaɗan cikin duka lambobi."
},
{
"role": "assistant",
"content": "Mataki na 1: A bincika kowane lokaci daban-daban a cikin karin magana.\n\n- Na farko, $(0.25)^{-2} = \\frac{1}{0.25^{2}} = \\frac{1}{(\\frac{1}{4})^{2}} = \\frac{1}{\\frac{1}{16}} = 16$.\n\n- Na biyu, $8^{\\frac {2}{3}} = (2^3)^{\\frac {2}{3}} = 2^{3 \\times \\frac{2}{3}} = 2^{2} = 4$.\n\n- Na uku, $\\lg 25 = \\lg (5^2) = 2 \\lg 5$.\n\n- Na ƙarshe, $2\\lg 2 = 2 \\times \\lg 2$.\n\nMataki na 2: Maye gurbin ƙima $\\lg 5$ da $\\lg 2$ sannan a gudanar da aiki.\n\nYawanci ana ɗauka cewa $\\lg 5 + \\lg 2 = \\lg 10$, wato $\\lg 5 = 0.69897$ da kuma $\\lg 2 = 0.30103$.\n\nDon haka:\n- $\\lg 25 = 2 \\times 0.69897 = 1.39794$\n- $2 \\lg 2 = 2 \\times 0.30103 = 0.60206$\n\nMataki na 3: Sanya ƙima cikin karin magana.\n$16 + 4 - 1.39794 - 0.60206$\n\n- Na farko, $16 + 4 = 20$.\n- Na biyu, $20 - 1.39794 = 18.60206$.\n- Na uku, $18.60206 - 0.60206 = 18$.\n\nMataki na ƙarshe: Don haka amsar ita ce: <answer>18</answer>"
}
] |
gpt-4o
|
HAUSA
|
End of preview. Expand
in Data Studio
Big Math Translated -- African Languages
This is a set of 41k SynthLabsAI/Big-Math-RL-Verified questions translated into 9 African languages using Azure/GPT-4o. We shuffle the dataset and then randomly sample a question without replacement, and then equally sample a language and then we translate the question and answer to that language.
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