instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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|---|---|---|---|
Simplify (b**(-20)/b)/b**(-7/6)*b**(2/5)/b*b*b*b/((b*b/((b/((b*b*b**(-1/3)*b)/b))/b))/b)*b assuming b is positive.\n | b**(-191/10)\n | ibivibiv/math_instruct | |
How many grams are there in twenty-seven quarters of a kilogram?\n | 6750\n | ibivibiv/math_instruct | |
Let r = 268.32 - 262. Let z = r + -0.12. What is z rounded to 0 decimal places?\n | 6\n | ibivibiv/math_instruct | |
Sort -2, -5, 0, 4, -85, 2 in decreasing order.\n | 4, 2, 0, -2, -5, -85\n | ibivibiv/math_instruct | |
List the prime factors of (0 + -52)*(42/(-4) - -2).\n | 2, 13, 17\n | ibivibiv/math_instruct | |
Simplify (o*o*(o/o**(-15))/o*o)/((o**(-2/15)/o*o*o)/o) assuming o is positive.\n | o**(272/15)\n | ibivibiv/math_instruct | |
Express 31 - 17 + 15*w + 10*w - 16 in the form q*w + g and give g.\n | -2\n | ibivibiv/math_instruct | |
What is one fifth of a centimeter in micrometers?\n | 2000\n | ibivibiv/math_instruct | |
Are -19832 and -79329/4 nonequal?\n | True\n | ibivibiv/math_instruct | |
What is the common denominator of -19/86253648 and 47/1428?\n | 603775536\n | ibivibiv/math_instruct | |
Let w(j) = j**2 + 6*j - 3. Let f be w(-6). Put 4, f, 3 in descending order.\n | 4, 3, f\n | ibivibiv/math_instruct | |
What is the highest common divisor of 6854 and 46?\n | 46\n | ibivibiv/math_instruct | |
Let y(r) = -2*r**3 - 3*r**2 + r + 2. What is the units digit of y(-2)?\n | 4\n | ibivibiv/math_instruct | |
Is 79 a factor of 1075017724?\n | False\n | ibivibiv/math_instruct | |
Which is the closest to -5? (a) 0 (b) 0.07 (c) -4 (d) -3 (e) 5\n | c\n | ibivibiv/math_instruct | |
Let p(k) be the third derivative of 11/12*k**4 + 1/60*k**5 + 0*k - 2*k**2 - 9 - 22/3*k**3. Let r be p(-25). Solve -3*h - 17 = -2*a + 3*a, -5*h - r = 3*a for a.\n | -2\n | ibivibiv/math_instruct | |
Calculate the remainder when 321 is divided by 109.\n | 103\n | ibivibiv/math_instruct | |
What is 39863 to the power of 1/2, to the nearest integer?\n | 200\n | ibivibiv/math_instruct | |
What is the value of (1*((-5)/1)/5)/5?\n | -1/5\n | ibivibiv/math_instruct | |
What is -6754 rounded to the nearest one thousand?\n | -7000\n | ibivibiv/math_instruct | |
Let c = -21 - -54. Suppose 3*n - 1 = 11. Let x = n + c. Does 12 divide x?\n | False\n | ibivibiv/math_instruct | |
Let l be 4 - (-4 + -3 + 6). Let s be (-23140)/(-5874) - (-4)/66. Let v = -5 + 5. Solve 4*o = l*o + s*p + 15, 4*o - 3*p - 35 = v for o.\n | 5\n | ibivibiv/math_instruct | |
-10436.28 + 0.03\n | -10436.25\n | ibivibiv/math_instruct | |
Let v(k) = -k - 3. Let y(h) = 5*h + 16. Let f(z) = 11*v(z) + 2*y(z). Let t(j) = -7*j - 4. Give 4*f(q) - t(q).\n | 3*q\n | ibivibiv/math_instruct | |
Is 151 a factor of 6372200?\n | True\n | ibivibiv/math_instruct | |
Suppose 474*n = 528*n + 125130 - 2054226. Is 78 a factor of n?\n | True\n | ibivibiv/math_instruct | |
Suppose -6 = -2*h - 2. Suppose -h = 2*p + 3*n, n - 6 = -0*p - 2*p. Solve 8 = -9*t + p*t for t.\n | -2\n | ibivibiv/math_instruct | |
Solve 10*g + 630 = -4*h, -5*h = 1232*g - 1231*g + 86 for h.\n | -5\n | ibivibiv/math_instruct | |
Let d(l) be the second derivative of -l**4/6 - l. Suppose -2*y + 6 = 2. Let n(b) = -5*b**2 + 9*b**y + 2*b**2. What is d(n(t))?\n | -72*t**4\n | ibivibiv/math_instruct | |
Suppose 2*i - 28 = -2*d, -2*i + 2*d + 19 = -17. Suppose i = 33*u - 29*u. Calculate the remainder when 23 is divided by u.\n | 3\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 16371 and 2907.\n | 153\n | ibivibiv/math_instruct | |
Evaluate 273/(-234)*9/(-42).\n | 1/4\n | ibivibiv/math_instruct | |
What is prob of sequence xkj when three letters picked without replacement from {e: 1, d: 4, x: 3, k: 2, j: 4}?\n | 1/91\n | ibivibiv/math_instruct | |
Let q(a) = 13*a**2 - a + 1. Let u(m) = 22*m**2 + 83*m + 3. Calculate 3*q(p) - u(p).\n | 17*p**2 - 86*p\n | ibivibiv/math_instruct | |
What comes next: -34, 126, 490, 1058, 1830, 2806?\n | 3986\n | ibivibiv/math_instruct | |
Suppose -z + 3*n + 90 = 0, 754 = 5*z + 4*n + 228. Let p(i) = 8*i**3 - 4*i**2 + 330*i - 654. What is the remainder when z is divided by p(2)?\n | 48\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 1083346 and 506.\n | 506\n | ibivibiv/math_instruct | |
Let j be (4/7)/(6/21). Suppose j*k = 4*r + 7*k - 15, 2*r + k = 3. Let q = 104 - 725/7. Which is smaller: q or r?\n | r\n | ibivibiv/math_instruct | |
Let u = 8/2805 - 1954/816255. Let t = u + 2099/5820. Find the common denominator of 47/10 and t.\n | 180\n | ibivibiv/math_instruct | |
17 (base 13) to base 9\n | 22\n | ibivibiv/math_instruct | |
Let w(s) = 9*s**2 + 18*s - 18. Let z be w(1). Let t(y) = -2*y**2 - y. Let n be t(1). Let g be (-60)/z + 4/n. Let l(r) = r**3 + 7*r**2 - 9*r - 9. Determine l(g).\n | -1\n | ibivibiv/math_instruct | |
Does 5 divide 501885?\n | True\n | ibivibiv/math_instruct | |
What is 6743.14 rounded to the nearest one hundred?\n | 6700\n | ibivibiv/math_instruct | |
Let u(o) = 104*o - 2. Let d(w) = 3 + 498*w - 499*w - 3. Calculate d(u(v)).\n | -104*v + 2\n | ibivibiv/math_instruct | |
Find the second derivative of 29*s**4 + 14*s + 69*s**3 - 69*s**3 wrt s.\n | 348*s**2\n | ibivibiv/math_instruct | |
Let g = 4.95 + 0.05. Let t = g + -4.92. Let h = -0.0846 + t. What is h rounded to 3 decimal places?\n | -0.005\n | ibivibiv/math_instruct | |
Factor -o**2/7 - 37746214*o/7 - 356194167833449/7.\n | -(o + 18873107)**2/7\n | ibivibiv/math_instruct | |
Simplify (h**(-1/4)*h*h*h**(-2))**(-27)*(((h*h**(2/15))/h)/(h/(h/(h/(h**5/h))*h)*h))**(-1/16) assuming h is positive.\n | h**(1573/240)\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 786421?\n | 7\n | ibivibiv/math_instruct | |
Let u be 4/(-3)*(-351)/(-18). Let f = u - -32. Let o be (3/2)/(f/12). Which is the third smallest value? (a) 2 (b) -4 (c) 0.3 (d) o\n | a\n | ibivibiv/math_instruct | |
Does 13 divide 246974?\n | True\n | ibivibiv/math_instruct | |
Let q be -13 + -2 + 2 + 2. Let a = q - -8. List the prime factors of -2 - 10*a/2.\n | 13\n | ibivibiv/math_instruct | |
What is 8188 (base 14) in base 2?\n | 101011011111100\n | ibivibiv/math_instruct | |
What is 25 minutes after 7:19 PM?\n | 7:44 PM\n | ibivibiv/math_instruct | |
Is 1396584 at most as big as 5586341/4?\n | True\n | ibivibiv/math_instruct | |
Calculate the remainder when 21617986 is divided by 463.\n | 53\n | ibivibiv/math_instruct | |
Suppose -302 = -w - 23*q + 19*q, -3*w + 851 = q. What is the remainder when w is divided by 57?\n | 54\n | ibivibiv/math_instruct | |
Let r(v) be the first derivative of 5*v**4/2 + 41*v**3/3 - 3*v**2/2 + 306*v + 562. Find the second derivative of r(t) wrt t.\n | 60*t + 82\n | ibivibiv/math_instruct | |
Simplify (sqrt(16) + -3*(sqrt(256) + sqrt(16)))/((sqrt(40) - (-1*sqrt(40) - sqrt(40)))/sqrt(5)).\n | -14*sqrt(2)/3\n | ibivibiv/math_instruct | |
Let x(d) = 4*d - 12. Let p(u) = -20*u + 57. Let s(h) = -3*p(h) - 14*x(h). Let l(b) = -11*b + 10. Give 3*l(k) + 8*s(k).\n | -k + 6\n | ibivibiv/math_instruct | |
Is 285745 a prime number?\n | False\n | ibivibiv/math_instruct | |
Calculate the remainder when 146 is divided by 15.\n | 11\n | ibivibiv/math_instruct | |
Let u = -53 + 89. What is the highest common divisor of u and 48?\n | 12\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Skew-symmetric matrices dot product condition
Denote with $\langle\cdot,\cdot\rangle$ the standard inner product on $\mathbb{R}^n$. The real $n$-by-$n$ matrix $A$ is skew-symmetric if and only if $\langle Ax, y\rangle = -\... | To understand the relationship between the definition of a skew-symmetric matrix, $A^{T} = -A$, and the dot product condition, $\langle Ax, y \rangle = -\langle x, Ay \rangle$, it is helpful to first review some fundamental linear algebra concepts. A matrix $A$ is said to be symmetric if $A^{T} = A$; conversely, it is... | ibivibiv/math_instruct | |
Round 475700 to the nearest ten thousand.\n | 480000\n | ibivibiv/math_instruct | |
Sort -0.1, -5, 6, 3, 2 in ascending order.\n | -5, -0.1, 2, 3, 6\n | ibivibiv/math_instruct | |
What is the second derivative of 164*c**2 - 1580*c**2 + c - 54 - 61 - 63 + 184 wrt c?\n | -2832\n | ibivibiv/math_instruct | |
Round -35.54078899 to 3 dps.\n | -35.541\n | ibivibiv/math_instruct | |
Let o(i) = -i**2 + 12*i - 14. Let w be o(11). Let t(z) = 2*z**2 - 3*z + 3. List the prime factors of t(w).\n | 2, 3, 5\n | ibivibiv/math_instruct | |
Express -c**3 + 47*c**2 + 0*c**3 - 13*c - 47*c**2 in the form n*c**2 + g + z*c + t*c**3 and give n.\n | 0\n | ibivibiv/math_instruct | |
What is 3680 rounded to the nearest 100?\n | 3700\n | ibivibiv/math_instruct | |
Two letters picked without replacement from eojjzzeoaeje. What is prob of picking 1 a and 1 z?\n | 1/33\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(53.9337 * -19.9956) - (-1.8847 / 45.5036) | -1078.3953 | ibivibiv/math_instruct | |
Solve -5*i + 41 = 4*m - 10*i, -5*m + 35 = -3*i for m.\n | 4\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 127310 and 20.\n | 10\n | ibivibiv/math_instruct | |
Expand (2*n**2 - 2 + 2)*(-11*n - 4*n + 11*n - 2*n**2).\n | -4*n**4 - 8*n**3\n | ibivibiv/math_instruct | |
Is -3/58399 <= -372/7?\n | False\n | ibivibiv/math_instruct | |
What is 1768 to the power of 1/2, to the nearest integer?\n | 42\n | ibivibiv/math_instruct | |
Let z be (-6 + 5 - -36)*(-2)/(-5). Suppose -4*g + 28 - 66 = 2*a, g - a = -z. Is -14 at most as big as g?\n | True\n | ibivibiv/math_instruct | |
What comes next: 31, -26, -181, -482, -977, -1714, -2741?\n | -4106\n | ibivibiv/math_instruct | |
Is 123 a factor of 714698?\n | False\n | ibivibiv/math_instruct | |
Let t(p) = p**3 - 8*p**2 + 9*p + 5. Let x be t(7). Suppose -4*f + x = d, -5*d - 4 = 2*f - 45. What are the prime factors of d?\n | 7\n | ibivibiv/math_instruct | |
Suppose -4*y = -12 + 4. Let s = 0 + y. Solve -s*q + 19 = 5*v, -v + 2*q + 5 = 3*q for v.\n | 3\n | ibivibiv/math_instruct | |
Let t = 8 - -5. Let u = -1 + t. Is u a multiple of 6?\n | True\n | ibivibiv/math_instruct | |
Is 7/290 at most 1?\n | True\n | ibivibiv/math_instruct | |
List the prime factors of 97074.\n | 2, 3, 5393\n | ibivibiv/math_instruct | |
List the prime factors of 529619.\n | 529619\n | ibivibiv/math_instruct | |
b"What is the ith term of -1, 15, 55, 131, 255, 439, 695?\n" | 2*i**3 + 2*i - 5\n | ibivibiv/math_instruct | |
What is the millions digit of 1888237?\n | 1\n | ibivibiv/math_instruct | |
What is 625 minutes before 12:13 PM?\n | 1:48 AM\n | ibivibiv/math_instruct | |
Solve -2*f**2/9 + 280*f/3 - 9800 = 0 for f.\n | 210\n | ibivibiv/math_instruct | |
What is the millions digit of 3977396725?\n | 7\n | ibivibiv/math_instruct | |
Suppose -2377 + 279 = -m. Is m prime?\n | False\n | ibivibiv/math_instruct | |
Let s = -1174.52827 - -1169.528. Let u = s - -5. Round u to four dps.\n | -0.0003\n | ibivibiv/math_instruct | |
b"What is the uth term of -63, -234, -523, -936, -1479?\n" | -u**3 - 53*u**2 - 5*u - 4\n | ibivibiv/math_instruct | |
Suppose -3*b = -5*z - 31, -5*b + 5*z = -0*b - 55. Let a = b + -1. What is the units digit of a?\n | 1\n | ibivibiv/math_instruct | |
Let g = 441081/44 - 10025. What is the common denominator of g and 3/22?\n | 44\n | ibivibiv/math_instruct | |
Rearrange 2*g**3 - 1 + 3 + 36*g**2 + 1 + g**4 - 2 - 2*g**4 to the form d*g**3 + p*g + y*g**4 + j + r*g**2 and give j.\n | 1\n | ibivibiv/math_instruct | |
Suppose -n = -3*k - 276, -5*n + 1444 = 10*k - 9*k. List the prime factors of n.\n | 2, 3\n | ibivibiv/math_instruct | |
What is the third derivative of -j**3*w**3 + 2*j**3*w**2 + 3*j**3*w - 9*j*w**4 + 8590*j*w + 10600*w**4 wrt w?\n | -6*j**3 - 216*j*w + 254400*w\n | ibivibiv/math_instruct |
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