instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What is prob of picking 1 b and 1 p when two letters picked without replacement from eqbypyp?\n | 2/21\n | ibivibiv/math_instruct | |
How many minutes are there between 12:41 AM and 3:45 AM?\n | 184\n | ibivibiv/math_instruct | |
Suppose -6*z + 156 = 24. Calculate the highest common factor of 88 and z.\n | 22\n | ibivibiv/math_instruct | |
What is -6 (base 15) in base 3?\n | -20\n | ibivibiv/math_instruct | |
Subtract -970 from -15542185.\n | -15541215\n | ibivibiv/math_instruct | |
Let s = 2 - 2. Let z = 47.9 - 48.3. Which is the nearest to 2? (a) -0.2 (b) z (c) s\n | c\n | ibivibiv/math_instruct | |
Calculate -3.153 - -2.\n | -1.153\n | ibivibiv/math_instruct | |
Is 9 a factor of 162?\n | True\n | ibivibiv/math_instruct | |
What is 236 minutes after 10:46 PM?\n | 2:42 AM\n | ibivibiv/math_instruct | |
Does 307 divide 405972502?\n | True\n | ibivibiv/math_instruct | |
Calculate 6 divided by 11407.\n | 6/11407\n | ibivibiv/math_instruct | |
Expand (-2 + 2 - b)*(-b + b - b**2) + 52*b**3 + 126*b**3 - 47*b**3.\n | 132*b**3\n | ibivibiv/math_instruct | |
Two letters picked without replacement from hwm. What is prob of sequence mw?\n | 1/6\n | ibivibiv/math_instruct | |
Let w(i) be the second derivative of -i**7/210 + i**6/90 + 2*i**3/3 - i. Let y(f) be the second derivative of w(f). What is the third derivative of y(t) wrt t?\n | -24\n | ibivibiv/math_instruct | |
Let s(m) = -m**2 - 40*m - 272. Determine s(-9).\n | 7\n | ibivibiv/math_instruct | |
What is prob of sequence ccp when three letters picked without replacement from {p: 1, c: 2}?\n | 1/3\n | ibivibiv/math_instruct | |
Let a(h) = -12*h. Suppose -p + c = -38, 109 = 10*p - 7*p - 2*c. Suppose -5*q = -3*k - 8*q - p, q = -5. Let f(t) = 6*t. What is k*a(m) - 11*f(m)?\n | 6*m\n | ibivibiv/math_instruct | |
Round 2167460 to the nearest ten thousand.\n | 2170000\n | ibivibiv/math_instruct | |
Add -9806 and 29.\n | -9777\n | ibivibiv/math_instruct | |
Let y(j) = -3*j**4 + 20*j**3 + 86*j**2 + 92*j + 41. Let w(q) = -3*q**4 + 19*q**3 + 85*q**2 + 91*q + 43. Let t(a) = 4*w(a) - 5*y(a). Factor t(r).\n | 3*(r - 11)*(r + 1)**3\n | ibivibiv/math_instruct | |
Let h(t) = 2*t + 5. Let n be h(-5). Let m = 11 + n. List the prime factors of m.\n | 2, 3\n | ibivibiv/math_instruct | |
What is 0.3 times -0.01?\n | -0.003\n | ibivibiv/math_instruct | |
Suppose -3*k + 5*t + 857 = 0, -5*k + 1383 = -49*t + 52*t. Calculate the least common multiple of k and 18.\n | 558\n | ibivibiv/math_instruct | |
Three letters picked without replacement from dfdfloffodoodfdf. Give prob of sequence dfd.\n | 1/28\n | ibivibiv/math_instruct | |
Let x = -0.115 - 58.885. Let u = 39.690572 - -19.309233. Let p = x + u. Round p to 4 decimal places.\n | -0.0002\n | ibivibiv/math_instruct | |
Let r = 22.3 + -22. Let z = 5 - 3. Which is the nearest to z? (a) -1 (b) -0.1 (c) r\n | c\n | ibivibiv/math_instruct | |
Find s such that 5*s**4 - 214320*s**3 + 2296438785*s**2 + 4593734890*s = 0.\n | -2, 0, 21433\n | ibivibiv/math_instruct | |
Let d = -102.9999427 + 103. What is d rounded to 5 decimal places?\n | 0.00006\n | ibivibiv/math_instruct | |
Find the second derivative of -23796*t**4 + 34238*t.\n | -285552*t**2\n | ibivibiv/math_instruct | |
What is the greatest common factor of 42 and 54?\n | 6\n | ibivibiv/math_instruct | |
Is 7 a factor of 3072438?\n | False\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"AR(1)-process: Conditional distribution
Consider I have an AR(p)-process $(X_{t})_{t\in Z }$, for example the following AR(1)-process:
$$X_{t}=\alpha_{0} + \alpha_{1}X_{t-1}+\epsilon_{t}$$ where $\epsilon_{t}\sim D(0,\sigma... | An autoregressive process of order p, denoted by AR(p), is a fundamental concept in time series analysis. It describes a type of stochastic process where the current value depends on its own past values and a random error term. A particularly important case is the AR(1) process, which has only one lagged term. Let's e... | ibivibiv/math_instruct | |
Calculate (-3)/(-7 - ((-6)/(-15) - (-345)/(-50))).\n | 6\n | ibivibiv/math_instruct | |
Which is greater: 8158 or 25?\n | 8158\n | ibivibiv/math_instruct | |
Express 11*l + 5 + 2*l - 20*l in the form v + k*l and give v.\n | 5\n | ibivibiv/math_instruct | |
Solve -764*l + 406512 = -1752*l + 9457*l for l.\n | 48\n | ibivibiv/math_instruct | |
Expand -s**4 - 2*s**4 + 6*s**4 + (10*s + 6*s - 5*s)*(-5*s**3 + 4*s**3 - s**3).\n | -19*s**4\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {i: 6, z: 6}. Give prob of picking 1 i and 1 z.\n | 6/11\n | ibivibiv/math_instruct | |
In 2005, 25 percent of the math department’s 60 students were female, and in 2007, 35 percent of the math department’s 65 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?
Answer Choices: (A) 15% (B) 51.7% (C) 62.5% (D) 115% (E) 160% | Lets reason about the multi-choice question.
Female students in 2005 = 25% of 60 = 15
Female students in 2007 = 35% of 65 = 22.75
Percentage increase = [(22.75- 15)/15] *100 % = 51.7%
The answer is B | ibivibiv/math_instruct | |
Let m = 44 + -42. Suppose 5*r - 2*d - 68 = 3*r, 0 = -2*r - m*d + 84. Calculate the greatest common divisor of 57 and r.\n | 19\n | ibivibiv/math_instruct | |
Which is the third biggest value? (a) -50 (b) 1/2 (c) 4\n | a\n | ibivibiv/math_instruct | |
Let u(w) = -4*w**2 + 10*w**2 - w - 4*w + w**3 - 5 + 0*w. Let q be (9/2)/(3/(-4)). Let p be u(q). Solve -p = 5*j - 0*j for j.\n | -5\n | ibivibiv/math_instruct | |
Let p(g) = -714783*g**2. Let t(h) = 31*h. What is t(p(i))?\n | -22158273*i**2\n | ibivibiv/math_instruct | |
Suppose 0 = -16*i - 29 + 77. Let a be i - 8 - 5/(-1). Sort 2, -4, a, -8.\n | -8, -4, a, 2\n | ibivibiv/math_instruct | |
Which is smaller: 2/13105 or 1?\n | 2/13105\n | ibivibiv/math_instruct | |
Let y = -1173/5 + 1883/8. Calculate the common denominator of 3/16 and y.\n | 80\n | ibivibiv/math_instruct | |
List the prime factors of 21720863.\n | 31, 700673\n | ibivibiv/math_instruct | |
What is the value of 24 - (-15 + 22 + 50)?\n | -33\n | ibivibiv/math_instruct | |
Suppose 4*b + 4 = g - 1, -5*g + 4*b = -9. Suppose -3*p + 4*p - 1 = 0. Let h be (-9)/(-3*p) - 2. Calculate the highest common divisor of g and h.\n | 1\n | ibivibiv/math_instruct | |
Let y = 29 - 57. Let x = -21 - -8. Let t = x - y. Calculate the remainder when 44 is divided by t.\n | 14\n | ibivibiv/math_instruct | |
Solve 0 = -4*z - 5*o - 25 - 7, -5*z = 5*o + 35 for z.\n | -3\n | ibivibiv/math_instruct | |
Find the common denominator of -67/222 and (21 - 9) + 7224/(-864).\n | 1332\n | ibivibiv/math_instruct | |
0.15989 + 137625.81\n | 137625.96989\n | ibivibiv/math_instruct | |
What is ((-3)/12)/((-1890)/(-560))?\n | -2/27\n | ibivibiv/math_instruct | |
Which is the third smallest value? (a) -0.1 (b) 73 (c) -0.0527\n | b\n | ibivibiv/math_instruct | |
Let b = -0.5 + -0.1. Let c = b + 0.682. Let r = c + -0.08. Round r to 2 decimal places.\n | 0\n | ibivibiv/math_instruct | |
Let q = -2018.7399 + 2019. Round q to two decimal places.\n | 0.26\n | ibivibiv/math_instruct | |
Let p(j) = -j**3 - 25*j**2 - 12*j - 252. Give p(-25).\n | 48\n | ibivibiv/math_instruct | |
What is 8352965 to the power of 1/3, to the nearest integer?\n | 203\n | ibivibiv/math_instruct | |
Collect the terms in 8167*l - 241*l**2 - 231*l**2 + 474*l**2 - 2.\n | 2*l**2 + 8167*l - 2\n | ibivibiv/math_instruct | |
Suppose 53*h - 56*h = -120. Suppose -h*v + 47*v = 35. Solve 5*c - v = -5*t, -5*c - 3 = 3*t - 0 for c.\n | -3\n | ibivibiv/math_instruct | |
153.896 * -0.3\n | -46.1688\n | ibivibiv/math_instruct | |
What comes next: -6420, -23752, -52630, -93048, -145000?\n | -208480\n | ibivibiv/math_instruct | |
What comes next: -1926, -1928, -1932, -1938, -1946, -1956, -1968?\n | -1982\n | ibivibiv/math_instruct | |
What is the value of -4 + 2 + 27/12?\n | 1/4\n | ibivibiv/math_instruct | |
Let k = 1.9817 + 0.0183. Let l = 0.33 - 0.13. Let z be (-3)/(-9)*(-4 - -1). Which is the nearest to z? (a) k (b) l (c) -6\n | b\n | ibivibiv/math_instruct | |
Let f = 10 - 5. Put -0.3, -0.12, f, 1 in decreasing order.\n | f, 1, -0.12, -0.3\n | ibivibiv/math_instruct | |
Suppose 14*b - 6454 = 11046. Calculate the remainder when b is divided by 37.\n | 29\n | ibivibiv/math_instruct | |
Simplify (((k/(k*k**7))/k)/k*k**(5/3)*k**4/((k*k**(1/2))/k))/((k*k**(2/17))/k*k**0*k*k*(k*k/(k/(k*k/k**3)))/(k/(k/(k**1/k))*k)) assuming k is positive.\n | k**(-505/102)\n | ibivibiv/math_instruct | |
Let q(u) be the second derivative of 0*u**3 - 2 + 0*u**2 - 1/6*u**4 + 7*u. Let t(c) = -c**2. What is q(t(j))?\n | -2*j**4\n | ibivibiv/math_instruct | |
(-53 - -36) + (10 - 74)\n | -81\n | ibivibiv/math_instruct | |
Let n(l) = -l**3 + 6*l**2 + 19*l - 135. Give n(6).\n | -21\n | ibivibiv/math_instruct | |
Simplify (l**8/l**(-1))**(-1) assuming l is positive.\n | l**(-9)\n | ibivibiv/math_instruct | |
Let y(l) be the first derivative of -2*l**3 - 2*l + 16 - 1/2*l**4 - 3*l**2. Factor y(a).\n | -2*(a + 1)**3\n | ibivibiv/math_instruct | |
What is -74 + 42 + (-2 - -21)?\n | -13\n | ibivibiv/math_instruct | |
Let t = -4 - -1. Let h be ((-2)/t)/(10/75). What is the derivative of 2 + h*i**3 - 90*i + 90*i wrt i?\n | 15*i**2\n | ibivibiv/math_instruct | |
Simplify (6*-1*sqrt(19)*-3 + -1)**2.\n | -36*sqrt(19) + 6157\n | ibivibiv/math_instruct | |
Solve 2*a + 67*d - 3 = 64*d, 0 = -14*a + 2*d - 2 for a.\n | 0\n | ibivibiv/math_instruct | |
Collect the terms in -15*i - 15*i - 39*i - 54*i**2 + 75*i - 7*i.\n | -54*i**2 - i\n | ibivibiv/math_instruct | |
What is the value of (18/(-15))/((-66)/120*(-12)/3)?\n | -6/11\n | ibivibiv/math_instruct | |
Let s(h) be the second derivative of h**5/20 + 5*h**4/12 - h**3 - 3*h**2/2 + 54*h. Let l(a) = -2*a. Let q be l(3). Calculate s(q).\n | -3\n | ibivibiv/math_instruct | |
Let a(o) = 2 - 3*o**2 - 2*o**2 + 3*o + 0 + 12*o**2 + o**3. Let i be a(-6). Calculate the greatest common divisor of 60 and i.\n | 20\n | ibivibiv/math_instruct | |
Convert -312 (base 4) to base 13.\n | -42\n | ibivibiv/math_instruct | |
Let p(w) = w**2 - 4*w - 3. Let c be p(6). Let o = -136 - -136.06. Suppose -u = 4*x + 7, -5*u + 30 = -5*x - 10. What is the second smallest value in x, c, o?\n | o\n | ibivibiv/math_instruct | |
Simplify 4 + (-5*((sqrt(33) + sqrt(165)/sqrt(5)*-3)/(sqrt(24)/sqrt(8)*-1) + 3) + -2)**2.\n | 340*sqrt(11) + 1393\n | ibivibiv/math_instruct | |
Let w = -26.10091825 + -1.899079. Let c = 28 + w. What is c rounded to 7 dps?\n | 0.0000028\n | ibivibiv/math_instruct | |
Convert -4 (base 12) to base 2.\n | -100\n | ibivibiv/math_instruct | |
Let u = 109.1 + -103. Let i = -5.51 + -1.09. Let v = u + i. What is the smallest value in v, 0, 1/6, 3?\n | v\n | ibivibiv/math_instruct | |
Four letters picked without replacement from oioddl. What is prob of picking 1 i, 1 d, and 2 o?\n | 2/15\n | ibivibiv/math_instruct | |
Collect the terms in 47*u**2 - 47*u**2 - 18*u**3.\n | -18*u**3\n | ibivibiv/math_instruct | |
How many minutes are there between 4:40 PM and 8:11 PM?\n | 211\n | ibivibiv/math_instruct | |
What is the value of (33/66)/((-3)/(-4))?\n | 2/3\n | ibivibiv/math_instruct | |
Let r(b) = -33*b + 52. Let t(q) = q**2 + 97*q - 164. Let m(z) = -7*r(z) - 2*t(z). Determine m(16).\n | 44\n | ibivibiv/math_instruct | |
Rearrange (3*r - 3*r + 2*r**2)*(8 - 15 + 8) + (-5*r + 23*r + 3*r)*(4*r - r - 6*r) + r**2 + 14*r**2 - r**2 to z + p*r + o*r**2 and give o.\n | -47\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 s, 2 y, and 1 u when four letters picked without replacement from dosyyeou.\n | 1/70\n | ibivibiv/math_instruct | |
In base 4, what is -10210 + -310233233?\n | -310310103\n | ibivibiv/math_instruct | |
Is 11945 composite?\n | True\n | ibivibiv/math_instruct | |
Differentiate -1 - 43*o**3 + 3*o**3 - o**3 - 17 - 49*o**3 with respect to o.\n | -270*o**2\n | ibivibiv/math_instruct | |
Is 13155743 prime?\n | True\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Achieving equality in the definition of the support function
Suppose that $B$ is a convex body (compact closed with nonempty interior), and let $$h_B(u) = \sup_{x \in B} \langle u,x\rangle$$ be its support function. Is the... | In convex analysis, the support function plays a crucial role in describing various properties of a convex body. Given a convex body $B$, its support function $h\_B(u)$ is defined as the supremum of the inner product of $u$ and all points $x$ within the set $B$:
$$h\_B(u) = \sup\_{x \in B} \langle u, x\rangle.$$
In ... | ibivibiv/math_instruct |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.