instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Let j be -4 + 12 + -1 - -1. List the prime factors of (38/j*2)/((-2)/(-24)).\n | 2, 3, 19\n | ibivibiv/math_instruct | |
Is 11107730563 composite?\n | False\n | ibivibiv/math_instruct | |
What is the distance between 12 and -0.298?\n | 12.298\n | ibivibiv/math_instruct | |
Suppose -91*p + 12 = -85*p. Solve -p*o - 5 + 1 = 0 for o.\n | -2\n | ibivibiv/math_instruct | |
Let g = -3 - -4. Let b be -2 + g + (-6)/(-2). What is the first derivative of 9*w**2 + 4 + 8*w**3 - 9*w**b wrt w?\n | 24*w**2\n | ibivibiv/math_instruct | |
Solve 0 = -600*l + 602*l - 3*d - 11, 0 = 3*l + 3*d + 21 for l.\n | -2\n | ibivibiv/math_instruct | |
Let r(c) = c**2 + 4*c + 13. List the prime factors of r(-6).\n | 5\n | ibivibiv/math_instruct | |
Solve 159 + 41 = -100*u for u.\n | -2\n | ibivibiv/math_instruct | |
In base 16, what is -4 + -2c?\n | -30\n | ibivibiv/math_instruct | |
Solve -448 = y - 4*u - 357, -4*u = 27*y - 119 for y.\n | 1\n | ibivibiv/math_instruct | |
What is 293 minutes after 1:26 AM?\n | 6:19 AM\n | ibivibiv/math_instruct | |
Suppose -2*q - x - 29 = 0, -66 = q + 2*q - 3*x. Let c = -45627 + 45622. Sort c, -4, q in decreasing order.\n | -4, c, q\n | ibivibiv/math_instruct | |
Sort -30, -1/4, -15.4, -0.5 in decreasing order.\n | -1/4, -0.5, -15.4, -30\n | ibivibiv/math_instruct | |
What comes next: 410, 838, 1058, 866, 58?\n | -1570\n | ibivibiv/math_instruct | |
What is the sixth root of 86 to the nearest integer?\n | 2\n | ibivibiv/math_instruct | |
Collect the terms in -34875*z**2 + 34874*z**2 - 1739 + 1746.\n | -z**2 + 7\n | ibivibiv/math_instruct | |
Find the third derivative of -3620*r**6 + 2*r**4 - 2*r**3 - 3*r**2 + 2701*r - 5 wrt r.\n | -434400*r**3 + 48*r - 12\n | ibivibiv/math_instruct | |
What is the ten millions digit of 107085075?\n | 0\n | ibivibiv/math_instruct | |
What are the prime factors of 5141866?\n | 2, 2570933\n | ibivibiv/math_instruct | |
What is the hundreds digit of 626?\n | 6\n | ibivibiv/math_instruct | |
Let t be (36/(-21))/(12/(-42)). Suppose -t*n + 36 = 6. Suppose 3*v - n*w - 35 = 0, w + 3 - 2 = 0. What is the greatest common factor of 20 and v?\n | 10\n | ibivibiv/math_instruct | |
Rearrange (-21*u + 9*u - 18*u)*(487*u + 2172 - 1086 + 488*u - 1086) to o*u + a*u**2 + g and give a.\n | -29250\n | ibivibiv/math_instruct | |
How many ways are there to put 5 balls in X boxes if the balls are not distinguishable but the boxes are? The answer is 21. What is the value of unknown variable X? | To solve this problem, we need to determine the value of x, which represents the number of boxes.
The problem states that there are 5 balls and X boxes.
We are told that there are 21 ways to distribute the 5 balls among the X boxes.
We can set up the equation as follows:
Number of ways to distribute 5 balls among X box... | ibivibiv/math_instruct | |
Expand (-2*t + 2*t + t**2)*(1 - 1 + 1) + 0*t**2 + 3*t**2 + 0*t**2 + 132 - 132 + 13*t**2 + (-2 + 3*t + 2)*(t + 0*t + 0*t).\n | 20*t**2\n | ibivibiv/math_instruct | |
Solve 790*b = 791*b + 2 for b.\n | -2\n | ibivibiv/math_instruct | |
b"What is the wth term of 11, -8, -47, -112, -209, -344?\n" | -w**3 - 4*w**2 + 16\n | ibivibiv/math_instruct | |
Let h(r) = -r + 2. Let m be h(0). Let t(i) = -3*i**2 - 224*i + 227*i + 2*i**2. Let k be t(3). Solve m*v - 6 = -k for v.\n | 3\n | ibivibiv/math_instruct | |
Suppose -143 = 5*n + 212. Let d = -42 - n. Is d a multiple of 22?\n | False\n | ibivibiv/math_instruct | |
Suppose -5*q + 0*q + 30 = 0. Suppose 191*m - 199*m = -8. Solve -q = -t - m for t.\n | 5\n | ibivibiv/math_instruct | |
Let l = 6131 + -6115.031. Let o = -15.9 + l. Let w = -0.229 + o. What is w rounded to 1 decimal place?\n | -0.2\n | ibivibiv/math_instruct | |
Let t(n) = -2*n**3 - 2*n**2 + n + 1. Let g be 3/(-5) + 14/(-10). Let p be t(g). Suppose 3*f + 0*f - 6 = 0. Solve f*c + 7 = -0*j + j, 0 = 4*j - c + p for j.\n | -3\n | ibivibiv/math_instruct | |
Sort 211, -10, 3, 2/3, 2/9, 4, 6.\n | -10, 2/9, 2/3, 3, 4, 6, 211\n | ibivibiv/math_instruct | |
Let n be 74/14 - (-2)/(-7). Suppose -2*q - 1 + n = 0. Suppose 3*v - 2*o = 19, v + 5*o = 6*o + 5. Solve s + 3*l - 1 + 13 = 0, -3*l = q*s + v for s.\n | 3\n | ibivibiv/math_instruct | |
What is (-15)/(-4) + 0 - (87 - 83)?\n | -1/4\n | ibivibiv/math_instruct | |
Suppose -5*b + j = -16933, 6*b = 11*b - 4*j - 16912. Calculate the greatest common factor of 28 and b.\n | 28\n | ibivibiv/math_instruct | |
Which is greater: -187347 or -187340?\n | -187340\n | ibivibiv/math_instruct | |
Calculate 406/(-133) + (-1557)/(-519).\n | -1/19\n | ibivibiv/math_instruct | |
What is the biggest value in 15, -1, 0.5?\n | 15\n | ibivibiv/math_instruct | |
Let b(k) = 40*k - 129*k + 47*k + 43*k. What is b(4)?\n | 4\n | ibivibiv/math_instruct | |
Add -0.4 and 0.0345.\n | -0.3655\n | ibivibiv/math_instruct | |
In base 6, what is 45135 + -3220?\n | 41515\n | ibivibiv/math_instruct | |
In base 12, what is 3 - -38?\n | 3b\n | ibivibiv/math_instruct | |
Let g(s) = -283*s**2 - 13*s - 7. Let w(h) = 190*h**2 + 9*h + 5. Let p(q) = -5*g(q) - 7*w(q). Let r(i) = 7*i**2. Calculate p(r(u)).\n | 4165*u**4 + 14*u**2\n | ibivibiv/math_instruct | |
What comes next: 24726, 98899, 222510, 395547, 617998?\n | 889851\n | ibivibiv/math_instruct | |
Solve 179*o - 182*o = 21, -4*o = 3*v + 43 for v.\n | -5\n | ibivibiv/math_instruct | |
Let a(m) = -7*m - 2. Let h be a(-1). Let y be 1*(h - -1) - 3. Find the second derivative of p**2 - 4*p**2 + 2*p + 0*p**2 - y*p wrt p.\n | -6\n | ibivibiv/math_instruct | |
What is the highest common divisor of 5142650 and 2?\n | 2\n | ibivibiv/math_instruct | |
What is the lowest common multiple of 10 and 1585?\n | 3170\n | ibivibiv/math_instruct | |
Let q be 3 - (15 - (-10 + 19)). Sort q, 0.18, 4, 0.2, -0.07 in increasing order.\n | q, -0.07, 0.18, 0.2, 4\n | ibivibiv/math_instruct | |
Collect the terms in 10*s**2 - 8*s + 3*s**2 + 8*s.\n | 13*s**2\n | ibivibiv/math_instruct | |
Calculate prob of sequence yyg when three letters picked without replacement from {g: 3, y: 6, r: 6, l: 3}.\n | 5/272\n | ibivibiv/math_instruct | |
What is the next term in 3444, 3416, 3404, 3414, 3452, 3524, 3636?\n | 3794\n | ibivibiv/math_instruct | |
What is the cube root of 1128 to the nearest integer?\n | 10\n | ibivibiv/math_instruct | |
What is the result of the following expression?
8.46 / 4.12 | 2.05 | ibivibiv/math_instruct | |
Express (96 + 8*b - 45 - 50)*(5 + 4*b**2 - 5) in the form q*b**2 + w*b**3 + h*b + f and give w.\n | 32\n | ibivibiv/math_instruct | |
Suppose -20 + 63 = 2*a + 3*j, 4*a - 156 = 4*j. Solve -74*f - a = -66*f for f.\n | -4\n | ibivibiv/math_instruct | |
Let v = 85 - -9. What is the remainder when v is divided by 19?\n | 18\n | ibivibiv/math_instruct | |
Which is the third smallest value? (a) 0.05 (b) 1 (c) 4\n | c\n | ibivibiv/math_instruct | |
What are the prime factors of 2800?\n | 2, 5, 7\n | ibivibiv/math_instruct | |
Suppose 2 = -3*f - 2*h, -12 = h + 2*h. Suppose -2*c - 2*p - f*p = -16, -4*p + 16 = -2*c. Solve -x + 2*x - 2 = c for x.\n | 2\n | ibivibiv/math_instruct | |
Factor -2/3*b**2 + 0 - 4/3*b.\n | -2*b*(b + 2)/3\n | ibivibiv/math_instruct | |
How many minutes are there between 5:54 AM and 2:02 PM?\n | 488\n | ibivibiv/math_instruct | |
Sort -77, -3, 23842, -2, 4, -4 in ascending order.\n | -77, -4, -3, -2, 4, 23842\n | ibivibiv/math_instruct | |
Let l(m) = 36*m**3 - 47*m**2 + 5*m - 53. Is l(13) prime?\n | True\n | ibivibiv/math_instruct | |
Let t(y) = -2*y - 3. Suppose 0*g + 6 = -2*g. Let j(b) = 2. Let a(v) = -v. Let i(o) = a(o) - j(o). Give g*t(h) + 4*i(h).\n | 2*h + 1\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 1173747030?\n | 4\n | ibivibiv/math_instruct | |
Suppose -6 = 6*f - 24. Suppose 2*i = -f*i. Suppose -2*z + 111 + 101 = i. What is the tens digit of z?\n | 0\n | ibivibiv/math_instruct | |
Suppose 3*h - 213 = -5*w, 5*h + 102 = -5*w + 447. Calculate the highest common factor of h and 1617.\n | 33\n | ibivibiv/math_instruct | |
Simplify (h/(h/(h*h/(h/(h*h**(-1/9)/h*h)))))/(h*h/h**(1/2))*h**2/h**(-2/9)*(h**(2/5))**(4/3)/(h/(h**(-1/3)/h*h))**(-34) assuming h is positive.\n | h**(4363/90)\n | ibivibiv/math_instruct | |
Simplify ((k**(1/4)*k*k*k)**(-40)*k**(-2/3)/k**5)**1 assuming k is positive.\n | k**(-407/3)\n | ibivibiv/math_instruct | |
Let l be (-11)/(-4) + 22/(-8) + 3. Let j be (-1 + (-3)/9)*l + 6. Solve d = j - 5 for d.\n | -3\n | ibivibiv/math_instruct | |
Let h(w) = w**2 - 2*w. Let d(j) = -j**3 - j**2 + j + 3. Let q be d(0). Let p be h(q). Find the second derivative of -g**3 + 6*g + 0*g**p - 5*g wrt g.\n | -6*g\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {u: 3, p: 9, w: 4}. What is prob of picking 3 p?\n | 3/20\n | ibivibiv/math_instruct | |
Suppose 11*z - 329 = 133. Is 21 a factor of z?\n | True\n | ibivibiv/math_instruct | |
Simplify (-4 + (1*(-1*sqrt(1100) + -2) + 5)*-5)**2.\n | -1900*sqrt(11) + 27861\n | ibivibiv/math_instruct | |
Let w = 4 - 10. Let v be (-2)/(-140) + w/(-21). Let n = v - 49/30. Are n and 0 unequal?\n | True\n | ibivibiv/math_instruct | |
What is the millions digit of 1124980805?\n | 4\n | ibivibiv/math_instruct | |
Solve -2228 = 108*r + z + 1769, -z - 186 = 5*r for r.\n | -37\n | ibivibiv/math_instruct | |
(-2)/((-68)/(-51)*6/(-28))\n | 7\n | ibivibiv/math_instruct | |
Let g(v) = v**2. Let o(y) be the third derivative of 2*y**4/3 - 4*y**2. Determine o(g(u)).\n | 16*u**2\n | ibivibiv/math_instruct | |
Let d(r) be the first derivative of -r**4/4 + 2*r**3 - 3*r**2 + 6*r - 17. Let w(i) = -2*i. Let h be w(-2). List the prime factors of d(h).\n | 2, 7\n | ibivibiv/math_instruct | |
Suppose 2*o**5 + 18*o**4 + 48*o**3 + 40*o**2 = 0. Calculate o.\n | -5, -2, 0\n | ibivibiv/math_instruct | |
What is the derivative of 268131*i - 662059 wrt i?\n | 268131\n | ibivibiv/math_instruct | |
Factor -2*r**3/3 - 16*r**2 + 18*r + 100/3.\n | -2*(r - 2)*(r + 1)*(r + 25)/3\n | ibivibiv/math_instruct | |
Let h be 364/18 + -2 + 32/(-144). Suppose 0 = 4*j + f + 16, -h = -4*f - 2. Let u = 6.1 + -6. Which is the nearest to j? (a) -2/19 (b) u (c) -1\n | c\n | ibivibiv/math_instruct | |
Suppose 0 = 5*g - 2*h - 2 - 0, -h = -4*g + 1. Let a(d) be the third derivative of 0 + 0*d + g*d**4 + 1/6*d**3 - d**2 - 1/30*d**5. Differentiate a(v) wrt v.\n | -4*v\n | ibivibiv/math_instruct | |
Does 32 divide 38176?\n | True\n | ibivibiv/math_instruct | |
39021.5+-45.4385\n | 38976.0615\n | ibivibiv/math_instruct | |
Expand -3*u**5 + 10*u - 10*u + (-1 - 1 + 1)*(2*u**5 + 0*u**5 - 3*u**5).\n | -2*u**5\n | ibivibiv/math_instruct | |
Let u(b) = 8*b. Let c(q) be the third derivative of 0*q**3 + 0 + 87*q**2 + 7/60*q**5 + 0*q + 0*q**4. What is u(c(f))?\n | 56*f**2\n | ibivibiv/math_instruct | |
How many millimeters are there in 15/4 of a meter?\n | 3750\n | ibivibiv/math_instruct | |
What is 5267 rounded to the nearest one thousand?\n | 5000\n | ibivibiv/math_instruct | |
What is the nearest to -1/2 in 2/3, -4, 30, 2/17, -2?\n | 2/17\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-83.211 + -0.554) * (17.032 % 98.266) | -1426.6855 | ibivibiv/math_instruct | |
Let x(s) = 51*s + 2423. What is x(-41)?\n | 332\n | ibivibiv/math_instruct | |
Let m(y) = y**2. Suppose 0 = s + s, -4 = -2*q - s. Let g(j) = 4*j - q*j - j - 2*j. Calculate m(g(x)).\n | x**2\n | ibivibiv/math_instruct | |
What is 207 minutes before 8:50 AM?\n | 5:23 AM\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"Quadratic Inequalities on [-1,1]
Solution 1
By substituting $x=1,x=-1,x=0,\,$ $|a+b+c|\le p,\,$ $|a-b+c|\le p,$ $|c|\le p.$
Now,
\begin{align} 2|a+c|&=|(a+b+c)+(a-b+c)|\\ &\le |a+b+c|+|a-b+c|\le 2p, \end{align}
so that $... | Quadratic Inequalities on the Interval [-1,1]: A Comprehensive Analysis
In this discussion, we will delve into quadratic inequalities on the interval [-1,1]. Specifically, we aim to understand how the properties of quadratic functions can help us determine constraints on their coefficients within this interval. The a... | ibivibiv/math_instruct | |
1623a (base 12) to base 3\n | 1121010101\n | ibivibiv/math_instruct | |
What is the greatest common factor of 65 and 42445?\n | 65\n | ibivibiv/math_instruct |
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