instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Does 8 divide 488?\n | True\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"1. Some calculus word problems
1The number of bus riders from the suburbs to downtown per day is represented by 1200(1.50-x), where x is the fare in dollars. What fare will maximize the total revenue?
#2 A large social part... | Calculus is a branch of mathematics that deals with rates of change and accumulation of quantities. It has numerous applications in various fields including physics, engineering, economics, and business. This piece aims to explore three calculus problems that are commonly encountered in college-level courses. We will ... | ibivibiv/math_instruct | |
Calculate the greatest common factor of 134007 and 38.\n | 19\n | ibivibiv/math_instruct | |
Suppose 3*i - 5*z = 26, -5*i + 0 + 6 = z. What is the units digit of (-4 + i)*(-3 + -106)?\n | 8\n | ibivibiv/math_instruct | |
Let i = 14 - 9. Suppose -29 = -w - w + v, 0 = -4*w + 3*v + 59. Suppose y + 2*h = -6 - 0, h + w = i*y. Sort 0, y, 1 in increasing order.\n | 0, 1, y\n | ibivibiv/math_instruct | |
-16306285.1 - 0.17\n | -16306285.27\n | ibivibiv/math_instruct | |
Let j(t) = 2*t - 51. Let q(h) = -8411*h. Determine j(q(n)).\n | -16822*n - 51\n | ibivibiv/math_instruct | |
Suppose 3*q = -2*q + 5*l - 425, -5*l = 5*q + 475. Is q*(-6 - (-80)/15) even?\n | True\n | ibivibiv/math_instruct | |
What is the common denominator of -93/1270 and -55/1016?\n | 5080\n | ibivibiv/math_instruct | |
Let h = 19 + -69. What is the common denominator of 1/(-2) - 74/h and -107/20?\n | 100\n | ibivibiv/math_instruct | |
Is 93728 a multiple of 26?\n | False\n | ibivibiv/math_instruct | |
What are the prime factors of 423803?\n | 423803\n | ibivibiv/math_instruct | |
Simplify 0 + (sqrt(88)*1)/sqrt(8).\n | sqrt(11)\n | ibivibiv/math_instruct | |
Let y = -10 + 14. Let m(b) = -3*b**3 - 3*b**2 - 4*b. Let o be m(y). Let l = o - -110. Round l to the nearest 10.\n | -150\n | ibivibiv/math_instruct | |
What is j in j**5/6 - 17*j**4/6 + 31*j**3/2 - 175*j**2/6 + 49*j/3 = 0?\n | 0, 1, 2, 7\n | ibivibiv/math_instruct | |
Let d(a) = 2119*a**2 + 3*a + 17. Let z be d(6). Let o = z - 699319. Round o to the nearest 100000.\n | -600000\n | ibivibiv/math_instruct | |
Collect the terms in 241964 - 39*o**3 - 241964.\n | -39*o**3\n | ibivibiv/math_instruct | |
What is 6772206059 to the power of 1/2, to the nearest integer?\n | 82293\n | ibivibiv/math_instruct | |
Is 7 a factor of 27951?\n | True\n | ibivibiv/math_instruct | |
Put 368, 68, -2, 5 in decreasing order.\n | 368, 68, 5, -2\n | ibivibiv/math_instruct | |
Solve 30*l + 207 = 237 for l.\n | 1\n | ibivibiv/math_instruct | |
Suppose -26*b + 19*b + 14 = 0. Let r(m) = -4 + 1092*m - 1092*m + m**2 + 10*m**b. What are the prime factors of r(2)?\n | 2, 5\n | ibivibiv/math_instruct | |
What is the third root of 3253708704 to the nearest integer?\n | 1482\n | ibivibiv/math_instruct | |
Let n(q) = 8*q + 16. Let d be n(11). Let s = d + -72. Let c = 18 - 7. What is the remainder when s is divided by c?\n | 10\n | ibivibiv/math_instruct | |
Rearrange -i - 3*i**2 + 35*i**4 - 2*i - 37*i**4 to b*i + u + n*i**2 + c*i**3 + s*i**4 and give n.\n | -3\n | ibivibiv/math_instruct | |
Is 45525913 prime?\n | True\n | ibivibiv/math_instruct | |
What are the prime factors of 2246152546?\n | 2, 11, 102097843\n | ibivibiv/math_instruct | |
Calculate prob of sequence fexf when four letters picked without replacement from {d: 1, e: 1, b: 2, x: 1, a: 1, f: 2}.\n | 1/840\n | ibivibiv/math_instruct | |
What is the ten millions digit of 23822920?\n | 2\n | ibivibiv/math_instruct | |
Is 2894813 composite?\n | False\n | ibivibiv/math_instruct | |
b"What is the rth term of -426, -2993, -7276, -13281, -21014, -30481, -41688, -54641?\n" | -r**3 - 852*r**2 - 4*r + 431\n | ibivibiv/math_instruct | |
Factor -15*w**4 + 13370*w**3 + 8920*w**2.\n | -5*w**2*(w - 892)*(3*w + 2)\n | ibivibiv/math_instruct | |
Let o(t) = -t**2 + 3*t + 20. Let x be o(6). Solve -2393*z**3 + 2399*z**3 - 6*z - 3*z**4 + 2*z**2 + z**x = 0.\n | -1, 0, 1, 2\n | ibivibiv/math_instruct | |
Solve -354 - 231 = -59*x + 123 for x.\n | 12\n | ibivibiv/math_instruct | |
Let a = 37 - 27. Suppose 11*x - 5 = a*x. Put x, -0.4, -0.1 in decreasing order.\n | x, -0.1, -0.4\n | ibivibiv/math_instruct | |
What is the hundreds digit of 12161?\n | 1\n | ibivibiv/math_instruct | |
Find the first derivative of -282*f*u**3 + 17*f*u**2 + u**3 - 40*u**2 - 2*u wrt f.\n | -282*u**3 + 17*u**2\n | ibivibiv/math_instruct | |
What is the third derivative of 4*q**2*u*w**3 - 2*q**2*u*w**2 - 2*q**2*w**4 - 2*q*w**2 - 2*u*w**3 - 9*u - 2*w wrt w?\n | 24*q**2*u - 48*q**2*w - 12*u\n | ibivibiv/math_instruct | |
What is 17696 to the power of 1/2, to the nearest integer?\n | 133\n | ibivibiv/math_instruct | |
Simplify -4 + 5*(3 + sqrt(1872) - sqrt(1872)).\n | 11\n | ibivibiv/math_instruct | |
Simplify 3 + (sqrt(891) + -1 - sqrt(891))**2*-5.\n | -2\n | ibivibiv/math_instruct | |
Let f(z) = 1 - z**2 - 20*z + 0*z**2 + 22*z - 3*z**3. Let k be f(5). Let h = 576 + k. Is h composite?\n | True\n | ibivibiv/math_instruct | |
Put 0.02, 63/2, 0.1, -0.2, -5 in ascending order.\n | -5, -0.2, 0.02, 0.1, 63/2\n | ibivibiv/math_instruct | |
Expand -772*g**4 + 772*g**4 - 44*g**5 + (g**3 - g**3 + 2*g**3)*(5 - 2*g**2 - 5) + g**2 - g**2 - g**5.\n | -49*g**5\n | ibivibiv/math_instruct | |
What is the nearest to 1 in 0, -112, 3, 5.89, 4?\n | 0\n | ibivibiv/math_instruct | |
Calculate prob of sequence sr when two letters picked without replacement from {x: 1, s: 1, r: 1}.\n | 1/6\n | ibivibiv/math_instruct | |
Divide -14366 by 5867.\n | -14366/5867\n | ibivibiv/math_instruct | |
Which is the closest to -1? (a) -68 (b) 165 (c) 2 (d) -2.8\n | d\n | ibivibiv/math_instruct | |
Round -7.9069845 to the nearest integer.\n | -8\n | ibivibiv/math_instruct | |
What is -1 (base 8) in base 3?\n | -1\n | ibivibiv/math_instruct | |
Let b(q) = 5*q + 1. Let u(n) = 2*n**2 - 45*n - 9. Let g(s) = -9*b(s) - u(s). Let i(r) = -2*r**2 - 39*r. Determine g(i(o)).\n | -8*o**4 - 312*o**3 - 3042*o**2\n | ibivibiv/math_instruct | |
Find p such that -2/3*p**2 + 24*p + 74/3 = 0.\n | -1, 37\n | ibivibiv/math_instruct | |
-2 * -1.7\n | 3.4\n | ibivibiv/math_instruct | |
Expand (2*r - r - 2*r)*(-5*r - 6*r + 2*r) + 2*r**2 - r**2 + r**2 + (-2 + 3 + 0)*(-2*r**2 + 1 - 1).\n | 9*r**2\n | ibivibiv/math_instruct | |
(-79 - 19) + 85 + (-44 - 4)\n | -61\n | ibivibiv/math_instruct | |
Find the common denominator of -4/15 and 52/75.\n | 75\n | ibivibiv/math_instruct | |
Find the second derivative of 0*j + 2*j**3 + j - 9*j**3 wrt j.\n | -42*j\n | ibivibiv/math_instruct | |
What is 341 minutes after 9:06 PM?\n | 2:47 AM\n | ibivibiv/math_instruct | |
Let i(d) = -d**3 + 9*d**2 - 2*d - 5. Let r be i(9). Let u = r - -42. Solve 3 = -4*x + u for x.\n | 4\n | ibivibiv/math_instruct | |
Rearrange (t + t - 3*t)*(t**2 - 16*t**2 - t**2) - 4*t**3 + 19*t**3 + 24*t**2 - 23*t**2 + 2*t**3 - t**3 - 2*t**3 to x + b*t**3 + f*t**2 + a*t and give b.\n | 30\n | ibivibiv/math_instruct | |
Solve -10*n + 126 = -28*n for n.\n | -7\n | ibivibiv/math_instruct | |
8.01 - 0.01\n | 8\n | ibivibiv/math_instruct | |
b"What is the dth term of 124, 157, 220, 319, 460, 649, 892, 1195?\n" | d**3 + 9*d**2 - d + 115\n | ibivibiv/math_instruct | |
Let y(u) = 1822*u - 257*u**2 - 1822*u. Let f(v) = 6*v. What is y(f(j))?\n | -9252*j**2\n | ibivibiv/math_instruct | |
Which is the closest to -12? (a) 6 (b) -22 (c) 1/8\n | b\n | ibivibiv/math_instruct | |
Put 7, 3, 185, -1 in descending order.\n | 185, 7, 3, -1\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {t: 4, u: 4, e: 8, z: 1, h: 2}. Give prob of picking 1 u, 1 t, and 1 h.\n | 32/969\n | ibivibiv/math_instruct | |
Suppose -6*n = -0*n - 18. What is the remainder when n is divided by 1?\n | 0\n | ibivibiv/math_instruct | |
Let f(s) = 60*s. Suppose 10*i = 11*i - 6. Suppose -2*d + 3*c - 11 = 0, -4*d + 5*c + 0 = 17. Let b(t) = 7*t - 10*t - d*t + i*t. Give b(f(m)).\n | 60*m\n | ibivibiv/math_instruct | |
Simplify (sqrt(77)*-2)/sqrt(7) + sqrt(88)/sqrt(128).\n | -7*sqrt(11)/4\n | ibivibiv/math_instruct | |
List the prime factors of 882.\n | 2, 3, 7\n | ibivibiv/math_instruct | |
Solve -4*i - 2*s - 20 = 0, 5*s = i - 0*s - 17 for i.\n | -3\n | ibivibiv/math_instruct | |
Let f(t) = 5*t - t**3 - 2*t**2 + 0 - 18*t - 11*t**2 - 13. Let n be f(-12). Let k be (1/(-1))/(-2 - -1). Is k smaller than n?\n | False\n | ibivibiv/math_instruct | |
Let i be ((-12)/9)/(4/(-6)). Let b be 0*((-5)/(-30) + (-3)/(-9)). Solve 3*v = -4*j + 14, -2*j + b*j = -i*v for j.\n | 2\n | ibivibiv/math_instruct | |
Is 2022217969 composite?\n | False\n | ibivibiv/math_instruct | |
Let t(w) be the third derivative of 0*w**3 - 1/12*w**4 + 0*w + 0 + 2*w**2. Let a(v) = v**2 + 2*v**2 - 5*v**2 + v**2. Determine a(t(l)).\n | -4*l**2\n | ibivibiv/math_instruct | |
Solve -9*i - 4 = -8*i - 3*q, -12 = -4*q for i.\n | 5\n | ibivibiv/math_instruct | |
Let t(o) = 5*o**2 - 2*o - 4. Let h be t(-2). List the prime factors of (-28)/h*2*-30.\n | 2, 3, 7\n | ibivibiv/math_instruct | |
Evaluate ((-32)/96)/((((-4)/3)/(-2))/46).\n | -23\n | ibivibiv/math_instruct | |
Calculate the remainder when 21731 is divided by 135.\n | 131\n | ibivibiv/math_instruct | |
Collect the terms in 221*s - 221*s + 143*s**3 + 22*s**3 - 137038 + 137038.\n | 165*s**3\n | ibivibiv/math_instruct | |
Let t(f) = -2*f - 1. Let l be t(-1). Let i(p) be the first derivative of p**2 - 2*p**2 - 2*p**2 + 5*p**2 + 4. What is i(l)?\n | 4\n | ibivibiv/math_instruct | |
Factor -289*i**4/2 + 1207*i**3 - 5449*i**2/2 + 852*i - 72.\n | -(i - 4)**2*(17*i - 3)**2/2\n | ibivibiv/math_instruct | |
What is 398 minutes before 4:30 AM?\n | 9:52 PM\n | ibivibiv/math_instruct | |
What is 103 minutes before 12:07 PM?\n | 10:24 AM\n | ibivibiv/math_instruct | |
What is the product of -0.47 and -30096?\n | 14145.12\n | ibivibiv/math_instruct | |
Suppose 2*s = 7*s + 5, -4*q - 3*s - 3640003 = 0. What is q rounded to the nearest 100000?\n | -900000\n | ibivibiv/math_instruct | |
What is the smallest value in 2, 5, 544, 4, 0.4?\n | 0.4\n | ibivibiv/math_instruct | |
Is 198851987 a prime number?\n | True\n | ibivibiv/math_instruct | |
Suppose -u = 2*d + 18, -5*u - 16 = -d - 3. Calculate the remainder when 43 is divided by (4/d)/(6/(-42)).\n | 3\n | ibivibiv/math_instruct | |
Calculate the common denominator of 43/21221736 and -61/5.\n | 106108680\n | ibivibiv/math_instruct | |
Suppose 29*m + 2859 = 5*i + 31*m, -3*i - m + 1716 = 0. Is i a multiple of 52?\n | False\n | ibivibiv/math_instruct | |
Let g(w) = -4*w**2 + 1 + 4*w**2 - 2*w**3. List the prime factors of g(-1).\n | 3\n | ibivibiv/math_instruct | |
What is the units digit of 593963?\n | 3\n | ibivibiv/math_instruct | |
Let h = 37588 + -9588. Round h to the nearest one thousand.\n | 28000\n | ibivibiv/math_instruct | |
Simplify ((sqrt(931)*-2*-4 - (4 + 1*sqrt(931)))*-4)**2 - (sqrt(2432)*3)/(sqrt(8) - (-1*sqrt(8) + sqrt(8))).\n | -6284*sqrt(19) + 730160\n | ibivibiv/math_instruct | |
Suppose 0 = l - 9 + 3. Let n = -1 + l. Solve -2*w - 3*v = 0, n*w - v - v = -19 for w.\n | -3\n | ibivibiv/math_instruct | |
Let r(a) = -a**3 + 4*a**2 + 6*a - 1. Suppose 0 = 4*f - 9 - 15. Let w be r(f). Let t = -18 - w. Does 19 divide t?\n | True\n | ibivibiv/math_instruct | |
-21 - (-47 + 48 + -17)\n | -5\n | ibivibiv/math_instruct | |
Round 38.8462133 to 0 dps.\n | 39\n | ibivibiv/math_instruct |
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