instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What is (-83*(-1900)/8300)/((0 - -2)/2)?\n | 19\n | ibivibiv/math_instruct | |
Let q(a) = a**2 - 8*a - 20. Let r be q(10). Suppose 59*b - 53*b - 1572 = r. What is the tens digit of b?\n | 6\n | ibivibiv/math_instruct | |
Let v(a) = 24*a**2 - 10. Let m(s) = -9*s**2 + 3. Let j(p) = 10*m(p) + 3*v(p). Let o(b) be the second derivative of -b**3/3 + b. What is o(j(n))?\n | 36*n**2\n | ibivibiv/math_instruct | |
Suppose 4 = 5*j - 11. Suppose -5*h + 69 = 3*n, -3 - 6 = -n + j*h. List the prime factors of n.\n | 2, 3\n | ibivibiv/math_instruct | |
Let l = 1.1 - -2.5. Let v = l - 3. Let t = 4.4 + v. What is the second smallest value in -2/19, t, 0.2?\n | 0.2\n | ibivibiv/math_instruct | |
What is the second derivative of 261*v**4 + 2*v + 33?\n | 3132*v**2\n | ibivibiv/math_instruct | |
Rearrange -v**4 + 9*v**3 - 89*v - v**3 - 10*v**3 - 2*v**2 to the form q + z*v + u*v**2 + n*v**3 + p*v**4 and give u.\n | -2\n | ibivibiv/math_instruct | |
How many millilitres are there in 18/5 of a litre?\n | 3600\n | ibivibiv/math_instruct | |
Collect the terms in 2080371766266 - 2*p - 2080371766266.\n | -2*p\n | ibivibiv/math_instruct | |
What is 430 minutes after 10:10 PM?\n | 5:20 AM\n | ibivibiv/math_instruct | |
What is the square root of 2207460 to the nearest integer?\n | 1486\n | ibivibiv/math_instruct | |
Let f(i) = -i**2 + 12*i - 10. Suppose -6*n = 4*g - 2*n - 160, 0 = -4*n. Suppose -g = -4*b - b. What are the prime factors of f(b)?\n | 2, 11\n | ibivibiv/math_instruct | |
List the prime factors of 58567.\n | 58567\n | ibivibiv/math_instruct | |
Simplify ((l/(l*l**15))/l)/(l**0/l) assuming l is positive.\n | l**(-15)\n | ibivibiv/math_instruct | |
Product of -0.0536 and 0.1.\n | -0.00536\n | ibivibiv/math_instruct | |
Expand (-3 + 2*w**2 + 3)*(-3 + w + 3) + 2 - 2 - 4*w**3 + (-663*w + 193*w**2 + 663*w)*(-2*w + 0*w - w).\n | -581*w**3\n | ibivibiv/math_instruct | |
What is 6/4 + 21/6?\n | 5\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 35088 and 16.\n | 16\n | ibivibiv/math_instruct | |
Let a = -36.42 - -37. What is a rounded to one decimal place?\n | 0.6\n | ibivibiv/math_instruct | |
What is the closest to 5.9 in 7, -4, -2/7?\n | 7\n | ibivibiv/math_instruct | |
In base 4, what is 2 + 201303323?\n | 201303331\n | ibivibiv/math_instruct | |
Expand (-94*g**2 + 231*g**2 + 105*g**2)*(2*g**3 + 0*g**3 + 3*g**3).\n | 1210*g**5\n | ibivibiv/math_instruct | |
Is 123082198823 composite?\n | False\n | ibivibiv/math_instruct | |
What is the units digit of 505484?\n | 4\n | ibivibiv/math_instruct | |
Is 680 a multiple of 34?\n | True\n | ibivibiv/math_instruct | |
Solve -7*x = -21*x + 45*x + 37*x + 2448 for x.\n | -36\n | ibivibiv/math_instruct | |
b"What is the mth term of 23, 31, 39, 47?\n" | 8*m + 15\n | ibivibiv/math_instruct | |
Let k = -27 - -27. Suppose -o + 2*a - 8789372 - 3910634 = k, 5*o + 2*a = -63499994. Round o to the nearest 1000000.\n | -13000000\n | ibivibiv/math_instruct | |
Convert -b88453 (base 14) to base 8.\n | -27647471\n | ibivibiv/math_instruct | |
Simplify (p/p**16*p)/p**10*(p**(-3/5)/p)**5 assuming p is positive.\n | p**(-32)\n | ibivibiv/math_instruct | |
What is the least common multiple of 189 and 189?\n | 189\n | ibivibiv/math_instruct | |
Let o be (-8)/(5/(15/(-6))). Suppose 12 + 12 = o*j. Calculate the least common multiple of j and 1.\n | 6\n | ibivibiv/math_instruct | |
What is the thousands digit of 1341?\n | 1\n | ibivibiv/math_instruct | |
Let l = -0.03 + 5.53. Let y = 2.5 - l. Let b = 3.4 - 2.9. Which is smaller: b or y?\n | y\n | ibivibiv/math_instruct | |
Calculate 5/6*33453/(-630)*1/((-9)/12).\n | 59\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Deriving posterior from a single observation z from a normal distribution (ESL book)
I am reading the book The Elements of Statistical Learning by Hastie, Tibshirani and Friedman. On page 271 the authors derive a posterior... | To understand the derivation provided in the text snippet, it's essential first to grasp some fundamental concepts about probability distributions, Bayes' theorem, and conjugate priors. We will cover these topics step-by-step, starting with probability distributions.
### Probability Distributions
A continuous random... | ibivibiv/math_instruct | |
What is the value of 8 - 2 - (2 - (11 + -3))?\n | 12\n | ibivibiv/math_instruct | |
What is the tens digit of 1110271169?\n | 6\n | ibivibiv/math_instruct | |
In base 13, what is -5 + -1bb?\n | -1c3\n | ibivibiv/math_instruct | |
Let i(z) = -z**3 - 10*z**2 + 3*z - 14. Let b be i(-10). Let p = b - -177/4. Is p less than 1/15?\n | False\n | ibivibiv/math_instruct | |
Let y be (1266/(-8))/((-6)/(-45)). Suppose -5*d + d = 4728. Let f = d - y. Find the common denominator of f and 19/22.\n | 88\n | ibivibiv/math_instruct | |
Calculate -2 divided by -24200.\n | 1/12100\n | ibivibiv/math_instruct | |
Evaluate (-10)/(80/(-24))*((-9620)/(-30))/(-26).\n | -37\n | ibivibiv/math_instruct | |
Round -9317650 to the nearest 100000.\n | -9300000\n | ibivibiv/math_instruct | |
Calculate 81187 divided by 4273.\n | 19\n | ibivibiv/math_instruct | |
What is -5 + 0.15244127927?\n | -4.84755872073\n | ibivibiv/math_instruct | |
What is the lowest common multiple of 350 and 3059650?\n | 21417550\n | ibivibiv/math_instruct | |
Let v(g) = -5*g + 116. Give v(19).\n | 21\n | ibivibiv/math_instruct | |
What is -2*72/18*-4*(-8)/(-576)?\n | 4/9\n | ibivibiv/math_instruct | |
Let u(z) = 2*z. Let x(b) = 109*b**2. What is u(x(v))?\n | 218*v**2\n | ibivibiv/math_instruct | |
Is 951 a factor of 1210394049?\n | False\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"• The knight’s tour problem is the mathematical problem of finding a knight’s tour, and probably making knight the most interesting piece on the chess board. The knight visits every square exactly once, if the knight ends on ... | The Knight's Tour Problem is a classic example of a mathematical problem in graph theory, which involves finding a sequence of moves for a knight piece on a chessboard that allows it to visit every square exactly once. This problem has fascinated mathematicians and computer scientists for centuries due to its complexi... | ibivibiv/math_instruct | |
Let n = 48 - 24. Let t(l) = l**3 + 11*l**2 + 20*l + 15. Calculate the remainder when t(-8) is divided by n.\n | 23\n | ibivibiv/math_instruct | |
What is 1896089843 plus -576.362?\n | 1896089266.638\n | ibivibiv/math_instruct | |
Is 2014433 prime?\n | False\n | ibivibiv/math_instruct | |
Let w = -7051870.99951 + 7051929. Let f = -0.017 - 57.983. Let j = w + f. Round j to 4 decimal places.\n | 0.0005\n | ibivibiv/math_instruct | |
What is -61030 rounded to the nearest ten thousand?\n | -60000\n | ibivibiv/math_instruct | |
Round 3335.0885 to 0 decimal places.\n | 3335\n | ibivibiv/math_instruct | |
Convert 8198.199ms to days.\n | 0.0000948865625\n | ibivibiv/math_instruct | |
Simplify (t**(-2)*t)**(-7/4)/(t*t**(-3/10)*t*t**16) assuming t is positive.\n | t**(-319/20)\n | ibivibiv/math_instruct | |
What are the prime factors of 2185065?\n | 3, 5, 59, 823\n | ibivibiv/math_instruct | |
Let v = 218 - 216. Suppose 4*b + v*k - 4468 = 0, -b + 48 + 1069 = -4*k. Is b composite?\n | False\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 16927881?\n | 2\n | ibivibiv/math_instruct | |
Suppose -4*p + 11423 = -3*n + 1477, -p + 3*n + 2482 = 0. List the prime factors of p.\n | 2, 311\n | ibivibiv/math_instruct | |
Simplify a**(-2/11)/(a*a*a**(-8)*a)*(a**(-1))**(-5/2) assuming a is positive.\n | a**(161/22)\n | ibivibiv/math_instruct | |
Simplify ((m*m**5)/(m**2/m))/(m*(m*m**2)/m*m)**(23/3) assuming m is positive.\n | m**(-77/3)\n | ibivibiv/math_instruct | |
Which is the fourth biggest value? (a) -1/7 (b) 10/9 (c) 3 (d) -2/13\n | d\n | ibivibiv/math_instruct | |
Product of -5 and -199888.\n | 999440\n | ibivibiv/math_instruct | |
Solve 14*f - 19*f = 15 for f.\n | -3\n | ibivibiv/math_instruct | |
b"What is the yth term of 517, 2010, 4495, 7978, 12465, 17962, 24475, 32010?\n" | y**3 + 490*y**2 + 16*y + 10\n | ibivibiv/math_instruct | |
Is ((-48)/72)/((-4)/5718) a prime number?\n | True\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 43430 and 215.\n | 43430\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 g and 1 x when two letters picked without replacement from {x: 5, g: 3, n: 3, d: 1}.\n | 5/22\n | ibivibiv/math_instruct | |
Let o(b) = 4 + 1 - b**3 - 2 - 4*b**2 + 1. Does 2 divide o(-4)?\n | True\n | ibivibiv/math_instruct | |
Let m(i) = 2*i + 1. What is m(12)?\n | 25\n | ibivibiv/math_instruct | |
Expand (-2*m + 5*m - 2*m)*(-3857*m**2 - 494*m**3 + 498*m**3 + 4*m + 4174*m**2).\n | 4*m**4 + 317*m**3 + 4*m**2\n | ibivibiv/math_instruct | |
In base 15, what is -189 + -68a8?\n | -6a42\n | ibivibiv/math_instruct | |
Let f(m) be the second derivative of 2*m + 0*m**2 + 0 + 1/2*m**4 + 0*m**3. Let w(r) = 0*r**2 + r**2 + 0*r**2. Calculate f(w(q)).\n | 6*q**4\n | ibivibiv/math_instruct | |
Divide -1 by 4284.\n | -1/4284\n | ibivibiv/math_instruct | |
What is 141673134 to the power of 1/2, to the nearest integer?\n | 11903\n | ibivibiv/math_instruct | |
Calculate (6/8)/((-48)/128).\n | -2\n | ibivibiv/math_instruct | |
Suppose -463*f + 1420946 = 301669 - 560024. What is the thousands digit of f?\n | 3\n | ibivibiv/math_instruct | |
Let b = 39 + -34. Suppose 0 = 2*n - 1 - 7. Solve -n*k - b = 11 for k.\n | -4\n | ibivibiv/math_instruct | |
Let z = 15.6 + -16.6. What is the smallest value in z, 0.1, 8, 1?\n | z\n | ibivibiv/math_instruct | |
What is the eighth root of 68787 to the nearest integer?\n | 4\n | ibivibiv/math_instruct | |
Which is the closest to 0.1? (a) 1 (b) -1.9 (c) 0.2 (d) -4\n | c\n | ibivibiv/math_instruct | |
Let d = -90873411.21999882 + 90873410. Let u = 1.22 + d. Round u to 7 decimal places.\n | 0.0000012\n | ibivibiv/math_instruct | |
What is the value of 491 + -629 + 33 + (4 - 1)?\n | -102\n | ibivibiv/math_instruct | |
Find the second derivative of -88751825*q**2*v - 5*q*v - 1325234*v wrt q.\n | -177503650*v\n | ibivibiv/math_instruct | |
Suppose -y + 0 = 7. Let h(a) = -19*a**3 + 10*a**2 + 2*a + 7. Let x be h(y). Round x to the nearest one thousand.\n | 7000\n | ibivibiv/math_instruct | |
Suppose 15 = -r - 4*r. Let b be (-77)/(-21) + 2/r. Solve 4*x + f + 0*f = 16, 0 = 4*x - b*f for x.\n | 3\n | ibivibiv/math_instruct | |
Does 909 divide 461598924?\n | False\n | ibivibiv/math_instruct | |
Simplify (h**(15/2)*h*h**(-7)/h)/(h*h**(-42)*h/h**(-2/19)) assuming h is positive.\n | h**(1535/38)\n | ibivibiv/math_instruct | |
In base 4, what is 1302012010323 - -1?\n | 1302012010330\n | ibivibiv/math_instruct | |
Expand (-6*a**4 + 2*a**4 + 2*a**4)*(5*a - 5 + 5) + (-7*a**3 - 20*a + 20*a)*(-2*a**2 + 4*a**2 - a**2).\n | -17*a**5\n | ibivibiv/math_instruct | |
Solve 0 = -59*i + 246*i - 374 for i.\n | 2\n | ibivibiv/math_instruct | |
Is 672703 a prime number?\n | True\n | ibivibiv/math_instruct | |
What are the prime factors of 30705717?\n | 3, 7, 31, 101, 467\n | ibivibiv/math_instruct | |
Let m be (804/24)/(1/6). Suppose 41 - m = -5*g. Calculate the common denominator of -7/12 and 354/g*(-3)/9.\n | 48\n | ibivibiv/math_instruct | |
775*-0.3\n | -232.5\n | ibivibiv/math_instruct |
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