instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Is 1053401 a composite number?\n | False\n | ibivibiv/math_instruct | |
Solve 83510 = 3374*j + 16030 for j.\n | 20\n | ibivibiv/math_instruct | |
Let o = 417 - -257. Is o a composite number?\n | True\n | ibivibiv/math_instruct | |
Let q(p) = 2 + 2*p + 0 - 7. Let l be q(9). Solve -l = c - 3*k, 3*c - k + 6 = c for c.\n | -1\n | ibivibiv/math_instruct | |
In base 14, what is -b - -4083?\n | 4076\n | ibivibiv/math_instruct | |
Let i(q) be the second derivative of q**5/120 - q**4/3 - 3*q**3/2 - 3*q. Let o(n) be the second derivative of i(n). What is o(0)?\n | -8\n | ibivibiv/math_instruct | |
b"What is the nth term of -5978, -6119, -6500, -7241, -8462, -10283?\n" | -20*n**3 - n - 5957\n | ibivibiv/math_instruct | |
Let t = -62 + 52. Suppose -3*p + 3*j - 17 = -56, -5*j + 10 = 0. Let x = t + p. Calculate the greatest common factor of x and 45.\n | 5\n | ibivibiv/math_instruct | |
Let j = 1575 + 985. Calculate the greatest common factor of j and 10.\n | 10\n | ibivibiv/math_instruct | |
Suppose -72/5 - 13/5*b**3 - 12/5*b + 1/5*b**4 + 46/5*b**2 = 0. What is b?\n | -1, 2, 6\n | ibivibiv/math_instruct | |
0.0187+-11042914.8\n | -11042914.7813\n | ibivibiv/math_instruct | |
Let j(i) = 148435*i + 2078100. Calculate j(-14).\n | 10\n | ibivibiv/math_instruct | |
What is the second smallest value in -247700.25, -0.4, 2/11?\n | -0.4\n | ibivibiv/math_instruct | |
Factor -3*h**3 - 414*h**2 + 2568*h - 3456.\n | -3*(h - 4)*(h - 2)*(h + 144)\n | ibivibiv/math_instruct | |
Factor -13295*w**3 - 132338435*w**2 - 329324232825*w - 123852645.\n | -5*(w + 4977)**2*(2659*w + 1)\n | ibivibiv/math_instruct | |
What is the fourth smallest value in -0.7, 3/19, -2, 0.3, 1?\n | 0.3\n | ibivibiv/math_instruct | |
Let g(f) = -f**3 - 70*f**2 - 172*f - 84. What is g(-67)?\n | -2027\n | ibivibiv/math_instruct | |
How many days are there in 12973535.1ns?\n | 0.00000015015665625\n | ibivibiv/math_instruct | |
What is -5872383 divided by -533853?\n | 11\n | ibivibiv/math_instruct | |
Evaluate -1 - 4 - (0 - (-17 + 15)).\n | -7\n | ibivibiv/math_instruct | |
What comes next: -2281, -2286, -2301, -2332, -2385, -2466, -2581?\n | -2736\n | ibivibiv/math_instruct | |
What comes next: -174, -351, -516, -663, -786, -879, -936?\n | -951\n | ibivibiv/math_instruct | |
Rearrange (7*u - 11 + 11)*(0 - 5 + 4) + 0 + 0 + 2*u + 4*u - 2*u + 4*u - 5 + u + 5 + (1 + 0 + 1)*(-3 + 3 - 2*u) - 2*u + 2*u - u to the form i + s*u and give s.\n | -3\n | ibivibiv/math_instruct | |
Let c(n) = -n**3 - 20*n**2 + 68*n - 2. Determine c(3).\n | -5\n | ibivibiv/math_instruct | |
What is 34541 to the power of 1/2, to the nearest integer?\n | 186\n | ibivibiv/math_instruct | |
Collect the terms in 4*s**2 + 0*s**2 - 47855*s**3 - 4*s**2 + 47887*s**3.\n | 32*s**3\n | ibivibiv/math_instruct | |
Which is the closest to -0.2? (a) -1 (b) 37 (c) -67 (d) 4 (e) -37\n | a\n | ibivibiv/math_instruct | |
What is 0.00000042655 rounded to seven dps?\n | 0.0000004\n | ibivibiv/math_instruct | |
Let i = -32 - -32.2. Sort -3, 2, i in decreasing order.\n | 2, i, -3\n | ibivibiv/math_instruct | |
Suppose 0 = o - 4 + 32. Let p = -42977/6 - -7147. Calculate the common denominator of p and (-78)/16*o/(-6).\n | 12\n | ibivibiv/math_instruct | |
Suppose -2*z + 36 = 2*j, -4*z + 3*j = -110 + 24. Suppose -2 = -2*k, 3*u + k - 14 = z. List the prime factors of u.\n | 11\n | ibivibiv/math_instruct | |
Let l(q) = -19*q - 14. What is l(-2)?\n | 24\n | ibivibiv/math_instruct | |
Let k = -159 + 213. Is 9 a factor of k?\n | True\n | ibivibiv/math_instruct | |
Let v = 1.17 + 0.03. Let m = v - -9. Round m to the nearest integer.\n | 10\n | ibivibiv/math_instruct | |
Is 6656713 a composite number?\n | True\n | ibivibiv/math_instruct | |
Let l(w) = -2*w**3 - 15*w**2 - 6*w + 10. Calculate l(-7).\n | 3\n | ibivibiv/math_instruct | |
How many minutes are there between 7:26 AM and 6:35 PM?\n | 669\n | ibivibiv/math_instruct | |
Let q(v) be the first derivative of -v**4/16 - 24*v**3 - 21021*v**2/8 - 20449*v/2 - 907. Factor q(r).\n | -(r + 2)*(r + 143)**2/4\n | ibivibiv/math_instruct | |
Evaluate -33 + -18 + (-6 - -19).\n | -38\n | ibivibiv/math_instruct | |
Let k = -3.95 + -0.05. Let j = k - -7. Let s be (-81)/9 + 284/32. Which is the nearest to j? (a) 0.5 (b) s (c) 5/4\n | c\n | ibivibiv/math_instruct | |
What is 9839 to the power of 1/9, to the nearest integer?\n | 3\n | ibivibiv/math_instruct | |
What are the prime factors of 16347360?\n | 2, 3, 5, 34057\n | ibivibiv/math_instruct | |
((-1)/3)/((-851)/(-8880)*-355 + 34)\n | 16\n | ibivibiv/math_instruct | |
Suppose 4*x - 35 + 231 = 0. Let p be 14/x - 26/7. Let s(y) = -4*y**3 + 9*y**2 - 9*y - 2. Let l(v) = 2*v**3 - 4*v**2 + 4*v + 1. Give p*s(a) - 9*l(a).\n | -2*a**3 - 1\n | ibivibiv/math_instruct | |
Is 157086278221 a composite number?\n | True\n | ibivibiv/math_instruct | |
-373704 divided by 552\n | -677\n | ibivibiv/math_instruct | |
Find the common denominator of 23/96 and 89/576.\n | 576\n | ibivibiv/math_instruct | |
Suppose 2*g + 14*s - 21 = 15*s, 6*g + 2*s - 98 = 0. What is the remainder when 247 is divided by g?\n | 9\n | ibivibiv/math_instruct | |
Suppose -6359*k + 6338*k = 84. What is the nearest to k in 12, -3, -1/10, 5?\n | -3\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 a and 1 m when two letters picked without replacement from {u: 2, a: 1, m: 1, j: 1, c: 1, y: 1}.\n | 1/21\n | ibivibiv/math_instruct | |
In base 6, what is -154 - 231132?\n | -231330\n | ibivibiv/math_instruct | |
Suppose -5*i + 4*b = -402, -i = 12*b - 14*b - 84. Let n be 2 + (-3 - 1) - i/(-21). Factor 0*t**2 - n*t**4 + 0 + 4/7*t**5 + 0*t + 8/7*t**3.\n | 4*t**3*(t - 2)*(t - 1)/7\n | ibivibiv/math_instruct | |
What is the second biggest value in 228, -3, -3/4, -2/41, -5?\n | -2/41\n | ibivibiv/math_instruct | |
Suppose 0 = -5*s + 15, -3*q - 180 + 63 = -3*s. Let n be (-10)/(-8) + 9/q. Let h = 19 - 12. Calculate the highest common factor of n and h.\n | 1\n | ibivibiv/math_instruct | |
Let f be (5 + -3 + -5)*-1. What is the closest to -5/3 in 1, 0.5, f?\n | 0.5\n | ibivibiv/math_instruct | |
What is the smallest value in -0.09, -2, 13/6?\n | -2\n | ibivibiv/math_instruct | |
What is the greatest common factor of 8 and 32?\n | 8\n | ibivibiv/math_instruct | |
Let l be ((-20)/(-6))/(-6*1/(-9)). List the prime factors of (l/25)/(-1) - 1342/(-10).\n | 2, 67\n | ibivibiv/math_instruct | |
Suppose 2*r = -5*g + 21, 2*g - 15 = -4*r - 13. What is the smallest value in r, -28, 1/4, 0.1?\n | -28\n | ibivibiv/math_instruct | |
Let w = -171 - -256. Let m = 84.16784 + 0.12216. Let b = w - m. Round b to one dp.\n | 0.7\n | ibivibiv/math_instruct | |
Calculate the common denominator of 65/102412 and -83/10.\n | 512060\n | ibivibiv/math_instruct | |
Let w be 56/96 + 1/4*-2. Which is the nearest to -2/5? (a) -0.3 (b) -3 (c) w\n | a\n | ibivibiv/math_instruct | |
Let v(u) = u**3 - 3*u**2 - 8*u + 3. Let y be v(5). Calculate the greatest common divisor of y and 39.\n | 13\n | ibivibiv/math_instruct | |
Work out -8059 * 78.\n | -628602\n | ibivibiv/math_instruct | |
Let k = 5.83 - 5.78. What is the fifth biggest value in 53, 0.4, -0.2, 0.1, k?\n | -0.2\n | ibivibiv/math_instruct | |
Calculate 11385 divided by -115.\n | -99\n | ibivibiv/math_instruct | |
What is the thousands digit of 101825861?\n | 5\n | ibivibiv/math_instruct | |
What is the cube root of 166791 to the nearest integer?\n | 55\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {u: 1, r: 3}. What is prob of sequence rrur?\n | 1/4\n | ibivibiv/math_instruct | |
Let n = 6.5 - -4. Let b = -10 + n. What is the closest to 3 in 1, -0.5, b?\n | 1\n | ibivibiv/math_instruct | |
Suppose 4*n + 16 = 0, -3*n = 3*p + 2*p - 13. Suppose -2*j = -j + p. Let m(l) be the first derivative of -l**2 - 5*l - 65. Give m(j).\n | 5\n | ibivibiv/math_instruct | |
Suppose -14 + 4 = -5*g - 4*n, -5*g + n = -10. Solve g*d - 28 = 5*u, 2*u - d + 16 = -u for u.\n | -4\n | ibivibiv/math_instruct | |
Let f = -0.3 + 0.6. Let t = 0.1 + 0.9. Put 3/4, t, f in decreasing order.\n | t, 3/4, f\n | ibivibiv/math_instruct | |
Let v be (5 - 4 - 2)/(6/4). Suppose -t - 4*o = -14, 2*o = 3*t - 7*t. Sort v, t, -0.2 in descending order.\n | -0.2, v, t\n | ibivibiv/math_instruct | |
Let b = -0.3 - -0.4. Let o = 2359 - 25973/11. Let l = o + 194/99. What is the closest to b in 0, l, -2/3?\n | 0\n | ibivibiv/math_instruct | |
What is the third smallest value in 0.3, 41, -4/5, -3/4, -4, 0.17?\n | -3/4\n | ibivibiv/math_instruct | |
Sort -2/11, -0.3, 38975537.\n | -0.3, -2/11, 38975537\n | ibivibiv/math_instruct | |
Convert 102 (base 4) to base 7.\n | 24\n | ibivibiv/math_instruct | |
Suppose 10*z - 3*z - 497 = 0. Suppose z - 17 = -3*g. Let d = 33/2 + g. Which is smaller: d or -3?\n | -3\n | ibivibiv/math_instruct | |
What comes next: 128, 256, 386, 524, 676?\n | 848\n | ibivibiv/math_instruct | |
Let y(u) be the third derivative of u**6/200 + 7*u**5/100 + 3*u**4/8 + 9*u**3/10 + 8*u**2. Factor y(g).\n | 3*(g + 1)*(g + 3)**2/5\n | ibivibiv/math_instruct | |
Sort -18, 11, 2, -5 in decreasing order.\n | 11, 2, -5, -18\n | ibivibiv/math_instruct | |
What is 250 minutes before 4:47 PM?\n | 12:37 PM\n | ibivibiv/math_instruct | |
Let c(m) = 21*m + 14. Let l be c(4). Suppose 5 = -5*d, 3*t - l = -d + 3*d. Which is smaller: t or 31?\n | 31\n | ibivibiv/math_instruct | |
Is 31472 smaller than 31467?\n | False\n | ibivibiv/math_instruct | |
Let d = 410.4 - 192.6. Round d to zero decimal places.\n | 218\n | ibivibiv/math_instruct | |
What is the units digit of 1636?\n | 6\n | ibivibiv/math_instruct | |
Sort 30, 2, -3 in increasing order.\n | -3, 2, 30\n | ibivibiv/math_instruct | |
Suppose -30*z - 7812 = -7872. Solve 3*k + z*i - 25 = -3*i, 5*i - 10 = 0 for k.\n | 5\n | ibivibiv/math_instruct | |
Let X be a normal, projective, and three-dimensional algebraic variety with a nef and big divisor D on it. Suppose that D generates an extremal ray, and let C be a curve in that ray with negative self-intersection. Show that the Mori dream space associated with the Zariski decomposition of D is birational to a blow-up ... | To show that the Mori dream space associated with the Zariski decomposition of D is birational to a blow-up of X along C, we will use the Cone Theorem and the contraction theorem.
By the Cone Theorem, the Mori cone of curves NE(X) is generated by the classes of curves contracted by extremal contractions. Since D gener... | ibivibiv/math_instruct | |
Let a be 3*4*2/6. Let i be (a - 1) + (4 - 5). Suppose 2*d - 1 = 2*g + g, 13 = 4*d + 5*g. Solve 4 = -d*c - i*c for c.\n | -1\n | ibivibiv/math_instruct | |
Suppose 15*i + 3*a + 58 = 5*a, 0 = -2*i - a - 9. Sort i, 1, 12, -5, -3 in descending order.\n | 12, 1, -3, i, -5\n | ibivibiv/math_instruct | |
Let t = -2620 + 2619.6. What is the nearest to 0.1 in -25, 4, 5, t?\n | t\n | ibivibiv/math_instruct | |
What is the value of 0 + (-53 - -56) + (-13 - -1)?\n | -9\n | ibivibiv/math_instruct | |
Let x = 2 + 10. Suppose -x = -4*j + j. Suppose p + p + 8 = j*m, 3*p - 3*m = -6. Solve -4*n + 16 = -p for n.\n | 4\n | ibivibiv/math_instruct | |
Solve 22*x + 48 = 6*x for x.\n | -3\n | ibivibiv/math_instruct | |
What are the prime factors of 23268391?\n | 23268391\n | ibivibiv/math_instruct | |
Let s(x) = -x**2 - 32*x - 34. Suppose 78 = 3*a - 5*y, 3*a - 33 = 2*y + 36. What is the remainder when (22/(-3))/((-2)/a) is divided by s(-30)?\n | 25\n | ibivibiv/math_instruct | |
Let s(p) = 11*p + 1 + 1 - 8*p + 6*p. Let j be s(2). Suppose -25*o - 25 = -j*o. What is the second biggest value in o, 0.5, -3/8, 0.1?\n | 0.1\n | ibivibiv/math_instruct | |
Let i = 343 - 434. Sort 0, -1, i in increasing order.\n | i, -1, 0\n | ibivibiv/math_instruct |
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