instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Does 198 divide 2848032?\n | True\n | ibivibiv/math_instruct | |
Let v(a) = -5*a**3 - a**2 + 1. Let u be v(-1). Let n = u - 5. Solve 4*k + n*j = 4*j - 24, -k - 2 = 3*j for k.\n | -5\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {e: 2, o: 5, u: 2, n: 2, p: 1, c: 1}. Give prob of picking 1 p, 1 c, and 1 o.\n | 5/286\n | ibivibiv/math_instruct | |
Let q(x) = -57*x. Let v(z) = 13*z**2 + 2*z. Determine v(q(k)).\n | 42237*k**2 - 114*k\n | ibivibiv/math_instruct | |
Is 0 > 54/67153?\n | False\n | ibivibiv/math_instruct | |
Simplify ((u*u**(5/4))/u**(-7))/(u**(-2/7))**(-2/65) assuming u is positive.\n | u**(16819/1820)\n | ibivibiv/math_instruct | |
Calculate (-1*18/(-15))/(-663*(-12)/780).\n | 2/17\n | ibivibiv/math_instruct | |
List the prime factors of 140.\n | 2, 5, 7\n | ibivibiv/math_instruct | |
Suppose 92 - 182 = 45*u. Let q = -0.1 + -0.9. What is the second smallest value in -4/3, u, q, 0.1?\n | -4/3\n | ibivibiv/math_instruct | |
List the prime factors of (3 + 14/(-4))/(14/(-4452)).\n | 3, 53\n | ibivibiv/math_instruct | |
Suppose -21 = -2*g - g. Suppose -573 = -g*f - 90. List the prime factors of f.\n | 3, 23\n | ibivibiv/math_instruct | |
Let t be -1 - -4 - 1 - -2. Suppose -t*i + 4*s + 42 = 6*s, -4*i - s + 37 = 0. Calculate the least common multiple of i and (-1 + 0 - -3) + 0.\n | 8\n | ibivibiv/math_instruct | |
Is 127340638 a multiple of 57?\n | False\n | ibivibiv/math_instruct | |
Let c(o) = 5*o**2 - 79*o + 12. What is the hundreds digit of c(-7)?\n | 8\n | ibivibiv/math_instruct | |
What is -0.031521 rounded to four decimal places?\n | -0.0315\n | ibivibiv/math_instruct | |
Calculate 4 divided by -33237.\n | -4/33237\n | ibivibiv/math_instruct | |
Let w(i) = i - 4*i - 9 - 4. Let f be w(-10). Solve 0 = 5*c - 3 - f for c.\n | 4\n | ibivibiv/math_instruct | |
Let x = -6.7 - -6.6. Let p = -1.3 + 0.3. Let d = p - -0.6. Which is the smallest value? (a) 5 (b) x (c) d\n | c\n | ibivibiv/math_instruct | |
Evaluate ((-3)/45)/(11/(-33)).\n | 1/5\n | ibivibiv/math_instruct | |
Suppose t + 67 = 5*k - 3*t, -5*t - 48 = -3*k. Let u(c) be the third derivative of c**5/60 - c**4/4 - 9*c**3/2 - c**2. Does 11 divide u(k)?\n | False\n | ibivibiv/math_instruct | |
Calculate -13401*-268.\n | 3591468\n | ibivibiv/math_instruct | |
What is 582 minutes before 6:43 PM?\n | 9:01 AM\n | ibivibiv/math_instruct | |
Does 145 divide 32970?\n | False\n | ibivibiv/math_instruct | |
Let f = 12 + 24. What are the prime factors of f?\n | 2, 3\n | ibivibiv/math_instruct | |
Total of 36.8 and -862704427.\n | -862704390.2\n | ibivibiv/math_instruct | |
What is 97 minutes after 8:32 PM?\n | 10:09 PM\n | ibivibiv/math_instruct | |
Rearrange (2*w - 7*w + w)*(w**2 + 2*w - 2*w) - 13 - w**3 + 13 to v*w**3 + i*w**2 + b + s*w and give v.\n | -5\n | ibivibiv/math_instruct | |
Expand (3*w - 6*w + w)*(2*w + 1 - 1 + (-1 - 1 + 5)*(-4*w + w - w)).\n | 20*w**2\n | ibivibiv/math_instruct | |
Which is smaller: 68 or -34?\n | -34\n | ibivibiv/math_instruct | |
What is the second derivative of 1903851*j**2 + 1280248*j?\n | 3807702\n | ibivibiv/math_instruct | |
Simplify (sqrt(38)/sqrt(2) + -2)**2 + 0 + -2.\n | -4*sqrt(19) + 21\n | ibivibiv/math_instruct | |
Let n be 12/18*(5/(-30) + 0). Is -6 equal to n?\n | False\n | ibivibiv/math_instruct | |
What is 3 divided by 1376?\n | 3/1376\n | ibivibiv/math_instruct | |
Let q(d) be the first derivative of 3*d**2 + 72*d + 72. Is q(4) a multiple of 12?\n | True\n | ibivibiv/math_instruct | |
Let f be 3/(-6)*(-8)/10. Let q = -57470 + 57468. Which is the biggest value? (a) f (b) -3/7 (c) -4 (d) q\n | a\n | ibivibiv/math_instruct | |
What is next in 1982, 1979, 1986, 2003?\n | 2030\n | ibivibiv/math_instruct | |
b"What is the nth term of 216570, 216569, 216570, 216573, 216578, 216585, 216594?\n" | n**2 - 4*n + 216573\n | ibivibiv/math_instruct | |
Let k(p) = 2*p + 12. Let a be k(-7). Calculate the common denominator of -93/4 and ((-1)/(-12))/(a/255).\n | 8\n | ibivibiv/math_instruct | |
Which is the closest to 0.3? (a) -3/5 (b) 0.1 (c) -5 (d) -8\n | b\n | ibivibiv/math_instruct | |
What is -0.0358 rounded to 2 dps?\n | -0.04\n | ibivibiv/math_instruct | |
Suppose -2*m - m = z - 628, 3*m + 3*z - 624 = 0. Let j be (-3)/(-15) + m/(-50). Which is the nearest to -1/2? (a) 0.5 (b) 0.02 (c) j\n | b\n | ibivibiv/math_instruct | |
Differentiate -515920*a*t**2 - 2*t**2 - 238337 with respect to a.\n | -515920*t**2\n | ibivibiv/math_instruct | |
Let f = -112 - -172. Let w = 45 + -14. Calculate the remainder when f is divided by w.\n | 29\n | ibivibiv/math_instruct | |
Suppose -29*a = -72*a + 2752. Let d(q) = -11*q**3 + 3*q**2 + 3*q - 3. Let j(p) = -232*p**3 + 64*p**2 + 64*p - 64. What is a*d(b) - 3*j(b)?\n | -8*b**3\n | ibivibiv/math_instruct | |
What is 3823938 to the power of 1/2, to the nearest integer?\n | 1955\n | ibivibiv/math_instruct | |
What is the tenth root of 15283 to the nearest integer?\n | 3\n | ibivibiv/math_instruct | |
Is 16116239 a composite number?\n | True\n | ibivibiv/math_instruct | |
Suppose 0*y + 3*y = 9. Let z be (3 - 0 - y)*1. Suppose d + 4*d - 5 = z. Calculate the least common multiple of d and 1.\n | 1\n | ibivibiv/math_instruct | |
Calculate the common denominator of 95/5452 and -6/6815.\n | 27260\n | ibivibiv/math_instruct | |
Let m be 0 + 2 + -3911 - 1. Let x be m/(-35) - 4/(-14). Let c = x - 78. Does 17 divide c?\n | True\n | ibivibiv/math_instruct | |
What is the third root of 655756 to the nearest integer?\n | 87\n | ibivibiv/math_instruct | |
Let h(t) be the second derivative of 0 + t - 2/3*t**3 + 3*t**2 + 1/3*t**4. Let w be (-4)/4 - (1 - 1). Let u(d) = -d**2 + d - 1. Calculate w*h(o) - 6*u(o).\n | 2*o**2 - 2*o\n | ibivibiv/math_instruct | |
Let z = -478.3 - -478. Suppose 4*w - i - 4 = 0, 7*w - 4*i - 16 = 2*w. Put 0.4, z, 3, w in ascending order.\n | z, w, 0.4, 3\n | ibivibiv/math_instruct | |
-3ef4bb (base 16) to base 14\n | -79585d\n | ibivibiv/math_instruct | |
Which is the third smallest value? (a) 3 (b) 5 (c) 0.4 (d) 1/43 (e) -2958\n | c\n | ibivibiv/math_instruct | |
Differentiate 665 - 9853*q**2 + 4786*q**2 + 4865*q**2 wrt q.\n | -404*q\n | ibivibiv/math_instruct | |
Express -2 + g + 2 + g + 0*g + 0*g + (0*g + 2*g - g)*(3 + 1 - 2) - 30266 + 1090*g + 30266 in the form c*g + j and give j.\n | 0\n | ibivibiv/math_instruct | |
Is 5174463547 composite?\n | True\n | ibivibiv/math_instruct | |
What is the millions digit of 15395845?\n | 5\n | ibivibiv/math_instruct | |
Let l be ((-39)/65)/((-1)/10). What is the highest common factor of l and 9?\n | 3\n | ibivibiv/math_instruct | |
Sort -1, -0.41, 3, -2/11, -3 in descending order.\n | 3, -2/11, -0.41, -1, -3\n | ibivibiv/math_instruct | |
Let p = 27 + 5. Let r be ((-1 - 0)*-1)/((-24)/(-552)). Suppose 3*d = -r + p. Calculate the greatest common factor of 3 and d.\n | 3\n | ibivibiv/math_instruct | |
Let n = -17 - -23. What is the third derivative of -2*f**n + 2*f**6 + 0*f**6 - 8*f**2 + 2*f**6 wrt f?\n | 240*f**3\n | ibivibiv/math_instruct | |
Let m = 71/185 + 8/37. Let v = -5801 + 5809. Which is the second smallest value? (a) v (b) 5 (c) m (d) -0.1\n | c\n | ibivibiv/math_instruct | |
Simplify ((4*(sqrt(48)/sqrt(2) + sqrt(24)))/sqrt(2))**2.\n | 768\n | ibivibiv/math_instruct | |
Calculate 102/27 - 16/(-72).\n | 4\n | ibivibiv/math_instruct | |
Calculate prob of sequence ovzv when four letters picked without replacement from {q: 1, o: 4, v: 2, u: 2, z: 2, w: 3}.\n | 2/3003\n | ibivibiv/math_instruct | |
What is the value of $m$ in the equation $(81)^{\frac{1}{2}} = 3^m$? | The equation $(81)^{\frac{1}{2}} = 3^m$ can be rewritten as $\sqrt{81} = 3^m$.
Since $\sqrt{81} = 9$, we have $9 = 3^m$.
Taking the logarithm base 3 of both sides, we get $\log_3{9} = \log_3{3^m}$.
Simplifying, we have $2 = m$.
Therefore, the value of $m$ is $\boxed{2}$.The answer is: 2 | ibivibiv/math_instruct | |
What is the nearest to 0.3 in -4, -13091, 2, 4, -0.4?\n | -0.4\n | ibivibiv/math_instruct | |
Is 157 != 157?\n | False\n | ibivibiv/math_instruct | |
Let b be (9 + -14)/(-2 - -1). Put 1, 4, b in decreasing order.\n | b, 4, 1\n | ibivibiv/math_instruct | |
What is the highest common factor of 3146 and 32318?\n | 286\n | ibivibiv/math_instruct | |
Multiply 3464 and -3.\n | -10392\n | ibivibiv/math_instruct | |
Let b(j) = 3*j - 3. Suppose -3*a - 2*g - 20 = 3*g, -a - 3*g - 4 = 0. Let z(o) = -o**3 - 11*o**2 - 10*o + 5. Let y be z(a). List the prime factors of b(y).\n | 2, 3\n | ibivibiv/math_instruct | |
Suppose 70*c - 22218 = 177492. List the prime factors of c.\n | 3, 317\n | ibivibiv/math_instruct | |
What is 43/2 of a centimeter in millimeters?\n | 215\n | ibivibiv/math_instruct | |
Let f be 540/(-1053) - 4/26. What is the third smallest value in 2/7, 3/5, f, -0.11?\n | 2/7\n | ibivibiv/math_instruct | |
What is the first derivative of 17*p**4 + 2*p + 235 wrt p?\n | 68*p**3 + 2\n | ibivibiv/math_instruct | |
Suppose -70 - 60 = -2*t. Suppose 5*z = -18 - 7, -t = -5*h - 2*z. What is the units digit of h?\n | 5\n | ibivibiv/math_instruct | |
Suppose -31 - 34 = -5*a. Differentiate -47 + 7*y**2 - 17*y**2 + a*y**2 wrt y.\n | 6*y\n | ibivibiv/math_instruct | |
Put 0.227, 4, -2/3 in descending order.\n | 4, 0.227, -2/3\n | ibivibiv/math_instruct | |
Evaluate -8 - 10 - -44 - 24.\n | 2\n | ibivibiv/math_instruct | |
Let v = 1 - -3. Suppose 0 = -5*d - v*b + 1039, -2*d + 641 = d - 2*b. Is d a composite number?\n | False\n | ibivibiv/math_instruct | |
Simplify (k*k**7)/((k/k**(-3)*k)/k) assuming k is positive.\n | k**4\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Using a recursive algorithm to find the value of a game
Tags:
1. Jun 28, 2017
### fignewtons
1. The problem statement, all variables and given/known data
Imagine you are playing a game with me, of drawing balls from a bo... | Recursion is a fundamental concept in mathematics and computer science, where a function solves a problem by solving smaller instances of the same problem. This approach simplifies complex problems into manageable pieces, making it easier to understand and solve them. Here, we'll discuss how to apply recursion to calc... | ibivibiv/math_instruct | |
Solve 114 = -22*d + 3*d for d.\n | -6\n | ibivibiv/math_instruct | |
What is -0.00003837922 rounded to 6 dps?\n | -0.000038\n | ibivibiv/math_instruct | |
Suppose -33 - 187 = -2*t - 3*z, -t - 4*z + 120 = 0. What is the common denominator of 55/3 and (-24)/8 + t/55?\n | 165\n | ibivibiv/math_instruct | |
Let d(u) = u**3 + 11*u**2 - u + 6. Let z be d(-11). Suppose -18*l = -z*l. Solve 0*n - 1/4*n**2 + l - 1/4*n**3 = 0 for n.\n | -1, 0\n | ibivibiv/math_instruct | |
Calculate 38/(-8) - 12/48.\n | -5\n | ibivibiv/math_instruct | |
Four letters picked without replacement from ziiizifiiiif. Give prob of picking 1 i, 1 f, and 2 z.\n | 16/495\n | ibivibiv/math_instruct | |
Evaluate -4 + (6 - (10 - (-2 + 5))).\n | -5\n | ibivibiv/math_instruct | |
Let c(z) = -z**3 - 30*z**2 - 29*z - 1. What is c(-29)?\n | -1\n | ibivibiv/math_instruct | |
Collect the terms in 11 + 6 + 12763*x + 20 - 37.\n | 12763*x\n | ibivibiv/math_instruct | |
In base 2, what is 10110100000 - -1101?\n | 10110101101\n | ibivibiv/math_instruct | |
What is 7*(-144)/56*(9/2)/3?\n | -27\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 64 and 13463672.\n | 8\n | ibivibiv/math_instruct | |
Let w = 87574828 - 47406843. Let n = w - 40168020.000106. Let v = -35 - n. What is v rounded to 5 dps?\n | 0.00011\n | ibivibiv/math_instruct | |
Simplify -2 + (sqrt(36)/sqrt(3) + sqrt(36)/(sqrt(12) + (sqrt(12) - sqrt(48)/sqrt(4)) + sqrt(12)))*-4.\n | -10*sqrt(3) - 2\n | ibivibiv/math_instruct | |
What is 14070476 to the power of 1/5, to the nearest integer?\n | 27\n | ibivibiv/math_instruct |
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