instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Which is the biggest value? (a) -5 (b) -1/5 (c) -0.04 (d) 0.03\n | d\n | ibivibiv/math_instruct | |
Let t(c) = 4*c**3 + 3*c**2 - 3*c. Let j(u) = -9*u**3 - 7*u**2 + 7*u. Let r(a) = a**3 - 4*a**2 - 4*a - 2. Let p be r(5). What is p*j(k) + 7*t(k)?\n | k**3\n | ibivibiv/math_instruct | |
Let i = -25.7 + 26. Let r = 4.11 + -0.11. What is the nearest to 1 in r, i, 2?\n | i\n | ibivibiv/math_instruct | |
Let y = 1958 + -918. Suppose 0*z - y = l - 3*z, 2*z - 2076 = 2*l. Let w = -2037 - l. What is w rounded to the nearest 100?\n | -1000\n | ibivibiv/math_instruct | |
Which is bigger: -0.4 or 4240?\n | 4240\n | ibivibiv/math_instruct | |
Collect the terms in 59632 + 12*c - 59632.\n | 12*c\n | ibivibiv/math_instruct | |
Let b be 6/(-4)*-2 + -1. Suppose 0 = -w + b. Solve 5*m - w*m = 0 for m.\n | 0\n | ibivibiv/math_instruct | |
Solve 160 - 4 = 39*x for x.\n | 4\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 3448 and 341816.\n | 8\n | ibivibiv/math_instruct | |
Let c = -197 + 562. Is c a composite number?\n | True\n | ibivibiv/math_instruct | |
Let m(w) be the second derivative of -w**4/12 + 4*w**3/3 + 11*w**2/2 - 3*w. Let g be m(9). Calculate the highest common divisor of g and 14.\n | 2\n | ibivibiv/math_instruct | |
Expand (-8 + 4*f + 8)*(4*f - f + 0*f) - 2*f**2 + 3*f**2 + 4*f**2 + (f - 6*f + 22*f)*(0 + 0 - 5*f).\n | -68*f**2\n | ibivibiv/math_instruct | |
Let a(v) be the first derivative of 6/5*v - 4/5*v**2 + 2/15*v**3 + 4. Factor a(q).\n | 2*(q - 3)*(q - 1)/5\n | ibivibiv/math_instruct | |
How many minutes are there between 12:28 PM and 7:08 PM?\n | 400\n | ibivibiv/math_instruct | |
Let q(t) be the first derivative of 2*t**3/3 + t**2/2 - 19*t - 20. Let g(c) be the first derivative of q(c). Determine g(1).\n | 5\n | ibivibiv/math_instruct | |
Let s = 160 - 106. Suppose -j - 16 = -s. Let u = j + 13. Is u a multiple of 17?\n | True\n | ibivibiv/math_instruct | |
What is the product of 27.1 and -2?\n | -54.2\n | ibivibiv/math_instruct | |
Find the length of the longest pole that can be placed in a room 12 m long 8m broad and 9m high.
Answer Choices: (A) 13 (B) 14 (C) 15 (D) 16 (E) 17 | Lets think about the multi-choice question.
Length of longest pole = Length of the diagonal of the room
= sqrt(12^2+8^2+9^2= sqrt(289)= 17 m.
The answer is E. | ibivibiv/math_instruct | |
Let z(h) be the third derivative of 0*h**6 - 1/735*h**7 + 0*h - 3*h**2 + 0 + 1/105*h**5 + 0*h**4 - 1/21*h**3. Factor z(b).\n | -2*(b - 1)**2*(b + 1)**2/7\n | ibivibiv/math_instruct | |
Solve 1606 = 5*h - 4*b + 1515, 4*h + 220 = -9*b for h.\n | -1\n | ibivibiv/math_instruct | |
Let d = -2 - -4. Suppose -10 = -5*w, 3*t - 4*w + 8 = -0*t. Suppose 3*o + r - 10 = 0, 2*r = -t - 4. Solve 4*s + 9 = -5*i, o*i - i = 5*s + d for i.\n | -1\n | ibivibiv/math_instruct | |
What is the closest to 1 in 784, -0.1, 2, -3, 0.4?\n | 0.4\n | ibivibiv/math_instruct | |
Suppose 0 = 3*d - d - 538. Suppose 272 = t - d. Is t composite?\n | False\n | ibivibiv/math_instruct | |
-1191939 divided by 4431\n | -269\n | ibivibiv/math_instruct | |
If Randy spent $10 on lunch and then used a quarter of the remaining money to buy a $5 ice cream cone, what was the initial amount of money that Randy had? | If Randy spent $10 on lunch, then the remaining money is the initial amount minus $10.
Lets call the initial amount of money x.
So, the remaining money is x - $10.
Randy used a quarter of the remaining money to buy a $5 ice cream cone.
A quarter of the remaining money is (x - $10)/4.
So, we have the equation (x - $10)/... | ibivibiv/math_instruct | |
950*0\n | 0\n | ibivibiv/math_instruct | |
Work out 319250301 - -55.6.\n | 319250356.6\n | ibivibiv/math_instruct | |
What is the second derivative of 55*b**2*r**3 - 2*b**2*r**2 - 3*b*r**3 + 27*b wrt b?\n | 110*r**3 - 4*r**2\n | ibivibiv/math_instruct | |
Does 33 divide 36333?\n | True\n | ibivibiv/math_instruct | |
Let u(g) = -g**2 - 4*g + 3. Let s be u(-4). Let z(v) = 2*v - 1. What are the prime factors of z(s)?\n | 5\n | ibivibiv/math_instruct | |
Find the third derivative of 1070*g**4*i - g**3*i + 48*g**2*i + g**2 + 3*g*i - 2*g wrt g.\n | 25680*g*i - 6*i\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 43311636 and 36.\n | 36\n | ibivibiv/math_instruct | |
Simplify (g**(-9)/g*g)/g**6*g*((g**(8/9)/g)/g)/g*g**4/g assuming g is positive.\n | g**(-118/9)\n | ibivibiv/math_instruct | |
What is the square root of 108707 to the nearest integer?\n | 330\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 1218 and 98.\n | 8526\n | ibivibiv/math_instruct | |
Let t = -1357 - -2133. Let b = 603 + t. What is the hundreds digit of b?\n | 3\n | ibivibiv/math_instruct | |
Let l(p) = 3*p**2 + 5*p - 6. Let a(z) be the second derivative of z**4/3 + z**3 - 3*z**2 + 1631*z. Give 6*a(n) - 7*l(n).\n | 3*n**2 + n + 6\n | ibivibiv/math_instruct | |
Let d(p) = p**3 + 6*p**2 + p - 6. Let x be d(1). Factor 2/5*z**x + 8/5 - 8/5*z.\n | 2*(z - 2)**2/5\n | ibivibiv/math_instruct | |
Suppose -3*v = 12 - 0, 0 = -q + 4*v + 17. Sort q, -2, -3, 7 in increasing order.\n | -3, -2, q, 7\n | ibivibiv/math_instruct | |
Let k be 0/3 + 4/(60 - 4). Let q(i) be the first derivative of -1 - k*i**2 + 1/21*i**3 - 2/7*i. Solve q(b) = 0 for b.\n | -1, 2\n | ibivibiv/math_instruct | |
Put -3, -7.3, -5/4 in ascending order.\n | -7.3, -3, -5/4\n | ibivibiv/math_instruct | |
What is -0.0535 take away 95177?\n | -95177.0535\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 12879 and 27.\n | 27\n | ibivibiv/math_instruct | |
Suppose that $f(x)$ and $g(x)$ are polynomials of degree $4$ and $5$ respectively. What is the degree of $f(x^3) \cdot g(x^2)$? | Since $f(x)$ is a polynomial of degree $4$, $f(x^3)$ is a polynomial of degree $(4)(3) = 12$.
Similarly, since $g(x)$ is a polynomial of degree $5$, $g(x^2)$ is a polynomial of degree $(5)(2) = 10$.
Therefore, $f(x^3) \cdot g(x^2)$ is a polynomial of degree $12 + 10 = \boxed{22}$.
The answer is: 22 | ibivibiv/math_instruct | |
Work out -25406 * -60.\n | 1524360\n | ibivibiv/math_instruct | |
In base 11, what is 9541 - 3?\n | 9539\n | ibivibiv/math_instruct | |
Let z(v) = -256*v - 432. Let x(t) = -27*t - 45. Let f(m) = 48*x(m) - 5*z(m). Let l(i) = 3*i**2 - 2*i**2 + 3*i**2. Determine l(f(n)).\n | 1024*n**2\n | ibivibiv/math_instruct | |
Does 26 divide 442?\n | True\n | ibivibiv/math_instruct | |
What is 0.000020143 rounded to 6 dps?\n | 0.00002\n | ibivibiv/math_instruct | |
Let p = 10 - 5. Suppose -3*d - p*q = 0, 0 = d + 3*q + 2*q. Solve 4*m + d*m = -4 for m.\n | -1\n | ibivibiv/math_instruct | |
What is the derivative of -817*i**4 + 6*i**3 - 66*i - 254656?\n | -3268*i**3 + 18*i**2 - 66\n | ibivibiv/math_instruct | |
Let s(u) = -u**2 - 11*u - 4. Let b be s(-10). Suppose -r = h + r - 13, -2*h + r = -b. Solve h*x - 15 = 4*z - 0*z, 2*x - 6 = 3*z for x.\n | 3\n | ibivibiv/math_instruct | |
What is the least common multiple of 206 and 2120?\n | 218360\n | ibivibiv/math_instruct | |
What is 448 minutes after 6:49 AM?\n | 2:17 PM\n | ibivibiv/math_instruct | |
What is the tens digit of 5695?\n | 9\n | ibivibiv/math_instruct | |
Let n = -1 - -2. Let x = -1.365 + 1.165. Let j = -176 - -180. Which is the fourth smallest value? (a) x (b) 5 (c) n (d) j\n | b\n | ibivibiv/math_instruct | |
Let i(w) = -2*w**4 + w**2. Let g(y) = 216*y**4 + 2*y**3 - 10*y**2 - 2*y + 43. Let s(j) = g(j) + 10*i(j). Find the second derivative of s(o) wrt o.\n | 2352*o**2 + 12*o\n | ibivibiv/math_instruct | |
Find the third derivative of 63*r**4*x**2 + 1790*r**3*x**3 - r**2*x**3 + 15*r**2*x**2 - 476*r*x**3 + 3*r - 3*x wrt r.\n | 1512*r*x**2 + 10740*x**3\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {a: 3, h: 1, r: 4, p: 5}. Give prob of picking 1 h and 1 p.\n | 5/78\n | ibivibiv/math_instruct | |
How many nanometers are there in 0.203634km?\n | 203634000000\n | ibivibiv/math_instruct | |
Calculate 8/64*((-1140)/(-100) - 9).\n | 3/10\n | ibivibiv/math_instruct | |
Let g be 119/11 - (-4)/22. Calculate the greatest common divisor of g and 33.\n | 11\n | ibivibiv/math_instruct | |
Suppose 2*k - 6 + 0 = 0. Let i be 464/4 + (2 - k). Let b = 162 - i. Does 14 divide b?\n | False\n | ibivibiv/math_instruct | |
What is -1011553.7 rounded to the nearest 10000?\n | -1010000\n | ibivibiv/math_instruct | |
What is next in -29356, -29391, -29426, -29461, -29496, -29531?\n | -29566\n | ibivibiv/math_instruct | |
Expand (-2*d - d + d)*(16 - 16 + 17*d + (-2 + 2 + 4*d)*(2 - 6 + 2))*((0*d + d + 5*d)*(-1 + 4 - 2) + 5*d - 2*d + 2*d)*(d - 4 + 4).\n | -198*d**4\n | ibivibiv/math_instruct | |
What is the value of (2/16)/(((-20)/(-4))/(-10))?\n | -1/4\n | ibivibiv/math_instruct | |
What is 2/(-23) + (-2730)/345?\n | -8\n | ibivibiv/math_instruct | |
Let x = 300 + -442. What are the prime factors of 4 - (x/2 - 3)?\n | 2, 3, 13\n | ibivibiv/math_instruct | |
Which is smaller: 161 or 2?\n | 2\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-90.5719 % 39.8613) * (10.0243 / -30.3073) | -9.5959 | ibivibiv/math_instruct | |
Let h(j) = -j**3 - 4*j**2 + 3*j - 6. Suppose n + 37*n - 608 = 0. What is the smallest common multiple of n and h(-5)?\n | 16\n | ibivibiv/math_instruct | |
Calculate prob of picking 3 z and 1 v when four letters picked without replacement from vqzhvh.\n | 0\n | ibivibiv/math_instruct | |
Suppose 2*f = -3*p + 13, -4*f + 2*f + 11 = 5*p. Let m(z) = -z**2 + 8*z. Let l be m(f). Solve -5*u = -u - 2*n - 18, 4*u + 3*n + 7 = l for u.\n | 2\n | ibivibiv/math_instruct | |
Suppose -5*k + o - 3*o + 5 = 0, -4*k - 4*o = -4. Suppose 3*f = k + 17. Calculate the common denominator of f/(-27) + (-1274)/180 and 119/6.\n | 30\n | ibivibiv/math_instruct | |
What is the value of 8/((-4900)/830 + 6)?\n | 83\n | ibivibiv/math_instruct | |
Which is the closest to 0? (a) 6028 (b) -0.1 (c) 0.213\n | b\n | ibivibiv/math_instruct | |
Let l = -52 - -55. Let p be -5*(l + 38/(-10)). Sort -1, -4, p, 8 in increasing order.\n | -4, -1, p, 8\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Inverse of non-square matrix
Is it true that a non-square matrix cannot have both the left and right inverse?
Consider an $m \times n$ matrix $A$. If $n \times m$ matrix $B$ is the right inverse of $A$, viz., $AB = I_m$. ... | A fundamental concept in linear algebra is the idea of a matrix inverse. For square matrices, this concept is relatively straightforward - a square matrix $A$ has an inverse (denoted as $A^{-1}$) if there exists another matrix such that their product equals the identity matrix ($AA^{-1} = A^{-1}A = I$). However, when ... | ibivibiv/math_instruct | |
Evaluate -9 + -4 + (5 - -2).\n | -6\n | ibivibiv/math_instruct | |
Solve -3*u = -6*j + 24, 41 - 27 = -5*u - 3*j for u.\n | -4\n | ibivibiv/math_instruct | |
What comes next: -82, -759, -2668, -6445, -12726?\n | -22147\n | ibivibiv/math_instruct | |
Calculate prob of sequence orra when four letters picked without replacement from riaaworirrriarrwi.\n | 3/1360\n | ibivibiv/math_instruct | |
What is next in -5265, -5264, -5263, -5262, -5261, -5260?\n | -5259\n | ibivibiv/math_instruct | |
Collect the terms in 104*d - 104*d + 844*d**2 + 1365*d**2.\n | 2209*d**2\n | ibivibiv/math_instruct | |
How many months are there in 7/15 of a millennium?\n | 5600\n | ibivibiv/math_instruct | |
What is 25/7 of a week in minutes?\n | 36000\n | ibivibiv/math_instruct | |
Solve 0 = -4*n - 0*n + 20 for n.\n | 5\n | ibivibiv/math_instruct | |
What is (27/6)/(28/(-16))*(-4)/12?\n | 6/7\n | ibivibiv/math_instruct | |
What is -11 (base 2) in base 8?\n | -3\n | ibivibiv/math_instruct | |
Find the third derivative of -b**5 + 2568*b**4 - b**3*y**3 + 2*b**2*y**2 - 24*b**2 + 18*b*y**3 wrt b.\n | -60*b**2 + 61632*b - 6*y**3\n | ibivibiv/math_instruct | |
Expand (-3*o**2 - 4*o**2 + 4*o**2)*(-3 + 3 - 6).\n | 18*o**2\n | ibivibiv/math_instruct | |
What is 17627581 to the power of 1/3, to the nearest integer?\n | 260\n | ibivibiv/math_instruct | |
What comes next: 2770, 2771, 2772, 2773, 2774, 2775?\n | 2776\n | ibivibiv/math_instruct | |
-46 - -81\n | 35\n | ibivibiv/math_instruct | |
0.6536 * 13323\n | 8707.9128\n | ibivibiv/math_instruct | |
What is the seventh root of 29189379 to the nearest integer?\n | 12\n | ibivibiv/math_instruct | |
Let j(r) = 43*r + 79. Is j(0) even?\n | False\n | ibivibiv/math_instruct | |
Let y = -20 - -34. Let a be (-3)/6*y + 3. Put a, 5, 2 in ascending order.\n | a, 2, 5\n | ibivibiv/math_instruct | |
Suppose -i - 13 = -3*r - 8, -5*i + r - 11 = 0. What is the hundreds digit of (-4)/(i/2)*(-335)/(-10)?\n | 1\n | ibivibiv/math_instruct |
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