instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Let c = 17 - -114. Suppose 2*t + 109 = 3*u, 4*u - 4*t = 21 + c. Suppose 3*z - 53 = -5*w, 3*w + 0*z + 3*z = u. What are the prime factors of w?\n | 2, 5\n | ibivibiv/math_instruct | |
Determine w, given that 2*w**5/7 + 4*w**4/7 - 36*w**3/7 + 64*w**2/7 - 46*w/7 + 12/7 = 0.\n | -6, 1\n | ibivibiv/math_instruct | |
Which is the second biggest value? (a) -1 (b) -2/9 (c) -4 (d) -6.095\n | a\n | ibivibiv/math_instruct | |
What is next in -2010, -2014, -2022, -2034, -2050, -2070, -2094?\n | -2122\n | ibivibiv/math_instruct | |
Let u be 2*1 - 4/4. Let v = u + -1. Suppose -3*h = 3*c - 168, v = -2*h - c - 5 + 112. Is h prime?\n | False\n | ibivibiv/math_instruct | |
Solve j**2/3 - 13202*j/3 + 43573201/3 = 0.\n | 6601\n | ibivibiv/math_instruct | |
b"What is the xth term of 1, -17, -61, -143, -275, -469?\n" | -2*x**3 - x**2 - x + 5\n | ibivibiv/math_instruct | |
In base 11, what is -1 - 58?\n | -59\n | ibivibiv/math_instruct | |
What is the ten thousands digit of 61349?\n | 6\n | ibivibiv/math_instruct | |
Let i = 0.1 - -0.4. Let h be 0*(8/6)/4. Which is the nearest to -1? (a) -3 (b) i (c) h\n | c\n | ibivibiv/math_instruct | |
What are the prime factors of 294287?\n | 7, 17, 2473\n | ibivibiv/math_instruct | |
What is prob of sequence vimk when four letters picked without replacement from {v: 1, m: 3, a: 2, i: 3, k: 2, n: 1}?\n | 1/660\n | ibivibiv/math_instruct | |
What is 2141223324 (base 5) in base 8?\n | 21530604\n | ibivibiv/math_instruct | |
Which is the fifth smallest value? (a) -1/4 (b) 0.1 (c) 7693 (d) 5/4 (e) -0.2 (f) 3\n | f\n | ibivibiv/math_instruct | |
Let z(t) be the third derivative of t**5/60 - 2*t**4/3 - 2*t**3/3 + 2*t**2 + t - 57. Give z(11).\n | -59\n | ibivibiv/math_instruct | |
Let o = 41 + -36. Sort o, -5, 3, 7 in descending order.\n | 7, o, 3, -5\n | ibivibiv/math_instruct | |
Put -2/3, 6, -1.88, 4, 1, -56 in increasing order.\n | -56, -1.88, -2/3, 1, 4, 6\n | ibivibiv/math_instruct | |
Let s(d) = -d + 6. Let o be ((-5 + 4)/(4/32))/(-1). What is s(o)?\n | -2\n | ibivibiv/math_instruct | |
How many minutes are there between 6:24 PM and 1:14 AM?\n | 410\n | ibivibiv/math_instruct | |
What is prob of sequence fjoa when four letters picked without replacement from jojwafooowjoooj?\n | 1/1170\n | ibivibiv/math_instruct | |
Calculate the remainder when 5600 is divided by 119.\n | 7\n | ibivibiv/math_instruct | |
Calculate prob of sequence nn when two letters picked without replacement from gmmmggnjpbn.\n | 1/55\n | ibivibiv/math_instruct | |
Simplify ((s/(s**(4/3)*s)*s)/s*s*s/(s**(-2/5)/s)*s*s)/(s**(-1))**(38/3)*(s**(2/15)*s*s/(s/s**(-3/2)*s))**38 assuming s is positive.\n | s**(-176/5)\n | ibivibiv/math_instruct | |
Let h(m) be the first derivative of m**2 - 3. Let b(n) = 6*n. Let x(j) = 4*j. Let f(t) = 5*b(t) - 8*x(t). What is h(f(v))?\n | -4*v\n | ibivibiv/math_instruct | |
Factor 5*f**2 + 33060*f - 99225.\n | 5*(f - 3)*(f + 6615)\n | ibivibiv/math_instruct | |
Let h = -2 - -6. Let v = 0.023 - -1.977. Let p = -5 - -10. Sort h, p, v in increasing order.\n | v, h, p\n | ibivibiv/math_instruct | |
Is 132446661 prime?\n | False\n | ibivibiv/math_instruct | |
Suppose 16 = 2*g + 48. Let k(t) = -2*t - 29. Suppose -11*w + w + 50 = 0. What is the least common multiple of w and k(g)?\n | 15\n | ibivibiv/math_instruct | |
Round 261.06043644 to 1 dp.\n | 261.1\n | ibivibiv/math_instruct | |
Find the third derivative of 7567*n**3*v**3 - n**3*v**2 - n*v**3 - 13408*n*v**2 - 3*v**3 - 2 wrt v.\n | 45402*n**3 - 6*n - 18\n | ibivibiv/math_instruct | |
Simplify 0 + sqrt(32)/sqrt(4) + -5*(1*sqrt(98) + sqrt(2))**2.\n | -640 + 2*sqrt(2)\n | ibivibiv/math_instruct | |
Put -5, -2/7, 0.24819, 1/5, -1/223 in ascending order.\n | -5, -2/7, -1/223, 1/5, 0.24819\n | ibivibiv/math_instruct | |
Suppose -13*l = -9*l - 16. Suppose -4*c - c + l*t = -54, -t + 19 = 2*c. List the prime factors of c.\n | 2, 5\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-98.615 * -9.816) - -36.011 | 1004.0158 | ibivibiv/math_instruct | |
Calculate the highest common divisor of 4028 and 12508.\n | 212\n | ibivibiv/math_instruct | |
Suppose 6*y = -42 + 576. Suppose y = 6*v - 163. Does 7 divide v?\n | True\n | ibivibiv/math_instruct | |
Let a be 60/(95/20 + -4). Calculate the greatest common divisor of a and 5.\n | 5\n | ibivibiv/math_instruct | |
What is the units digit of 23102?\n | 2\n | ibivibiv/math_instruct | |
Let a(f) be the second derivative of f**6/30 - f**4/2 - 4*f**3/3 - 3*f**2/2 - 25*f - 1. Factor a(z).\n | (z - 3)*(z + 1)**3\n | ibivibiv/math_instruct | |
Solve -2*t + 62 = 18*y, -5*y + 419 = -3*t + 384 for y.\n | 4\n | ibivibiv/math_instruct | |
Are -12172.945 and 2/11 non-equal?\n | True\n | ibivibiv/math_instruct | |
What is -0.0330599 rounded to 4 decimal places?\n | -0.0331\n | ibivibiv/math_instruct | |
Suppose 13*f + 838509 = 34*f. Is f a prime number?\n | True\n | ibivibiv/math_instruct | |
Simplify (z/(z/(z*z**(-18))))/z**(2/29) assuming z is positive.\n | z**(-495/29)\n | ibivibiv/math_instruct | |
Let p = -41 + 40. Sort 6, 5, p in decreasing order.\n | 6, 5, p\n | ibivibiv/math_instruct | |
b"What is the zth term of 35, 134, 299, 530?\n" | 33*z**2 + 2\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 70967 and 795366.\n | 42154398\n | ibivibiv/math_instruct | |
Calculate prob of picking 2 a when two letters picked without replacement from {e: 2, a: 9, i: 2}.\n | 6/13\n | ibivibiv/math_instruct | |
What is the first derivative of -z**4 - 325 + 323 + 3*z**4 wrt z?\n | 8*z**3\n | ibivibiv/math_instruct | |
Two letters picked without replacement from xgasrmmg. What is prob of picking 1 x and 1 a?\n | 1/28\n | ibivibiv/math_instruct | |
Express 2 + 4*a + 4*a**4 - 4*a**3 + 5*a**3 + 8*a - 15*a in the form z*a**4 + q*a + m*a**3 + t + l*a**2 and give t.\n | 2\n | ibivibiv/math_instruct | |
Suppose 0 = -4*y - 5 + 1. Let a(q) = 3*q**2 - 4*q + 2. Let h be a(2). Let n(z) = 5*z**2 + h - 2*z + z - 7. What is n(y)?\n | 5\n | ibivibiv/math_instruct | |
Is 19378896 a multiple of 229?\n | True\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Tag Info
5
Let's solve a more general problem (Least Squares with Linear Equality Constraints): \begin{alignat*}{3} \arg \min_{x} & \quad & \frac{1}{2} \left\| A x - b \right\|_{2}^{2} \\ \text{subject to} & \quad & C x =... | Let us begin by discussing the concept of Least Squares with Linear Equality Constraints. This optimization problem involves finding a vector $x$ that minimizes the squared Euclidean norm $\| Ax - b \|\_2^2$, where $A$ is an m x n matrix and $b$ is an m x 1 column vector, subject to the constraint $Cx = d$. Here, $C$ ... | ibivibiv/math_instruct | |
Let c be (3/((-9)/2))/((-8)/12). Suppose 1 = n - c. Solve 0 = 2*g + n*v + 4, -5*g - v - 2 - 4 = 0 for g.\n | -1\n | ibivibiv/math_instruct | |
Calculate the least common multiple of 2718 and 28086.\n | 84258\n | ibivibiv/math_instruct | |
What is the fourth smallest value in -1/10, -17, -70, 2/19, 3?\n | 2/19\n | ibivibiv/math_instruct | |
Collect the terms in -165*q - 16 - 680*q - 18 + 34.\n | -845*q\n | ibivibiv/math_instruct | |
Solve 51204*t - 51182*t - 924 = 0 for t.\n | 42\n | ibivibiv/math_instruct | |
What is the value of (-448)/(-6)*(-5514)/(-6433)?\n | 64\n | ibivibiv/math_instruct | |
Expand (30 - 8 + 10)*(3*x - 2*x + 0*x)*(-3 + 4 + 3).\n | 128*x\n | ibivibiv/math_instruct | |
Suppose 1505*k - 1498*k - 7 = 0. Suppose -3*m + 7*m = i + 27, 3*m - k = -2*i. Let c(z) = z**2 + 9*z - 3. What is c(i)?\n | -17\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {s: 5}. What is prob of picking 4 s?\n | 1\n | ibivibiv/math_instruct | |
Rearrange -1 + w + 1 + 7*w - 3*w - 2*w + (-4 + 3 + 4)*(w - 4*w + 2*w) + (5 - 2 - 2)*(2*w + 5*w - 5*w) - 3 + 3 - w + 6 - 6 + w to the form k + o*w and give o.\n | 2\n | ibivibiv/math_instruct | |
Suppose -540 = -6*o - 0*o. Does 11 divide o?\n | False\n | ibivibiv/math_instruct | |
-286556 times -0.28\n | 80235.68\n | ibivibiv/math_instruct | |
Which is bigger: -326 or 91?\n | 91\n | ibivibiv/math_instruct | |
Let c = 1.459 + 2.541. What is the closest to -1/4 in -3/5, c, 10, -3/2?\n | -3/5\n | ibivibiv/math_instruct | |
What is nineteen quarters of a litre in millilitres?\n | 4750\n | ibivibiv/math_instruct | |
Let q(x) = 3*x**2 + 269*x + 2776. What is q(-12)?\n | -20\n | ibivibiv/math_instruct | |
Suppose 25 - 3 = -2*v + 4*q, -20 = -4*q. Let b = -2.8 + 2. Let r = -0.8 - b. Put -1/12, v, 2/17, r in increasing order.\n | v, -1/12, r, 2/17\n | ibivibiv/math_instruct | |
-47026 divided by -23513\n | 2\n | ibivibiv/math_instruct | |
Is 12 a factor of 26868?\n | True\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-0.7358 % 74.8719) / (55.213 / -72.0292) | -96.7157 | ibivibiv/math_instruct | |
Let c(h) = h**2 + 8*h. Let j = 55 - 59. Calculate c(j).\n | -16\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 18 and 144?\n | 18\n | ibivibiv/math_instruct | |
Find o such that 2*o**3/5 + 4*o**2/5 - 14*o/5 + 8/5 = 0.\n | -4, 1\n | ibivibiv/math_instruct | |
What is 29/2 of a micrometer in nanometers?\n | 14500\n | ibivibiv/math_instruct | |
What is prob of picking 3 r when three letters picked without replacement from {m: 2, s: 7, p: 5, r: 3, l: 1, q: 2}?\n | 1/1140\n | ibivibiv/math_instruct | |
Round -0.083276783 to 4 decimal places.\n | -0.0833\n | ibivibiv/math_instruct | |
What is 88154 to the power of 1/3, to the nearest integer?\n | 45\n | ibivibiv/math_instruct | |
Let c(w) = 4*w. Let t be c(-1). Let o = -4 - t. Suppose 0 = 4*n - 7*n + 2*d + 56, 4*d + 16 = o. Calculate the least common multiple of 2 and n.\n | 16\n | ibivibiv/math_instruct | |
What is the tens digit of (196/8)/(2/4)?\n | 4\n | ibivibiv/math_instruct | |
Let p(u) = 2*u**3 - 6*u**2 + 3*u + 3. Let o be p(4). Let w = -7 + o. Calculate the common denominator of 41/2 and 86/w - (0 + 0).\n | 20\n | ibivibiv/math_instruct | |
Suppose 0 = 24*k - 934 - 1034. What is the greatest common factor of 205 and k?\n | 41\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {d: 4, i: 1, u: 1, l: 3, f: 4, t: 1}. Give prob of picking 1 i, 1 d, and 2 f.\n | 24/1001\n | ibivibiv/math_instruct | |
Let s(j) = -8*j. Let f be 2/(-3) + 2/(-6). Let q be s(f). Calculate the highest common divisor of q and 8.\n | 8\n | ibivibiv/math_instruct | |
Factor -d**3/2 - 5*d**2 + 23*d/2 - 6.\n | -(d - 1)**2*(d + 12)/2\n | ibivibiv/math_instruct | |
Let i be 0 - -5*(3 + -4). Let k = 32 + i. Let j(m) = 12*m - 5. What is the remainder when k is divided by j(1)?\n | 6\n | ibivibiv/math_instruct | |
Collect the terms in -30*r**2 + 30*r**2 - 5*r**3.\n | -5*r**3\n | ibivibiv/math_instruct | |
Evaluate 4/32*5/(-5)*2.\n | -1/4\n | ibivibiv/math_instruct | |
b"What is the dth term of -707, -1452, -2197?\n" | -745*d + 38\n | ibivibiv/math_instruct | |
Calculate the remainder when 1224 is divided by ((-115)/345)/(1/(-147)).\n | 48\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 747 and 27.\n | 9\n | ibivibiv/math_instruct | |
Let b(v) = 2*v**2. Suppose 4*d - 2 = 2. Let z(u) = -8*u**2 + 12*u. Let a(l) = l**2 - l. Let w(o) = d*z(o) + 12*a(o). Determine w(b(g)).\n | 16*g**4\n | ibivibiv/math_instruct | |
Is 10487 a composite number?\n | False\n | ibivibiv/math_instruct | |
Calculate the least common multiple of 221580 and 12984588.\n | 64922940\n | ibivibiv/math_instruct | |
Express -2348 - 122*o + 2348 in the form a + u*o and give a.\n | 0\n | ibivibiv/math_instruct | |
Does 3 divide 49080514?\n | False\n | ibivibiv/math_instruct | |
Convert 4c (base 14) to base 7.\n | 125\n | ibivibiv/math_instruct |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.