instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Let n = 26753/2360 - 17/472. Find the common denominator of n and 37/1157.\n | 11570\n | ibivibiv/math_instruct | |
Let u = 0.6 + -2.15. Let b = -2.55 - u. What is the nearest to 0.1 in -1/7, b, -2/5?\n | -1/7\n | ibivibiv/math_instruct | |
Differentiate 347*i**3 - 4*i**2 - 6*i - 40677 with respect to i.\n | 1041*i**2 - 8*i - 6\n | ibivibiv/math_instruct | |
Let r(p) = -p**2 - 5*p + 8. Let k be r(-6). Suppose 2*l + 50 = 5*m, -4*l = -m + k*m - 32. Calculate the greatest common factor of 84 and m.\n | 12\n | ibivibiv/math_instruct | |
Let r(b) = -b. Let x(o) = -1285*o**2 - 4265*o + 3. What is x(r(v))?\n | -1285*v**2 + 4265*v + 3\n | ibivibiv/math_instruct | |
How many minutes are there between 12:56 PM and 6:56 PM?\n | 360\n | ibivibiv/math_instruct | |
Let p = -4 - -4. Which is smaller: -3 or p?\n | -3\n | ibivibiv/math_instruct | |
Rearrange 3*a**4 + 0*a**2 - a**4 + 2 - 1 - a**2 to the form s + k*a**4 + t*a**3 + g*a**2 + b*a and give g.\n | -1\n | ibivibiv/math_instruct | |
Does 64 divide 4941062633?\n | False\n | ibivibiv/math_instruct | |
Let f = 0.3 + 0.1. Let y = f + 0.1. Let l = -0.3 + y. Which is the closest to l? (a) -0.3 (b) 0 (c) 0.1\n | c\n | ibivibiv/math_instruct | |
Calculate prob of sequence fwk when three letters picked without replacement from fkkcggpw.\n | 1/168\n | ibivibiv/math_instruct | |
Let b(u) = 4*u**2 - 9*u + 41. Let d(l) = -39 - 2*l**2 - 68*l + 37*l - l**2 + 41*l. Let h(a) = 6*b(a) + 7*d(a). Find the first derivative of h(q) wrt q.\n | 6*q + 16\n | ibivibiv/math_instruct | |
Calculate ((-3416)/5978)/((-120)/7).\n | 1/30\n | ibivibiv/math_instruct | |
Is 57215 prime?\n | False\n | ibivibiv/math_instruct | |
Let n(m) = m**3 - 17*m**2 + 21*m - 92. Determine n(16).\n | -12\n | ibivibiv/math_instruct | |
Simplify (((b**2)**50)**42)**(-3/29) assuming b is positive.\n | b**(-12600/29)\n | ibivibiv/math_instruct | |
1154880 divided by -60\n | -19248\n | ibivibiv/math_instruct | |
What is prob of picking 2 k and 2 g when four letters picked without replacement from {k: 2, e: 1, r: 1, t: 1, g: 2}?\n | 1/35\n | ibivibiv/math_instruct | |
Divide -4 by -1451.\n | 4/1451\n | ibivibiv/math_instruct | |
Is -17213334/23 < -748405?\n | True\n | ibivibiv/math_instruct | |
Evaluate 61*(-73)/8906*(-5)/(10/(-72)).\n | -18\n | ibivibiv/math_instruct | |
Expand (1 + 4 - 3)*(-c**2 - 3*c**2 + 6*c**2)*(-1 + 1 + 1 + (-2 + 5 - 4)*(-1 + 5 - 2) + 2 + 3 - 3).\n | 4*c**2\n | ibivibiv/math_instruct | |
Are -63 and -1586632 non-equal?\n | True\n | ibivibiv/math_instruct | |
Collect the terms in 1596*f**2 - 1602*f**2 + 0*f - 2*f.\n | -6*f**2 - 2*f\n | ibivibiv/math_instruct | |
What is -120 (base 16) in base 4?\n | -10200\n | ibivibiv/math_instruct | |
Solve -1516*l = 100024 + 53092 for l.\n | -101\n | ibivibiv/math_instruct | |
Evaluate 30/75*(-5)/(-3).\n | 2/3\n | ibivibiv/math_instruct | |
In base 12, what is -159 - -215a67?\n | 21590a\n | ibivibiv/math_instruct | |
Let f(v) = v**2 - 4*v - 16. What is the units digit of f(8)?\n | 6\n | ibivibiv/math_instruct | |
Expand (b**3 - 3*b**3 - b**3)*(9 - 6 - 1 + 1 - 2 + 0 + (0 + 2 + 0)*(-6 + 3 + 4) - 3 + 1 + 1 + 2 - 2 - 1 + (-1 + 3 - 4)*(0 - 2 + 4) + 3 - 1 - 4 + 5 - 1 - 2).\n | 9*b**3\n | ibivibiv/math_instruct | |
Suppose 15*z + 7515 + 5581 = 52516. What is the remainder when z is divided by 31?\n | 24\n | ibivibiv/math_instruct | |
Find the third derivative of -1106*m**5*r**2 - m**4*r - 27*m**2*r**2 - 5*m**2 wrt m.\n | -66360*m**2*r**2 - 24*m*r\n | ibivibiv/math_instruct | |
Convert 775 (base 10) to base 12.\n | 547\n | ibivibiv/math_instruct | |
Let o(g) = g**2 - 6*g + 1. Let q be o(6). Suppose -5*n = 0, -5*w = 2*n + q - 21. Solve 3*k + 1 = w*z - 10, 6 = -2*k + 2*z for k.\n | -1\n | ibivibiv/math_instruct | |
Let i(b) = -b**2 + 11*b + 1. What are the prime factors of i(6)?\n | 31\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Derivative w.r.t another function [duplicate]
Find $\frac{dv}{du}$ if $v=\sin^{-1}\frac{2x}{1+x^2}$ w.r.t $u=\tan^{-1}\frac{2x}{1-x^2}$
$$v=\sin^{-1}\frac{2x}{1+x^2}=\begin{cases}2\tan^{-1}x&\text{, if }|x|<1\\ \pm\pi-2\t... | The problem you've presented is about finding the derivative of one function with respect to another function, specifically when both functions are expressed in terms of a third variable (in this case, x). This concept involves applying the chain rule from calculus, which states that the derivative of a composite func... | ibivibiv/math_instruct | |
What is the square root of 399 to the nearest integer?\n | 20\n | ibivibiv/math_instruct | |
Collect the terms in 390 - k**2 - 52*k + 52*k - 390.\n | -k**2\n | ibivibiv/math_instruct | |
What is the closest to -0.1 in 45, 0.1, 1?\n | 0.1\n | ibivibiv/math_instruct | |
Let f = 24861146/131243 - -4/18749. Let c = -73 - 229/2. Let s = f + c. What is the common denominator of s and -37/14?\n | 14\n | ibivibiv/math_instruct | |
Three letters picked without replacement from hjhjwwwwhhwwwwww. What is prob of sequence hwh?\n | 1/28\n | ibivibiv/math_instruct | |
What is next in 10389, 20776, 31163, 41550, 51937, 62324?\n | 72711\n | ibivibiv/math_instruct | |
8*(-4)/(64/(-6))\n | 3\n | ibivibiv/math_instruct | |
Let o = -15 + 26. Let u = 3 + 0. Suppose -89 = -u*j + 1. What is the remainder when j is divided by o?\n | 8\n | ibivibiv/math_instruct | |
What is 1/10 of a kilogram in milligrams?\n | 100000\n | ibivibiv/math_instruct | |
What are the prime factors of 17154026?\n | 2, 71, 107, 1129\n | ibivibiv/math_instruct | |
A right circular cone has a volume of $12\pi$ cubic centimeters. The height of the cone is 4 cm. How many centimeters is the circumference of the base of the cone, in terms of $\pi$? | The volume of a cone is given by the formula $\frac{1}{3}\pi r^2 h$, where $r$ is the radius of the base and $h$ is the height.
We are given that the volume is $12\pi$ and the height is 4 cm, so we can solve for the radius as follows:
$12\pi = \frac{1}{3}\pi r^2 \cdot 4$
Simplifying, we find $r^2 = 9$.
Taking the posit... | ibivibiv/math_instruct | |
In base 7, what is 1442504 - 5?\n | 1442466\n | ibivibiv/math_instruct | |
Differentiate -38250141*g + 38238296 with respect to g.\n | -38250141\n | ibivibiv/math_instruct | |
Let u be (-2)/8*-3*24. Let i = 13 - u. Let y(m) = m**3 + 4*m**2 - 4*m + 7. Let v be y(i). Solve a = v*a for a.\n | 0\n | ibivibiv/math_instruct | |
What is prob of picking 1 h and 1 j when two letters picked without replacement from {j: 9, d: 2, h: 5}?\n | 3/8\n | ibivibiv/math_instruct | |
What is 888 + -895 - (-2 + 2 - (0 + 6))?\n | -1\n | ibivibiv/math_instruct | |
Let b = -249 - -321. Let r = b - 71.999791. Round r to four decimal places.\n | 0.0002\n | ibivibiv/math_instruct | |
Let v = -8 + 12. Suppose 4*b - v*n = 520, -1 + 11 = -5*n. Let u = 179 - b. What is the tens digit of u?\n | 5\n | ibivibiv/math_instruct | |
Is 69 a factor of 422?\n | False\n | ibivibiv/math_instruct | |
Differentiate -p**3 + 803004*p - 6803879 wrt p.\n | -3*p**2 + 803004\n | ibivibiv/math_instruct | |
What is the least common multiple of 2232 and 44?\n | 24552\n | ibivibiv/math_instruct | |
Is 105558371 composite?\n | False\n | ibivibiv/math_instruct | |
Are 29 and -1541 equal?\n | False\n | ibivibiv/math_instruct | |
Let i = -41.05 - -49. What is i rounded to zero decimal places?\n | 8\n | ibivibiv/math_instruct | |
Collect the terms in 20*j + 5*j - 17*j.\n | 8*j\n | ibivibiv/math_instruct | |
Let o(j) = 147*j**3 - 9*j**2 - 9*j + 9. Let m(p) = 37*p**3 - 2*p**2 - 2*p + 2. Calculate 9*m(u) - 2*o(u).\n | 39*u**3\n | ibivibiv/math_instruct | |
Let a be (14/10)/(1/5). Let p(y) = 3*y - 5. List the prime factors of p(a).\n | 2\n | ibivibiv/math_instruct | |
Calculate ((-60)/45)/((-186)/(-9)).\n | -2/31\n | ibivibiv/math_instruct | |
Let z(k) = -6*k - 5. Let c be z(3). Let g(w) = 3*w - 4. Let l be g(-6). Which is smaller: l or c?\n | c\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Extracting parameters from a fitted function
Lets say I have written a function which performs convolution and returns value calculated for the time, t.
CalculateConvolution[length_, aifMatrix_, Ktrans_, Kep_, dt_, t_] :=... | Now let's delve into the process of extracting parameters from a fitted function using your provided example. We will discuss the components involved, their roles, and how they contribute to obtaining optimal values for our desired parameters.
### Convolutional Function `CalculateConvolution`
Your first custom funct... | ibivibiv/math_instruct | |
13223 * 1.4\n | 18512.2\n | ibivibiv/math_instruct | |
Let k be (-12)/(-18)*(-9 - -3). Let b be 1232/12*(-6)/k. Calculate the highest common divisor of b and 22.\n | 22\n | ibivibiv/math_instruct | |
What is the tens digit of 378031?\n | 3\n | ibivibiv/math_instruct | |
Find the second derivative of 50*q**3 - 17790*q**2 - 2462183*q + 1 wrt q.\n | 300*q - 35580\n | ibivibiv/math_instruct | |
Let n be (34 + -37)*(-716)/(-3). Let v = 722 + n. Solve 18 = -4*i + j, -i + v*i = -4*j - 12 for i.\n | -4\n | ibivibiv/math_instruct | |
Let f(a) = -2*a + 5. Let o be f(-4). Let t = o + 2. What are the prime factors of t?\n | 3, 5\n | ibivibiv/math_instruct | |
Let t(w) = -2*w**2 + 111*w + 56. Calculate t(56).\n | 0\n | ibivibiv/math_instruct | |
Solve y - 18*p = 831 - 879, 4*p = 4*y - 12 for y.\n | 6\n | ibivibiv/math_instruct | |
(-510)/(-952) + (-32)/896\n | 1/2\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {y: 7, e: 1, u: 6}. What is prob of picking 1 e and 2 y?\n | 3/52\n | ibivibiv/math_instruct | |
Let w be -4 - ((-402)/18 + 19). Which is the nearest to -0.1? (a) -4 (b) w (c) -28 (d) 0\n | d\n | ibivibiv/math_instruct | |
Let m = -160 + 161. Suppose 0 = -16*k - 248 - 56. Sort -1, k, m, 5 in descending order.\n | 5, m, -1, k\n | ibivibiv/math_instruct | |
Suppose 13 - 5 = -2*r. Suppose -4*b - 401 = -413. Let y(u) = 11*u**2 + 3*u**3 - 9*u**2 - 4*u + 5*u**3 - 7*u**b. Calculate y(r).\n | -16\n | ibivibiv/math_instruct | |
Suppose 3 = -3*y - 6. Let b = 3 + y. Suppose b = -2*w - 1 + 5. Sort -3, 4, w in decreasing order.\n | 4, w, -3\n | ibivibiv/math_instruct | |
Simplify -4 + 1 + sqrt(128) + sqrt(128) + sqrt(128) + 4 + 0 - -5*(-3*(2 + sqrt(128)))**2*3.\n | 4344*sqrt(2) + 17821\n | ibivibiv/math_instruct | |
What is the least common multiple of 104 and 520?\n | 520\n | ibivibiv/math_instruct | |
Let t = 229511/4 - 57366. Suppose -5*p = -54 + 204. What is the common denominator of t and (22/p)/((-4)/3)?\n | 20\n | ibivibiv/math_instruct | |
Let v be 5*3/((-60)/(-8)). Find the second derivative of 8*o**5 - 46*o**5 + 0 + 2*o**5 + 37*o - v wrt o.\n | -720*o**3\n | ibivibiv/math_instruct | |
Simplify (t/((t**(-5)*t)/t)*t**(-3)*(t*(t*t**(-1/3))/t)**(-48))**(-1) assuming t is positive.\n | t**29\n | ibivibiv/math_instruct | |
Suppose -10 = -3*j - 2*r, -3*j - 4 = 5*r - 10*r. Solve 1 = -2*f + 7, -4*u + j*f + 2 = 0 for u.\n | 2\n | ibivibiv/math_instruct | |
Simplify (-5 + sqrt(39)/sqrt(3) - (sqrt(13) + 1*sqrt(13) + 3))**2.\n | 16*sqrt(13) + 77\n | ibivibiv/math_instruct | |
What is the distance between 190962812277 and 1.31?\n | 190962812275.69\n | ibivibiv/math_instruct | |
What is the thousands digit of 56052191?\n | 2\n | ibivibiv/math_instruct | |
Multiply -4 and -646.\n | 2584\n | ibivibiv/math_instruct | |
Solve -2*r + 15 - 10 = -3*y, 3*y - 3*r = -9 for y.\n | 1\n | ibivibiv/math_instruct | |
What is 0.097461 - -1604384.9?\n | 1604384.997461\n | ibivibiv/math_instruct | |
Put 426, 1, 5, 4, -5 in descending order.\n | 426, 5, 4, 1, -5\n | ibivibiv/math_instruct | |
Find the common denominator of (10/(-528))/(657/(-11388)) and 40/333.\n | 7326\n | ibivibiv/math_instruct | |
Let m(c) = -7*c**2 + 6*c + 8. Let z be (-5)/(-3)*(432/(-15))/(-8). Let o(k) = k**2 + k + 1. Give z*o(u) - m(u).\n | 13*u**2 - 2\n | ibivibiv/math_instruct | |
What is -24020.6723 rounded to the nearest 100?\n | -24000\n | ibivibiv/math_instruct | |
Solve -16 = -6*t + 2 for t.\n | 3\n | ibivibiv/math_instruct | |
2 + 1 + 1 + -4\n | 0\n | ibivibiv/math_instruct | |
Simplify -4 + ((sqrt(110) - (-6*-1*sqrt(110) + sqrt(110))) + 2*sqrt(110)*6)/(-5*sqrt(50)/sqrt(5) - sqrt(90)/(sqrt(9)*-2)) + 2.\n | -4*sqrt(11)/3 - 2\n | ibivibiv/math_instruct | |
Suppose -i + 0*i = 2*d + 8, 5*d + 20 = i. Let 0*b + i + 2/3*b**4 - 4/3*b**2 + 2/3*b**3 = 0. Calculate b.\n | -2, 0, 1\n | ibivibiv/math_instruct |
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