instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Is 9/79298 != 1?\n | True\n | ibivibiv/math_instruct | |
Suppose 376 = 4*a - 0*a. Let f = a - 52. Is f a multiple of 6?\n | True\n | ibivibiv/math_instruct | |
Let k = -1.08 + -0.12. Let q = -2.526 - -0.926. Let n = k - q. What is the second smallest value in -0.1, n, 0.3, 1/4?\n | 1/4\n | ibivibiv/math_instruct | |
How many minutes are there between 6:02 PM and 5:56 AM?\n | 714\n | ibivibiv/math_instruct | |
Do 3529514 and 3529515 have the same value?\n | False\n | ibivibiv/math_instruct | |
Let j(q) be the second derivative of q**5/50 + q**4/15 + 3*q - 27. Factor j(m).\n | 2*m**2*(m + 2)/5\n | ibivibiv/math_instruct | |
Let l(q) = q**2. Suppose -4*u - 8 = -2*d - 0*u, 5*d - 35 = -5*u. Let y(r) be the first derivative of 1 + d*r**3 - 2 + 0. Give l(y(w)).\n | 324*w**4\n | ibivibiv/math_instruct | |
Two letters picked without replacement from neiae. What is prob of sequence ei?\n | 1/10\n | ibivibiv/math_instruct | |
Calculate -8 - 1 - ((33/(-4))/((-1329)/1772) + -34).\n | 14\n | ibivibiv/math_instruct | |
Let k = -2 - -7. Let z(s) = 10*s + 4. Let d be z(k). Is (d/24)/((-3)/(-16)) a multiple of 12?\n | True\n | ibivibiv/math_instruct | |
Expand (-3*v - 2*v + 6*v)*(0*v - 3*v + v) - 58 + 58 + 19*v**2 + (-2*v + 4 - 4)*(2*v - 1 + 1).\n | 13*v**2\n | ibivibiv/math_instruct | |
Collect the terms in 64*u - 16*u - 13*u.\n | 35*u\n | ibivibiv/math_instruct | |
Let 20*k**3 + 516*k**2 - 2304*k + 2384 = 0. What is k?\n | -149/5, 2\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 119840?\n | 1\n | ibivibiv/math_instruct | |
Let j(i) = i**2 - 6*i + 3. Let k be j(2). Let f = -3 - k. Find the third derivative of 2 - 2 + a**2 + 3*a**3 + 3*a**f wrt a.\n | 18\n | ibivibiv/math_instruct | |
Solve 4*c = 5*s + 20 - 54, -3*s - 18*c = 204 for s.\n | -2\n | ibivibiv/math_instruct | |
(-1)/((-1)/(-3)*9/(-6))\n | 2\n | ibivibiv/math_instruct | |
Determine j so that -3*j**4/7 + 54*j**3 - 4947*j**2/7 - 5328*j/7 = 0.\n | -1, 0, 16, 111\n | ibivibiv/math_instruct | |
Solve -12 = -6*w + 12*w for w.\n | -2\n | ibivibiv/math_instruct | |
Express -6*s**3 - 2*s**2 + 7*s**3 - 3*s + 3*s**2 in the form i*s + p*s**3 + w*s**2 + x and give p.\n | 1\n | ibivibiv/math_instruct | |
Calculate prob of sequence vo when two letters picked without replacement from kxovvvvov.\n | 5/36\n | ibivibiv/math_instruct | |
b"What is the jth term of -107, -106, -113, -134, -175, -242, -341?\n" | -j**3 + 2*j**2 + 2*j - 110\n | ibivibiv/math_instruct | |
Two letters picked without replacement from oooaao. What is prob of picking 1 a and 1 o?\n | 8/15\n | ibivibiv/math_instruct | |
Suppose -2*y - 41255 - 228745 = 0. Round y to the nearest 10000.\n | -140000\n | ibivibiv/math_instruct | |
Convert 4ac2ee (base 15) to base 12.\n | 124a738\n | ibivibiv/math_instruct | |
Let c be 416 - -3 - (-137 - -151). What is the greatest common factor of 10 and c?\n | 5\n | ibivibiv/math_instruct | |
Let x = 14.151 + 0.049. Let t be 60/24 - (-9)/(-6)*2. Is x bigger than t?\n | True\n | ibivibiv/math_instruct | |
How many seconds are there in nine tenths of a hour?\n | 3240\n | ibivibiv/math_instruct | |
Let t = 2151937 - 1225304. Is t composite?\n | False\n | ibivibiv/math_instruct | |
Express (-43 + 43 + 4*f + 24*f**3)*(2*f + 4*f - 4*f) in the form p*f**3 + a*f**2 + u*f + j*f**4 + w and give j.\n | 48\n | ibivibiv/math_instruct | |
Let z(d) = 4*d**2 + 494*d - 755. What is z(-125)?\n | -5\n | ibivibiv/math_instruct | |
Let l = 8 - 8. Suppose l = -2*b - 2*b + 28. Suppose 15 = 3*g - 21. Calculate the remainder when g is divided by b.\n | 5\n | ibivibiv/math_instruct | |
What is -0.005045175 rounded to four dps?\n | -0.005\n | ibivibiv/math_instruct | |
Suppose 19 = -7*z - 30. Let j(x) be the first derivative of -x**3/3 - 7*x**2/2 + 3*x + 2. Let l be j(z). Solve 2*k - u = 1, 2*k + 0 + 3 = -l*u for k.\n | 0\n | ibivibiv/math_instruct | |
Four letters picked without replacement from ppetgpgqpgpgqpq. Give prob of sequence tpge.\n | 1/1365\n | ibivibiv/math_instruct | |
Is 8899 a prime number?\n | False\n | ibivibiv/math_instruct | |
Let v(n) = 73*n**3 - 2957*n**2 + 1468*n + 484. What is v(40)?\n | 4\n | ibivibiv/math_instruct | |
Let h(l) = -3. Let a(j) = -11. Let s(n) = 2*a(n) - 7*h(n). Let c(f) = 9 + 16*f - 32*f + 15*f. Suppose y + 2*m = 18, -2 = -y + 5*m + 2. Give y*s(u) + 2*c(u).\n | -2*u + 4\n | ibivibiv/math_instruct | |
Let l = 94/3 + -476/15. Which is the biggest value? (a) -0.1 (b) l (c) 0.5\n | c\n | ibivibiv/math_instruct | |
Let g(r) = r**3 + 2*r**2 + 2*r - 6. Determine g(0).\n | -6\n | ibivibiv/math_instruct | |
Collect the terms in 0*t**2 + 9*t**2 - 9*t**2 + 9*t**3.\n | 9*t**3\n | ibivibiv/math_instruct | |
Sort -188, -139, -2 in descending order.\n | -2, -139, -188\n | ibivibiv/math_instruct | |
Let u(q) = q**3 - q**2 - 3*q - 2. Let r be u(-1). What is the common denominator of -151/30 and 37/(-15) + r + 0 + 0?\n | 30\n | ibivibiv/math_instruct | |
What is the third root of 722806130 to the nearest integer?\n | 897\n | ibivibiv/math_instruct | |
Is 21977 a prime number?\n | True\n | ibivibiv/math_instruct | |
Simplify ((1*-1*sqrt(252) + sqrt(252))/(sqrt(72)/(sqrt(16)/sqrt(2))))/(4*(-3*-5*sqrt(400) + sqrt(400))).\n | 0\n | ibivibiv/math_instruct | |
Find v, given that -48*v**4 - 30840*v**3 - 15363*v**2 + 28917*v + 17334 = 0.\n | -642, -3/4, 1\n | ibivibiv/math_instruct | |
What is the third root of 8083057 to the nearest integer?\n | 201\n | ibivibiv/math_instruct | |
Divide -7865334 by 6.\n | -1310889\n | ibivibiv/math_instruct | |
Collect the terms in -17*n - 8*n**3 + 0*n**3 + 7*n.\n | -8*n**3 - 10*n\n | ibivibiv/math_instruct | |
Let y = 135 + -133. Solve y*x = 4*x for x.\n | 0\n | ibivibiv/math_instruct | |
Solve -7*f + 22*f + 4*f + 95 = 0 for f.\n | -5\n | ibivibiv/math_instruct | |
Three letters picked without replacement from kzzjjzzjjzz. Give prob of picking 3 z.\n | 4/33\n | ibivibiv/math_instruct | |
Solve 3*a - i = -10, -3*i - 35 = -30*a + 34*a for a.\n | -5\n | ibivibiv/math_instruct | |
Simplify ((-2*sqrt(2695)*-2)/(sqrt(45)/sqrt(144)*5))**2.\n | 137984/25\n | ibivibiv/math_instruct | |
Four letters picked without replacement from hgxhxhxxhxaxhhxwhhw. What is prob of picking 1 a, 1 x, and 2 w?\n | 7/3876\n | ibivibiv/math_instruct | |
Let r be (240/(-35))/(2/(-14)). Calculate the common denominator of -79/76 and ((-3)/r)/((-3)/(-606)).\n | 152\n | ibivibiv/math_instruct | |
Is 1 smaller than -1/3342155?\n | False\n | ibivibiv/math_instruct | |
Let s(r) be the third derivative of -r**7/42 - 47*r**6/40 + r**5/30 - r**4/8 - 115*r**3/2 - 8323*r**2. What is the third derivative of s(u) wrt u?\n | -120*u - 846\n | ibivibiv/math_instruct | |
Let o(u) = -10*u + 12*u - 15*u + 5. Let n(z) = -14*z - 3. Let j(l) = 7*l + 1. Let k(i) = 7*j(i) + 3*n(i). Let g(v) = 11*k(v) + 6*o(v). Calculate g(4).\n | 4\n | ibivibiv/math_instruct | |
10/(1080/(-96)*7/(-21))\n | 8/3\n | ibivibiv/math_instruct | |
Which is smaller: -1 or -4/1039485?\n | -1\n | ibivibiv/math_instruct | |
Let k be (-3 - (-1)/5)/(2/(-60)). Let u = k + -81. Solve 0*w - 1/4*w**u + 0 + 1/4*w**2 = 0 for w.\n | 0, 1\n | ibivibiv/math_instruct | |
Let t(v) = 1446*v - 64. Let u(z) = 10122*z - 432. Give 27*t(c) - 4*u(c).\n | -1446*c\n | ibivibiv/math_instruct | |
Let q(v) = -v. Let c(l) = 13*l. Let a(k) = c(k) + 4*q(k). Suppose 3*f - w + 3*w = -19, 5*w + 16 = 3*f. Let o = -2 - f. Calculate a(o).\n | 9\n | ibivibiv/math_instruct | |
Suppose j + 164 = 5*j. Let y = j - 41. Let s(w) = w**3 - w + 3. Give s(y).\n | 3\n | ibivibiv/math_instruct | |
Let p(y) = -2*y. Let h(t) be the first derivative of 11*t**5/60 - 4*t**3 - 17. Let z(c) be the third derivative of h(c). Give p(z(d)).\n | -44*d\n | ibivibiv/math_instruct | |
What is the closest to -2/7 in -1, -4, -12, 184.83, -3, 3?\n | -1\n | ibivibiv/math_instruct | |
What is 158 minutes before 3:53 AM?\n | 1:15 AM\n | ibivibiv/math_instruct | |
Does 7 divide 164766?\n | True\n | ibivibiv/math_instruct | |
What is the greatest common factor of 4955 and 149?\n | 1\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 268816597 and 147.\n | 49\n | ibivibiv/math_instruct | |
Let k be ((-6)/(-195))/(24/(-35575)). Let q = k + 555/13. Let a = 46/3 - 991/66. Calculate the common denominator of a and q.\n | 132\n | ibivibiv/math_instruct | |
Suppose k = l - 1 + 5, -3*l - 15 = -4*k. Let v(b) = b + k*b - 5 + 4. Give v(3).\n | 11\n | ibivibiv/math_instruct | |
Work out -7.822 * 0.025.\n | -0.19555\n | ibivibiv/math_instruct | |
Suppose -38*h = 2 - 344. Let z(v) = -v**3 - 7*v**2 - 7*v + 2. What is the smallest common multiple of h and z(-7)?\n | 153\n | ibivibiv/math_instruct | |
Let x(c) be the first derivative of c**5/70 + 17*c**4/42 - 6*c**3/7 + 51*c - 183. Let t(s) be the first derivative of x(s). Determine z so that t(z) = 0.\n | -18, 0, 1\n | ibivibiv/math_instruct | |
What is the third root of 147281257 to the nearest integer?\n | 528\n | ibivibiv/math_instruct | |
Let q = -76/49 - -55/49. What is the nearest to q in 0.3, -29, -3, 0?\n | 0\n | ibivibiv/math_instruct | |
What is 94821742 to the power of 1/2, to the nearest integer?\n | 9738\n | ibivibiv/math_instruct | |
Let c = -296/5 + 59. Let x = -0.2245 - 0.7755. Let u be 1/(-9) + 4/(-18). What is the closest to u in x, 3, c?\n | c\n | ibivibiv/math_instruct | |
Is 34 a factor of 6778716?\n | True\n | ibivibiv/math_instruct | |
Let a(r) = 32*r + 2150. What is a(-61)?\n | 198\n | ibivibiv/math_instruct | |
Collect the terms in 1 + 25*q**2 + 8 + 4 - 13.\n | 25*q**2\n | ibivibiv/math_instruct | |
In base 10, what is 387 - -2?\n | 389\n | ibivibiv/math_instruct | |
Let u(k) be the second derivative of -7*k**6/120 + 5*k**3/6 + k**2/2 - 6*k. Let j(w) be the first derivative of u(w). Differentiate j(v) with respect to v.\n | -21*v**2\n | ibivibiv/math_instruct | |
What are the prime factors of 517930164?\n | 2, 3, 941, 15289\n | ibivibiv/math_instruct | |
211003033 (base 4) to base 3\n | 21201011201\n | ibivibiv/math_instruct | |
Put -3/5, -15, 4, -2 in increasing order.\n | -15, -2, -3/5, 4\n | ibivibiv/math_instruct | |
What is the units digit of 11812444?\n | 4\n | ibivibiv/math_instruct | |
What is the next term in 30, 19, 10, 3, -2, -5, -6?\n | -5\n | ibivibiv/math_instruct | |
What is the value of (-48)/(-28) - 392409/201747?\n | -3/13\n | ibivibiv/math_instruct | |
Suppose -458 = -3*b - 4*p + 62, -5*b + 820 = -5*p. Let u = 22 - 36. Let s = 35 + u. Calculate the greatest common factor of b and s.\n | 21\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 m, 2 v, and 1 p when four letters picked without replacement from mvbbmvbpmvvmhm.\n | 30/1001\n | ibivibiv/math_instruct | |
Let z(j) be the first derivative of 8*j**6/15 + 3*j**5 + 8*j**4/3 - 2*j**3 - 71*j + 22. Let n(q) be the first derivative of z(q). Suppose n(w) = 0. What is w?\n | -3, -1, 0, 1/4\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Tag Info
7
First of all, interpolation and approximation are slightly different from each other. Given a sufficiently smooth function $f$ (sufficiently smooth just means that I am covering my bases, there are many theorem... | Interpolation and approximation are fundamental concepts in numerical analysis, often used to estimate the values of functions at certain points based on known data. While they may seem similar, they differ in their approaches to estimating these unknown values.
Interpolation involves constructing a new function tha... | ibivibiv/math_instruct | |
In base 10, what is 359 - -1?\n | 360\n | ibivibiv/math_instruct | |
Let i = -7.12 + 9.12. Which is the closest to -10? (a) i (b) -0.4 (c) -0.2 (d) 2/9\n | b\n | ibivibiv/math_instruct | |
Let q(x) = -x**3 - 3*x**2 + 5*x. Let t be q(-5). Suppose 4*r = t + 23. Solve 0 = -h - 3*h - r for h.\n | -3\n | ibivibiv/math_instruct | |
Which is the closest to 2? (a) 5/23 (b) -4 (c) 1/4 (d) 0.1\n | c\n | ibivibiv/math_instruct |
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