instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Put -0.3, -2, 3/16, 2/11 in descending order.\n | 3/16, 2/11, -0.3, -2\n | ibivibiv/math_instruct | |
Add together 1 and 3815016536096.\n | 3815016536097\n | ibivibiv/math_instruct | |
Let y(q) = -6*q + 5. Let z(w) = 3*w - 2. Let k(u) = 2*y(u) + 5*z(u). Let v(j) = 10*j**2. Give v(k(p)).\n | 90*p**2\n | ibivibiv/math_instruct | |
Let i be 4/(-8)*-6 + 2. Suppose 0 = -i*g - 3*g + 26048. Suppose 16563 = 7*s + g. Is s prime?\n | True\n | ibivibiv/math_instruct | |
Sort 3, 6, 0, -9.\n | -9, 0, 3, 6\n | ibivibiv/math_instruct | |
14 + 0 - (-26 + 38)\n | 2\n | ibivibiv/math_instruct | |
What is prob of sequence qr when two letters picked without replacement from {r: 9, q: 10}?\n | 5/19\n | ibivibiv/math_instruct | |
What is 158 minutes after 10:33 AM?\n | 1:11 PM\n | ibivibiv/math_instruct | |
Sort 46, -1/7, -0.4 in descending order.\n | 46, -1/7, -0.4\n | ibivibiv/math_instruct | |
List the prime factors of 5041.\n | 71\n | ibivibiv/math_instruct | |
Let l(r) be the second derivative of 0*r**2 + 0 + 5*r - 1/24*r**5 + 1/8*r**4 - 1/3*r**3. Let x(z) be the second derivative of l(z). Differentiate x(h) wrt h.\n | -5\n | ibivibiv/math_instruct | |
Is 9967 a composite number?\n | False\n | ibivibiv/math_instruct | |
Let n be (0 - -1) + (0 - -1). Suppose 4*w = 3*g - 5, -w + n*g = -5*w + 10. Suppose -v = -w - 2. Which is the second biggest value? (a) v (b) 2/17 (c) -0.1\n | b\n | ibivibiv/math_instruct | |
Let r(s) = 37*s + 41. What is r(-1)?\n | 4\n | ibivibiv/math_instruct | |
Let m(x) be the second derivative of -7*x + 1/12*x**4 + 1/2*x**2 + 0 - x**3. Calculate m(4).\n | -7\n | ibivibiv/math_instruct | |
What is the millions digit of 35379865?\n | 5\n | ibivibiv/math_instruct | |
Is 64 a factor of 3970?\n | False\n | ibivibiv/math_instruct | |
Let w(t) = t**2 - 35*t. Let i(l) be the first derivative of l**2/2 - 296. Give w(i(o)).\n | o**2 - 35*o\n | ibivibiv/math_instruct | |
Sort -7, -21, 795, 31, 8.\n | -21, -7, 8, 31, 795\n | ibivibiv/math_instruct | |
Collect the terms in 5 + 403*h - 5.\n | 403*h\n | ibivibiv/math_instruct | |
Expand (73 - 33 - 1827*q - 42)*(3 - 5 + 1).\n | 1827*q + 2\n | ibivibiv/math_instruct | |
Let c(q) = 2*q**2 - 25*q - 25. Calculate the remainder when c(15) is divided by (-4)/12 + 61/3.\n | 10\n | ibivibiv/math_instruct | |
Let f = -661 - -679. Suppose 12*m - f*m = 42. Let x(t) = -2*t + 2. Let i(g) = -5*g + 7. What is m*x(j) + 2*i(j)?\n | 4*j\n | ibivibiv/math_instruct | |
Which is the nearest to -2/9? (a) -19 (b) -1/7 (c) -530 (d) -1.6\n | b\n | ibivibiv/math_instruct | |
How many minutes are there in 3/10 of a week?\n | 3024\n | ibivibiv/math_instruct | |
Divide -4885936 by 55522.\n | -88\n | ibivibiv/math_instruct | |
Let p = 70.83 + 0.17. Let m = -75 + p. Put m, 2/11, 3/4 in descending order.\n | 3/4, 2/11, m\n | ibivibiv/math_instruct | |
Calculate 259907.1 - 7.56.\n | 259899.54\n | ibivibiv/math_instruct | |
Solve 0 = -0*o + 3*o + 12 for o.\n | -4\n | ibivibiv/math_instruct | |
Let c = -138 + 142. Let w(i) be the second derivative of 3/2*i**2 + 0*i**3 + 0*i**c + 4*i + 0 + 1/5*i**5. Differentiate w(v) with respect to v.\n | 12*v**2\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 40 and 20.\n | 40\n | ibivibiv/math_instruct | |
Is 496 a multiple of 31?\n | True\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Network Flow Optimization
1. Suppose we have a network with node set $$N = \{1,\dots, n\}$$ and arc set $$E$$. $$(i, j) \in E$$ if there is a link between node $$i$$ and node $$j$$. We need to send $$L$$ commodities from t... | Let's begin by discussing the concept of network flow optimization and its significance in various fields. A network can be thought of as a graph where nodes represent entities, and arcs denote communication or interaction between these entities. For instance, in transportation networks, nodes could signify cities, wh... | ibivibiv/math_instruct | |
Let d(x) be the third derivative of 49*x**5/60 + 7*x**3/6 + 301*x**2. Let p(v) = -2*v. Give p(d(j)).\n | -98*j**2 - 14\n | ibivibiv/math_instruct | |
Let k(p) = 2*p**2. Let h(x) = 100*x - 15. Let r(o) = -o + 1. Let g(v) = -4*h(v) - 60*r(v). Give g(k(j)).\n | -680*j**2\n | ibivibiv/math_instruct | |
Evaluate -11 + 24 - (17 + -15).\n | 11\n | ibivibiv/math_instruct | |
Let c = -6 - -8. Let z be -3*(8/(-4))/6. Which is smaller: z or c?\n | z\n | ibivibiv/math_instruct | |
Let u = 0.28 + 0.02. Let d = 0.9587 + 5.0413. Let v = 0.2 + 0.2. Sort v, u, d in descending order.\n | d, v, u\n | ibivibiv/math_instruct | |
-42 (base 14) to base 11\n | -53\n | ibivibiv/math_instruct | |
Let j = -480 - -480. Is j at most -0.162?\n | False\n | ibivibiv/math_instruct | |
b"What is the dth term of 288, 286, 284, 282, 280?\n" | -2*d + 290\n | ibivibiv/math_instruct | |
What is -11033 (base 6) in base 13?\n | -90c\n | ibivibiv/math_instruct | |
Let m be ((-1)/4)/((-2)/(-4))*-8. Let d(a) = 27*a**2 + 7*a - 6. Let c be d(m). Suppose -5*t + 0*z = -z - 748, 3*t + 2*z = c. Does 30 divide t?\n | True\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 666 and 27.\n | 1998\n | ibivibiv/math_instruct | |
Let x(z) = -7*z**3 - z - 4. Suppose -5*v = 4*q - 0*q + 18, 4 = -3*q + v. What is the least common multiple of x(q) and 12?\n | 108\n | ibivibiv/math_instruct | |
What is the value of (-80)/(-100)*(-15)/2?\n | -6\n | ibivibiv/math_instruct | |
Let z(c) be the second derivative of -c**3/6 + 6*c**2 - 19*c. Let h be z(-15). Suppose h*k = 24*k + 171. Is 19 a factor of k?\n | True\n | ibivibiv/math_instruct | |
Collect the terms in -3206*a + 1607*a + 1612*a.\n | 13*a\n | ibivibiv/math_instruct | |
What is the biggest value in 258/25, -5684, 0.5, 4/5, -0.3?\n | 258/25\n | ibivibiv/math_instruct | |
Which is the second biggest value? (a) 3.4 (b) 190 (c) -5 (d) 1 (e) -2/5\n | a\n | ibivibiv/math_instruct | |
What is the thousands digit of 6050?\n | 6\n | ibivibiv/math_instruct | |
Rearrange 3*d**3 - 4*d**3 + 14*d + 18*d + 2 - 46*d - 10 to the form u*d**2 + s + b*d + h*d**3 and give b.\n | -14\n | ibivibiv/math_instruct | |
Simplify (2 + (sqrt(242) - (2 + sqrt(242)))**2 + sqrt(242))*-5 + ((sqrt(288)*-1*-1 - sqrt(288))*-4)**2.\n | -55*sqrt(2) - 30\n | ibivibiv/math_instruct | |
((-30450)/200)/(-87)*(-4)/3\n | -7/3\n | ibivibiv/math_instruct | |
Let r be 3 + -10 + 7 + -7. Let p be (r - (-215)/30)/(3/135). Solve 55/6*o**2 - 5/3 - p*o = 0.\n | -2/11, 1\n | ibivibiv/math_instruct | |
-4 + -72.434\n | -76.434\n | ibivibiv/math_instruct | |
How many kilograms are there in six fifths of a tonne?\n | 1200\n | ibivibiv/math_instruct | |
Suppose 264 = 4*r - 3*b, -b = -3*b. Let h be 1/(2*3/r). Suppose -7914 = h*j - 17*j. Is j a prime number?\n | True\n | ibivibiv/math_instruct | |
Add together 112362 and -13415.\n | 98947\n | ibivibiv/math_instruct | |
Solve -6*m + 12 = 6, -3*u + 6 = -3*m for u.\n | 3\n | ibivibiv/math_instruct | |
What is 371 minutes before 9:07 AM?\n | 2:56 AM\n | ibivibiv/math_instruct | |
Let l(w) = -w**2 - w + 1. Let n(m) = 3*m**2 + 4*m - 2. Let r be 4 + -5*(-20)/25 + -4. What is r*l(o) + n(o)?\n | -o**2 + 2\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"Show that $\cos(A-B)-\cos(A+B)=2\sin A\sin B.$
Using compound angle and identity for $\cos.$
Anybody have an idea how to solve this question?
Cheers all...
-
What do you mean by "compound angle and identity for cosine"? Do... | To begin, let us clarify what is meant by "compound angle and identity for cosine." Compound angles refer to expressions involving multiple trigonometric functions added together, specifically those formed from the sum or difference of two angles. An identity, in this context, is an equation that holds true for any va... | ibivibiv/math_instruct | |
What is -0.00000000040096 rounded to seven dps?\n | 0\n | ibivibiv/math_instruct | |
Let h(r) = -r**3 - 17*r**2 - 34*r + 10. Let b be h(-15). Calculate the greatest common factor of b and 20.\n | 10\n | ibivibiv/math_instruct | |
Suppose -5*u + a = -433, 3*u - 5*a = -a + 253. Is (u/9)/((-1)/(-267)) a prime number?\n | False\n | ibivibiv/math_instruct | |
Let i be (4/10)/(-4 + 63/15). Solve i*n = 2*c + 6, 4*c - 10 = -c for n.\n | 5\n | ibivibiv/math_instruct | |
Let u(w) = 1. Let n(k) = -41*k + 1840. Let i be n(45). Let f(y) = -y - 27. Calculate i*u(r) - f(r).\n | r + 22\n | ibivibiv/math_instruct | |
Solve 9667*c - 1044 = 9725*c for c.\n | -18\n | ibivibiv/math_instruct | |
Suppose -196 = -66*l + 17*l. Suppose l*y = 2*b - 12280, 4*y + 6140 = b + 7*y. What is b rounded to the nearest 1000?\n | 6000\n | ibivibiv/math_instruct | |
What is next in 519188, 1038387, 1557582, 2076773, 2595960?\n | 3115143\n | ibivibiv/math_instruct | |
(20/(-150))/((35/15)/1)\n | -2/35\n | ibivibiv/math_instruct | |
Suppose -s + 243 - 226 = -4*u, 2*u + 11 = s. Let h(q) = -6*q**2 - 3*q - 1. Give h(u).\n | -46\n | ibivibiv/math_instruct | |
Three letters picked without replacement from dzwdzzzzdzzzwdwdd. What is prob of picking 1 z and 2 w?\n | 3/85\n | ibivibiv/math_instruct | |
Let h = 159 - 45. Let k = h - 26. List the prime factors of k.\n | 2, 11\n | ibivibiv/math_instruct | |
Let j be (3 - 1)/2 - 20/12. Suppose -m = -p + 11 + 3, 0 = -2*m + 2. Let i be 17/p + 8/(-60). Which is the nearest to j? (a) i (b) 4 (c) -0.4\n | c\n | ibivibiv/math_instruct | |
What is the highest common divisor of 52975160 and 274?\n | 274\n | ibivibiv/math_instruct | |
Product of -296 and 163394.\n | -48364624\n | ibivibiv/math_instruct | |
What is the thousands digit of 3334036?\n | 4\n | ibivibiv/math_instruct | |
Find the first derivative of -2268 - 8144*u - 1853 - 3145 wrt u.\n | -8144\n | ibivibiv/math_instruct | |
What is (-10101)/1131 + (-6)/(-4)*6?\n | 2/29\n | ibivibiv/math_instruct | |
Let c(g) be the second derivative of g**3/6 - g**2/2 + g. Let o be c(3). Determine a, given that -13*a**3 + 16*a**3 - 4*a**2 + a**o = 0.\n | 0, 1\n | ibivibiv/math_instruct | |
What comes next: 63486331, 126972659, 190458987?\n | 253945315\n | ibivibiv/math_instruct | |
Work out -42401.147 * 0.2.\n | -8480.2294\n | ibivibiv/math_instruct | |
What comes next: -40234, -40170, -40062, -39910, -39714?\n | -39474\n | ibivibiv/math_instruct | |
Suppose 50 = 7*k - 2*k. Suppose 0 = -d + 4*h + k, 2*d + 5*h + 8 = 2. Calculate the remainder when (d + -1)/(2/20) is divided by 7.\n | 3\n | ibivibiv/math_instruct | |
Let z(d) = 423*d + 55301. What is z(-142)?\n | -4765\n | ibivibiv/math_instruct | |
List the prime factors of 1330.\n | 2, 5, 7, 19\n | ibivibiv/math_instruct | |
Let s = -2332 - -2336. Which is the nearest to -5? (a) -2.5 (b) -1 (c) s\n | a\n | ibivibiv/math_instruct | |
Let f be ((-920)/(-6))/((-4)/(11 - 47)). Suppose -18*x = -6*x - f. Does 57 divide x?\n | False\n | ibivibiv/math_instruct | |
Solve 6*k - 426 = 0, -2*u - 2*k = -832 + 684 for u.\n | 3\n | ibivibiv/math_instruct | |
Is 4 a factor of 75844?\n | True\n | ibivibiv/math_instruct | |
Suppose v = -2*d - 24, -30*v + 28*v = -3*d - 8. Let a(w) = -62*w - 492. What is a(v)?\n | 4\n | ibivibiv/math_instruct | |
Let a(z) be the third derivative of -40*z**4/3 + 209*z**3/6 + 29*z**2. What is the derivative of a(g) wrt g?\n | -320\n | ibivibiv/math_instruct | |
Let j(p) = -p**3 - 93*p**2 + 74*p - 2086. Calculate j(-94).\n | -206\n | ibivibiv/math_instruct | |
Let f = 16.91 + -17. Let h = -0.61 + f. What is h rounded to 0 dps?\n | -1\n | ibivibiv/math_instruct | |
Solve 44*m - 45 = 35*m for m.\n | 5\n | ibivibiv/math_instruct | |
Suppose 2*v + 3*x = 21565, -54*v = -50*v + x - 43135. Suppose -18*f - 4358 = -v. What is the greatest common factor of f and 21?\n | 21\n | ibivibiv/math_instruct | |
Calculate prob of sequence aa when two letters picked without replacement from lalaalalkalllaaakk.\n | 28/153\n | ibivibiv/math_instruct | |
Solve -4*t + 7957*k + 21 = 15921*k - 7965*k, 4*t = 4*k + 12 for t.\n | 6\n | ibivibiv/math_instruct |
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