instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Three letters picked without replacement from {q: 2, u: 1, g: 1, s: 1, p: 1, t: 1}. Give prob of picking 1 u, 1 p, and 1 t.\n | 1/35\n | ibivibiv/math_instruct | |
Let f(x) = 3*x**2 - x - 1. Calculate f(-2).\n | 13\n | ibivibiv/math_instruct | |
Expand -t - 22*t**2 - t**3 + 2*t**3 + 32*t**2 + (0*t + 2*t - 3*t)*(-2*t**2 + 1 - 1) + 2*t**3 + t**3 - 2*t**3 - 5*t**3 + 3*t**3 + t**3.\n | 3*t**3 + 10*t**2 - t\n | ibivibiv/math_instruct | |
What is the next term in 392, 782, 1174, 1568, 1964?\n | 2362\n | ibivibiv/math_instruct | |
What is the third root of 458270 to the nearest integer?\n | 77\n | ibivibiv/math_instruct | |
Collect the terms in 41*j**2 - 24*j**2 - 405*j**2 + 43*j**2 + j - 2*j.\n | -345*j**2 - j\n | ibivibiv/math_instruct | |
What is the third derivative of r**4*y**2 - 7*r**4 + 12*r**3*y**2 - 22*r**2*y**2 + r**2 + r*y**2 wrt r?\n | 24*r*y**2 - 168*r + 72*y**2\n | ibivibiv/math_instruct | |
Rearrange (-4*g**2 + 3*g**2 - g**2)*((-149 - 16*g + 149)*(-4 + 1 + 1) + 3*g + g + g) to p*g**3 + i*g + m + w*g**2 and give p.\n | -74\n | ibivibiv/math_instruct | |
Let w = -5/584 + 43261/5256. Let i be (-4)/(-2) + (-7706)/4028. Let g = i - -1/38. Calculate the common denominator of w and g.\n | 477\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 4358809 and 38.\n | 19\n | ibivibiv/math_instruct | |
What is prob of sequence gms when three letters picked without replacement from {r: 1, n: 1, g: 3, m: 2, s: 4}?\n | 4/165\n | ibivibiv/math_instruct | |
-0.13*0.6\n | -0.078\n | ibivibiv/math_instruct | |
Solve z = -x + 5*z + 13, -5*x = -3*z - 14 for x.\n | 1\n | ibivibiv/math_instruct | |
Collect the terms in 112 - 110 + 12*w**2 - 15998*w + 15999*w - 2.\n | 12*w**2 + w\n | ibivibiv/math_instruct | |
What is 46/5 of a millisecond in microseconds?\n | 9200\n | ibivibiv/math_instruct | |
Let j(t) = 2*t. Let q(l) = -2*l**2. Let p be (2 - 0)*(-1)/1. Let r(u) = -3*u**2. Let f(o) = p*r(o) + 5*q(o). What is f(j(g))?\n | -16*g**2\n | ibivibiv/math_instruct | |
Sort -505, 4, -5, -6, 39 in increasing order.\n | -505, -6, -5, 4, 39\n | ibivibiv/math_instruct | |
Round -19210.8 to the nearest 100.\n | -19200\n | ibivibiv/math_instruct | |
What is 0.5029 times -0.29?\n | -0.145841\n | ibivibiv/math_instruct | |
What is the next term in 11, -21, -101, -235, -429, -689, -1021?\n | -1431\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 l, 1 m, and 2 j when four letters picked without replacement from {u: 2, l: 4, m: 3, j: 2, o: 1, v: 2}.\n | 12/1001\n | ibivibiv/math_instruct | |
Calculate -60*(-11)/858*(39*(-4)/4)/(-9).\n | 10/3\n | ibivibiv/math_instruct | |
Work out 6283319942 - -1.772.\n | 6283319943.772\n | ibivibiv/math_instruct | |
Let f be 5 - (-10)/(-5) - (-2 + 17). Is (-36)/(-4)*(-112)/f a multiple of 6?\n | True\n | ibivibiv/math_instruct | |
Let h(r) = r**3 + 26*r**2 - 13*r - 36. What are the prime factors of h(-26)?\n | 2, 151\n | ibivibiv/math_instruct | |
Let m(w) = -w**2 - 1. Let a(p) = -7*p**2 + 2*p - 10. Give a(c) - 6*m(c).\n | -c**2 + 2*c - 4\n | ibivibiv/math_instruct | |
Let x(v) = v**2 + 9*v + 10. Suppose o - 10*n = -8*n - 3, -3*n = -3*o - 15. Determine x(o).\n | -4\n | ibivibiv/math_instruct | |
Let f = 0 + 13. Let y(x) = 7*x**3 - 2*x**2 + x. Let w be y(1). Let j = f + w. Is 16 a factor of j?\n | False\n | ibivibiv/math_instruct | |
Suppose -2*n = -7*n + 25. Let h(t) = t**2 - 5*t + 3. Let o be h(n). Solve -o*y = 2*p + 1, 19 = 4*p - 0*p - y for p.\n | 4\n | ibivibiv/math_instruct | |
What is 1195 to the power of 1/10, to the nearest integer?\n | 2\n | ibivibiv/math_instruct | |
Let f be (-528)/3432 - (-64)/78. Solve -1/3*i + 1/3*i**2 - f = 0 for i.\n | -1, 2\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Equivalence of Definitions of Locally Path-Connected Space/Definition 1 implies Definition 2
## Theorem
Let $T = \struct{S, \tau}$ be a topological space.
Let each point of $T$ have a local basis consisting entirely of p... | Topological spaces are fundamental structures in mathematics, used to describe continuity, convergence, and proximity. They consist of a set S together with a topology tau, which is a collection of subsets of S satisfying certain axioms. Two important properties of topological spaces are path-connectedness and local p... | ibivibiv/math_instruct | |
Suppose s = -2*s. Let t = -26 + 43. Let v = t - 16.96. Is s less than v?\n | True\n | ibivibiv/math_instruct | |
Solve -5*l = -3*x - l + 10, 10*x + 8*l = -28*x + 68 for x.\n | 2\n | ibivibiv/math_instruct | |
What is 11 - (-10 + 1337/63)?\n | -2/9\n | ibivibiv/math_instruct | |
What is -23 (base 7) in base 14?\n | -13\n | ibivibiv/math_instruct | |
Express (-w - 5 + 5)*(-2 + 2 + 1) + (0 + 0 - 2)*(0*w - 5*w + 0*w) + 4*w - w - 2*w as m*w + g and give m.\n | 10\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 462 and 9870?\n | 108570\n | ibivibiv/math_instruct | |
Let b(r) = -r**3 - 8*r**2 - 8*r. What are the prime factors of b(-8)?\n | 2\n | ibivibiv/math_instruct | |
Let j(v) = 8*v**2 + 56*v + 180. Determine j(-6).\n | 132\n | ibivibiv/math_instruct | |
Let i be 1 + (-3 - 60/(-24))*18. Let o(c) = c**2 - 6*c + 2. Let t be o(5). Which is bigger: t or i?\n | t\n | ibivibiv/math_instruct | |
Let g = 2.8 + 1.2. Let z = 3.85 - g. Let d = -0.05 + z. Sort -0.1, 2/25, d.\n | d, -0.1, 2/25\n | ibivibiv/math_instruct | |
Let v(f) = f - 2. Let m be v(-2). Let s(h) = h**3 - 29*h**2 - 4*h + 126. Let d be s(29). Sort m, -3, d in ascending order.\n | m, -3, d\n | ibivibiv/math_instruct | |
Let v(x) = x**2 - x + 1. Let m be v(1). Let r = 0.05 - -0.04. Let a = -0.01 - r. Which is greater: m or a?\n | m\n | ibivibiv/math_instruct | |
Simplify 2*(2*sqrt(343) + -4) + (-3 + sqrt(7) + -4 - (sqrt(7) - (sqrt(21)/sqrt(3) + -2)))**2.\n | 10*sqrt(7) + 80\n | ibivibiv/math_instruct | |
Suppose -12 = 15*n - 19*n. Find j, given that 3*j**3 + 757*j**2 - 749*j**2 + 0*j**3 + n*j**3 - 2*j**3 = 0.\n | -2, 0\n | ibivibiv/math_instruct | |
10.129*10.97\n | 111.11513\n | ibivibiv/math_instruct | |
Evaluate ((-1)/(-15))/(357/765)*(-87 + -1).\n | -88/7\n | ibivibiv/math_instruct | |
Round -28.54 to the nearest ten.\n | -30\n | ibivibiv/math_instruct | |
Does 26 divide 48 + (-4 - -1) + 7?\n | True\n | ibivibiv/math_instruct | |
Put 3, -2/103, 0.14, 2 in decreasing order.\n | 3, 2, 0.14, -2/103\n | ibivibiv/math_instruct | |
What are the prime factors of 786777?\n | 3, 17, 15427\n | ibivibiv/math_instruct | |
Let m be -1 - ((-14)/(-2) + -2). Let c = -194 + 204. Suppose -2*y - c = 2. Is m at most as big as y?\n | True\n | ibivibiv/math_instruct | |
Suppose -43*n + 8125 + 24254 = 0. What is the highest common divisor of n and 3?\n | 3\n | ibivibiv/math_instruct | |
Suppose 4909 = -3*t + 2*x, 4*t - 38*x = -39*x - 6560. Let h = t - -1642. Suppose 0*n + 30 = 3*n. Solve h*k + 2 + n = 0 for k.\n | -4\n | ibivibiv/math_instruct | |
Let h = -45 - -47. Suppose 0 = -2*t + h*g + 342, 4*t + 175 = 5*t + 3*g. What are the prime factors of t?\n | 2, 43\n | ibivibiv/math_instruct | |
b"What is the hth term of -192984, -192665, -192348, -192033, -191720, -191409?\n" | -h**2 + 322*h - 193305\n | ibivibiv/math_instruct | |
Let z be (-1 - -2)/(1/(-7)). Let w be 1/(-4) + z/(-4). Let q = -121 + 120. Is w bigger than q?\n | True\n | ibivibiv/math_instruct | |
Let o be (-7)/(-4) + -2 + (-957)/44. Let b = o - -26. Let x be (5/30 + 0)/((-1)/b). Which is bigger: x or -1?\n | x\n | ibivibiv/math_instruct | |
Simplify (v**(17/4)/(v/(v/(v/(v**19*v)*v))))/((v**14*v)/(v/v**(-1/38))) assuming v is positive.\n | v**(629/76)\n | ibivibiv/math_instruct | |
Let z(y) = y + 32. Let o be z(-14). Let s(m) = m**3 + 3*m + 1. Let n(h) = 3*h + 17*h**3 + 10*h - 12*h**3 + 5. Determine o*s(t) - 4*n(t).\n | -2*t**3 + 2*t - 2\n | ibivibiv/math_instruct | |
How many millilitres are there in seven eighths of a litre?\n | 875\n | ibivibiv/math_instruct | |
Let g(d) = d**2 + 5*d + 1. Let h be g(-5). Which is the closest to h? (a) -0.6 (b) 0.3 (c) -0.1\n | b\n | ibivibiv/math_instruct | |
b"What is the tth term of -97, -159, -177, -145, -57, 93?\n" | t**3 + 16*t**2 - 117*t + 3\n | ibivibiv/math_instruct | |
What is the highest common factor of 4 and 1265204?\n | 4\n | ibivibiv/math_instruct | |
Four letters picked without replacement from vuvw. What is prob of sequence vuvw?\n | 1/12\n | ibivibiv/math_instruct | |
What is the second derivative of 2*g**3*m**3 - 107*g**3*m - 31*g*m**2 + 2*m**3 - 6*m wrt g?\n | 12*g*m**3 - 642*g*m\n | ibivibiv/math_instruct | |
Evaluate 3 + -3 + -7 + 2.\n | -5\n | ibivibiv/math_instruct | |
What is the highest common factor of 16591 and 47?\n | 47\n | ibivibiv/math_instruct | |
Calculate -4075476 divided by -20276.\n | 201\n | ibivibiv/math_instruct | |
Is 409 a multiple of 5?\n | False\n | ibivibiv/math_instruct | |
Express (2*z**2 + 0*z**2 + z**2)*(4*z**2 - 7*z + 0*z**2 + 4*z) - 49*z**4 - 996*z**3 + 996*z**3 as m*z**2 + b*z + p*z**4 + f + g*z**3 and give p.\n | -37\n | ibivibiv/math_instruct | |
Let c = 1349/5 - 270. Let z be 3/4 - 916/1136. Let a = z + 178/639. What is the second biggest value in a, 2/13, c?\n | 2/13\n | ibivibiv/math_instruct | |
Rearrange 0 - 162*p + 7*p**2 - p**3 + 6 + 83*p + 81*p to k*p**2 + g*p + m*p**3 + i and give g.\n | 2\n | ibivibiv/math_instruct | |
Suppose -5*d + 2*d = -15. Suppose -d*h + 10 = i, i = -i. What is y in -4*y**h - 12*y - 13 + y**2 + y**2 - 5 = 0?\n | -3\n | ibivibiv/math_instruct | |
-1149 + -816\n | -1965\n | ibivibiv/math_instruct | |
Put 2, -0.2, 1/21888 in increasing order.\n | -0.2, 1/21888, 2\n | ibivibiv/math_instruct | |
Is 294514357 a prime number?\n | False\n | ibivibiv/math_instruct | |
What is the third derivative of 73*c**5*n - c**2*n + 3*c**2 - 5*c*n wrt c?\n | 4380*c**2*n\n | ibivibiv/math_instruct | |
Calculate the remainder when 123 is divided by 12.\n | 3\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {y: 2, z: 1, c: 1, r: 1, b: 1, o: 2}. Give prob of sequence yco.\n | 1/84\n | ibivibiv/math_instruct | |
b"What is the cth term of -22, -24, -26, -28, -30?\n" | -2*c - 20\n | ibivibiv/math_instruct | |
Let a(x) = 6*x**2 + 151*x + 715. Determine a(-19).\n | 12\n | ibivibiv/math_instruct | |
What is the cube root of 753041599 to the nearest integer?\n | 910\n | ibivibiv/math_instruct | |
What is the nearest to 4/15 in 7/6, 8, 0.3, 2/13, -45?\n | 0.3\n | ibivibiv/math_instruct | |
Is 743 bigger than 741?\n | True\n | ibivibiv/math_instruct | |
What are the prime factors of 48958790?\n | 2, 5, 59, 82981\n | ibivibiv/math_instruct | |
Calculate 8/(-10)*(-75)/15.\n | 4\n | ibivibiv/math_instruct | |
What is the tens digit of 366?\n | 6\n | ibivibiv/math_instruct | |
Evaluate -30 + 23 - (-2 + -1).\n | -4\n | ibivibiv/math_instruct | |
Let n(b) = -b**3 + 9*b**2 + 21*b - 17. Let o be n(13). List the prime factors of 7*36/o + 4368/5.\n | 3, 97\n | ibivibiv/math_instruct | |
Is 26 a factor of 520?\n | True\n | ibivibiv/math_instruct | |
Factor -4*v**3 + 36592*v**2 - 83649300*v - 167445000.\n | -4*(v - 4575)**2*(v + 2)\n | ibivibiv/math_instruct | |
Suppose 788 = 6*g - 1066. Is g composite?\n | True\n | ibivibiv/math_instruct | |
How many tonnes are there in 72641.66 milligrams?\n | 0.00007264166\n | ibivibiv/math_instruct | |
Is 16221 a prime number?\n | False\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {f: 1, r: 1, u: 3, l: 1, q: 2, h: 4}. What is prob of sequence lq?\n | 1/66\n | ibivibiv/math_instruct | |
Evaluate (-47)/94*(-142)/10 - 7.\n | 1/10\n | ibivibiv/math_instruct | |
What is 7/2 of a second in milliseconds?\n | 3500\n | ibivibiv/math_instruct | |
Let j = -0.0549 + 0.045. Round j to three dps.\n | -0.01\n | ibivibiv/math_instruct |
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