instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Let i = 325 + -165. Suppose 0*r = 3*r - 192. Calculate the highest common factor of i and r.\n | 32\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {i: 7, z: 2, e: 2, c: 6, r: 1}. Give prob of picking 1 e and 1 c.\n | 4/51\n | ibivibiv/math_instruct | |
Let a(t) = -2*t**3 + 20*t**2 + t - 7. Give a(10).\n | 3\n | ibivibiv/math_instruct | |
Expand k**3 + 0*k**3 - 4*k**3 + (3*k - 2*k + 0*k)*((3*k - 2*k + k)*(-1 + 1 + k) + 35*k**2 - 32*k**2 - 35*k**2).\n | -33*k**3\n | ibivibiv/math_instruct | |
Let z(c) = 385*c - 13267. Let r(q) = 2*q. Calculate r(z(l)).\n | 770*l - 26534\n | ibivibiv/math_instruct | |
Round -11.57369564 to 3 decimal places.\n | -11.574\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 619345103?\n | 3\n | ibivibiv/math_instruct | |
Simplify (((j*j**(-11)*j)**(-44/5))**(-7/8))**22 assuming j is positive.\n | j**(-7623/5)\n | ibivibiv/math_instruct | |
Simplify ((o/o**(-14))**14)**(2/17) assuming o is positive.\n | o**(420/17)\n | ibivibiv/math_instruct | |
What is the lowest common multiple of 417 and 15?\n | 2085\n | ibivibiv/math_instruct | |
Let i = 3.7 + -3.7095. Round i to 3 decimal places.\n | -0.01\n | ibivibiv/math_instruct | |
Let x = -12 - -17. Let j(g) = -2463*g - 54187. Let i be j(-22). Sort 1, i, x, -4 in descending order.\n | x, 1, i, -4\n | ibivibiv/math_instruct | |
Convert -121202031 (base 4) to base 8.\n | -314215\n | ibivibiv/math_instruct | |
Let z(l) be the first derivative of -l**5/60 - 2*l**3/3 + 2. Let s(c) be the third derivative of z(c). Let v(y) = 4*y + 5*y**2 - 4*y - 3*y**2. Give s(v(n)).\n | -4*n**2\n | ibivibiv/math_instruct | |
-110010 (base 2) to base 10\n | -50\n | ibivibiv/math_instruct | |
Expand (-l**3 + 0*l**3 + 0*l**3)*(-369 + 1465 + 68055*l - 362 - 369 - 365).\n | -68055*l**4\n | ibivibiv/math_instruct | |
-222019978.434 - -12\n | -222019966.434\n | ibivibiv/math_instruct | |
What is the third root of 5792 to the nearest integer?\n | 18\n | ibivibiv/math_instruct | |
-15 (base 11) to base 2\n | -10000\n | ibivibiv/math_instruct | |
What are the prime factors of 3409?\n | 7, 487\n | ibivibiv/math_instruct | |
Let y(w) = -w + 1. Let h(x) = 3*x - 6. Let n(t) = h(t) + 2*y(t). Let p be n(7). Suppose -102 = -p*l - 0*l. Is l a composite number?\n | True\n | ibivibiv/math_instruct | |
What is the third derivative of 539880*c**3 + 2*c**2 + 9*c + 1369 wrt c?\n | 3239280\n | ibivibiv/math_instruct | |
What is 0.0120455783 rounded to four decimal places?\n | 0.012\n | ibivibiv/math_instruct | |
Let u(s) = -149*s**3 - 9*s**2 + 54*s + 196. What is the units digit of u(-5)?\n | 6\n | ibivibiv/math_instruct | |
Let d = 66 + -242. Let x = d + 166.7. Let c = 9.5 + x. What is the nearest to -0.05 in 4, 5, c?\n | c\n | ibivibiv/math_instruct | |
Simplify ((a*a**6)/((a*a**(-3))/a))/(a*a/a**2)**(-15)*((a/(a/((a**3*a)/a)))**(6/25))**(-2/47) assuming a is positive.\n | a**(11714/1175)\n | ibivibiv/math_instruct | |
Let k be ((-4)/(-3))/((-102)/(-16371)). What is the highest common factor of k and 4?\n | 2\n | ibivibiv/math_instruct | |
Let x = 370420 - 370414.00108. Let q = x - 6. Round q to four decimal places.\n | -0.0011\n | ibivibiv/math_instruct | |
Suppose 0 = 4*c - 6*c. Let d be (c + -3 - -3) + 3. Suppose 0 = -d*i + 8*i + 20. Sort 1, i, 3.\n | i, 1, 3\n | ibivibiv/math_instruct | |
Rearrange -2*m - 2 - 3*m**4 + 8*m**2 - 4*m**2 + 0*m - 6*m**2 to n*m + y*m**4 + w*m**2 + g + b*m**3 and give y.\n | -3\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {b: 6, l: 4, e: 7}. Give prob of sequence bbe.\n | 7/136\n | ibivibiv/math_instruct | |
Which is the second biggest value? (a) 5.4 (b) -1/6 (c) -4842\n | b\n | ibivibiv/math_instruct | |
Solve 34*d + 10 - 1 = 2*y + 39*d, 20*y + 2*d = 42 for y.\n | 2\n | ibivibiv/math_instruct | |
Let x = -146 - -76. Let t = x + 105. Is t a multiple of 13?\n | False\n | ibivibiv/math_instruct | |
Suppose 4*a + 3*q = 37, -3*a + 12 = -3*q - 0*q. Let j = a + 7. Suppose 2 = 2*i, -j = 5*z - z - 2*i. What is the nearest to 1 in z, 0.3, 0?\n | 0.3\n | ibivibiv/math_instruct | |
Let r(m) be the third derivative of m**9/241920 + m**8/80640 + 4*m**5/15 + 13*m**2. Let n(x) be the third derivative of r(x). Find w, given that n(w) = 0.\n | -1, 0\n | ibivibiv/math_instruct | |
Does 1513 divide 28876192?\n | False\n | ibivibiv/math_instruct | |
What is the highest common divisor of 54206208 and 312?\n | 24\n | ibivibiv/math_instruct | |
Express (544*i**4 - 507*i**4 + 12*i - 14*i)*(-273 - 323 + 552) as b*i**4 + f*i + w + m*i**2 + a*i**3 and give f.\n | 88\n | ibivibiv/math_instruct | |
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"# infinitely-differentiable function that is not analytic
If $f\in\mathcal{C}^{\infty}$, then we can certainly write a Taylor series for $f$. However, analyticity requires that this Taylor series actually converge (at least ... | Let's begin by discussing what an infinitely-differentiable function is. A function $f$ is said to be infinitely-differentiable if its derivative of every order exists at every point in its domain. This means that you can find the first, second, third, and so on derivatives of $f$ ad infinitum, without encountering an... | ibivibiv/math_instruct | |
What is prob of sequence pezl when four letters picked without replacement from pdplpkeklpzd?\n | 1/1485\n | ibivibiv/math_instruct | |
Let z = -18.06 + 18.3122. What is z rounded to 2 dps?\n | 0.25\n | ibivibiv/math_instruct | |
What is the nearest to 4/241 in -5.4, 0.2, -54, -5?\n | 0.2\n | ibivibiv/math_instruct | |
Let o(j) = j**2 - 10*j - 3. Let y be (-3)/6 + 51/6. Suppose -2 = -p + y. Let d be o(p). Let g(r) = r**2 + r - 3. Calculate g(d).\n | 3\n | ibivibiv/math_instruct | |
Calculate (-2)/1*(0 - -35)*(26 - (-7030)/(-259)).\n | 80\n | ibivibiv/math_instruct | |
Suppose -94*q + 344984 + 95477 = -49373. Is 27 a factor of q?\n | True\n | ibivibiv/math_instruct | |
Suppose -5*y + 4*t = 9, -y + 5*t + 40 = -5*y. Let n = 7 + y. Let a = n - 0. Solve -12 = -a*l - 4 for l.\n | 4\n | ibivibiv/math_instruct | |
Which is the nearest to 3? (a) -3/14 (b) 6532 (c) 0.3 (d) 1\n | d\n | ibivibiv/math_instruct | |
Suppose -3*w + d + 3 = 0, 19 = 5*w - d + 4*d. Suppose -w*z + 501 = -3*l - 5*z, -3*z + 359 = -2*l. Let h = 321 + l. Does 8 divide h?\n | False\n | ibivibiv/math_instruct | |
What is seven halves of a kilogram in grams?\n | 3500\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {g: 2, a: 3}. Give prob of picking 2 g and 1 a.\n | 3/10\n | ibivibiv/math_instruct | |
What is the value of (36 - 34) + (-1 - -6)?\n | 7\n | ibivibiv/math_instruct | |
Let m(b) = -8*b**2 + 10*b + 10. Let i(t) = t**2 - t - 1. Let a(c) = 10*i(c) + m(c). Let g(x) = 30*x. Give a(g(p)).\n | 1800*p**2\n | ibivibiv/math_instruct | |
Does 20 divide 40?\n | True\n | ibivibiv/math_instruct | |
What is the smallest value in 5, -21, -1545421?\n | -1545421\n | ibivibiv/math_instruct | |
Let x(q) = q**3 + q**2 - 2*q + 6. Let m be x(-3). Suppose -145 = -7*o - 19. Let w be 12/o - (-1 + 1). Which is greater: w or m?\n | w\n | ibivibiv/math_instruct | |
Is (-7*(-16)/(-56))/((-4)/20714)*2 composite?\n | True\n | ibivibiv/math_instruct | |
Evaluate (-10)/8*((-16)/(-6))/(-4).\n | 5/6\n | ibivibiv/math_instruct | |
5847 - 5762 - (0 + -2)\n | 87\n | ibivibiv/math_instruct | |
Calculate 1.3*-32874526.\n | -42736883.8\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {r: 6, i: 4}. Give prob of sequence rrir.\n | 2/21\n | ibivibiv/math_instruct | |
Suppose 97*l = 1514882 + 858611. List the prime factors of l.\n | 24469\n | ibivibiv/math_instruct | |
Let c(v) = v**3 - 7*v**2 - 7. Let f be c(7). Let u = f + 50. Calculate the remainder when u is divided by 22.\n | 21\n | ibivibiv/math_instruct | |
Let c(u) = 86024*u**2 + 8*u - 9. Is c(1) a composite number?\n | True\n | ibivibiv/math_instruct | |
Let w = -2.492 - -0.996. What is w rounded to 0 dps?\n | -1\n | ibivibiv/math_instruct | |
Suppose 3*h = -0 - 6. Let w be (-28)/(-6) + (h - (-21)/9). Solve 2*s + 0*c - 5*c + 25 = 0, 10 = -w*s - 5*c for s.\n | -5\n | ibivibiv/math_instruct | |
Which is the nearest to 0? (a) -0.3 (b) -11/5 (c) -2\n | a\n | ibivibiv/math_instruct | |
What is the thousands digit of 82958?\n | 2\n | ibivibiv/math_instruct | |
Is -1 less than or equal to -389/907427?\n | True\n | ibivibiv/math_instruct | |
Let o(v) = 320*v**2 - 468*v + 125. Is o(-46) a composite number?\n | False\n | ibivibiv/math_instruct | |
Let c be 1*(-1)/(-1)*1. Let m be (0 - c) + -1 + 1. Sort m, -2, -0.3.\n | -2, m, -0.3\n | ibivibiv/math_instruct | |
What is the third smallest value in 14.32, -0.196, -0.012, 1/4?\n | 1/4\n | ibivibiv/math_instruct | |
Calculate 24795 divided by 19.\n | 1305\n | ibivibiv/math_instruct | |
What is prob of picking 1 j, 1 s, 1 u, and 1 f when four letters picked without replacement from ejefunfs?\n | 1/35\n | ibivibiv/math_instruct | |
Express 168*q**2 - 337*q**2 + 0 + 166*q**2 + q - 2*q + q**4 - 1 - 5*q**3 in the form h*q**4 + u + z*q + r*q**3 + s*q**2 and give u.\n | -1\n | ibivibiv/math_instruct | |
Work out 0.1 * 0.631.\n | 0.0631\n | ibivibiv/math_instruct | |
Expand -3*r + 93 - 6*r - 91 - 2*r**2 + (-1 - 2*r + 1)*(2*r + 0 + 0) - 2*r**2 + r**2 + 0*r**2 + 0 + 0 - r**2 - 2*r**2 - r + r + (r + 0*r + r)*(2*r - 17*r + 5*r).\n | -30*r**2 - 9*r + 2\n | ibivibiv/math_instruct | |
Put -63, -2563, 1, 60, 5, -5, 4 in decreasing order.\n | 60, 5, 4, 1, -5, -63, -2563\n | ibivibiv/math_instruct | |
Find the third derivative of -467*y**6 + 5*y**3 - 18797*y**2.\n | -56040*y**3 + 30\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 767720 and 88264.\n | 136\n | ibivibiv/math_instruct | |
What is the value of (8/18)/(24/(-36))*((-310284)/(-17))/(-78)?\n | 156\n | ibivibiv/math_instruct | |
Four letters picked without replacement from vvuuwwquwuuwwvv. Give prob of sequence vvwq.\n | 1/546\n | ibivibiv/math_instruct | |
Calculate the remainder when 3/((-45)/(-760))*9/6 is divided by 26.\n | 24\n | ibivibiv/math_instruct | |
Simplify (((u*u/(u/u**(1/5)))/u)**(-2/135)*u*u**(1/3)*u*(u**5*u)/u)**29 assuming u is positive.\n | u**(143492/675)\n | ibivibiv/math_instruct | |
Suppose 69 = 3*g - 3. Suppose -7*o = -3*o - g. What are the prime factors of o?\n | 2, 3\n | ibivibiv/math_instruct | |
What is the third derivative of 1198*u**3 + 1846*u**2 wrt u?\n | 7188\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 12593 and 49.\n | 12593\n | ibivibiv/math_instruct | |
Let o(w) = 2*w**3 + 7*w**2 + 7*w + 11. What is the smallest common multiple of o(4) and 90?\n | 2790\n | ibivibiv/math_instruct | |
Let m = -136.8 + 49.34. What is m rounded to the nearest 10?\n | -90\n | ibivibiv/math_instruct | |
Suppose -3*h - 3*y = 21 - 18, 3*y = 4*h - 31. Suppose h*t - 10 = -z, -14 = 2*t - 3*z - 12. Solve u = 2*r + 2*u - t, -10 = 2*r - 5*u for r.\n | 0\n | ibivibiv/math_instruct | |
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"# Tag Info
7
We have \begin{align} \sum_{i=1}^n\sum_{j=1}^i(2^j-1) &=\sum_{i=1}^n\sum_{j=1}^i2^j-\sum_{i=1}^n\sum_{j=1}^i1\\ &=\sum_{i=1}^n(2^{i+1}-2)-\sum_{i=1}^ni\\ &=2\sum_{i=1}^n2^{i}-\sum_{i=1}^n2-\sum_{i=1}^ni\\ &=2(2... | Let's begin by analyzing the given equation involving double summations:
∑i=1n∑j=1i(2j−1)=∑i=1n(2i+1−2)−∑i=1ni−∑i=1nij=2∑i=1n2i−∑i=1n2−∑i=1ni−12i(i+1)=2(2n+1−2)−2n−12n(n+1)=2n+2−4−n2−n=2n+2−n2−3n−4
This result demonstrates how multiple summation signs can be simplified into a single expression through algebraic mani... | ibivibiv/math_instruct | |
Let i(d) = -4*d - 3. Let a be i(-3). Let q be 213/a - (-4)/12. Calculate the greatest common factor of 120 and q.\n | 24\n | ibivibiv/math_instruct | |
What is the hundreds digit of 23197?\n | 1\n | ibivibiv/math_instruct | |
Simplify -4*((sqrt(26) - (sqrt(26) - sqrt(78)/sqrt(3) - sqrt(26)))*-2)/((sqrt(384) - sqrt(24))/sqrt(12)).\n | 16*sqrt(13)/3\n | ibivibiv/math_instruct | |
Suppose -24 = 3*f, -131*a + 126*a - 3*f = -320861. What is the units digit of a?\n | 7\n | ibivibiv/math_instruct | |
Sort -2, 49781, -1 in ascending order.\n | -2, -1, 49781\n | ibivibiv/math_instruct | |
Which is the nearest to -0.1? (a) -24 (b) -3/5 (c) 2 (d) 4\n | b\n | ibivibiv/math_instruct | |
Suppose -7*f = -46 - 45. Let v(n) = -14 + 29 + 3502*n - f. Let h be v(-1). What is h rounded to the nearest one thousand?\n | -4000\n | ibivibiv/math_instruct | |
Work out 0.89 * -0.5.\n | -0.445\n | ibivibiv/math_instruct | |
What is the least common multiple of 280 and 4?\n | 280\n | ibivibiv/math_instruct |
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