instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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|---|---|---|---|
Simplify (b*b**(-1/6)*b*b/b**7)/(b**1)**16*(((b/(b/b**0))/b)**(-3))**3 assuming b is positive.\n | b**(-67/6)\n | ibivibiv/math_instruct | |
Round 0.04803 to 2 dps.\n | 0.05\n | ibivibiv/math_instruct | |
Let b(m) be the first derivative of m**4/12 - 4*m + 29. Let q(h) be the first derivative of b(h). Let y(w) = 6*w**2. What is q(y(r))?\n | 36*r**4\n | ibivibiv/math_instruct | |
Suppose -2*l + 13146 = -26*q + 31*q, -2*q + 5260 = l. What is the smallest common multiple of 156 and q?\n | 15756\n | ibivibiv/math_instruct | |
Is 6198893 a composite number?\n | True\n | ibivibiv/math_instruct | |
Let w(f) be the third derivative of 0 + 0*f - f**2 - 1/24*f**4 - 1/60*f**5 + 2/3*f**3. Let b be w(0). Solve j = b*j - 12 for j.\n | 4\n | ibivibiv/math_instruct | |
Which is smaller: -4 or -437231?\n | -437231\n | ibivibiv/math_instruct | |
What is 1133 divided by 1?\n | 1133\n | ibivibiv/math_instruct | |
Let y = 2247551766360014 - 2247551566712034.99999992. Let j = y - 199647946. Let o = j + -33. What is o rounded to seven dps?\n | 0.0000001\n | ibivibiv/math_instruct | |
Product of -4129 and 1673.\n | -6907817\n | ibivibiv/math_instruct | |
What is the second smallest value in -5, 1/3, -46, 2/7?\n | -5\n | ibivibiv/math_instruct | |
What is the hundred millions digit of 224473103?\n | 2\n | ibivibiv/math_instruct | |
Is 2815497 a multiple of 921?\n | True\n | ibivibiv/math_instruct | |
Let d = -254 - -744. Suppose -m = -6*m + d. What is the highest common divisor of 14 and m?\n | 14\n | ibivibiv/math_instruct | |
What is the cube root of 2942964491 to the nearest integer?\n | 1433\n | ibivibiv/math_instruct | |
Let k(q) = -q**3 + 7*q**2 - 7*q + 8. Let o be k(4). What is the greatest common factor of 28 and o?\n | 28\n | ibivibiv/math_instruct | |
Simplify ((sqrt(36) - sqrt(216)/(sqrt(6)*2))/((sqrt(18)/sqrt(2))/sqrt(3)))/(-5*(sqrt(726) - (sqrt(726)*1 - sqrt(726))*-5)).\n | -sqrt(2)/110\n | ibivibiv/math_instruct | |
Let x(f) = -f**2 + 23*f - 107. Suppose 0 = -7*m + 2*m + 470. What is the remainder when m is divided by x(14)?\n | 18\n | ibivibiv/math_instruct | |
Which is the nearest to -3? (a) 0.5 (b) 0.08 (c) 1 (d) 0.6\n | b\n | ibivibiv/math_instruct | |
Let l(z) = -z - 10. Suppose -5*q - 5*n + 100 = 0, n - 41 = -4*q + 33. Let b(u) = 18 + 5*u**2 - 3*u**2 - 3*u**2 + 17*u. Let v be b(q). Give l(v).\n | -10\n | ibivibiv/math_instruct | |
Expand (3*a**2 + 2 - 2)*(4 - 3 - 3)*(0*a**3 + 4*a**3 + 0*a**3).\n | -24*a**5\n | ibivibiv/math_instruct | |
Simplify 2*-6*((sqrt(243) - (sqrt(243) - sqrt(243)*4))/sqrt(9) + 3 + 5)*2.\n | -288*sqrt(3) - 192\n | ibivibiv/math_instruct | |
Let h(i) = -2*i**3 + 12*i**2 + 4*i - 20. Let x be h(6). Solve -2*v = -3*v + x for v.\n | 4\n | ibivibiv/math_instruct | |
Let y = -0.529 + -77.751. Let x = y + 0.28. Let k = -77.9876 - x. What is k rounded to 3 decimal places?\n | 0.012\n | ibivibiv/math_instruct | |
How many months are there in eleven quarters of a decade?\n | 330\n | ibivibiv/math_instruct | |
Let w(u) = -u**2 + 13*u - 4. Let s be w(13). Is -5 < s?\n | True\n | ibivibiv/math_instruct | |
Calculate 520/4922 - (-378)/(-4347).\n | 2/107\n | ibivibiv/math_instruct | |
What is the third smallest value in -0.1, 0, 5, -15, -5, 3.475?\n | -0.1\n | ibivibiv/math_instruct | |
Calculate the remainder when 744687 is divided by 2523.\n | 402\n | ibivibiv/math_instruct | |
Calculate -542952 divided by 18.\n | -30164\n | ibivibiv/math_instruct | |
Simplify -5*(4 + -2*sqrt(612))**2.\n | -12320 + 480*sqrt(17)\n | ibivibiv/math_instruct | |
Which is greater: 291300/7 or 41615?\n | 41615\n | ibivibiv/math_instruct | |
What is 4/7 of a week in hours?\n | 96\n | ibivibiv/math_instruct | |
Suppose 16*f + 5250 = 30*f. Is f a multiple of 7?\n | False\n | ibivibiv/math_instruct | |
Solve 4*g + 8 = 19*i - 21*i, 9 = -3*g - 3*i for g.\n | -1\n | ibivibiv/math_instruct | |
Solve -4*i + 4 = 4*u, i = 2*u - 5*u + 11 for u.\n | 5\n | ibivibiv/math_instruct | |
Collect the terms in y - y**2 + 1 + 7*y**2 - 10*y + 4*y.\n | 6*y**2 - 5*y + 1\n | ibivibiv/math_instruct | |
What is the second derivative of -14713*k**3*m + 3*k*m + 2084*k wrt k?\n | -88278*k*m\n | ibivibiv/math_instruct | |
Express (0*g + 0*g - 2*g)*(-8 - 7 - 6) + 1 - 4*g - 1 as l + r*g and give r.\n | 38\n | ibivibiv/math_instruct | |
What is prob of sequence rw when two letters picked without replacement from {k: 2, w: 2, e: 3, r: 5, s: 6}?\n | 5/153\n | ibivibiv/math_instruct | |
Is 1463447 prime?\n | True\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"The details don’t matter. Students can serve on either or both committees, but Rocco refuses to serve on both - he will only serve on one or the other. 2 n! Active 6 years, 3 months ago. Remaining 1 can be occupied by anybody... | Let's delve into some fundamental counting principles, specifically focusing on permutations and combinations with restrictions. These concepts arise often in discrete mathematics and have various applications in computer science, statistics, and engineering. We aim to provide clarity, rigor, and engagement throughout... | ibivibiv/math_instruct | |
Calculate -433 divided by 77.\n | -433/77\n | ibivibiv/math_instruct | |
What is (14/(-5))/(1547/(-442))?\n | 4/5\n | ibivibiv/math_instruct | |
Convert 3565 (base 8) to base 12.\n | 1131\n | ibivibiv/math_instruct | |
What is prob of picking 1 s and 1 c when two letters picked without replacement from cssscsscddcds?\n | 4/13\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {r: 3, t: 1}. What is prob of picking 1 t and 1 r?\n | 1/2\n | ibivibiv/math_instruct | |
b"What is the qth term of -369, -847, -1311, -1755, -2173, -2559?\n" | q**3 + q**2 - 488*q + 117\n | ibivibiv/math_instruct | |
What is the common denominator of 19/5 and (-4 - 18/(-5)) + 3?\n | 5\n | ibivibiv/math_instruct | |
Let d = 0.162 + -0.2114. Let q = 0.1494 + d. Which is the third biggest value? (a) 3/2 (b) q (c) 23\n | b\n | ibivibiv/math_instruct | |
Let f be 22/(-4) + 33/22. Let a = f - -37. Is a a prime number?\n | False\n | ibivibiv/math_instruct | |
What is the value of -5 - ((0 - -4) + 1) - -5?\n | -5\n | ibivibiv/math_instruct | |
What is 300 minutes after 10:53 PM?\n | 3:53 AM\n | ibivibiv/math_instruct | |
Put 45, -5, 5 in decreasing order.\n | 45, 5, -5\n | ibivibiv/math_instruct | |
Is 21 at most as big as -37942?\n | False\n | ibivibiv/math_instruct | |
Let b = 63 + -60. Suppose -b*i + 5*u + 68 = -25, 0 = 2*i + u - 62. Suppose 0 = -26*v + i*v - 1110. What is the remainder when v is divided by 45?\n | 42\n | ibivibiv/math_instruct | |
Solve 5 + 0 = 5*d for d.\n | 1\n | ibivibiv/math_instruct | |
Round -2.8451 to zero decimal places.\n | -3\n | ibivibiv/math_instruct | |
Let m(f) = -9*f**3. Let j = 15 + -14. What is m(j)?\n | -9\n | ibivibiv/math_instruct | |
Suppose 0 = 2*t + 834 + 7344. Let h = t + 1124. Is (1 + h + 2)*4/(-8) a composite number?\n | False\n | ibivibiv/math_instruct | |
Round -1075.78941 to the nearest ten.\n | -1080\n | ibivibiv/math_instruct | |
Suppose -180 = -38*q + 2*q. Let z(h) be the first derivative of -h**3/3 - 3*h**2/2 + 7*h - 149. Give z(q).\n | -33\n | ibivibiv/math_instruct | |
Let b(q) = -289*q - 2010. Let f be b(-7). Solve f = v - 4*x, 4*v - x = 11 - 4 for v.\n | 1\n | ibivibiv/math_instruct | |
Let a(o) be the third derivative of 19*o**9/252 + 19*o**8/336 - 2539*o**5/60 + 13244*o**2. What is the third derivative of a(d) wrt d?\n | 4560*d**3 + 1140*d**2\n | ibivibiv/math_instruct | |
What is -14437721 (base 8) in base 10?\n | -3293137\n | ibivibiv/math_instruct | |
Suppose -3*z - 2*m = -10170 - 1751, -z + 5*m = -3968. Is z composite?\n | True\n | ibivibiv/math_instruct | |
What is the value of -2 + (-1 - 45) + (-1 - (7 - (-1 + 1)))?\n | -56\n | ibivibiv/math_instruct | |
Let h = -444 - -447.1. Which is the fourth smallest value? (a) h (b) -2/7 (c) 0.5 (d) -3\n | a\n | ibivibiv/math_instruct | |
What is 23097701 to the power of 1/4, to the nearest integer?\n | 69\n | ibivibiv/math_instruct | |
In base 6, what is 2 - 11504454?\n | -11504452\n | ibivibiv/math_instruct | |
Find the second derivative of 23*y + 2*y**4 + 19*y**4 - 4*y wrt y.\n | 252*y**2\n | ibivibiv/math_instruct | |
Let m(n) = -n**2 - 2*n + 2. Let v be m(0). Suppose 5*d = -0*d - 4*j - 12, 3*j + 9 = 2*d. Solve v*t = -d*t - 4 for t.\n | -2\n | ibivibiv/math_instruct | |
Calculate 68.1252*231.\n | 15736.9212\n | ibivibiv/math_instruct | |
Factor 2*d**4/7 - 32*d**3/7 + 156*d**2/7 - 32*d + 14.\n | 2*(d - 7)**2*(d - 1)**2/7\n | ibivibiv/math_instruct | |
Suppose 160 = 4*f - u, -2*f - 2*f + 4*u + 148 = 0. Suppose -5*y + f + 99 = 0. What is the greatest common divisor of y and 140?\n | 28\n | ibivibiv/math_instruct | |
Solve -60*s - 202 - 57 + 19 = 0 for s.\n | -4\n | ibivibiv/math_instruct | |
Let s(c) be the first derivative of 13*c**3/3 + c**2 + c - 1. Does 6 divide s(-1)?\n | True\n | ibivibiv/math_instruct | |
Let m(h) = 3*h**3 - 4*h**2 + 6*h - 3. List the prime factors of m(6).\n | 3, 179\n | ibivibiv/math_instruct | |
Let y(p) be the first derivative of 0*p**4 + 5*p + 7/5*p**5 + 0*p**3 + 0*p**2 + 5. What is the first derivative of y(c) wrt c?\n | 28*c**3\n | ibivibiv/math_instruct | |
Convert 8.19387 kilometers to centimeters.\n | 819387\n | ibivibiv/math_instruct | |
Suppose 4*a + 4 + 0 = 0. Let n(o) = -13*o**3 - o**2 + o + 1. What is the tens digit of n(a)?\n | 1\n | ibivibiv/math_instruct | |
What is 7.683037 years in centuries?\n | 0.07683037\n | ibivibiv/math_instruct | |
Solve -1083 = -11*s - 1028 for s.\n | 5\n | ibivibiv/math_instruct | |
What is next in 2962, 6217, 9472, 12727, 15982, 19237?\n | 22492\n | ibivibiv/math_instruct | |
What is the next term in -8612, -8641, -8674, -8699, -8704, -8677?\n | -8606\n | ibivibiv/math_instruct | |
What is -52 + 57 + (0 - 9)?\n | -4\n | ibivibiv/math_instruct | |
What is the fourth smallest value in 26, -5, 1/7, 0.2, -950/83, 1?\n | 0.2\n | ibivibiv/math_instruct | |
Let l be 4/((-20)/(-15)) + -2. Let i be -21 - l/2*-10. Is 13 a factor of ((-507)/(-52))/((-3)/i)?\n | True\n | ibivibiv/math_instruct | |
What is -4520736600 rounded to the nearest one million?\n | -4521000000\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 j and 1 u when two letters picked without replacement from {s: 7, u: 2, m: 1, j: 4}.\n | 8/91\n | ibivibiv/math_instruct | |
What is the biggest value in 0.4, -32, 2/9, 6?\n | 6\n | ibivibiv/math_instruct | |
Suppose 5*g - 5*i = 3*g - 15, 2*i = g + 5. Suppose 46 = -v + 4*v - u, 0 = v + g*u - 26. Suppose 72 = 4*m - 8. Calculate the smallest common multiple of m and v.\n | 80\n | ibivibiv/math_instruct | |
Expand (0*g - g**3 - g + 0*g)*(-23*g**2 - 55 + 55 + (g - 2*g + 0*g)*(-4 + 2*g + 4)).\n | 25*g**5 + 25*g**3\n | ibivibiv/math_instruct | |
In the coordinate plane, one of the vertices of a square is the point (-6, -4). If the diagonals of that square intersect at point (3, 2), what is the area of that square? | The diagonals of a square intersect at the center of the square, and they are perpendicular bisectors of each other. This means that the center of the square is the midpoint of any diagonal.
Given that one of the vertices of the square is (-6, -4) and the diagonals intersect at (3, 2), we can find the length of the di... | ibivibiv/math_instruct | |
Three letters picked without replacement from {s: 6, n: 12}. Give prob of picking 1 s and 2 n.\n | 33/68\n | ibivibiv/math_instruct | |
Suppose -10 - 100 = -5*x. Calculate the greatest common divisor of x and 253.\n | 11\n | ibivibiv/math_instruct | |
What is the third root of 452705 to the nearest integer?\n | 77\n | ibivibiv/math_instruct | |
Simplify (l**(2/51)/((l*l**(-1/15)*l)/l))/(l/(l/(l*l**(3/2)/l)))**(5/9) assuming l is positive.\n | l**(-881/510)\n | ibivibiv/math_instruct | |
Let y(d) = 5*d**3 + 1344*d**2 + 24650*d - 245. Determine y(-249).\n | 4\n | ibivibiv/math_instruct | |
Calculate prob of sequence vl when two letters picked without replacement from vlllvlvvlvvvlllvlv.\n | 9/34\n | ibivibiv/math_instruct |
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