instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Divide -426 by -8971.\n | 426/8971\n | ibivibiv/math_instruct | |
Convert 38 (base 10) to base 12.\n | 32\n | ibivibiv/math_instruct | |
Let m = -5.277 - -4.577. Which is the smallest value? (a) 5 (b) -4/7 (c) 0.2 (d) m\n | d\n | ibivibiv/math_instruct | |
6 (base 13) to base 12\n | 6\n | ibivibiv/math_instruct | |
Is 6219551 prime?\n | False\n | ibivibiv/math_instruct | |
Let g = 5.4 + -0.4. Let q be 17/15 + (-66)/198. What is the second smallest value in -4, g, q?\n | q\n | ibivibiv/math_instruct | |
What is the highest common factor of 24464 and 263824?\n | 176\n | ibivibiv/math_instruct | |
Let h(o) = 2*o**3 + 5*o - o**3 + 36 + 0*o**3 + 5*o**2 - 30. Let x be h(-4). Which is smaller: 7 or x?\n | x\n | ibivibiv/math_instruct | |
Let w(z) = z - 5. Let j be -1*(-3 + 0 + 24). Let t = -10 - j. Suppose 15*k - t*k - 24 = 0. Calculate w(k).\n | 1\n | ibivibiv/math_instruct | |
What is 178307469 to the power of 1/5, to the nearest integer?\n | 45\n | ibivibiv/math_instruct | |
Expand (3 - 5 + 1)*(-5*m + 4*m - 28 - 13).\n | m + 41\n | ibivibiv/math_instruct | |
List the prime factors of 21282.\n | 2, 3, 3547\n | ibivibiv/math_instruct | |
What is the millions digit of 38284245?\n | 8\n | ibivibiv/math_instruct | |
What is the greatest common factor of 48 and 264?\n | 24\n | ibivibiv/math_instruct | |
Suppose -90*a = -119*a + 342287. List the prime factors of a.\n | 11, 29, 37\n | ibivibiv/math_instruct | |
Let s = 14 - -8. What is the smallest common multiple of s and 6?\n | 66\n | ibivibiv/math_instruct | |
Expand (-21 + 0 + 2)*(2*l - 1 + 1)*((-3 + 5 - 1)*(-3 + 4 - 2) + 3 - 1 + 0).\n | -38*l\n | ibivibiv/math_instruct | |
Calculate ((-52)/(-715))/(-1)*30/(-4).\n | 6/11\n | ibivibiv/math_instruct | |
Let d = 0.42 - 3.42. What is the smallest value in 2/21, d, -0.2, 5?\n | d\n | ibivibiv/math_instruct | |
Collect the terms in -207*c - 7 + 27 + 194*c - 8 - 10.\n | -13*c + 2\n | ibivibiv/math_instruct | |
Collect the terms in -146 + 272 + 2*j**2 - 126.\n | 2*j**2\n | ibivibiv/math_instruct | |
Let n(y) = -y**3 + 9*y**2 - 17*y - 4. Let i be n(6). Suppose -d = -5*z + 11, 4*d = i*z + 25 - 69. Let m = d - -14. Are 4 and m non-equal?\n | True\n | ibivibiv/math_instruct | |
Let t(z) = 3145*z + 2. Let k(v) = 2*v**2 + 281*v. Calculate t(k(h)).\n | 6290*h**2 + 883745*h + 2\n | ibivibiv/math_instruct | |
What is -67 (base 12) in base 15?\n | -54\n | ibivibiv/math_instruct | |
Suppose -450*q + 449*q = -39. Calculate the remainder when 66 is divided by q.\n | 27\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 456484 and 12553310?\n | 25106620\n | ibivibiv/math_instruct | |
Let o = 7752 + -4106. Suppose 70*d - 72*d = -o. Is d a prime number?\n | True\n | ibivibiv/math_instruct | |
Let s(n) = 9*n**3 + 2*n**2 - 84*n + 567. Is s(6) a multiple of 7?\n | True\n | ibivibiv/math_instruct | |
Is 244 a factor of 372588?\n | True\n | ibivibiv/math_instruct | |
Let q = 57 + 2. List the prime factors of q.\n | 59\n | ibivibiv/math_instruct | |
What is the common denominator of 71/249280 and -27/1744960?\n | 1744960\n | ibivibiv/math_instruct | |
Let l(t) be the second derivative of 3*t + 0*t**4 + 0*t**2 + 0 - 1/3*t**3 - 1/4*t**5. Find the second derivative of l(h) wrt h.\n | -30*h\n | ibivibiv/math_instruct | |
Suppose 2*b - 760 = -0*t - 4*t, -2*t + 5*b + 356 = 0. Suppose 3*v - t = -68. What is the tens digit of v?\n | 4\n | ibivibiv/math_instruct | |
List the prime factors of 1973332863.\n | 3, 23, 79, 120671\n | ibivibiv/math_instruct | |
(-37 - (-11718)/294)/((-2)/7)\n | -10\n | ibivibiv/math_instruct | |
What is 3 (base 7) in base 2?\n | 11\n | ibivibiv/math_instruct | |
Suppose -4*a + 4*n + 12 = -a, -4*a = -3*n - 9. Which is smaller: a or 14/173?\n | a\n | ibivibiv/math_instruct | |
Let c(u) = -13 + u + 0*u + 14 + 0*u. Let x(p) = -p - 1. Let v be x(-6). Let i(b) = -b**2 + 5*b + 5. Calculate v*c(o) - i(o).\n | o**2\n | ibivibiv/math_instruct | |
11 + (-16 - -10) - 6\n | -1\n | ibivibiv/math_instruct | |
Calculate the common denominator of -1/80928 and -55/21.\n | 566496\n | ibivibiv/math_instruct | |
What is the third biggest value in -4/27, 3/11, -5?\n | -5\n | ibivibiv/math_instruct | |
Let v be ((-16525)/(-9915))/(8/6 - 1). What is the nearest to v in 1/3, -0.5, -74, -2/3?\n | 1/3\n | ibivibiv/math_instruct | |
Let a = -7 + 12. Suppose a*c = 4*c - 15. Let v = 15 + c. Solve -5*p - r = -22, v = -2*p + 2*r + r + 2 for p.\n | 4\n | ibivibiv/math_instruct | |
-5355760 (base 8) to base 5\n | -331320220\n | ibivibiv/math_instruct | |
Find the second derivative of -2*a**5 - 17469*a**4 + 8*a + 150 wrt a.\n | -40*a**3 - 209628*a**2\n | ibivibiv/math_instruct | |
2039 divided by -2039\n | -1\n | ibivibiv/math_instruct | |
How many nanometers are there in 8/25 of a micrometer?\n | 320\n | ibivibiv/math_instruct | |
Let y = -5.9 + 5.4. Let o = -0.2 - -0.2. Let l = o + 1. What is the third biggest value in -5, l, y?\n | -5\n | ibivibiv/math_instruct | |
What comes next: 1052, 1040, 1032, 1028, 1028?\n | 1032\n | ibivibiv/math_instruct | |
Let m(b) = 203 - 198 + 4*b**3 - b**3 - 2*b**2 + 2*b**2. Let i(r) = 3*r**3 + 6. Give 3*i(l) - 4*m(l).\n | -3*l**3 - 2\n | ibivibiv/math_instruct | |
Add -52 and 0.0707.\n | -51.9293\n | ibivibiv/math_instruct | |
What are the prime factors of 20976?\n | 2, 3, 19, 23\n | ibivibiv/math_instruct | |
What is (-5)/(200/15)*21/((-2520)/320)?\n | 1\n | ibivibiv/math_instruct | |
What is the units digit of 274982?\n | 2\n | ibivibiv/math_instruct | |
Let t = -7 + 7.03. Let w = -3.97 - t. Let z = -1339 + 1351. Which is the nearest to z? (a) w (b) -0.2 (c) 2\n | c\n | ibivibiv/math_instruct | |
What is 16574 plus 1161?\n | 17735\n | ibivibiv/math_instruct | |
Let v be (1 + 0)*(3 + -6). Let a be (1 + 0)*(-17 - -20). Sort v, -5, a in ascending order.\n | -5, v, a\n | ibivibiv/math_instruct | |
What is prob of sequence canv when four letters picked without replacement from cvacnccaccnaaaaaaa?\n | 1/680\n | ibivibiv/math_instruct | |
What is the value of -12 + (7 + 1 - 2)?\n | -6\n | ibivibiv/math_instruct | |
Expand (-3 - 4 + 1)*(-13*w**2 - 6398*w**3 + 1 + 3358*w**3 + 3170*w**3).\n | -780*w**3 + 78*w**2 - 6\n | ibivibiv/math_instruct | |
Factor 4*t**2 + 62976*t + 1257920.\n | 4*(t + 20)*(t + 15724)\n | ibivibiv/math_instruct | |
Let v(s) = s**3 - s**2 + 15*s - 257. What is v(0)?\n | -257\n | ibivibiv/math_instruct | |
Suppose 3*z = 4*w + 25, z - 4*w - 10 = 3*z. Suppose 5*a - 3*a + 2*n = 28, z*a - 30 = n. List the prime factors of a.\n | 11\n | ibivibiv/math_instruct | |
What is the billions digit of 2806116639?\n | 2\n | ibivibiv/math_instruct | |
Let y = -19 + 54. What is the tens digit of (-10)/y + 849/7?\n | 2\n | ibivibiv/math_instruct | |
Let k(h) = -h**3 - 125*h**2 + 100*h - 3289. Calculate k(-126).\n | -13\n | ibivibiv/math_instruct | |
Let z(x) = -39137*x**2. Let u(f) = -3*f. Calculate z(u(c)).\n | -352233*c**2\n | ibivibiv/math_instruct | |
Calculate -867595 divided by -5.\n | 173519\n | ibivibiv/math_instruct | |
Evaluate -1*4/1*((-14688)/128)/17.\n | 27\n | ibivibiv/math_instruct | |
How many minutes are there between 6:18 AM and 8:21 AM?\n | 123\n | ibivibiv/math_instruct | |
What is next in 58752, 58099, 57446, 56793, 56140?\n | 55487\n | ibivibiv/math_instruct | |
Let v(l) = l**2 + 4*l + 22. Let d = 7 - 24. What are the prime factors of v(d)?\n | 3\n | ibivibiv/math_instruct | |
Does 9 divide 5544?\n | True\n | ibivibiv/math_instruct | |
Evaluate (-3)/((936/(-390))/((-112)/3570)).\n | -2/51\n | ibivibiv/math_instruct | |
Calculate the remainder when 422 is divided by 75.\n | 47\n | ibivibiv/math_instruct | |
Collect the terms in 11 - 5 + 9*k - 6.\n | 9*k\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# 1.3: Procedure
## Part A: Calculating Force and Pressure
1. Calculate the expected force for the 1000 g (1 kilogram) mass based on the acceleration due to Earth’s gravity and record in Table 1.
2. Repeat step one for th... | The study of physics involves exploring various phenomena and their interactions, including the principles surrounding force, pressure, and deformation. This piece aims to delve deeper into these fundamental topics using a hands-on approach by guiding you through a series of calculations and observations. We'll start ... | ibivibiv/math_instruct | |
Suppose -31 = 4*o - 3*u, 3*o + 7*u = 3*u + 8. Let y be 7*(3427 + (4 - 1)). Let r be o/(-10) + y/(-25). Round r to the nearest 100.\n | -1000\n | ibivibiv/math_instruct | |
Is 178374930 a multiple of 6?\n | True\n | ibivibiv/math_instruct | |
Collect the terms in 1 - 1251846*u**2 - 1 + 1251840*u**2.\n | -6*u**2\n | ibivibiv/math_instruct | |
Let y be 5/(-10)*12/(-21). Let v = -0.01 + 2.01. What is the third smallest value in 0.5, y, v?\n | v\n | ibivibiv/math_instruct | |
Suppose 315 = -7*r + 308. What is the second biggest value in 6, 1/3, r?\n | 1/3\n | ibivibiv/math_instruct | |
What is the sixth root of 8449 to the nearest integer?\n | 5\n | ibivibiv/math_instruct | |
What is prob of picking 2 w when two letters picked without replacement from {t: 7, w: 6}?\n | 5/26\n | ibivibiv/math_instruct | |
In how many different ways can a sequence of four letters be formed using the letters in EQUALS, given that each sequence must start with L, end with Q, and no letter can be repeated within a sequence? | Since each sequence must start with L and end with Q, we only need to choose the two remaining letters.
From the given letters in EQUALS, there are 4 choices for the second letter (E, U, A, or S) and 3 choices for the third letter (the remaining letters after using L and Q).
Therefore, there are $4 \times 3 = \boxed{12... | ibivibiv/math_instruct | |
Factor 4*h**3 + 124*h**2 + 1020*h + 900.\n | 4*(h + 1)*(h + 15)**2\n | ibivibiv/math_instruct | |
Suppose j = 2*j. Suppose j*i + 375 = 5*i. Calculate the greatest common divisor of i and 15.\n | 15\n | ibivibiv/math_instruct | |
Let t = -10 - -10. Suppose -7*a + 12*a - 20 = t. Let q(y) = 2*y + 9. Let x(r) = r + 5. Let h(f) = a*q(f) - 7*x(f). What is h(5)?\n | 6\n | ibivibiv/math_instruct | |
Calculate the remainder when 486 is divided by 17.\n | 10\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 15946 and 13668?\n | 95676\n | ibivibiv/math_instruct | |
Evaluate (-28)/(-15) - (13 - (-1 - (-18 + 6))).\n | -2/15\n | ibivibiv/math_instruct | |
Calculate prob of sequence ykh when three letters picked without replacement from yykyhyyykyyyhyyhyyyy.\n | 1/76\n | ibivibiv/math_instruct | |
Let s(t) = 3*t + 1081 - 529 + 6*t**2 - 537. Let p be s(-4). Calculate the greatest common divisor of 66 and p.\n | 33\n | ibivibiv/math_instruct | |
Simplify (sqrt(1900) + -1 + -1 + sqrt(1900) - sqrt(1900)) + 4.\n | 2 + 10*sqrt(19)\n | ibivibiv/math_instruct | |
Suppose -16 = -7*j + 3*j. Let a = -1710.9 + 1713. What is the nearest to a in j, -0.2, -0.1?\n | j\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Direct proof that, in a commutative ring with only one prime ideal $P$, every element of $P$ is nilpotent
Let $R$ be a commutative ring with identity such that $R$ has exactly one prime ideal $P$.
Prove: all elements in $... | To directly prove that every element of the prime ideal P in a commutative ring R with identity and only one prime ideal P is nilpotent, we can argue by contradiction. Suppose there exists an element a in P that is not nilpotent. This means that for all positive integers n, the power an does not belong to P.
Since P ... | ibivibiv/math_instruct | |
Let y = -73433735 + 73433775.999917. Let n = -41 + y. Round n to four decimal places.\n | -0.0001\n | ibivibiv/math_instruct | |
Let v = -87 - -90. Does 10 divide v/(-6)*(-2 + -132)?\n | False\n | ibivibiv/math_instruct | |
Suppose 2628 = -8*n + 26*n. What are the prime factors of n?\n | 2, 73\n | ibivibiv/math_instruct | |
Let x(t) = -t**3 + 2*t**2 + 2*t - 2. Let m be x(3). Let l = 4 - m. Is l prime?\n | False\n | ibivibiv/math_instruct |
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