instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Calculate prob of sequence sz when two letters picked without replacement from {h: 2, z: 5, s: 2}.\n | 5/36\n | ibivibiv/math_instruct | |
Three letters picked without replacement from gjppjjpnjfnyjpj. Give prob of sequence nng.\n | 1/1365\n | ibivibiv/math_instruct | |
How many centimeters are there in 57.91658 micrometers?\n | 0.005791658\n | ibivibiv/math_instruct | |
What is 1.435 rounded to 1 decimal place?\n | 1.4\n | ibivibiv/math_instruct | |
Suppose -2*z = 4*p - 187 + 41, -2*p = -5*z - 79. What is the units digit of p?\n | 7\n | ibivibiv/math_instruct | |
What is p in -189*p**3 - 663711*p**2 - 582588120*p + 175761552 = 0?\n | -1756, 19/63\n | ibivibiv/math_instruct | |
Let u = 3813/4 - 959. What is the common denominator of u and 131/18?\n | 36\n | ibivibiv/math_instruct | |
Suppose -1248 = 460*u - 464*u. Calculate the highest common divisor of u and 52.\n | 52\n | ibivibiv/math_instruct | |
Factor 1/6 + 1/2*j**2 - 1/2*j - 1/6*j**3.\n | -(j - 1)**3/6\n | ibivibiv/math_instruct | |
What is the second derivative of 238*s**5 + 322*s?\n | 4760*s**3\n | ibivibiv/math_instruct | |
Let f = 64 - 0. Is 8 a factor of f?\n | True\n | ibivibiv/math_instruct | |
b"What is the vth term of -259944, -259929, -259914, -259899, -259884?\n" | 15*v - 259959\n | ibivibiv/math_instruct | |
Collect the terms in 12*d**3 + 124*d**3 - 66*d**3 + 70*d**3.\n | 140*d**3\n | ibivibiv/math_instruct | |
What is 1243 to the power of 1/8, to the nearest integer?\n | 2\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {m: 4, u: 1, l: 1, v: 4, g: 1, x: 4}. Give prob of picking 1 g and 1 m.\n | 4/105\n | ibivibiv/math_instruct | |
Put 7, 0.03, 2, 0, -5 in descending order.\n | 7, 2, 0.03, 0, -5\n | ibivibiv/math_instruct | |
Calculate 4/(-48)*-4*(-2)/1.\n | -2/3\n | ibivibiv/math_instruct | |
What are the prime factors of 590?\n | 2, 5, 59\n | ibivibiv/math_instruct | |
b"What is the gth term of -13, -56, -129, -232?\n" | -15*g**2 + 2*g\n | ibivibiv/math_instruct | |
Simplify -5 + sqrt(60)/(sqrt(24)/sqrt(2)) + -6*(sqrt(5) - (sqrt(5) - (5 + (sqrt(5) + -1 + sqrt(5))**2) - sqrt(5) - sqrt(5)) - sqrt(5)).\n | -161 + 19*sqrt(5)\n | ibivibiv/math_instruct | |
Simplify 3 + -3 + -3*(-1*sqrt(1300) - sqrt(1300))**2*6 + 0 + 1.\n | -93599\n | ibivibiv/math_instruct | |
Sort 4183, 4, -0.3, -0.4 in descending order.\n | 4183, 4, -0.3, -0.4\n | ibivibiv/math_instruct | |
Simplify (x**(-1/10)*x**8)/((x*x**(15/4)*x)/(x*x**(9/4)*x)) assuming x is positive.\n | x**(32/5)\n | ibivibiv/math_instruct | |
Calculate 60/108*(-6)/15.\n | -2/9\n | ibivibiv/math_instruct | |
Sort 3, -2/9, 4, -1, -1/3 in ascending order.\n | -1, -1/3, -2/9, 3, 4\n | ibivibiv/math_instruct | |
Let f(n) = -235*n - 11701. Determine f(-50).\n | 49\n | ibivibiv/math_instruct | |
What is the ten millions digit of 101895530?\n | 0\n | ibivibiv/math_instruct | |
Is 31 a factor of 2790?\n | True\n | ibivibiv/math_instruct | |
Let s(m) = -9*m**2 - 17*m - 15. Let v(i) = i**2 + i + 1. Let b(w) = 2*s(w) + 14*v(w). Factor b(q).\n | -4*(q + 1)*(q + 4)\n | ibivibiv/math_instruct | |
Let f(l) be the first derivative of -416*l**3/3 - 253*l - 945. Find the first derivative of f(q) wrt q.\n | -832*q\n | ibivibiv/math_instruct | |
Solve 10*n - 3*n + 7 = 0 for n.\n | -1\n | ibivibiv/math_instruct | |
Sort 2, 5, -3, -4, 1 in ascending order.\n | -4, -3, 1, 2, 5\n | ibivibiv/math_instruct | |
Suppose -31 = -9*y + 86. Suppose 9 = 3*i + y*t - 16*t, 0 = i - 5*t + 1. Solve 0 = -i*c + 5*c + 2 for c.\n | -2\n | ibivibiv/math_instruct | |
What is 50.6728 rounded to zero dps?\n | 51\n | ibivibiv/math_instruct | |
Put -59, 3, 74163 in descending order.\n | 74163, 3, -59\n | ibivibiv/math_instruct | |
How many minutes are there between 8:06 PM and 10:45 PM?\n | 159\n | ibivibiv/math_instruct | |
Calculate 87908 divided by -1233.\n | -87908/1233\n | ibivibiv/math_instruct | |
Suppose 2*f - 59 = 1. Suppose 10 + f = 4*y. Suppose 4*s - 6 = y. What are the prime factors of s?\n | 2\n | ibivibiv/math_instruct | |
Let j be -4 + 245/60 - 5/(-60)*-4. Sort -195, -2, 1, j, -3/8 in decreasing order.\n | 1, j, -3/8, -2, -195\n | ibivibiv/math_instruct | |
Let i = -5053 + 5052. What is the second biggest value in -1/49, i, 0.04?\n | -1/49\n | ibivibiv/math_instruct | |
Let x = 53.46 - 53. Let z = x - 0.4388. What is z rounded to 2 decimal places?\n | 0.02\n | ibivibiv/math_instruct | |
Round -6286 to the nearest 1000.\n | -6000\n | ibivibiv/math_instruct | |
Let l = -753 + 753.1125. What is l rounded to 2 decimal places?\n | 0.11\n | ibivibiv/math_instruct | |
Is 1923 a prime number?\n | False\n | ibivibiv/math_instruct | |
Let y = 18 - 18. Let p(v) be the third derivative of 1/168*v**8 - v**2 + 0 + 0*v**5 + 0*v**6 + y*v + 0*v**3 + 0*v**4 + 0*v**7. Factor p(q).\n | 2*q**5\n | ibivibiv/math_instruct | |
Let n be -2 + 0 + -2*11. Let s be (-10)/n - 8/12. Let d = 1/12 + s. Which is the third biggest value? (a) d (b) 3 (c) -5\n | c\n | ibivibiv/math_instruct | |
Expand -2*h + 4*h - h - 17 + 17 - 18*h + (5*h - 5*h - h)*(1 + 3 - 5).\n | -16*h\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {e: 6, c: 4}. Give prob of sequence ccc.\n | 1/30\n | ibivibiv/math_instruct | |
Is 9753940577 a prime number?\n | True\n | ibivibiv/math_instruct | |
Expand (-5*z**2 + 3*z**2 + 0*z**2)*(-89*z + 454 - 454).\n | 178*z**3\n | ibivibiv/math_instruct | |
Suppose -2*s - 1 = 2*i + 9, -2*s = -i + 10. Suppose -561 = 7*p + 1112. Which is bigger: i or p?\n | i\n | ibivibiv/math_instruct | |
Suppose 3*z = -k + 44386, -3*k + 2*k + 44381 = 4*z. Is k composite?\n | True\n | ibivibiv/math_instruct | |
Let w be 1/(4*(-1)/(-12)). Let o be (-4)/(-1) + -2 + w. Suppose 3*i + 16 = -5*j + 2, i = -j - 2. Solve i*c + o = -3*c for c.\n | -1\n | ibivibiv/math_instruct | |
What is the value of -9 + 2 + -7 - (-16 + 32)?\n | -30\n | ibivibiv/math_instruct | |
In base 7, what is -15 + 146465?\n | 146450\n | ibivibiv/math_instruct | |
Let t(m) = -44*m - 3. Let x(r) = -86*r - 7. Calculate -7*t(j) + 3*x(j).\n | 50*j\n | ibivibiv/math_instruct | |
Calculate the remainder when 7296 is divided by 1822.\n | 8\n | ibivibiv/math_instruct | |
Suppose 0 = -n + 5*n + 5*h - 68, -5*h = 2*n - 44. Let j(m) = m**2 - 3*m - 3. Let a be j(-3). Calculate the remainder when 66/(-4)*(-20)/a is divided by n.\n | 10\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"Finding the upper tight bound of a mathematical function. (Big O)
I am trying to understand Big-$O$ notation through a book I have and it is covering Big-$O$ by using functions although I am a bit confused. The book says tha... | Now, let's unravel the mystery behind the example you provided step by step. This will help clarify your confusion regarding finding the upper bound of a given function using Big O notation.
Firstly, recall the definition of Big O notation: if f(n) and g(n) are two functions, we say that f(n) is O(g(n)), if there exi... | ibivibiv/math_instruct | |
Let u(f) = 6. Let y(x) = -2260*x - 2712. Calculate 452*u(k) + y(k).\n | -2260*k\n | ibivibiv/math_instruct | |
What is the derivative of h*n**3 - 91994*h*n*p - 2*n**3 + 13*n**2 - 5*n*p wrt h?\n | n**3 - 91994*n*p\n | ibivibiv/math_instruct | |
Find the third derivative of -336847*a**6 + 674194*a**2.\n | -40421640*a**3\n | ibivibiv/math_instruct | |
Suppose 3*u + 6 = 0, 10*u = -5*w + 9*u + 663. Let f be 2/12 - (-332)/24. Let x = w - f. What are the prime factors of x?\n | 7, 17\n | ibivibiv/math_instruct | |
Let $\mathbf{v}_0$ be a vector. The vector $\mathbf{v}_0$ is projected onto $\begin{pmatrix} 3 \\ 1 \end{pmatrix},$ resulting in the vector $\mathbf{v}_1.$ The vector $\mathbf{v}_1$ is then projected onto $\begin{pmatrix} 1 \\ X \end{pmatrix},$ resulting in the vector $\mathbf{v}_2.$ Find the matrix that takes $\mat... | To solve this problem, we need to determine the value of x, which represents the entry in the matrix that takes $\mathbf{v}_0$ to $\mathbf{v}_2$.
We know that $\mathbf{v}_0$ is projected onto $\begin{pmatrix} 3 \\ 1 \end{pmatrix}$ to get $\mathbf{v}_1$, and $\mathbf{v}_1$ is projected onto $\begin{pmatrix} 1 \\ X \end{... | ibivibiv/math_instruct | |
Let l(x) be the second derivative of -1/5*x**5 + 0 + 0*x**2 + 8/9*x**3 - 2*x - 2/9*x**4 + 1/9*x**6 - 1/63*x**7. Solve l(h) = 0 for h.\n | -1, 0, 2\n | ibivibiv/math_instruct | |
Suppose -20*y + 71 = -29. Suppose -3 - 2 = y*i + 3*r, -3*i = -2*r + 3. Sort -26, 5, i, 4 in ascending order.\n | -26, i, 4, 5\n | ibivibiv/math_instruct | |
Suppose 4*f = 17 + 7. Suppose b + f = -b. Suppose 2*o + o = 5*l + 29, l = o - 7. Let i(s) = -s**3 - 2*s + 2. Let k(u) = u**3 + u - 2. What is b*i(a) + l*k(a)?\n | -a**3 + 2*a + 2\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-39.2707 - 65.5801 | -104.8508 | ibivibiv/math_instruct | |
In base 2, what is 10011 + 11000?\n | 101011\n | ibivibiv/math_instruct | |
Let s = -0.36 + 6.36. Let v = -54 - s. Let p = -59.6 - v. Sort -2, p, -1/2, -0.2.\n | -2, -1/2, -0.2, p\n | ibivibiv/math_instruct | |
Let n = -114030 + 228063/2. Factor n*u + 3/2*u**3 + 0 - 3*u**2.\n | 3*u*(u - 1)**2/2\n | ibivibiv/math_instruct | |
Is 88165273 composite?\n | True\n | ibivibiv/math_instruct | |
(10/(-60))/(((-275)/(-90))/(-11))\n | 3/5\n | ibivibiv/math_instruct | |
Calculate the remainder when 42556 is divided by 235.\n | 21\n | ibivibiv/math_instruct | |
Three letters picked without replacement from ppkpqppbqbtpptk. What is prob of picking 2 k and 1 b?\n | 2/455\n | ibivibiv/math_instruct | |
What is next in 92, 1611, 5756, 13841, 27180, 47087, 74876?\n | 111861\n | ibivibiv/math_instruct | |
Let b be 6*(4 - (-20)/(-12)). Suppose n = 3*i - b, -3*i + 4*n = i - 16. Suppose -i*j + 184 = -76. Does 26 divide j?\n | True\n | ibivibiv/math_instruct | |
Solve 6*d - 18 = -0*d for d.\n | 3\n | ibivibiv/math_instruct | |
b"What is the hth term of -12883, -10524, -6589, -1078, 6009, 14672?\n" | 788*h**2 - 5*h - 13666\n | ibivibiv/math_instruct | |
Let k = 4 - -1. Suppose d = -o - 11, k*d + 5*o + 48 = d. Let h be ((-62)/d)/((-24)/(-84)). Solve -3*n = q + 6 + 6, 5*n = 2*q - h for q.\n | 3\n | ibivibiv/math_instruct | |
Suppose 4*a + 0*a = -4*n + 20, 0 = 5*n - 4*a + 2. Suppose s = -z + 6*z - 85, -n*z = -4*s - 52. Calculate the lowest common multiple of z and 18.\n | 144\n | ibivibiv/math_instruct | |
Let y = -454 + 454. Solve 0*o - 4 = -o, h - 3*o + 11 = y for h.\n | 1\n | ibivibiv/math_instruct | |
Let t(l) = 30*l + 5. Let r(f) = 30*f + 4. Let c(n) = -3*r(n) + 2*t(n). Is c(-4) a composite number?\n | True\n | ibivibiv/math_instruct | |
Let d = 36475/4 - 9192. Let b = d - -64. What is the common denominator of 65/32 and b?\n | 32\n | ibivibiv/math_instruct | |
What is the value of 7 + (1 - -2) + (101 - (25 + 17 + -44))?\n | 113\n | ibivibiv/math_instruct | |
Simplify (sqrt(64)/sqrt(2)*1)**2 + 3.\n | 35\n | ibivibiv/math_instruct | |
Which is the closest to 0? (a) 5 (b) 0.2 (c) 10 (d) -3\n | b\n | ibivibiv/math_instruct | |
Let t(j) = 2 - 22 - 3*j - 19. Let q be (-39 - -1)/2 - (49 - 54). Let s be t(q). Let c(b) = -b**3 + b**2 + 5*b - 2. What is c(s)?\n | -5\n | ibivibiv/math_instruct | |
Let p(i) be the first derivative of i**7/210 + 13*i**3/3 - i**2/2 + 31. Let g(n) be the second derivative of p(n). Find the first derivative of g(y) wrt y.\n | 4*y**3\n | ibivibiv/math_instruct | |
What is the next term in -2513964, -5027921, -7541866, -10055793, -12569696, -15083569?\n | -17597406\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 2880 and 61632.\n | 576\n | ibivibiv/math_instruct | |
Suppose 7*i + 180 = 11*i. Suppose -i = 12*s - 27*s. Determine v so that 18/5*v**4 + 4/5*v**2 + 0 + 22/5*v**s + 0*v = 0.\n | -1, -2/9, 0\n | ibivibiv/math_instruct | |
Round -883060 to the nearest one hundred thousand.\n | -900000\n | ibivibiv/math_instruct | |
Collect the terms in 145*j**2 - 129*j**2 + 1 + 1.\n | 16*j**2 + 2\n | ibivibiv/math_instruct | |
Let b be (3 - 0/(2/1)) + 0. Suppose -l + 1 + 8 = b*w, w + l = 1. Solve 0*h + w*h = 0 for h.\n | 0\n | ibivibiv/math_instruct | |
What is the next term in -141, -175, -209, -243?\n | -277\n | ibivibiv/math_instruct | |
Calculate (-25 - 38) + 54 + 68.\n | 59\n | ibivibiv/math_instruct | |
828/(-690) + (-9178)/(-7540)\n | 1/58\n | ibivibiv/math_instruct | |
the sum of 4 consecutive even numbers is 36 . find the sum of the squares of these numbers ? Lets write a Python program. | n0 = 36.0
t0 = n0 - 10.0
t1 = t0 - 2.0
t2 = t1 / 4.0
t3 = t2 + 2.0
t4 = t2**min(2.0, 5)
t5 = t3 + 2.0
t6 = t3**min(2.0, 5)
t7 = t5 + 2.0
t8 = t4 + t6
t9 = t5**min(2.0, 5)
t10 = t7**min(2.0, 5)
t11 = t9 + t10
answer = t11 + t8
print(answer) | ibivibiv/math_instruct | |
Calculate -1035 divided by 4.\n | -1035/4\n | ibivibiv/math_instruct |
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