instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Solve 21 = 324*y - 327*y for y.\n | -7\n | ibivibiv/math_instruct | |
Let a be (-10)/(-2) - (3 + -1). Suppose t = a*t - 8. What is the greatest common divisor of 28 and t?\n | 4\n | ibivibiv/math_instruct | |
What is the remainder when 7579 is divided by 3776?\n | 27\n | ibivibiv/math_instruct | |
Let s = -24 + 21. Let o = -1 - -1. Which is the biggest value? (a) s (b) o (c) -2\n | b\n | ibivibiv/math_instruct | |
22/(572/(-39))*(-5)/((-90)/(-4))\n | 1/3\n | ibivibiv/math_instruct | |
What is the thousands digit of 471296?\n | 1\n | ibivibiv/math_instruct | |
What is -174f1 (base 16) in base 10?\n | -95473\n | ibivibiv/math_instruct | |
What is 4594804316 to the power of 1/2, to the nearest integer?\n | 67785\n | ibivibiv/math_instruct | |
(-266045)/(-23205) + 6/(-7) + (-28)/(-476)\n | 32/3\n | ibivibiv/math_instruct | |
Let v be 197 - 5/(2 - -3). Suppose 0 = h + 2*h + 2*i + v, -5*h + 2*i = 300. Is (-2)/1 - h/1 a multiple of 12?\n | True\n | ibivibiv/math_instruct | |
Let i(x) = -x**2 + 61*x - 125. Calculate i(59).\n | -7\n | ibivibiv/math_instruct | |
Rearrange (-8*n**2 + n**3 + 4*n**2 + 6*n**2)*(n + n - 4*n) to f*n**2 + d*n + y*n**3 + r*n**4 + g and give y.\n | -4\n | ibivibiv/math_instruct | |
What is the greatest common factor of 95 and 73321?\n | 19\n | ibivibiv/math_instruct | |
Let u = -0.0319 + 0.1319. What is the fourth smallest value in -25, u, 1, -3/7?\n | 1\n | ibivibiv/math_instruct | |
Calculate 1*(-4 + -1) + (-1088)/(-192).\n | 2/3\n | ibivibiv/math_instruct | |
Is 7105 a multiple of 29?\n | True\n | ibivibiv/math_instruct | |
What is the fourth smallest value in -0.2, 17, -2, 10?\n | 17\n | ibivibiv/math_instruct | |
b"What is the lth term of 21498, 21504, 21512, 21522?\n" | l**2 + 3*l + 21494\n | ibivibiv/math_instruct | |
Collect the terms in -476*r**3 - 1247*r**3 + 188*r**3.\n | -1535*r**3\n | ibivibiv/math_instruct | |
Let k(s) = 8*s + 53. Calculate k(-6).\n | 5\n | ibivibiv/math_instruct | |
Calculate prob of sequence xllm when four letters picked without replacement from {l: 2, x: 2, c: 1, i: 2, m: 7, y: 1}.\n | 1/1170\n | ibivibiv/math_instruct | |
Collect the terms in -7646*q**2 + 7646*q**2 - 8*q**3 + 5.\n | -8*q**3 + 5\n | ibivibiv/math_instruct | |
Suppose -34*n + 855988 = -48*n. What is n rounded to the nearest 10000?\n | -60000\n | ibivibiv/math_instruct | |
Which is smaller: 1 or -154/3099?\n | -154/3099\n | ibivibiv/math_instruct | |
What is -269 divided by 3603?\n | -269/3603\n | ibivibiv/math_instruct | |
What is the seventh root of 65510632 to the nearest integer?\n | 13\n | ibivibiv/math_instruct | |
Let t(m) = 244*m + 4017. Calculate the remainder when t(-9) is divided by 61.\n | 52\n | ibivibiv/math_instruct | |
How many minutes are there between 8:48 AM and 12:12 PM?\n | 204\n | ibivibiv/math_instruct | |
List the prime factors of 98440688.\n | 2, 67, 229, 401\n | ibivibiv/math_instruct | |
Let r(q) = q**3 + q**2 + q + 1. Let f be r(0). Let d be (-4)/(1/(f/2)). Let z be d/(-12)*9/(-4). Is -1 less than z?\n | True\n | ibivibiv/math_instruct | |
Suppose -4*u = -j - 8*u - 52, -3*j = 4*u + 132. Let d = j + 42. Is d even?\n | True\n | ibivibiv/math_instruct | |
List the prime factors of 52351.\n | 13, 4027\n | ibivibiv/math_instruct | |
Let l(q) = -2*q**2 + 189*q + 3. Let c(m) = -2*m**2 + 187*m + 4. Calculate -3*c(y) + 4*l(y).\n | -2*y**2 + 195*y\n | ibivibiv/math_instruct | |
Suppose 0 = -6*u + 2*u + 36. Let q = 5 + -1. Calculate the least common multiple of q and u.\n | 36\n | ibivibiv/math_instruct | |
Let q = 0.10685 + 0.79315. Which is the nearest to 2/7? (a) q (b) 4 (c) -1/9 (d) -0.5\n | c\n | ibivibiv/math_instruct | |
Suppose -9*r + 16*r = 3*r. Suppose 5*a - l - 26 = -0*l, -2*a - 3*l + 7 = r. Solve -5*h = -4*h - a for h.\n | 5\n | ibivibiv/math_instruct | |
Put 9, -62, 1, 3, -15 in ascending order.\n | -62, -15, 1, 3, 9\n | ibivibiv/math_instruct | |
Let j(b) = b**3 + 3*b + 4. Let t(y) = y**3 + 10*y**2 - 2*y - 21. Let z be t(-10). Let n(m) = -m**3 - m - 1. Give z*j(p) - 4*n(p).\n | 3*p**3 + p\n | ibivibiv/math_instruct | |
How many minutes are there between 1:59 PM and 6:23 PM?\n | 264\n | ibivibiv/math_instruct | |
Let f = -23 - -22. Let m be f/(-5) + 258/(-15). Let s = -17 - m. Does 1/21 = s?\n | False\n | ibivibiv/math_instruct | |
Solve 2*i - 15 + 8 = 3*n, 4*n - 24 = -4*i for n.\n | 1\n | ibivibiv/math_instruct | |
Is 1448/3 less than 157122?\n | True\n | ibivibiv/math_instruct | |
Is -3/16 at most as big as 0?\n | True\n | ibivibiv/math_instruct | |
Let b be (21/(-5))/((-13)/520). Suppose -66*l - b = -72*l. Calculate the highest common divisor of l and 7.\n | 7\n | ibivibiv/math_instruct | |
Let y = -203.8 + 200.8. Which is the fifth biggest value? (a) -430 (b) -2/3 (c) y (d) -5 (e) -4\n | a\n | ibivibiv/math_instruct | |
List the prime factors of 157438.\n | 2, 223, 353\n | ibivibiv/math_instruct | |
What comes next: 10874, 10872, 10870, 10868, 10866?\n | 10864\n | ibivibiv/math_instruct | |
What is the units digit of (-10)/85 - 5616/(-51)?\n | 0\n | ibivibiv/math_instruct | |
Find the second derivative of -38320*d**5 - 25112*d wrt d.\n | -766400*d**3\n | ibivibiv/math_instruct | |
What is -101.255109 rounded to the nearest 10?\n | -100\n | ibivibiv/math_instruct | |
Factor 2*z**2 + 2534884*z + 803204611682.\n | 2*(z + 633721)**2\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"Mathematical induction inequality proofs
## Mathematical induction inequality proofs
<
to their mathematical induction proofs on the Mathematical Induction
(a) (2^n) ≤ n! , n≥4 Base Step: sub in n=1 and yes, it works! How... | Mathematical induction is a powerful proof technique used to establish that a given statement is true for all natural numbers. It consists of two steps: the base case and the inductive step. The base case involves verifying the truth of the statement for the smallest possible value of the integer (usually n = 1). The ... | ibivibiv/math_instruct | |
List the prime factors of 211.\n | 211\n | ibivibiv/math_instruct | |
Solve 4*a = 2*a - 0*a for a.\n | 0\n | ibivibiv/math_instruct | |
Evaluate 1*((-130)/221)/10.\n | -1/17\n | ibivibiv/math_instruct | |
Let j = -480 + 1720. Is j a multiple of 16?\n | False\n | ibivibiv/math_instruct | |
Calculate the remainder when 960819 is divided by 985.\n | 444\n | ibivibiv/math_instruct | |
Let g = -0.306 + -0.064. Let t = -2.07 - g. Let h = t + 1.764. What is h rounded to 2 decimal places?\n | 0.06\n | ibivibiv/math_instruct | |
Let x(y) = -y**3 + 5*y**2 - 3*y + 1. Let i(t) = t**3 - 6*t**2 + 4*t - 2. Calculate -3*i(v) - 4*x(v).\n | v**3 - 2*v**2 + 2\n | ibivibiv/math_instruct | |
Simplify (sqrt(720) + (sqrt(720) + (sqrt(720) - (sqrt(720) - 2*sqrt(720))) + sqrt(720) - sqrt(720)))/(sqrt(4) + (sqrt(400)*-1 - sqrt(4))).\n | -12*sqrt(5)/5\n | ibivibiv/math_instruct | |
Which is the nearest to 2/5? (a) 4 (b) 6.4679 (c) -2/7 (d) -2/3 (e) -0.1\n | e\n | ibivibiv/math_instruct | |
Suppose j - 8*j + 35 = 0. Solve j*r - 28 = -8 for r.\n | 4\n | ibivibiv/math_instruct | |
What is 0.00227629 rounded to 5 decimal places?\n | 0.00228\n | ibivibiv/math_instruct | |
Let a(y) = -y**2 + 3622*y + 146478. Calculate a(-40).\n | -2\n | ibivibiv/math_instruct | |
What is 10 divided by -31873980?\n | -1/3187398\n | ibivibiv/math_instruct | |
Solve -513 - 158 - 209 = -110*o for o.\n | 8\n | ibivibiv/math_instruct | |
What is the cube root of 5130384998 to the nearest integer?\n | 1725\n | ibivibiv/math_instruct | |
Let d(y) = -y**2 + y + 1. Let k(f) = -2*f**4 + 8*f**3 - 10*f**2 - 2*f + 12. Let c(j) = -6*d(j) + k(j). Factor c(g).\n | -2*(g - 3)*(g - 1)**2*(g + 1)\n | ibivibiv/math_instruct | |
Let v = 10 - 12. Let n = 37.18 - 37. What is the third smallest value in n, -1/4, v?\n | n\n | ibivibiv/math_instruct | |
Let o(k) = -k**2 + k + 1. Let d(a) = 12*a**2 + a + 1. Calculate -d(h) + o(h).\n | -13*h**2\n | ibivibiv/math_instruct | |
Suppose 0 = 50*f - 66*f + 32. Solve 2*l + 10 = f for l.\n | -4\n | ibivibiv/math_instruct | |
Suppose 0 = -2*m - s - s + 430, -185 = -m + 5*s. List the prime factors of m.\n | 2, 3, 5, 7\n | ibivibiv/math_instruct | |
What is 704/160*(-380)/76?\n | -22\n | ibivibiv/math_instruct | |
Expand -4*r**3 + 4*r**3 - r**3 + (1 - r**2 - 1)*(-2*r + 3 - 3) + 27*r**3 + 14*r**3 + 25*r**3.\n | 67*r**3\n | ibivibiv/math_instruct | |
List the prime factors of 4227.\n | 3, 1409\n | ibivibiv/math_instruct | |
-81569159 divided by 6\n | -81569159/6\n | ibivibiv/math_instruct | |
What is the thousands digit of 32664?\n | 2\n | ibivibiv/math_instruct | |
Let w be (-2)/2 - (-9)/(-3). Let b(x) = x**3 + 4*x**2 - 2*x. Give b(w).\n | 8\n | ibivibiv/math_instruct | |
What is the closest to 1/3 in -0.4, -3/5, -3, 3?\n | -0.4\n | ibivibiv/math_instruct | |
What is the next term in -175156, -174933, -174710, -174487, -174264?\n | -174041\n | ibivibiv/math_instruct | |
Let y(i) = -i**3 - 7*i**2 - 7*i - 1. Let s be y(-6). Let l be 9/s + (-2)/(-10). What is the third derivative of 2*q**5 + 0*q**5 + l*q**2 - 4*q**5 wrt q?\n | -120*q**2\n | ibivibiv/math_instruct | |
Do 1 and -18/5281 have the same value?\n | False\n | ibivibiv/math_instruct | |
Suppose 113*b - 36*b - 185955 = 0. What is the thousands digit of b?\n | 2\n | ibivibiv/math_instruct | |
Let x(z) be the second derivative of z**7/42 - z**6/60 - 19*z**5/40 - 31*z**4/24 - 19*z**3/12 - z**2 + 378*z. Suppose x(v) = 0. Calculate v.\n | -1, -1/2, 4\n | ibivibiv/math_instruct | |
List the prime factors of 1169.\n | 7, 167\n | ibivibiv/math_instruct | |
Let i be 70 - (8 - (0 - -4)). Suppose i = 4*w + p, 5*p = 4*w - 0*w - 78. Does 7 divide w?\n | False\n | ibivibiv/math_instruct | |
Which is the nearest to -2/19? (a) 0 (b) 3 (c) 0.14 (d) 5\n | a\n | ibivibiv/math_instruct | |
Let n(o) = 6*o - 63. Let x be n(15). Let b be 2/2*(x - 14). Let m(g) = -7*g**2 + 6*g + 3. Let i(f) = -15*f**2 + 13*f + 6. Give b*m(y) - 6*i(y).\n | -y**2 + 3\n | ibivibiv/math_instruct | |
-469451484 divided by 13040319\n | -36\n | ibivibiv/math_instruct | |
What is -2.390973 rounded to 1 dp?\n | -2.4\n | ibivibiv/math_instruct | |
What is the third root of 6492 to the nearest integer?\n | 19\n | ibivibiv/math_instruct | |
What is the next term in -356057, -356060, -356063, -356066, -356069, -356072?\n | -356075\n | ibivibiv/math_instruct | |
Suppose -5*n - 2*d - 18 = 0, n + 30 = 10*d - 6*d. Let v(x) = x**2 - 7*x - 3. Give v(n).\n | 75\n | ibivibiv/math_instruct | |
List the prime factors of 1398.\n | 2, 3, 233\n | ibivibiv/math_instruct | |
Suppose 2*g - 480 = 52. Is ((-2)/(-4))/(7/g) a composite number?\n | False\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {a: 3, e: 5, j: 1}. Give prob of picking 3 a.\n | 1/84\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {k: 3, w: 8}. Give prob of sequence wkww.\n | 7/55\n | ibivibiv/math_instruct | |
Suppose 0 = -10*t - t + 5797. Suppose 2*f + u - 129 = 500, 2*u = -10. Let w = t - f. What is the hundreds digit of w?\n | 2\n | ibivibiv/math_instruct | |
Suppose -y - 5*z + 9 = -4*y, 0 = 5*z. Let k be 2/((-8)/12060*y). Let q = k + -51253/51. Which is smaller: 1 or q?\n | q\n | ibivibiv/math_instruct | |
What is 328 minutes after 3:41 PM?\n | 9:09 PM\n | ibivibiv/math_instruct |
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