instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Calculate the greatest common factor of 1576 and 12725412.\n | 788\n | ibivibiv/math_instruct | |
Suppose -5*t + 65 = 2*y, 2*y = 6*y + 4*t - 112. Is 4 + 1*(y + 0) a multiple of 16?\n | False\n | ibivibiv/math_instruct | |
Calculate (-144)/(-32)*10/45.\n | 1\n | ibivibiv/math_instruct | |
Let u = 7197 + -16437. Round u to the nearest one thousand.\n | -9000\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 582435624 and 276.\n | 276\n | ibivibiv/math_instruct | |
Suppose -7*r = -3*r. Suppose r = 4*d - 33 - 3. Calculate the smallest common multiple of 11 and d.\n | 99\n | ibivibiv/math_instruct | |
What is 67 + -71 - (0 + -6)?\n | 2\n | ibivibiv/math_instruct | |
Two letters picked without replacement from rlutuauarauu. Give prob of sequence ar.\n | 1/22\n | ibivibiv/math_instruct | |
Expand 3*g**5 - 3*g**5 + g**5 + g**5 - 4*g**5 + g**5 + (g**4 + 2*g**4 - 2*g**4)*(-g - 5 + 5) - g**4 + 3*g**4 - 129*g**5 + 105*g**5.\n | -26*g**5 + 2*g**4\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {a: 6, t: 1, b: 5, u: 2, g: 3}. What is prob of picking 1 a and 1 g?\n | 9/68\n | ibivibiv/math_instruct | |
In base 5, what is -1031 + 423?\n | -103\n | ibivibiv/math_instruct | |
Let h(a) = 38*a**2 - 243*a - 41. Suppose 897 = -42*w - 825. Let k be h(w). What is k rounded to the nearest 10000?\n | 70000\n | ibivibiv/math_instruct | |
Does 7 divide 3507?\n | True\n | ibivibiv/math_instruct | |
Simplify -4 + (sqrt(2) + sqrt(72) + sqrt(2))*5.\n | -4 + 40*sqrt(2)\n | ibivibiv/math_instruct | |
Let v(h) = 4*h. Let j(o) = -3*o + 12. Suppose 0 = 3*w + 9*w - 60. Let n be j(w). Let a(k) = -k. Let p(d) = n*a(d) - v(d). Determine p(1).\n | -1\n | ibivibiv/math_instruct | |
Suppose -4*s + 6*s = 24. What is the lowest common multiple of 1*(6 + -3 + 1) and s?\n | 12\n | ibivibiv/math_instruct | |
Is 24857563 a prime number?\n | True\n | ibivibiv/math_instruct | |
Let k be (-3)/(18 - 3) - (-16770)/(-25). Does 28 divide k/(-4) - (2 + (-36)/16)?\n | True\n | ibivibiv/math_instruct | |
In base 4, what is 2 + 23120?\n | 23122\n | ibivibiv/math_instruct | |
Convert 4b48 (base 15) to base 6.\n | 202135\n | ibivibiv/math_instruct | |
What is the tenth root of 917013885 to the nearest integer?\n | 8\n | ibivibiv/math_instruct | |
Let g(x) = -x**2 + 14*x - 2. Determine g(12).\n | 22\n | ibivibiv/math_instruct | |
Express -12*b**2 - 21*b + 4*b**2 - 14*b + 10*b**2 as v*b**2 + g + d*b and give v.\n | 2\n | ibivibiv/math_instruct | |
Let m(g) = -6 + 3*g + 7 + 19*g - 27*g. Let f(d) be the third derivative of d**5/60 - 5*d**4/6 + 5*d**3/6 - 2*d**2. Calculate -2*f(v) + 9*m(v).\n | -2*v**2 - 5*v - 1\n | ibivibiv/math_instruct | |
Sort 0, -1, 9697 in increasing order.\n | -1, 0, 9697\n | ibivibiv/math_instruct | |
Rearrange -40*q**2 + 40*q**2 - 30*q**2 + 2 to i*q + h*q**2 + b and give b.\n | 2\n | ibivibiv/math_instruct | |
Let p(f) = -13*f - 3. Let t(s) = 384*s. Give p(t(z)).\n | -4992*z - 3\n | ibivibiv/math_instruct | |
Which is the closest to 1/8? (a) -95 (b) 0.1 (c) 0.4\n | b\n | ibivibiv/math_instruct | |
Simplify (((u/(u*u**(1/5)*u)*u)/u**(-6))/((u*u*u/(u*u*u**(-1)*u*u)*u*u*u)/u**(-6)))**43 assuming u is positive.\n | u**(-688/5)\n | ibivibiv/math_instruct | |
Factor -3*d**3 + 3303*d**2 + 114903*d + 984045.\n | -3*(d - 1135)*(d + 17)**2\n | ibivibiv/math_instruct | |
Suppose 0 = -6*i + 4986 + 5688. Is i a prime number?\n | False\n | ibivibiv/math_instruct | |
Is 9501934565 a composite number?\n | True\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(15.992 + 20.427) * (-27.558 - 60.648) | -3212.3743 | ibivibiv/math_instruct | |
Find the first derivative of -7 + 3 + 5 - 5*z**3 + 6 wrt z.\n | -15*z**2\n | ibivibiv/math_instruct | |
What is the next term in -138444, -1107539, -3737940, -8860299, -17305268?\n | -29903499\n | ibivibiv/math_instruct | |
Let v(l) = -l**2 - 2*l + 4. Let u(p) = -p**3 + p - 4. Suppose c - 10 = -2*j, 4*c + 5 = c + j. Let k be u(c). Calculate v(k).\n | -4\n | ibivibiv/math_instruct | |
List the prime factors of 127919.\n | 11, 29, 401\n | ibivibiv/math_instruct | |
What comes next: 236, -956, -4234, -10642, -21224, -37024, -59086?\n | -88454\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {y: 7, r: 2, q: 4, z: 1, o: 1}. Give prob of sequence qoq.\n | 2/455\n | ibivibiv/math_instruct | |
What is the tens digit of 149?\n | 4\n | ibivibiv/math_instruct | |
Let p(t) be the first derivative of -50998*t**2 + 20*t + 21. Let n be p(-5). What is n rounded to the nearest one hundred thousand?\n | 500000\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 16935582?\n | 9\n | ibivibiv/math_instruct | |
b"What is the pth term of -540616, -540612, -540606, -540598, -540588?\n" | p**2 + p - 540618\n | ibivibiv/math_instruct | |
What is 104 minutes before 7:05 PM?\n | 5:21 PM\n | ibivibiv/math_instruct | |
Suppose 10*l - 25 = 5*l. Let i(h) be the second derivative of -h**4/12 + 2*h**3/3 + 3*h**2 + h. Calculate i(l).\n | 1\n | ibivibiv/math_instruct | |
Express -9*y - 4*y - 12*y as c + f*y and give c.\n | 0\n | ibivibiv/math_instruct | |
In base 11, what is -1 + 12594527?\n | 12594526\n | ibivibiv/math_instruct | |
Let h = -4 + 7. Let s(j) = 11*j**2. Let g(r) = 4*r**2. Let c(v) = h*s(v) - 8*g(v). Let b(u) = -7*u**2. Give b(c(z)).\n | -7*z**4\n | ibivibiv/math_instruct | |
Simplify ((sqrt(288) - (1 + sqrt(288))*-5) + sqrt(2)*1*-3*4)**2 + (sqrt(4)/sqrt(2)*-1 - (1*(0 + sqrt(2)))**2) + sqrt(4)/(sqrt(8)/sqrt(4))*-3.\n | 596*sqrt(2) + 7223\n | ibivibiv/math_instruct | |
Calculate the remainder when 951 is divided by 119.\n | 118\n | ibivibiv/math_instruct | |
Suppose -8 - 7 = -g - 3*p, -3*p + 15 = 0. Suppose 0 = 4*n - 76 - 88. Suppose 4*w - n = -2*v + 97, -5*w = g. Does 38 divide v?\n | False\n | ibivibiv/math_instruct | |
Find the first derivative of 165*m**2 - 409 wrt m.\n | 330*m\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 85 and 24565.\n | 85\n | ibivibiv/math_instruct | |
Is 42 a factor of 378?\n | True\n | ibivibiv/math_instruct | |
Solve -75*s + 136*s - 119*s + 665 = 37*s for s.\n | 7\n | ibivibiv/math_instruct | |
Round -3572420 to the nearest one hundred thousand.\n | -3600000\n | ibivibiv/math_instruct | |
Solve 916 = 42*n - 295*n + 965 + 4505 for n.\n | 18\n | ibivibiv/math_instruct | |
Let q(i) = 11*i**2 + i**3 + 27 - 4*i**2 - 4*i + 4*i**2 - 6*i. Let k be q(-12). Suppose 28 = -k*s + 5*s. What is the remainder when 221 is divided by s?\n | 11\n | ibivibiv/math_instruct | |
Solve 0 = 12*f - 30*f - 18 for f.\n | -1\n | ibivibiv/math_instruct | |
What is -490603 (base 10) in base 7?\n | -4112221\n | ibivibiv/math_instruct | |
Let l = 16 + -31. Let s = -42 + 75. What is the remainder when (48/l)/((-4)/120) is divided by s?\n | 30\n | ibivibiv/math_instruct | |
What is the second derivative of -640*u**3 + 915*u wrt u?\n | -3840*u\n | ibivibiv/math_instruct | |
What is 46.46 rounded to the nearest ten?\n | 50\n | ibivibiv/math_instruct | |
Let m(j) = j. Let t(k) = -k**2 + 4*k - 1. What is 9*m(f) - 2*t(f)?\n | 2*f**2 + f + 2\n | ibivibiv/math_instruct | |
Let w(i) = 141*i**2. Let k(o) = -5*o + 39. What is k(w(l))?\n | -705*l**2 + 39\n | ibivibiv/math_instruct | |
Collect the terms in 3*a + 7*a + 66*a**3 - 12*a**2 - 9*a + 328*a**3 + 4*a**2.\n | 394*a**3 - 8*a**2 + a\n | ibivibiv/math_instruct | |
Let v(y) = -2*y**3 - 20*y**2 + 207*y + 848. Calculate v(-15).\n | -7\n | ibivibiv/math_instruct | |
Express (c**2 + c**2 - c**2)*((2*c - 3*c + 3*c)*(-2 + 0 + 4) + 3*c - 7*c + 3*c) + 5*c**3 + 22*c**3 - 6*c**3 in the form w*c**3 + x + f*c + y*c**2 and give w.\n | 24\n | ibivibiv/math_instruct | |
What is the thousands digit of 664184441?\n | 4\n | ibivibiv/math_instruct | |
Let i = 147429 + 51466. Is i prime?\n | False\n | ibivibiv/math_instruct | |
Differentiate -4860*h*l**2 - 53*h*l - 14*h + 1680*l**2 + 7921*l with respect to h.\n | -4860*l**2 - 53*l - 14\n | ibivibiv/math_instruct | |
Let j = 1.12221 + -1.116. Round j to three decimal places.\n | 0.006\n | ibivibiv/math_instruct | |
Evaluate (-8820)/3675*(-100)/6.\n | 40\n | ibivibiv/math_instruct | |
Let g = -72 - -158. Let v = -84 + g. Solve -v*h + 4 = -3*h for h.\n | -4\n | ibivibiv/math_instruct | |
Let t be (-252)/(-4) + -4 + 9. Is t bigger than 70?\n | False\n | ibivibiv/math_instruct | |
What is the value of 1*(-2)/(-36)*1616/(-404)?\n | -2/9\n | ibivibiv/math_instruct | |
Two letters picked without replacement from lll. Give prob of picking 2 l.\n | 1\n | ibivibiv/math_instruct | |
What is 92/(-74704)*-112*(-3)/6?\n | -2/29\n | ibivibiv/math_instruct | |
(-42*(-8)/(-12))/(126/7560*-440)\n | 42/11\n | ibivibiv/math_instruct | |
Let j(o) = -o**3 - 11*o**2 - 13*o + 57. Determine j(-8).\n | -31\n | ibivibiv/math_instruct | |
Let p be -17 + 3 - (-425)/30. Suppose 0 = 3*g - 2 - 7. Which is the nearest to 2? (a) p (b) g (c) 5\n | b\n | ibivibiv/math_instruct | |
What is prob of sequence fffk when four letters picked without replacement from {k: 4, e: 3, f: 7}?\n | 5/143\n | ibivibiv/math_instruct | |
What is the units digit of 474751?\n | 1\n | ibivibiv/math_instruct | |
What is the closest to -0.2 in 13, 0.1, -2.83?\n | 0.1\n | ibivibiv/math_instruct | |
Suppose 58*i - 1175251 - 1175431 = 0. What is the hundreds digit of i?\n | 5\n | ibivibiv/math_instruct | |
How many grams are there in 1/5 of a kilogram?\n | 200\n | ibivibiv/math_instruct | |
Let d(s) = 10793 + 12*s**2 - 10793 + 2*s. Let r(u) = 203*u**2 + 35*u. Determine 70*d(g) - 4*r(g).\n | 28*g**2\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {i: 2, s: 5, x: 6}. What is prob of sequence isx?\n | 5/143\n | ibivibiv/math_instruct | |
Two letters picked without replacement from ubqoioip. Give prob of picking 1 i and 1 u.\n | 1/14\n | ibivibiv/math_instruct | |
What is the units digit of 2*(-5 - (-38)/2)?\n | 8\n | ibivibiv/math_instruct | |
Simplify -6*(3 + -5 + (sqrt(117) + sqrt(117)*3)**2 + -1 + -3 + -3)*3.\n | -33534\n | ibivibiv/math_instruct | |
Put -767, 31, 1, -1, 158 in descending order.\n | 158, 31, 1, -1, -767\n | ibivibiv/math_instruct | |
Solve -6*a + 5 + 7 = 0 for a.\n | 2\n | ibivibiv/math_instruct | |
Divide 73785757 by -4.\n | -73785757/4\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# The meaning of notation $\subset\subset$ in complex analysis
I have read the book Function Theory of Several Complex Variables of Krantz. But there is a notation the meaning of which I don't know. The notation is $\subset\... | In complex analysis, when dealing with sets, you may encounter the notation $\subset \subset$, also known as "compactly contained in." This term is used to describe a particular relationship between two sets, specifically when one set is a subset of another and any closure of the smaller set is still within the larger... | ibivibiv/math_instruct | |
(((-11820)/(-5319))/(20/3))/((-2)/(-492))\n | 82\n | ibivibiv/math_instruct | |
Does 62 divide 112811232?\n | True\n | ibivibiv/math_instruct | |
Simplify ((1*sqrt(168))/sqrt(12))/(sqrt(7) + sqrt(63)*-3).\n | -sqrt(2)/8\n | ibivibiv/math_instruct | |
Let d(p) = 27*p. Let s(a) be the second derivative of -a**5/60 + 125*a**2/2 - 94*a. Let l(w) be the first derivative of s(w). What is l(d(h))?\n | -729*h**2\n | ibivibiv/math_instruct | |
Does 559 divide 1110174?\n | True\n | ibivibiv/math_instruct |
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