instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Let s = 12 - 12. Suppose s = 7*t + 98 - 350. Let p = -6 + 10. Calculate the greatest common factor of t and p.\n | 4\n | ibivibiv/math_instruct | |
Suppose -4*a + 2 + 6 = 0. Solve 0 = a*d + 3*d + 5 for d.\n | -1\n | ibivibiv/math_instruct | |
Let u(q) be the first derivative of q**4/4 + 2*q**3/3 + q**2/2 + 2*q - 1. Let l be u(-2). Suppose l = -6*t + 2*t. Solve 4*m - 5*x = t, x = -4*m + 5*x for m.\n | 0\n | ibivibiv/math_instruct | |
Let u = 30784 - 9793. Suppose 3*b - u = -o + 4*o, 5*b + o - 34967 = 0. Is 5/((-20)/(-12)) + b prime?\n | True\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-58.792 / 24.666) * (45.109 - -62.71) | -256.9892 | ibivibiv/math_instruct | |
Does 30 divide 752?\n | False\n | ibivibiv/math_instruct | |
Let r = 56/11 - -17113/33. Let m = r + -6557/12. What is the common denominator of m and 139/24?\n | 24\n | ibivibiv/math_instruct | |
What is the third derivative of 1307*f**3*l**5 + 1686*f**3*l**3 - 11174*f**3*l**2 - 2*f**3 - 2*f**2*l**2 - f*l**2 + 3*l**2 wrt l?\n | 78420*f**3*l**2 + 10116*f**3\n | ibivibiv/math_instruct | |
What is the third derivative of 5251*d**2*y**3 - 2320007*d**2*y**2 - 107*d*y**3 + y**3 wrt y?\n | 31506*d**2 - 642*d + 6\n | ibivibiv/math_instruct | |
Which is the biggest value? (a) 4/3 (b) 1 (c) -9\n | a\n | ibivibiv/math_instruct | |
What is the closest to -9 in 5, -3, -18/23, -0.5?\n | -3\n | ibivibiv/math_instruct | |
Is 2024147 a prime number?\n | True\n | ibivibiv/math_instruct | |
What is the closest to -32 in -1/4, 1.156, -4, 79?\n | -4\n | ibivibiv/math_instruct | |
Let h be (-6)/(-21) + (-13240)/(-14). Let q = h - 2884/3. Let o = 15286/6903 + 6/767. Find the common denominator of q and o.\n | 9\n | ibivibiv/math_instruct | |
Let d(u) = 20*u**2 - 8*u - 8*u**2 - 13*u**2. What is the tens digit of d(-6)?\n | 1\n | ibivibiv/math_instruct | |
What is -103101630 (base 7) in base 11?\n | -3510527\n | ibivibiv/math_instruct | |
Simplify sqrt(756)/(2*sqrt(108)).\n | sqrt(7)/2\n | ibivibiv/math_instruct | |
Find the second derivative of 4*k**3*z**4 + k**3*z - 9*k**2*z**4 - 67*z wrt z.\n | 48*k**3*z**2 - 108*k**2*z**2\n | ibivibiv/math_instruct | |
Is 38279 a composite number?\n | True\n | ibivibiv/math_instruct | |
Expand -2*y**3 - y**4 + 2*y**3 + (-1 + 2*y**2 + 1)*(-2*y - 6*y**2 + 2*y) - 9*y**4 + 4*y**4 + 23*y**4.\n | 5*y**4\n | ibivibiv/math_instruct | |
Factor -79/4*h**2 + 57/2*h - 2 - 27/4*h**3.\n | -(h - 1)*(h + 4)*(27*h - 2)/4\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"Lemma 13.28.2. Let $\mathcal{A}$ be an abelian category. Then there is a canonical identification $K_0(D^ b(\mathcal{A})) = K_0(\mathcal{A})$ of zeroth $K$-groups.
Proof. Given an object $A$ of $\mathcal{A}$ denote $A[0]$ th... | We begin by defining what an abelian category is. An abelian category $\mathcal{A}$ is a category where finite limits and colimits exist, morphisms have kernels and cokernels, and every monomorphism is the kernel of its cokernel and every epimorphism is the cokernel of its kernel. The prototypical example of an abelia... | ibivibiv/math_instruct | |
Let d = -9 - -14. Suppose -5*i = -4*q + 25, 0*q - 10 = -q + d*i. Factor 24*x**3 - 9*x**2 + x - 39*x**3 + q*x.\n | -3*x*(x + 1)*(5*x - 2)\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-29.4416 + 15.2404) % (-24.5303 / 93.022) | -0.2249 | ibivibiv/math_instruct | |
What is the result of the following expression?
-13.762 / -0.5516 | 24.9492 | ibivibiv/math_instruct | |
Put -0.5, 30, -1/6 in ascending order.\n | -0.5, -1/6, 30\n | ibivibiv/math_instruct | |
b"What is the vth term of 32936, 132863, 299780, 533687, 834584, 1202471?\n" | 33495*v**2 - 558*v - 1\n | ibivibiv/math_instruct | |
Find the common denominator of -1/1251700 and -11/2002720.\n | 10013600\n | ibivibiv/math_instruct | |
Which is the fifth biggest value? (a) 0 (b) 13146 (c) 3 (d) 5 (e) -85\n | e\n | ibivibiv/math_instruct | |
Is 8807061 a prime number?\n | False\n | ibivibiv/math_instruct | |
Is 80004989 a prime number?\n | False\n | ibivibiv/math_instruct | |
Simplify (((o**(-1/4)*o*o**(3/10))/(o**(-12)*o*o*o*o**(-10)))**(-26))**(-4/9) assuming o is positive.\n | o**(10426/45)\n | ibivibiv/math_instruct | |
Differentiate -5*j**3 + 2170 - 1924 - 2573 + 33*j - 105*j with respect to j.\n | -15*j**2 - 72\n | ibivibiv/math_instruct | |
Evaluate -2 + 23 - (-3 + 15).\n | 9\n | ibivibiv/math_instruct | |
Let z = 0 - -12. Suppose 4*n = 5*w - 38, 4*n - 7*n - z = -w. Let u be 470/(-4)*(w - 8). What is u rounded to the nearest 10?\n | 240\n | ibivibiv/math_instruct | |
Let r(d) be the first derivative of 3*d**5/20 - d**3/6 + 2*d - 2. Let p(y) be the first derivative of r(y). What is the second derivative of p(o) wrt o?\n | 18*o\n | ibivibiv/math_instruct | |
b"What is the qth term of -26, -111, -252, -449?\n" | -28*q**2 - q + 3\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 d, 1 u, and 1 y when three letters picked without replacement from {y: 4, d: 1, u: 3, s: 4, f: 1}.\n | 6/143\n | ibivibiv/math_instruct | |
What is one tenth of a century in months?\n | 120\n | ibivibiv/math_instruct | |
Which is the nearest to 2? (a) 8/3 (b) 44 (c) -29\n | a\n | ibivibiv/math_instruct | |
Divide -192700 by -1927.\n | 100\n | ibivibiv/math_instruct | |
Suppose -5*n + 1656 = -0*g - 4*g, 4*g + 1680 = -n. Let w = g + 427. Calculate the highest common divisor of 6 and w.\n | 2\n | ibivibiv/math_instruct | |
b"What is the fth term of 1863, 1912, 2007, 2154, 2359, 2628?\n" | f**3 + 17*f**2 - 9*f + 1854\n | ibivibiv/math_instruct | |
Suppose 144*z = 141*z + 915. Suppose -z = -3*o + 2995. What is the units digit of o?\n | 0\n | ibivibiv/math_instruct | |
What is 240234 (base 6) in base 11?\n | 14717\n | ibivibiv/math_instruct | |
Let i = -61 - -64. Let r(m) = -2*m + 3. Let n(q) be the third derivative of -q**4/8 + 5*q**3/6 - 20*q**2. Give i*n(j) - 5*r(j).\n | j\n | ibivibiv/math_instruct | |
(-16 - 1) + 1 + (-64 - 14 - -27)\n | -67\n | ibivibiv/math_instruct | |
What is the value of 181 + -95 + (-23 - -13)?\n | 76\n | ibivibiv/math_instruct | |
What is 273335.3013 rounded to the nearest 10?\n | 273340\n | ibivibiv/math_instruct | |
Let t be (-1 + (0 - -1))/3. Suppose 0 = 4*u - 5*d + 97, 3*d = -t*u + 3*u + 69. What is the remainder when 95 is divided by 4/u - (-872)/36?\n | 23\n | ibivibiv/math_instruct | |
What is the tenth root of 66362857 to the nearest integer?\n | 6\n | ibivibiv/math_instruct | |
Suppose 5*a = 3*k + 34084, 12 = 96*k - 100*k. List the prime factors of a.\n | 5, 29, 47\n | ibivibiv/math_instruct | |
Factor 4*p**3 + 478*p**2 + 710*p + 236.\n | 2*(p + 1)*(p + 118)*(2*p + 1)\n | ibivibiv/math_instruct | |
What is the millions digit of 1856576?\n | 1\n | ibivibiv/math_instruct | |
What is the highest common divisor of 10 and 257903590?\n | 10\n | ibivibiv/math_instruct | |
What is 632 divided by 18?\n | 316/9\n | ibivibiv/math_instruct | |
Calculate the remainder when 25 is divided by (-9)/(-6)*10/1.\n | 10\n | ibivibiv/math_instruct | |
What is -3.215 rounded to one decimal place?\n | -3.2\n | ibivibiv/math_instruct | |
Simplify ((sqrt(99)*-2)/sqrt(11))/sqrt(192) + 2.\n | -sqrt(3)/4 + 2\n | ibivibiv/math_instruct | |
Which is the third biggest value? (a) -59 (b) -1/363 (c) 1/4\n | a\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-41.1675 % -50.6301) + 11.378 | -29.7895 | ibivibiv/math_instruct | |
What is the units digit of 1920?\n | 0\n | ibivibiv/math_instruct | |
Sort -2, -0.4, 12.5.\n | -2, -0.4, 12.5\n | ibivibiv/math_instruct | |
What is 8375.014t in milligrams?\n | 8375014000000\n | ibivibiv/math_instruct | |
What is seven eighths of a litre in millilitres?\n | 875\n | ibivibiv/math_instruct | |
What is -3 - -97759036?\n | 97759033\n | ibivibiv/math_instruct | |
Let o(z) = -4*z - 3. Let d(w) = 4*w + 3. Let f(p) = -3*d(p) - 2*o(p). Let s be f(-3). Suppose s*k + 4*k = 676. What is the units digit of k?\n | 2\n | ibivibiv/math_instruct | |
Let i = 4318 - 4311. Solve -w - 14 = -4*q, 0 = 3*w - 2*w + 3*q - i for w.\n | -2\n | ibivibiv/math_instruct | |
Factor 152/3 - 224/3*j + 2/3*j**3 + 70/3*j**2.\n | 2*(j - 2)*(j - 1)*(j + 38)/3\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(17.973 * 23.399) % -42.875 | -8.1998 | ibivibiv/math_instruct | |
Let s be -3*((-8)/6 + 0). Suppose -r = 3*r - s. Let f be -2 + 0 - (32/12 - 5). Do f and r have different values?\n | True\n | ibivibiv/math_instruct | |
Suppose -11 = -3*f + 2*x, -4*f + 5*x = -2*f - 11. Suppose -f*w + 6*w = -4*s + 44, 4*s + 2*w - 48 = 0. What is the remainder when 26 is divided by s?\n | 12\n | ibivibiv/math_instruct | |
Expand (-3 + 4 - 3)*(-2 + 2 + 8*n)*(2 - n - 2 + (3*n + 2*n - 3*n)*(-2 + 1 + 0)).\n | 48*n**2\n | ibivibiv/math_instruct | |
Suppose 0 = 4*g + 12, -3*t - 12 = -g - 36. Let y(o) = o**3 - 9*o**2 + 12*o + 16. Let a be y(t). Solve -5*n - 4*b - 15 = 0, a*n + 27 = -5*b + 4 for n.\n | 1\n | ibivibiv/math_instruct | |
Rearrange 4*o + 7*o + 10*o**2 - 12*o**2 to i + v*o**2 + p*o and give p.\n | 11\n | ibivibiv/math_instruct | |
b"What is the oth term of -2529, -2545, -2565, -2589, -2617, -2649, -2685?\n" | -2*o**2 - 10*o - 2517\n | ibivibiv/math_instruct | |
How many minutes are there between 7:01 AM and 2:01 PM?\n | 420\n | ibivibiv/math_instruct | |
Sort 5, 4, -2/3, 1/26 in decreasing order.\n | 5, 4, 1/26, -2/3\n | ibivibiv/math_instruct | |
Work out 10.3228 + -11.\n | -0.6772\n | ibivibiv/math_instruct | |
Calculate ((-2708)/14894)/(3/825).\n | -50\n | ibivibiv/math_instruct | |
Simplify (4*(2*(sqrt(4200) - sqrt(4200)*2 - sqrt(4200) - sqrt(42) - sqrt(42))/sqrt(6) - (0 + 1 + sqrt(7) + sqrt(28)/sqrt(4)*-2)))**2.\n | 1376*sqrt(7) + 207104\n | ibivibiv/math_instruct | |
-5127 times -0.3\n | 1538.1\n | ibivibiv/math_instruct | |
What is the third root of 47304866 to the nearest integer?\n | 362\n | ibivibiv/math_instruct | |
Is -19949 equal to -19945?\n | False\n | ibivibiv/math_instruct | |
Let j(q) = -9*q - 7. Let s(o) = o + 2. Let r(t) = -j(t) - 2*s(t). What is r(-2)?\n | -11\n | ibivibiv/math_instruct | |
Let i(t) = -90*t + 1615. What is i(18)?\n | -5\n | ibivibiv/math_instruct | |
What is the common denominator of 119/22434 and 55/48?\n | 179472\n | ibivibiv/math_instruct | |
Collect the terms in 28*x**2 + 13*x - 11*x**2 - 16*x**2 - 13*x.\n | x**2\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {t: 1, v: 1, i: 2, p: 1, l: 2, n: 1}. Give prob of sequence pi.\n | 1/28\n | ibivibiv/math_instruct | |
Is 5991637231 a prime number?\n | False\n | ibivibiv/math_instruct | |
Expand -o - 3*o + 0*o + (-o + 0 + 0)*(-1 + 0 + 2) + 15*o + 3*o - 2*o.\n | 11*o\n | ibivibiv/math_instruct | |
What comes next: -65, -51, -37?\n | -23\n | ibivibiv/math_instruct | |
Suppose 9 + 3 = 4*l. Let i be (-6)/(10 + -4)*l/9. Which is smaller: -2/17 or i?\n | i\n | ibivibiv/math_instruct | |
Suppose 50 - 274 = -2*d. Let v(q) = -56*q + d*q - 57*q + 1. Suppose 28 = 5*a - 4*i + 78, 25 = -5*a - i. What is v(a)?\n | 7\n | ibivibiv/math_instruct | |
Convert 14 (base 15) to base 13.\n | 16\n | ibivibiv/math_instruct | |
How many kilometers are there in 6.31298nm?\n | 0.00000000000631298\n | ibivibiv/math_instruct | |
What is the units digit of 165525?\n | 5\n | ibivibiv/math_instruct | |
What are the prime factors of 441?\n | 3, 7\n | ibivibiv/math_instruct | |
Suppose 3*q - 29 = 5*v, 21 = -q + 2*q + 4*v. Calculate the remainder when 25 is divided by q.\n | 12\n | ibivibiv/math_instruct | |
Let f = 130199/120 - 1085. Let z = f + 101/120. Which is the smallest value? (a) -0.12 (b) z (c) 1\n | a\n | ibivibiv/math_instruct |
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