instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What is -11896133610 rounded to the nearest 1000000?\n | -11896000000\n | ibivibiv/math_instruct | |
Suppose 400678 = 3*g + 400642. Let b(k) = k - 1. Let u(p) = -2*p + 19. Let w(q) = b(q) + u(q). What is w(g)?\n | 6\n | ibivibiv/math_instruct | |
What is the nearest to -31 in 33, -0.2, 131.5?\n | -0.2\n | ibivibiv/math_instruct | |
Suppose -3 = -7*n + 46. Let d(i) = -i**3 + 10*i**2 - 10*i + 19. Is 20 a factor of d(n)?\n | False\n | ibivibiv/math_instruct | |
What comes next: -13952693, -27905392, -41858091, -55810790, -69763489, -83716188?\n | -97668887\n | ibivibiv/math_instruct | |
Suppose 11*l = 8*l + 12. Let t(y) = -y. Let s be t(-3). Let v = 6 - s. Calculate the lowest common multiple of l and v.\n | 12\n | ibivibiv/math_instruct | |
Calculate (-81)/(-3807) + 24/34216.\n | 2/91\n | ibivibiv/math_instruct | |
What is prob of sequence tbbb when four letters picked without replacement from {t: 3, b: 9}?\n | 7/55\n | ibivibiv/math_instruct | |
Let o = -1734/29455 + 1/1370. Calculate the common denominator of 5/4 and o.\n | 172\n | ibivibiv/math_instruct | |
What is the cube root of 10575 to the nearest integer?\n | 22\n | ibivibiv/math_instruct | |
Collect the terms in 0 + 0 - 2935556*u**3 + 2933513*u**3.\n | -2043*u**3\n | ibivibiv/math_instruct | |
Suppose -5*d + 164*g + 32 = 161*g, 0 = -2*g - 8. Sort 3, d, -47 in ascending order.\n | -47, 3, d\n | ibivibiv/math_instruct | |
Let o(k) = k**3 + 11*k**2 + 9*k - 9. What is o(-7)?\n | 124\n | ibivibiv/math_instruct | |
Let x(w) = -28*w**3 - 8*w**2 + 59*w + 390. Let o be x(7). What is o rounded to the nearest 100?\n | -9200\n | ibivibiv/math_instruct | |
Suppose 2*b - 780 = -3*p, 0 = 2*p + 3*p + 20. Let h = 399 - b. Solve 1 = -5*u + a - 3, -h*a + 12 = -3*u for u.\n | 0\n | ibivibiv/math_instruct | |
Product of -34847 and -6.3.\n | 219536.1\n | ibivibiv/math_instruct | |
Let b(s) = -s**3 - 3*s**2 - 4*s - 4. What is the remainder when (-201)/335 + 118/5 is divided by b(-3)?\n | 7\n | ibivibiv/math_instruct | |
Let r be -5 + (6 + -3)/(-1). Let d be r/28 + 16/14. Determine n so that -4/7*n**3 + d*n**4 - 2/7 - 2/7*n**5 - 4/7*n**2 + 6/7*n = 0.\n | -1, 1\n | ibivibiv/math_instruct | |
Let t = 2.22 + -1.3. Let a = 1.12 - t. Sort -3, a, 0.07.\n | -3, 0.07, a\n | ibivibiv/math_instruct | |
Suppose 0 = 312*h - 295*h - 17119. Is 19 a factor of h?\n | True\n | ibivibiv/math_instruct | |
Which is the closest to -2/9? (a) 258 (b) -0.1 (c) -16 (d) 9/4\n | b\n | ibivibiv/math_instruct | |
Calculate 272 divided by -17.\n | -16\n | ibivibiv/math_instruct | |
What comes next: 11, -216, -681, -1384, -2325, -3504, -4921?\n | -6576\n | ibivibiv/math_instruct | |
Let w(x) be the first derivative of -2*x**3/21 + 10*x**2 - 350*x - 501. Factor w(i).\n | -2*(i - 35)**2/7\n | ibivibiv/math_instruct | |
Let h(p) = 3*p**3 - 63*p**2 + 2*p - 2. Let t(k) = k - 1. Let c(d) = h(d) - 2*t(d). Let c(b) = 0. What is b?\n | 0, 21\n | ibivibiv/math_instruct | |
Solve -361 = -2089*n + 2070*n for n.\n | 19\n | ibivibiv/math_instruct | |
b"What is the gth term of -48, -53, -42, -15, 28, 87, 162?\n" | 8*g**2 - 29*g - 27\n | ibivibiv/math_instruct | |
Calculate 59.4 - 4427.\n | -4367.6\n | ibivibiv/math_instruct | |
What is -0.000000038851207 rounded to 7 dps?\n | 0\n | ibivibiv/math_instruct | |
Let j = -0.2 + 0.3. Let i = 4.54 - 4.547. Let z = i - -0.037. What is the closest to z in -3, -2/23, j?\n | j\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {y: 4, i: 3, s: 2, f: 3, a: 1, l: 4}. Give prob of sequence si.\n | 3/136\n | ibivibiv/math_instruct | |
Suppose 2*k + 857 = -2*c - 321, 0 = -c - 5*k - 589. Let b = c + 1783/3. Let -7/3*o**2 - b*o - 4/3 = 0. Calculate o.\n | -2, -2/7\n | ibivibiv/math_instruct | |
How many minutes are there between 3:10 PM and 2:20 AM?\n | 670\n | ibivibiv/math_instruct | |
Let n(q) = -5*q**2 + 6*q**2 - 236 + 455 + 3*q - 231. Calculate n(-8).\n | 28\n | ibivibiv/math_instruct | |
Solve -3*t + 23 = -2*o + 16, -t + 1 = -o for o.\n | 4\n | ibivibiv/math_instruct | |
Which is the nearest to -2/7? (a) 20 (b) -3 (c) -0.01 (d) 1/4\n | c\n | ibivibiv/math_instruct | |
What is 72/5 of a decade in months?\n | 1728\n | ibivibiv/math_instruct | |
Let q(z) be the third derivative of -z**6/180 + z**5/120 - z**3/3 + z**2. Let t(k) be the first derivative of q(k). Determine t(2).\n | -6\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 181505812 and 20.\n | 907529060\n | ibivibiv/math_instruct | |
What is the second derivative of -239*h*r**2*u + 5*h*r*u**3 - 11*h*r*u + 2*h - 636*r**2*u**2 - r**2 + 8*r*u**3 wrt u?\n | 30*h*r*u - 1272*r**2 + 48*r*u\n | ibivibiv/math_instruct | |
Suppose 0 = -8*v + 9*v + 4*j - 207, 999 = 5*v + 2*j. Is 200 <= v?\n | False\n | ibivibiv/math_instruct | |
What is 32/5 of a litre in millilitres?\n | 6400\n | ibivibiv/math_instruct | |
What is the greatest common factor of 1068 and 10591?\n | 89\n | ibivibiv/math_instruct | |
Three letters picked without replacement from roozlozrozrioq. Give prob of sequence qoi.\n | 5/2184\n | ibivibiv/math_instruct | |
What is 0 - 1 - ((2 - 6) + 1)?\n | 2\n | ibivibiv/math_instruct | |
Let j = -0.05215 - -0.029317. Round j to 4 dps.\n | -0.0228\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 500 and 170.\n | 8500\n | ibivibiv/math_instruct | |
Factor -30318123*y**4 - 30470715*y**3 - 152784*y**2 - 192*y.\n | -3*y*(y + 1)*(3179*y + 8)**2\n | ibivibiv/math_instruct | |
Suppose 24*n = 27*n - 48. What is the lowest common multiple of n and 36?\n | 144\n | ibivibiv/math_instruct | |
Let s(r) = r**2 + 19*r + 28. Let h be s(-21). Suppose h*t = 72*t - 10. Solve 5*p - t*l - 5 = -0*l, -5*l = -4*p + 4 for p.\n | 1\n | ibivibiv/math_instruct | |
What is the hundreds digit of 1095121?\n | 1\n | ibivibiv/math_instruct | |
Suppose 5*p - 11 = -1. Suppose p*j = -5*j - 1022. What is the tens digit of (-2)/((16/j)/4)?\n | 7\n | ibivibiv/math_instruct | |
Let d be ((-6)/(-5))/(9/(-30)). Let n = -113 - -29. Calculate the common denominator of 77/20 and (-34)/n*(d + -5).\n | 140\n | ibivibiv/math_instruct | |
Let a(r) = 268*r + 370. List the prime factors of a(4).\n | 2, 7, 103\n | ibivibiv/math_instruct | |
Expand -2 - 1 - i**2 - 6 + (3 + i**2 - 3)*(3 - 1 - 4) - 13*i**2 - 5*i**2 + 11*i**2.\n | -10*i**2 - 9\n | ibivibiv/math_instruct | |
What is the nearest to -2 in -0.2, 18, -0.4?\n | -0.4\n | ibivibiv/math_instruct | |
Is 1142777 prime?\n | True\n | ibivibiv/math_instruct | |
Calculate the least common multiple of 160688 and 3652.\n | 160688\n | ibivibiv/math_instruct | |
Is 360107527 a multiple of 1633?\n | True\n | ibivibiv/math_instruct | |
A and B can together finish the work in 12 days. If B can complete the work in 36 days independently, what is the ratio of A's work speed to Bs work speed? | Let's denote the work speed of A as A_work_speed and the work speed of B as B_work_speed.
Since A and B together can finish the work in 12 days, their combined work speed is 1/12 of the work per day.
B can complete the work in 36 days independently, so B's work speed is 1/36 of the work per day.
Now, let's find A's ... | ibivibiv/math_instruct | |
Add 575610261 and -0.6153.\n | 575610260.3847\n | ibivibiv/math_instruct | |
Suppose -4*y + 5*a = -198 + 4, 4*a = -y + 59. Let m = -46 + y. Suppose 2*n + 3 = 3*x - n, -m*n - 1 = -4*x. Solve x = -w - w for w.\n | -2\n | ibivibiv/math_instruct | |
Evaluate 8/(-1)*(-28)/(-28).\n | -8\n | ibivibiv/math_instruct | |
What is prob of sequence fb when two letters picked without replacement from cfbbbfbfbcfcbc?\n | 12/91\n | ibivibiv/math_instruct | |
List the prime factors of 318599.\n | 199, 1601\n | ibivibiv/math_instruct | |
Let p(d) be the second derivative of -3*d**4/2 - d**3/6 + d**2/2 - 24*d. Determine p(1).\n | -18\n | ibivibiv/math_instruct | |
Let r(d) = -8*d + 5970838 - 5970838. Let f(l) = -l**2. What is f(r(k))?\n | -64*k**2\n | ibivibiv/math_instruct | |
Solve -318*t + 12958 = -3*t + 274*t for t.\n | 22\n | ibivibiv/math_instruct | |
What is the product of 15 and -9.069?\n | -136.035\n | ibivibiv/math_instruct | |
Calculate (-10)/(2/(-16) - (-105)/(-56)).\n | 5\n | ibivibiv/math_instruct | |
Solve -59*z - 1686 = -2158 for z.\n | 8\n | ibivibiv/math_instruct | |
How many seconds are there in 54/5 of a minute?\n | 648\n | ibivibiv/math_instruct | |
Work out -0.1 * 363.\n | -36.3\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Thread: IVP using Leibniz formula
1. ## IVP using Leibniz formula
How does one formulate this integral equation as an initial value problem?
u(t)=1 + integral from 0 to t (s ln (s/t) u(s) ds)
we're supposed to use Leibn... | The thread at hand deals with converting an integral equation into an initial value problem (IVP) using the Leibniz Formula. Let us first establish the necessary background and then delve deeper into applying the Leibniz Formula to solve the given problem.
Integration by parts provides a fundamental method for solvin... | ibivibiv/math_instruct | |
Simplify ((w**14*w*w**(-2/101)*w)**41)**(-11/4) assuming w is positive.\n | w**(-363957/202)\n | ibivibiv/math_instruct | |
What is the highest common divisor of 2412 and 36?\n | 36\n | ibivibiv/math_instruct | |
Determine l so that 604323889*l**3 - 604520553*l**2 + 196680*l - 16 = 0.\n | 4/24583, 1\n | ibivibiv/math_instruct | |
Suppose 15 = 37*l - 34*l. What is the third derivative of -231*b**2 + 117*b**2 + 119*b**2 + 0*b**l - b**5 wrt b?\n | -60*b**2\n | ibivibiv/math_instruct | |
b"What is the fth term of 36, 155, 354, 633, 992, 1431?\n" | 40*f**2 - f - 3\n | ibivibiv/math_instruct | |
Convert 8751 (base 9) to base 12.\n | 3891\n | ibivibiv/math_instruct | |
Let z(b) = -2*b - 4. Let a be z(-4). Suppose -94*c = -93*c - a. Let l(i) = 15*i**2 - 5*i. Let t(q) = 14*q**2 - 4*q. What is c*l(r) - 5*t(r)?\n | -10*r**2\n | ibivibiv/math_instruct | |
b"What is the wth term of -7193, -7195, -7197, -7199, -7201, -7203?\n" | -2*w - 7191\n | ibivibiv/math_instruct | |
Solve -231605 = 405*d - 240110 for d.\n | 21\n | ibivibiv/math_instruct | |
Let h(r) = -7*r**3 - 39*r**2 - 52*r + 161. Is h(-43) a prime number?\n | False\n | ibivibiv/math_instruct | |
What is -13 + (-1 - -13) + 6?\n | 5\n | ibivibiv/math_instruct | |
Let p = 25.4 + -25. Let s = 0.3 - 0.9. Which is the closest to -0.2? (a) p (b) -2/3 (c) s\n | c\n | ibivibiv/math_instruct | |
In base 13, what is -82c - -32373?\n | 31844\n | ibivibiv/math_instruct | |
Solve 3*x = -2*y - 2, 0 = 626*x - 627*x - 3*y - 3 for x.\n | 0\n | ibivibiv/math_instruct | |
Which is the nearest to 1? (a) 36 (b) 0.4 (c) -21/5 (d) 0 (e) 6005\n | b\n | ibivibiv/math_instruct | |
Let n(b) = b**3 + 49*b**2 + 38*b - 468. What is n(-48)?\n | 12\n | ibivibiv/math_instruct | |
In base 8, what is -12447 + 473?\n | -11754\n | ibivibiv/math_instruct | |
Let l(c) = 1. Let x(p) be the third derivative of p**7/2520 + p**6/720 + p**5/60 - 9*p**2. Let h(m) be the third derivative of x(m). What is 2*h(u) - 2*l(u)?\n | 4*u\n | ibivibiv/math_instruct | |
Calculate the remainder when 2551 is divided by 608.\n | 119\n | ibivibiv/math_instruct | |
In base 15, what is 290 + 9?\n | 299\n | ibivibiv/math_instruct | |
Convert 2421.589mg to nanograms.\n | 2421589000\n | ibivibiv/math_instruct | |
Let g = 730 - 728. What is the fourth biggest value in g, -0.2, -0.6, 0.2?\n | -0.6\n | ibivibiv/math_instruct | |
Divide 192154365 by 38430873.\n | 5\n | ibivibiv/math_instruct | |
Let m(n) = 25*n**3 + 5*n**2 + 5*n - 33. Let j(f) = 13*f**3 + 3*f**2 + 3*f - 17. Let v(o) = 5*j(o) - 3*m(o). Find the first derivative of v(q) wrt q.\n | -30*q**2\n | ibivibiv/math_instruct | |
What is the next term in -886, -1792, -2702, -3616, -4534, -5456, -6382?\n | -7312\n | ibivibiv/math_instruct | |
Evaluate 120/(-70)*(525/(-100))/((-3)/8).\n | -24\n | ibivibiv/math_instruct |
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