instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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|---|---|---|---|
Express (-5 - 2 - 3)*(2*x**3 - 2*x**3 - x**3) - x**3 + x**3 - x**3 + 4*x**3 - x**3 - 5*x**3 in the form q*x + i + h*x**3 + g*x**2 and give h.\n | 7\n | ibivibiv/math_instruct | |
Sort 5, 29, -7, -5, -2 in ascending order.\n | -7, -5, -2, 5, 29\n | ibivibiv/math_instruct | |
Let a(q) = 2*q - 7. Let g be a(6). Let p = g + 4. Suppose 107 = 132*h - 157. Solve h*c - 2*f = -2*c - 10, 3*c - 3*f + p = 0 for c.\n | -2\n | ibivibiv/math_instruct | |
b"What is the oth term of -2683, -5367, -8063, -10777, -13515, -16283, -19087, -21933?\n" | -o**3 - 2677*o - 5\n | ibivibiv/math_instruct | |
What is -3.96 times 2025?\n | -8019\n | ibivibiv/math_instruct | |
What is the value of -6 - (-30 - -8 - -27)?\n | -11\n | ibivibiv/math_instruct | |
Let i(g) = 2*g**3 + g**2 - 9*g + 3. Give i(2).\n | 5\n | ibivibiv/math_instruct | |
Let p = 11.3 - 11. Let l = -0.2 - 0. Suppose k - 4 = 0, 2*t + 5*k = -3*t + 5. Which is the closest to t? (a) l (b) -1/7 (c) p\n | a\n | ibivibiv/math_instruct | |
What is the tens digit of 2065?\n | 6\n | ibivibiv/math_instruct | |
Let r be 3 + (-4 - -5) + -3 + -119. Let s = 138 + r. Let l be 9/(-15)*s/32. Which is the third smallest value? (a) -0.33 (b) -5 (c) l\n | a\n | ibivibiv/math_instruct | |
What is 69250.079 + 211908.49?\n | 281158.569\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {r: 1, c: 2, u: 4, p: 4, q: 1, a: 2}. Give prob of sequence cqu.\n | 1/273\n | ibivibiv/math_instruct | |
What is the common denominator of -89/2265291 and 23/4?\n | 9061164\n | ibivibiv/math_instruct | |
Let x(i) = -201*i + 16. Let m(w) = 134*w - 10. Give -8*m(o) - 5*x(o).\n | -67*o\n | ibivibiv/math_instruct | |
What is the tens digit of 2536769555?\n | 5\n | ibivibiv/math_instruct | |
Let d = -164 + 166. Let i(z) = -4*z**2 - d*z**2 + 13*z**2 - 5*z**2. Let c(s) = 4*s. What is c(i(b))?\n | 8*b**2\n | ibivibiv/math_instruct | |
Calculate 0.132*-0.5.\n | -0.066\n | ibivibiv/math_instruct | |
Is 22498099 composite?\n | True\n | ibivibiv/math_instruct | |
What is -2a364 (base 11) in base 14?\n | -11973\n | ibivibiv/math_instruct | |
Let c(d) = -2*d**2 - 5 + d - 6*d + 4*d**3 + 8 - 1. Let u(r) = 4*r**3 - 2*r**2 - 4*r + 1. Let b(h) = -2*c(h) + 3*u(h). Determine b(-1).\n | -5\n | ibivibiv/math_instruct | |
Simplify (-2 + (0 + sqrt(147))*-3 + 2 + 6*sqrt(9)/sqrt(3) + -5 + sqrt(27))**2.\n | 120*sqrt(3) + 457\n | ibivibiv/math_instruct | |
Evaluate 3 + -6 + -3 + 4.\n | -2\n | ibivibiv/math_instruct | |
Convert 2 (base 4) to base 8.\n | 2\n | ibivibiv/math_instruct | |
Let w = -148 + 148. Let y = -5 - -7.04. Let d = y + -0.04. What is the closest to w in -2/13, d, -2/5?\n | -2/13\n | ibivibiv/math_instruct | |
How many minutes are there between 9:49 PM and 5:36 AM?\n | 467\n | ibivibiv/math_instruct | |
What is the greatest common factor of 32129 and 1083?\n | 361\n | ibivibiv/math_instruct | |
Factor -2*s**3/5 - 2394*s**2 + 9142146*s/5 - 1647690174/5.\n | -2*(s - 351)**2*(s + 6687)/5\n | ibivibiv/math_instruct | |
Let f(m) = 5*m**2 - 187*m + 13563. Let q(g) = -g**2 + 34*g - 2713. Determine 2*f(x) + 11*q(x).\n | -x**2 - 2717\n | ibivibiv/math_instruct | |
What is the common denominator of 163/162792 and 37/14112?\n | 4558176\n | ibivibiv/math_instruct | |
Is 66239518453 a prime number?\n | True\n | ibivibiv/math_instruct | |
What is the value of (-10)/((-100)/15) + 4/(-8)*5?\n | -1\n | ibivibiv/math_instruct | |
(2 - -19 - -39) + 2 + 0 + (-3 - -2)\n | 61\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"How to prove convex+concave=affine?
Suppose $f:\mathbb{R}^n\to \mathbb{R}$ is both convex and concave, how to prove that $f$ is linear? or exactly speaking, $f$ is affine?
I thought for the whole day, but I cannot figure it... | To prove that a function $f: mathbb{R}^n rightarrow mathbb{R}$, which is both convex and concave, is affine, let's begin by establishing some properties of such functions. First, recall the definitions of convexity and concavity using the notation provided:
* A function $f$ is convex if for all $\mathbf{x}, extbf{y} ... | ibivibiv/math_instruct | |
1394441268905 + -18\n | 1394441268887\n | ibivibiv/math_instruct | |
What is the value of -12 + (-4140)/(-322) - 186/21?\n | -8\n | ibivibiv/math_instruct | |
b"What is the ith term of 9246, 9159, 9016, 8817?\n" | -28*i**2 - 3*i + 9277\n | ibivibiv/math_instruct | |
Let q = -2 - -4. Let u(c) = 2 + 0 + q + 32*c - 3. What is the tens digit of u(1)?\n | 3\n | ibivibiv/math_instruct | |
Calculate -47 divided by 1153075.\n | -47/1153075\n | ibivibiv/math_instruct | |
Calculate 1*-7.\n | -7\n | ibivibiv/math_instruct | |
Which is the closest to 162? (a) -24 (b) -1 (c) 9\n | c\n | ibivibiv/math_instruct | |
Factor 5*u**2/4 - 5*u/2 - 15/4.\n | 5*(u - 3)*(u + 1)/4\n | ibivibiv/math_instruct | |
Let s be (-298)/745 - (-1 - 1112/5). Let z = 228 - s. Solve 5*q - 5*u = 30, -u + 2*u = -z*q + 24 for q.\n | 5\n | ibivibiv/math_instruct | |
Let x be 3*(-3 + 2)*-1. Suppose 2*j - j - 5*w = 84, -3*j - x*w = -324. Suppose 3*z + 6 = 0, 2*h - 6*z + 2*z = j. Does 16 divide h?\n | True\n | ibivibiv/math_instruct | |
What is -21729828.42 rounded to the nearest one thousand?\n | -21730000\n | ibivibiv/math_instruct | |
((2 - 1)/((-650)/(-8775)))/(4/8)\n | 27\n | ibivibiv/math_instruct | |
Let y(v) = 12*v + 67. Let z be y(-5). Suppose 1689 = z*s + 506. Is 12 a factor of s?\n | False\n | ibivibiv/math_instruct | |
Suppose 3*m = -m + 5*d - 94, -3*m - 72 = -3*d. Let z = 28 + m. Is (z/3)/(42/9387) composite?\n | False\n | ibivibiv/math_instruct | |
Calculate the common denominator of -71/708 and 149/17700.\n | 17700\n | ibivibiv/math_instruct | |
List the prime factors of 2710.\n | 2, 5, 271\n | ibivibiv/math_instruct | |
Is 21292476811 a composite number?\n | False\n | ibivibiv/math_instruct | |
Solve -s + 3*s + 63*w + 251 - 29 = 0, 0*s - 5*s = -5*w + 555 for s.\n | -111\n | ibivibiv/math_instruct | |
What is the nearest to 5 in 13, 2, -0.3, 4?\n | 4\n | ibivibiv/math_instruct | |
Let x(f) = -155*f**3 + 4*f**2 - 26*f - 83. Let i be x(-19). Round i to the nearest one hundred thousand.\n | 1100000\n | ibivibiv/math_instruct | |
Suppose 48 = 5*r + 7*j, -20 = -r - 2*r - 2*j. Solve 0 = -4*u + 4*w - 20 + r, -2*w = -5*u - 8 for u.\n | 0\n | ibivibiv/math_instruct | |
What is the product of 315.256 and -0.3?\n | -94.5768\n | ibivibiv/math_instruct | |
What is the smallest common multiple of (-1816)/(-14) - 5/((-140)/8) and 240?\n | 3120\n | ibivibiv/math_instruct | |
Solve -8 = z + 4*s, 803*s - 408*s - 28 = -z + 400*s for z.\n | 8\n | ibivibiv/math_instruct | |
Multiply 0.2 and 267174.\n | 53434.8\n | ibivibiv/math_instruct | |
Factor 4*n**2 - 21420*n - 21424.\n | 4*(n - 5356)*(n + 1)\n | ibivibiv/math_instruct | |
What is the highest common divisor of 9892 and 16?\n | 4\n | ibivibiv/math_instruct | |
Does 27 divide 1701?\n | True\n | ibivibiv/math_instruct | |
Sort 2/13, 1/3, 5056, -0.2, 0 in descending order.\n | 5056, 1/3, 2/13, 0, -0.2\n | ibivibiv/math_instruct | |
-4790.9 * 0.3\n | -1437.27\n | ibivibiv/math_instruct | |
Determine r, given that 15*r**4 + 45/4*r**5 - 25*r**3 + 55/4*r - 25/2*r**2 - 5/2 = 0.\n | -2, -1, 1/3, 1\n | ibivibiv/math_instruct | |
What is (-6)/(-30)*(-5)/(-1)?\n | 1\n | ibivibiv/math_instruct | |
Simplify (((b**(1/7)*b*b)/b**(-1))/(b**(-2/13)/(b*b**(-6)/b)))/(b/(b/(b/b**4))*b*b**(2/5))**13 assuming b is positive.\n | b**(8234/455)\n | ibivibiv/math_instruct | |
Solve -5*g**4 + 800*g**3 - 40620*g**2 + 611840*g + 1392640 = 0.\n | -2, 34, 64\n | ibivibiv/math_instruct | |
Evaluate (-4 - (-6 - 5)) + -7.\n | 0\n | ibivibiv/math_instruct | |
Does 94 divide 955726952?\n | True\n | ibivibiv/math_instruct | |
Suppose 0 = b + 4*b + 15, -2*v + 7 = 3*b. What is the greatest common divisor of v and 88?\n | 8\n | ibivibiv/math_instruct | |
Calculate the common denominator of 47/6912 and 161/3432.\n | 988416\n | ibivibiv/math_instruct | |
Let r(s) = -2*s**2 + 74*s + 1. Let w(h) = -h**2 + 25*h. Give -3*r(d) + 8*w(d).\n | -2*d**2 - 22*d - 3\n | ibivibiv/math_instruct | |
Is 9/2260 greater than or equal to 1?\n | False\n | ibivibiv/math_instruct | |
Evaluate (((-9)/9)/(90/(-2340)))/((-1)/(-1)).\n | 26\n | ibivibiv/math_instruct | |
Let y(g) = -6*g + 144. Let p be y(23). Solve 0 = 2*d - 0*d + p for d.\n | -3\n | ibivibiv/math_instruct | |
In base 8, what is -42 + 44206?\n | 44144\n | ibivibiv/math_instruct | |
Let b be 18/135 + (-116)/(-30). What is the third derivative of 74*m**b - 48*m**2 + 6*m**2 - 75*m**4 + 60*m**3 - 16*m**3 wrt m?\n | -24*m + 264\n | ibivibiv/math_instruct | |
Simplify 6*(sqrt(5)*3*-5 + 3).\n | -90*sqrt(5) + 18\n | ibivibiv/math_instruct | |
Suppose -s = -n + 2*s + 11, -1 = 4*n + 3*s. Let b(g) be the first derivative of 0*g**n + 5 + g - 2/3*g**3. Differentiate b(u) with respect to u.\n | -4*u\n | ibivibiv/math_instruct | |
Let g = -331 + 337. Determine u, given that -14*u**3 - 2*u**2 - 3*u**4 - g*u**5 + 14*u**5 + 5*u**4 + 6*u**5 + 0*u**5 = 0.\n | -1, -1/7, 0, 1\n | ibivibiv/math_instruct | |
What is 0.000198348 rounded to 6 decimal places?\n | 0.000198\n | ibivibiv/math_instruct | |
Suppose -3*i - 13 = -8*i + 2*x, 8 = -4*i - 3*x. Suppose -p = i - 2. Let f = 21/935 - 1103/7480. Which is the nearest to 13? (a) p (b) f (c) 5/3\n | c\n | ibivibiv/math_instruct | |
Solve 107*z - 12 = 5*k + 105*z, -k = z + 8 for k.\n | -4\n | ibivibiv/math_instruct | |
What is the next term in 131993, 131995, 131995, 131993?\n | 131989\n | ibivibiv/math_instruct | |
Expand (2*c + 0*c + 0*c)*(3 - 11 + 2)*(-1 + 0 + 0).\n | 12*c\n | ibivibiv/math_instruct | |
What is ninety-three quarters of a litre in millilitres?\n | 23250\n | ibivibiv/math_instruct | |
Jimmy wants to play in the inflatable swimming pool in his backyard. The swimming pool is empty and the garage is locked, so he cannot use the hose to fill the pool. He finds a 2 gallon bucket and calculates that it takes x seconds to fill the bucket from the tap and carry it to the pool where he pours in the water. If... | To solve this problem, we need to determine the value of x, which represents the time it takes for Jimmy to fill the bucket from the tap and carry it to the pool.
We know that it takes x seconds to fill the bucket from the tap.
We also know that the pool holds 84 gallons of water.
We can set up the equation as follows:... | ibivibiv/math_instruct | |
What is the smallest common multiple of 163 and 6?\n | 978\n | ibivibiv/math_instruct | |
Three letters picked without replacement from zmdccccdcmzzdzzzmc. What is prob of picking 1 z and 2 d?\n | 3/136\n | ibivibiv/math_instruct | |
Sort -3, 1, -3139, 25, 5 in increasing order.\n | -3139, -3, 1, 5, 25\n | ibivibiv/math_instruct | |
Let n be ((-24)/(-60))/((-32)/869738). Let c = n + 10871. What is the common denominator of -99/16 and c?\n | 80\n | ibivibiv/math_instruct | |
What is the remainder when 1274 is divided by (4 - 363/(-6)) + (-33)/66?\n | 58\n | ibivibiv/math_instruct | |
Solve 0 = -5*z - 4*i + 44, -27*i = -4*z - 25*i + 4 for z.\n | 4\n | ibivibiv/math_instruct | |
Collect the terms in w**3 + 30 + 15*w**2 - 3*w**3 - 104 - 5*w**2 + w - 9*w**2.\n | -2*w**3 + w**2 + w - 74\n | ibivibiv/math_instruct | |
Solve -72 = -19*r + 42 for r.\n | 6\n | ibivibiv/math_instruct | |
Suppose -7*o - o**2 - 1 - o**3 - 3*o**2 + o**2 + 4*o = 0. What is o?\n | -1\n | ibivibiv/math_instruct | |
Suppose y - 34 + 27 = 2*f, -15 = -3*y + 3*f. Solve -g - 23 = 3*p, -8*g = -5*p - y*g - 25 for p.\n | -7\n | ibivibiv/math_instruct | |
52877 (base 9) to base 7\n | 203662\n | ibivibiv/math_instruct | |
Simplify ((sqrt(119)*-4*6)/(sqrt(14)/sqrt(2)*5))**2 - 4*(-5*sqrt(153)*5*3)**2.\n | -86052708/25\n | ibivibiv/math_instruct | |
What is 3/8 of a microsecond in nanoseconds?\n | 375\n | ibivibiv/math_instruct |
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