instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Calculate ((-21)/(-9) - 3 - -4) + -4.\n | -2/3\n | ibivibiv/math_instruct | |
Two letters picked without replacement from qcqcscqicqccssicsiq. Give prob of picking 2 q.\n | 10/171\n | ibivibiv/math_instruct | |
Is 62933 a multiple of 22?\n | False\n | ibivibiv/math_instruct | |
Expand (4*g**3 - 3*g**3 + 0*g**3)*(-g**2 + 4*g**2 - 4*g**2) + 4*g**5 - 3*g**5 - 4*g**5 + 2 + (3*g**4 - 4*g**4 + 3*g**4)*(0*g + g - 2*g).\n | -6*g**5 + 2\n | ibivibiv/math_instruct | |
Collect the terms in 9*l**2 - 2*l**3 - 80961 - 23*l**2 - 34*l**2 + 80961.\n | -2*l**3 - 48*l**2\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 881155 and 7073.\n | 11\n | ibivibiv/math_instruct | |
Let q = -6 - -11. Suppose -16 = -4*s, 2*z + 32 = 5*s - s. Let v be 18/4 - (-4)/z. Solve v*h = q*h for h.\n | 0\n | ibivibiv/math_instruct | |
In base 6, what is 313 - 20344003?\n | -20343250\n | ibivibiv/math_instruct | |
Suppose 0*d - 5*d = 0. Let s be (2/(-3) - -1)*221. Let a = s + -73. What is the nearest to a in 2/7, 5, d?\n | 2/7\n | ibivibiv/math_instruct | |
Suppose g - 2*k = 2*k + 3, 4*g = -k + 12. Suppose g*h - 10 = 2*t, t + 15 = 4*t + 3*h. Is t at least 5/9?\n | True\n | ibivibiv/math_instruct | |
Suppose 0 = 15*o - 8*o - 56. Calculate the lowest common multiple of 24 and o.\n | 24\n | ibivibiv/math_instruct | |
Is 217453 composite?\n | True\n | ibivibiv/math_instruct | |
Let s(n) = -293*n - 431. What is the units digit of s(-13)?\n | 8\n | ibivibiv/math_instruct | |
Calculate the remainder when 21608368 is divided by 309.\n | 307\n | ibivibiv/math_instruct | |
Convert -11 (base 2) to base 10.\n | -3\n | ibivibiv/math_instruct | |
What is prob of picking 1 l, 1 n, and 1 v when three letters picked without replacement from nlnnkllnnvkk?\n | 3/44\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(73.389 + 44.295) - -62.391 | 180.0750 | ibivibiv/math_instruct | |
Let h = -451 - -450.669. Let u = h + 0.33099583. What is u rounded to 7 decimal places?\n | -0.0000042\n | ibivibiv/math_instruct | |
Calculate the least common multiple of 3570 and 1746.\n | 1038870\n | ibivibiv/math_instruct | |
Let q(t) = -13*t**2. Let r(y) = 4*y - 293*y**2 - 4*y + 296*y**2. Give r(q(k)).\n | 507*k**4\n | ibivibiv/math_instruct | |
Suppose 30 = 4*w - 2*a, -4*w - 15 = -5*a - 42. Find the third derivative of w*i**2 - i**3 + 14*i**3 + 7*i**2 wrt i.\n | 78\n | ibivibiv/math_instruct | |
Let o = 24 + -26. Is (-3)/((-6)/(-223))*o a prime number?\n | True\n | ibivibiv/math_instruct | |
Let j be -1*(1 - 0)*-3. Let b(x) = j*x + 4 - 3 - x. Let f(i) = 4*i + 2. Give 5*b(n) - 2*f(n).\n | 2*n + 1\n | ibivibiv/math_instruct | |
Suppose 0 = 4*q - 34 - 2. Let p = q + -4. Let o(s) = s**3 + 5*s**2 - 5*s. Let d(u) = -u**3 - 6*u**2 + 6*u. Give p*d(f) + 6*o(f).\n | f**3\n | ibivibiv/math_instruct | |
What is the next term in -22393, -22146, -21725, -21124, -20337, -19358?\n | -18181\n | ibivibiv/math_instruct | |
What is 4 - 809843862?\n | -809843858\n | ibivibiv/math_instruct | |
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"# Making Friends around a Circular Table
I have $n$ people seated around a circular table, initially in arbitrary order. At each step, I choose two people and switch their seats. What is the minimum number of steps required ... | Let's delve into the problem presented, which involves rearranging people seated around a circular table. We will explore the conditions for minimizing the number of steps required so that every person sits adjacent to all others at least once, considering both restrictions on switching neighbors versus non-neighbors.... | ibivibiv/math_instruct | |
Let v(j) = j**3 + 5*j**2 + 3*j - 3. Let c(f) = 2*f**2 - 3*f + 1. Let z be c(2). Suppose 2*r + 4*d = 14, 5*r = 3*d - 1 - z. Let l be (-16)/6 + r/(-3). Give v(l).\n | 6\n | ibivibiv/math_instruct | |
b"What is the wth term of 35, 67, 99, 131, 163?\n" | 32*w + 3\n | ibivibiv/math_instruct | |
Nadia was sent to the flower shop to buy 20 roses and 3/4 times as many Lillies as roses. If roses cost $x each and lilies cost twice as much each, calculate the total amount of money Nadia used to buy the flowers.
If we know the answer to the above question is 250, what is the value of unknown variable x? | Nadia bought 20 roses, so the cost of the roses is 20 * $x = $20x.
She also bought 3/4 times as many Lilies as roses, which means she bought (3/4) * 20 = 15 Lilies.
Each Lily costs twice as much as a rose, so the cost of the Lilies is 15 * 2 * $x = $30x.
The total amount of money Nadia used to buy the flowers is the su... | ibivibiv/math_instruct | |
Let x(t) = -t. Let a be 1 + 2/(4/(-14)). Let q(m) = -7*m**2 + 6*m + 6. Let v(l) = -l + 8 - 9 - 3*l**2 + 4*l**2. Let w(g) = a*v(g) - q(g). Calculate x(w(h)).\n | -h**2\n | ibivibiv/math_instruct | |
Calculate ((-516)/((-66)/11))/(6/(-84)*-7*4).\n | 43\n | ibivibiv/math_instruct | |
Calculate ((-1)/(-10))/(-2*(-2)/(-16)).\n | -2/5\n | ibivibiv/math_instruct | |
What is the cube root of 84604765 to the nearest integer?\n | 439\n | ibivibiv/math_instruct | |
Simplify -4 + (sqrt(6)/sqrt(3) - sqrt(2)) + -2 + 2.\n | -4\n | ibivibiv/math_instruct | |
Solve -3 = 5*i - i - 12*a + 16*a + 5, 2*i + 5*a + 19 = 0 for i.\n | 3\n | ibivibiv/math_instruct | |
What is 64/5 of a century in months?\n | 15360\n | ibivibiv/math_instruct | |
Differentiate 2*m**4 - 3*m**2*z + 54*m*s - 11009*s*z with respect to m.\n | 8*m**3 - 6*m*z + 54*s\n | ibivibiv/math_instruct | |
Let k be 7 + (195/(-10))/3. Let t = -1 + 2. Sort t, 14.5, k in ascending order.\n | k, t, 14.5\n | ibivibiv/math_instruct | |
Expand ((-r**2 + r - r)*(-2 + 0 + 0) + r - r - 3*r**2)*(8*r + 3*r + 5*r).\n | -16*r**3\n | ibivibiv/math_instruct | |
How many minutes are there between 8:51 PM and 7:54 AM?\n | 663\n | ibivibiv/math_instruct | |
Solve -12215 = -3776*n + 4394*n + 5707 for n.\n | -29\n | ibivibiv/math_instruct | |
Suppose -2*r + 2 + 2 = 0. Suppose -r*m + 0 - 4 = 0. Let w = 2 + -3. Which is bigger: w or m?\n | w\n | ibivibiv/math_instruct | |
Find the second derivative of 5*y**4 + 250*y**2 - 39*y + 4.\n | 60*y**2 + 500\n | ibivibiv/math_instruct | |
Let j(v) = v**3 - 10*v**2 + 2*v - 21. Let u be j(10). Let w = -65 - -68. Let t be 0/(3 - w - 1*u). Which is greater: t or 4/27?\n | 4/27\n | ibivibiv/math_instruct | |
What is the nearest to -6 in 0.05, -2, -0.5, -3?\n | -3\n | ibivibiv/math_instruct | |
Solve 3*d + 2*r + 2 + 4 = 0, 4*d + 8 = 3*r for d.\n | -2\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {v: 3, i: 4, u: 7, j: 2, a: 2}. Give prob of picking 3 v.\n | 1/816\n | ibivibiv/math_instruct | |
Sort 4, 0, -2, -17, -1013, 5 in decreasing order.\n | 5, 4, 0, -2, -17, -1013\n | ibivibiv/math_instruct | |
Find the second derivative of 185353082*f**3 + 4*f + 12756601 wrt f.\n | 1112118492*f\n | ibivibiv/math_instruct | |
Put -10, -5, -3/4, -1/2 in decreasing order.\n | -1/2, -3/4, -5, -10\n | ibivibiv/math_instruct | |
Suppose 3*m - 6 = -39. Is m greater than -12?\n | True\n | ibivibiv/math_instruct | |
Let b(a) = -3*a**2 + 13. Let u be b(0). Let r be (-1)/(-3)*(40 - u). Put -1, 1/8, r in descending order.\n | r, 1/8, -1\n | ibivibiv/math_instruct | |
Suppose 0 = 3*o - 2 + 5. Let m = -37.48 + 37. Let j = m + 0.18. Which is the closest to o? (a) -5 (b) j (c) -0.2\n | b\n | ibivibiv/math_instruct | |
Put 4, -4/11, -1/3, -4 in increasing order.\n | -4, -4/11, -1/3, 4\n | ibivibiv/math_instruct | |
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"# Integration math question
1. May 26, 2008
### Gear300
If we were to integrate 1/x by parts using u = 1/x and dv = 1dx, then it would end up as:
Int(dx/x) = 1 + Int(dx/x), ending up with 1 = 0. Why was there a discrepancy... | The initial post from "Gear300" presents an interesting conundrum regarding integration by parts of the function 1/x. At first glance, it seems like the process yields an incorrect equality (1 = 0). However, let us examine the steps more closely and address any potential misconceptions.
Integration by parts is a tech... | ibivibiv/math_instruct | |
-226 divided by -2251\n | 226/2251\n | ibivibiv/math_instruct | |
What is 4 divided by 49?\n | 4/49\n | ibivibiv/math_instruct | |
What is the closest to 0.03 in -4, -0.2, -0.11, -1976.49?\n | -0.11\n | ibivibiv/math_instruct | |
Rearrange (-2*j + 7*j + 0*j)*(-5 + 2 + 1)*(j - 4*j + 2*j)*(49*j + 191 - 191 - 2*j**2) to p*j + b*j**4 + c*j**3 + v + x*j**2 and give b.\n | -20\n | ibivibiv/math_instruct | |
Let t = -1255.08 - -1255. Which is the nearest to 3? (a) 0.4 (b) t (c) 4\n | c\n | ibivibiv/math_instruct | |
Let g be 3 + -2 - (-2)/1. Suppose t = -4, -2*t = g*r - 7*r + 68. What is the remainder when r is divided by 8?\n | 7\n | ibivibiv/math_instruct | |
Is 6 a factor of 451243640?\n | False\n | ibivibiv/math_instruct | |
10 divided by 16\n | 5/8\n | ibivibiv/math_instruct | |
b"What is the lth term of 2885, 2730, 2597, 2480, 2373, 2270, 2165, 2052?\n" | -l**3 + 17*l**2 - 199*l + 3068\n | ibivibiv/math_instruct | |
Is 583 != -12?\n | True\n | ibivibiv/math_instruct | |
Does 516 divide 21166320?\n | True\n | ibivibiv/math_instruct | |
Let a(d) = d**2 + 10*d + 3. Let c be a(-10). Suppose 0 = -2*k + 2*v - 14, -c*v + 17 + 8 = -5*k. What is k rounded to the nearest 10?\n | 0\n | ibivibiv/math_instruct | |
Solve 266 = 38*i - 0*i for i.\n | 7\n | ibivibiv/math_instruct | |
Is 40 a factor of 5718200?\n | True\n | ibivibiv/math_instruct | |
Let a(q) = 16*q**2 - 18*q**2 - 20*q**2 - 16*q**2 + 26*q**2. Suppose -5*g = 10, 0 = 2*j - 0*g - 2*g - 16. Let f(i) = i - j*i + 3*i. Give f(a(h)).\n | 24*h**2\n | ibivibiv/math_instruct | |
Let f = -150096/685 + 756/137. Let x = f - -214. Determine u so that -2/5*u**4 + 6/5*u**2 + x*u - 2/5*u**3 - 4/5 = 0.\n | -2, -1, 1\n | ibivibiv/math_instruct | |
Let c(o) be the second derivative of -o**5/120 + 31*o**4/9 + o**3/36 - 62*o**2/3 - 4091*o. Let c(i) = 0. What is i?\n | -1, 1, 248\n | ibivibiv/math_instruct | |
Collect the terms in -22*i**3 - 401 - 112*i**2 - 108*i**2 + 220*i**2 + 401.\n | -22*i**3\n | ibivibiv/math_instruct | |
Suppose -2*c + 27 + 3 = 0. Suppose c + 0 = 5*h, 7 = 2*a + h. Let x(m) = -2*m - 1 - 1 + 0*m**2 + 2*m**a. Calculate x(2).\n | 2\n | ibivibiv/math_instruct | |
Solve -p + 5*p - 4 = 0, -3*y + 4*p = 4 for y.\n | 0\n | ibivibiv/math_instruct | |
Let w be (-6)/(-21) + (-148)/28. Let x be (3 + -1 - 0)/(48/120). Sort w, -2, -1, x in increasing order.\n | w, -2, -1, x\n | ibivibiv/math_instruct | |
What are the prime factors of 45390?\n | 2, 3, 5, 17, 89\n | ibivibiv/math_instruct | |
What is 1196 to the power of 1/2, to the nearest integer?\n | 35\n | ibivibiv/math_instruct | |
Let m(g) = -g**3 - 12*g**2 + 12*g - 12. Let q(c) = 4*c**3 + 35*c**2 - 34*c + 40. Let n(z) = 7*m(z) + 2*q(z). Give n(13).\n | 35\n | ibivibiv/math_instruct | |
Let h(a) = 2*a - 19. Suppose -24 + 19 = c. Let q be h(c). Which is bigger: -25 or q?\n | -25\n | ibivibiv/math_instruct | |
Calculate prob of sequence bu when two letters picked without replacement from uuasnsblnun.\n | 3/110\n | ibivibiv/math_instruct | |
Let p = -3718 - -89293/24. Let f = p - 8/3. Which is the second biggest value? (a) f (b) 0.1 (c) 5\n | b\n | ibivibiv/math_instruct | |
Let u be -24*(-3 - 27/(-12)). Suppose -u*k + 1402 = -974. What is the highest common divisor of 44 and k?\n | 44\n | ibivibiv/math_instruct | |
Convert 22 (base 3) to base 14.\n | 8\n | ibivibiv/math_instruct | |
Let q(l) = -l**2 - l + 23. Let u(y) = -y - 9. Let o be u(-9). Let k be q(o). Solve -5*h - 2*t + k = 0, -3*t + 20 = 4*h - t for h.\n | 3\n | ibivibiv/math_instruct | |
Let n = 1214 + -1215. What is the closest to n in -1/2, -0.4, -1/3?\n | -1/2\n | ibivibiv/math_instruct | |
What is the nearest to -5 in -0.8, -1/2, 15, 0.4?\n | -0.8\n | ibivibiv/math_instruct | |
What is the third smallest value in 9, 3821, 1/5, -619, 0.3?\n | 0.3\n | ibivibiv/math_instruct | |
Is 23 a factor of 1039922?\n | True\n | ibivibiv/math_instruct | |
Suppose 5 = -3*c - 19. Let y(w) = -7*w**2 - 23*w + 24. Let z(d) = 20*d**2 + 68*d - 72. Let b(f) = c*y(f) - 3*z(f). Find r, given that b(r) = 0.\n | -6, 1\n | ibivibiv/math_instruct | |
-972751740 divided by -95\n | 10239492\n | ibivibiv/math_instruct | |
What is next in -10591, -10586, -10583, -10582, -10583, -10586?\n | -10591\n | ibivibiv/math_instruct | |
Which is the fourth smallest value? (a) -1/7 (b) -140 (c) -9 (d) -8716\n | a\n | ibivibiv/math_instruct | |
Work out -55882 * 0.058.\n | -3241.156\n | ibivibiv/math_instruct | |
Is -10521720 bigger than -10521720?\n | False\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {l: 4, p: 1, b: 2}. What is prob of sequence plb?\n | 4/105\n | ibivibiv/math_instruct | |
Suppose -g - 3 = -6. Let w(l) be the third derivative of 1/120*l**6 + 0*l**4 + 0 + 0*l + 1/2*l**g - l**2 + 0*l**5. Find the first derivative of w(q) wrt q.\n | 3*q**2\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 p, 2 q, and 1 a when four letters picked without replacement from qappqpqaqqppqqqpqp.\n | 14/85\n | ibivibiv/math_instruct | |
Convert 87.92595 nanograms to micrograms.\n | 0.08792595\n | ibivibiv/math_instruct |
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