instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What are the prime factors of 135189?\n | 3, 1669\n | ibivibiv/math_instruct | |
Let f = -93 + 95. Let m be 1*(3 + (4 - f)). Suppose -5*g + 3 = 8, 5*g = m*j - 220. What is the remainder when 213 is divided by j?\n | 41\n | ibivibiv/math_instruct | |
Is 25115383 prime?\n | False\n | ibivibiv/math_instruct | |
(58/3)/(-2) - 32/24\n | -11\n | ibivibiv/math_instruct | |
List the prime factors of 70420.\n | 2, 5, 7, 503\n | ibivibiv/math_instruct | |
Is -7 bigger than -12?\n | True\n | ibivibiv/math_instruct | |
Calculate 1 + -9 - (-142 - -115).\n | 19\n | ibivibiv/math_instruct | |
How many minutes are there between 8:14 AM and 10:21 AM?\n | 127\n | ibivibiv/math_instruct | |
Let n = 57372 - 39077. Is n a prime number?\n | False\n | ibivibiv/math_instruct | |
Let y be (3 - 788/260)/((-15)/75). Let q = -57 - -169/3. Let r = 11 + -11.5. Which is the fourth smallest value? (a) y (b) -5 (c) r (d) q\n | a\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {m: 3, i: 3, w: 1, b: 3}. Give prob of picking 2 b and 2 i.\n | 3/70\n | ibivibiv/math_instruct | |
Round 78779.728 to the nearest ten.\n | 78780\n | ibivibiv/math_instruct | |
What is 186 minutes after 9:08 PM?\n | 12:14 AM\n | ibivibiv/math_instruct | |
Suppose -2*q - 18 = 4*j, 5 = -2*q + j + 2. Let m be (-7)/((-7)/q) - -39. Solve -m = 4*r - 32 for r.\n | -1\n | ibivibiv/math_instruct | |
Find the common denominator of 31/5790492 and 65/40533444.\n | 40533444\n | ibivibiv/math_instruct | |
Solve -11*z = -14*z - 12 for z.\n | -4\n | ibivibiv/math_instruct | |
What is the next term in -5728, -11340, -16952, -22564?\n | -28176\n | ibivibiv/math_instruct | |
Let a(f) = 2*f. Let g(v) = v**2 - 30*v + 11. Let s be g(30). Let y(z) = z - 9. Let r be y(s). Let j(k) = 60*k**r + 0 + 9 - 9. Give j(a(b)).\n | 240*b**2\n | ibivibiv/math_instruct | |
A company produces two types of products, Product A and Product B. Each unit of Product A requires 3 hours of labor and 4 hours of machine time, while each unit of Product B requires 5 hours of labor and 2 hours of machine time. The company has 400 labor hours and 240 machine hours available. If the profit from each un... | Let x be the number of units of Product A and y be the number of units of Product B.
Objective function (profit): P = 50x + 60y
Constraints:
1. Labor hours: 3x + 5y ≤ 400
2. Machine hours: 4x + 2y ≤ 240
We can rewrite the constraints in matrix form as:
| 3 5 | | x | ≤ | 400 |
| 4 2 | | y | ≤ | 240 |
Now, we need... | ibivibiv/math_instruct | |
Let f be (-1 + 0)/(5/(-10)). Let b be (1/f*-2)/1. Let j be (b/1)/((-2)/20). Calculate the greatest common factor of j and 4.\n | 2\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 8 and 2064?\n | 2064\n | ibivibiv/math_instruct | |
Suppose 6*l = 4*l + c + 16, 4*c + 10 = -l. Solve 3*x = l + 3 for x.\n | 3\n | ibivibiv/math_instruct | |
Is 7827695 a composite number?\n | True\n | ibivibiv/math_instruct | |
What are the prime factors of (-15390)/(-665) + 12/14 + -1?\n | 23\n | ibivibiv/math_instruct | |
Let w(s) be the third derivative of 0*s + 13/6*s**3 + 3*s**2 + 0 - 1/12*s**4. Calculate the remainder when 48 is divided by w(3).\n | 6\n | ibivibiv/math_instruct | |
What is the value of (8 - (-10 + 2 + 13)) + (-1 - -2)?\n | 4\n | ibivibiv/math_instruct | |
Solve -a + 2575*l = 2572*l + 21, 5*a + 25 = 5*l for a.\n | 3\n | ibivibiv/math_instruct | |
Rearrange -66 - 449*g**2 + 143*g**2 + 66 to u*g + k + t*g**2 and give t.\n | -306\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {n: 2, c: 2, m: 13, w: 3}. What is prob of picking 1 m and 1 n?\n | 13/95\n | ibivibiv/math_instruct | |
Is 533543 a composite number?\n | False\n | ibivibiv/math_instruct | |
Let p be (60/560)/((1/8)/1). Which is the nearest to -2/5? (a) -5 (b) -1 (c) p\n | b\n | ibivibiv/math_instruct | |
What is the value of (14/18)/(-13 - (-1547)/117)?\n | 7/2\n | ibivibiv/math_instruct | |
20.849 * 13\n | 271.037\n | ibivibiv/math_instruct | |
What are the prime factors of 1678340?\n | 2, 5, 31, 2707\n | ibivibiv/math_instruct | |
Suppose -2*g + 358162 = -5*d, -g = 914*d - 915*d - 179075. Is g a composite number?\n | True\n | ibivibiv/math_instruct | |
(-208)/(-22)*(-123)/12 + 7470/(-82170)\n | -97\n | ibivibiv/math_instruct | |
Let u(b) = -b**3 - b**2 + 2*b - 3. Let a = 40 + -33. Let z = a + -10. Calculate u(z).\n | 9\n | ibivibiv/math_instruct | |
What is the thousands digit of 2012824?\n | 2\n | ibivibiv/math_instruct | |
Collect the terms in -192*q + 97*q + 90*q.\n | -5*q\n | ibivibiv/math_instruct | |
What is 18845 to the power of 1/2, to the nearest integer?\n | 137\n | ibivibiv/math_instruct | |
Let m = 0.5 + 16.5. Let h = 11 - m. Let p = h - -5.8. Which is the second smallest value? (a) p (b) 0.2 (c) 2/19\n | c\n | ibivibiv/math_instruct | |
Suppose -25 = -3*i - 2*i - 2*b, -10 = -2*b. Let t = -9199 + 9201. What is the closest to t in -4/7, 4, i?\n | i\n | ibivibiv/math_instruct | |
Let y(v) = -53*v**2 + 7*v - 1212. Let k(g) = 9*g**2 - g. Give 6*k(w) + y(w).\n | w**2 + w - 1212\n | ibivibiv/math_instruct | |
Suppose 4*p - 12 = 8. Which is the closest to 4? (a) 2 (b) 0.5 (c) p\n | c\n | ibivibiv/math_instruct | |
Determine n so that -78*n**2 - 501*n**3 - 25229 + 25229 + 39*n**4 = 0.\n | -2/13, 0, 13\n | ibivibiv/math_instruct | |
Product of 1003 and 0.4.\n | 401.2\n | ibivibiv/math_instruct | |
Factor -3*b**3 + 21048*b**2 - 899385*b - 920436.\n | -3*(b - 6973)*(b - 44)*(b + 1)\n | ibivibiv/math_instruct | |
What is next in -34711482, -69422966, -104134450, -138845934, -173557418?\n | -208268902\n | ibivibiv/math_instruct | |
Find the second derivative of -14397541*w**2 - 31519577*w wrt w.\n | -28795082\n | ibivibiv/math_instruct | |
What is 132 minutes after 4:26 PM?\n | 6:38 PM\n | ibivibiv/math_instruct | |
Let b = 2.26 - 2.76. Sort -3, b, 0.5, 0.37.\n | -3, b, 0.37, 0.5\n | ibivibiv/math_instruct | |
Which is the nearest to 3/5? (a) -0.094 (b) -0.1 (c) -3 (d) 258\n | a\n | ibivibiv/math_instruct | |
Put -1.0978, -12, 2/7 in increasing order.\n | -12, -1.0978, 2/7\n | ibivibiv/math_instruct | |
What is the tens digit of 120414?\n | 1\n | ibivibiv/math_instruct | |
Let k = 976 + -946. Suppose 94 - 7 = o. Let f = o - k. Calculate the remainder when f is divided by 12.\n | 9\n | ibivibiv/math_instruct | |
How many minutes are there between 7:01 AM and 11:57 AM?\n | 296\n | ibivibiv/math_instruct | |
What is the hundreds digit of 16076?\n | 0\n | ibivibiv/math_instruct | |
In base 3, what is 1012000 + -10100200?\n | -2011200\n | ibivibiv/math_instruct | |
Let c = 64 + 195. What are the prime factors of c?\n | 7, 37\n | ibivibiv/math_instruct | |
List the prime factors of 8603429.\n | 8603429\n | ibivibiv/math_instruct | |
Calculate 16854.97 + 134116902.\n | 134133756.97\n | ibivibiv/math_instruct | |
Let y(j) = -196*j + 5. Let h be (-120)/(-54) - (-6)/(-27). Let v be y(h). Let f be -5*(-3 + v/15). What is the greatest common divisor of f and 36?\n | 36\n | ibivibiv/math_instruct | |
Let u(g) be the first derivative of 0*g + 0*g**2 - 14/3*g**3 + 101. Let p(c) be the first derivative of -c**2/2 + 3. Calculate p(u(x)).\n | 14*x**2\n | ibivibiv/math_instruct | |
b"What is the sth term of -45, -189, -429, -765, -1197, -1725, -2349?\n" | -48*s**2 + 3\n | ibivibiv/math_instruct | |
What is 18*(-7)/(-189)*(3576/(-36) - (-3)/9)?\n | -66\n | ibivibiv/math_instruct | |
What is 88928769 to the power of 1/3, to the nearest integer?\n | 446\n | ibivibiv/math_instruct | |
What is the greatest common factor of 17317282 and 31?\n | 31\n | ibivibiv/math_instruct | |
Let u be 9854/(-117) - 2/(-9). Let l = -82 - u. Solve 0*s = l*s - 2 for s.\n | 1\n | ibivibiv/math_instruct | |
What is the value of 89 + -64 - (1 - -27)?\n | -3\n | ibivibiv/math_instruct | |
Divide -340 by 85.\n | -4\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-88.8622 % -61.1739 | -27.6883 | ibivibiv/math_instruct | |
Is 12678233 composite?\n | True\n | ibivibiv/math_instruct | |
Suppose -4*u + 887 = 375. Calculate the remainder when u is divided by 10.\n | 8\n | ibivibiv/math_instruct | |
Rearrange (-4*m + m + 5*m)*(4*m + m**2 - 4*m) - 6 + 6 - m**3 + (-m + 0*m + 3*m)*(222*m + 89*m**2 - 222*m) to f*m**2 + k*m**3 + p + d*m and give k.\n | 179\n | ibivibiv/math_instruct | |
Solve 5*f**5 - 60*f**4 + 230*f**3 - 300*f**2 + 125*f = 0 for f.\n | 0, 1, 5\n | ibivibiv/math_instruct | |
Sort 5, -1, 4, -142200, -3 in ascending order.\n | -142200, -3, -1, 4, 5\n | ibivibiv/math_instruct | |
Rearrange -36*c**2 - 21*c + 16*c - 24*c + 2*c**2 - 5*c to b + k*c**2 + p*c and give k.\n | -34\n | ibivibiv/math_instruct | |
Suppose -5409114 = -2*z - 3*b + 2770892, 2*z = 2*b + 8179996. What is z rounded to the nearest 100000?\n | 4100000\n | ibivibiv/math_instruct | |
Collect the terms in c**3 - 6260*c**2 + 13133*c**2 - 6873*c**2 + 6*c**3.\n | 7*c**3\n | ibivibiv/math_instruct | |
Let i(v) be the third derivative of 673*v**7/70 + 1363*v**3/6 + 223*v**2 + 3*v. Differentiate i(r) with respect to r.\n | 8076*r**3\n | ibivibiv/math_instruct | |
Let q = 99 + -105.3. Let d = q + -0.7. Let c = -6.9 - d. Sort -0.2, c, -2.\n | -2, -0.2, c\n | ibivibiv/math_instruct | |
What is -44220044677 minus -401.3?\n | -44220044275.7\n | ibivibiv/math_instruct | |
Suppose -3*c = 4*p - 6393590, 797756 = 3*c - 4*p - 5595842. Let d = c + -3831198. What is d rounded to the nearest 1000000?\n | -2000000\n | ibivibiv/math_instruct | |
Put -95, 1, 0, -1, 17, 21 in decreasing order.\n | 21, 17, 1, 0, -1, -95\n | ibivibiv/math_instruct | |
What is the third smallest value in -1/2, -179691685, 0?\n | 0\n | ibivibiv/math_instruct | |
Simplify (sqrt(72)*-1 + 1)**2 + (6*(sqrt(72) + 1))**2 - (sqrt(72) + 6*(sqrt(72) + sqrt(72)*-3) + sqrt(72)*3*-1)**2.\n | -11411 + 420*sqrt(2)\n | ibivibiv/math_instruct | |
Let h = -11 - -219. Suppose 3*p = -p + h. What are the prime factors of p?\n | 2, 13\n | ibivibiv/math_instruct | |
What is the fifth smallest value in 4, 7, -1/5, -2, 1/6688, 0.14, -4?\n | 0.14\n | ibivibiv/math_instruct | |
List the prime factors of 4555278.\n | 2, 3, 7, 13, 103\n | ibivibiv/math_instruct | |
Solve -5*p = -3*m - 70, -1464*p - 28*m - 836 = -1465*p for p.\n | -4\n | ibivibiv/math_instruct | |
Suppose 70*f - 60*f - 18650 = 0. Is f a composite number?\n | True\n | ibivibiv/math_instruct | |
Collect the terms in 822*u**2 - 7*u + 4*u + 3943*u**2.\n | 4765*u**2 - 3*u\n | ibivibiv/math_instruct | |
Suppose 2*t + 2*t = -3*j + 13, -3*t - 9 = -4*j. Suppose 2*w = 2*c - 1 - 7, -j*c - 12 = 3*w. Suppose -4*u - 18 + 86 = c. What is the units digit of u?\n | 7\n | ibivibiv/math_instruct | |
Let f be ((-96)/(-18))/((-4)/(-186)). Calculate the highest common factor of 31 and f.\n | 31\n | ibivibiv/math_instruct | |
What is the ten millions digit of 22115844?\n | 2\n | ibivibiv/math_instruct | |
Is 1020927007 a prime number?\n | False\n | ibivibiv/math_instruct | |
Solve 7*q + 47 = -8611*y + 8622*y + 4*q, -5*q + 11 = 4*y for y.\n | 4\n | ibivibiv/math_instruct | |
Which is the closest to -2/5? (a) -8 (b) 0.3 (c) 21 (d) 18/5 (e) -0.3\n | e\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"The Abelian Group of the Product of Abelian Subgroups
# The Abelian Group of the Product of Abelian Subgroups
Definition: Let $(G, \cdot)$ be an abelian group and let $(S, \cdot)$ and $(T, \cdot)$ be (abelian) subgroups of... | Now that we have established the definition of the product of two abelian subgroups $S$ and $T$, it's essential to understand why this concept is crucial in abstract algebra and mathematics at large. Before delving into its significance, let us first explore some key properties of the product of abelian subgroups.
Fi... | ibivibiv/math_instruct | |
Let q = -7.3 - -6.3. Let t be 2/(-3)*(-348)/(-58). Which is the fourth smallest value? (a) q (b) -2/9 (c) t (d) 1.1\n | d\n | ibivibiv/math_instruct |
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