instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Calculate the least common multiple of 12338 and 123380.\n | 123380\n | ibivibiv/math_instruct | |
Let c(g) = -13*g**2 + 2927*g + 2614. Give c(226).\n | 128\n | ibivibiv/math_instruct | |
What is 9.48283nm in kilometers?\n | 0.00000000000948283\n | ibivibiv/math_instruct | |
Suppose 0*d = 3*d. Suppose d = -5*p - 20, 4*q - 3*q = 4*p + 4. Let y = -16 - q. Let a(i) = -2*i - 4. What is a(y)?\n | 4\n | ibivibiv/math_instruct | |
What is 1321 (base 10) in base 12?\n | 921\n | ibivibiv/math_instruct | |
Let u(s) = -2*s**5 + 10*s**4 + 10*s**3 + 14*s**2 - 8*s. Let l(a) = a**5 - 3*a**4 - 3*a**3 - 5*a**2 + 3*a. Let n(t) = -8*l(t) - 3*u(t). Factor n(i).\n | -2*i**2*(i + 1)**3\n | ibivibiv/math_instruct | |
9 + (-8 - 3 - (4 + 14 + -24 + 88))\n | -84\n | ibivibiv/math_instruct | |
Find the common denominator of 131/4860 and 143/24.\n | 9720\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Derivative of continuous function exists if limit of derivative exists
I'm stuck on this old qualifier problem. I suppose one could do it using the basic definitions of continuity and differentiability, but is there a simp... | We will delve into the problem of demonstrating that if a function $f: ooll R ooll R$ is continuous and differentiable everywhere except at 0, and the limit of its derivative as x approaches 0 exists, then the derivative of f at 0 also exists. To begin, let's establish the fundamental definitions of continuity and dif... | ibivibiv/math_instruct | |
What is the ten thousands digit of 1716722?\n | 1\n | ibivibiv/math_instruct | |
What is the least common multiple of 20 and 102?\n | 1020\n | ibivibiv/math_instruct | |
b"What is the mth term of -10, -18, -24, -22, -6, 30, 92, 186?\n" | m**3 - 5*m**2 - 6\n | ibivibiv/math_instruct | |
Let o(h) = 13*h**2 + 14*h - 21. Let r(y) = 3*y**2 - y - 1. Let v = 675 - 681. Let b(u) = v*r(u) + o(u). Solve b(t) = 0.\n | 1, 3\n | ibivibiv/math_instruct | |
List the prime factors of 3777534331.\n | 3777534331\n | ibivibiv/math_instruct | |
What is the hundreds digit of 189141?\n | 1\n | ibivibiv/math_instruct | |
Let k = -9 + 4. Suppose 4*m = -0*m. Let x be 1 - (m - (-1)/4). Put k, -2, x in increasing order.\n | k, -2, x\n | ibivibiv/math_instruct | |
Let a(b) = b**2 + 3*b + 3. Let k be a(0). Solve 0 = -k*n - 13 + 1 for n.\n | -4\n | ibivibiv/math_instruct | |
Collect the terms in -43 - 4*p + 13 - 49.\n | -4*p - 79\n | ibivibiv/math_instruct | |
Rearrange -17*k**2 + 4*k**2 + 3*k - k + 3*k**3 - 4*k**3 to o*k**3 + n*k**2 + i + t*k and give t.\n | 2\n | ibivibiv/math_instruct | |
Is 24233 prime?\n | False\n | ibivibiv/math_instruct | |
Is 15915693 equal to 15915696?\n | False\n | ibivibiv/math_instruct | |
Let z = -1.71 + 0.84. Let b = -619174.41999947 - -619175.29. Let m = b + z. Round m to seven dps.\n | 0.0000005\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 154 and 110?\n | 22\n | ibivibiv/math_instruct | |
Let q(i) = -3 + 648*i + 634*i - 1281*i. Give q(5).\n | 2\n | ibivibiv/math_instruct | |
Let t be (-1)/(0 + 4/(-8)). Solve 8/5 + 32/5*h - 10*h**3 + 2*h**t = 0.\n | -2/5, 1\n | ibivibiv/math_instruct | |
Solve -5*z = -20, -722*s - 40 = -727*s + 5*z for s.\n | 12\n | ibivibiv/math_instruct | |
What is ((-4)/(-10))/(195/(-1950))?\n | -4\n | ibivibiv/math_instruct | |
Expand (3 - 3 - 2*h)*(-5*h + 5*h + 2*h**2)*(-296 - 689 + 27).\n | 3832*h**3\n | ibivibiv/math_instruct | |
What comes next: -67, -40, 13, 98, 221, 388, 605?\n | 878\n | ibivibiv/math_instruct | |
Find the common denominator of 106/(-48) - 3/(-9) and 24/(-66240)*-1990 + (-2)/3.\n | 184\n | ibivibiv/math_instruct | |
Is -15/156641 at most 1?\n | True\n | ibivibiv/math_instruct | |
Sort -0.1796, -3, 17, -0.1 in ascending order.\n | -3, -0.1796, -0.1, 17\n | ibivibiv/math_instruct | |
Let s(z) = 2*z**2 + 23*z - 22. Let x be s(-12). Is x greater than or equal to -10?\n | True\n | ibivibiv/math_instruct | |
Let s be (-231 - -3)/(-3) + 2. Let q be (s/9)/((-2)/(-24)). Suppose 0 = -5*y - 2*k + 67, y = -2*k - 3*k + 18. What is the greatest common divisor of y and q?\n | 13\n | ibivibiv/math_instruct | |
Let l be (-2)/((-2)/9) + 1. Suppose 5*q + l = 0, -2*q - 26 = -4*s + 22. What is the highest common factor of s and 88?\n | 11\n | ibivibiv/math_instruct | |
Let g = -3 - -5. Let u be 15/(-9) + g/(-6). Let i(p) = -2*p**3 - 4*p**2 - 3*p - 1. What is the units digit of i(u)?\n | 5\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 803 and 374271.\n | 73\n | ibivibiv/math_instruct | |
Simplify (5*sqrt(4)/sqrt(2))**2 + sqrt(12)/sqrt(150).\n | sqrt(2)/5 + 50\n | ibivibiv/math_instruct | |
Let n = -0.160301811 - -0.1603. What is n rounded to seven dps?\n | -0.0000018\n | ibivibiv/math_instruct | |
Which is the fifth biggest value? (a) -3 (b) 664 (c) 1 (d) -4 (e) 2/3\n | d\n | ibivibiv/math_instruct | |
1244413244 (base 5) to base 4\n | 23322130011\n | ibivibiv/math_instruct | |
How many nanograms are there in 59856.78 grams?\n | 59856780000000\n | ibivibiv/math_instruct | |
Evaluate (5 - 9) + 0 + 1.\n | -3\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 1421523 and 350613.\n | 1467\n | ibivibiv/math_instruct | |
What is 96/(-40)*(-110)/(-33)?\n | -8\n | ibivibiv/math_instruct | |
What is the millions digit of 2193669432?\n | 3\n | ibivibiv/math_instruct | |
What is 270 minutes before 7:41 AM?\n | 3:11 AM\n | ibivibiv/math_instruct | |
Let a(k) = -3*k - 13. Let v be a(-6). Let l = 95 - 87. Let -14*r**4 - 4*r + 8*r**2 + 8*r**v + l*r**2 - 4*r**3 + 5 - 7 = 0. Calculate r.\n | -1, -1/4, 1\n | ibivibiv/math_instruct | |
Simplify (sqrt(275) + 1 + sqrt(275) + 1 - 2*sqrt(275)*-2)**2*-4 + 6*((sqrt(275) + 0 - sqrt(275)) + 5 + 4)**2.\n | -39130 - 480*sqrt(11)\n | ibivibiv/math_instruct | |
Calculate prob of sequence ffss when four letters picked without replacement from fffffffsfffsf.\n | 1/78\n | ibivibiv/math_instruct | |
Suppose 3*y - 5*y = -6. Suppose 0*g + g - 6 = -y*l, 4*l + 20 = 0. Is g a multiple of 9?\n | False\n | ibivibiv/math_instruct | |
Expand -5 + a**2 + 5 + (1 + 3 - 5)*(5*a + 3*a**2 - 5*a) - 1709*a**2 + 98*a + 1710*a**2 - 568*a.\n | -a**2 - 470*a\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 77 and 35.\n | 7\n | ibivibiv/math_instruct | |
Evaluate (-7714)/114*(-603)/1407.\n | 29\n | ibivibiv/math_instruct | |
Let y = -261 + 266. What is the closest to 0 in 15, 2, y?\n | 2\n | ibivibiv/math_instruct | |
Divide 34804696 by -178.\n | -195532\n | ibivibiv/math_instruct | |
What is (-53)/((-2120)/(-560))*-1?\n | 14\n | ibivibiv/math_instruct | |
What is the next term in 242788506, 242788505, 242788504?\n | 242788503\n | ibivibiv/math_instruct | |
Work out 6 * 0.7.\n | 4.2\n | ibivibiv/math_instruct | |
What is the biggest value in 67, -3/7, 3, -1/5?\n | 67\n | ibivibiv/math_instruct | |
Let o = 6 + -2. Sort o, 2, -5 in decreasing order.\n | o, 2, -5\n | ibivibiv/math_instruct | |
Let i(a) = 2*a**3 - a**2 - 2*a - 3. Let r(f) = -f**3 + f**2 + f + 2. Let t(g) = 2*i(g) + 3*r(g). Let p be t(2). Factor 4 + p*c + 30*c - 12*c + 49*c**2.\n | (7*c + 2)**2\n | ibivibiv/math_instruct | |
Is 215383261 a composite number?\n | True\n | ibivibiv/math_instruct | |
Let n(r) = 3*r + 121. Let t be n(-39). Suppose -t*p = -2*w - 32832, -2*w = -3*p - 2*p + 41041. Is p prime?\n | True\n | ibivibiv/math_instruct | |
In base 16, what is -7fd + 2?\n | -7fb\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Approximating when variable to infinity
In a book on algorithms I read that $$n^2 (1+\log n)$$ as $$n$$ approaches infinity is approximated to $$n^2 \log n$$.
I am not sure if I understand reasoning in this. Is it because... | When discussing the approximation of mathematical expressions involving variables approaching infinity, it's important to first establish a fundamental concept from calculus: limits. The limit of a function describes its behavior as the input (in this case, the variable "n") gets arbitrarily close to a certain value, ... | ibivibiv/math_instruct | |
b"What is the fth term of -300, 591, 3354, 8925, 18240, 32235?\n" | 156*f**3 - 201*f - 255\n | ibivibiv/math_instruct | |
Let y(v) be the third derivative of 1/60*v**4 + 3*v**2 - 1/300*v**5 + 0*v + 0 + 0*v**3. Factor y(w).\n | -w*(w - 2)/5\n | ibivibiv/math_instruct | |
Let w = -4 - 19. Let c = -21 - w. What is the first derivative of -16*n**3 + 6 + 2*n - c*n wrt n?\n | -48*n**2\n | ibivibiv/math_instruct | |
Is (2*(-1)/3)/((-178)/731847) prime?\n | True\n | ibivibiv/math_instruct | |
Let j(n) = 26723*n + 133956. Determine j(-5).\n | 341\n | ibivibiv/math_instruct | |
Solve -3*n**5 - 1749*n**4 - 252225*n**3 + 800805*n**2 + 4141848*n + 3090564 = 0 for n.\n | -293, -2, -1, 6\n | ibivibiv/math_instruct | |
Suppose -2*x + 173 = -5*z, 4*z - 271 = x - 4*x. Suppose 5*w - 2*l - x = 0, 2*w + 21 = 3*w - 2*l. Does 16 divide w?\n | False\n | ibivibiv/math_instruct | |
Solve 65523*u + 20*h = 65528*u - 195, -3*u + 47 = -5*h for u.\n | -1\n | ibivibiv/math_instruct | |
b"What is the xth term of 2411, 2414, 2417?\n" | 3*x + 2408\n | ibivibiv/math_instruct | |
Is 1388867536 a multiple of 14?\n | True\n | ibivibiv/math_instruct | |
Three letters picked without replacement from blbklplll. What is prob of sequence kpl?\n | 5/504\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Is zero vector always present in any n-dimensional space?
The book "Introduction to Linear Algebra" by Gilbert Strang says that every time we see a space of vectors, the zero vector will be included in it.
I reckon that t... | A vector space is a fundamental concept in linear algebra, and it is defined as a set of vectors that can be added together and multiplied by scalars while preserving certain properties. These properties include closure under addition and scalar multiplication, associativity, commutativity, existence of an additive id... | ibivibiv/math_instruct | |
Is 44912 a multiple of 32?\n | False\n | ibivibiv/math_instruct | |
Let z(x) = -13*x - 27. Let d be z(10). Let l = -34 - d. What are the prime factors of l?\n | 3, 41\n | ibivibiv/math_instruct | |
Solve 0 = -18*s + 162 - 288 for s.\n | -7\n | ibivibiv/math_instruct | |
b"What is the tth term of 59066, 59071, 59076, 59081, 59086, 59091?\n" | 5*t + 59061\n | ibivibiv/math_instruct | |
Let g be -2*-22*(-6)/(-24). Let n(j) = j**3 - 10*j**2 - 10*j - 8. Give n(g).\n | 3\n | ibivibiv/math_instruct | |
In base 12, what is a156 - 477?\n | 989b\n | ibivibiv/math_instruct | |
Evaluate (-13)/(-4992)*64 + (-2)/3.\n | -1/2\n | ibivibiv/math_instruct | |
Suppose 3*h + 5*o - 14 = 0, 2*h + 7*o - 6*o = 7. Let a = 2 + -2. Suppose -h*m + 2 + 4 = a. Solve 3*l - 8*l = -t - 10, 5*l = -m*t + 25 for l.\n | 3\n | ibivibiv/math_instruct | |
Subtract -4573372 from 1357.7.\n | 4574729.7\n | ibivibiv/math_instruct | |
Sort -5, -3/10, 4, -0.2, 0.2 in increasing order.\n | -5, -3/10, -0.2, 0.2, 4\n | ibivibiv/math_instruct | |
Calculate (-52)/((-39)/(-3))*6/(-56).\n | 3/7\n | ibivibiv/math_instruct | |
Convert 4.95351ml to litres.\n | 0.00495351\n | ibivibiv/math_instruct | |
Does 1278 divide 19855543?\n | False\n | ibivibiv/math_instruct | |
What is the value of ((-15)/(-9) + -2)*3 - -2?\n | 1\n | ibivibiv/math_instruct | |
Let t(o) = -o**2 + 635*o + 7116. Determine t(-11).\n | 10\n | ibivibiv/math_instruct | |
Expand (2*k**2 + 9*k**2 + 4*k**2)*(4*k**2 + k**2 - k**2) + 2*k**4 - 2*k**4 - 2*k**4 + (-2*k**2 - k**2 - 2*k**2)*(k**2 - k**2 - k**2).\n | 63*k**4\n | ibivibiv/math_instruct | |
What is the value of (-5 + 3)*1892/(-344)?\n | 11\n | ibivibiv/math_instruct | |
Let n = -19 + 26. Solve 0 = -4*r + 3 - n for r.\n | -1\n | ibivibiv/math_instruct | |
Is -26.308 at least as big as -8?\n | False\n | ibivibiv/math_instruct | |
Let h be (-60)/(-18)*46908/12. Suppose -h = -b + 8*r - 7*r, -3*r + 9 = 0. Is b a prime number?\n | True\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-85.2823 % 61.2587) + (77.2257 - -45.7945) | 160.2553 | ibivibiv/math_instruct | |
What is the nearest to 4/1253 in -49, 0.5, 1/3?\n | 1/3\n | ibivibiv/math_instruct |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.