instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Suppose f = 2*w - 0*f + 21, -4*w - 4*f = 12. Does 6 divide w + (-2250)/(-81) + (-6)/(-27)?\n | False\n | ibivibiv/math_instruct | |
Suppose -a + 4 = 8. Let w be (3/(-6))/((a/(-1))/(-8)). Which is greater: w or -8/23?\n | w\n | ibivibiv/math_instruct | |
Solve 0 = 2*f - 12 + 10 for f.\n | 1\n | ibivibiv/math_instruct | |
What is -121.8478 + 0.1?\n | -121.7478\n | ibivibiv/math_instruct | |
Let f(o) = 36*o**2 - 5*o - 45. Let y = 37 - 45. Let v be f(y). What is v rounded to the nearest one hundred?\n | 2300\n | ibivibiv/math_instruct | |
Sort -3, 178, 1, 2 in increasing order.\n | -3, 1, 2, 178\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Limit of $L^p$ norm
Could someone help me prove that given a finite measure space $$(X, \mathcal{M}, \sigma)$$ and a measurable function $$f:X\to\mathbb{R}$$ in $$L^\infty$$ and some $$L^q$$, $$\displaystyle\lim_{p\to\inft... | The question you're asking about is a fundamental result in the theory of Lebesgue integration, which establishes the relationship between the L^p norm of a measurable function f with respect to a finite measure space (X, M, σ) and its essential supremum norm, denoted by ||f||∞. Before proving this result, let's first... | ibivibiv/math_instruct | |
Calculate the remainder when 1059 is divided by 98.\n | 79\n | ibivibiv/math_instruct | |
Let x(m) = -71*m + 34*m + 34*m + 2. Determine x(2).\n | -4\n | ibivibiv/math_instruct | |
Is 356341 prime?\n | False\n | ibivibiv/math_instruct | |
Let j(n) be the third derivative of -n**6/3 + n**5/10 + n**4/6 + 62*n**2. What is the third derivative of j(a) wrt a?\n | -240\n | ibivibiv/math_instruct | |
Solve -3434 = -274*d - 694 for d.\n | 10\n | ibivibiv/math_instruct | |
What is 22130322 (base 5) in base 14?\n | 50283\n | ibivibiv/math_instruct | |
Let u = -0.4 + 0. Let h = -43.52 - 0.48. Let j = 43.8 + h. Which is the nearest to -0.1? (a) u (b) -4 (c) j\n | c\n | ibivibiv/math_instruct | |
What are the prime factors of 99616293?\n | 3, 7, 1581211\n | ibivibiv/math_instruct | |
What is the cube root of 623 to the nearest integer?\n | 9\n | ibivibiv/math_instruct | |
Which is the nearest to -3.68? (a) 5 (b) -0.1 (c) -1/4\n | c\n | ibivibiv/math_instruct | |
Sort -5, 4, 6, 5 in descending order.\n | 6, 5, 4, -5\n | ibivibiv/math_instruct | |
Collect the terms in 10806342*n**3 - 21612671*n**3 + 10806327*n**3.\n | -2*n**3\n | ibivibiv/math_instruct | |
Let d(m) = -41718*m**2 + 561*m - 1122. Let x(l) = -149*l**2 + 2*l - 4. Let z(y) = 2*d(y) - 561*x(y). Let t(a) = 17*a + 1. What is z(t(r))?\n | 44217*r**2 + 5202*r + 153\n | ibivibiv/math_instruct | |
Rearrange 2 + 7*o + 5*o**2 - 8*o + o**4 + o - 2*o to b*o**2 + t + l*o**4 + m*o**3 + q*o and give m.\n | 0\n | ibivibiv/math_instruct | |
What is 616 minutes after 1:58 AM?\n | 12:14 PM\n | ibivibiv/math_instruct | |
Let f be (-4)/(-3)*(-18)/(-4). Suppose -3*j + 4*m = -56, f*j - 2*j - m - 79 = 0. List the prime factors of j.\n | 2, 5\n | ibivibiv/math_instruct | |
Suppose 3192 = 3*u - 104*k + 101*k, -4*k - 5323 = -5*u. Calculate the greatest common divisor of u and 194.\n | 97\n | ibivibiv/math_instruct | |
Calculate -4 - (-6 - (-3 - 1))/(-1).\n | -6\n | ibivibiv/math_instruct | |
Suppose -5*m + 6 = -u, 274*m = 278*m - u - 5. What is the second smallest value in -0.2, m, -26/7, -2/3?\n | -2/3\n | ibivibiv/math_instruct | |
(2 + 1152/960*(-620)/6)*-1\n | 122\n | ibivibiv/math_instruct | |
For 5 days, Chantel makes 2 friendship bracelets every day. She gives away x bracelets to her friends at school. Then for four days, she makes 3 friendship bracelets every day. Then she gives away 6 bracelets to her friends at soccer practice. How many bracelets does Chantel have in the end?
If we know the answer to th... | For the first 5 days, Chantel makes 2 bracelets every day, so she has 5 * 2 = 10 bracelets.
She gives away x bracelets to her friends at school, so she has 10 - x bracelets left.
For the next 4 days, she makes 3 bracelets every day, so she has 4 * 3 = 12 bracelets.
She gives away 6 bracelets to her friends at soccer pr... | ibivibiv/math_instruct | |
Is 962809 composite?\n | True\n | ibivibiv/math_instruct | |
Total of 125863 and 0.2222268.\n | 125863.2222268\n | ibivibiv/math_instruct | |
What is the next term in -36, -66, -96, -126?\n | -156\n | ibivibiv/math_instruct | |
Expand (-3*c + 4*c + 5*c**2 + 0*c)*(-4 + 4 - 7*c**2) + (2 + 2 - 5)*(-2*c**4 + 21*c - 21*c).\n | -33*c**4 - 7*c**3\n | ibivibiv/math_instruct | |
Let u(i) = 4*i - 1. Let y(b) = 29*b + 9. Let w(c) = -4*c - 2 + 7*c - 5*c - 5*c. Let n(v) = -9*w(v) - 2*y(v). Give 2*n(g) - 3*u(g).\n | -2*g + 3\n | ibivibiv/math_instruct | |
Suppose r = -r + 26. Suppose 2*k - 19 - 14 = -5*f, -3*k + 17 = f. Calculate the remainder when r is divided by f.\n | 3\n | ibivibiv/math_instruct | |
Collect the terms in 297 - 19*y**3 + 315 - 612.\n | -19*y**3\n | ibivibiv/math_instruct | |
Let k(w) = -25589*w - 8. Let a be 30/4*(-8)/5. Let n be k(a). Let m = n - -14792940. What is m rounded to the nearest 1000000?\n | 15000000\n | ibivibiv/math_instruct | |
Is 4305127013 composite?\n | True\n | ibivibiv/math_instruct | |
Let p = -18 - -52. Let h = 103 + p. Let z(v) = -v**3 + 3*v**2 + 10*v + 23. Calculate the remainder when h is divided by z(0).\n | 22\n | ibivibiv/math_instruct | |
Is 70351 a prime number?\n | True\n | ibivibiv/math_instruct | |
Collect the terms in 0*f + 32*f**3 + 0*f + 0*f.\n | 32*f**3\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-49.014 + (59.883 - -43.485) | 54.3540 | ibivibiv/math_instruct | |
Let r be (-12)/(-8)*(-13 - -2). Let k = -16 - r. Which is the closest to -1? (a) k (b) -2/15 (c) 0.4\n | b\n | ibivibiv/math_instruct | |
What is 17656 to the power of 1/4, to the nearest integer?\n | 12\n | ibivibiv/math_instruct | |
In base 7, what is 33 - 3221?\n | -3155\n | ibivibiv/math_instruct | |
Let i(w) = -121*w + 368. Let x be i(3). Factor -2/11*t**x + 16/11*t**2 + 4/11 + 4/11*t**3 - 4/11*t**4 + 14/11*t.\n | -2*(t - 2)*(t + 1)**4/11\n | ibivibiv/math_instruct | |
Which is the closest to 1/9? (a) -13 (b) -1/181 (c) 0.5\n | b\n | ibivibiv/math_instruct | |
What is the units digit of 304314?\n | 4\n | ibivibiv/math_instruct | |
Let n = 1727 + -1726. Which is the smallest value? (a) 1/2 (b) n (c) -200\n | c\n | ibivibiv/math_instruct | |
What is the highest common factor of 41 and 2?\n | 1\n | ibivibiv/math_instruct | |
Simplify sqrt(45) - -4*sqrt(405) - (1*sqrt(270)/sqrt(6) + sqrt(45)).\n | 33*sqrt(5)\n | ibivibiv/math_instruct | |
Suppose 4*n - 251 = 9. Suppose n = 7*j - 20*j. Let t = 0.12 + 4.88. Which is the closest to t? (a) j (b) 4 (c) 2\n | b\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 99800 and 3100.\n | 100\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {f: 2, c: 1, g: 1, s: 1, a: 4, j: 3}. Give prob of picking 1 j, 1 a, 1 g, and 1 c.\n | 4/165\n | ibivibiv/math_instruct | |
How many minutes are there between 3:40 PM and 3:44 PM?\n | 4\n | ibivibiv/math_instruct | |
Suppose -2*f = -0*z + 5*z - 18, -5*z + 14 = f. Let h(g) = 2*g**2 - 2 - 15*g**3 - 6*g**2 - 2 + 26*g**3. Let s(m) = 23*m**3 - 9*m**2 - 9. What is f*s(o) - 9*h(o)?\n | -7*o**3\n | ibivibiv/math_instruct | |
What is 49/4 of a micrometer in nanometers?\n | 12250\n | ibivibiv/math_instruct | |
Let g(k) be the second derivative of 254*k + 0 - 71/2*k**2 - 23/2*k**3. Find the first derivative of g(r) wrt r.\n | -69\n | ibivibiv/math_instruct | |
Simplify (i**1)**48/(i**0/i*i*i**2) assuming i is positive.\n | i**46\n | ibivibiv/math_instruct | |
Let x(p) = p**3 - 17*p**2 + 178*p - 823. Give x(5).\n | -233\n | ibivibiv/math_instruct | |
Which is the second biggest value? (a) -4 (b) -9857.32 (c) 0\n | a\n | ibivibiv/math_instruct | |
Evaluate ((2/(-16))/((-381)/5080))/(10/6).\n | 1\n | ibivibiv/math_instruct | |
What is 699.6887 microseconds in seconds?\n | 0.0006996887\n | ibivibiv/math_instruct | |
Let g(f) be the third derivative of f**8/48 - 19*f**5/20 + 1033*f**4/12 + 1999*f**2. Find the second derivative of g(n) wrt n.\n | 140*n**3 - 114\n | ibivibiv/math_instruct | |
Let d = -9 - -11. Suppose -3*c = -4*p + 14 - d, 4*p + 4*c = 40. Solve -4*g = -p*g for g.\n | 0\n | ibivibiv/math_instruct | |
Let i = 0 + 4. Let w be 30/i*12/9. What is the units digit of ((-9)/(-15))/(1/w)?\n | 6\n | ibivibiv/math_instruct | |
Let t = 3 - -2. Suppose -p = -t*p + 8. What is g in g**p + 2/3 - 7/3*g = 0?\n | 1/3, 2\n | ibivibiv/math_instruct | |
Expand (-1 + 526*y - 525*y + 2)*(-y**4 + y**4 + 2*y**4).\n | 2*y**5 + 2*y**4\n | ibivibiv/math_instruct | |
Simplify (((r*r**(-1)*r)/r)**27/(r*r*r**(-1)*r*r)**(1/24))/((r**(2/7))**23*(r**1)**41) assuming r is positive.\n | r**(-2671/56)\n | ibivibiv/math_instruct | |
Let q = 2563.691 + -2560. Round q to one dp.\n | 3.7\n | ibivibiv/math_instruct | |
Let w(r) = -746*r - 733. Let f be w(-3). What is the highest common factor of f and 43?\n | 43\n | ibivibiv/math_instruct | |
Round -0.010541763956 to three dps.\n | -0.011\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"## Problem
Calculate the energy $E_\infty$ and the average power $P_\infty$ for the CT signal $x(t)=\sqrt{2t}u(t)$
## Solution 1
Compute $E\infty$
$E\infty=\int_{-\infty}^\infty |x(t)|^2dt$
$E\infty=\int_{-\infty}^\infty... | This educational piece will delve into the problem of calculating the energy ($E\_∞$) and the average power ($P\_∞$) for the CT (continuous-time) signal x(t)=√2t * u(t), where u(t) represents the unit step function. We'll discuss essential concepts in signals and systems, focusing on rigorous mathematical derivations ... | ibivibiv/math_instruct | |
Calculate prob of sequence tpp when three letters picked without replacement from {t: 5, p: 2, i: 6}.\n | 5/858\n | ibivibiv/math_instruct | |
Suppose -51*b - 44*b = -285. Solve 3/5*v**5 + b*v**4 + 21/5*v**2 + 6/5*v + 27/5*v**3 + 0 = 0.\n | -2, -1, 0\n | ibivibiv/math_instruct | |
Suppose 3*i - 15 = -h, 0*i + i - 5 = 2*h. Suppose i*t = -24 - 1. Let q be 1*2*(-345)/30. Sort 4, t, q in increasing order.\n | q, t, 4\n | ibivibiv/math_instruct | |
Solve -4364*s = -4372*s - 40 for s.\n | -5\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 13 and 2582759101.\n | 13\n | ibivibiv/math_instruct | |
Put 2/5, 1, 3/5, -1, 6/113 in increasing order.\n | -1, 6/113, 2/5, 3/5, 1\n | ibivibiv/math_instruct | |
Let l(z) = -z. Let m = 44 + -41. Suppose 0 = -8*d + 13 + m. Let h(x) = 22 + 2*x**d + 6*x**2 - 22. Give h(l(v)).\n | 8*v**2\n | ibivibiv/math_instruct | |
What is the third smallest value in 42, -2, -0.2, -1?\n | -0.2\n | ibivibiv/math_instruct | |
Which is the third biggest value? (a) -1/9 (b) 5 (c) -284\n | c\n | ibivibiv/math_instruct | |
Calculate -3*(-30)/(-45)*1/12.\n | -1/6\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 8070 and 33.\n | 88770\n | ibivibiv/math_instruct | |
Let a = -0.02 - -0.42. Let m = -8.353 - -8.653. Put m, a, -7/5, 2 in decreasing order.\n | 2, a, m, -7/5\n | ibivibiv/math_instruct | |
What is 6865 to the power of 1/10, to the nearest integer?\n | 2\n | ibivibiv/math_instruct | |
Rearrange (-12*m - m + 37*m)*(-5*m + 5*m - 4*m)*(-4*m - 2*m + 2*m)*(2*m + 1 - 1) to the form w*m**3 + f*m**4 + a*m + d*m**2 + y and give f.\n | 768\n | ibivibiv/math_instruct | |
Let k(v) = -v + 10. Let b(x) = x - 8. Let i(j) = -5*b(j) - 4*k(j). Let r(t) = -98*t. What is r(i(q))?\n | 98*q\n | ibivibiv/math_instruct | |
0.1 * -388595\n | -38859.5\n | ibivibiv/math_instruct | |
How many minutes are there in fourty-two fifths of a day?\n | 12096\n | ibivibiv/math_instruct | |
Is 215407 composite?\n | True\n | ibivibiv/math_instruct | |
Two-fifths of the seats in an auditorium that holds 500 people are currently taken. It was found that 1/10 of the seats are broken. How many seats are still available? | The auditorium has 500/ 2/5 = 200 seats that are already taken.
The auditorium has 500/ 1/10 = 50 broken seats.
The total number of unavailable seats is 200 + 50 = 250.
There are 500 - 250 = 250 seats still available.
The answer is 250 | ibivibiv/math_instruct | |
Work out 81 * -12990.\n | -1052190\n | ibivibiv/math_instruct | |
Let o be (-1)/((6/(-2))/(-39)). Let m be 2/1 - (-2 - 0)/1. Put o, 3, m in descending order.\n | m, 3, o\n | ibivibiv/math_instruct | |
Let i(h) = -10*h**3 - 3*h**2 + 33*h - 12. What are the prime factors of i(-6)?\n | 2, 3, 307\n | ibivibiv/math_instruct | |
What is -406396.82 rounded to the nearest one thousand?\n | -406000\n | ibivibiv/math_instruct | |
Simplify (r**(-6)/r)/(r/(r**(-3/8)/r))*(r*r**(-9/5)*r*r)/(r*r/r**(-3)) assuming r is positive.\n | r**(-527/40)\n | ibivibiv/math_instruct | |
Find the second derivative of f**2*r**3 + 5*f**2*r**2 + 9*f**2*r + 159*f**2 - 8*f*r**3 + 10*f - 7*r**3 - 13*r**2 wrt f.\n | 2*r**3 + 10*r**2 + 18*r + 318\n | ibivibiv/math_instruct | |
Solve 29*y = -5*s + 17*y + 24, 77484*s - 77484*s - 5*y = -10 for s.\n | 0\n | ibivibiv/math_instruct | |
What is 3456 (base 10) in base 16?\n | d80\n | ibivibiv/math_instruct | |
What is the square root of 8209834064 to the nearest integer?\n | 90608\n | ibivibiv/math_instruct |
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