instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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|---|---|---|---|
Let b(h) = 84*h + 8. Let j(y) = 28*y + 3. What is -4*b(k) + 11*j(k)?\n | -28*k + 1\n | ibivibiv/math_instruct | |
Convert 2302 (base 6) to base 13.\n | 329\n | ibivibiv/math_instruct | |
Let i(q) = -q**2 + 3*q. Let j(r) = -r**2 + 5*r + 1. Let b = 1 - -3. Let w(z) = 3 + b*z**2 - z**3 - 3 - 3*z + 3. Let o be w(3). Calculate o*j(a) - 5*i(a).\n | 2*a**2 + 3\n | ibivibiv/math_instruct | |
Sort -16, -2/9, 2.\n | -16, -2/9, 2\n | ibivibiv/math_instruct | |
What is the second smallest value in -2, -9/20, -5?\n | -2\n | ibivibiv/math_instruct | |
What is 0.1930894 nanometers in meters?\n | 0.0000000001930894\n | ibivibiv/math_instruct | |
Which is smaller: 46 or 47?\n | 46\n | ibivibiv/math_instruct | |
Let c(t) = 2*t. Let l(p) = p - 1. Let i(q) = -81*q + 5. Let s(x) = -2*i(x) - 10*l(x). What is c(s(o))?\n | 304*o\n | ibivibiv/math_instruct | |
Suppose -5*a - a - 18 = 0. What is the second biggest value in 3/2, a, 0.3?\n | 0.3\n | ibivibiv/math_instruct | |
Solve 5*j - 21 = -2*f, 69*j - 68*j = -4*f - 3 for j.\n | 5\n | ibivibiv/math_instruct | |
Let o(g) = g**3 - 144*g**2 + 300*g + 883. What are the prime factors of o(142)?\n | 5, 631\n | ibivibiv/math_instruct | |
Suppose 6*z**4 - 321*z**3 + 414*z**2 + 2784*z + 1248 = 0. What is z?\n | -2, -1/2, 4, 52\n | ibivibiv/math_instruct | |
Two letters picked without replacement from upuuuuup. Give prob of picking 2 p.\n | 1/28\n | ibivibiv/math_instruct | |
Let p = 9567.5 - 9567. Suppose 4*i + 8 = 8*i. Which is the third biggest value? (a) -4/3 (b) 5 (c) i (d) p\n | d\n | ibivibiv/math_instruct | |
What is the cube root of 2872766 to the nearest integer?\n | 142\n | ibivibiv/math_instruct | |
What is prob of sequence www when three letters picked without replacement from wdwwwwwdw?\n | 5/12\n | ibivibiv/math_instruct | |
Round 0.00364582 to five decimal places.\n | 0.00365\n | ibivibiv/math_instruct | |
Let y be -1 + 4*(-3)/(-4). Let f be (15 + -13)*(-1)/y. Which is smaller: f or -2/73?\n | f\n | ibivibiv/math_instruct | |
Add -27 and 0.013037151.\n | -26.986962849\n | ibivibiv/math_instruct | |
Calculate (-31 - -39) + 5 + (-1 - 21).\n | -9\n | ibivibiv/math_instruct | |
Subtract 0.7 from 0.142963145669.\n | -0.557036854331\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 24166 and 86.\n | 86\n | ibivibiv/math_instruct | |
Suppose -w**5 - 55*w**4 + 16861*w**3 + 51247*w**2 - 68052*w = 0. Calculate w.\n | -159, -4, 0, 1, 107\n | ibivibiv/math_instruct | |
Suppose 2*i = 4 + 2. Let f(d) = -2 + i*d**2 + 0*d**2 - 2*d**2 - 5*d - 6. What is the units digit of f(8)?\n | 6\n | ibivibiv/math_instruct | |
Suppose -22*d = -49*d - 49*d + 11151860. Is d prime?\n | False\n | ibivibiv/math_instruct | |
Let a(x) = -2*x**2 - 3*x + 3. Let o(y) = y**2 + y + 1. Let i(s) = -2*a(s) - 6*o(s). What is the derivative of i(m) wrt m?\n | -4*m\n | ibivibiv/math_instruct | |
The cube below has sides of length 4 feet. If a cylindrical section of radius X feet is removed from the solid, what is the total remaining volume of the cube? Express your answer in cubic feet in terms of $\pi$.
[asy]
import solids; size(150); import three; defaultpen(linewidth(0.8)); currentprojection = orthographic... | We are given that the cube has sides of length 4 feet and a cylindrical section of radius X feet is removed from the solid.
To find the total remaining volume of the cube, we need to calculate the volume of the cube and subtract the volume of the removed cylindrical section.
The volume of the cube is given by the formu... | ibivibiv/math_instruct | |
Let j be 2/(-8) - (-21)/(-28). Let w = j - -3. Suppose -5*f - 2 = -k, 2*f - 4*f + 2*k - 4 = 0. Sort w, 5, f in increasing order.\n | f, w, 5\n | ibivibiv/math_instruct | |
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"# Math Help - URGENT Parametrics
1. ## URGENT Parametrics
Let be the graph of the parametric equations
What is the length of the smallest interval
such that the graph of these equations for all produces the entire graph ?
... | When working with parametric curves, it is often necessary to determine the period or interval required to produce a complete graph. This can be achieved by finding the least common multiple (LCM) of the periods associated with each independent variable. The individual periods are determined by analyzing the arguments... | ibivibiv/math_instruct | |
What is the next term in 493, 621, 1019, 1831, 3201, 5273?\n | 8191\n | ibivibiv/math_instruct | |
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"# Fibs Our Geometry Teachers Told Us: SSA
There is a standard litany of theorems involving proving triangle congruence that has remained largely unchanged since my high school days. I was told that, to prove that two triangl... | Congruency of triangles is a fundamental concept in geometry, which helps us understand whether two triangles have the same size and shape. To establish this congruency, various sets of conditions have been laid out, such as SSS (Side-Side-Side), SAS (Side-Angle-Side), AAS (Angle-Angle-Side), and ASA (Angle-Side-Angle... | ibivibiv/math_instruct | |
Let m(k) = k**3 - 2*k**2 - k + 1. Let v(x) = 2*x**3 - 104*x**2 + 782*x - 678. Let f(n) = -2*m(n) - v(n). Factor f(z).\n | -4*(z - 13)**2*(z - 1)\n | ibivibiv/math_instruct | |
Let d(q) = -2*q**2 + 6*q + 0*q + 3*q**2 + 0*q**2 + 7. Let o be d(-5). Find the second derivative of 0*w - 3*w + w**4 + o*w wrt w.\n | 12*w**2\n | ibivibiv/math_instruct | |
Round 5642042 to the nearest 1000.\n | 5642000\n | ibivibiv/math_instruct | |
Expand (-2 - 3*u + 2*u - 2*u)*(-1 - 13 - 6)*(0*u**2 + 3*u**2 - u**2 + 5*u**2 + u**2 + 2*u**2 + (1 - 1 + 2*u)*(5*u - 2*u - 4*u)).\n | 480*u**3 + 320*u**2\n | ibivibiv/math_instruct | |
What is the third smallest value in 8957/14, 0, 10/3?\n | 8957/14\n | ibivibiv/math_instruct | |
Solve -808*u + 28767 - 10062 + 12807 = 0 for u.\n | 39\n | ibivibiv/math_instruct | |
Let m(a) = 2*a**3 - 7*a**2 - 5*a - 1. What is m(4)?\n | -5\n | ibivibiv/math_instruct | |
Suppose y + 1526 = 4*k, k - 3*y = 674 - 298. Solve -k*c = -381*c - 1, 4*c = 4*v + 4 for v.\n | 0\n | ibivibiv/math_instruct | |
Let t(y) = -17*y + 5*y**2 + 39*y - 61*y. Let c be t(8). Which is greater: 9 or c?\n | 9\n | ibivibiv/math_instruct | |
Simplify (0 + sqrt(405) + 3*sqrt(405)*-1 + 1 + sqrt(405) + -2*(sqrt(405) + -1*sqrt(405)))**2.\n | -18*sqrt(5) + 406\n | ibivibiv/math_instruct | |
Evaluate 64/(-1008)*7*1/(-2).\n | 2/9\n | ibivibiv/math_instruct | |
Let m = 2137 + -1190. Suppose -4*f - m = -q - 2*q, -4*f - 20 = 0. What is the tens digit of q?\n | 0\n | ibivibiv/math_instruct | |
Let j(y) be the first derivative of -5/2*y**2 - 5/6*y**6 + 0*y**3 + 0*y + 0*y**4 + 4 + 0*y**5. What is the second derivative of j(i) wrt i?\n | -100*i**3\n | ibivibiv/math_instruct | |
Suppose -43*k + 47*k = 32. Suppose -33*s - k = -37*s. Factor 0 + 2*m**s - 4/7*m.\n | 2*m*(7*m - 2)/7\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 660360562?\n | 6\n | ibivibiv/math_instruct | |
In base 13, what is 7 - 49?\n | -42\n | ibivibiv/math_instruct | |
Let r(z) = 16*z**2 - 2*z + 1. Let y be r(1). Let j(f) = -f**3 + 5*f + 4. Let l be j(-3). Solve -5*i - 2*p - y = 0, -4*i = -0*p - 4*p - l for i.\n | -1\n | ibivibiv/math_instruct | |
Calculate 1.3*2561126.\n | 3329463.8\n | ibivibiv/math_instruct | |
Factor -a**4 - 49*a**3 + 166*a**2 + 3424*a + 8160.\n | -(a - 10)*(a + 4)**2*(a + 51)\n | ibivibiv/math_instruct | |
Let k(y) = 35*y + 3. Let j be k(3). Let t = -76 + j. Suppose 15 + 18 = 3*p. Calculate the remainder when t is divided by p.\n | 10\n | ibivibiv/math_instruct | |
Sort 3/7, 4/7, -17, -1, -68/7.\n | -17, -68/7, -1, 3/7, 4/7\n | ibivibiv/math_instruct | |
What is the value of -1 - (-2 + (-208)/(-60) - 4/6)?\n | -9/5\n | ibivibiv/math_instruct | |
What is the product of -21799 and 22?\n | -479578\n | ibivibiv/math_instruct | |
Let h = -11 - 8. Let i = h + 28. Let m be (-16)/(-9) - ((-170)/(-45) - 4). Solve i = m*f + f for f.\n | 3\n | ibivibiv/math_instruct | |
Is 10.05511 smaller than -1/37?\n | False\n | ibivibiv/math_instruct | |
Suppose 21 + 7 = 7*t. Solve 8 + 2 = 2*w + 2*u, 0 = -4*w + t*u - 12 for w.\n | 1\n | ibivibiv/math_instruct | |
Let l = -451.00346 + 451. What is l rounded to three decimal places?\n | -0.003\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {f: 3, z: 2}. What is prob of sequence zz?\n | 1/10\n | ibivibiv/math_instruct | |
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"In other words, this theorem specifies that the shortest distance between two distinct points is always a straight line. A scalene triangle is a triangle in which all three sides have different lengths. Now why is it called t... | The theorem stating that the shortest distance between two distinct points is always a straight line is a fundamental concept in Euclidean geometry, which deals with flat surfaces. This idea can be applied to various mathematical and scientific fields, including physics, engineering, and computer science. For instance... | ibivibiv/math_instruct | |
What is the third smallest value in 1/3, -3/4, -1/7, -6, -2/41?\n | -1/7\n | ibivibiv/math_instruct | |
Let t be 30/(-12) - ((-2)/4 + -2). Solve 0 = -4*l - d - 1, t = 4*d - 2*d - 6 for l.\n | -1\n | ibivibiv/math_instruct | |
Let m be 8/44 - (-966)/11. Let c = 88 + -139. Let q = m + c. What are the prime factors of q?\n | 37\n | ibivibiv/math_instruct | |
Suppose -3*y + 150 = 3*y. List the prime factors of y.\n | 5\n | ibivibiv/math_instruct | |
Is 151 a factor of 78095237?\n | True\n | ibivibiv/math_instruct | |
List the prime factors of 5289474.\n | 2, 3, 47, 18757\n | ibivibiv/math_instruct | |
Let y(j) = 70*j + 35. Let d(b) = -b + 13. Let n be d(6). Let p(q) = -23*q - 12. Let o(i) = n*p(i) + 2*y(i). Is o(-13) a composite number?\n | True\n | ibivibiv/math_instruct | |
What is 1874270479 to the power of 1/10, to the nearest integer?\n | 8\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 14365 and 340.\n | 85\n | ibivibiv/math_instruct | |
1/(132/(-88))*-66*(-3)/48\n | -11/4\n | ibivibiv/math_instruct | |
Expand ((-1 - 2 + 4)*(4 - 1 - 4) - 2 + 0 + 0 - 1 + 1 + 1)*(-395 + 365*a**2 + 395).\n | -730*a**2\n | ibivibiv/math_instruct | |
(-18)/(-48) + (-105)/24\n | -4\n | ibivibiv/math_instruct | |
Differentiate -10*a**2*w**4 + 113*a**2 + 6*a + 600*w**4 - 2 with respect to w.\n | -40*a**2*w**3 + 2400*w**3\n | ibivibiv/math_instruct | |
Let t(c) = -3*c - 5*c**2 + 2*c**3 - 7 - 3*c**3 + 4*c**2 - c**2. Let b be t(-5). Suppose -66 - b = -a. Is a composite?\n | False\n | ibivibiv/math_instruct | |
What is 16077000 rounded to the nearest one million?\n | 16000000\n | ibivibiv/math_instruct | |
How many minutes are there between 1:19 AM and 6:08 AM?\n | 289\n | ibivibiv/math_instruct | |
Simplify (r**(-1))**(1/14)*(r*r**(-2/3))**(3/20)*(r*(r/(r**7/r*r))/r)/r*r**(1/5)*r*r*r*r*r**3*r*r*r*r**(-1/3) assuming r is positive.\n | r**(239/84)\n | ibivibiv/math_instruct | |
Find the third derivative of 1529582*h*x**6 + 124841*h*x**2 + 20*h - x**6 wrt x.\n | 183549840*h*x**3 - 120*x**3\n | ibivibiv/math_instruct | |
Let o(k) = -29*k + 1839. Let d(p) = -48*p + 3679. Give -3*d(c) + 5*o(c).\n | -c - 1842\n | ibivibiv/math_instruct | |
Let t = -41/5 - -359/45. Let f = -0.23 + 18.23. Let l = f + -22. Which is the closest to -0.1? (a) l (b) 0.1 (c) t\n | c\n | ibivibiv/math_instruct | |
Let n = 720 + -414. Let s = n + 11. What is the hundreds digit of s?\n | 3\n | ibivibiv/math_instruct | |
Let d(z) = -159*z - 7. Let n be d(-3). Suppose k - 4*y = n, -2*k = 2*y - 193 - 697. Suppose -4*x + 2*h = -k - 12, 5*x = -5*h + 570. Is x a composite number?\n | True\n | ibivibiv/math_instruct | |
Solve -11*h = -351*h + 1700 for h.\n | 5\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-68.029 / (-12.508 % 11.75) | -6.1890 | ibivibiv/math_instruct | |
How many minutes are there between 8:03 AM and 8:51 AM?\n | 48\n | ibivibiv/math_instruct | |
Let n be (-7428)/(-60) + ((-130)/(-25) - 4). Which is smaller: 123 or n?\n | 123\n | ibivibiv/math_instruct | |
-3.4 * -0.0482\n | 0.16388\n | ibivibiv/math_instruct | |
-71 (base 11) to base 4\n | -1032\n | ibivibiv/math_instruct | |
Solve -1463 + 943 + 521 = -225*o + 4051 for o.\n | 18\n | ibivibiv/math_instruct | |
1323031200 (base 4) to base 2\n | 1111011001101100000\n | ibivibiv/math_instruct | |
Let g(s) = 3*s + 718841 - 718841. Let b(z) = -1264*z**2. Calculate g(b(v)).\n | -3792*v**2\n | ibivibiv/math_instruct | |
Find the common denominator of -7/2460 and 39/1640.\n | 4920\n | ibivibiv/math_instruct | |
Let q(g) be the first derivative of 47*g**4/4 - g**3/3 + 17. Determine q(1).\n | 46\n | ibivibiv/math_instruct | |
Suppose -m - 2 = -2*h + 2, 0 = h - 4*m + 5. Let l be h + 1 + 2 + -7. Let i = -1 - -2. Sort i, 5, l in ascending order.\n | l, i, 5\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 11154 and 132.\n | 66\n | ibivibiv/math_instruct | |
What is the third biggest value in 6, 0.01, -3?\n | -3\n | ibivibiv/math_instruct | |
Let v(u) = u**2 - 6*u + 517. Suppose -4*h + 16 = 3*l, 2*l - 20 = 6*l - 5*h. Is v(l) a prime number?\n | False\n | ibivibiv/math_instruct | |
What comes next: 70532, 141095, 211688, 282311?\n | 352964\n | ibivibiv/math_instruct | |
Expand (-4 + 4 + 5*i)*(2 - 7 + 1)*(-2*i**2 - 2 + 2).\n | 40*i**3\n | ibivibiv/math_instruct | |
Collect the terms in 5*h + 19*h + 7*h + 214*h**2 - 38*h + 7*h.\n | 214*h**2\n | ibivibiv/math_instruct |
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