instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Solve -2*u + 4*z = -20, 5*z = 3*u - 28 + 1 for u.\n | 4\n | ibivibiv/math_instruct | |
Find the common denominator of -1/101 and -59/2.\n | 202\n | ibivibiv/math_instruct | |
What is (40/(-640)*6/4)/(2/8)?\n | -3/8\n | ibivibiv/math_instruct | |
Collect the terms in 3510614*o**2 + 23709*o**3 - 2589*o**3 - 3510614*o**2.\n | 21120*o**3\n | ibivibiv/math_instruct | |
Collect the terms in -4*a**2 - 712591 + 712591.\n | -4*a**2\n | ibivibiv/math_instruct | |
Let a = -679 - -678.6798. Let y = -0.08 - 0.24. Let j = y - a. What is j rounded to four dps?\n | 0.0002\n | ibivibiv/math_instruct | |
Let b(o) = o**2 - 2*o + 2. Let t be b(2). Let p be 100/10*(-4)/(-10). Solve t*d - p - 6 = 0 for d.\n | 5\n | ibivibiv/math_instruct | |
Simplify (((k*k/k**(4/11)*k)/k)/k*k*k*k**(4/13))**(-30) assuming k is positive.\n | k**(-12630/143)\n | ibivibiv/math_instruct | |
Put -0.1, 0.1, 1/3, -5, -0.04 in decreasing order.\n | 1/3, 0.1, -0.04, -0.1, -5\n | ibivibiv/math_instruct | |
What is the square root of 26929 to the nearest integer?\n | 164\n | ibivibiv/math_instruct | |
What is 691 minutes before 3:54 AM?\n | 4:23 PM\n | ibivibiv/math_instruct | |
Express -27*p + 82*p - 408*p - 137*p in the form w*p + r and give w.\n | -490\n | ibivibiv/math_instruct | |
Let l(o) = o**2. Let x(f) = 28774459*f**2. Calculate l(x(d)).\n | 827969490742681*d**4\n | ibivibiv/math_instruct | |
Let h = -28513991 - -28513977.499937. Let q = -51 + 64.5. Let y = q + h. Round y to 5 decimal places.\n | -0.00006\n | ibivibiv/math_instruct | |
What is the value of (-128)/72*243/(-378)?\n | 8/7\n | ibivibiv/math_instruct | |
Express -232*l**3 - 648*l + 117*l**3 - 795*l + 114*l**3 - 4 as t*l**3 + i + v*l**2 + r*l and give r.\n | -1443\n | ibivibiv/math_instruct | |
-3102240 divided by 460\n | -6744\n | ibivibiv/math_instruct | |
Is 46262392 a multiple of 41?\n | False\n | ibivibiv/math_instruct | |
What is 107106356.7 microseconds in weeks?\n | 0.00017709384375\n | ibivibiv/math_instruct | |
Let y = -6 + 3. Let h = y + 5. Suppose -h = -3*g + 1. Is -2/11 bigger than g?\n | False\n | ibivibiv/math_instruct | |
Which is smaller: -1 or 589031?\n | -1\n | ibivibiv/math_instruct | |
Suppose 6*m = 25 + 11. Solve m*g = 2*g for g.\n | 0\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {g: 5, a: 2, c: 5, z: 5, r: 1, m: 1}. Give prob of sequence czgg.\n | 125/23256\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {k: 6, l: 6}. What is prob of picking 4 k?\n | 1/33\n | ibivibiv/math_instruct | |
Which is the biggest value? (a) -0.8 (b) 1 (c) -2 (d) -0.114\n | b\n | ibivibiv/math_instruct | |
Let c = 4 + -1. Let u(w) = 2*w - 4. Let v be u(3). What is the highest common factor of v and c?\n | 1\n | ibivibiv/math_instruct | |
Let c be ((-20)/6)/((-6)/9). Suppose 46 = 5*i + 2*v, 0 = 4*i + 2*v + 3*v - 47. Let l = i - c. Put -3/2, l, 2 in descending order.\n | l, 2, -3/2\n | ibivibiv/math_instruct | |
Let k(d) be the third derivative of 0*d**4 + 3*d + 0*d**3 + 13/20*d**6 - 32*d**2 + 0 + 7/15*d**5. What is the third derivative of k(f) wrt f?\n | 468\n | ibivibiv/math_instruct | |
Find the third derivative of -756507*n**6 + 298968*n**2.\n | -90780840*n**3\n | ibivibiv/math_instruct | |
Let n = 411 - 571. Suppose -730 = -5*s + 395. Let c = n + s. What are the prime factors of c?\n | 5, 13\n | ibivibiv/math_instruct | |
Let l = 40 + -256. Suppose -2*d = -w + 250 - 74, d + 2*w + 93 = 0. Let r = d - l. What is the units digit of r?\n | 7\n | ibivibiv/math_instruct | |
Suppose -3*w + 3*j = 2*j + 13, 5*j = -4*w - 11. Let l be (2 + 1/2)/(2/w). Put l, -3, 3, 0 in decreasing order.\n | 3, 0, -3, l\n | ibivibiv/math_instruct | |
Let d(w) = 630*w**2. Let y(p) be the third derivative of -p**4/12 - 2*p**2 - 36. Give d(y(i)).\n | 2520*i**2\n | ibivibiv/math_instruct | |
Expand -2*u - 2*u**2 + 2*u + (-3*u + 12*u + 0*u)*(-250*u + 138*u - 346*u).\n | -4124*u**2\n | ibivibiv/math_instruct | |
Which is the smallest value? (a) -4 (b) -1/2 (c) 31 (d) 21\n | a\n | ibivibiv/math_instruct | |
Let a be 6/4*16/12. Suppose 4*d + 2*z + 2*z + 100 = 0, a*d = z - 35. What are the prime factors of (-156)/(-10) - 8/d?\n | 2\n | ibivibiv/math_instruct | |
Multiply 11180 and 3.\n | 33540\n | ibivibiv/math_instruct | |
Let s(d) = -2*d**2 + 4*d + 1. Let a(x) be the third derivative of -x**5/60 + x**4/12 + 20*x**2. What is -5*a(q) + 2*s(q)?\n | q**2 - 2*q + 2\n | ibivibiv/math_instruct | |
Solve 0 = 3*d - 2*z + 43, -5*d - 2622*z + 2627*z = 75 for d.\n | -13\n | ibivibiv/math_instruct | |
Let o(g) be the second derivative of -g**7/126 + 7*g**6/90 + g**5/2 + g**4/9 - 20*g**3/9 + 1457*g. Determine r so that o(r) = 0.\n | -2, 0, 1, 10\n | ibivibiv/math_instruct | |
Simplify (-6*(1 + (5 + sqrt(117) + sqrt(117)*1 + sqrt(117) + -4)*6 + -1 + 1))**2.\n | 27216*sqrt(13) + 1366452\n | ibivibiv/math_instruct | |
Which is the biggest value? (a) -2/3 (b) -1/5 (c) -1/232 (d) 2\n | d\n | ibivibiv/math_instruct | |
Arrange Trishas five test scores, separated by commas, in descending order. The scores on her first three tests were 88, 73, and 70, and after two more tests, the mean score for all five tests was 81. All test scores are different integers and less than 90. | The sum of Trishas five test scores is $81 \times 5 = 405$.
The sum of her first three test scores is $88+73+70 = 231$.
The sum of her last two test scores is $405-231 = 174$.
Since all the test scores are different integers and less than 90,
the two smallest possible test scores that sum to 174 are 85 and 89.
Therefor... | ibivibiv/math_instruct | |
Solve 6*o - 9*o + 3 = -3*y, -5*o = 2*y + 23 for o.\n | -3\n | ibivibiv/math_instruct | |
Suppose z - 3*u + 4*u = 231000, 692996 = 3*z - u. Is z a prime number?\n | True\n | ibivibiv/math_instruct | |
How many centuries are there in sixty-four fifths of a millennium?\n | 128\n | ibivibiv/math_instruct | |
b"What is the nth term of -181, -719, -1617, -2875?\n" | -180*n**2 + 2*n - 3\n | ibivibiv/math_instruct | |
What is the value of 3 + (-1 - 4) + 1 + -1?\n | -2\n | ibivibiv/math_instruct | |
What is the thousands digit of 43397?\n | 3\n | ibivibiv/math_instruct | |
Simplify (-1 + 3 + sqrt(1053) + sqrt(1053)*2*4)**2.\n | 324*sqrt(13) + 85297\n | ibivibiv/math_instruct | |
Let o(k) = -2*k + 2. Let h be o(5). Let v = 7 + h. Suppose f = -f - 6. What is the nearest to 0.2 in f, 2, v?\n | v\n | ibivibiv/math_instruct | |
What is prob of sequence yyv when three letters picked without replacement from {y: 6, v: 1, i: 4}?\n | 1/33\n | ibivibiv/math_instruct | |
Expand (91*y - 1142 + 1142)*(-156 + 156 - 25*y**3).\n | -2275*y**4\n | ibivibiv/math_instruct | |
Suppose -2*u - 563 = -3*j, -5*j - 390 + 1327 = -2*u. Solve -3 = 5*s - 4*g, 186*s - j*s - 4*g = -9 for s.\n | 1\n | ibivibiv/math_instruct | |
What is the highest common factor of 11581682 and 174034?\n | 5614\n | ibivibiv/math_instruct | |
Let u(c) = c**2 + 1. Let k(h) = h**3 - 8*h**2 + 14*h - 9. Let q(i) = k(i) - 4*u(i). Let t be q(11). Let v(r) = 14*r + 0 - t*r - 3 + r**2 - 5. Give v(7).\n | -1\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 2289 and 3924.\n | 27468\n | ibivibiv/math_instruct | |
Suppose -4*n - h + 1416 = -6*h, 2*n - 3*h - 708 = 0. List the prime factors of n.\n | 2, 3, 59\n | ibivibiv/math_instruct | |
Let d(i) = -2*i**3 - 1024*i**2 + 1056*i + 15387. What is d(-513)?\n | -3\n | ibivibiv/math_instruct | |
Let f(n) = -2*n + 12. Suppose 11*u = 22 + 11. Is 3 a factor of f(u)?\n | True\n | ibivibiv/math_instruct | |
Collect the terms in 11030959*v + v**3 - 11030959*v + 13*v**3.\n | 14*v**3\n | ibivibiv/math_instruct | |
Divide 36 by 12.\n | 3\n | ibivibiv/math_instruct | |
Let s(i) = i**2 - 15*i + 608. Let a be s(0). Let o = a - 262. Is 8 a factor of o?\n | False\n | ibivibiv/math_instruct | |
Let q(x) = x**3 - 51*x**2 - 47*x - 242. What is the remainder when 4316 is divided by q(52)?\n | 14\n | ibivibiv/math_instruct | |
What is the second derivative of 701*c**4*i + 2*c*i + 167*c - i wrt c?\n | 8412*c**2*i\n | ibivibiv/math_instruct | |
Calculate -106.104 + 3810262.\n | 3810155.896\n | ibivibiv/math_instruct | |
Let d = -1053 - -1053.2. Which is the second smallest value? (a) d (b) -5 (c) 9\n | a\n | ibivibiv/math_instruct | |
What is 9/10 of a gram in milligrams?\n | 900\n | ibivibiv/math_instruct | |
Let x be 6/(-35) - 2/5. Let l = 3 + -3.9. Let p = -1 - l. What is the closest to p in x, 1/2, -1?\n | x\n | ibivibiv/math_instruct | |
b"What is the dth term of -4809, -9604, -14341, -18990, -23521?\n" | 5*d**3 - d**2 - 4827*d + 14\n | ibivibiv/math_instruct | |
Suppose -3*o + 42 = 3*r, -o + 3*r + 29 = -r. Suppose 59*n + 3 = 58*n, 70 = p + 5*n. What is the highest common factor of o and p?\n | 17\n | ibivibiv/math_instruct | |
Put -5, 0, 4, -7 in decreasing order.\n | 4, 0, -5, -7\n | ibivibiv/math_instruct | |
Simplify (q*q**(-5/3))**(2/5)/(q/(q*q/q**(2/23)))**(2/11) assuming q is positive.\n | q**(-382/3795)\n | ibivibiv/math_instruct | |
Which is the second smallest value? (a) -1/6 (b) 1567 (c) 0.0245\n | c\n | ibivibiv/math_instruct | |
Two letters picked without replacement from xpppxxzlhpp. What is prob of sequence xz?\n | 3/110\n | ibivibiv/math_instruct | |
Let b(v) = 999*v - 16. Calculate b(0).\n | -16\n | ibivibiv/math_instruct | |
b"What is the pth term of 2011, 2015, 2019, 2023?\n" | 4*p + 2007\n | ibivibiv/math_instruct | |
Simplify (5*(sqrt(1573) + 0)*6 + -5*(sqrt(1573) + 0 + -1))**2.\n | 2750*sqrt(13) + 983150\n | ibivibiv/math_instruct | |
Is 21064/2*(-2)/(-8) a prime number?\n | True\n | ibivibiv/math_instruct | |
What is prob of sequence zzzm when four letters picked without replacement from mzmszzmpmnzhhss?\n | 4/1365\n | ibivibiv/math_instruct | |
Let o(c) = 14*c - 29. Let a(v) = 3*v - 7. Let k(q) = 9*a(q) - 2*o(q). Suppose r = -2*j + 9, 0*j = -5*j - r + 24. Suppose -s + j*s + 28 = 0. Give k(s).\n | 2\n | ibivibiv/math_instruct | |
What are the prime factors of 904916?\n | 2, 29, 269\n | ibivibiv/math_instruct | |
(148 - 118) + (2 - (2 - (0 - -11)))\n | 41\n | ibivibiv/math_instruct | |
Let a(j) = -27*j + 20. Let y be a(8). Let l = 201 + y. Solve -4*x + 3*n + 13 = 0, l = -0*x - 4*x - 3*n for x.\n | 1\n | ibivibiv/math_instruct | |
Let l = 470 - 467. Solve k + 5 = -k - f, -f + 5 = -l*k for k.\n | -2\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Why didn't Voyager 1 and Voyager 2 crash on into Jupiter or Uranus when they approached near to these massive planets?
I was reading about gravity assist and I read that both the Voyagers used gravitational force of these ... | Gravitational forces are central to our understanding of celestial motion and were key in enabling the Voyager 1 and 2 spacecraft to reach their current locations in interstellar space. The concept of escape velocity is crucial to addressing your question. Escape velocity (ve) represents the minimum speed required for... | ibivibiv/math_instruct | |
Let o(r) = 23*r**2 + 2*r + 4. Let n be o(-2). Let b(w) = -836*w**2 + 4*w + 4. Let g be b(3). Let x = g - n. Round x to the nearest 1000.\n | -8000\n | ibivibiv/math_instruct | |
Simplify ((i**18*i)/i)/i*i/(i*i**21*i) assuming i is positive.\n | i**(-5)\n | ibivibiv/math_instruct | |
What is the next term in 2, -6, -20, -40?\n | -66\n | ibivibiv/math_instruct | |
What is 3/40 of a micrometer in nanometers?\n | 75\n | ibivibiv/math_instruct | |
Find the second derivative of 11914402*u**4 + 909304*u wrt u.\n | 142972824*u**2\n | ibivibiv/math_instruct | |
Is 34 a factor of 4453320?\n | True\n | ibivibiv/math_instruct | |
Round -0.263911086 to one dp.\n | -0.3\n | ibivibiv/math_instruct | |
Let r be (-4)/(-18) + (-76)/18. Let t be (-2)/r - 4/16. Suppose 4*v = -11 - 5. Which is the nearest to t? (a) 3 (b) v (c) -5/4\n | c\n | ibivibiv/math_instruct | |
What is 0.58 minus 11?\n | -10.42\n | ibivibiv/math_instruct | |
Let n be 3*4/4*1. Let p be (-1)/2*(n - 2)*-6. Solve 0 = -p*m - m for m.\n | 0\n | ibivibiv/math_instruct | |
In base 15, what is -51c + -c?\n | -529\n | ibivibiv/math_instruct | |
0.5*-256759.2\n | -128379.6\n | ibivibiv/math_instruct | |
Let n = -473 + 473. Suppose 0 = -3*z + 2*k + 976, n = -k + 1. Calculate the remainder when z is divided by 107.\n | 5\n | ibivibiv/math_instruct | |
Suppose 2*k - 12 = 5*w - w, -5*k = w - 19. Put 10, 2, -3, w in decreasing order.\n | 10, 2, w, -3\n | ibivibiv/math_instruct |
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