instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
-4768*2.76\n | -13159.68\n | ibivibiv/math_instruct | |
What is next in 132, 137, 146, 159?\n | 176\n | ibivibiv/math_instruct | |
Let p be ((-2)/4)/((-2)/8). Suppose -4*u + t = -3, t = p + 3. Let x(y) = -3*y + 3*y + 3*y**2 - 2*y**u. Let n(f) = -5*f. What is x(n(q))?\n | 25*q**2\n | ibivibiv/math_instruct | |
What is the greatest common factor of 69 and 23?\n | 23\n | ibivibiv/math_instruct | |
What is next in -393, -2901, -9349, -21597, -41505, -70933?\n | -111741\n | ibivibiv/math_instruct | |
Let o = 0.1 + -0.2. Let l = 0.2 + o. Let p = 2 - 4. What is the closest to l in p, -1, 2/5?\n | 2/5\n | ibivibiv/math_instruct | |
What is 1/(60/(-118)) + (-1987)/59610?\n | -2\n | ibivibiv/math_instruct | |
Sort 76, 2, -0.05, 3, 7, -15 in decreasing order.\n | 76, 7, 3, 2, -0.05, -15\n | ibivibiv/math_instruct | |
What is the value of ((-715)/(-650) - (-2)/(-20))*25?\n | 25\n | ibivibiv/math_instruct | |
Solve -11*m + c = 28, 3*m + 2*c - 64104 = -64123 for m.\n | -3\n | ibivibiv/math_instruct | |
What is 0.00000031594 rounded to 7 dps?\n | 0.0000003\n | ibivibiv/math_instruct | |
Collect the terms in 2*n - 2336 + 2336 + 36*n**2.\n | 36*n**2 + 2*n\n | ibivibiv/math_instruct | |
Let j(u) = u**3 - 4*u**2 + 5*u - 6. Suppose l = 3*l - 10. Let f(y) = 5*y - 10. Calculate the remainder when j(5) is divided by f(l).\n | 14\n | ibivibiv/math_instruct | |
In base 13, what is 32 - 87?\n | -55\n | ibivibiv/math_instruct | |
Let a = 119/38 - -23/114. What is the fourth smallest value in -29/5, 4, 0.2, a?\n | 4\n | ibivibiv/math_instruct | |
Let l be 20/(-25) + (-29)/(-5). Let c be (1 + 0 - l) + 7. Suppose -51 = -x + c*b + 9, 3*x = 5*b + 180. Is 13 a factor of x?\n | False\n | ibivibiv/math_instruct | |
Calculate prob of picking 2 t when two letters picked without replacement from {t: 15, f: 3, a: 2}.\n | 21/38\n | ibivibiv/math_instruct | |
Let n(s) = -9*s**3 + 58*s**2 - 1802*s + 12853. Determine n(7).\n | -6\n | ibivibiv/math_instruct | |
Let o = 7 + -10. Let t = o - -7. Suppose 0 = -4*s - t*u + 40, 5*s - 21 = 4*u + 29. What is the units digit of s?\n | 0\n | ibivibiv/math_instruct | |
Let w = 12 + 3. Let k be 184/18 - 4/18. Let x(s) = 4*s - 11. What is the remainder when x(k) is divided by w?\n | 14\n | ibivibiv/math_instruct | |
Let s = 28 + -13. Suppose s = 4*m + m. Let z(r) = m*r + 9 - 9 + r. Let g(y) = -3*y**2. Give z(g(k)).\n | -12*k**2\n | ibivibiv/math_instruct | |
Does 17 divide 5038433?\n | False\n | ibivibiv/math_instruct | |
Evaluate (5/5)/(56/38080*68).\n | 10\n | ibivibiv/math_instruct | |
Let w be (-2 + 8)/((-1)/1). Let r(m) = -3*m + 29. Let h be r(8). Suppose -a - 48 = h*a. Do w and a have different values?\n | True\n | ibivibiv/math_instruct | |
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"# Tension / Equilibrium Question
## Homework Statement
A load on which the force of gravity is 46 N hands from the centre of a frictionless clothesline, pulling its centre down so that each half of the line makes an angle o... | When analyzing mechanical systems in physics, it is common to break down forces into their components along different axes. This allows us to simplify complex problems by considering only the relevant forces acting in each direction separately. In your problem, the forces are broken down into horizontal (X) and vertic... | ibivibiv/math_instruct | |
What is the next term in 4579, 9167, 13755?\n | 18343\n | ibivibiv/math_instruct | |
Suppose 5*h + 2*c + 13 = -2, 0 = 3*c. Is 228*6/(-27)*h a multiple of 38?\n | True\n | ibivibiv/math_instruct | |
How many minutes are there between 12:36 PM and 12:07 AM?\n | 691\n | ibivibiv/math_instruct | |
-8.08+0.7\n | -7.38\n | ibivibiv/math_instruct | |
Express (2 - 2 - 1)*(-g - 4 + 4) - 2 + g + 2 + (2 - g - 2)*(-1 - 1 + 0) + 10*g - 4*g + 17*g + (-1 + 25 + 17)*(-5 + 5 - 2*g) in the form y*g + d and give y.\n | -55\n | ibivibiv/math_instruct | |
What is the value of (-135)/21*(-6356)/(-2270)?\n | -18\n | ibivibiv/math_instruct | |
Calculate prob of sequence fyw when three letters picked without replacement from {n: 1, l: 4, y: 1, w: 1, f: 4}.\n | 2/495\n | ibivibiv/math_instruct | |
Two letters picked without replacement from clvcwqii. What is prob of picking 2 i?\n | 1/28\n | ibivibiv/math_instruct | |
Let i(z) be the third derivative of z**5/60 + z**2. Let c(r) = 8*r**2 - r + 1. Let p be c(-1). Let m(j) = 34 - 34 + p*j. Determine i(m(u)).\n | 100*u**2\n | ibivibiv/math_instruct | |
Let k be 0 + -1 + -6 + -1. Let a(y) = y**3 + 11*y**2 + 7*y - 18. Is a(k) composite?\n | True\n | ibivibiv/math_instruct | |
What is the greatest common factor of 868 and 13600692?\n | 868\n | ibivibiv/math_instruct | |
Let p(q) = -q**3 + 11*q**2 - 30*q + 22. Determine p(6).\n | 22\n | ibivibiv/math_instruct | |
Work out -1.0086 * 45.\n | -45.387\n | ibivibiv/math_instruct | |
Collect the terms in -1 + 1 - 33002*o + 66116*o - 33111*o.\n | 3*o\n | ibivibiv/math_instruct | |
What is the result of the following expression?
67.595 % -25.2945 | -8.2885 | ibivibiv/math_instruct | |
Suppose 0 = 3*z - 6*z. Let i(t) = 20*t. Let p be i(z). Solve -4*c = -s + 20, -3*c = -p*s + 5*s - 8 for s.\n | 4\n | ibivibiv/math_instruct | |
Let y(i) = i. Let g(f) = 2*f + 2. Let q(h) = -g(h) + 5*y(h). What is q(2)?\n | 4\n | ibivibiv/math_instruct | |
Let a(d) = d**3 + 38*d**2 + 25*d + 26. What is the hundreds digit of a(-37)?\n | 4\n | ibivibiv/math_instruct | |
Suppose 0 = 4*m + 8*m + 1368. Let b be (-4)/(-16) + m/(-24). Solve -5 - b = -2*c for c.\n | 5\n | ibivibiv/math_instruct | |
Let q(b) = 10*b**3 - 3*b**2 - 7*b + 8. Suppose -41 = -3*z + 46. Calculate the remainder when z is divided by q(1).\n | 5\n | ibivibiv/math_instruct | |
What is -8963898 divided by -6?\n | 1493983\n | ibivibiv/math_instruct | |
Let w = -202 + 22. Let p = 899/5 + w. Which is greater: p or -2?\n | p\n | ibivibiv/math_instruct | |
Solve 2*f = 5*x, 26 = -4*f + 67*x - 70*x for f.\n | -5\n | ibivibiv/math_instruct | |
Suppose -5*w - q + 32 = -2, -2*q - 16 = -4*w. Calculate the smallest common multiple of 8 and w.\n | 24\n | ibivibiv/math_instruct | |
What is 3/16 of a centimeter in micrometers?\n | 1875\n | ibivibiv/math_instruct | |
Simplify ((-1*(sqrt(7) + -2) + sqrt(7) - sqrt(7)) + sqrt(21)/sqrt(75))*-3.\n | -6 + 12*sqrt(7)/5\n | ibivibiv/math_instruct | |
Let q be (-15)/25*5*-1. Let l(x) = -4*x**3 - 4*x**2 - 2*x - 6. Let s(f) = 11*f**3 + 12*f**2 + 6*f + 17. Let k(t) = q*s(t) + 8*l(t). Determine k(-4).\n | -5\n | ibivibiv/math_instruct | |
Let y = -78 - -77. Let r be -1 + (2 - (0 + y)). What is the third derivative of -36*z**2 + r*z**2 - 8*z**2 - 14*z**6 + 4*z**2 wrt z?\n | -1680*z**3\n | ibivibiv/math_instruct | |
What comes next: 101, 226, 339, 434, 505?\n | 546\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 35 and 16363?\n | 1\n | ibivibiv/math_instruct | |
Simplify (-1 + (sqrt(208)*1 - sqrt(208)) + sqrt(208)*2*3 - (-4 + (-1*(sqrt(208) + sqrt(208) + 0) - (4 + sqrt(208) + 0))))**2.\n | 504*sqrt(13) + 16897\n | ibivibiv/math_instruct | |
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"# How to show that the Jeans Criterion for Mass, Radius and Density are equivalent?
The gravitational collapse of a gas cloud can be described by the Jeans Criterion for mass, radius and density of the gas cloud, which is (c... | To demonstrate the equivalence of the Jeans Criteria for Mass, Radius, and Density, let's begin by examining the given equations more closely:
1. Jeans Mass: $$M_J = (\frac{5kT}{G\mu m_H})^\frac{3}{2}(\frac{3}{4\pi\rho_c})^{\frac{1}{2}}$$
2. Jeans Radius: $$R_J=(\frac{15kT}{4\pi G\mu m_H\rho_c})^\frac{1}{2}$$
3. Jean... | ibivibiv/math_instruct | |
What is the nearest to -1 in 0.2, -3, 2/19, 0.19, -27?\n | 2/19\n | ibivibiv/math_instruct | |
(806/(-6324))/((-104)/24)*-24\n | -12/17\n | ibivibiv/math_instruct | |
Solve 0*y - 2*y = -2*g + 2, y + 113 = 97*g + 128 - 496 for y.\n | 4\n | ibivibiv/math_instruct | |
Which is the second smallest value? (a) 2/13 (b) 2 (c) -0.3\n | a\n | ibivibiv/math_instruct | |
Let g be (132/(-198))/((-16)/(-6)). Which is bigger: g or -5/14?\n | g\n | ibivibiv/math_instruct | |
Convert -3 (base 8) to base 2.\n | -11\n | ibivibiv/math_instruct | |
Suppose -4*l - 8 = -24. Suppose -5*p + l = 19. Let c be p/(-2)*(3 + 1). What is the highest common factor of c and 2?\n | 2\n | ibivibiv/math_instruct | |
Let w be 39/15 + (-4)/(-10). Suppose 5*h - 2*l - 8 - 6 = 0, -3*h = -w*l - 12. Let r be -2 + 0 + 4*h. Solve 0 = -2*g - x + 7, -r = 2*g - 3*x + 7 for g.\n | 1\n | ibivibiv/math_instruct | |
Let s(d) be the third derivative of 0*d + 5/24*d**4 + 1/6*d**3 + 0 - d**2. Give s(1).\n | 6\n | ibivibiv/math_instruct | |
What is next in -2196, -4378, -6548, -8706, -10852?\n | -12986\n | ibivibiv/math_instruct | |
Product of -0.02 and -3.\n | 0.06\n | ibivibiv/math_instruct | |
In base 5, what is -33121 - -320130?\n | 232004\n | ibivibiv/math_instruct | |
Factor -3*l**4/5 + 231*l**3/5 - 912*l**2 + 4332*l/5.\n | -3*l*(l - 38)**2*(l - 1)/5\n | ibivibiv/math_instruct | |
Let h be (0 + -2)/(3/5 - 1). Let k = 3.67 - 0.17. Let v = -0.5 + k. Which is the biggest value? (a) -0.3 (b) h (c) v\n | b\n | ibivibiv/math_instruct | |
Let b = 14 + -16. Let q be (-3 - -3)/(4/b). Is 21/(q + (4 - 3)) a multiple of 7?\n | True\n | ibivibiv/math_instruct | |
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"# Who is Schroder Bernstein?
## Main Question or Discussion Point
Who is this person?
The theorem says as long as there is a one-to-one map from X to Y and a one-to-one map from Y to X, there will be a one-to-one and onto ... | The Schröder-Bernstein Theorem is a fundamental principle in set theory, a branch of mathematical logic that studies sets, which are collections of objects. This theorem was proven by German mathematicians Ernst Schröder and Felix Bernstein independently around 1897. It provides conditions under which two sets have th... | ibivibiv/math_instruct | |
Let n(x) = -x**2 + 2. Let h(d) = -3*d**2 + 5. Let w(q) = -2*h(q) + 5*n(q). Let z(t) be the first derivative of 5*t**2/2 + 16. Calculate z(w(m)).\n | 5*m**2\n | ibivibiv/math_instruct | |
Let z = -211 - 110. Let x = z - -304.9. What is x rounded to 0 dps?\n | -16\n | ibivibiv/math_instruct | |
Calculate -43 - ((27 - 44) + -45).\n | 19\n | ibivibiv/math_instruct | |
Which is the nearest to -0.2? (a) -3 (b) -41/76 (c) -2/11 (d) 2\n | c\n | ibivibiv/math_instruct | |
Suppose 0 = -2*i + 3*q + 36, -2*q - 2*q - 68 = -4*i. Let m be 4203/i - (-2)/(-10). Suppose -4*k = -m - 440. Does 13 divide k?\n | False\n | ibivibiv/math_instruct | |
What is the product of 0.039 and 1057437?\n | 41240.043\n | ibivibiv/math_instruct | |
Solve -2*s = 2*g - 2, 2*g - 54 = 5*g - 6*s - 93 for g.\n | 5\n | ibivibiv/math_instruct | |
Calculate 876/(-657)*(-3)/16*-20.\n | -5\n | ibivibiv/math_instruct | |
What is prob of picking 2 f when two letters picked without replacement from {f: 3}?\n | 1\n | ibivibiv/math_instruct | |
Simplify 0 + -4 + ((sqrt(1458) - -2*sqrt(1458)) + -2)**2 + -1 + -2.\n | -324*sqrt(2) + 13119\n | ibivibiv/math_instruct | |
Calculate prob of sequence qs when two letters picked without replacement from cnqso.\n | 1/20\n | ibivibiv/math_instruct | |
Is 4841 prime?\n | False\n | ibivibiv/math_instruct | |
Let w(f) = -2*f**3 + 23*f**2 - 1700*f + 37712. Calculate w(19).\n | -3\n | ibivibiv/math_instruct | |
List the prime factors of 1331.\n | 11\n | ibivibiv/math_instruct | |
Sort 0, 1.14, 35, 4, 474, -1 in ascending order.\n | -1, 0, 1.14, 4, 35, 474\n | ibivibiv/math_instruct | |
Is 3640409 a composite number?\n | False\n | ibivibiv/math_instruct | |
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"# Pair wise disjoint open balls
Let $(X,ρ)$ be a metric space and $A$ is a subset of $X$. How do I prove that there exists a family $(B(t,r_{t}))_{t\in\operatorname{Iso}A}$ of pair wise disjoint open balls?
• What is $IsoA$... | Before diving into the main topic, let's review some fundamental definitions from metric spaces. A metric space (X,ρ) consists of a set X together with a function ρ, called a metric, that assigns to every pair of elements x, y in X a nonnegative real number ρ(x,y), called the distance between x and y, satisfying three... | ibivibiv/math_instruct | |
Expand -125*r**2 + 1981608 - 1981608 + (0 - r + 0)*(4*r - 5*r - r).\n | -123*r**2\n | ibivibiv/math_instruct | |
Simplify (r*r**(2/11))**34/(r**(3/5))**(-24) assuming r is positive.\n | r**(3002/55)\n | ibivibiv/math_instruct | |
What is the nearest to 2.4 in 0, 0.2, -1/4, 0.3?\n | 0.3\n | ibivibiv/math_instruct | |
What is the smallest value in -14, -0.09, -0.2?\n | -14\n | ibivibiv/math_instruct | |
-145 (base 7) to base 5\n | -312\n | ibivibiv/math_instruct | |
Express -2299 + 25*b + 2299 + (2 - 2*b - 2)*(-3 + 0 + 1) in the form s + f*b and give f.\n | 29\n | ibivibiv/math_instruct | |
Let w = 611 + -580. Solve w = -2*p + 23 for p.\n | -4\n | ibivibiv/math_instruct | |
Sort 5, 217, -15765.\n | -15765, 5, 217\n | ibivibiv/math_instruct | |
Let s(t) = t**3 + t**2 + 2*t + 1. Let c be s(-1). Let r = 6 - c. Solve -r*z + 12 = -3*z for z.\n | 3\n | ibivibiv/math_instruct | |
Suppose -10*j + 7*j = -27. Let c be (-34)/(-2)*-1 - -2. Is (c/10)/(j/(-1284)) a prime number?\n | False\n | ibivibiv/math_instruct |
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