instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Which is the third smallest value? (a) -9 (b) 0.16 (c) -1 (d) -0.4\n | d\n | ibivibiv/math_instruct | |
Suppose 3*f = 5*q + 58521367 + 50478636, 0 = 3*q + 3*f + 65399997. What is q rounded to the nearest 1000000?\n | -22000000\n | ibivibiv/math_instruct | |
Let u = 567 + -567. Suppose -5*w + u*p + 2*p = -31, 3*w - 24 = 3*p. Solve 0 = 3*c - 0 + 3, -w*h - 5*c = 0 for h.\n | 1\n | ibivibiv/math_instruct | |
Suppose 42*b + 2618 = 56*b. What are the prime factors of b?\n | 11, 17\n | ibivibiv/math_instruct | |
Let q = 1673 - 1673.1329. Let d = -0.143 - q. What is d rounded to 2 dps?\n | -0.01\n | ibivibiv/math_instruct | |
Simplify ((y**(-13)/y)/(((y**(-2)*y)/y)/y))**(1/9)/((y/(y/(y**15/y)*y))/((y*y/(y/(y/(((y*y/y**(-1/20)*y)/y*y)/y)))*y)/y))**(12/7) assuming y is positive.\n | y**(-7432/315)\n | ibivibiv/math_instruct | |
(42/42)/(-9*(-7)/126)\n | 2\n | ibivibiv/math_instruct | |
Let m(n) be the second derivative of -n**7/840 - n**6/120 - n**5/30 + n**4/24 + 17*n**3/6 - 24*n. Let a(k) be the second derivative of m(k). What is a(-3)?\n | 13\n | ibivibiv/math_instruct | |
Is -72 < -1301/18?\n | False\n | ibivibiv/math_instruct | |
Calculate prob of sequence vk when two letters picked without replacement from {k: 2, v: 9}.\n | 9/55\n | ibivibiv/math_instruct | |
What is 130 minutes after 2:22 AM?\n | 4:32 AM\n | ibivibiv/math_instruct | |
Suppose -f = f. Let o(z) = 3*z - 51. Let r be o(18). Factor f + 2 + 0*t - t**2 - r + 2*t.\n | -(t - 1)**2\n | ibivibiv/math_instruct | |
Work out -29972.5 * 0.2.\n | -5994.5\n | ibivibiv/math_instruct | |
Expand 3632*j + 5*j**4 - 3576*j + j**3 + j**3 + j**2 + (3*j**2 + j**2 - j**2)*(0 - 3*j**2 + 0).\n | -4*j**4 + 2*j**3 + j**2 + 56*j\n | ibivibiv/math_instruct | |
Is -58754 > -58808?\n | True\n | ibivibiv/math_instruct | |
Calculate prob of sequence rrbr when four letters picked without replacement from {b: 4, h: 2, r: 11, s: 2}.\n | 55/1292\n | ibivibiv/math_instruct | |
Expand 3*x - 2*x - 2*x + (0 - 1 + 3)*(2*x + x - 6*x + (1 - 1 + 2)*(x - 3*x + x) + x - 2*x - 2*x).\n | -17*x\n | ibivibiv/math_instruct | |
Let v = -221190 - -312717. Is v composite?\n | True\n | ibivibiv/math_instruct | |
-3 (base 6) to base 9\n | -3\n | ibivibiv/math_instruct | |
Find the second derivative of -28883*v**2*w**2 + 8*v**2*w + 3*v**2 + 138*v*w wrt w.\n | -57766*v**2\n | ibivibiv/math_instruct | |
Suppose -m = 4*m - 10. Suppose m*z = -b - 138 - 41, 5*b = -15. What is the common denominator of ((-6)/z)/((-9)/(-642)) and -21/20?\n | 220\n | ibivibiv/math_instruct | |
Let s(l) = -l**3 + 2. Let k be s(0). Suppose f = 4*w - 4*f - 23, -k*w - 5*f - 11 = 0. Solve 0 = h + w*h for h.\n | 0\n | ibivibiv/math_instruct | |
Let o = -4.5 + -13.3. Let k = 18 + o. Which is the closest to -0.2? (a) -1/2 (b) 0.5 (c) k\n | a\n | ibivibiv/math_instruct | |
What is 386 minutes before 5:55 AM?\n | 11:29 PM\n | ibivibiv/math_instruct | |
Which is greater: -4318316/5 or -2?\n | -2\n | ibivibiv/math_instruct | |
Let i(h) = -13*h - 34. Let n be i(-3). Suppose 0 = -n*u - 190 + 2850. List the prime factors of u.\n | 2, 7, 19\n | ibivibiv/math_instruct | |
Convert -52e4e (base 16) to base 7.\n | -2612616\n | ibivibiv/math_instruct | |
What is the third biggest value in -3/5, 0.2, 4154?\n | -3/5\n | ibivibiv/math_instruct | |
Suppose 28 = -4*v - 20. Suppose 0 = 5*s + 3*t - 10, -6 = 3*s - 2*s - t. Let r be 18/v*s*10. Calculate the greatest common divisor of 30 and r.\n | 15\n | ibivibiv/math_instruct | |
Suppose 106 - 12 = 2*x. Let t = x - 41. Solve -t = -5*h + 9 for h.\n | 3\n | ibivibiv/math_instruct | |
What is 373 minutes after 3:58 PM?\n | 10:11 PM\n | ibivibiv/math_instruct | |
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"# How to find Residue of Power Integer
I found congruence like below in various note-
$$6^x \equiv 16 \pmod{20}$$
$$5^z\equiv 5 \pmod{20}$$
For any $$z,x$$ (perhaps, I didn't see any other condition).
How residues $$16, ... | Congruences are a fundamental concept in Number Theory, which is a branch of mathematics that studies properties and relationships between integers. The notation $a o b$ means that $a$ and $b$ leave the same remainder when divided by $m$, where $m > 0$. This relation is called congruence modulo $m$. Two important pro... | ibivibiv/math_instruct | |
What comes next: 1096, 2143, 3144, 4099, 5008, 5871, 6688?\n | 7459\n | ibivibiv/math_instruct | |
What is the second derivative of 5937*m**4 - 14463*m wrt m?\n | 71244*m**2\n | ibivibiv/math_instruct | |
Factor z**5 - 4*z**4 - 6*z**3 + 4*z**2 + 5*z.\n | z*(z - 5)*(z - 1)*(z + 1)**2\n | ibivibiv/math_instruct | |
Let o(j) = 6*j**2 + 14*j - 13. Let p(s) = -3*s**2 - 7*s + 6. Let h = -7 + 1. Let x(f) = h*o(f) - 13*p(f). Find the second derivative of x(u) wrt u.\n | 6\n | ibivibiv/math_instruct | |
Expand (v + 0 + 0)*(2*v + 1 - 1) + (0*v + 2*v + 0*v)*(-3*v + 4*v - 3*v) - 162*v + 162*v + 112*v**2.\n | 110*v**2\n | ibivibiv/math_instruct | |
Solve 1261657 = -18*u + 1260757 for u.\n | -50\n | ibivibiv/math_instruct | |
Simplify (x/(x/(x**(1/9)*x))*x/(x**39*x))/(x**28*x/(x/(x**(7/4)/x))) assuming x is positive.\n | x**(-2399/36)\n | ibivibiv/math_instruct | |
Let j(d) be the first derivative of -7/32*d**4 + 37/24*d**3 - 19/8*d**2 + 15 + d. Factor j(r).\n | -(r - 4)*(r - 1)*(7*r - 2)/8\n | ibivibiv/math_instruct | |
Round 62980000 to the nearest 1000000.\n | 63000000\n | ibivibiv/math_instruct | |
What is the closest to -11 in -2, -30.36, 13?\n | -2\n | ibivibiv/math_instruct | |
Let v = 184 + -172. Suppose 2*g + 4*f - 520 = 0, 7 = f + v. What is g rounded to the nearest one hundred?\n | 300\n | ibivibiv/math_instruct | |
In base 13, what is 6 - -16851586?\n | 1685158c\n | ibivibiv/math_instruct | |
Simplify (j**(-11)/(j/j**(-4/11)))/(j*j*j/(j/(j**(-1/7)/j*j)*j))**(-21) assuming j is positive.\n | j**(62/11)\n | ibivibiv/math_instruct | |
What is -11195 rounded to the nearest one thousand?\n | -11000\n | ibivibiv/math_instruct | |
1647044 divided by 411761\n | 4\n | ibivibiv/math_instruct | |
-6 * -118.33\n | 709.98\n | ibivibiv/math_instruct | |
Suppose t = 4*z + 4, 3*z = -t + 2*t - 3. Let c(r) = 11*r**2 + 2*r + 1. Calculate the lowest common multiple of c(-1) and (0 + 16 - 4) + z.\n | 110\n | ibivibiv/math_instruct | |
1281 divided by 520\n | 1281/520\n | ibivibiv/math_instruct | |
Sort 2/9, 12, -2/21, 6, 1/2, 3332 in ascending order.\n | -2/21, 2/9, 1/2, 6, 12, 3332\n | ibivibiv/math_instruct | |
What is (((-4)/30)/((-156)/702))/(17/(-5))?\n | -3/17\n | ibivibiv/math_instruct | |
Let s(c) be the third derivative of -c**8/20160 - 13*c**7/7560 + 37*c**4/24 - 2*c**2 - 32. Let n(m) be the second derivative of s(m). What is f in n(f) = 0?\n | -13, 0\n | ibivibiv/math_instruct | |
Sort -496, -1, 4, -4, -72, -3 in decreasing order.\n | 4, -1, -3, -4, -72, -496\n | ibivibiv/math_instruct | |
Calculate prob of sequence hrhw when four letters picked without replacement from {m: 1, u: 1, d: 5, w: 2, r: 6, h: 2}.\n | 1/2380\n | ibivibiv/math_instruct | |
Simplify l**(2/9)/(l/(((l/(l*l**(1/11)/l*l))/l)/l))*(l**(2/3)*l)**23 assuming l is positive.\n | l**(3511/99)\n | ibivibiv/math_instruct | |
Multiply -6 and 5760204.\n | -34561224\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 182410 and 422762?\n | 2146\n | ibivibiv/math_instruct | |
Is 6201319 a composite number?\n | True\n | ibivibiv/math_instruct | |
Divide 146 by 5.\n | 146/5\n | ibivibiv/math_instruct | |
Which is greater: 0 or 0.114164?\n | 0.114164\n | ibivibiv/math_instruct | |
Suppose -4*o + 2*d + 10 = -2, -3*o + 3*d = -6. Suppose -o = 2*s, -3*k + 2*s = k - 36. Suppose -12 - k = -4*m + 2*t, -m = 3*t - 5. What is the units digit of m?\n | 5\n | ibivibiv/math_instruct | |
Let r be -2*1*2/(-4). Let z be -2*(0 + r) - -7. Suppose -8 = -z*i + 4*i. What is the units digit of i?\n | 8\n | ibivibiv/math_instruct | |
Expand (-123*p + 2 + 132*p - 1)*(p**3 - 3*p**3 + p**3).\n | -9*p**4 - p**3\n | ibivibiv/math_instruct | |
What is the common denominator of 19/69675 and 55/21?\n | 487725\n | ibivibiv/math_instruct | |
Find d, given that 5*d**3/2 - 54*d**2 + 61*d/2 + 21 = 0.\n | -2/5, 1, 21\n | ibivibiv/math_instruct | |
Expand (4 - 4 - 2*a)*(4 + 7 - 2 + (2 + 5 - 2)*(-1 + 4 - 2)).\n | -28*a\n | ibivibiv/math_instruct | |
Two letters picked without replacement from vevteetvevbevevve. Give prob of sequence bt.\n | 1/136\n | ibivibiv/math_instruct | |
Let x(o) = 18*o - 1. Let t be x(3). Suppose 3*n + 3*j - 57 + 24 = 0, j - t = -4*n. List the prime factors of n.\n | 2, 7\n | ibivibiv/math_instruct | |
Let d = 0.006 - 5.006. Let i = 103.96 - 103. Let q = -2.96 + i. Which is the second smallest value? (a) d (b) q (c) 0.1\n | b\n | ibivibiv/math_instruct | |
Simplify (((t**(-3/2))**49*t*t/t**(-10)*t**(12/5))**(-35))**(10/3) assuming t is positive.\n | t**6895\n | ibivibiv/math_instruct | |
Round 244.0296 to one decimal place.\n | 244\n | ibivibiv/math_instruct | |
What is the fifth root of 55412 to the nearest integer?\n | 9\n | ibivibiv/math_instruct | |
Let j(s) = 3*s**2 - 12*s + 15. Let d be j(2). Suppose -1320 = -d*g - 4*i, 6*g + 3*i - 2200 = g. What are the prime factors of g?\n | 2, 5, 11\n | ibivibiv/math_instruct | |
Let n be (2/(-8))/(7/(-84)). Suppose -3*q = -n*k - 168, q + 29 - 91 = -k. Is q a prime number?\n | True\n | ibivibiv/math_instruct | |
Let d be 9 - (0 + 4) - 0. Suppose -4*i + 5269 = -d*k, 1286 = i - 2*k + 7*k. Calculate the greatest common factor of i and 57.\n | 57\n | ibivibiv/math_instruct | |
Let l(b) = 3*b**2. Let o(g) be the first derivative of 3/2*g**2 + 0*g - 101. Calculate o(l(w)).\n | 9*w**2\n | ibivibiv/math_instruct | |
What is 20303114 to the power of 1/3, to the nearest integer?\n | 273\n | ibivibiv/math_instruct | |
What is ((-36)/(-6) - 7)/((-64)/(-2240))?\n | -35\n | ibivibiv/math_instruct | |
Round -185.95566 to two dps.\n | -185.96\n | ibivibiv/math_instruct | |
What is the biggest value in -0.02, -1/41, 202147?\n | 202147\n | ibivibiv/math_instruct | |
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"# New families in Bambi
In this third post about my work during this Google Summer of Code I describe two families of models recently added. The first one, is the Student T family, used to make linear regressions more robust... | In the field of statistical modeling, a key concept is the use of likelihood functions to estimate parameters and make predictions based on data. A likelihood function describes the probability of observing the data given certain parameter values. Different types of likelihood functions correspond to different distrib... | ibivibiv/math_instruct | |
Divide -115 by 10.\n | -23/2\n | ibivibiv/math_instruct | |
Express (-z**2 + 0 + 0)*(5*z + 0*z + 0*z)*(-113*z - 111*z - 66*z - 188*z) as o + r*z**2 + l*z**4 + n*z + p*z**3 and give l.\n | 2390\n | ibivibiv/math_instruct | |
Solve 42*g - 43*g + 792 = 197*g for g.\n | 4\n | ibivibiv/math_instruct | |
Let o(d) = 6*d**2 + 66*d + 9. Give o(-12).\n | 81\n | ibivibiv/math_instruct | |
Let h be ((-112)/24)/7*-1. Which is the third smallest value? (a) h (b) 10 (c) -0.2 (d) 0.3\n | a\n | ibivibiv/math_instruct | |
What is the hundreds digit of 4737?\n | 7\n | ibivibiv/math_instruct | |
Let r(n) = n**3 + 10*n**2 - 910*n - 8267. Give r(-9).\n | 4\n | ibivibiv/math_instruct | |
Calculate -43 + 71 - 17 - (1 + (-1 - -8)).\n | 3\n | ibivibiv/math_instruct | |
Suppose -5*k + 7*k = 0. Let r be (1 - 1) + (k + 2 - 2). Let u(p) = p - 3. Let s be u(3). Solve r*w - w - 5 = s for w.\n | -5\n | ibivibiv/math_instruct | |
Let i = 29122 - 191620/7. Let l = i - 1751. Let a = 10808 + -183790/17. Find the common denominator of l and a.\n | 119\n | ibivibiv/math_instruct | |
Calculate prob of sequence tb when two letters picked without replacement from {t: 1, i: 1, b: 2, m: 2}.\n | 1/15\n | ibivibiv/math_instruct | |
In base 7, what is 11 + 26?\n | 40\n | ibivibiv/math_instruct | |
Solve 2*a**5 + 818*a**4 + 96558*a**3 + 2499606*a**2 - 5691600*a - 8095464 = 0.\n | -186, -39, -1, 3\n | ibivibiv/math_instruct | |
Simplify (r**(-2/65)/(r*r*(r/(r*r*r**(-2/73)))/r*r*r))/(r**(-5/9)*r**(-3)) assuming r is positive.\n | r**(63946/42705)\n | ibivibiv/math_instruct | |
What is -1770.221133 rounded to 1 dp?\n | -1770.2\n | ibivibiv/math_instruct | |
In base 15, what is -87e + 7?\n | -877\n | ibivibiv/math_instruct | |
Let t(g) = 1218*g + 2. Let h(o) = 37*o - 25. Let a(c) = 59*c - 40. Let b(r) = 5*a(r) - 8*h(r). Determine b(t(d)).\n | -1218*d - 2\n | ibivibiv/math_instruct | |
Let w = -10701/8 - -12055/9. What is the common denominator of -131/72 and w?\n | 72\n | ibivibiv/math_instruct |
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