instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Collect the terms in -343514458200*o + 28*o**2 + 343514458200*o.\n | 28*o**2\n | ibivibiv/math_instruct | |
Let b = 23864/3 - 7944. Let g(y) = -y**3 + 5*y**2 - 4*y. Let h be g(3). Factor -h*p**2 + b*p + 8/3.\n | -2*(p - 2)*(9*p + 2)/3\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 240 and 240.\n | 240\n | ibivibiv/math_instruct | |
Let h = -42608 - -221091. Is h composite?\n | True\n | ibivibiv/math_instruct | |
Is 821175899 composite?\n | False\n | ibivibiv/math_instruct | |
What is prob of sequence ww when two letters picked without replacement from ppwpwp?\n | 1/15\n | ibivibiv/math_instruct | |
Let q(i) be the first derivative of i**3/3 - 6*i**2 + 13*i + 1. Let r be q(11). Let h(l) = -l**3 - 6*l**r - 5*l + 0 + 0 + 3. Give h(-5).\n | 3\n | ibivibiv/math_instruct | |
Calculate the remainder when 421 is divided by 13.\n | 5\n | ibivibiv/math_instruct | |
Put together 2325 and -60.\n | 2265\n | ibivibiv/math_instruct | |
Let g be -115 + 112 - (-2 + -18 + 1). Solve 204 = -g*y - 18*y for y.\n | -6\n | ibivibiv/math_instruct | |
Calculate the common denominator of -65/86114 and -11/49.\n | 602798\n | ibivibiv/math_instruct | |
Product of -5 and 0.43.\n | -2.15\n | ibivibiv/math_instruct | |
Express -o + o + 2*o as c + i*o and give i.\n | 2\n | ibivibiv/math_instruct | |
Simplify v**8/(v**(1/5)*v) assuming v is positive.\n | v**(34/5)\n | ibivibiv/math_instruct | |
Put 2, 10, -19, 5, -3, 13, -8 in decreasing order.\n | 13, 10, 5, 2, -3, -8, -19\n | ibivibiv/math_instruct | |
The ratio of two natural numbers is 5:6. If a certain number is added to both the numbers, the ratio becomes 7:8. If the larger number exceeds the smaller number by 10, find the number added?
Answer Choices: (A) 10 (B) 87 (C) 20 (D) 72 (E) 74 | Lets think about the multi-choice question.
Let the two numbers be 5x and 6x.
Let the number added to both so that their ratio becomes 7:8 be k.
(5x + k)/(6x + k) = 7/8
42x = 7k => k = 2x.
6x - 5x = 10 => x = 10
k = 2x = 20.
The answer is C | ibivibiv/math_instruct | |
How many millimeters are there in 3/10 of a centimeter?\n | 3\n | ibivibiv/math_instruct | |
Let l = 5951.6229 + -5952. Let m = -0.0219 + l. Round m to 1 decimal place.\n | -0.4\n | ibivibiv/math_instruct | |
In base 9, what is 1 + 21825322?\n | 21825323\n | ibivibiv/math_instruct | |
What is next in -823, -820, -817?\n | -814\n | ibivibiv/math_instruct | |
b"What is the rth term of 160194090, 320388177, 480582264, 640776351, 800970438, 961164525?\n" | 160194087*r + 3\n | ibivibiv/math_instruct | |
Let l be (-27)/(-5) + 6/(-15). Let b(o) = l*o**3 - 4*o**3 + 6 - 14*o**2 + o + 20*o**2. Calculate b(-6).\n | 0\n | ibivibiv/math_instruct | |
Calculate -29*6/(-1740) - ((-955)/(-50))/1.\n | -19\n | ibivibiv/math_instruct | |
Calculate (5892/(-11784))/((2 - 2/4)/(6/89)).\n | -2/89\n | ibivibiv/math_instruct | |
What is 972.5706 days in hours?\n | 23341.6944\n | ibivibiv/math_instruct | |
What is 10637 rounded to the nearest 100?\n | 10600\n | ibivibiv/math_instruct | |
What is the smallest value in 94, 1, -0.3, 4?\n | -0.3\n | ibivibiv/math_instruct | |
Let b(d) = -2*d + 1. Let h be b(4). What is the smallest value in h, 4, 0.4?\n | h\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {f: 1, e: 1, h: 1, a: 1, j: 1}. Give prob of sequence fj.\n | 1/20\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {c: 3, k: 1, z: 4}. Give prob of picking 1 c and 1 z.\n | 3/7\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-38.2393 / 22.4531 | -1.7031 | ibivibiv/math_instruct | |
Is 27563 prime?\n | False\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {i: 2, j: 6}. Give prob of sequence jji.\n | 5/28\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 1712 and 26943028?\n | 428\n | ibivibiv/math_instruct | |
Suppose -2 = -2*x + 3*s, 3*x + 0*x - 4 = 4*s. Suppose -2*h + 4*i - 14 = 0, -7*h = -6*h - i + x. Which is bigger: -2/485 or h?\n | -2/485\n | ibivibiv/math_instruct | |
In base 14, what is bd - 55c3a?\n | -55b5b\n | ibivibiv/math_instruct | |
What is the second derivative of 3*u**3 - 368315*u**2 + 491670*u?\n | 18*u - 736630\n | ibivibiv/math_instruct | |
-3699206166 - -0.011\n | -3699206165.989\n | ibivibiv/math_instruct | |
Solve -2*s - 4*h + 20 = 0, 12*s + 3*h = 15*s + 6 for s.\n | 2\n | ibivibiv/math_instruct | |
In base 14, what is d + -4d443?\n | -4d434\n | ibivibiv/math_instruct | |
Calculate 339/(-7)*87/7569 - 112/(-784).\n | -12/29\n | ibivibiv/math_instruct | |
Let c(t) = t**2 - 3645*t - 66240. What is c(-18)?\n | -306\n | ibivibiv/math_instruct | |
What is the closest to 0.1 in -57, -1/70, -0.1?\n | -1/70\n | ibivibiv/math_instruct | |
Calculate prob of picking 2 u, 1 n, and 1 a when four letters picked without replacement from yvuaauuuuyvvvnu.\n | 2/91\n | ibivibiv/math_instruct | |
-40 divided by 15\n | -8/3\n | ibivibiv/math_instruct | |
Let g be 7/(((-60)/(-18))/(-10)). What is the hundreds digit of 7464/18 + g/(-9)?\n | 4\n | ibivibiv/math_instruct | |
Suppose -10*v + 6*v + 16 = 0. Solve -3*o + 1 = 5*d, -v*d - o + 0*o = 2 for d.\n | -1\n | ibivibiv/math_instruct | |
Let g = -40043572 + 27633572. What is g rounded to the nearest one million?\n | -12000000\n | ibivibiv/math_instruct | |
Convert -164 (base 11) to base 2.\n | -10111111\n | ibivibiv/math_instruct | |
Is 7844 a factor of 1111887000?\n | True\n | ibivibiv/math_instruct | |
Let i = 0.63 - -3.37. Let r = -2.2 + 2. What is the smallest value in r, i, -1?\n | -1\n | ibivibiv/math_instruct | |
Let g(b) = -8*b**2 - 14*b + 5. Let v(i) = -9*i**2 - 15*i + 6. Calculate -6*g(y) + 5*v(y).\n | 3*y**2 + 9*y\n | ibivibiv/math_instruct | |
What is (-1)/6*6/(-4)*12?\n | 3\n | ibivibiv/math_instruct | |
Suppose -326 = -2*g + 324. Let a be 3/(-1) + g/117. Put a, 4, -0.3 in descending order.\n | 4, a, -0.3\n | ibivibiv/math_instruct | |
Which is greater: -71968 or -71922?\n | -71922\n | ibivibiv/math_instruct | |
Suppose 7*b - 3*h = 100852 + 151845, -2*b = 4*h - 72238. List the prime factors of b.\n | 79, 457\n | ibivibiv/math_instruct | |
Let y = -9881 + 9879. Which is the third biggest value? (a) 4 (b) y (c) -1.46\n | b\n | ibivibiv/math_instruct | |
Solve 32*p - 1647 + 2443 = 1308 for p.\n | 16\n | ibivibiv/math_instruct | |
Simplify 0 + 1 + sqrt(108) + 1 + 4 + -1*sqrt(48)*-5.\n | 6 + 26*sqrt(3)\n | ibivibiv/math_instruct | |
Which is the nearest to -2/7? (a) -124 (b) 1/13 (c) -3/7 (d) 0.04\n | c\n | ibivibiv/math_instruct | |
Put 4/5, 4, -13142, 1, -0.73 in ascending order.\n | -13142, -0.73, 4/5, 1, 4\n | ibivibiv/math_instruct | |
Let q = 198 + 1756. Is q a prime number?\n | False\n | ibivibiv/math_instruct | |
What is the ten millions digit of 18645976?\n | 1\n | ibivibiv/math_instruct | |
Which is the closest to -1? (a) 3 (b) -0.03 (c) -4\n | b\n | ibivibiv/math_instruct | |
What is the nearest to -828 in 1/5, 5, 18/11, 1?\n | 1/5\n | ibivibiv/math_instruct | |
What is 2789 to the power of 1/3, to the nearest integer?\n | 14\n | ibivibiv/math_instruct | |
In base 7, what is 463 - 1?\n | 462\n | ibivibiv/math_instruct | |
Solve -7 = 5*a + 8 for a.\n | -3\n | ibivibiv/math_instruct | |
What is (560 + -524)*(33/9 + -4) + 1899/159?\n | -3/53\n | ibivibiv/math_instruct | |
In base 16, what is -3 - -16?\n | 13\n | ibivibiv/math_instruct | |
What is 11762368 rounded to the nearest 1000?\n | 11762000\n | ibivibiv/math_instruct | |
Let z(v) = -v**2 - 12*v + 68. What are the prime factors of z(-12)?\n | 2, 17\n | ibivibiv/math_instruct | |
Let h(a) be the second derivative of -7*a**5/50 - 67*a**4/3 - 5312*a**3/5 + 4608*a**2/5 - 4931*a. Factor h(q).\n | -2*(q + 48)**2*(7*q - 2)/5\n | ibivibiv/math_instruct | |
Simplify ((v**(2/9)/v)/((v/v**(-2/17))/v))/(v**(-1/4))**(-2/139) assuming v is positive.\n | v**(-38239/42534)\n | ibivibiv/math_instruct | |
Is -14/43 at most 1?\n | True\n | ibivibiv/math_instruct | |
Let o = -89231051/15640 + 96988/17. Find the common denominator of -127/168 and o.\n | 19320\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Partial-Fraction Decomposition
So I was doing some integrals and ran across this one: $$\int{\frac{3x+1}{x^2+4x+4}}dx=\int{\frac{3x+1}{(x+2)(x+2)}}dx$$
Of course, I started decomposing the fraction and immediately realize... | In calculus, partial fraction decomposition is a technique used to break down complex rational functions into simpler ones, making integration easier. This method involves expressing a single fraction as the sum of several fractions, where the denominators are simplified expressions compared to the original denominato... | ibivibiv/math_instruct | |
Expand (u + u**2 - u - 2*u**3)*((3 - 3 - 2)*(-6 + 8 + 8) - 208 - 337 + 436).\n | 258*u**3 - 129*u**2\n | ibivibiv/math_instruct | |
How many minutes are there between 9:21 AM and 11:16 AM?\n | 115\n | ibivibiv/math_instruct | |
Simplify ((y*y/(y*y*y/(y**16*y)*y*y*y))**(-1/53)/(y**(-3)*y**(1/15)))**(46/5) assuming y is positive.\n | y**(98302/3975)\n | ibivibiv/math_instruct | |
Three letters picked without replacement from llllll. Give prob of sequence lll.\n | 1\n | ibivibiv/math_instruct | |
What is the value of ((-30)/1863*(-3)/(-2))/(13815/(-16578))?\n | 2/69\n | ibivibiv/math_instruct | |
Evaluate (-19)/(152/47)*(-112)/14.\n | 47\n | ibivibiv/math_instruct | |
Simplify x/x**17*x*x**22 assuming x is positive.\n | x**7\n | ibivibiv/math_instruct | |
Simplify 1*((sqrt(252) - -1*sqrt(252)) + -4 + ((sqrt(252) + (sqrt(252) + 0)**2)*-3 - sqrt(252))) - -2*(1*(sqrt(252) + -3)*3)**2.\n | -660*sqrt(7) + 3938\n | ibivibiv/math_instruct | |
Simplify ((m*m/(m/(m**(-2/15)/m*m))*m)/(m*m**(-9)*m))/(m**13/(m/(m/(m/(m*(m*m/((m/(m*m/(m/(m*m**15)*m)*m)*m)/m))/m*m)*m)))) assuming m is positive.\n | m**(-317/15)\n | ibivibiv/math_instruct | |
Suppose 6 = 3*n, 4*n + 0*n = -5*j + 8. What is the nearest to -4 in j, -0.2, 2/15?\n | -0.2\n | ibivibiv/math_instruct | |
Let v be 14/(4 - -3) + 293. Let i = 495 - v. What is the hundreds digit of i?\n | 2\n | ibivibiv/math_instruct | |
Let l = 56 - 59.1. Let g = -3 - l. Let c be 22/8 - 2/(-8). Is c greater than g?\n | True\n | ibivibiv/math_instruct | |
Simplify sqrt(20) - ((sqrt(20) - -1*sqrt(20)) + -1).\n | -2*sqrt(5) + 1\n | ibivibiv/math_instruct | |
Sort -0.2, 0.4, -1/7, 56.\n | -0.2, -1/7, 0.4, 56\n | ibivibiv/math_instruct | |
Let y(t) = -11*t**3 + 6*t + 6. Let n(i) = 2*i**3 + i**2 + i + 1. Let x(v) = -8*v**3 + v**2 + 6*v + 6. Let r(u) = -n(u) + x(u). Give -6*r(c) + 5*y(c).\n | 5*c**3\n | ibivibiv/math_instruct | |
Is 161091729 a multiple of 15?\n | False\n | ibivibiv/math_instruct | |
Evaluate 2 + (-1 - -9) + (-22 - -16).\n | 4\n | ibivibiv/math_instruct | |
Calculate -203 divided by -30505.\n | 203/30505\n | ibivibiv/math_instruct | |
5590 divided by -1118\n | -5\n | ibivibiv/math_instruct | |
Which is bigger: -2092 or -2091?\n | -2091\n | ibivibiv/math_instruct | |
Factor 5*i**3/4 + 13*i**2/4 - 13*i/2 + 2.\n | (i - 1)*(i + 4)*(5*i - 2)/4\n | ibivibiv/math_instruct | |
Calculate prob of picking 2 k and 1 v when three letters picked without replacement from nnvkkksrnrk.\n | 2/55\n | ibivibiv/math_instruct | |
Suppose 15 = -0*t + t + 3*l, l - 33 = -5*t. Suppose -p - 4*n = -t, -n = -p - 3 + 4. Find j, given that 4*j**p + j + 2*j - 5*j - 5*j**2 = 0.\n | -2, 0\n | ibivibiv/math_instruct |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.