instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Which is the third biggest value? (a) 552 (b) -1 (c) 2/7 (d) 6/29 (e) 5\n | c\n | ibivibiv/math_instruct | |
Let m(c) = -c**2 - 5*c + 7. Let p be m(-6). Let v be p - (-1 + 1*-8). Let w = v + 4. Is w a composite number?\n | True\n | ibivibiv/math_instruct | |
Collect the terms in -123*v + 64*v + 45*v.\n | -14*v\n | ibivibiv/math_instruct | |
Simplify 1 + (sqrt(68)*1 - sqrt(68))**2.\n | 1\n | ibivibiv/math_instruct | |
Let r = 2 + -3. Let n(k) be the second derivative of k**4/3 + k**3/6 - 4*k. Is n(r) a multiple of 3?\n | True\n | ibivibiv/math_instruct | |
What is -0.0686455 rounded to 3 decimal places?\n | -0.069\n | ibivibiv/math_instruct | |
Let g be (3*(0 + -1))/1. Let w = -4 - g. Let h(d) = -9*d + 2. Let c(t) = 5*t - 1. Let b(x) = -5*c(x) - 2*h(x). Determine b(w).\n | 8\n | ibivibiv/math_instruct | |
Simplify (((f*f/f**(-2/5)*f)/(f*f/f**11))/(f**7*f*f**(-10)))**(-28) assuming f is positive.\n | f**(-2016/5)\n | ibivibiv/math_instruct | |
What is 422981 to the power of 1/10, to the nearest integer?\n | 4\n | ibivibiv/math_instruct | |
Let q = 218.869 - 219. Round q to 2 dps.\n | -0.13\n | ibivibiv/math_instruct | |
Let c(l) = l**3 + 13*l**2 - l - 27. Suppose 7*v - 49 = -126. Let r be c(v). What is the second derivative of 36*n - 23*n**3 + 226 - r + 4*n wrt n?\n | -138*n\n | ibivibiv/math_instruct | |
What is the units digit of 10241?\n | 1\n | ibivibiv/math_instruct | |
b"What is the vth term of 140453, 561671, 1263651, 2246393, 3509897, 5054163, 6879191?\n" | 140381*v**2 + 75*v - 3\n | ibivibiv/math_instruct | |
Express (-96*a + 1101 - 1101)*(-3*a - 5 - 5*a - 1 + 5) as j*a**2 + m*a + c and give m.\n | 96\n | ibivibiv/math_instruct | |
Let v be 43 + -49 + 13 + 3/3. What is the greatest common factor of v and 1668?\n | 4\n | ibivibiv/math_instruct | |
Let h = 1.98 - 2. Let g = h + 4.02. Suppose -16*k - 22*k = 114. What is the biggest value in g, k, 0?\n | g\n | ibivibiv/math_instruct | |
Let m(u) = -4*u**2. Let f(i) = -243*i. Calculate f(m(n)).\n | 972*n**2\n | ibivibiv/math_instruct | |
Let z(x) = -x**3 + 15*x**2 + 17*x - 14. What is the least common multiple of 5 and z(16)?\n | 10\n | ibivibiv/math_instruct | |
Is 1796825587 prime?\n | False\n | ibivibiv/math_instruct | |
Suppose 4*d = 665 + 779. What is the remainder when d is divided by 98?\n | 67\n | ibivibiv/math_instruct | |
What is the ten millions digit of 172347434?\n | 7\n | ibivibiv/math_instruct | |
Let l = -21245.8 + 21246. Let a = -10 - -7. What is the second smallest value in l, -1/22, a?\n | -1/22\n | ibivibiv/math_instruct | |
Is 22483393189 a composite number?\n | True\n | ibivibiv/math_instruct | |
List the prime factors of 92397903.\n | 3, 13, 887, 2671\n | ibivibiv/math_instruct | |
Let o(f) = 33*f + 11. Let n(r) = 11*r + 3. Let p(m) = -8*n(m) + 3*o(m). What is p(-1)?\n | -2\n | ibivibiv/math_instruct | |
Let q = -47 + 52. Let y be (-11)/(33/(-60)) - (q + -2). Let m = y - -4. What is the remainder when 40 is divided by m?\n | 19\n | ibivibiv/math_instruct | |
Is 25151 a composite number?\n | True\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 39802396 and 674?\n | 674\n | ibivibiv/math_instruct | |
Collect the terms in 7013*a - 9334*a + 15980*a + 4923*a + 24452*a.\n | 43034*a\n | ibivibiv/math_instruct | |
What is the thousands digit of 1221?\n | 1\n | ibivibiv/math_instruct | |
What is the next term in 112, 98, 84, 70, 56, 42?\n | 28\n | ibivibiv/math_instruct | |
What is the millions digit of 11195644?\n | 1\n | ibivibiv/math_instruct | |
Let k = 14743 - 191661/13. Which is the closest to -5? (a) -3 (b) k (c) 113 (d) 0.2\n | a\n | ibivibiv/math_instruct | |
Let m be 27/(-6) - -4 - (-2044)/8. Let l = -250 + m. Let f = 1 - 1. Solve f = -l*u + 20 for u.\n | 4\n | ibivibiv/math_instruct | |
Let n be (13 - 10)/(3/52). Let s = n - 37. Is 2*s*(-1)/(-2) a multiple of 15?\n | True\n | ibivibiv/math_instruct | |
Collect the terms in 4586 + 23328 + 3*s**2 - 3204.\n | 3*s**2 + 24710\n | ibivibiv/math_instruct | |
Let f(g) = -7*g**2 - 4*g + 3. Let n be f(1). Let v(l) = -15 - 6*l + 2*l**2 + 5*l - 34. What is the tens digit of v(n)?\n | 8\n | ibivibiv/math_instruct | |
List the prime factors of 9670.\n | 2, 5, 967\n | ibivibiv/math_instruct | |
Let n(f) = 8 - f - 3*f + 2*f + 0*f. Give n(7).\n | -6\n | ibivibiv/math_instruct | |
Let n(u) = -3*u**3 + 2*u**2 - 3*u**2 - 4*u**3 + 2*u. Let b(s) = s**2 - s. Let t = 20 + -19. Let x(l) = t*n(l) + b(l). What is x(1)?\n | -6\n | ibivibiv/math_instruct | |
Collect the terms in -8*n - 62 + 18 - 112 + 6*n.\n | -2*n - 156\n | ibivibiv/math_instruct | |
Is 4177237 a prime number?\n | False\n | ibivibiv/math_instruct | |
Calculate -15*(-2)/(-3)*57*3/513.\n | -10/3\n | ibivibiv/math_instruct | |
Calculate prob of sequence zaa when three letters picked without replacement from aadaaddzaadddddaaaa.\n | 5/323\n | ibivibiv/math_instruct | |
Suppose -3*f + 602 = -0*b + 4*b, 0 = -5*f - 2*b + 1008. Is f prime?\n | False\n | ibivibiv/math_instruct | |
11222 (base 3) to base 2\n | 10000110\n | ibivibiv/math_instruct | |
What is (6 - 1) + -26 + 10 + 9?\n | -2\n | ibivibiv/math_instruct | |
Simplify 5 + (-2*sqrt(7) - sqrt(7)) - (sqrt(700) + 3)**2 - (sqrt(84) + 6*(sqrt(84) + (sqrt(84) - (-1*sqrt(84) + sqrt(84)))))/(2*sqrt(1452)).\n | -704 - 1399*sqrt(7)/22\n | ibivibiv/math_instruct | |
Let y(f) = f - 59. Let s(t) = 13*t**2 + 9*t. Let c(j) = 3*j**2 + 2*j. Let x be 0*(-1)/2 - (-12)/3. Let h(g) = x*s(g) - 18*c(g). Determine y(h(p)).\n | -2*p**2 - 59\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 2/5 - (-28265940)/900?\n | 3\n | ibivibiv/math_instruct | |
Suppose 34 - 16 = -67*q + 18. Solve -3 = f, q*s + 2 = s - 2*f for s.\n | -4\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-70.4323 + (72.5188 / -86.5524) | -71.2702 | ibivibiv/math_instruct | |
Multiply 2837 and -0.16046.\n | -455.22502\n | ibivibiv/math_instruct | |
Suppose -30*q - 1258 = 512. Let b be 54 - (0 + -3 - -2). Let k = b - q. What is the hundreds digit of k?\n | 1\n | ibivibiv/math_instruct | |
Sort 10, 53, 3, -2, -5 in ascending order.\n | -5, -2, 3, 10, 53\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 60 and 7160.\n | 20\n | ibivibiv/math_instruct | |
What is the units digit of 7554440?\n | 0\n | ibivibiv/math_instruct | |
11 - -16 - 0 - -11\n | 38\n | ibivibiv/math_instruct | |
Let t(g) = -1422 - 9*g + 1422 - g - 3*g. Let l(i) be the second derivative of i**5/120 - i**3/3 - i. Let q(r) be the second derivative of l(r). What is t(q(j))?\n | -13*j\n | ibivibiv/math_instruct | |
What is the least common multiple of 105 and 210?\n | 210\n | ibivibiv/math_instruct | |
Which is the nearest to -1/2? (a) 1.2 (b) -312 (c) -6 (d) -2\n | d\n | ibivibiv/math_instruct | |
0.871*-576.447\n | -502.085337\n | ibivibiv/math_instruct | |
Suppose 0*g = 2*g - 4. List the prime factors of g.\n | 2\n | ibivibiv/math_instruct | |
Collect the terms in 31*j + 46*j + 20*j - 8169 + 8167 - 127*j + 20*j + 48*j.\n | 38*j - 2\n | ibivibiv/math_instruct | |
Sum -39551 and -172.6.\n | -39723.6\n | ibivibiv/math_instruct | |
Suppose -2*d + 0*d = -4. Let v be 1 + (1*-2)/(-1). Suppose -3 = 3*f + v. Sort -1, f, d.\n | f, -1, d\n | ibivibiv/math_instruct | |
Let m(y) = y**2 - 2*y - 1. Let a be m(-1). Let s(q) = -13*q**2 + 3 + 12*q**a - 3*q + 0 + q**3. Suppose 4*n - 5*d = -2, 3*d = 5*n - 3 - 1. Calculate s(n).\n | 1\n | ibivibiv/math_instruct | |
Work out -0.85965 + -32442.8.\n | -32443.65965\n | ibivibiv/math_instruct | |
Let p be (-1 + (-14)/(-6))/((-8)/36). Let n be -849 + 3 + p/6. What is n rounded to the nearest one hundred?\n | -800\n | ibivibiv/math_instruct | |
Let a be ((-3)/(-108)*3)/((-14)/(-28)). Put 3, 4/5, a, -1/5 in decreasing order.\n | 3, 4/5, a, -1/5\n | ibivibiv/math_instruct | |
Divide 160411584 by 18912.\n | 8482\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {d: 4}. Give prob of picking 2 d.\n | 1\n | ibivibiv/math_instruct | |
Convert -321 (base 15) to base 3.\n | -222011\n | ibivibiv/math_instruct | |
Two letters picked without replacement from ocmeckcmomoccy. Give prob of sequence ke.\n | 1/182\n | ibivibiv/math_instruct | |
Expand (-v + 3*v - 4*v - 3*v - v + v + (-3*v - v + 2*v)*(6 - 4 - 4))*(-2 - 4 + 5).\n | v\n | ibivibiv/math_instruct | |
Suppose -204 = -10*q + 36. Solve -24 = 12*w + q for w.\n | -4\n | ibivibiv/math_instruct | |
Divide -2 by 492432.\n | -1/246216\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 448456 and 616627?\n | 4933016\n | ibivibiv/math_instruct | |
-56454436 (base 8) to base 10\n | -12212510\n | ibivibiv/math_instruct | |
Suppose 1641 = 2*i - 5*z, -4*z = 2*i - 1331 - 337. What is the tens digit of i?\n | 2\n | ibivibiv/math_instruct | |
What is 1010213340 (base 5) in base 16?\n | 1f1b43\n | ibivibiv/math_instruct | |
Expand d**3 - 2*d**4 - d**3 + (d**2 + 2*d - 2*d)*(-4*d**2 + 3*d**2 - 9*d**2) + (5*d + 6*d - 2*d)*(-3*d + 3*d - 3*d**3) - 6*d**2 + 8*d**4 + 6*d**2.\n | -31*d**4\n | ibivibiv/math_instruct | |
What is 454 minutes after 4:19 AM?\n | 11:53 AM\n | ibivibiv/math_instruct | |
Suppose -2*o - y = -8, -4*o + o + 13 = 2*y. Suppose 2*x - 95 = -o*g + x, -2*g + 66 = -2*x. Does 16 divide g?\n | True\n | ibivibiv/math_instruct | |
Expand ((2 - 1 - 2)*(-2*y + 3 - 3) + 5*y - 1 + 1)*(-4*y + 3 - 3).\n | -28*y**2\n | ibivibiv/math_instruct | |
Which is smaller: 799 or 798?\n | 798\n | ibivibiv/math_instruct | |
Let h = -63 - -62.5. What is the second biggest value in -1/5, 3/7, -0.8, h?\n | -1/5\n | ibivibiv/math_instruct | |
Suppose 0*m**2 - 1/4*m + 0 + 1/4*m**3 = 0. What is m?\n | -1, 0, 1\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Does $\sum\limits_{k=1}^n 1 / k ^ 2$ converge when $n\rightarrow\infty$?
I can prove this sum has a constant upper bound like this:
$$\sum_{k=1}^n \frac1{k ^ 2} \lt 1 + \sum_{k=2}^n \frac 1 {k (k - 1)} = 2 - \frac 1 n \lt... | The question posed is whether the sum of the series 1/k² converges as n approaches infinity. A user named J.M. proves that this sum has a constant upper bound of 2 through the inequality stated above. Another user, Arturo Magidin, confirms the convergence of the sum and identifies it as a special case of a p-series, w... | ibivibiv/math_instruct | |
Solve -1607*p = -778*p - 792*p + 185 for p.\n | -5\n | ibivibiv/math_instruct | |
Let h = -0.54 - 0.46. Let q = 8 - h. Let k = -8 - -5. What is the biggest value in 4, k, q?\n | q\n | ibivibiv/math_instruct | |
What is the second smallest value in 0.3, -2, -0.04, 42?\n | -0.04\n | ibivibiv/math_instruct | |
What is 1171344147 to the power of 1/8, to the nearest integer?\n | 14\n | ibivibiv/math_instruct | |
Let n(q) = 146*q**3 - 5671*q**2 - 16. Let x(l) = -293*l**3 + 11344*l**2 + 40. Let p(o) = -5*n(o) - 2*x(o). Find the third derivative of p(k) wrt k.\n | -864\n | ibivibiv/math_instruct | |
Factor -3*f**2 + 54*f - 51.\n | -3*(f - 17)*(f - 1)\n | ibivibiv/math_instruct | |
Suppose 14*w - 17*w + 27 = 0. Suppose 4*p + 27 = -w. Is 11 a factor of p + 7 + 24*1?\n | True\n | ibivibiv/math_instruct | |
Let c(s) = -s**2 - 9*s + 3. Let t be c(-9). Let h = 13 - t. What is the units digit of h?\n | 0\n | ibivibiv/math_instruct | |
Let l = -5 + 15. Let z(w) = 14*w**2 - w. Let k be z(-1). Calculate the lowest common multiple of (55/k + -1)*6 and l.\n | 80\n | ibivibiv/math_instruct | |
Rearrange 33*o**2 - 21*o**2 - 20*o - 14*o**2 - 10*o**2 to the form x*o**2 + u*o + z and give x.\n | -12\n | ibivibiv/math_instruct | |
What comes next: -4781, -4782, -4781, -4778, -4773, -4766?\n | -4757\n | ibivibiv/math_instruct |
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