instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Let f(y) = -y**3 - 22*y**2 - 39*y + 23. Let v be f(-20). Put 111, 2, v in descending order.\n | 111, v, 2\n | ibivibiv/math_instruct | |
Let a(z) be the third derivative of -z**5/60 - z**4/3 + 5*z**3/6 + 2*z**2. Is 2 a factor of a(-8)?\n | False\n | ibivibiv/math_instruct | |
Let o(p) = -p**2 - 123*p + 2387. Calculate o(17).\n | 7\n | ibivibiv/math_instruct | |
Calculate 20831 divided by -2.\n | -20831/2\n | ibivibiv/math_instruct | |
How many minutes are there between 10:42 AM and 1:27 PM?\n | 165\n | ibivibiv/math_instruct | |
Round 0.001586 to four dps.\n | 0.0016\n | ibivibiv/math_instruct | |
Suppose -2*v + 3 = 33. Let q be (0 - v)*(-32)/(-12). Suppose 2*m - q = -2*m. Calculate the greatest common factor of m and 5.\n | 5\n | ibivibiv/math_instruct | |
Let x(t) be the third derivative of t**5/60 - t**4/12 - t**3/2 - 2222*t**2. Determine x(4).\n | 5\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 779 and 41.\n | 41\n | ibivibiv/math_instruct | |
Factor 5*o**3 - 213780*o**2 + 2285308185*o - 4569761290.\n | 5*(o - 21377)**2*(o - 2)\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {e: 1, f: 1, q: 2, a: 3}. What is prob of picking 2 a?\n | 1/7\n | ibivibiv/math_instruct | |
What is the Euler characteristic of a Torus with two holes?
Solution:
Using the formula for Euler characteristic:
χ = V - E + F,
where χ is the Euler characteristic, V is the number of vertices, E is the number of edges, and F is the number of faces.
For a torus with two holes, it has 2 handles, which means:
V ... | The provided solution is incorrect. Lets solve the problem again.
A torus with two holes is a surface of genus 2. The Euler characteristic of a surface of genus g can be calculated using the formula:
χ = 2 - 2g
For a torus with two holes (genus 2), we have:
χ = 2 - 2(2) = 2 - 4 = -2
Therefore, the Euler characteri... | ibivibiv/math_instruct | |
What is 999182 to the power of 1/2, to the nearest integer?\n | 1000\n | ibivibiv/math_instruct | |
Calculate the least common multiple of (-33)/4*4*(-16)/4 and 110.\n | 660\n | ibivibiv/math_instruct | |
Find the third derivative of -588190*o*t**4 + 27*o*t**3 + 4290136*o + 4*t**2 wrt t.\n | -14116560*o*t + 162*o\n | ibivibiv/math_instruct | |
Which is the closest to 27? (a) 1 (b) 3/7 (c) 42 (d) -2\n | c\n | ibivibiv/math_instruct | |
Simplify ((m/(m*m/(m/(m**(-2/9)*m))))/m*m)**(-21)*m**29/m**(-6/7) assuming m is positive.\n | m**(970/21)\n | ibivibiv/math_instruct | |
Let l be (6/(-8))/((-2)/(-8)). Let f = 2.3 + -0.3. Let o be 54/15*1/6. Which is the nearest to f? (a) l (b) -2/5 (c) o\n | c\n | ibivibiv/math_instruct | |
Solve 5*v + 317*z = 320*z + 29, -2*v - 2*z + 2 = 0 for v.\n | 4\n | ibivibiv/math_instruct | |
Let b(h) = -h**2 - 9*h - 14. Suppose z + 4*p + 6 = 0, 2*z + 24 = -2*z - p. Let c be b(z). Suppose -15 = c*m - 11. Is 0 less than or equal to m?\n | False\n | ibivibiv/math_instruct | |
Sort -5, -101038, -2, -0.4 in descending order.\n | -0.4, -2, -5, -101038\n | ibivibiv/math_instruct | |
What is 10 - 448/819*18?\n | 2/13\n | ibivibiv/math_instruct | |
Solve 2*k + 3*f + 8 = 4, 2*f = -4*k for k.\n | 1\n | ibivibiv/math_instruct | |
Add -72537856 and 20.7.\n | -72537835.3\n | ibivibiv/math_instruct | |
Evaluate ((9 + -4)/(-5))/1*-7.\n | 7\n | ibivibiv/math_instruct | |
What is the second derivative of -244*j**5 - 2*j**3 - 109*j?\n | -4880*j**3 - 12*j\n | ibivibiv/math_instruct | |
Evaluate (18/(-540)*18)/(3/10*-2).\n | 1\n | ibivibiv/math_instruct | |
Let l(i) = 11*i**3 - 9*i**2 + 15*i - 15. Let r = -251 + 246. Let c(u) = -2*u**3 - u + 1. Let y(k) = r*c(k) - l(k). Calculate y(8).\n | -6\n | ibivibiv/math_instruct | |
b"What is the rth term of 89, 341, 593, 845, 1097, 1349?\n" | 252*r - 163\n | ibivibiv/math_instruct | |
Simplify 3 + -1 + (-5 + sqrt(153)*-1 + sqrt(153) + sqrt(153))**2 - -4*2*sqrt(187)/(sqrt(176)*-3).\n | -92*sqrt(17)/3 + 180\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 2414 and 187.\n | 17\n | ibivibiv/math_instruct | |
Suppose -168 = -24*g + 28*g. Round g to the nearest 10.\n | -40\n | ibivibiv/math_instruct | |
Put 1, 2, 359, 4, -2, -7 in descending order.\n | 359, 4, 2, 1, -2, -7\n | ibivibiv/math_instruct | |
What is 43/6 of a minute in seconds?\n | 430\n | ibivibiv/math_instruct | |
Let o(k) = 4*k**2 + 81*k + 1. Let g(j) = -30*j. Calculate g(o(f)).\n | -120*f**2 - 2430*f - 30\n | ibivibiv/math_instruct | |
Rearrange 79*r**3 - 4*r - r**4 - 78*r**3 - r**4 - 2 + 4*r**4 to g*r**3 + v*r**2 + b*r**4 + x + y*r and give y.\n | -4\n | ibivibiv/math_instruct | |
Let b(g) = -g**3 + 214*g**2 + 1544*g + 869. Determine b(221).\n | 206\n | ibivibiv/math_instruct | |
Let o(l) = -l**2 - 1 + 2 - 1. Let m(d) = -10*d. Give o(m(b)).\n | -100*b**2\n | ibivibiv/math_instruct | |
Suppose 2*f - 3 - 3 = 0. What is the tens digit of 20 - (f + -4 - -3)?\n | 1\n | ibivibiv/math_instruct | |
What is the eighth root of 845 to the nearest integer?\n | 2\n | ibivibiv/math_instruct | |
Let y = -5171 - -12614. Let c be (322/(-4))/((-3)/(-438)). Let d = y + c. What is d rounded to the nearest 100?\n | -4300\n | ibivibiv/math_instruct | |
What is the cube root of 63237837 to the nearest integer?\n | 398\n | ibivibiv/math_instruct | |
What is -24.545 rounded to zero decimal places?\n | -25\n | ibivibiv/math_instruct | |
Let q(r) = -26*r**2 - 5. Let b(h) = -69*h - 10*h + 77*h. What is q(b(n))?\n | -104*n**2 - 5\n | ibivibiv/math_instruct | |
Expand (-6 - 3*p + 6)*(259 - 5 + 321 - 113).\n | -1386*p\n | ibivibiv/math_instruct | |
Suppose 117 = 4*m - o, -4*m + 51 = -2*m + o. Is 16 a factor of m?\n | False\n | ibivibiv/math_instruct | |
Put 22, 4759, -1 in decreasing order.\n | 4759, 22, -1\n | ibivibiv/math_instruct | |
What is 0.0000015118 rounded to seven decimal places?\n | 0.0000015\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 1002 and 88?\n | 44088\n | ibivibiv/math_instruct | |
Let h(o) be the first derivative of -26*o**3/3 - 8*o**2 + 24. What is the second derivative of h(l) wrt l?\n | -52\n | ibivibiv/math_instruct | |
Let m = 5.0228 + -0.0228. What is the third smallest value in -14, -0.02, m?\n | m\n | ibivibiv/math_instruct | |
Are -3322217 and -3321600 unequal?\n | True\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 i, 2 m, and 1 e when four letters picked without replacement from {m: 4, e: 7, i: 4}.\n | 8/65\n | ibivibiv/math_instruct | |
What is (32 - 36 - (4 - (-2 - -3))) + 3?\n | -4\n | ibivibiv/math_instruct | |
Let n = 0.1 - 0.6. Let t = -1 - n. Let u be (-2)/3 + 0 - -2. What is the second smallest value in u, 0.2, t?\n | 0.2\n | ibivibiv/math_instruct | |
Express 47*h**2 - 14*h**2 - 15*h**2 - 3*h**2 - 28 - 483*h + 486*h as s*h + q*h**2 + u and give u.\n | -28\n | ibivibiv/math_instruct | |
Find the common denominator of -21/8 and 19/2683.\n | 21464\n | ibivibiv/math_instruct | |
What is 735493 to the power of 1/2, to the nearest integer?\n | 858\n | ibivibiv/math_instruct | |
Suppose 1 = -3*m + 7. Suppose 0 = -c + 4*h + 1, m*h = -0 + 2. Suppose c*t + 13 = -n, -2*n + 5 = -t - 2. Solve 0 = 2*d + 2 + n for d.\n | -2\n | ibivibiv/math_instruct | |
Let o = -833 + 836. Solve -25*u - o*t = -30*u - 10, 0 = 5*t for u.\n | -2\n | ibivibiv/math_instruct | |
Let z = -0.042 + 203.042. Let c = -27448644.999798 + 27448848. Let w = z - c. Round w to five decimal places.\n | -0.0002\n | ibivibiv/math_instruct | |
Suppose g = -3*j + 5*g + 5, -3 = -5*j + 4*g. Let p = -3 + 5. Let z = p + j. What is the highest common divisor of z and 8?\n | 1\n | ibivibiv/math_instruct | |
Let p(s) = -15*s + 11. Determine p(2).\n | -19\n | ibivibiv/math_instruct | |
Let w be (-2)/(-4) - (-75)/(-10). Let b = w + 11. Suppose -7*n + 3*n + 2*q + 144 = 0, 4*n + 4*q = 144. What is the greatest common factor of b and n?\n | 4\n | ibivibiv/math_instruct | |
Let g = 161771276.4275145 - 161776675.99. Let t = g + 5384.5625. Let m = -15 - t. Round m to six dps.\n | -0.000015\n | ibivibiv/math_instruct | |
Let k(h) = -15*h - 34. Let l(r) = 1. Let m(c) = -k(c) - l(c). Let z(s) = -s - 2. Calculate 2*m(d) + 33*z(d).\n | -3*d\n | ibivibiv/math_instruct | |
Find the second derivative of 645*c**2 - 188*c + 14 + 83*c + 89*c - 3 wrt c.\n | 1290\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {i: 10, c: 2}. Give prob of sequence cc.\n | 1/66\n | ibivibiv/math_instruct | |
Factor 2*y**4/3 + 4*y**3/3 + 2*y**2/3.\n | 2*y**2*(y + 1)**2/3\n | ibivibiv/math_instruct | |
Let n(m) be the third derivative of -29*m**4/4 + 10*m**3/3 - 54*m**2. List the prime factors of n(-2).\n | 2, 23\n | ibivibiv/math_instruct | |
Three letters picked without replacement from ccfff. What is prob of sequence ffc?\n | 1/5\n | ibivibiv/math_instruct | |
Is 416239 a composite number?\n | False\n | ibivibiv/math_instruct | |
Put 4, 9, -5, 0 in ascending order.\n | -5, 0, 4, 9\n | ibivibiv/math_instruct | |
Work out 1432973671 + 8.1316.\n | 1432973679.1316\n | ibivibiv/math_instruct | |
Simplify ((y/(y/(y**(2/5)*y))*y**(-10)*y**(-2/5)/(y/(y*y*(y/(y*y*y**(-5)))/y*y)))**(3/34))**(4/11) assuming y is positive.\n | y**(-24/187)\n | ibivibiv/math_instruct | |
Let l(a) = 4*a. Let s(h) = 5132293*h**2. Calculate s(l(d)).\n | 82116688*d**2\n | ibivibiv/math_instruct | |
Which is the fifth biggest value? (a) 359 (b) 3 (c) -2/17 (d) -3 (e) -2/5\n | d\n | ibivibiv/math_instruct | |
60 - (-33 - (3 + -34) - (-8 + (-2 - -1)))\n | 53\n | ibivibiv/math_instruct | |
Suppose -3*x + 0 = 12. What are the prime factors of -3 - 8/x*15?\n | 3\n | ibivibiv/math_instruct | |
What is the cube root of 45190 to the nearest integer?\n | 36\n | ibivibiv/math_instruct | |
Let f be (7 - 18)/((-9)/2). Is 1 smaller than f?\n | True\n | ibivibiv/math_instruct | |
Let x = 1 + -1. Let p(f) = -f**2 - 4*f + 13. Let j be p(-8). Let n = j - -22. Put n, x, 2 in descending order.\n | n, 2, x\n | ibivibiv/math_instruct | |
List the prime factors of 350717583.\n | 3, 89, 151, 8699\n | ibivibiv/math_instruct | |
Is 9921 prime?\n | False\n | ibivibiv/math_instruct | |
What is the millions digit of 730472875?\n | 0\n | ibivibiv/math_instruct | |
Simplify -4 + sqrt(130)/(sqrt(10)*-1).\n | -4 - sqrt(13)\n | ibivibiv/math_instruct | |
Let w be ((-12)/(-50))/(19 + (-2431)/130). Let k be (-4 - 2)*(-4)/18. Let v = 14/15 - k. Which is the closest to v? (a) -0.2 (b) w (c) 0.3\n | a\n | ibivibiv/math_instruct | |
What is the thousands digit of 315726?\n | 5\n | ibivibiv/math_instruct | |
Let k = 0 - 0. Let s = 0 + k. Let u = 6.9 + -5.9. Which is the second biggest value? (a) -2/3 (b) u (c) s\n | c\n | ibivibiv/math_instruct | |
In base 7, what is -21 - 511?\n | -532\n | ibivibiv/math_instruct | |
Let o(r) = -6*r + 10. Let x(w) = -7*w + 11. Let q(u) = 6*o(u) - 5*x(u). Suppose -4*l - 4 + 16 = 0. Let b be q(l). Solve 0 = -4*y + b*y - 6 for y.\n | -3\n | ibivibiv/math_instruct | |
What is the thousands digit of 187982?\n | 7\n | ibivibiv/math_instruct | |
Let v(i) = i**3 - 44*i**2 + 2*i - 85. Calculate v(44).\n | 3\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 586278 and 752?\n | 4690224\n | ibivibiv/math_instruct | |
Which is the nearest to -0.4? (a) 68 (b) 5 (c) 0.35\n | c\n | ibivibiv/math_instruct | |
Let x(o) = -o**3 + 7*o**2 + 11*o - 5. Let s be x(8). Suppose 0 = -d + s + 5. Calculate the highest common divisor of 3 and d.\n | 3\n | ibivibiv/math_instruct | |
Let h(x) = -2*x**3 - 220*x**2 - 918*x + 4784. What is h(3)?\n | -4\n | ibivibiv/math_instruct | |
Let x = 4 + -3.4. Let v = x - 0.5. Let u = -15.14 - -18.14. Which is greater: v or u?\n | u\n | ibivibiv/math_instruct | |
Let t(c) = c**2 + 5*c + 4. Let g be t(-1). Suppose 5*r + 6 = 3*p + 27, -2*r - 5*p - 4 = g. Solve r*l + b = -b + 14, -3*b - 5 = -2*l for l.\n | 4\n | ibivibiv/math_instruct | |
Let l(a) be the third derivative of 0*a + 0*a**3 - a**2 + 7/60*a**5 + 0 + 0*a**6 - 1/14*a**7 + 0*a**4. What is the third derivative of l(c) wrt c?\n | -360*c\n | ibivibiv/math_instruct |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.