instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What are the prime factors of 17823 - 21/3 - 27/(-3)?\n | 5, 23, 31\n | ibivibiv/math_instruct | |
Which is the fifth biggest value? (a) 1 (b) -1/5 (c) -3/4 (d) -0.0596 (e) 2/5\n | c\n | ibivibiv/math_instruct | |
Sort -3/2, -0.1, -5 in increasing order.\n | -5, -3/2, -0.1\n | ibivibiv/math_instruct | |
What is the value of (-15 + (-550)/(-50))*(-6)/56?\n | 3/7\n | ibivibiv/math_instruct | |
Suppose -3*o + 95 = 2*o. What is the remainder when 72 is divided by o?\n | 15\n | ibivibiv/math_instruct | |
List the prime factors of 407983.\n | 17, 103, 233\n | ibivibiv/math_instruct | |
Evaluate -1 + (7 - 4) - -2.\n | 4\n | ibivibiv/math_instruct | |
Find the common denominator of (1/(-5))/(216/(-3285)) and 67/12.\n | 24\n | ibivibiv/math_instruct | |
What is the biggest value in -2/29, 0, 7, 5?\n | 7\n | ibivibiv/math_instruct | |
Let p(i) be the third derivative of 0*i**3 + 1/30*i**5 + 1/8*i**4 + 3*i**2 + 0*i + 0. Find the second derivative of p(q) wrt q.\n | 4\n | ibivibiv/math_instruct | |
Let w(q) = 3*q - 6. Let v be w(3). What is the units digit of v*(14/6 + -1)?\n | 4\n | ibivibiv/math_instruct | |
Let s(n) = 49*n**2 + 54*n + 2. Let z(r) = -r**2 + r + 2. Suppose -11*b = -29*b - 18. Let t(g) = b*s(g) + z(g). Find the second derivative of t(l) wrt l.\n | -100\n | ibivibiv/math_instruct | |
Rearrange -k + k + 2*k**2 + (-4*k + 0*k + 0*k)*(-272*k - 1112*k - 4303*k + 1023*k - 1993*k) to the form w*k**2 + m + j*k and give w.\n | 26630\n | ibivibiv/math_instruct | |
Convert 73306.21 millilitres to litres.\n | 73.30621\n | ibivibiv/math_instruct | |
Suppose 59 = -2*u + 2959. Calculate the greatest common divisor of 100 and u.\n | 50\n | ibivibiv/math_instruct | |
What is -0.0001635149 rounded to four dps?\n | -0.0002\n | ibivibiv/math_instruct | |
Does 107 divide 19926981?\n | False\n | ibivibiv/math_instruct | |
Let z(p) = -5*p**2 + 3*p - 5. Let r(w) = -9*w**2 + 6*w - 9. Let b(g) = -4*r(g) + 7*z(g). What is b(4)?\n | 5\n | ibivibiv/math_instruct | |
List the prime factors of 36294957.\n | 3, 4032773\n | ibivibiv/math_instruct | |
Let j be (-240)/234 - 8/(-6). Is j at most 0?\n | False\n | ibivibiv/math_instruct | |
Expand 4 - 3*y**2 + 2*y**2 - 3 + (-4*y + y + y)*(-2 + 0 - 94*y + 121*y).\n | -55*y**2 + 4*y + 1\n | ibivibiv/math_instruct | |
Solve -2*m**4/11 + 142*m**3/11 + 22824*m**2/11 - 1726920*m/11 - 1749600/11 = 0.\n | -108, -1, 90\n | ibivibiv/math_instruct | |
Simplify (1 + ((sqrt(1872)*1)/sqrt(4))**2 - (sqrt(78)/(sqrt(42)/(-2*sqrt(7))) + 4)**2) + 1.\n | 16*sqrt(13) + 402\n | ibivibiv/math_instruct | |
Expand -4*l - l - 2*l + (0 + 2*l + 0)*(46 - 86 + 73).\n | 59*l\n | ibivibiv/math_instruct | |
What are the prime factors of 7004?\n | 2, 17, 103\n | ibivibiv/math_instruct | |
Calculate the common denominator of 98/(-882)*1/(-1)*30 and -53/1527.\n | 1527\n | ibivibiv/math_instruct | |
Suppose j**3/5 - 81*j**2/5 - 33*j - 83/5 = 0. Calculate j.\n | -1, 83\n | ibivibiv/math_instruct | |
What is the units digit of 2061?\n | 1\n | ibivibiv/math_instruct | |
Calculate -440.6861 + -0.16.\n | -440.8461\n | ibivibiv/math_instruct | |
b"What is the ith term of 2959, 2955, 2949, 2941, 2931?\n" | -i**2 - i + 2961\n | ibivibiv/math_instruct | |
Calculate 6231090 divided by -1246218.\n | -5\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 7 and 12.\n | 84\n | ibivibiv/math_instruct | |
What is ((-224)/(-8))/(-7)*42*(-2)/16?\n | 21\n | ibivibiv/math_instruct | |
Simplify t**32/(t**25*t) assuming t is positive.\n | t**6\n | ibivibiv/math_instruct | |
Rearrange -8*v - 7*v - 4 + 24*v to the form x + o*v and give x.\n | -4\n | ibivibiv/math_instruct | |
Suppose -s + 16 = 3*s. Let i = s + -16. Let h = -7 - i. What are the prime factors of h?\n | 5\n | ibivibiv/math_instruct | |
Calculate prob of sequence ies when three letters picked without replacement from {s: 3, l: 1, e: 1, b: 2, i: 4}.\n | 2/165\n | ibivibiv/math_instruct | |
Is 81062141 a composite number?\n | False\n | ibivibiv/math_instruct | |
A biologist is studying a population growth of bacteria that follows the Mackey-Glass equation:
dx/dt = 0.2x(t-τ) / [1 + x(t-τ)^10] - 0.1x(t)
where x(t) is the population density at time t and τ is the time delay. If the initial population density is x(0) = 0.5 and the time delay is τ = 17, what is the population den... | To find the population density at t = 30, we need to solve the Mackey-Glass equation numerically. This is because the equation is a nonlinear delay differential equation, which cannot be solved analytically. We can use numerical methods like the Euler method or the Runge-Kutta method to approximate the solution.
Here,... | ibivibiv/math_instruct | |
Suppose 2*m - 1861 = 5*s - 10*s, -s = -4*m - 381. Is s a composite number?\n | False\n | ibivibiv/math_instruct | |
Let u(l) = -43*l**2. Let c(d) be the third derivative of -d**4/24 - d**2 - 43*d. Calculate u(c(s)).\n | -43*s**2\n | ibivibiv/math_instruct | |
Suppose -y = 4*y - 10. Find the third derivative of -12*w**3 - 9*w**3 + 15*w**2 - w**3 + w**y wrt w.\n | -132\n | ibivibiv/math_instruct | |
Solve 0 = -294*z - 146*z + 12745 - 4825 for z.\n | 18\n | ibivibiv/math_instruct | |
Let n be 481/37 + 3*-3. Let g(i) = i**2. Let a(p) = 2*p**2 - 1. Let f(b) = -2*a(b) + 5*g(b). Give f(n).\n | 18\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 5026 and 542449.\n | 359\n | ibivibiv/math_instruct | |
Rearrange (0 - 2 - 2 - 2)*(2 - 1 - 2)*(-576*k - 710*k + 185*k) to y*k + r and give y.\n | -6606\n | ibivibiv/math_instruct | |
How many minutes are there between 11:26 AM and 1:42 PM?\n | 136\n | ibivibiv/math_instruct | |
Collect the terms in 0*n + 6*n + 3*n - 2*n - n.\n | 6*n\n | ibivibiv/math_instruct | |
In base 13, what is -1778 - -89b6?\n | 723b\n | ibivibiv/math_instruct | |
Convert 2122 (base 3) to base 14.\n | 51\n | ibivibiv/math_instruct | |
(126720/(-11880))/((-3)/36)\n | 128\n | ibivibiv/math_instruct | |
Let f = 535 + -267. Let s = f - 153. Calculate the highest common divisor of 46 and s.\n | 23\n | ibivibiv/math_instruct | |
Which is bigger: 27/2352745 or 1?\n | 1\n | ibivibiv/math_instruct | |
What is the value of (-4 + 10 + -4 - 7) + 3?\n | -2\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"## What Is a Fréchet Derivative?
Let $U$ and $V$ be Banach spaces (complete normed vector spaces). The Fréchet derivative of a function $f:U \to V$ at $X\in U$ is a linear mapping $L:U\to V$ such that
$f(X+E) - f(X) - L(X,E... | A fundamental concept in advanced calculus and mathematical analysis is the notion of a derivative. While most students are familiar with the basic definition of a derivative from single-variable calculus, the idea generalizes smoothly to functions between more abstract spaces known as Banach spaces. This is where the... | ibivibiv/math_instruct | |
What is the value of 40*(141/1504)/(6/8)?\n | 5\n | ibivibiv/math_instruct | |
Calculate prob of sequence eyzz when four letters picked without replacement from {z: 5, w: 3, y: 4, e: 3, x: 3}.\n | 1/306\n | ibivibiv/math_instruct | |
Let i = 3521 - 3520.9998571. What is i rounded to 4 dps?\n | 0.0001\n | ibivibiv/math_instruct | |
Suppose f + 69 = 4*f. Suppose -78 = -5*i - f. Is i prime?\n | True\n | ibivibiv/math_instruct | |
Let u = 88 + -84. Solve -a - 3*p - 7 = 0, u*a - 3*p - 32 = -0*p for a.\n | 5\n | ibivibiv/math_instruct | |
3/(3/3*9/12)\n | 4\n | ibivibiv/math_instruct | |
Convert 3.01035 days to milliseconds.\n | 260094240\n | ibivibiv/math_instruct | |
Solve -4 = 4*j - 3*k + 5, -959 = 141*j + 178*j + 2*k for j.\n | -3\n | ibivibiv/math_instruct | |
What is the lowest common multiple of 270 and 2130?\n | 19170\n | ibivibiv/math_instruct | |
Let p = 33.5 + -34. Let v = 0.06 + 1.94. Which is the closest to 2? (a) v (b) p (c) -4\n | a\n | ibivibiv/math_instruct | |
What is prob of sequence oq when two letters picked without replacement from {o: 4, e: 7, q: 4}?\n | 8/105\n | ibivibiv/math_instruct | |
Let a(m) = -11*m**2 + 99*m - 338. What is a(5)?\n | -118\n | ibivibiv/math_instruct | |
Suppose -4*h + 43 = h + n, -5*n - 37 = -3*h. Suppose -48 = h*a - 93. Solve 0 = 4*u + a*y + 35, u + 3*y + 24 = -2*u for u.\n | -5\n | ibivibiv/math_instruct | |
What are the prime factors of 874?\n | 2, 19, 23\n | ibivibiv/math_instruct | |
(-5)/40*12*320/(-40)\n | 12\n | ibivibiv/math_instruct | |
What is the result of the following expression?
58.1216 - 56.4976 | 1.6240 | ibivibiv/math_instruct | |
Convert -6 (base 13) to base 14.\n | -6\n | ibivibiv/math_instruct | |
Two letters picked without replacement from pspsopssdwpkpwspowos. What is prob of picking 2 w?\n | 3/190\n | ibivibiv/math_instruct | |
Is 413 greater than or equal to 413?\n | True\n | ibivibiv/math_instruct | |
What is the common denominator of -25/8492 and 61/3088?\n | 33968\n | ibivibiv/math_instruct | |
Simplify (((k**(-15)/k)**(-10/7))**41)**33 assuming k is positive.\n | k**(216480/7)\n | ibivibiv/math_instruct | |
Suppose 3*p = p + 24. Suppose -311 + 1 = -47*x + 113. Calculate the least common multiple of x and p.\n | 36\n | ibivibiv/math_instruct | |
What is 40646038 to the power of 1/4, to the nearest integer?\n | 80\n | ibivibiv/math_instruct | |
In base 6, what is -3132 + 101400?\n | 54224\n | ibivibiv/math_instruct | |
Does 47 divide (-3)/15 + ((-259464)/20)/(-6)?\n | True\n | ibivibiv/math_instruct | |
Let w = -1.6 - -1.6007. What is w rounded to three dps?\n | 0.001\n | ibivibiv/math_instruct | |
Which is the biggest value? (a) 4/7 (b) -12 (c) 7.30672\n | c\n | ibivibiv/math_instruct | |
Suppose 198 = 13*b - 10*b. Let t = 117 - 109. What is the remainder when 494/t - (-2 - b/(-24)) is divided by 9?\n | 7\n | ibivibiv/math_instruct | |
What is the hundreds digit of 11083?\n | 0\n | ibivibiv/math_instruct | |
What is the hundreds digit of 2617?\n | 6\n | ibivibiv/math_instruct | |
What is the difference between 29457.69063 and -1?\n | 29458.69063\n | ibivibiv/math_instruct | |
(3/26*(-144)/432)/1\n | -1/26\n | ibivibiv/math_instruct | |
Suppose 3*d**2 - 194751*d - 779052 = 0. What is d?\n | -4, 64921\n | ibivibiv/math_instruct | |
Expand (-4*r + 5*r + 0*r)*(-11*r**2 - 3*r**2 - r**2) + (-4*r**2 + 3*r**2 + 5*r**2)*(3 + r - 3).\n | -11*r**3\n | ibivibiv/math_instruct | |
Solve -1157*r - 55491 = 2157*r + 116837 for r.\n | -52\n | ibivibiv/math_instruct | |
Suppose 3008 = 2*l + 340. What are the prime factors of l?\n | 2, 23, 29\n | ibivibiv/math_instruct | |
Let u = 1 + 3. Suppose 7*s = u*s + 6. What is the third derivative of 0*z**s - 2*z**4 + 6*z**4 + z**2 + 6*z**2 wrt z?\n | 96*z\n | ibivibiv/math_instruct | |
Collect the terms in 12*k**2 + 5*k + 19*k + 55*k**2 + 10*k**2 - 91*k**2 + 10*k**2 + 8*k**2.\n | 4*k**2 + 24*k\n | ibivibiv/math_instruct | |
What is 36196.64 litres in millilitres?\n | 36196640\n | ibivibiv/math_instruct | |
What is the least common multiple of 2774790 and 3194235?\n | 274704210\n | ibivibiv/math_instruct | |
Let p(o) = -o**2. Let g(f) = -3*f - 142 + 142. Calculate p(g(x)).\n | -9*x**2\n | ibivibiv/math_instruct | |
Solve -5*i - 28 = 2*i for i.\n | -4\n | ibivibiv/math_instruct | |
Expand (981*l - 981*l + 221*l**2)*(1 + 2 - 5).\n | -442*l**2\n | ibivibiv/math_instruct | |
Calculate (-54)/30*-2*15/72.\n | 3/4\n | ibivibiv/math_instruct | |
Is 7033 a prime number?\n | False\n | ibivibiv/math_instruct |
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