instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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|---|---|---|---|
Suppose 4*k + 2*f = -8, 5*f + 6 = -3*k + 7*k. Let w(x) = -145*x + 8. What are the prime factors of w(k)?\n | 3, 17\n | ibivibiv/math_instruct | |
Simplify (-1*sqrt(6655))/(1*sqrt(80) + sqrt(80) - sqrt(80)) + -2 + (sqrt(176) - (-1 + sqrt(176) - sqrt(176))) + (sqrt(176) - -1*sqrt(176)*-3).\n | -27*sqrt(11)/4 - 1\n | ibivibiv/math_instruct | |
Let i be 2365/25 - (-10)/25. Suppose -5*g - 5*z = -i, -11*g + z = -6*g - 95. Solve 2*h + 2 = -4*u, -2*u + 5*u + g = 2*h for u.\n | -3\n | ibivibiv/math_instruct | |
What is the least common multiple of 108648 and 1774584?\n | 5323752\n | ibivibiv/math_instruct | |
Convert 9.470877 years to millennia.\n | 0.009470877\n | ibivibiv/math_instruct | |
Solve 15*v - 2*v = 74*v + 61 for v.\n | -1\n | ibivibiv/math_instruct | |
Let m(r) = -3068*r. Let j(i) = -19*i**2. Determine j(m(n)).\n | -178839856*n**2\n | ibivibiv/math_instruct | |
Find the third derivative of 1810*h**2 - 97*h**3 - 3565*h**2 + 1992*h**2 wrt h.\n | -582\n | ibivibiv/math_instruct | |
Solve -16*b = -15*b + 4 for b.\n | -4\n | ibivibiv/math_instruct | |
Determine l so that -5*l**2 - 295*l - 840 = 0.\n | -56, -3\n | ibivibiv/math_instruct | |
Suppose 6 = 5*a + 1, 5 = -f + a. Sort 2, f, -2 in decreasing order.\n | 2, -2, f\n | ibivibiv/math_instruct | |
In base 3, what is 1020 - -1001011120?\n | 1001012210\n | ibivibiv/math_instruct | |
Let s(j) = 1162914302*j. Let w(d) = -d**2. Calculate s(w(u)).\n | -1162914302*u**2\n | ibivibiv/math_instruct | |
Round -0.0012121194 to 5 decimal places.\n | -0.00121\n | ibivibiv/math_instruct | |
Express 133*i**2 + i - 2 - 5 - i + 4 as a*i**2 + q*i + u and give a.\n | 133\n | ibivibiv/math_instruct | |
Is 6347 a prime number?\n | False\n | ibivibiv/math_instruct | |
Expand (0 + 3 - 1)*(-1 + 1 - 2*a) - 2*a - 3*a - a - 2 + 3*a + 2.\n | -7*a\n | ibivibiv/math_instruct | |
What is the closest to 2/3 in 4, -2/69, 1/12, 63, -4?\n | 1/12\n | ibivibiv/math_instruct | |
Simplify (v*v**(-8)*v*v)**(-3/4) assuming v is positive.\n | v**(15/4)\n | ibivibiv/math_instruct | |
How many minutes are there between 4:05 AM and 8:31 AM?\n | 266\n | ibivibiv/math_instruct | |
Find the second derivative of 2203960*m**5 + m - 124422 wrt m.\n | 44079200*m**3\n | ibivibiv/math_instruct | |
Solve -49*c + 42*c = -21 for c.\n | 3\n | ibivibiv/math_instruct | |
Let d(k) = k**3 + 10*k**2 - 24*k + 4. Suppose 3*j = -8 - 28. Let q be d(j). Solve 0*z + q*z = 20, -10 = y - z for y.\n | -5\n | ibivibiv/math_instruct | |
Let w = -5.4667 - -5.396. What is w rounded to three decimal places?\n | -0.071\n | ibivibiv/math_instruct | |
What is the common denominator of 43/7400 and 61/544990?\n | 403292600\n | ibivibiv/math_instruct | |
Solve -274*m - 83619 + 88551 = 0 for m.\n | 18\n | ibivibiv/math_instruct | |
Collect the terms in 1 - 191*u + 30*u - 1.\n | -161*u\n | ibivibiv/math_instruct | |
Put -139, 4, 1, 6/13 in ascending order.\n | -139, 6/13, 1, 4\n | ibivibiv/math_instruct | |
Factor 5*u**3 - 740*u**2 + 25645*u - 24910.\n | 5*(u - 94)*(u - 53)*(u - 1)\n | ibivibiv/math_instruct | |
List the prime factors of 3323355.\n | 3, 5, 7, 31, 1021\n | ibivibiv/math_instruct | |
Let t(v) = 2*v**3 - 61*v**2 - 35*v + 145. Determine t(31).\n | 21\n | ibivibiv/math_instruct | |
What is 144 minutes after 4:19 AM?\n | 6:43 AM\n | ibivibiv/math_instruct | |
Let f(k) = -k**2 - 4*k + 15. Let m be f(-6). Let y(i) = 2*i - 4. Let x be y(-3). What are the prime factors of m*x/(-6) - 1?\n | 2\n | ibivibiv/math_instruct | |
List the prime factors of 263.\n | 263\n | ibivibiv/math_instruct | |
Suppose 2*q + 18 - 36 = -2*b, 2*q - 26 = -4*b. What is the fourth biggest value in 0, q, -0.13, 1?\n | -0.13\n | ibivibiv/math_instruct | |
Let r(q) = -q**2 + 8*q - 5. Let w be r(6). Solve -w*g + 3*g = -20 for g.\n | 5\n | ibivibiv/math_instruct | |
Suppose -q - 2*i = 2*i - 17, -5*i = 4*q - 24. Solve q = p - 4 for p.\n | 5\n | ibivibiv/math_instruct | |
What is 305.13 rounded to the nearest 10?\n | 310\n | ibivibiv/math_instruct | |
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### Does $\varphi_{X+Y}(t)=\varphi_X(t)\varphi_Y(t)$ imply independence of $X$ and $Y$? [duplicate]
It shouldn't, but I am blanking on a counterexample. ETA: Note that the $t$ is shared on both sides - which diffe... | In probability theory, the concept of independence between two random variables is a fundamental notion that has various equivalent formulations. One common characterization involves the use of cumulative distribution functions (CDFs), where X and Y are said to be independent if and only if their joint CDF factors int... | ibivibiv/math_instruct | |
Two letters picked without replacement from {f: 1, q: 1, v: 3}. Give prob of picking 1 f and 1 v.\n | 3/10\n | ibivibiv/math_instruct | |
In base 5, what is 4 - 23?\n | -14\n | ibivibiv/math_instruct | |
What is 3 + 59 + 38 + -37 - (-6 + 0)?\n | 69\n | ibivibiv/math_instruct | |
Let x(j) = j**2 - j. Let s(n) = n**2 - 3*n - 1. Let l(r) = s(r) - 3*x(r). What is l(1)?\n | -3\n | ibivibiv/math_instruct | |
Suppose u = -2*p - 50, -3*u = 3*p - 5*p - 66. Let l = p - -32. What is the units digit of l?\n | 5\n | ibivibiv/math_instruct | |
What is 76.23388 rounded to the nearest 10?\n | 80\n | ibivibiv/math_instruct | |
Which is the nearest to 3? (a) 3 (b) -3/8 (c) -6 (d) 4\n | a\n | ibivibiv/math_instruct | |
Let s = 3.34 + -1.54. Round s to the nearest integer.\n | 2\n | ibivibiv/math_instruct | |
What is 51909136 to the power of 1/2, to the nearest integer?\n | 7205\n | ibivibiv/math_instruct | |
Which is smaller: 695 or 1230297/1769?\n | 695\n | ibivibiv/math_instruct | |
Solve 152*w + 120 = 176*w for w.\n | 5\n | ibivibiv/math_instruct | |
What is 0.3 times -354572?\n | -106371.6\n | ibivibiv/math_instruct | |
Let a = -3 - 0. Let t be 4/5 - ((-340)/(-17))/(-100). Let p be -4 + a*(t + -17*8). What is p rounded to the nearest one hundred?\n | 400\n | ibivibiv/math_instruct | |
Which is smaller: 10332656 or 175655132/17?\n | 175655132/17\n | ibivibiv/math_instruct | |
In base 14, what is 41468 - d67?\n | 40501\n | ibivibiv/math_instruct | |
Let h = 65234 + -717234. Round h to the nearest one thousand.\n | -652000\n | ibivibiv/math_instruct | |
Let n(f) = -6*f + 9. Let i(r) = r + 1. Let y(p) = 6*i(p) - n(p). Let z be y(-2). What is z rounded to the nearest 10?\n | -30\n | ibivibiv/math_instruct | |
Suppose -1321 = -4*f + p - 6*p, -5*f + 4*p = -1641. What is the remainder when f is divided by 102?\n | 23\n | ibivibiv/math_instruct | |
Let a = 20.583 + -0.143. Let q = 20.4 - a. Let d = 0.03 + -0.33. What is the nearest to d in -4, 0.1, q?\n | q\n | ibivibiv/math_instruct | |
Let h = -181 - -172. Let f(g) = 2*g**2 - 5*g - 8. Is f(h) a multiple of 5?\n | False\n | ibivibiv/math_instruct | |
Simplify ((n**(-1/7)/((n*n**(-6))/n))/(n**(-4)/(n*n**(-6))))/(((n*n**6)/(n*n**(1/3)*n))/(n**(-2/3))**(-47)) assuming n is positive.\n | n**(662/21)\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 1799 and 395266.\n | 257\n | ibivibiv/math_instruct | |
Let g = 0.0204 - 0.1989. Let d = g - -0.18. Round d to 4 decimal places.\n | 0.0015\n | ibivibiv/math_instruct | |
Solve 13*h + 17*h = 17*h - 338 for h.\n | -26\n | ibivibiv/math_instruct | |
Let l(q) = 2*q - 2. Let g(o) = -4*o + 1 + 7*o - 5*o + 1. What is 5*g(b) + 4*l(b)?\n | -2*b + 2\n | ibivibiv/math_instruct | |
Let m = 18 + -20. Let t(w) = -4*w - 1. Let n be t(m). Suppose 0 = 3*z - n + 1. Solve a + 0*a = -z for a.\n | -2\n | ibivibiv/math_instruct | |
Express -2*v - 2*v + 2*v + 7*v + 2*v**4 - 2*v - 95*v**2 + v**3 in the form t*v**4 + n*v + r*v**2 + u + a*v**3 and give t.\n | 2\n | ibivibiv/math_instruct | |
Is 9 a factor of 431?\n | False\n | ibivibiv/math_instruct | |
Let k(z) = 0*z + 2*z + 2*z. Let i(a) = -5*a. What is i(k(y))?\n | -20*y\n | ibivibiv/math_instruct | |
Sort -50, -307, 5 in ascending order.\n | -307, -50, 5\n | ibivibiv/math_instruct | |
Simplify 3 + ((sqrt(108) + 0)*-2)**2*-1.\n | -429\n | ibivibiv/math_instruct | |
Is 71606540669 prime?\n | True\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-85.267 * 22.734) % (-46.051 - -63.16) | 11.9660 | ibivibiv/math_instruct | |
What is 180802856 to the power of 1/5, to the nearest integer?\n | 45\n | ibivibiv/math_instruct | |
-17.308 times -0.12\n | 2.07696\n | ibivibiv/math_instruct | |
Collect the terms in 69*z - 28*z - 214*z.\n | -173*z\n | ibivibiv/math_instruct | |
-7*((-3)/(-21))/((88/96)/11)\n | -12\n | ibivibiv/math_instruct | |
Let c(j) = 3*j. Let m be c(4). Solve -3*q + 6*q = -m for q.\n | -4\n | ibivibiv/math_instruct | |
How many months are there in 7/6 of a year?\n | 14\n | ibivibiv/math_instruct | |
Suppose -10*t + 6*t = -2*t. Let f(z) = -z + t*z - z. Let r(n) = 27*n**2. Calculate f(r(o)).\n | -54*o**2\n | ibivibiv/math_instruct | |
How many centuries are there in 0.6292337 millennia?\n | 6.292337\n | ibivibiv/math_instruct | |
b"What is the zth term of -9568, -9636, -9728, -9844, -9984, -10148?\n" | -12*z**2 - 32*z - 9524\n | ibivibiv/math_instruct | |
Let t(a) = -14*a - 39. Does 15 divide t(-6)?\n | True\n | ibivibiv/math_instruct | |
Calculate 9/15 + -1 - (-11)/(-110)*186.\n | -19\n | ibivibiv/math_instruct | |
Simplify (z*(z/(z**1*z))/z*z*z/(z**(2/49)/z)*z*((z/((z*z**(3/2))/z*z))/z)/((z/((z/(z/(z*z**(-9))*z))/z))/z*z*z))**17 assuming z is positive.\n | z**(-19227/98)\n | ibivibiv/math_instruct | |
28182 divided by 154\n | 183\n | ibivibiv/math_instruct | |
Let p = -0.94 - -0.04. Which is the closest to p? (a) 3 (b) 2/3 (c) 2/9\n | c\n | ibivibiv/math_instruct | |
What is one quarter of a millennium in decades?\n | 25\n | ibivibiv/math_instruct | |
Calculate the least common multiple of 605214 and 90.\n | 3026070\n | ibivibiv/math_instruct | |
What is 23650 rounded to the nearest 100?\n | 23700\n | ibivibiv/math_instruct | |
What is the second derivative of -51447408*l**2 - 22*l - 250611?\n | -102894816\n | ibivibiv/math_instruct | |
Let a = -688 + -1033. Let t = a - -2768. What are the prime factors of t?\n | 3, 349\n | ibivibiv/math_instruct | |
What is the least common multiple of 22 and 922?\n | 10142\n | ibivibiv/math_instruct | |
What is the value of 26/3*881475/66430?\n | 115\n | ibivibiv/math_instruct | |
b"What is the ath term of 9, 32, 65, 102, 137, 164, 177, 170?\n" | -a**3 + 11*a**2 - 3*a + 2\n | ibivibiv/math_instruct | |
b"What is the nth term of 491, 2006, 4533, 8078, 12647, 18246?\n" | n**3 + 500*n**2 + 8*n - 18\n | ibivibiv/math_instruct | |
Suppose 4 = -4*v - k, -15*v - 2*k - 5 = -10*v. Which is bigger: 5/12 or v?\n | 5/12\n | ibivibiv/math_instruct | |
Let v(s) = -3*s**3 - 3*s**2 + 4*s**3 - 6 + 10*s**2 + 0*s - 2*s. What is the remainder when v(-4) is divided by 17?\n | 16\n | ibivibiv/math_instruct | |
Three letters picked without replacement from njajncjjojojo. What is prob of sequence jcj?\n | 5/286\n | ibivibiv/math_instruct | |
Solve -50*q - 2*g + 105 = -g, 0 = -q - 3*g + 17 for q.\n | 2\n | ibivibiv/math_instruct | |
Find the second derivative of 3618458*s**3 - 12536772*s wrt s.\n | 21710748*s\n | ibivibiv/math_instruct |
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