instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Solve 5*v = -5*w - 0*w + 10, -2*w - 4*v - 32 = -36 for w.\n | 2\n | ibivibiv/math_instruct | |
What is the cube root of 12032 to the nearest integer?\n | 23\n | ibivibiv/math_instruct | |
Let p be (865/175 - 4) + -1. Which is the third biggest value? (a) 0 (b) p (c) 1\n | b\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"Lemma 17.5.2. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $\mathcal{F}$ be a sheaf of $\mathcal{O}_ X$-modules. Let $U \subset X$ open.
1. The support of $s \in \mathcal{F}(U)$ is closed in $U$.
2. The support of $fs$ ... | We will delve into Lemma 17.5.2, which discusses essential properties of the support of sections in sheaves of modules over a ringed space. To understand this lemma, let us first define some terms:
* **Ringed Space:** A ringed space $(X,\mathcal{O}_X)$ consists of a topological space $X$ along with a sheaf of rings $... | ibivibiv/math_instruct | |
Collect the terms in -28*m**2 + 15*m**2 - 14*m**2.\n | -27*m**2\n | ibivibiv/math_instruct | |
Let x(j) = -18*j - 124. Let y be x(-7). Suppose -y*i - 84 = -30*i. What is the smallest common multiple of i and 33?\n | 33\n | ibivibiv/math_instruct | |
Let s(j) = -j. Let f(g) = 74*g - 50. Determine f(s(r)).\n | -74*r - 50\n | ibivibiv/math_instruct | |
What is the second derivative of s**3*v**2 - 1368*s**3*v + 17*s**2*v + 2872521*s*v**2 + 3*v + 15 wrt v?\n | 2*s**3 + 5745042*s\n | ibivibiv/math_instruct | |
Let a(z) = 7*z**2 + 7*z - 33. List the prime factors of a(8).\n | 3, 157\n | ibivibiv/math_instruct | |
Sort 0, 0.4, -3, -5 in decreasing order.\n | 0.4, 0, -3, -5\n | ibivibiv/math_instruct | |
Solve 1586 = 35*n + 431 for n.\n | 33\n | ibivibiv/math_instruct | |
What is the tens digit of 16579084?\n | 8\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 9 and 228.\n | 684\n | ibivibiv/math_instruct | |
What is the product of 0.1 and -353179?\n | -35317.9\n | ibivibiv/math_instruct | |
Let m be 1/(-15)*(-310)/93. Let r = -42563/424 + -715/53. Let f = r - -114. Which is the fourth smallest value? (a) f (b) 1/11 (c) m (d) 0.16\n | c\n | ibivibiv/math_instruct | |
Find the third derivative of -2730306*g*l**3*t + 2*g*l**3 + 93004*g*t - 9*l**3*t**2 + 187*l**2*t - l*t**2 wrt l.\n | -16381836*g*t + 12*g - 54*t**2\n | ibivibiv/math_instruct | |
Let g(t) = t - 6. Suppose 0*k + 5*k = 2*j - 51, 0 = j - 2*k - 23. Calculate the smallest common multiple of g(j) and 3.\n | 21\n | ibivibiv/math_instruct | |
Let k(r) be the second derivative of r**6/30 + r**5/60 - r**4/12 - r**3/18 - 6*r. Factor k(m).\n | m*(m - 1)*(m + 1)*(3*m + 1)/3\n | ibivibiv/math_instruct | |
Let p be (-42)/(-7) + (2 - -18). What is the closest to -5/8 in -1, 2, p?\n | -1\n | ibivibiv/math_instruct | |
Expand 4 - 4 + 2*u**4 + (-2*u**2 - 3*u**2 + 3*u**2)*(-2*u**2 - 5*u**2 - u**2).\n | 18*u**4\n | ibivibiv/math_instruct | |
Is 37429767283 a prime number?\n | True\n | ibivibiv/math_instruct | |
Is 3645 a multiple of 5?\n | True\n | ibivibiv/math_instruct | |
Evaluate -84 - -45 - -260 - 43 - 50.\n | 128\n | ibivibiv/math_instruct | |
Which is the third biggest value? (a) -1 (b) 0.4 (c) 1/4 (d) -5/4 (e) -4 (f) 9/2\n | c\n | ibivibiv/math_instruct | |
Which is the closest to 1? (a) 16/13 (b) 0.2 (c) -4 (d) 4 (e) 258/13 (f) -1.4\n | a\n | ibivibiv/math_instruct | |
In base 6, what is 1322 + -10?\n | 1312\n | ibivibiv/math_instruct | |
Simplify sqrt(27) + sqrt(27)*-2 - 6*sqrt(3)*-3.\n | 15*sqrt(3)\n | ibivibiv/math_instruct | |
Is 0 equal to 1/677?\n | False\n | ibivibiv/math_instruct | |
Let s(t) be the second derivative of 5*t**4/3 - 29*t**3/6 - 19*t. Find the second derivative of s(f) wrt f.\n | 40\n | ibivibiv/math_instruct | |
Let m(w) = 142*w**2 - 4098*w - 575. Determine m(29).\n | 5\n | ibivibiv/math_instruct | |
Let b(q) = q**3 + 2*q**2 - 236*q - 1094. Give b(-5).\n | 11\n | ibivibiv/math_instruct | |
Let r be (3/(-3))/(2*5/(-50)). Sort 3/8, 28, r in decreasing order.\n | 28, r, 3/8\n | ibivibiv/math_instruct | |
What is 36 minutes after 3:17 AM?\n | 3:53 AM\n | ibivibiv/math_instruct | |
In base 7, what is -6304216 - 4?\n | -6304223\n | ibivibiv/math_instruct | |
Let c(d) = -3*d - 4*d + 1 + 6*d + 58 - d**2. Let a = 0 - 0. Is 22 a factor of c(a)?\n | False\n | ibivibiv/math_instruct | |
What is next in 6726, 13131, 19540, 25953, 32370?\n | 38791\n | ibivibiv/math_instruct | |
What is the result of the following expression?
8.9619 * (-91.1784 % 53.4661) | 141.1840 | ibivibiv/math_instruct | |
Let c be (12/4 + -23)/(1*-2). Suppose -2*b = 2*b, -4*b + c = 2*a. Suppose a*g - 1 = -5*v - 11, 0 = 4*v + 5*g + 5. What is the smallest value in -6/23, -1, v?\n | v\n | ibivibiv/math_instruct | |
Expand (3 + 15*y**2 - 3)*((1 + 1 + 1)*(-y**2 + 5 - 5) + (-10*y + 3 - 3)*(0*y + y + y)).\n | -345*y**4\n | ibivibiv/math_instruct | |
Is (54/9)/((-2)/(-37)) a composite number?\n | True\n | ibivibiv/math_instruct | |
Calculate -3410580 divided by -6.\n | 568430\n | ibivibiv/math_instruct | |
What is the tens digit of 22750?\n | 5\n | ibivibiv/math_instruct | |
Differentiate -2*h**2*u**4 + 2*h**2 + 11*h*u**4 + 179 wrt u.\n | -8*h**2*u**3 + 44*h*u**3\n | ibivibiv/math_instruct | |
Let y = -1456673553683.000000297 + 1456673553015. Let g = y + 668. What is g rounded to seven decimal places?\n | -0.0000003\n | ibivibiv/math_instruct | |
How many kilograms are there in 207.3331 milligrams?\n | 0.0002073331\n | ibivibiv/math_instruct | |
Let m = -1005162.599935 - -1005169. Let p = 5 + -11.4. Let o = m + p. What is o rounded to five dps?\n | 0.00007\n | ibivibiv/math_instruct | |
Simplify (((o**4/o)/(o*o**6))/(o**6*o*o)**(-25))**(-1) assuming o is positive.\n | o**(-196)\n | ibivibiv/math_instruct | |
Simplify -6*(-2 + -2*sqrt(2448) + -5 + sqrt(2448) + 5*(2 + sqrt(2448)) + sqrt(2448) + 1 + -2)**2.\n | -367224 - 1440*sqrt(17)\n | ibivibiv/math_instruct | |
Let n be 528/(-200)*-30 - ((-76)/20 - -3). Solve -33*w = n + 151 for w.\n | -7\n | ibivibiv/math_instruct | |
What is the hundreds digit of 33842?\n | 8\n | ibivibiv/math_instruct | |
What is the product of 82.62 and 0.5?\n | 41.31\n | ibivibiv/math_instruct | |
Does 532 divide 552748?\n | True\n | ibivibiv/math_instruct | |
Which is smaller: 6/29 or -1?\n | -1\n | ibivibiv/math_instruct | |
Solve 4*z + 962*p - 958*p + 24 = 0, 33 = -4*z - p for z.\n | -9\n | ibivibiv/math_instruct | |
Solve -85 = -14*m - 243 + 32 for m.\n | -9\n | ibivibiv/math_instruct | |
b"What is the fth term of -57, -55, -53, -51, -49?\n" | 2*f - 59\n | ibivibiv/math_instruct | |
Calculate ((-68)/(-1122))/((48/21)/(3/(-7))).\n | -1/88\n | ibivibiv/math_instruct | |
Let k = -2589002982390/461 - -5616054179. Let i = k - -17016789652/3909741. Let q = i - 17/257. What is the common denominator of 35/39 and q?\n | 429\n | ibivibiv/math_instruct | |
Is -283297 < 2?\n | True\n | ibivibiv/math_instruct | |
Let l = 5.409 + -5.408996577. What is l rounded to 6 dps?\n | 0.000003\n | ibivibiv/math_instruct | |
Calculate 468 + -469 - (-48 - (3 - (2 - 4))).\n | 52\n | ibivibiv/math_instruct | |
Let c(j) = j**3 - 58*j**2 - 2*j + 130. Calculate c(58).\n | 14\n | ibivibiv/math_instruct | |
Simplify (l**10*l**10/l)/(l**(-1)/l**(-4)) assuming l is positive.\n | l**16\n | ibivibiv/math_instruct | |
Let k be 26 + (-4)/14 + (-416)/112. Let y be (-4)/k - (-600)/275. Solve y - 27 = -5*r for r.\n | 5\n | ibivibiv/math_instruct | |
What is 3792/(-237)*(-6)/2208?\n | 1/23\n | ibivibiv/math_instruct | |
Suppose 3*o = -4*o + 2121. Is o a prime number?\n | False\n | ibivibiv/math_instruct | |
Let s(w) = -w**3 + 11*w**2 + 13*w + 3. Let n be s(12). Suppose -2*b = b - n. Solve 2*j + 3*x - 7 = 0, 4*x + 4 = b*j - 2 for j.\n | 2\n | ibivibiv/math_instruct | |
Solve 0 = 39*q - 26*q - 117 for q.\n | 9\n | ibivibiv/math_instruct | |
Is 44167905569 composite?\n | False\n | ibivibiv/math_instruct | |
Calculate (-68)/357*9*14/(-44).\n | 6/11\n | ibivibiv/math_instruct | |
Solve -37*d = 36 - 221 for d.\n | 5\n | ibivibiv/math_instruct | |
Is 47124 a multiple of 201?\n | False\n | ibivibiv/math_instruct | |
Let a = 134 + -85. What is the greatest common factor of a and 1?\n | 1\n | ibivibiv/math_instruct | |
Let s = -33153 + 33154. Solve s = 4*r - 19 for r.\n | 5\n | ibivibiv/math_instruct | |
Let y(w) = w**2 - 3*w - 8. Suppose 0*c + c + 4 = -5*q, -3*q = 3*c - 12. Calculate the remainder when (1 + 1)/(2/28) is divided by y(c).\n | 8\n | ibivibiv/math_instruct | |
What is 0.1225616t in nanograms?\n | 122561600000000\n | ibivibiv/math_instruct | |
What is the square root of 628342 to the nearest integer?\n | 793\n | ibivibiv/math_instruct | |
Suppose t - 9231733 = -30*t + 5778777. What is t rounded to the nearest 100000?\n | 500000\n | ibivibiv/math_instruct | |
What is the thousands digit of 241920?\n | 1\n | ibivibiv/math_instruct | |
-142 (base 15) to base 12\n | -1bb\n | ibivibiv/math_instruct | |
What is 149823 rounded to the nearest 10000?\n | 150000\n | ibivibiv/math_instruct | |
Suppose 3*v = -4*v. Solve -f + v*f = -4 for f.\n | 4\n | ibivibiv/math_instruct | |
Expand (-535*m - 36*m + 59*m)*(m**2 + 0*m**2 - 3*m**2)*(-m + 0*m + 2*m).\n | 1024*m**4\n | ibivibiv/math_instruct | |
Suppose -13*h + 14*h = -85. Let i = -83 - h. Calculate the smallest common multiple of i and 30.\n | 30\n | ibivibiv/math_instruct | |
Let y = -1 - -1. Let x = -2880/1807 + 21/13. Let z = -1417/1251 + x. Is z bigger than y?\n | False\n | ibivibiv/math_instruct | |
Sum 4 and 5261.\n | 5265\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {i: 4, q: 6, k: 5}. Give prob of sequence kkq.\n | 4/91\n | ibivibiv/math_instruct | |
Sort -729537, 0, -4.\n | -729537, -4, 0\n | ibivibiv/math_instruct | |
Suppose 2*x + 3*r = -2*r + 34, x + r = 23. Solve 4*b - 2*y = -6, -2*b - x = 5*y + 6 for b.\n | -4\n | ibivibiv/math_instruct | |
Let t = -2.6 + 0.6. Which is the closest to 1/4? (a) -0.5 (b) -5 (c) t\n | a\n | ibivibiv/math_instruct | |
What is the eighth root of 12843757 to the nearest integer?\n | 8\n | ibivibiv/math_instruct | |
In base 6, what is -2 + -3141?\n | -3143\n | ibivibiv/math_instruct | |
What is the third smallest value in -4, 0.1, -0.111, 3, -8/5?\n | -0.111\n | ibivibiv/math_instruct | |
Let g(v) = 3*v**2 - 187*v - 625. What is g(75)?\n | 2225\n | ibivibiv/math_instruct | |
Suppose v**4 - 24981*v**3 + 207966801*v**2 - 576552694951*v - 3466808371734 = 0. What is v?\n | -6, 8329\n | ibivibiv/math_instruct | |
Does 13 divide (-16)/(-440)*-5 + 7726/22?\n | True\n | ibivibiv/math_instruct | |
In base 12, what is 46 - -b?\n | 55\n | ibivibiv/math_instruct | |
Rearrange -9 + 62*p**3 - 18 - 11 - 3*p + 40 + 0*p to q*p**3 + x*p**2 + k*p + s and give s.\n | 2\n | ibivibiv/math_instruct | |
Let t(k) = -k**3 + 9*k**2 - 9*k + 7. Let q be t(7). Suppose -4*d + 80 = -4*z - 8, q = 3*d + 3*z. Solve o - 5*j + 5 = -d, -2*o - 10 = -j for o.\n | -3\n | ibivibiv/math_instruct | |
In base 5, what is -1 + 2320043?\n | 2320042\n | ibivibiv/math_instruct |
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