instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What is 1.6913724 months in years?\n | 0.1409477\n | ibivibiv/math_instruct | |
b"What is the wth term of 729, 733, 737, 741?\n" | 4*w + 725\n | ibivibiv/math_instruct | |
List the prime factors of 67191576.\n | 2, 3, 47, 59567\n | ibivibiv/math_instruct | |
Suppose 3*k = -x - 18, 0*k + 3*k = 0. Let v be -1*(-3)/(-15) - x/140. Which is the biggest value? (a) -2/3 (b) 0.3 (c) v\n | b\n | ibivibiv/math_instruct | |
Suppose -4*z - 25 = -2*s - z, -s + 15 = -2*z. Suppose s*j - 4*l - 5117 = 0, 5*l + 3081 = 3*j + 8*l. What is the tens digit of j?\n | 2\n | ibivibiv/math_instruct | |
Simplify (-3*-1*sqrt(77)*-1)/(1*sqrt(539)*1).\n | -3*sqrt(7)/7\n | ibivibiv/math_instruct | |
Suppose 0 = -11*s + 34134 + 10064. What are the prime factors of s?\n | 2, 7, 41\n | ibivibiv/math_instruct | |
Let i(m) = -33*m**3 + 11*m**2 + 12*m + 3. Let k be i(-1). What is the greatest common factor of k and 445?\n | 5\n | ibivibiv/math_instruct | |
Is 4789 a multiple of 24?\n | False\n | ibivibiv/math_instruct | |
Let g(j) = -j**3 + j**2 + 2*j + 6. Let h(t) = t**3 - 19*t**2 + 21*t - 24. Calculate the lowest common multiple of h(18) and g(0).\n | 30\n | ibivibiv/math_instruct | |
Solve -1597 = -146*p - 137 for p.\n | 10\n | ibivibiv/math_instruct | |
What is prob of sequence ee when two letters picked without replacement from {e: 3}?\n | 1\n | ibivibiv/math_instruct | |
Simplify (-3*(2*sqrt(432) + -4 + -2 - (sqrt(432)*-1 + -3)*1))**2.\n | -1944*sqrt(3) + 35073\n | ibivibiv/math_instruct | |
Let f(l) be the third derivative of 0*l - 1/60*l**5 - 1/3*l**3 + 0 - 3*l**2 + 1/24*l**4. Let c(x) = -3*x**2 + 2*x - 5. Let b(p) = 2*c(p) - 5*f(p). Factor b(w).\n | -w*(w + 1)\n | ibivibiv/math_instruct | |
List the prime factors of 539.\n | 7, 11\n | ibivibiv/math_instruct | |
What is the thousands digit of 627877?\n | 7\n | ibivibiv/math_instruct | |
Let j = -12263 + 27570. List the prime factors of j.\n | 15307\n | ibivibiv/math_instruct | |
Let i(a) = -a. Let g(b) = -4*b - 12. Let p(c) = -8*c - 26. Let x(v) = -13*g(v) + 6*p(v). Determine -28*i(d) - 6*x(d).\n | 4*d\n | ibivibiv/math_instruct | |
Let y = 99.00175 - 70.00154. Let j = y + -29. Round j to four decimal places.\n | 0.0002\n | ibivibiv/math_instruct | |
Let h = 9615 + -9586. Solve 5*u = -4*x - h, -2*x - 3*u - 6 = 9 for x.\n | -6\n | ibivibiv/math_instruct | |
Sort 1, -2555/2, 2/15, -0.1, 4 in descending order.\n | 4, 1, 2/15, -0.1, -2555/2\n | ibivibiv/math_instruct | |
Let m = 5 + -4.9999928. Round m to 6 decimal places.\n | 0.000007\n | ibivibiv/math_instruct | |
Let s be -1*(0 - -2 - 4). Let o(j) = 10*j + 2*j - 3*j - j**2 + s. Let f be o(9). Solve 0 = -3*n - 2*t + 9, 3*n - 2*t = -f*n + 15 for n.\n | 3\n | ibivibiv/math_instruct | |
Simplify q**(-2/3)/(q/(q/(((q**27/q)/q)/q))) assuming q is positive.\n | q**(-74/3)\n | ibivibiv/math_instruct | |
Let z = -2013 + 2038. Solve -r = 3*m - 8, -11 - z = -4*m + 5*r for m.\n | 4\n | ibivibiv/math_instruct | |
Is 15940051 prime?\n | False\n | ibivibiv/math_instruct | |
What is the value of -2 - (7 + -3) - (-1 + -11)?\n | 6\n | ibivibiv/math_instruct | |
Let q = -0.003 - 0.297. Let s = 16.9 + -18. Let u = s + 1.1. Which is the nearest to -1? (a) q (b) 3 (c) u\n | a\n | ibivibiv/math_instruct | |
Let a be (-4)/10 + (348/20 - 5). Suppose a*b - 6 = 9*b. Let q(z) = -3 - z**b - 12*z**2 + 12*z**2 - 7*z. What is q(-4)?\n | 9\n | ibivibiv/math_instruct | |
Suppose 0 = -4*u + 8*u - 32. Suppose 16 = -4*t + 4*z, 22 = -3*t + 5*z + u. Is ((-26)/(-2))/(t/(-669) + 0) a prime number?\n | False\n | ibivibiv/math_instruct | |
Let r = 84 + -36. Let u = r - 381/8. Sort -2/13, u, 5.\n | -2/13, u, 5\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Analysis of algorithms, 'big O' question
The main question is, how exactly is the big O analysis calculated on routines? Is there a specific formula that relates what each function in a program does to a big O calculation?... | The analysis of algorithms through Big O notation is a fundamental aspect of computer science that helps us understand the efficiency and performance of different algorithmic solutions. However, contrary to what you might hope, there isn't a specific formula to calculate Big O directly from a given function or routine... | ibivibiv/math_instruct | |
What is the hundred thousands digit of 727983?\n | 7\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 3 and 7671?\n | 7671\n | ibivibiv/math_instruct | |
Let o = 56.8 + -57. Which is the closest to -3? (a) 2 (b) o (c) 4/3\n | b\n | ibivibiv/math_instruct | |
Sort 33, -15, 0.1 in descending order.\n | 33, 0.1, -15\n | ibivibiv/math_instruct | |
Solve -m - 4 = -5, 4*h - 60 = 4*m for h.\n | 16\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Floor function of powers of $2$
Is there any way to know the exact value of
$$\left(\left\lfloor 2^{\frac{n}{2}} \right\rfloor\right)^2$$
for $n$ an integer $n>0$?
When $n$ is even, the solution is trivial, since we do ... | The floor function, denoted by ⌊x⌋, returns the largest integer less than or equal to x. When dealing with powers of 2 raised to a half integer n/2, where n > 0, finding the exact value of (⌊2^(n/2)⌋)^2 can be approached differently depending on whether n is even or odd. We will explore this concept in detail and prov... | ibivibiv/math_instruct | |
Suppose -4*i + 96 = 24. Suppose -d + s + 2*s = -8, -4*s - 4 = 0. Let h be (13/1 + d)*(-7 - -9). What is the highest common factor of i and h?\n | 18\n | ibivibiv/math_instruct | |
What is the first derivative of -2*w**4 - 7054*w - 94574 wrt w?\n | -8*w**3 - 7054\n | ibivibiv/math_instruct | |
Let y = 26 + -4. Suppose 6*z - 10*z = -80. Let a = z - 14. Calculate the remainder when y is divided by a.\n | 4\n | ibivibiv/math_instruct | |
What is the nearest to 37 in 476, 3/7, 0.5, -7.2, 0, 5?\n | 5\n | ibivibiv/math_instruct | |
Let r be (-3540)/2124 - 5*(-2)/(-4). Which is the nearest to 0? (a) -0.2 (b) r (c) 3 (d) 1\n | a\n | ibivibiv/math_instruct | |
What is prob of picking 1 s, 1 d, 1 m, and 1 e when four letters picked without replacement from {m: 4, u: 5, e: 1, d: 4, y: 1, s: 3}?\n | 4/255\n | ibivibiv/math_instruct | |
2 divided by -270438\n | -1/135219\n | ibivibiv/math_instruct | |
What is 618 minutes before 11:00 PM?\n | 12:42 PM\n | ibivibiv/math_instruct | |
What is ((-9)/(-15))/(165/(-1650))?\n | -6\n | ibivibiv/math_instruct | |
What is the third derivative of 223038806*h**2*t**4 + 3*h**2*t - 633*h*t**2 - 71054*t**2 wrt t?\n | 5352931344*h**2*t\n | ibivibiv/math_instruct | |
Round -0.0000075945394 to seven dps.\n | -0.0000076\n | ibivibiv/math_instruct | |
Let f = 18 + -16. Suppose -v = 7 - f. Let s(p) = -p**3 - 2*p**2 + 12*p. What is the units digit of s(v)?\n | 5\n | ibivibiv/math_instruct | |
Is -9296/13 > -714?\n | False\n | ibivibiv/math_instruct | |
Solve -3*x + 52*d - 53*d + 4 = 0, 14*x + 8*d = 3*d + 22 for x.\n | -2\n | ibivibiv/math_instruct | |
Let i = -24.09 - -24.09. Which is the third smallest value? (a) -2445 (b) i (c) 0.5\n | c\n | ibivibiv/math_instruct | |
What is the least common multiple of 916 and 26370?\n | 12077460\n | ibivibiv/math_instruct | |
Solve 70 = 1183*z - 1169*z for z.\n | 5\n | ibivibiv/math_instruct | |
Is 2039905 a multiple of 63?\n | False\n | ibivibiv/math_instruct | |
Let b(j) = -15*j**2 - 9*j + 6. Let c(y) = 10*y**2 + 6*y - 4. Suppose -2*p + 6 = -8. Let x(v) = p*c(v) + 5*b(v). Let x(h) = 0. What is h?\n | -1, 2/5\n | ibivibiv/math_instruct | |
What is the value of $(-27)^{5/3}$ when evaluated? | Since $\left((-27)^{\frac{1}{3}}\right)^5=(-27)^{\frac{5}{3}}$, we have \[\left((-27)^{\frac{1}{3}}\right)^5 = (-3)^5 = \boxed{-243}.\]
The answer is: -243 | ibivibiv/math_instruct | |
Is 14 a factor of 1736?\n | True\n | ibivibiv/math_instruct | |
What is 2134 to the power of 1/4, to the nearest integer?\n | 7\n | ibivibiv/math_instruct | |
Rearrange (-1 + 0*s + s + 2*s)*(-s + 1 - 4 + 0) to the form r + j*s + z*s**2 and give r.\n | 3\n | ibivibiv/math_instruct | |
Let y(c) be the second derivative of 0*c**3 + 0*c**2 + 4/3*c**4 + 0 - 7/20*c**5 + 7*c. What is the third derivative of y(p) wrt p?\n | -42\n | ibivibiv/math_instruct | |
Sort 4, -9, -2, -29, -1.\n | -29, -9, -2, -1, 4\n | ibivibiv/math_instruct | |
Solve -5*v - 2 = -4*q, -3*q = -2*v + 6 - 4 for q.\n | -2\n | ibivibiv/math_instruct | |
Let n(b) = -b - 10*b + 1 + 0*b. Let q = 1 - 2. Calculate the remainder when 22 is divided by n(q).\n | 10\n | ibivibiv/math_instruct | |
Simplify z**(1/2)*z**(-3)/z*z**(-4)*z/(z*z**(2/7))*(z/z**0)**(-2/29)/(z**(-1)*z/(z*z**(-3))) assuming z is positive.\n | z**(-4001/406)\n | ibivibiv/math_instruct | |
Sort 83, 10, -18 in decreasing order.\n | 83, 10, -18\n | ibivibiv/math_instruct | |
Suppose 121*q = 113*q + 4616. List the prime factors of q.\n | 577\n | ibivibiv/math_instruct | |
Evaluate -1 - -13 - (-415 + 413).\n | 14\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 97437079 and 15653.\n | 1423\n | ibivibiv/math_instruct | |
Simplify (-5 + -3*sqrt(931)*2)**2 + -5*(sqrt(931) + 3 + (sqrt(931)*2 - sqrt(931)))**2.\n | 14876\n | ibivibiv/math_instruct | |
Use each of the five digits $2, 4, X, 7$ and $9$ only once to form a three-digit integer and a two-digit integer which will be multiplied together. What is the three-digit integer that results in the greatest product?
If we know the answer to the above question is 762, what is the value of unknown variable X? | We want to find the value of $X$ in the given situation.
We are given the digits $2, 4, X, 7$ and $9$ and we need to form a three-digit integer and a two-digit integer using these digits.
To maximize the product of the two numbers, we want the largest possible digit in the hundreds place of the three-digit number.
Sinc... | ibivibiv/math_instruct | |
Simplify ((n*n**18/n*n)/n**(1/6))/((n/(n/n**(-7/5)))/n**(-2/3)) assuming n is positive.\n | n**(587/30)\n | ibivibiv/math_instruct | |
What is seventy-five halves of a tonne in kilograms?\n | 37500\n | ibivibiv/math_instruct | |
Calculate (1/(-2))/(174/(-336) - 2/(-14)).\n | 4/3\n | ibivibiv/math_instruct | |
Calculate the remainder when 45 is divided by 13.\n | 6\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {o: 3, m: 3, u: 1, a: 4}. Give prob of sequence um.\n | 3/110\n | ibivibiv/math_instruct | |
What is the biggest value in 4, 2, -2, -3, -0.1008, 0?\n | 4\n | ibivibiv/math_instruct | |
Which is the nearest to 1? (a) 0.1 (b) 4/13 (c) 1 (d) -724385\n | c\n | ibivibiv/math_instruct | |
What is the cube root of 40674 to the nearest integer?\n | 34\n | ibivibiv/math_instruct | |
Calculate 4/((5/5)/1*-1).\n | -4\n | ibivibiv/math_instruct | |
Solve 3*a = -3354*q + 3350*q + 32 + 168, -8*a = -4*q - 460 for q.\n | 5\n | ibivibiv/math_instruct | |
Which is the third smallest value? (a) 177 (b) -5 (c) -3/7 (d) 5\n | d\n | ibivibiv/math_instruct | |
Let a(w) = -2*w**2 - 16*w - 25. Let c(d) = d**2 + 8*d + 13. Let f(k) = -4*a(k) - 7*c(k). Calculate f(-6).\n | -3\n | ibivibiv/math_instruct | |
What is the third smallest value in -5, -4, -1, 1, -2/63?\n | -1\n | ibivibiv/math_instruct | |
What is 7655 (base 16) in base 6?\n | 352125\n | ibivibiv/math_instruct | |
Let r(y) = -6*y**3 + 2*y. Let x(u) = -u**2 - 22*u + 50. Let c be x(-24). Let p be c/3 - (-70)/(-15). Let v(m) = -5*m**3 + 2*m. Determine p*r(q) + 5*v(q).\n | -q**3 + 2*q\n | ibivibiv/math_instruct | |
Let r = 4 + 8. Let a = 13 + r. Let d = -25.0157 + a. What is d rounded to three dps?\n | -0.016\n | ibivibiv/math_instruct | |
Evaluate (18 - (-19 - (-35 + -1))) + -4.\n | -3\n | ibivibiv/math_instruct | |
Which is the second biggest value? (a) 35 (b) 35987 (c) -0.3\n | a\n | ibivibiv/math_instruct | |
In base 3, what is 1111102010 - -221?\n | 1111110001\n | ibivibiv/math_instruct | |
Suppose -d + 11 - 4 = 0. Let l(s) = 10 - s - 2*s + 2*s. What is the units digit of l(d)?\n | 3\n | ibivibiv/math_instruct | |
Let h(v) = v**2 - 20*v + 16. Calculate h(11).\n | -83\n | ibivibiv/math_instruct | |
Expand (5 - 2 - 1 + (1 - 3 + 3)*(0 - 2 + 1) + (-2 - 1 + 0)*(0 + 2 - 3))*(2*u - u + 2*u).\n | 12*u\n | ibivibiv/math_instruct | |
Which is the closest to -6? (a) 0.1 (b) 9 (c) -0.5\n | c\n | ibivibiv/math_instruct | |
Simplify (((sqrt(325) - (sqrt(325) + 1)) + sqrt(325))**2 + -3)*-5.\n | -1615 + 50*sqrt(13)\n | ibivibiv/math_instruct | |
Calculate 2/(36/(-16)*242/1089).\n | -4\n | ibivibiv/math_instruct | |
Does 9 divide 1253?\n | False\n | ibivibiv/math_instruct | |
What is 63250087 to the power of 1/7, to the nearest integer?\n | 13\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {y: 3, p: 2, s: 2, n: 6, g: 2}. What is prob of picking 2 s and 2 p?\n | 1/1365\n | ibivibiv/math_instruct |
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