instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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|---|---|---|---|
Let r be (2/4)/(1/268). Let h(y) = -134 + r - 5*y. Let p(s) be the first derivative of s**2 - 1. Calculate h(p(j)).\n | -10*j\n | ibivibiv/math_instruct | |
What is 454 minutes after 6:09 AM?\n | 1:43 PM\n | ibivibiv/math_instruct | |
What is 3191175 to the power of 1/5, to the nearest integer?\n | 20\n | ibivibiv/math_instruct | |
b"What is the rth term of -15, -37, -69, -111, -163, -225?\n" | -5*r**2 - 7*r - 3\n | ibivibiv/math_instruct | |
Put 6, 1, 10, -2 in descending order.\n | 10, 6, 1, -2\n | ibivibiv/math_instruct | |
Three letters picked without replacement from yvzvjjjjjjyy. Give prob of sequence zjj.\n | 1/44\n | ibivibiv/math_instruct | |
Solve -156*o - 155*o = -309*o + 24 for o.\n | -12\n | ibivibiv/math_instruct | |
Let v be 15/(-10) - (4386/(-4) + 0). Suppose -5*y = -4*r - v, -3*y - y = 5*r - 917. Is y a composite number?\n | False\n | ibivibiv/math_instruct | |
Collect the terms in -319 - 326 - 316 - 3*r + 2*r**2 + 1268 - 307.\n | 2*r**2 - 3*r\n | ibivibiv/math_instruct | |
b"What is the nth term of 11, 34, 87, 182, 331?\n" | 2*n**3 + 3*n**2 + 6\n | ibivibiv/math_instruct | |
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"# Test of divisibility of 3, 9, 27, 37, 111, 333 or 999
Find test of divisibility of 9138431772
Step 1 Make groups of 3 digits from the end groups are as 9 138 431 772
Step 2 add all groups 9 + 138 + 431 + 772 = 1350
Step... | Divisibility tests are methods used to determine if a given integer can be evenly divided by another integer (the divisor) without leaving a remainder. These tests come in handy when dealing with large numbers, saving us the trouble of performing long division. Here, we'll focus on the divisibility tests mentioned in ... | ibivibiv/math_instruct | |
Suppose -2*i + 21 = 5. Solve 0 = -i*n + 21 + 11 for n.\n | 4\n | ibivibiv/math_instruct | |
Put together -4 and 1721.\n | 1717\n | ibivibiv/math_instruct | |
Is 194 a factor of 479805?\n | False\n | ibivibiv/math_instruct | |
Let q = 332 + -328. Suppose -32*i + 29*i = -q*z + 2447, z - i - 612 = 0. What is the tens digit of z?\n | 1\n | ibivibiv/math_instruct | |
Is 967702595 a multiple of 12?\n | False\n | ibivibiv/math_instruct | |
Round -3369.831289 to one decimal place.\n | -3369.8\n | ibivibiv/math_instruct | |
Convert 4033 (base 10) to base 16.\n | fc1\n | ibivibiv/math_instruct | |
What is (((-2623)/(-366))/43)/(((-9)/(-30))/3)?\n | 5/3\n | ibivibiv/math_instruct | |
Let q = 204 + -204. Which is the fourth smallest value? (a) -0.2 (b) 34 (c) q (d) -5/4\n | b\n | ibivibiv/math_instruct | |
What is 461 (base 16) in base 5?\n | 13441\n | ibivibiv/math_instruct | |
Determine w so that -6*w**5 + 112*w**4 - 66*w**3 - 112*w**2 + 72*w = 0.\n | -1, 0, 2/3, 1, 18\n | ibivibiv/math_instruct | |
Total of -58437 and -0.2.\n | -58437.2\n | ibivibiv/math_instruct | |
What is the closest to -0.19 in 10416, 0, 13?\n | 0\n | ibivibiv/math_instruct | |
What is the common denominator of -49/9699156 and -191/2790?\n | 48495780\n | ibivibiv/math_instruct | |
What is 862700 rounded to the nearest 100000?\n | 900000\n | ibivibiv/math_instruct | |
How many months are there in 85/4 of a decade?\n | 2550\n | ibivibiv/math_instruct | |
b"What is the mth term of -128, -449, -946, -1589, -2348, -3193, -4094?\n" | 5*m**3 - 118*m**2 - 2*m - 13\n | ibivibiv/math_instruct | |
What is the value of ((-52626)/(-2184) - 24)/(7/2 + -1)?\n | 1/26\n | ibivibiv/math_instruct | |
What is the fifth root of 38100 to the nearest integer?\n | 8\n | ibivibiv/math_instruct | |
What comes next: -2249, -2251, -2253?\n | -2255\n | ibivibiv/math_instruct | |
What is the common denominator of 139/57206520 and 71/3384?\n | 57206520\n | ibivibiv/math_instruct | |
Is 1194 a multiple of 39?\n | False\n | ibivibiv/math_instruct | |
Subtract -5 from -17.062.\n | -12.062\n | ibivibiv/math_instruct | |
Suppose 9*i - 9373 = -2118 + 2690. Solve -i*s + 1111*s = 12 for s.\n | 2\n | ibivibiv/math_instruct | |
Simplify (-2*(sqrt(18)*-2*-1 + -5*sqrt(36)/sqrt(2)))/(2*6*5*(sqrt(6) + sqrt(12)/sqrt(2))).\n | sqrt(3)/20\n | ibivibiv/math_instruct | |
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"# A Metre Long Narrow Bore Held Horizontally (And Closed at One End) Contains a 76 Cm Long Mercury Thread, Which Traps a 15 Cm Column of Air. What Happens If the Tube is Held Vertically with the Open End at the Bottom - Physi... | This physics problem involves several fundamental principles, including fluid dynamics and the behavior of gases under different conditions. When dealing with liquids in a confined space like a tube, it's important to consider factors such as height, cross-sectional area, and pressure. These quantities are all interco... | ibivibiv/math_instruct | |
Find the second derivative of 43247544*i**2*n**2 + 331292642*i**2*n wrt n.\n | 86495088*i**2\n | ibivibiv/math_instruct | |
b"What is the kth term of -10390, -10411, -10454, -10525, -10630?\n" | -k**3 - 5*k**2 + k - 10385\n | ibivibiv/math_instruct | |
Suppose 5*s + 24 + 111 = 0. What are the prime factors of -69*-6*(-12)/s?\n | 2, 23\n | ibivibiv/math_instruct | |
Let z(j) = j**3 - 9*j**2 - 31*j + 145. Give z(3).\n | -2\n | ibivibiv/math_instruct | |
Put -4, -390, 3277 in decreasing order.\n | 3277, -4, -390\n | ibivibiv/math_instruct | |
Let g(h) = -h - 3*h**2 + 2*h**2 + 6 - 7 + 0. Let v(l) = 5*l**3 + 20*l**2 + 20*l + 20. What is -20*g(k) - v(k)?\n | -5*k**3\n | ibivibiv/math_instruct | |
Suppose -2*u + 0 = -6. Suppose 7 = -u*n + 1. Is 293/((-1)/(1 + n)) prime?\n | True\n | ibivibiv/math_instruct | |
Collect the terms in -1883 + 1883 + 31*r**2.\n | 31*r**2\n | ibivibiv/math_instruct | |
Let n(s) = s + 3 + 3 + 15. Let z be n(-13). Factor -2*l**2 - 2*l**2 + z*l + 8*l + 18 - 30.\n | -4*(l - 3)*(l - 1)\n | ibivibiv/math_instruct | |
Expand (5*g**2 - g**2 + 5*g**5 - 2*g**5)*(-568 + 409 - 917).\n | -3228*g**5 - 4304*g**2\n | ibivibiv/math_instruct | |
Let t(u) = -17*u + 104. Let l = 142 - 136. Let k be t(l). Which is the second smallest value? (a) -3 (b) 0 (c) k (d) -6\n | a\n | ibivibiv/math_instruct | |
Are -2/2749 and -1 unequal?\n | True\n | ibivibiv/math_instruct | |
Collect the terms in 103*n + 11 + 23*n - 64*n + 89*n.\n | 151*n + 11\n | ibivibiv/math_instruct | |
Suppose 5*w = 15 + 80. Let i = w + 0. Does 5 divide i?\n | False\n | ibivibiv/math_instruct | |
Let i = 1418 - 1415. Factor -4/7*f**2 - 2/7*f + 0 - 2/7*f**i.\n | -2*f*(f + 1)**2/7\n | ibivibiv/math_instruct | |
What is next in 3231205, 3231269, 3231323, 3231361, 3231377, 3231365, 3231319, 3231233?\n | 3231101\n | ibivibiv/math_instruct | |
Suppose -35*t + 258 = 8*t. Let c(g) be the second derivative of 0 - 1/150*g**t - 1/15*g**3 + 1/50*g**5 - g + 0*g**2 + 1/60*g**4. Determine r so that c(r) = 0.\n | -1, 0, 1, 2\n | ibivibiv/math_instruct | |
Work out -9965 * 882.\n | -8789130\n | ibivibiv/math_instruct | |
Express (2 + 2 - 3 + (1 - 2 + 0)*(1 + 0 + 1) + 2 + 1 - 5)*(0*o**4 - 3*o**4 + o**4) as v*o + u*o**3 + s*o**4 + d*o**2 + g and give u.\n | 0\n | ibivibiv/math_instruct | |
Let t(l) = -117*l + 2769. What is the remainder when t(23) is divided by 28?\n | 22\n | ibivibiv/math_instruct | |
How many minutes are there between 11:25 PM and 5:10 AM?\n | 345\n | ibivibiv/math_instruct | |
Convert 0.515929 litres to millilitres.\n | 515.929\n | ibivibiv/math_instruct | |
Let v = 0.1194 + -9.8594. Let q = -0.26 + v. Which is the third smallest value? (a) -1/10 (b) -1 (c) q\n | a\n | ibivibiv/math_instruct | |
Simplify (4*-2*(sqrt(102) - (sqrt(102)*-3*2 - sqrt(102))))/(((2*sqrt(864) - sqrt(864)) + sqrt(864))*-6 - 2*sqrt(864)*1).\n | 8*sqrt(17)/21\n | ibivibiv/math_instruct | |
If Scott won 4 athletic awards and Jessie won 3 times as many awards as Scott, how many awards did the best athlete at the rival high school win, considering they won twice as many awards as Jessie? | If Scott won 4 athletic awards, and Jessie won 3 times as many awards as Scott, then Jessie won 3 * 4 = <<3*4=12>>12 awards.
If the best athlete at the rival high school won twice as many awards as Jessie, then they won 2 * 12 = <<2*12=24>>24 awards.
#### 24
The answer is: 24 | ibivibiv/math_instruct | |
What is the thousands digit of 4902?\n | 4\n | ibivibiv/math_instruct | |
An empty bottle weighs 1/6th of the full bottle. When a certain percent of water was removed and the bottle was weighed, the weight of the bottle turned out to be 1/3rd of the bottle when it was full. What is the percent of water removed?
Answer Choices: (A) 89% (B) 82% (C) 81% (D) 50% (E) 80% | Lets think about the multi-choice question.
Let the weight of full bottle be 6kg.
Therefore, weight of empty bottle is 1kg and that of water is 5kg.
If x% of water is removed, the weight of the bottle becomes 2kg.
Therefore, the amount of water removed is 4kg.
% of water removed = 4/5 *100 = 80%
The answer is E | ibivibiv/math_instruct | |
Let x = -26 + 29. Let q(g) be the third derivative of 0*g**x + 1/12*g**4 - g**2 + 0 + 0*g. Let l(i) = -4*i**2. Determine l(q(a)).\n | -16*a**2\n | ibivibiv/math_instruct | |
Let j = -66.00444 - -66. Round j to three decimal places.\n | -0.004\n | ibivibiv/math_instruct | |
Suppose -8 = -2*u - 2. Let f(k) = k - 4. Let d be f(u). Let i be d - 1*9/(-3). Solve -i*v + 6 = 0, 2*l - v = -5*v + 20 for l.\n | 4\n | ibivibiv/math_instruct | |
Let q = -4067/26520 - 1/2040. Which is the biggest value? (a) q (b) -0.06 (c) 5/2 (d) 3/4 (e) -0.5\n | c\n | ibivibiv/math_instruct | |
Let u(q) = q**2 - 16*q - 26 - 2*q**2 + q. Does 5 divide u(-7)?\n | True\n | ibivibiv/math_instruct | |
Let u = 0.063 + 0.054. Round u to 2 dps.\n | 0.12\n | ibivibiv/math_instruct | |
What comes next: -10, -19, -28, -37, -46, -55?\n | -64\n | ibivibiv/math_instruct | |
What is 5/8 of a millennium in months?\n | 7500\n | ibivibiv/math_instruct | |
Suppose 12 = -5*z - 3*r, 4*z + 8 = -z - 2*r. Let u be z + (-1)/(1/(-81000)). What is u rounded to the nearest 10000?\n | 80000\n | ibivibiv/math_instruct | |
Let f(o) = -88*o + 16. Let n(s) = 18*s - 3. Let t(k) = 9*f(k) + 48*n(k). Let y(i) = -10*i**2. Calculate y(t(m)).\n | -51840*m**2\n | ibivibiv/math_instruct | |
Let h = -51266/23 + 2227. Calculate the common denominator of 2*-1 - (-343)/(-14) and h.\n | 46\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {q: 2, k: 3, g: 1, s: 1, x: 5, p: 1}. What is prob of picking 1 s and 1 k?\n | 1/26\n | ibivibiv/math_instruct | |
Differentiate -2*r**3 + 89*r**2 - 53 wrt r.\n | -6*r**2 + 178*r\n | ibivibiv/math_instruct | |
5160 divided by -129\n | -40\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {m: 3, n: 2}. What is prob of sequence nmmn?\n | 1/10\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 2105157?\n | 0\n | ibivibiv/math_instruct | |
What is ((-9)/(-3))/(6 + (-2 - 5))?\n | -3\n | ibivibiv/math_instruct | |
What is 0.000382 rounded to 5 dps?\n | 0.00038\n | ibivibiv/math_instruct | |
Evaluate -8 + 6 + 1 + 0 + 3.\n | 2\n | ibivibiv/math_instruct | |
Let u = 71 + -43. Let r(z) = -z**2 + 8*z + 3. Let k(b) = -3*b - 3. Let t be k(-3). What is the remainder when u is divided by r(t)?\n | 13\n | ibivibiv/math_instruct | |
Let o be 8/(-18) + 15/8100*24. Let z = -0.02 + -17.98. Put z, -4, o in decreasing order.\n | o, -4, z\n | ibivibiv/math_instruct | |
Calculate (15 - 11) + -2 + -10 + -3 - 23.\n | -34\n | ibivibiv/math_instruct | |
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"# Interesting series involving factorials and logarithms
Not sure if the following is easy to prove or not, I obtained the result using probabilistic arguments exclusively.
Define $$x_1 = 2; x_2 = 4/3; x_3 = (8\cdot 6) / (7... | Let's delve into the interesting series involving factorials and logarithms as presented by Vincent Granville. We will explore two claims and discuss an unsolved problem regarding these sequences. Additionally, we will examine how these concepts relate to familiar ideas from calculus and combinatorics.
First, let us ... | ibivibiv/math_instruct | |
What is prob of picking 1 g and 3 z when four letters picked without replacement from zggzz?\n | 2/5\n | ibivibiv/math_instruct | |
b"What is the uth term of -3618983, -3618984, -3618985, -3618986, -3618987?\n" | -u - 3618982\n | ibivibiv/math_instruct | |
Let f be 468/38 - 4/2. Let u = 1452/95 + f. Factor -u*m**3 - 24/5*m - 2/5 - 96/5*m**2.\n | -2*(4*m + 1)**3/5\n | ibivibiv/math_instruct | |
What is the value of (-306)/(-17)*90/(-108)?\n | -15\n | ibivibiv/math_instruct | |
742294876 divided by -185573719\n | -4\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 274774?\n | 2\n | ibivibiv/math_instruct | |
In base 4, what is -33 + 33?\n | 0\n | ibivibiv/math_instruct | |
Suppose 2*y = 3*s - 2, 4*y + y + 5 = -3*s. Let c be 102/24 - (-2)/(-8). Calculate the smallest common multiple of 7 and (-5)/c - y/4 - -15.\n | 14\n | ibivibiv/math_instruct | |
Madeline wants to drink 100 ounces of water in a day. Her water bottle can hold 12 ounces of water. She refills her water bottle 7 times. How much more water does she need to drink? | Madelines water bottle can hold 12 ounces of water.
She refills her water bottle 7 times, so she drinks 12 ounces x 7 = 84 ounces of water from her water bottle.
She wants to drink 100 ounces of water in total, so she needs to drink an additional 100 ounces - 84 ounces = 16 ounces of water.
Therefore, Madeline needs to... | ibivibiv/math_instruct | |
What is 0.0338243 rounded to 4 dps?\n | 0.0338\n | ibivibiv/math_instruct | |
What is 0.9 times -479?\n | -431.1\n | ibivibiv/math_instruct | |
What is the third root of 5309 to the nearest integer?\n | 17\n | ibivibiv/math_instruct | |
Let k(b) = -47*b - 104. What are the prime factors of k(-16)?\n | 2, 3\n | ibivibiv/math_instruct |
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