instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Let k = 4612 - 2558. What is the units digit of k?\n | 4\n | ibivibiv/math_instruct | |
Is 14980067339 prime?\n | False\n | ibivibiv/math_instruct | |
Rearrange 5053*k**3 - 10095*k**3 + 5042*k**3 - 3*k**4 + 13*k**2 - 33 to w*k**2 + j*k**3 + x + z*k**4 + i*k and give x.\n | -33\n | ibivibiv/math_instruct | |
What is prob of sequence hhh when three letters picked without replacement from {d: 3, h: 12}?\n | 44/91\n | ibivibiv/math_instruct | |
Simplify 4 + ((sqrt(1300) - 6*sqrt(1300)*-1)*-3)/(sqrt(144)*-1 + (sqrt(400) - (sqrt(400) + sqrt(400)*1 + sqrt(400)))).\n | 4 + 105*sqrt(13)/26\n | ibivibiv/math_instruct | |
Calculate the remainder when (-2)/(-7) - (5394/(-42) - (-225)/(-175)) is divided by 68.\n | 62\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 43 and 172?\n | 43\n | ibivibiv/math_instruct | |
Is 2773 composite?\n | True\n | ibivibiv/math_instruct | |
Suppose 14*a = 5*x + 16*a - 2950, -3*x + 2*a = -1754. What is the hundreds digit of x?\n | 5\n | ibivibiv/math_instruct | |
Round -178987091 to the nearest one hundred thousand.\n | -179000000\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {m: 9, f: 2}. Give prob of sequence mffm.\n | 1/55\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Why must a function be closed for descent methods to work?
At the beginning of chapter 9 of Boyd & Vandenberghe's Convex Optimization, about unconstrained minimization, it is said:
The starting point $$x^{(0)}$$ for a met... | To begin with, let's define what it means for a function to be "closed." A function $f : X \to \mathbb{R} \cup \{+\infty\}$ is said to be closed if its epigraph $\text{epi}(f)$, which is defined as the set $\{ (x,\alpha) \in X \times \mathbb{R} : f(x) \le \alpha \}$, is a closed subset of $X \times \mathbb{R}$. Intuit... | ibivibiv/math_instruct | |
Suppose -4 = -4*u, -c + 0 = -4*u - 5. What is the remainder when 26 is divided by c?\n | 8\n | ibivibiv/math_instruct | |
In base 16, what is -a0 + 8?\n | -98\n | ibivibiv/math_instruct | |
What are the prime factors of 1062?\n | 2, 3, 59\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 x, 1 g, and 2 q when four letters picked without replacement from {g: 5, c: 3, q: 9, x: 1}.\n | 1/17\n | ibivibiv/math_instruct | |
Suppose -21 = -2*m + 5*q - 0*q, 3*q + 23 = 2*m. Let c(n) = -2*n**3 + 28*n**2 - 20*n + 18. List the prime factors of c(m).\n | 2, 3\n | ibivibiv/math_instruct | |
Suppose -4*g + 5*z + 321 = 0, -4*g + 2*g + 3*z + 159 = 0. What is the units digit of g?\n | 4\n | ibivibiv/math_instruct | |
Which is smaller: 5021 or 5020?\n | 5020\n | ibivibiv/math_instruct | |
Let h = 35 - 49. Let a = 29 + h. What are the prime factors of a?\n | 3, 5\n | ibivibiv/math_instruct | |
Suppose -9*x + 5270 = -6178. What is the derivative of -38 + x*h - 17 - 1226*h wrt h?\n | 46\n | ibivibiv/math_instruct | |
b"What is the nth term of 1849524, 1849481, 1849438?\n" | -43*n + 1849567\n | ibivibiv/math_instruct | |
Let k = -39/170 + 1/34. Is k != -33.7?\n | True\n | ibivibiv/math_instruct | |
Solve 3*x - 3*i = -10 + 13, -4*i + 1 = x for x.\n | 1\n | ibivibiv/math_instruct | |
What is the second derivative of 4*l**2*m**3 - 32*l**2*m**2 - 5*l**2*m - l*m**3 + 209*l wrt l?\n | 8*m**3 - 64*m**2 - 10*m\n | ibivibiv/math_instruct | |
Simplify a**(6/11)*a**(-3/7) assuming a is positive.\n | a**(9/77)\n | ibivibiv/math_instruct | |
Is 878 bigger than -9694?\n | True\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 v and 1 t when two letters picked without replacement from tttvtttttttt.\n | 1/6\n | ibivibiv/math_instruct | |
Let j(g) = -3*g. Let w = 3 + -3. Let q(o) = -6*o**2 + w*o**2 + 4*o**2. Calculate j(q(t)).\n | 6*t**2\n | ibivibiv/math_instruct | |
Which is greater: -31 or -1672/53?\n | -31\n | ibivibiv/math_instruct | |
Let g(p) = -p**2 - 12*p - 8. Let r be g(-9). Let m = 63 - r. Is 45 at least as big as m?\n | True\n | ibivibiv/math_instruct | |
Express 12*z**3 - 3*z**2 - 23*z**3 + 6 + 12*z**3 + 2*z in the form m*z + u*z**3 + j + a*z**2 and give m.\n | 2\n | ibivibiv/math_instruct | |
Let g(y) be the second derivative of y**3/2 + y. Let u(p) be the first derivative of -2*p**2 + 31. Calculate g(u(j)).\n | -12*j\n | ibivibiv/math_instruct | |
Calculate (9 - (2 - -7)) + (-6)/4.\n | -3/2\n | ibivibiv/math_instruct | |
Let r(z) = -1034*z + 125118. What is r(121)?\n | 4\n | ibivibiv/math_instruct | |
What is the common denominator of 51/562 and -61/10?\n | 2810\n | ibivibiv/math_instruct | |
What is -1475355.6 rounded to the nearest one hundred thousand?\n | -1500000\n | ibivibiv/math_instruct | |
Sort 4, -4/11, -5, -4, 5 in ascending order.\n | -5, -4, -4/11, 4, 5\n | ibivibiv/math_instruct | |
What is the least common multiple of 1382 and 188643?\n | 377286\n | ibivibiv/math_instruct | |
Suppose 3*w = h - 4*h - 15, -5*h = 4*w + 22. Let q be -2 - w - 15/3. Let t = -1 - q. Is t a composite number?\n | False\n | ibivibiv/math_instruct | |
Let g(n) = n**2. Let r(v) = -v - 18. Let l be r(-20). Let w(i) = -4*i - l*i**2 + 4*i + i. Calculate w(g(c)).\n | -2*c**4 + c**2\n | ibivibiv/math_instruct | |
What is (-1)/3*1266/1477?\n | -2/7\n | ibivibiv/math_instruct | |
What comes next: -2679, -2488, -2297, -2106, -1915, -1724?\n | -1533\n | ibivibiv/math_instruct | |
Is 60006467 composite?\n | False\n | ibivibiv/math_instruct | |
Divide 5595 by 7.\n | 5595/7\n | ibivibiv/math_instruct | |
Let h = -6862 + 13295. Suppose 0 = -5*a + 4*t + h + 8063, -2*a = 3*t - 5803. Round a to the nearest 1000.\n | 3000\n | ibivibiv/math_instruct | |
Let x = -10 - -3. Let j = -6.4 - x. Let v = j + -0.60001. What is v rounded to 4 dps?\n | 0\n | ibivibiv/math_instruct | |
Round 0.067 to the nearest integer.\n | 0\n | ibivibiv/math_instruct | |
Divide -325539411 by 1.\n | -325539411\n | ibivibiv/math_instruct | |
Let r(b) = -2 + 64*b + b**2 + 7 - 54*b. Let l be r(-10). Calculate the highest common factor of l and 25.\n | 5\n | ibivibiv/math_instruct | |
Let z(h) = -30*h**2 + 128*h + 292. Let k(t) = -17*t**2 + 73*t + 167. Let l(g) = -16*k(g) + 9*z(g). Calculate l(10).\n | -4\n | ibivibiv/math_instruct | |
Does 16 divide 3336?\n | False\n | ibivibiv/math_instruct | |
Suppose 3*r - 4 = -r. Let y(b) = 3*b**2 - 3*b. Let d(t) = -t**2 + t. Let m(g) = -8*d(g) - 3*y(g). Let u be m(r). Is u less than -2/5?\n | False\n | ibivibiv/math_instruct | |
Calculate -13.4741032*0.3.\n | -4.04223096\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 999697?\n | 9\n | ibivibiv/math_instruct | |
In base 11, what is -3 + -41814?\n | -41817\n | ibivibiv/math_instruct | |
Factor -3*x**3 + 657*x**2 + 267075*x - 267729.\n | -3*(x - 427)*(x - 1)*(x + 209)\n | ibivibiv/math_instruct | |
Collect the terms in -62*x**3 - 22*x**2 + 180*x**3 - 393*x**3 - 421*x**3.\n | -696*x**3 - 22*x**2\n | ibivibiv/math_instruct | |
What is the square root of 3027 to the nearest integer?\n | 55\n | ibivibiv/math_instruct | |
What is prob of picking 2 m when two letters picked without replacement from mmrr?\n | 1/6\n | ibivibiv/math_instruct | |
Convert -28 (base 13) to base 8.\n | -42\n | ibivibiv/math_instruct | |
Let i(p) = p**3 + 14*p**2 - 2*p - 411. What is i(-11)?\n | -26\n | ibivibiv/math_instruct | |
Let k = -1378 + 774. List the prime factors of (6/(-1))/(3 - k/(-200)).\n | 2, 3, 5\n | ibivibiv/math_instruct | |
Suppose 0 = 2*n + 3*n + c - 9, -n + 5 = -3*c. Suppose 3*f - n*f = 2*j + 118, -3*f = -3*j - 369. List the prime factors of f.\n | 2\n | ibivibiv/math_instruct | |
Differentiate 2985*g*v + 7*v - 38 with respect to g.\n | 2985*v\n | ibivibiv/math_instruct | |
Collect the terms in 2721*z**2 - 173*z + 786*z**2 + 176*z.\n | 3507*z**2 + 3*z\n | ibivibiv/math_instruct | |
What is next in -1726, -6798, -15260, -27118, -42378?\n | -61046\n | ibivibiv/math_instruct | |
Convert 5.735457 nanometers to centimeters.\n | 0.0000005735457\n | ibivibiv/math_instruct | |
What comes next: 163, 139, 93, 19, -89, -237, -431?\n | -677\n | ibivibiv/math_instruct | |
Expand -227*m - 48*m**2 + 226*m + 8*m**2 - m**3 + (2*m + 4 - 4)*(2*m**2 + 4*m**2 - 5*m**2) + 2*m**2 + 2*m**3 - 2*m**2.\n | 3*m**3 - 40*m**2 - m\n | ibivibiv/math_instruct | |
Let v(z) = 232*z. Let x(n) be the first derivative of -38*n**3/3 - 565. Determine x(v(b)).\n | -2045312*b**2\n | ibivibiv/math_instruct | |
Let s = -582 - -445. Let m = s - -138. Is m at least -131?\n | True\n | ibivibiv/math_instruct | |
Which is the fifth smallest value? (a) -1 (b) 153 (c) 1/7 (d) 3 (e) -0.29\n | b\n | ibivibiv/math_instruct | |
Simplify (k*k*k/(k**(5/3)/k)*k*k)/k**(6/13)*(k**0)**(-10/3) assuming k is positive.\n | k**(151/39)\n | ibivibiv/math_instruct | |
Suppose 5*k - 26 = -4*y, -10*k - 5*y + 14 = -13*k. Let a be -1 + 0 - (1 + -2). Solve 2*z = -a*z + k for z.\n | 1\n | ibivibiv/math_instruct | |
-26 times 695\n | -18070\n | ibivibiv/math_instruct | |
Solve 2207 = -3*d + r + 2190, 2*d + 3*r - 7 = 0 for d.\n | -4\n | ibivibiv/math_instruct | |
What is the tenth root of 10660 to the nearest integer?\n | 3\n | ibivibiv/math_instruct | |
Let v = -1 + 4. Let b = 1 - v. Let a = -2.9417 - -4.9417. Sort 0.4, b, a in decreasing order.\n | a, 0.4, b\n | ibivibiv/math_instruct | |
Let h be (0 + 4/20)/(4/260). Solve 11*y = -h*y + 72 for y.\n | 3\n | ibivibiv/math_instruct | |
Simplify (((k*(k/(k/k**16))/k)/k**(-20))**(39/2))**(36/5) assuming k is positive.\n | k**(25272/5)\n | ibivibiv/math_instruct | |
In base 13, what is 3085 + -4?\n | 3081\n | ibivibiv/math_instruct | |
Let v(s) = -s**3 + 4*s**2 + 4. Let i be v(4). Let b = 6 - i. Suppose g = 4 - b. Solve 3*u + 3*l = 0, -g*u + 14 = 5*l - 1 for u.\n | -5\n | ibivibiv/math_instruct | |
What is -34 times -20.3?\n | 690.2\n | ibivibiv/math_instruct | |
Factor 3*x**2/4 - 42*x - 87.\n | 3*(x - 58)*(x + 2)/4\n | ibivibiv/math_instruct | |
Let d(n) = -7*n**3 - n + 1. Let g be d(1). Let s(a) be the first derivative of a**4/4 + 7*a**3/3 + 8*a - 1. What is the units digit of s(g)?\n | 8\n | ibivibiv/math_instruct | |
Let r(o) = -229*o + 3. Let d(k) = k + 1. Let v(t) = -5*d(t) + r(t). Let y be v(5). What is the remainder when 12/16 + y/(-16) is divided by 25?\n | 24\n | ibivibiv/math_instruct | |
What is the square root of 7982 to the nearest integer?\n | 89\n | ibivibiv/math_instruct | |
Is 3881 > 3969?\n | False\n | ibivibiv/math_instruct | |
What is ((-432)/63)/(-12)*-1?\n | -4/7\n | ibivibiv/math_instruct | |
What is the greatest common factor of 29 and 75661?\n | 29\n | ibivibiv/math_instruct | |
Let q(w) = -737*w**3 + 12*w**2 + 6*w + 239. Let z(f) = 3682*f**3 - 62*f**2 - 31*f - 1197. Let k(j) = -31*q(j) - 6*z(j). Find the first derivative of k(c) wrt c.\n | 2265*c**2\n | ibivibiv/math_instruct | |
Simplify 2*(sqrt(15)/sqrt(3)*-4 + 5)**2*-3 - -3*(-1 + (sqrt(50)/sqrt(2))/sqrt(5))*6.\n | -648 + 258*sqrt(5)\n | ibivibiv/math_instruct | |
Is -16140 at most as big as -5955116/369?\n | True\n | ibivibiv/math_instruct | |
Is 935029 prime?\n | False\n | ibivibiv/math_instruct | |
Let y = 3735 + -3733. Let r = 8.048 - 0.048. What is the biggest value in -4, y, r?\n | r\n | ibivibiv/math_instruct | |
Is 911993 a prime number?\n | False\n | ibivibiv/math_instruct | |
Let q = 210 + -140. Calculate the greatest common factor of q and 14.\n | 14\n | ibivibiv/math_instruct | |
Is 31 a factor of 6727?\n | True\n | ibivibiv/math_instruct | |
4748 divided by -4461\n | -4748/4461\n | ibivibiv/math_instruct |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.