instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Suppose 2*f + 248*i = 251*i + 99571, 4*i = -f + 49769. Is f composite?\n | True\n | ibivibiv/math_instruct | |
Which is smaller: 1 or -778?\n | -778\n | ibivibiv/math_instruct | |
Solve 211*o - 214*o + q - 8 = 0, -5*q + 97 = 4*o for o.\n | 3\n | ibivibiv/math_instruct | |
Expand -10*l**5 - 14*l**5 + 23*l**5 + 36 + (0 + 0 - 2*l)*(-2*l**3 + 3*l**4 + 2*l**3) + (-2*l**5 + 2*l**5 + l**5)*(5 - 1 - 1).\n | -4*l**5 + 36\n | ibivibiv/math_instruct | |
Collect the terms in -985888*u**2 - 20*u + 230302*u**2 + 48*u - 26*u + 3.\n | -755586*u**2 + 2*u + 3\n | ibivibiv/math_instruct | |
What is the tens digit of 379?\n | 7\n | ibivibiv/math_instruct | |
Which is the closest to -1? (a) 0.5 (b) 3/4 (c) 4.3 (d) -4\n | a\n | ibivibiv/math_instruct | |
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"The Completion of a Measure Space
The Completion of a Measure Space
Recall from the Complete Measure Spaces page that a measure space $(X, \mathcal, \mu)$ is said to be complete if for every measurable set $E \in \mathcal P... | Now, lets delve into the concept of completing a measure space. We will explore what it means for a measure space to be complete, how to construct a larger measure space that is complete, and the significance of this completion process.
A measure space $(X,mathcal{A},\ mu)$ is said to be complete if for every measur... | ibivibiv/math_instruct | |
Calculate the common denominator of 157/30 and -49/20.\n | 60\n | ibivibiv/math_instruct | |
Let m(z) = 23*z. Let a(s) be the second derivative of 14*s**3 - 813*s. Determine a(m(x)).\n | 1932*x\n | ibivibiv/math_instruct | |
Simplify (w**0/w)**(-37)*(w**(-1))**(-18) assuming w is positive.\n | w**55\n | ibivibiv/math_instruct | |
What is eleven quarters of a tonne in kilograms?\n | 2750\n | ibivibiv/math_instruct | |
Solve -4 = 361*a - 359*a for a.\n | -2\n | ibivibiv/math_instruct | |
What is (2/8)/(119/56 + -2)?\n | 2\n | ibivibiv/math_instruct | |
Collect the terms in -t + 6*t - 2*t - t - 6*t.\n | -4*t\n | ibivibiv/math_instruct | |
Expand (-2 + 3 + 1)*(1 + 3 - 5)*(-f - f + 7*f).\n | -10*f\n | ibivibiv/math_instruct | |
What is h in 3*h**4 - 2146968*h**3 + 384111897654*h**2 + 3841357293648*h - 4225467044337 = 0?\n | -11, 1, 357833\n | ibivibiv/math_instruct | |
Which is the nearest to 0.1? (a) 1/8 (b) -189881 (c) 0.4\n | a\n | ibivibiv/math_instruct | |
Suppose 0 = 2*o - 5*h - 2080, 2*h + 1019 = 2*o - 1079. What is the highest common divisor of 5 and o?\n | 5\n | ibivibiv/math_instruct | |
Rearrange -9 + 7 + 0 - 2*x**3 + 4*x + 1 to t*x + v + i*x**3 + a*x**2 and give v.\n | -1\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {k: 2, w: 1}. Give prob of sequence wk.\n | 1/3\n | ibivibiv/math_instruct | |
Three letters picked without replacement from snnyanqyyqnaqcynyna. What is prob of sequence any?\n | 5/323\n | ibivibiv/math_instruct | |
Collect the terms in -118*m - 151*m + 559*m - 146*m - 144*m - 27*m**3.\n | -27*m**3\n | ibivibiv/math_instruct | |
Suppose 4*m = 10*m - 66. Let g(f) = -2*f**3 + 8. Let c(q) = q**3 - 3. What is m*c(w) + 4*g(w)?\n | 3*w**3 - 1\n | ibivibiv/math_instruct | |
What is the common denominator of 20/7946361 and -26/259685?\n | 39731805\n | ibivibiv/math_instruct | |
How many seconds are there in three eighths of a day?\n | 32400\n | ibivibiv/math_instruct | |
What is the cube root of 488928854 to the nearest integer?\n | 788\n | ibivibiv/math_instruct | |
What is the common denominator of -89/70 and -99/13496?\n | 67480\n | ibivibiv/math_instruct | |
Is 4413594/5 at most 882718?\n | False\n | ibivibiv/math_instruct | |
Simplify (((s**9/s)/s**8*(s/s**(2/11))**22)**(-8/9))**(17/3) assuming s is positive.\n | s**(-272/3)\n | ibivibiv/math_instruct | |
Let s = 816 + -820. Sort -2/7, 25, s, 1.\n | s, -2/7, 1, 25\n | ibivibiv/math_instruct | |
What is prob of picking 3 s when three letters picked without replacement from sss?\n | 1\n | ibivibiv/math_instruct | |
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"## Convert Cartesian To Polar Unit Vectors
http://en.wikipedia.org/wiki/Vector_fiel… The 2nd website is also helpful. it teaches you the conversion lesson and then you have problems to figure .
Spherical Unit Vectors in rela... | Let's delve into converting Cartesian unit vectors to polar unit vectors, focusing on spherical coordinate systems. This topic is essential for advanced mathematics courses and applications in physics and engineering. We will discuss definitions, derive conversion formulas, provide detailed examples, and highlight the... | ibivibiv/math_instruct | |
What is the biggest value in 7, -2, -4, -16.3, -2/13, 2/7?\n | 7\n | ibivibiv/math_instruct | |
What comes next: -28, -123, -268, -451, -660, -883, -1108, -1323?\n | -1516\n | ibivibiv/math_instruct | |
Is 7829 composite?\n | False\n | ibivibiv/math_instruct | |
What are the prime factors of 3816363915?\n | 3, 5, 7, 13, 17, 4217\n | ibivibiv/math_instruct | |
Let h = 0.164081 - 0.164. Round h to five dps.\n | 0.00008\n | ibivibiv/math_instruct | |
Let f(d) be the second derivative of d**3/6 - 11*d**2/2 - 86*d + 1. What is f(6)?\n | -5\n | ibivibiv/math_instruct | |
Is -4236 less than -0.08?\n | True\n | ibivibiv/math_instruct | |
b"What is the th term of 427109, 854188, 1281219, 1708178, 2135041, 2561784?\n" | -4*b**3 + 427107*b + 6\n | ibivibiv/math_instruct | |
Factor -5*s**4 - 1160*s**3 - 61105*s**2 + 732050*s.\n | -5*s*(s - 10)*(s + 121)**2\n | ibivibiv/math_instruct | |
What is the tens digit of ((-1)/(1/4787))/(1154/(-2308))?\n | 7\n | ibivibiv/math_instruct | |
Which is the fourth biggest value? (a) 2/11 (b) 3/4 (c) 1 (d) 0 (e) 10 (f) 65\n | b\n | ibivibiv/math_instruct | |
Let w = 10 - 7. Suppose 0*m = w*m - 27. Solve -t - 2*t = m for t.\n | -3\n | ibivibiv/math_instruct | |
Which is the closest to -69/2? (a) 2/213 (b) 5 (c) 2/9\n | a\n | ibivibiv/math_instruct | |
What is the value of 7/14*30*(-10)/(-60)?\n | 5/2\n | ibivibiv/math_instruct | |
What is next in -37895, -65394, -92893, -120392, -147891?\n | -175390\n | ibivibiv/math_instruct | |
Suppose 0 = w - 5*w + 16, 21 = l + w. Let y = 27 - l. Suppose 3*k - 8*k - 5 = 4*d, 5*d + 5*k = -y. Put d, 19, 5 in decreasing order.\n | 19, 5, d\n | ibivibiv/math_instruct | |
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"# Showing that $k | 12$ given $k$ is the order of $2$ mod $13$.
I am trying to show that $k | 12$ given $k$ is the order of $2$ mod $13$. Is it sufficient if I use Euler's theorem like this: By Euler's theorem, since (2,13) ... | You are off to a good start when it comes to showing that $k$ divides 12, given that $k$ is the order of 2 modulo 13. Your intuition regarding using Euler's Theorem is correct! However, let me provide some more details to solidify your argument.
Euler's Totient Function, denoted by $\phi(n)$, gives us the count of po... | ibivibiv/math_instruct | |
Let o(i) = -4*i - 981. Let f be o(0). Let z = f - -1391. What is the hundreds digit of z?\n | 4\n | ibivibiv/math_instruct | |
b"What is the sth term of 94, 374, 834, 1468, 2270, 3234, 4354?\n" | -s**3 + 96*s**2 - s\n | ibivibiv/math_instruct | |
Let v(h) = -2725002*h - 16. Let x(l) = -1362501*l - 8. Let s(z) = -3*v(z) + 7*x(z). Let o be s(-8). Round o to the nearest one million.\n | 11000000\n | ibivibiv/math_instruct | |
Divide -65942 by 1.\n | -65942\n | ibivibiv/math_instruct | |
Suppose 641*g = 642*g + 5*y + 10, g - 5*y - 10 = 0. Sort -3.3, -1, 2/9, 0.1, g in descending order.\n | 2/9, 0.1, g, -1, -3.3\n | ibivibiv/math_instruct | |
Multiply 85 and 154.\n | 13090\n | ibivibiv/math_instruct | |
Let c(o) = 6*o + 1. Let v be c(-14). Let i = v + 82. Which is bigger: 0.002 or i?\n | 0.002\n | ibivibiv/math_instruct | |
Calculate (((-438)/27 + 6)*9)/(-4).\n | 23\n | ibivibiv/math_instruct | |
Let f(v) be the second derivative of -14*v**3/3 - 81*v**2/2 - 147*v. Let n be f(-3). Solve -5*y + 6 = -n*y for y.\n | 3\n | ibivibiv/math_instruct | |
Convert 20 (base 6) to base 8.\n | 14\n | ibivibiv/math_instruct | |
What is -1.081875 times 0.6?\n | -0.649125\n | ibivibiv/math_instruct | |
Let o be (-90510)/(-24) - (6/(-8))/(-1). Let v = o - 3941. Let u = 127 + v. Calculate the common denominator of u and 74/9.\n | 18\n | ibivibiv/math_instruct | |
Let z(n) = -14*n**3 - 8*n - 8. Let g be (-4)/8 - (2 - 15/2). Let w(l) = -9*l**3 - 5*l - 5. What is g*z(h) - 8*w(h)?\n | 2*h**3\n | ibivibiv/math_instruct | |
What is (-22)/(-33)*(-274)/(-3425)*30/(-16)?\n | -1/10\n | ibivibiv/math_instruct | |
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"# Chapter 7 - Section 7.7 - Basics of Probability - 7.7 Exercises - Page 689: 5
The sample space is $S=\left\{(3,3), (3,2), (3,1), (2,3), (2,2), (2,1), (1,3), (1,2), (1,1)\right\}$
#### Work Step by Step
The sample space i... | Probability theory is a fundamental branch of mathematics that deals with quantifying uncertainty. It forms the backbone of many fields, including statistics, data science, engineering, and physics. One key concept in probability theory is the sample space, which is the set of all possible outcomes of a random experim... | ibivibiv/math_instruct | |
What is -22220 (base 6) in base 8?\n | -6044\n | ibivibiv/math_instruct | |
(6/5)/(-9*(-3)/(-30))\n | -4/3\n | ibivibiv/math_instruct | |
-4321 (base 5) to base 8\n | -1112\n | ibivibiv/math_instruct | |
Let q(s) = 9*s - 5. Let m be (-184)/(-44) - (-12)/(-66). What is the remainder when q(m) is divided by 8?\n | 7\n | ibivibiv/math_instruct | |
Find the second derivative of -b**2*k**2 - 2*b**2*k - 3*b**2 - 6*b*k - 999*k**3 + 63*k**2 + 15583*k wrt k.\n | -2*b**2 - 5994*k + 126\n | ibivibiv/math_instruct | |
Is -969 >= -965?\n | False\n | ibivibiv/math_instruct | |
Let o(j) = 5*j - 4. Let x be o(3). Let d(h) = h**2 - 13*h - 2. Let n be d(11). Let q = -23 - n. Which is smaller: q or x?\n | q\n | ibivibiv/math_instruct | |
Evaluate 4 - 7 - (-12 - -9).\n | 0\n | ibivibiv/math_instruct | |
Let j be (2 - 0)/(5/35). What is the highest common divisor of 56 and j?\n | 14\n | ibivibiv/math_instruct | |
Simplify ((a**(-3/5)/a)/a**(12/11))**(-6)*a**(-8)/(a/(a/a**(-4/3)*a))*(a*a*a**(2/13)*a)/a**(-2/9) assuming a is positive.\n | a**(89156/6435)\n | ibivibiv/math_instruct | |
Let s = 250 - 240. Solve 2 = 2*c + s for c.\n | -4\n | ibivibiv/math_instruct | |
Suppose -3*y + 4*o = 1 - 12, 0 = 3*o + 15. Let u(c) = c**3 + 4*c**2 + 3*c + 4. Give u(y).\n | 4\n | ibivibiv/math_instruct | |
List the prime factors of 1057.\n | 7, 151\n | ibivibiv/math_instruct | |
Solve 5*o - b + 14 = 67, 0 = -53*o + b + 581 for o.\n | 11\n | ibivibiv/math_instruct | |
Four letters picked without replacement from dfdfdddfo. Give prob of sequence ofoo.\n | 0\n | ibivibiv/math_instruct | |
Simplify ((sqrt(3600) - 1*sqrt(3600)) + sqrt(3600))/(sqrt(45)/(-2*sqrt(9))).\n | -24*sqrt(5)\n | ibivibiv/math_instruct | |
Suppose -5*a + 373 - 48 = 0. Suppose 9*f - 1066 = -72*f - f. What is the greatest common factor of f and a?\n | 13\n | ibivibiv/math_instruct | |
94127 times 3\n | 282381\n | ibivibiv/math_instruct | |
Express d**4 - 4*d**4 - 11*d**4 + (18 - 65 - 29)*(-d**3 + 2*d**4 + d**3) in the form i*d**3 + g + u*d**4 + h*d**2 + w*d and give u.\n | -166\n | ibivibiv/math_instruct | |
In base 13, what is 876 + 2?\n | 878\n | ibivibiv/math_instruct | |
Let h(s) = -2*s**3 + 70*s**2 + 87*s + 52. What is the units digit of h(36)?\n | 2\n | ibivibiv/math_instruct | |
Let t(z) = 4*z**2 - 56*z + 32. Suppose 5*g - 78 = 62. What is the units digit of t(g)?\n | 0\n | ibivibiv/math_instruct | |
Find f such that -3*f**5 - 20427*f**4/7 + 882*f**3 + 326832*f**2/7 - 13344*f = 0.\n | -973, -4, 0, 2/7, 4\n | ibivibiv/math_instruct | |
Suppose -l - 5*z + 3 = 0, -79*l + 76*l + 2*z = 8. Is 2/l + -1 + 13311 a composite number?\n | False\n | ibivibiv/math_instruct | |
Which is smaller: 1221 or 1225?\n | 1221\n | ibivibiv/math_instruct | |
What is 265 minutes after 4:21 AM?\n | 8:46 AM\n | ibivibiv/math_instruct | |
Let j = 4442 - 4431. Solve 0 = -12*i + j*i for i.\n | 0\n | ibivibiv/math_instruct | |
Let i be -1*(-792)/(-135) - (2 + (-6 - 2)). What is the fifth biggest value in i, 6/7, 1, 0.1, 1/8?\n | 0.1\n | ibivibiv/math_instruct | |
Let p(x) = -3*x**3 + x**2 - 2*x + 4. Let r(g) be the second derivative of g**5/10 - g**4/12 + g**3/3 - 3*g**2/2 + g + 17. Calculate -3*p(u) - 4*r(u).\n | u**3 + u**2 - 2*u\n | ibivibiv/math_instruct | |
Find the first derivative of 2326*i*y - 32110084*i + 1727*y wrt y.\n | 2326*i + 1727\n | ibivibiv/math_instruct | |
What is the value of (2 + -13 + 7)/26 + 835/(-65)?\n | -13\n | ibivibiv/math_instruct | |
What is 24919139 to the power of 1/2, to the nearest integer?\n | 4992\n | ibivibiv/math_instruct | |
Rearrange (45*n**2 - 8*n**3 - 45*n**2)*(-1 + 3 - 4) + 206 + n**3 - 100 - 96 to d + w*n**3 + q*n**2 + v*n and give d.\n | 10\n | ibivibiv/math_instruct | |
Simplify -3 + (4 + sqrt(252) + sqrt(112) + 0 + sqrt(112))**2.\n | 112*sqrt(7) + 1385\n | ibivibiv/math_instruct | |
Let o = 505 + -441. Let g = o - 48. Which is the smallest value? (a) -3 (b) -0.1 (c) g\n | a\n | ibivibiv/math_instruct |
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