instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Suppose -4*o = 4*b - 2204, 530 - 3275 = -5*o - 3*b. Let z = 1519 - o. Is z composite?\n | True\n | ibivibiv/math_instruct | |
Solve -k - 3*p + 9 = 0, 0 = -3*k - k + 2*p - 6 for k.\n | 0\n | ibivibiv/math_instruct | |
Expand (-2 + 0 + 1)*(3*q - q - 3*q) - 3*q + q + 0*q - 2*q + 0*q + 0*q + (2*q - 3*q + 0*q)*(-1 + 0 - 1) - q - 3*q + 3*q - 3*q - 2*q + 6*q + 6*q + 0*q - q.\n | 4*q\n | ibivibiv/math_instruct | |
Is 2 a factor of 2/15 + 624/45?\n | True\n | ibivibiv/math_instruct | |
Collect the terms in -85*m + 30*m - 87*m**2 + 24*m + 31*m - 37*m**2.\n | -124*m**2\n | ibivibiv/math_instruct | |
Simplify ((sqrt(170) - (6*-1*sqrt(170) - sqrt(170)))*5 + -4*sqrt(170)*2*-5)/(-1*(3*(sqrt(1000) + sqrt(1000)*-2) + sqrt(1000) + sqrt(1000)*2*3)).\n | -2*sqrt(17)\n | ibivibiv/math_instruct | |
What is the sixth root of 79946512 to the nearest integer?\n | 21\n | ibivibiv/math_instruct | |
Is 9923 composite?\n | False\n | ibivibiv/math_instruct | |
Let a = 2 - 1. Suppose -2 = -l + a. Suppose -3*b - 22 = -5*r, 1 = r - l*b - 13. Solve 0 = t - r + 4 for t.\n | -2\n | ibivibiv/math_instruct | |
Let l(b) = -2*b**2 - 20*b - 22. Give l(-10).\n | -22\n | ibivibiv/math_instruct | |
Calculate prob of sequence vv when two letters picked without replacement from {l: 2, i: 1, v: 4, y: 4}.\n | 6/55\n | ibivibiv/math_instruct | |
Which is greater: 0.5 or -417.348?\n | 0.5\n | ibivibiv/math_instruct | |
In base 15, what is -4 - 6ee0c?\n | -6ee11\n | ibivibiv/math_instruct | |
What is the value of 0 - (9 + -4 + -6)?\n | 1\n | ibivibiv/math_instruct | |
Let o(q) = -q**3 + 8*q**2 + 183*q - 4. Let g be o(-13). What is the highest common factor of g and 22?\n | 22\n | ibivibiv/math_instruct | |
0.2*11213.4\n | 2242.68\n | ibivibiv/math_instruct | |
Suppose -9 = -4*t - 3*i - 27, -i - 17 = 5*t. Let r be 316/28 + -4 + -4. Let g = t + r. Which is the biggest value? (a) g (b) 0.5 (c) -0.4 (d) -3\n | b\n | ibivibiv/math_instruct | |
Is 28463 prime?\n | True\n | ibivibiv/math_instruct | |
Collect the terms in 121*z - 238*z + 127*z.\n | 10*z\n | ibivibiv/math_instruct | |
What is the smallest value in -1333, 0.5, 12?\n | -1333\n | ibivibiv/math_instruct | |
Suppose -11 = -3*x + 1. Suppose -2*r + 690 = 2*l + 72, x*r + 1554 = 5*l. Does 47 divide l?\n | False\n | ibivibiv/math_instruct | |
Let a(v) = 6*v**2 - 2*v + 3. Let j be a(-3). Calculate the greatest common factor of j and 7.\n | 7\n | ibivibiv/math_instruct | |
Suppose 0 = -2*c, -c = -4*u + 728 - 132. Is u composite?\n | False\n | ibivibiv/math_instruct | |
What are the prime factors of 83545505?\n | 5, 16709101\n | ibivibiv/math_instruct | |
Evaluate 216/(-12) - (-24 + 18).\n | -12\n | ibivibiv/math_instruct | |
-0.9 * 1164\n | -1047.6\n | ibivibiv/math_instruct | |
Let l be (-1635)/40 - (-1)/(-8). Let c = l - -47. Solve -4*m = -6*m + c for m.\n | 3\n | ibivibiv/math_instruct | |
Does 7 divide 14?\n | True\n | ibivibiv/math_instruct | |
Let y(g) = g**3 + 8*g**2 + 3*g + 6. Let k be y(-7). Let o be k/4*10/5. What is the units digit of o/4 - (-9)/12?\n | 5\n | ibivibiv/math_instruct | |
Simplify ((o**3*o)/o*o*o)/o**(1/4)*(o/o**(3/7)*o)/(o*o**(-5/2)/o*o) assuming o is positive.\n | o**(219/28)\n | ibivibiv/math_instruct | |
Is 3553 a multiple of 19?\n | True\n | ibivibiv/math_instruct | |
Solve 0 = g - 5*f - 12, 10 = -g + 5*g - f for g.\n | 2\n | ibivibiv/math_instruct | |
Let t(c) be the first derivative of -2*c**5/45 + c**4/18 + 4*c**3/27 + 5. Find k such that t(k) = 0.\n | -1, 0, 2\n | ibivibiv/math_instruct | |
Suppose 5*z + 117 = 2*z. Let w = 58 + z. Suppose 3*d + 2*x + 34 = 5*d, 0 = -3*d + 2*x + 53. Calculate the greatest common factor of d and w.\n | 19\n | ibivibiv/math_instruct | |
Let t(y) = -338*y + 4*y**2 - 341*y - 340*y + 1019*y. Let n(h) = -1011*h. Determine n(t(z)).\n | -4044*z**2\n | ibivibiv/math_instruct | |
b"What is the ith term of -8032, -16052, -24060, -32050, -40016, -47952?\n" | i**3 - 8027*i - 6\n | ibivibiv/math_instruct | |
Find the first derivative of -2350 + 55320*u**3 - 34*u - 43*u - 27*u - 55319*u**3 wrt u.\n | 3*u**2 - 104\n | ibivibiv/math_instruct | |
Find the third derivative of 484*h**3*j**3 - 13*h**2*j**2 - 2*h*j + 7*j**3 wrt h.\n | 2904*j**3\n | ibivibiv/math_instruct | |
In base 13, what is 1 - -31?\n | 32\n | ibivibiv/math_instruct | |
Suppose -2*y + 10 = -7*y, -26 = d + 5*y. Let o be 1/((d/20)/(-4)). Find the third derivative of 318 - 3*l**2 - 318 + 3*l**o wrt l.\n | 180*l**2\n | ibivibiv/math_instruct | |
Let t be (-24)/2*((-102)/24 + 4). Let r be (-4 + t)*(0/(-1) - 4). Calculate the highest common factor of r and 16.\n | 4\n | ibivibiv/math_instruct | |
Suppose -5*l + 5*u + 95 = 0, 70 = 5*l - 4*u - 23. What is the remainder when l/2 - (-5)/(-10) is divided by 3?\n | 2\n | ibivibiv/math_instruct | |
What is the millions digit of 1574631?\n | 1\n | ibivibiv/math_instruct | |
25b994 (base 16) to base 2\n | 1001011011100110010100\n | ibivibiv/math_instruct | |
What are the prime factors of 63808?\n | 2, 997\n | ibivibiv/math_instruct | |
What is 1960 rounded to the nearest 10000?\n | 0\n | ibivibiv/math_instruct | |
Expand -41*a**5 + 77*a**2 - 148*a**2 + 71*a**2 + (18*a**5 + 9*a**5 + 11*a**5)*(2 + 12 - 3).\n | 377*a**5\n | ibivibiv/math_instruct | |
Convert 62405.74ml to litres.\n | 62.40574\n | ibivibiv/math_instruct | |
What comes next: -168, -374, -598, -840, -1100, -1378?\n | -1674\n | ibivibiv/math_instruct | |
Let b be -5 + 4 - (-5 + 1). Suppose 0 = b*k + 32 - 5. List the prime factors of 6/(-4)*48/k.\n | 2\n | ibivibiv/math_instruct | |
Let p = -67234411/2671 - -25172. Let y = p - -130864/40065. Find the common denominator of (-1)/(-8) + 18424/2112 + -7 and y.\n | 165\n | ibivibiv/math_instruct | |
Let o(m) = -7*m**2. Let j(h) = 3*h - 6*h + h. Determine j(o(b)).\n | 14*b**2\n | ibivibiv/math_instruct | |
5 drainage pipes , each draining water from a pool at the same constant rate , together can drain a certain pool in 16 days . how many additional pipes , each draining water at the same constant rate , will be needed to drain the pool in 4 days ? Lets program in Python in the response. | n0 = 5.0
n1 = 16.0
n2 = 4.0
t0 = n0 * n2
answer = t0 - n0
print(answer) | ibivibiv/math_instruct | |
Let b(m) = m**2 + m + 79. Suppose -24*k + 19*k + 2545 = 5*d, -3*k + 1543 = -d. Suppose -100*w + 81*w + k = 0. Calculate the remainder when b(0) is divided by w.\n | 25\n | ibivibiv/math_instruct | |
Sort 48, 0.3, -2/11, 0.\n | -2/11, 0, 0.3, 48\n | ibivibiv/math_instruct | |
Let r be (4/51)/(16/24). Let i = -3 + 5. Which is the nearest to 0? (a) -2/7 (b) r (c) i\n | b\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {s: 1, u: 3, o: 1, x: 2, r: 5}. Give prob of picking 1 x, 1 u, and 2 r.\n | 4/33\n | ibivibiv/math_instruct | |
Let l(j) be the first derivative of 32 - 13/30*j**3 - 2/5*j - 1/50*j**5 - 3/20*j**4 - 3/5*j**2. Solve l(x) = 0 for x.\n | -2, -1\n | ibivibiv/math_instruct | |
What is the thousands digit of (2 - (-13728)/18)*(-588)/(-56)?\n | 8\n | ibivibiv/math_instruct | |
Simplify (sqrt(90)/(-4*sqrt(3)) - sqrt(30) - (2*sqrt(210) + sqrt(210) - sqrt(210))/sqrt(7))/((3*2*sqrt(40))/(sqrt(216)/sqrt(6))).\n | -13*sqrt(3)/8\n | ibivibiv/math_instruct | |
If $(x,y)$ is a solution to the system
\begin{align*}
xy &= 6, \\
x^2 y + xy^2 + x + y &= 63,
\end{align*}find $x^2 + y^2.$ | We can rewrite the second equation as $xy(x+y) + (x+y) = 63$ and factor out $(x+y)$ to get $(xy+1)(x+y)=63$.
Since we know that $xy=6$, we can substitute to get $(6+1)(x+y)=63$.
Simplifying, we have $7(x+y)=63$, so $x+y=9$.
We are asked to find $x^2+y^2$, which we can rewrite as $(x+y)^2-2xy$.
Substituting the values w... | ibivibiv/math_instruct | |
What is the next term in 217, 313, 395, 457, 493, 497?\n | 463\n | ibivibiv/math_instruct | |
Let y(t) = 69*t + 59*t + 70*t - 245*t + 63*t. Let f(l) = -21*l. What is f(y(k))?\n | -336*k\n | ibivibiv/math_instruct | |
What is f in 3*f**4 - 747*f**3 + 45729*f**2 + 145875*f - 6187500 = 0?\n | -12, 11, 125\n | ibivibiv/math_instruct | |
Let m = -150 + -22. Let c = 177 + m. Solve c = -2*p + 3*p - 2*h, 2*p = 2*h + 6 for p.\n | 1\n | ibivibiv/math_instruct | |
Simplify (w**(1/8)/w)**(-16)*w**11/(w**5/w) assuming w is positive.\n | w**21\n | ibivibiv/math_instruct | |
Let g(y) = -6*y**3 - 2. Let s(q) = q**3 + 1. Suppose -4*f + 5 = -3*z + 4*z, -2*f + 7 = -z. Let v(t) = f*s(t) + 2*g(t). Differentiate v(l) wrt l.\n | -30*l**2\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# CIRCUIT ANALYSIS: 8 Resistors, 1 IVS, 1 Differential Op-Amp - Find Vo
1. Feb 5, 2007
### VinnyCee
1. The problem statement, all variables and given/known data
The circuit below is a differential amplifier driven by a br... | Circuit analysis is a fundamental skill in electrical engineering, and it involves applying various techniques to determine unknown voltages and currents in circuits based on known ones. This task requires a deep understanding of circuit theory, Kirchhoff's laws, Ohm's law, and other relevant equations. Let's dive int... | ibivibiv/math_instruct | |
-14361 times 74935\n | -1076141535\n | ibivibiv/math_instruct | |
Expand (622*b**2 - 300*b**2 - 304*b**2 + 3 + b**4)*(-1 + 1 - 2*b).\n | -2*b**5 - 36*b**3 - 6*b\n | ibivibiv/math_instruct | |
Expand (4 - 5*g**2 - 4 + (-1 + 0 - 1)*(-20*g + 6*g**2 + 20*g))*(-6 + 2 + 2).\n | 34*g**2\n | ibivibiv/math_instruct | |
Let a be (-24)/156 - 264/(-26). Calculate the remainder when (-13981)/(-55) + (-2)/a is divided by 51.\n | 50\n | ibivibiv/math_instruct | |
Let d(b) = 20*b**2 + 10*b + 4. Let j be d(4). What is the highest common divisor of 56 and j?\n | 28\n | ibivibiv/math_instruct | |
Suppose -3*p + 5 = 2*p. Let z be (2 + p - 4)*-1. Is 1 at most z?\n | True\n | ibivibiv/math_instruct | |
A shopkeeper forced to sell at cost price, uses a 850 grams weight for a kilogram. What is his gain percent?
Answer Choices: (A) 17.65% (B) 9% (C) 11.11% (D) 12 % (E) None of these | Lets solve the multi-choice question step by step.
Shopkeeper sells 850g instead of 1000g.
So, his gain = 1000 - 850 = 150g.
Thus, %Gain = (150 *100)/850 = 17.65%.
The answer is OPTION A | ibivibiv/math_instruct | |
Let s = 6212/15 - 414. Let g = 3470/19 - 548/3. Which is the third biggest value? (a) s (b) 0.1 (c) g\n | c\n | ibivibiv/math_instruct | |
Let s be (-2)/(-9) - (-292)/(-18). Let y be (s - -31) + 1/2*0. Solve -y = -5*l - 0*l for l.\n | 3\n | ibivibiv/math_instruct | |
Calculate prob of picking 2 b when two letters picked without replacement from {f: 9, k: 1, b: 6, a: 3}.\n | 5/57\n | ibivibiv/math_instruct | |
Let q**4/2 - 3*q**3 - 7*q**2/2 = 0. Calculate q.\n | -1, 0, 7\n | ibivibiv/math_instruct | |
Simplify (4*-1*sqrt(2)*1 + -3 + sqrt(32) + sqrt(8)/sqrt(4)*-1)**2.\n | 6*sqrt(2) + 11\n | ibivibiv/math_instruct | |
Let i(s) = -4*s + 3*s - 1 + 2*s. Let p(u) = 2*u - 2. Let l(m) = -11*i(m) + 6*p(m). Let g = 1 - -3. What is l(g)?\n | 3\n | ibivibiv/math_instruct | |
What are the prime factors of 18098?\n | 2, 9049\n | ibivibiv/math_instruct | |
What is 676 minutes after 12:27 PM?\n | 11:43 PM\n | ibivibiv/math_instruct | |
(3/156)/((((-527)/(-612))/(-31))/((-6)/27))\n | 2/13\n | ibivibiv/math_instruct | |
Is 183 a factor of 431171?\n | False\n | ibivibiv/math_instruct | |
Let a(v) = 91*v + 121. Let s(w) = 18*w + 1. Let k be s(2). Let u = -19 + k. What is the lowest common multiple of a(-1) and u?\n | 90\n | ibivibiv/math_instruct | |
Simplify c**(2/9)*c*c*c*c/(c/(c/c**2))*c**(2/17)*c*c**(-1) assuming c is positive.\n | c**(358/153)\n | ibivibiv/math_instruct | |
Suppose 4*c - 4*d = 24, 5*c = -4*d + 21 + 9. Let k be 3/c + 52/8. Let i(x) = k + 0*x - 8 - x + 7*x**2. Calculate i(-1).\n | 7\n | ibivibiv/math_instruct | |
Is 4617108521 a prime number?\n | False\n | ibivibiv/math_instruct | |
What is 211 minutes after 8:33 PM?\n | 12:04 AM\n | ibivibiv/math_instruct | |
What are the prime factors of 3926603?\n | 3926603\n | ibivibiv/math_instruct | |
Let k = 730 - 499. Let f = 31 - -2. What is the highest common divisor of f and k?\n | 33\n | ibivibiv/math_instruct | |
What is the nearest to 4/5 in 2, -8/5, 2/9, -6/7, -0.04?\n | 2/9\n | ibivibiv/math_instruct | |
What is prob of sequence gh when two letters picked without replacement from {g: 2, h: 2, v: 8}?\n | 1/33\n | ibivibiv/math_instruct | |
Put -3, 5, 6, 16, 1, -5 in increasing order.\n | -5, -3, 1, 5, 6, 16\n | ibivibiv/math_instruct | |
Let o be 1*((4 - -3) + -2). Solve -o = -3*a - 2*a for a.\n | 1\n | ibivibiv/math_instruct | |
4/5*(-25)/(-280)*-4*-1\n | 2/7\n | ibivibiv/math_instruct | |
Which is the nearest to 1/31? (a) 0.08 (b) -1/6 (c) 2\n | a\n | ibivibiv/math_instruct | |
What is 7/2 of a litre in millilitres?\n | 3500\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 163107 and 567.\n | 189\n | ibivibiv/math_instruct |
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