instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Suppose 3*p = -3*s + 192, -10 - 174 = -3*s - p. Calculate the least common multiple of s and 14.\n | 420\n | ibivibiv/math_instruct | |
810/420*800/1350\n | 8/7\n | ibivibiv/math_instruct | |
Let z(a) = -3*a**3 - 7*a - 3. Let d(f) = -f**3 - f - 1. Let b(c) = 2*c + 31. Let h be b(-16). Determine h*z(l) + 5*d(l).\n | -2*l**3 + 2*l - 2\n | ibivibiv/math_instruct | |
Calculate prob of picking 3 q when three letters picked without replacement from {q: 3}.\n | 1\n | ibivibiv/math_instruct | |
What are the prime factors of 36982930?\n | 2, 5, 19, 194647\n | ibivibiv/math_instruct | |
Four letters picked without replacement from nmnyxxyxxyyxxx. What is prob of picking 1 x, 1 m, 1 n, and 1 y?\n | 8/143\n | ibivibiv/math_instruct | |
Suppose 0 = -p + 2*i + 6, 2*i - 2 = -5*p - 2*i. Let r(s) = -5 + 11*s + s**2 + s**2 - p. Let w(v) = 0*v + v**2 + 4*v - 4 + 2*v. Determine -6*r(q) + 11*w(q).\n | -q**2 - 2\n | ibivibiv/math_instruct | |
Suppose 18 - 38 = -4*g, -5*c = -g - 120. Suppose -c*j - 6 = -28*j. Sort 1, 7, -1, j in descending order.\n | 7, j, 1, -1\n | ibivibiv/math_instruct | |
Factor 3*a**2/5 + 474*a/5 + 18723/5.\n | 3*(a + 79)**2/5\n | ibivibiv/math_instruct | |
Henry went to the beach and picked up 17 perfect shells and 52 broken shells. Out of those 52 broken shells, half of them were spiral. Out of the 17 perfect shells, 12 of them were not spiral. How many more broken spiral shells were there than perfect spiral shells? Lets program in Python in the response. | # define the number of shells
perfect_shells = 17
broken_shells = 52
broken_spiral_shells = broken_shells / 2
perfect_not_spiral_shells = 12
perfect_spiral_shells = perfect_shells - perfect_not_spiral_shells
difference = broken_spiral_shells - perfect_spiral_shells
print(int(difference)) | ibivibiv/math_instruct | |
Factor -3*v**3/8 + 3*v**2/8 + 51*v/8 + 45/8.\n | -3*(v - 5)*(v + 1)*(v + 3)/8\n | ibivibiv/math_instruct | |
What is 61.82043l in millilitres?\n | 61820.43\n | ibivibiv/math_instruct | |
What is the third derivative of -2*r**6*u + 57107*r**6 + 5150*r**2*u - r**2 + 3*r*u - r wrt r?\n | -240*r**3*u + 6852840*r**3\n | ibivibiv/math_instruct | |
Suppose 2*i + 12 = 4*i. What is the third derivative of i*k**2 + k**2 + 3*k**4 + 16*k**6 - 3*k**4 wrt k?\n | 1920*k**3\n | ibivibiv/math_instruct | |
Suppose 0 = 7*z - 2*z + 1050. Let j = z - -55. Let f = j + 218. What are the prime factors of f?\n | 3, 7\n | ibivibiv/math_instruct | |
Suppose 2*r + 152 = -4*c - 0*c, -4*r = -3*c + 348. Let t = 109 + r. What are the prime factors of t?\n | 5\n | ibivibiv/math_instruct | |
Expand -29*l**2 - l**2 + 8*l**2 + (2*l - l - 2*l)*(-3*l + 0*l + 4*l) - 2*l**2 - l**2 + 5*l**2.\n | -21*l**2\n | ibivibiv/math_instruct | |
Let q = 947/55 + -87/5. Suppose w - 20 = 5*c, w = -4*c - 15 - 1. Which is smaller: q or w?\n | q\n | ibivibiv/math_instruct | |
Let x(w) = -w + 16. Let t = 6 - 6. Let i be x(t). Solve -b = -5*b - i for b.\n | -4\n | ibivibiv/math_instruct | |
What is -5 + (6 - -6 - 2)?\n | 5\n | ibivibiv/math_instruct | |
Collect the terms in -7619*j + 5*j**3 - 7619*j + 15238*j.\n | 5*j**3\n | ibivibiv/math_instruct | |
Simplify ((f*f/f**(-2/7))/f*(f/(f/f**(-4)))/f)**(-11/2) assuming f is positive.\n | f**(143/7)\n | ibivibiv/math_instruct | |
Sum -3 and -379.1910266667.\n | -382.1910266667\n | ibivibiv/math_instruct | |
Let t = 1.63 - 15.73. Let k = -14.2 - t. Which is the nearest to k? (a) -1 (b) 5 (c) -2/17\n | c\n | ibivibiv/math_instruct | |
Which is the second biggest value? (a) -2/19 (b) 0.5 (c) 12\n | b\n | ibivibiv/math_instruct | |
Find the third derivative of 38697835*c**6 - 5*c**2 - 1804*c + 30.\n | 4643740200*c**3\n | ibivibiv/math_instruct | |
Express -2*j**2 + 0*j**2 - 5*j**2 + (2*j + 2*j - 6*j)*(j - 3*j + 0*j) + (0 + 1 - 5)*(0*j**2 + 2*j**2 + 0*j**2) in the form f*j**2 + z + p*j and give f.\n | -11\n | ibivibiv/math_instruct | |
Which is the closest to 0.1? (a) -1 (b) -1/4 (c) 1483\n | b\n | ibivibiv/math_instruct | |
What is 616 minutes before 3:19 PM?\n | 5:03 AM\n | ibivibiv/math_instruct | |
Suppose -m = 2*r - 164, -m + 48*r - 46*r + 164 = 0. What is the hundreds digit of m?\n | 1\n | ibivibiv/math_instruct | |
In base 13, what is -1c5 + -7c?\n | -274\n | ibivibiv/math_instruct | |
Which is the second smallest value? (a) -1 (b) -0.05 (c) 2 (d) 0 (e) -2/11\n | e\n | ibivibiv/math_instruct | |
Expand (-1 - 3 + 3 + (-7 - 3 + 9 + (2 - 4 - 1)*(3 - 1 + 1))*(-5 + 4 - 1) + 4 + 2 - 5)*(3*s - 6*s + 0*s).\n | -60*s\n | ibivibiv/math_instruct | |
Calculate the remainder when 768 is divided by 4/(-6)*(-3)/((10/59)/10).\n | 60\n | ibivibiv/math_instruct | |
Sort -696, 120, 7 in ascending order.\n | -696, 7, 120\n | ibivibiv/math_instruct | |
What is 12173 to the power of 1/2, to the nearest integer?\n | 110\n | ibivibiv/math_instruct | |
In base 11, what is -15a - 3?\n | -162\n | ibivibiv/math_instruct | |
Expand (0 + m**5 + 0)*(3 - 2 - 3) + 12*m - 12*m - 4*m + 14*m**5.\n | 12*m**5 - 4*m\n | ibivibiv/math_instruct | |
Find the common denominator of (-849)/(-2830) - (-613)/(-1660) and 49/8.\n | 664\n | ibivibiv/math_instruct | |
Let f(i) = i + 3. Let g(u) = 2*u + 7. Let l(x) = 7*f(x) - 3*g(x). Let a(m) be the third derivative of 0 + 1/24*m**4 + 0*m + 7*m**2 + 0*m**3. Determine l(a(j)).\n | j\n | ibivibiv/math_instruct | |
Let z(n) = n**2 - 3*n - 1. Let t be (2/(-6))/(5/(-150)). Suppose y + y = t. Is 6 a factor of z(y)?\n | False\n | ibivibiv/math_instruct | |
Collect the terms in 3*j**2 + 7 - 4 - j**2 - 2.\n | 2*j**2 + 1\n | ibivibiv/math_instruct | |
Solve 0 = 100*v - 91*v + 36 for v.\n | -4\n | ibivibiv/math_instruct | |
Let t = 569/6 - 462/5. What is the common denominator of t and -149/126?\n | 630\n | ibivibiv/math_instruct | |
What is the thousands digit of 121149395?\n | 9\n | ibivibiv/math_instruct | |
Let c = 80 + 32. Is 7 a factor of c?\n | True\n | ibivibiv/math_instruct | |
Let r = 3623852507 + -3623852522.59999937. Let j = r + 15.6. What is j rounded to seven dps?\n | 0.0000006\n | ibivibiv/math_instruct | |
What is 149 minutes before 4:47 PM?\n | 2:18 PM\n | ibivibiv/math_instruct | |
What is the highest common factor of 546326 and 113278?\n | 418\n | ibivibiv/math_instruct | |
Suppose -4*i = b - 4055, 4*b + 1929 = 3*i - 1117. What is the thousands digit of i?\n | 1\n | ibivibiv/math_instruct | |
Convert 769.8375 micrometers to meters.\n | 0.0007698375\n | ibivibiv/math_instruct | |
If $n$ is an integer, what is the remainder when the sum of $7 - n$ and $n + 3$ is divided by $7$? | The sum of $7 - n$ and $n + 3$ is $10$,
and the remainder when $10$ is divided by $7$ is $\boxed{3}$.
The answer is: 3 | ibivibiv/math_instruct | |
Product of 1.8828 and 0.15.\n | 0.28242\n | ibivibiv/math_instruct | |
Which is the third biggest value? (a) 50 (b) 624 (c) 0.5 (d) 0\n | c\n | ibivibiv/math_instruct | |
Sort 1/2, 3, -1.2.\n | -1.2, 1/2, 3\n | ibivibiv/math_instruct | |
What is the thousands digit of 1158?\n | 1\n | ibivibiv/math_instruct | |
Let f = 1.3 + 86.7. Let t = 46 - f. Let g = 41.17 + t. What is g rounded to one dp?\n | -0.8\n | ibivibiv/math_instruct | |
Suppose -h + 160 = -k, -4*k - 55 = 4*h + 569. Let x = 246 + k. List the prime factors of x.\n | 2, 11\n | ibivibiv/math_instruct | |
Let z(j) = -j. Let m be z(2). Let n = -0.601 + 0.501. What is the closest to m in 2/7, n, -1?\n | -1\n | ibivibiv/math_instruct | |
Let a(c) = -26 + 1 + 11*c + 3*c**2 + 11. What is the hundreds digit of a(9)?\n | 3\n | ibivibiv/math_instruct | |
What is 52/((15 + -14 - 3)/(2 - 0))?\n | -52\n | ibivibiv/math_instruct | |
Let g(i) = 2*i**3 - 4*i**2 + 3*i. Suppose 0 = -5*z + 7 + 3. What is the units digit of g(z)?\n | 6\n | ibivibiv/math_instruct | |
Let y(s) = 60*s**3 + 2*s**2 - 3*s + 1. List the prime factors of y(1).\n | 2, 3, 5\n | ibivibiv/math_instruct | |
Is 18 a factor of 5328?\n | True\n | ibivibiv/math_instruct | |
What is next in -1277492, -2554989, -3832486?\n | -5109983\n | ibivibiv/math_instruct | |
Determine r, given that r**4/6 + 26*r**3/3 + 437*r**2/6 + 361*r/3 + 56 = 0.\n | -42, -8, -1\n | ibivibiv/math_instruct | |
Let v = -37.017 + 37. Let l = 205.103 + -205. Let f = v + l. Round f to 2 dps.\n | 0.09\n | ibivibiv/math_instruct | |
Suppose -3*t - 18 = -5*t. Calculate the least common multiple of t and 2.\n | 18\n | ibivibiv/math_instruct | |
Suppose 2*o - u - 5 = 3*o, 3*u + 15 = -2*o. Let w(j) = -2*j**2 - 3*j - 374. Let r(k) = 3*k**2 + 4*k + 375. Let t(i) = -3*r(i) - 4*w(i). Is t(o) composite?\n | True\n | ibivibiv/math_instruct | |
Calculate 584180241*-0.1.\n | -58418024.1\n | ibivibiv/math_instruct | |
How many minutes are there between 9:21 AM and 3:47 PM?\n | 386\n | ibivibiv/math_instruct | |
Suppose 3*l + 0*l = t - 11, -3*t = -3*l - 45. Let z be (-4)/18 + (-2)/(-9). Suppose z = -5*n + 19 + 26. What is the remainder when t is divided by n?\n | 8\n | ibivibiv/math_instruct | |
Is 18414/14 + (-8)/28 composite?\n | True\n | ibivibiv/math_instruct | |
-256 + 239 - (2 - 6)\n | -13\n | ibivibiv/math_instruct | |
What is -0.001395798 rounded to six decimal places?\n | -0.001396\n | ibivibiv/math_instruct | |
Suppose -30*j - 34 = -32*j. Calculate the remainder when 62 is divided by j.\n | 11\n | ibivibiv/math_instruct | |
Let n(i) be the second derivative of -6*i - 9/16*i**5 + 0 + 0*i**2 - 7/80*i**6 - 1/4*i**4 + 0*i**3. Determine o so that n(o) = 0.\n | -4, -2/7, 0\n | ibivibiv/math_instruct | |
What is the derivative of -811593*b**3*o**2 + 100*b*o**3 + 147*o**3 + 2*o**2 + 309*o - 20 wrt b?\n | -2434779*b**2*o**2 + 100*o**3\n | ibivibiv/math_instruct | |
(-1 - -26) + ((-66)/18 - 26/(-39))\n | 22\n | ibivibiv/math_instruct | |
List the prime factors of 146903918.\n | 2, 7, 1201, 8737\n | ibivibiv/math_instruct | |
b"What is the wth term of 32, 49, 92, 173, 304?\n" | 2*w**3 + w**2 + 29\n | ibivibiv/math_instruct | |
As a high school Calculus teacher, Stacy assigns 45 homework problems. The number of multiple choice problems is twice the number of free response problems, and there are 7 more free response problems than true/false. How many true/false questions are there in total? | Lets say the number of true/false questions is x.
The number of free response problems is x + 7 (since there are 7 more free response problems than true/false).
The number of multiple choice problems is 2 * (x + 7) (since the number of multiple choice problems is twice the number of free response problems).
So the tota... | ibivibiv/math_instruct | |
What is 111 minutes after 5:20 PM?\n | 7:11 PM\n | ibivibiv/math_instruct | |
Let z = 2691.68 - 2636. Let w = 393.92 + z. Round w to the nearest one hundred.\n | 400\n | ibivibiv/math_instruct | |
Let i(j) = 2*j**3 - 14*j**2 + 8*j - 25. Let n be 1023/99 - (-4)/6. Is i(n) prime?\n | True\n | ibivibiv/math_instruct | |
Does 14 divide (0 - 5)*122*-31?\n | False\n | ibivibiv/math_instruct | |
Express 15 - 367*d - 389*d + 24 + 109*d - 38 as s + n*d and give n.\n | -647\n | ibivibiv/math_instruct | |
Let c(b) = -b**3 + 25*b**2 + 27*b + 53. Let k be c(26). Let s = 79 - k. Solve s = -5*y - m - 2, 6 = -y - 2*y + m for y.\n | -1\n | ibivibiv/math_instruct | |
Let -p**3/4 - 17*p**2/2 = 0. What is p?\n | -34, 0\n | ibivibiv/math_instruct | |
Calculate prob of sequence akak when four letters picked without replacement from kaakaaaaakakkakaaa.\n | 11/204\n | ibivibiv/math_instruct | |
Calculate prob of sequence avbh when four letters picked without replacement from vbhhavvvvvza.\n | 1/495\n | ibivibiv/math_instruct | |
Let x(n) = n**3 + n**2 + 2*n + 5. Let h be x(0). Solve 5*s - h = 5*j, s + 2*j = -s - 10 for s.\n | -2\n | ibivibiv/math_instruct | |
What is -0.84 plus -0.4?\n | -1.24\n | ibivibiv/math_instruct | |
Simplify (sqrt(405) + -1)*-4 - (-1 + sqrt(405))**2*5.\n | -2026 + 54*sqrt(5)\n | ibivibiv/math_instruct | |
Suppose -430 = i - 223. Is -209 greater than i?\n | False\n | ibivibiv/math_instruct | |
-33110321 (base 5) to base 14\n | -75c74\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Lecture 16: Review of the First 15 Lectures¶
In the first 15 lectures we explored the extensive number system of Sage, manipulated polynomials and general expressions.
Below is a first, preliminary list of questions to re... | Let's delve into the questions presented in the lecture snippet and explore the underlying mathematical and computational concepts. We will cover numerical precision, algebraic numbers, polynomial handling, and hardware floating point evaluation.
1. Floating Point Precision in Sage:
Sage, like other computer algebra ... | ibivibiv/math_instruct | |
Let b be (-23)/(-7) + 10/(-35). Let y(a) = -a - a**b + 3*a - 2*a**2 - 3*a. List the prime factors of y(-3).\n | 2, 3\n | ibivibiv/math_instruct | |
Let h = -12 + 6. Let g = h - -11. Suppose -42 = 2*k - 5*k - 3*s, -g*k + 62 = s. Calculate the remainder when k is divided by 7.\n | 5\n | ibivibiv/math_instruct | |
Suppose -3*d + 4*q - 41 = 0, 4*d - 4*q = -0*d - 48. Let o = -6 - d. Is o less than 1?\n | False\n | ibivibiv/math_instruct |
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