instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Evaluate (290/60)/(((-70)/12)/7*(-42)/210).\n | 29\n | ibivibiv/math_instruct | |
Let a(k) = -5*k - 3. Let j(w) = -2*w - 1. What is -6*a(f) + 17*j(f)?\n | -4*f + 1\n | ibivibiv/math_instruct | |
Suppose t = -2*t - 3. Is -1/28 < t?\n | False\n | ibivibiv/math_instruct | |
Let v be 2/(-3*(-2)/12). Suppose -v*a = -8*a + 16. Suppose -a*n + 0 + 12 = 0. What is the units digit of n?\n | 3\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 1852244?\n | 8\n | ibivibiv/math_instruct | |
Let g(r) = -3404*r + 17023. Determine g(5).\n | 3\n | ibivibiv/math_instruct | |
Is 6 a factor of 7406?\n | False\n | ibivibiv/math_instruct | |
Suppose -1340*u + 1331*u + 693 = 0. What is the remainder when 253 is divided by u?\n | 22\n | ibivibiv/math_instruct | |
Let s(r) = -3*r - 21. Let u be s(-7). Suppose u = 3*l - 3*t + 7*t - 2, 0 = -l + 3*t + 5. Put l, -0.09, 1/11, -4 in decreasing order.\n | l, 1/11, -0.09, -4\n | ibivibiv/math_instruct | |
Let a be ((-14)/42)/(1/(-15)). Let h(w) = 2*w - 5. Calculate h(a).\n | 5\n | ibivibiv/math_instruct | |
Suppose 2*h + 3*h = -180. Let f be 4/18 + (-172)/h. Solve -f*c - 9 = -3*a, 4*a + c + 23 = -4*c for a.\n | -2\n | ibivibiv/math_instruct | |
Simplify (-2 + (sqrt(468) + (sqrt(468) - -3*sqrt(468)) + 0 - sqrt(468)) + sqrt(468) + -4 - ((2 + sqrt(468))*2 + sqrt(468)*1*-1)*-4)**2.\n | 1080*sqrt(13) + 38008\n | ibivibiv/math_instruct | |
Simplify (-2*1*sqrt(833) - (1*sqrt(833)*-1)**2)*6.\n | -4998 - 84*sqrt(17)\n | ibivibiv/math_instruct | |
Let o(q) be the first derivative of q + 2 + 2/3*q**3 - 1/2*q**2. Suppose 2*n = -3*k - k - 6, -3*k = -3*n + 9. Give o(n).\n | 2\n | ibivibiv/math_instruct | |
Evaluate -2 - ((-1 - 0) + -3) - -2.\n | 4\n | ibivibiv/math_instruct | |
Suppose -m - 2318 = -9601. Is m a composite number?\n | False\n | ibivibiv/math_instruct | |
Suppose 77 = 2*m - 5*p, 2*m = -3*p + 70 + 15. Suppose 4*y - 23 = -d, m = d + 5*y + 13. Solve -d*a = -2*a - 4 for a.\n | 4\n | ibivibiv/math_instruct | |
Four letters picked without replacement from tgttvvvvgtvtttt. What is prob of sequence ggtv?\n | 2/819\n | ibivibiv/math_instruct | |
What is 16155/(-1620) + 2/(-72)?\n | -10\n | ibivibiv/math_instruct | |
What is the second derivative of -2965845*v**2*w**3 - v + 6195*w**3 + 2*w**2 + 52*w wrt v?\n | -5931690*w**3\n | ibivibiv/math_instruct | |
What comes next: 1084, 1418, 1706, 1924, 2048, 2054?\n | 1918\n | ibivibiv/math_instruct | |
Sort 4/13, -0.549538, -0.3, -3.\n | -3, -0.549538, -0.3, 4/13\n | ibivibiv/math_instruct | |
-0.14+-1320292\n | -1320292.14\n | ibivibiv/math_instruct | |
Let y = -4.54 - -195.54. Let n = y - 190.99867. Round n to four decimal places.\n | 0.0013\n | ibivibiv/math_instruct | |
How many minutes are there in 3/10 of a day?\n | 432\n | ibivibiv/math_instruct | |
Is 4547 a prime number?\n | True\n | ibivibiv/math_instruct | |
What is the value of 15 + (45 - 55) + 0 + 3?\n | 8\n | ibivibiv/math_instruct | |
Calculate -1 + -109 + (-6392 - -6606).\n | 104\n | ibivibiv/math_instruct | |
Solve -v + 3*v - v + 0*a = -0*v - 3*a - 5, -1127*v + a = 9017 for v.\n | -8\n | ibivibiv/math_instruct | |
In base 13, what is 2b - 2901?\n | -28a3\n | ibivibiv/math_instruct | |
b"What is the yth term of 158318, 309791, 461274, 612773, 764294, 915843?\n" | y**3 - y**2 + 151469*y + 6849\n | ibivibiv/math_instruct | |
Suppose -t + 14 = -3*k, -t + 2*t = 4*k + 17. Let o = -2 - -3. Suppose f = o - 5. Is k != f?\n | True\n | ibivibiv/math_instruct | |
Let i be (-2 + 3)/(1/(-19)). Let l = 38 + i. What are the prime factors of l?\n | 19\n | ibivibiv/math_instruct | |
Let k be 3/(-9) + 1/3. Suppose 44*h = 41*h + 9. Let d = 9 + -9. Solve d = -n - h - k for n.\n | -3\n | ibivibiv/math_instruct | |
Dr. Banks had 480 toothbrushes to give away to his patients over a 6-month period. He gave away 65 toothbrushes in January. In February, the number of toothbrushes he gave away increased by 10%, and he continued to increase the number of toothbrushes given away by 10% each subsequent month. In June, he gave away the re... | Let's calculate the number of toothbrushes Dr. Banks gave away each month, starting with January and increasing by 10% each month.
January: 65 toothbrushes
For February, we increase the number by 10%:
February: 65 + (10% of 65) = 65 + 6.5 = 71.5 (since we can't give away half a toothbrush, we'll round to the nearest ... | ibivibiv/math_instruct | |
Let j(p) = p**2 - 8*p - 8. Let r be j(9). Suppose 5*d - r = -s - 20, -9 = 3*s + 3*d. Which is smaller: s or -2?\n | -2\n | ibivibiv/math_instruct | |
Let h = 89 - 87. Let y(l) = -10*l**2 + 5*l - 4 + 18*l**2 + 0*l - h*l**3. What is the least common multiple of 20 and y(4)?\n | 80\n | ibivibiv/math_instruct | |
Let d(h) = h - 6. Let m(c) = c**2 - 2. Let i be m(2). Suppose v + i*s = 6, -4*v + s = -2*s - 35. Let p be d(v). Solve -p*w = z + 1 + 6, 3*w - 3 = 3*z for z.\n | -3\n | ibivibiv/math_instruct | |
Let i(f) = -3*f**2. Let r(d) = -201*d + 125*d + 10 + 58*d. What is r(i(m))?\n | 54*m**2 + 10\n | ibivibiv/math_instruct | |
Suppose 21*k - 23*k = -196. Let c = k + -60. Is 15 a factor of c?\n | False\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-99.076 + -9.0348) % (75.9176 / 36.5186) | 2.0696 | ibivibiv/math_instruct | |
Let c(b) = -2*b**3 + 2*b**2 - 4*b + 7. Calculate c(3).\n | -41\n | ibivibiv/math_instruct | |
Is -2/5 at most as big as -89949955?\n | False\n | ibivibiv/math_instruct | |
Calculate 518 divided by -259.\n | -2\n | ibivibiv/math_instruct | |
Let v be 1*((-42)/45)/7. Which is the nearest to -1/2? (a) v (b) 2/9 (c) -3\n | a\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(66.575 + -38.323) * (2.164 * 99.847) | 6104.3788 | ibivibiv/math_instruct | |
Let p be 1*3/((-6)/56). Let c be p/154 + (-128)/22. Let h(n) = 2*n**2 + 10*n - 7. Let k be h(c). Solve 4*u = k*w - 21, -u = -w - 2 + 6 for w.\n | 5\n | ibivibiv/math_instruct | |
Solve i - j = 4*i - 9, 1 = -i + j for i.\n | 2\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {k: 2, m: 5, s: 2, v: 4}. What is prob of picking 1 s and 1 m?\n | 5/39\n | ibivibiv/math_instruct | |
Let o(k) be the second derivative of 2*k**3/3 - k**2/2 - 35*k - 2. Calculate o(2).\n | 7\n | ibivibiv/math_instruct | |
Let r(a) = -a**3 + 3*a**2 + 2*a + 5. Let d be r(4). Is 18 a factor of d - -3 - 1 - -136?\n | False\n | ibivibiv/math_instruct | |
Rearrange -2 - 3*k**2 - 3*k**2 + 2*k**3 + 0*k**2 + 4*k**2 to the form o*k**3 + n + q*k**2 + v*k and give o.\n | 2\n | ibivibiv/math_instruct | |
Three letters picked without replacement from gggkxkgxggxkg. What is prob of picking 1 k and 2 x?\n | 9/286\n | ibivibiv/math_instruct | |
Round 468859.93 to the nearest one hundred thousand.\n | 500000\n | ibivibiv/math_instruct | |
How many nanograms are there in 36848.14 milligrams?\n | 36848140000\n | ibivibiv/math_instruct | |
Let g(p) = -p**2 - 34*p - 35. Let t be g(-33). Let k be t/15*171/(-114). Let o = 2 - 2. What is the biggest value in -0.3, k, o, -5?\n | k\n | ibivibiv/math_instruct | |
Let m(j) = 1286*j - 10317. Give m(8).\n | -29\n | ibivibiv/math_instruct | |
-2 * -7840\n | 15680\n | ibivibiv/math_instruct | |
In base 9, what is -13601 + 6?\n | -13584\n | ibivibiv/math_instruct | |
Express 2 + 3*h + 3*h**3 - 2*h**3 - 3*h + 14*h**2 as r*h**3 + v*h**2 + w + f*h and give w.\n | 2\n | ibivibiv/math_instruct | |
Round -30509000 to the nearest one hundred thousand.\n | -30500000\n | ibivibiv/math_instruct | |
Simplify (((((y*y/(y/y**(-2))*y)/y*y)/y*y)/y*y)/(y*y*y**2))/(y*y*y*y**(2/7)*y*y*y**(2/11)*y*y*y) assuming y is positive.\n | y**(-960/77)\n | ibivibiv/math_instruct | |
Is 1557033361 prime?\n | False\n | ibivibiv/math_instruct | |
Let -w**4 - 2150840*w**3 + 12905076*w**2 = 0. What is w?\n | -2150846, 0, 6\n | ibivibiv/math_instruct | |
Does 14 divide 8667?\n | False\n | ibivibiv/math_instruct | |
Solve -h - 5 = f, -101*f - 70 = -4*h - 123*f for h.\n | -10\n | ibivibiv/math_instruct | |
Factor 5*i**2 - 105060*i + 551880180.\n | 5*(i - 10506)**2\n | ibivibiv/math_instruct | |
Let m(a) be the first derivative of -141 + 7/4*a**4 - 9*a**2 + 0*a**3 - a. Find the second derivative of m(d) wrt d.\n | 42*d\n | ibivibiv/math_instruct | |
Let g be 48/10 - (-1)/5. Let r = g - 3. Find the second derivative of 2*a + 7*a - 6*a + 2*a**r wrt a.\n | 4\n | ibivibiv/math_instruct | |
Rearrange (-45 - 52 + 2402*j + 100 - 3)*(-2*j + 3*j + j) to the form i*j + b*j**2 + a and give b.\n | 4804\n | ibivibiv/math_instruct | |
Let d be (-28)/(-27)*-2 + 48/24. What is the nearest to -1 in d, 1, 4?\n | d\n | ibivibiv/math_instruct | |
Simplify (d**5*d**(-4))/(d/(d/(d*d**(-4/5)))*d*d*d**(-5)*d) assuming d is positive.\n | d**(14/5)\n | ibivibiv/math_instruct | |
Simplify 2 + (1 + sqrt(363))**2 + -1 + 0.\n | 22*sqrt(3) + 365\n | ibivibiv/math_instruct | |
Calculate 974133325 + 15.\n | 974133340\n | ibivibiv/math_instruct | |
Let p(i) = i**3 - 3*i**2 + 5*i + 3. Let r(u) = -2*u**3 + 2 + 0 + 5*u**2 - 9*u - 7. Suppose -26*l = 66 + 12. Let m = -5 + 0. Give l*r(b) + m*p(b).\n | b**3 + 2*b\n | ibivibiv/math_instruct | |
What is the ten millions digit of 15817742?\n | 1\n | ibivibiv/math_instruct | |
Convert 1410ba (base 14) to base 13.\n | 1b40b1\n | ibivibiv/math_instruct | |
Let t be ((-4598)/133 - (-6)/(-14))/(-1). Suppose -2*y + 2*b = -0*y - 12, -b = -5*y + 22. Suppose -o + y*o = 0, -j - 5*o + t = 0. Is j a multiple of 10?\n | False\n | ibivibiv/math_instruct | |
What is the value of (1/(-6))/(12*17/2040)?\n | -5/3\n | ibivibiv/math_instruct | |
What is 0.6081185ug in nanograms?\n | 608.1185\n | ibivibiv/math_instruct | |
Suppose 1680 = 4*i - v + 5*v, -3*i + 3*v + 1278 = 0. Suppose -q + i = 420. Calculate the highest common divisor of 2 and q.\n | 1\n | ibivibiv/math_instruct | |
What is the value of ((-2)/7)/(-140*(-178)/3115)?\n | -1/28\n | ibivibiv/math_instruct | |
What is the value of 20/(-8)*(-6)/(12/4)?\n | 5\n | ibivibiv/math_instruct | |
Let d = -21814527.22999576 + 21814528. Let k = -1129.23 + 1130. Let u = k - d. Round u to six dps.\n | -0.000004\n | ibivibiv/math_instruct | |
Calculate 987 divided by 47.\n | 21\n | ibivibiv/math_instruct | |
Solve -145*z + 101*z + 1447 = 117*z - n, -z - 3*n + 13 = -n for z.\n | 9\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 d and 1 i when two letters picked without replacement from {i: 1, q: 7, f: 3, d: 4, w: 4}.\n | 4/171\n | ibivibiv/math_instruct | |
Let n = 27 - 23. Let t(b) = 6*b**2 - 408*b + b**3 + 2*b**3 + 0*b**3 + 400*b + 10 - n*b**3. What is t(5)?\n | -5\n | ibivibiv/math_instruct | |
What comes next: -6, 2, 10?\n | 18\n | ibivibiv/math_instruct | |
b"What is the xth term of 108640305, 108640308, 108640311, 108640314, 108640317, 108640320?\n" | 3*x + 108640302\n | ibivibiv/math_instruct | |
Does 32 divide 2886397888?\n | True\n | ibivibiv/math_instruct | |
What is the smallest value in -2, 0.5, -0.1, 1/3, -28/5207, -1/9?\n | -2\n | ibivibiv/math_instruct | |
Express 90 - 177 + 76*a**3 + 90 in the form d*a**3 + w + v*a**2 + k*a and give k.\n | 0\n | ibivibiv/math_instruct | |
What is the third smallest value in -7, -0.12, 1/2, -1, 0.7?\n | -0.12\n | ibivibiv/math_instruct | |
Let u be (3 + 0)*(3 + -2). Let f(m) = m**3 - 2*m**2 - 2*m + 3. What is f(u)?\n | 6\n | ibivibiv/math_instruct | |
Round -18967.03 to the nearest one thousand.\n | -19000\n | ibivibiv/math_instruct | |
Let u = 19 + -17. Does 2 divide u?\n | True\n | ibivibiv/math_instruct | |
Solve -536967 = 196*c - 524619 for c.\n | -63\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Sampling for ML/AI Engineers
### Central Limit Theorem
According to the Central Limit Theorem, the sampling distribution of the mean:
• is normally distributed
• has a mean equal to the population mean
• has standard dev... | The Central Limit Theorem is a fundamental concept in statistics that underpins much of the work done by machine learning and artificial intelligence engineers when they are building models based on sampled data. At its core, this theorem describes the behavior of the sampling distribution of the mean, which is crucia... | ibivibiv/math_instruct | |
Let t = 1250 - 1245. What is the nearest to -4 in t, 32, -1/4?\n | -1/4\n | ibivibiv/math_instruct |
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