instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Let i be (-9680)/(-35) + 3/7. Suppose 4*j - 103 = i. What is the greatest common divisor of j and 19?\n | 19\n | ibivibiv/math_instruct | |
What is the second derivative of 2935*m**4 - 13*m**3 - 23*m**2 - 4175437*m?\n | 35220*m**2 - 78*m - 46\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 b and 1 o when two letters picked without replacement from {b: 11, o: 3, j: 4, q: 1}.\n | 11/57\n | ibivibiv/math_instruct | |
What is the result of the following expression?
89.501 / 46.065 | 1.9429 | ibivibiv/math_instruct | |
Simplify (d**8*d)**(-1/27)*(d**(5/4))**38 assuming d is positive.\n | d**(283/6)\n | ibivibiv/math_instruct | |
What is the cube root of 5528069861 to the nearest integer?\n | 1768\n | ibivibiv/math_instruct | |
Solve 89*j - 267 = 21*j + 481 for j.\n | 11\n | ibivibiv/math_instruct | |
What is 49.14479 rounded to one decimal place?\n | 49.1\n | ibivibiv/math_instruct | |
Solve 3*z - 27 = -5*b, -4196*b + 4224*b + 2*z = -2*z + 100 for b.\n | 3\n | ibivibiv/math_instruct | |
In the city, there is a block of flats. This block has 12 floors. Half of the floors have 6 apartments and the other half have x apartments. One apartment can accommodate a maximum of 4 residents. What is the maximum number of residents that can live in this block of flats?
If we know the answer to the above question i... | We know that half of the floors have 6 apartments, so the number of apartments on these floors is (12/2) * 6 = 36.
The other half of the floors have x apartments, so the number of apartments on these floors is (12/2) * x = 6x.
The total number of apartments in the block of flats is 36 + 6x.
Each apartment can accommoda... | ibivibiv/math_instruct | |
Let k be (-9)/(72/16)*(-7 - 2). Solve 4*s - 10*s = k for s.\n | -3\n | ibivibiv/math_instruct | |
Find the common denominator of 206/28 + (-98)/(-196) and -3 + 5 + 172/(-18).\n | 63\n | ibivibiv/math_instruct | |
Which is the nearest to -1/3? (a) -1/3 (b) -1 (c) -0.1 (d) 4\n | a\n | ibivibiv/math_instruct | |
Solve 20 = -40*o + 35*o, 3*o - o = -16*x - 2*o + 32 for x.\n | 3\n | ibivibiv/math_instruct | |
How many minutes are there between 3:38 PM and 2:57 AM?\n | 679\n | ibivibiv/math_instruct | |
What is (60/7)/((-5406)/(-12614))?\n | 20\n | ibivibiv/math_instruct | |
Does 59 divide 32865?\n | False\n | ibivibiv/math_instruct | |
Is -1 < -44/197?\n | True\n | ibivibiv/math_instruct | |
If there are seven distinct points on the circumference of a circle, how many different triangles can be formed if each vertex must be one of these seven points? | To form a triangle, we need to choose 3 points from the 7 distinct points on the circumference of the circle.
The number of ways to choose 3 points from a set of 7 is given by $\binom{7}{3} = \frac{7!}{3!4!} = 35$.
Therefore, there are $\boxed{35}$ different triangles that can be formed.The answer is: 35 | ibivibiv/math_instruct | |
Calculate prob of picking 1 i and 1 m when two letters picked without replacement from {m: 2, c: 5, i: 3}.\n | 2/15\n | ibivibiv/math_instruct | |
What is 7/4 of a microgram in nanograms?\n | 1750\n | ibivibiv/math_instruct | |
What is -4750 (base 9) in base 12?\n | -2060\n | ibivibiv/math_instruct | |
Suppose -n + 3 = 7. Let b(c) = 2*c - 3. Let m be b(-4). Let o = n - m. Is o composite?\n | False\n | ibivibiv/math_instruct | |
Let r = 831175/36 - 23088. Which is the nearest to 0? (a) 4 (b) -0.5 (c) r\n | c\n | ibivibiv/math_instruct | |
Suppose 4*s + 5 - 25 = 0, 4*i = -s + 605. Let t be (2/3)/(i/(-45)). Let k = 201 + -2209/11. Which is the third smallest value? (a) t (b) -7/3 (c) k\n | c\n | ibivibiv/math_instruct | |
Simplify ((sqrt(240)*-1)/sqrt(12))/((-1*sqrt(40))/sqrt(10) - sqrt(4)).\n | sqrt(5)/2\n | ibivibiv/math_instruct | |
-633 divided by -18\n | 211/6\n | ibivibiv/math_instruct | |
Suppose 15 = -21*x + 26*x. Find the third derivative of -49*f**2 - 5 + 14*f**3 - 12*f**x + 5 wrt f.\n | 12\n | ibivibiv/math_instruct | |
Is 1680837799 prime?\n | False\n | ibivibiv/math_instruct | |
Put 107, 9, 5, -2, 0, 2 in decreasing order.\n | 107, 9, 5, 2, 0, -2\n | ibivibiv/math_instruct | |
How many millilitres are there in 13/5 of a litre?\n | 2600\n | ibivibiv/math_instruct | |
Let g(m) be the second derivative of m**2 + 6*m + 0 + 1/6*m**3 + 1/12*m**4 - 2/5*m**5. What are the prime factors of g(-2)?\n | 2, 17\n | ibivibiv/math_instruct | |
What is -11ac7e (base 16) in base 13?\n | -317289\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 y, 1 v, 1 o, and 1 w when four letters picked without replacement from {w: 1, y: 1, o: 1, v: 2}.\n | 2/5\n | ibivibiv/math_instruct | |
Let u = 41 - 36. Let v(g) = 4*g**2 - 3*g. What are the prime factors of v(u)?\n | 5, 17\n | ibivibiv/math_instruct | |
Simplify u**1/(u**(-7/3)/u) assuming u is positive.\n | u**(13/3)\n | ibivibiv/math_instruct | |
Calculate 49 divided by 332.\n | 49/332\n | ibivibiv/math_instruct | |
Let y(t) = t**3 - t**2 - 34*t + 6. Determine y(0).\n | 6\n | ibivibiv/math_instruct | |
Let v = 551 - 546. Sort 4, 22, -2, v in ascending order.\n | -2, 4, v, 22\n | ibivibiv/math_instruct | |
Let h(u) be the second derivative of u**4/12 - 7*u**2/2 - u. Suppose -21*k = -11*k + 60. Does 25 divide h(k)?\n | False\n | ibivibiv/math_instruct | |
What is the ten millions digit of 1593238400?\n | 9\n | ibivibiv/math_instruct | |
Let b = 268 + -264. Suppose -3*t + 474 = -3*m, b*t - m - 4*m - 629 = 0. Is t a multiple of 24?\n | False\n | ibivibiv/math_instruct | |
What is the lowest common multiple of 8 and 110?\n | 440\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# I cannot prove that if f(x) is convex on [a,b]
I cannot prove that if $$\displaystyle{f{{\left({x}\right)}}}$$ is convex on $$\displaystyle{\left[{a},{b}\right]}$$ then
$$\displaystyle{f{{\left({\frac{{{a}+{b}}}{{{2}}}}\ri... | The statement presented in the initial text snippet is an application of Jensen's Inequality, which holds true when dealing with a convex function. Before delving into Jensen's Inequality and its significance within this context, let us first understand what it means for a function to be convex.
A real-valued functio... | ibivibiv/math_instruct | |
Let l(j) be the third derivative of j**4/8 + j**2. Let q(k) be the first derivative of -k**3/3 + 70. What is q(l(t))?\n | -9*t**2\n | ibivibiv/math_instruct | |
Let u(c) = c**3 - 2*c**2 + c + 2. Let v be u(2). Suppose i - 274 = -4*h, -v*i - 79 = -h - 2. What is the tens digit of h?\n | 6\n | ibivibiv/math_instruct | |
Suppose 0 = -2*g - 0*g + 3*u - 1, g = 4*u - 3. Let w = 195.4 - 995.4. Let p = 800.01 + w. Which is the closest to g? (a) -2/9 (b) p (c) -2\n | b\n | ibivibiv/math_instruct | |
Suppose -4*w = -11*w - 7. Let p be (-6)/33*(-1)/w. Let l = 3 + 1. Put 0.4, p, l in increasing order.\n | p, 0.4, l\n | ibivibiv/math_instruct | |
Solve -5*t + 5*a = 0, -a - 221 = -4*t - 212 for t.\n | 3\n | ibivibiv/math_instruct | |
Round -0.0000401022193 to 7 dps.\n | -0.0000401\n | ibivibiv/math_instruct | |
Let y(r) = -1130*r + 53. Let g = 89 - 64. Calculate the remainder when y(0) is divided by g.\n | 3\n | ibivibiv/math_instruct | |
What is the units digit of 6652?\n | 2\n | ibivibiv/math_instruct | |
Let b(s) = -24*s. Let n(x) be the first derivative of x**2/2 - 385. Determine -5*b(j) - 90*n(j).\n | 30*j\n | ibivibiv/math_instruct | |
What is the tens digit of 8426?\n | 2\n | ibivibiv/math_instruct | |
Sort -17, 10, 4, -25, -2, 1.\n | -25, -17, -2, 1, 4, 10\n | ibivibiv/math_instruct | |
b"What is the zth term of -346, -314, -280, -244, -206?\n" | z**2 + 29*z - 376\n | ibivibiv/math_instruct | |
Express -8857*n + 17710*n - 8854*n + 8968*n**2 in the form w*n + x*n**2 + l and give x.\n | 8968\n | ibivibiv/math_instruct | |
Let c(a) = a + 177. Let x be c(-13). Let u be (41/x)/(-1*4). Which is smaller: u or -9/4?\n | -9/4\n | ibivibiv/math_instruct | |
Is -0.161 > -0.6?\n | True\n | ibivibiv/math_instruct | |
Let k(o) = -o - 31. Let s be k(0). Let b = s + 169. What are the prime factors of b?\n | 2, 3, 23\n | ibivibiv/math_instruct | |
Expand (3*s**2 + 3*s**2 - 4*s**2 + (0 - s + 0)*(-5*s + s + 5*s))*(-17 + 20 - 12) + 4*s**2 - 5*s**2 - 2*s**2.\n | -12*s**2\n | ibivibiv/math_instruct | |
Let o = -779/3 - -261. What is the smallest value in 4, -2/7, 5, o?\n | -2/7\n | ibivibiv/math_instruct | |
Let j be ((-6)/4)/((-9)/48). Suppose 7*c - j = 3*c. Solve 2*a - 18 = -c*r, -3*r + 23 = a + a for a.\n | 4\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-4.8276 / 22.6446) % (-92.1937 % 46.7205) | 1.0341 | ibivibiv/math_instruct | |
What are the prime factors of 27014?\n | 2, 13, 1039\n | ibivibiv/math_instruct | |
Let j(u) = -4*u**2 - 130*u + 224. Let s be j(-34). Solve 22*k = 26*k + s for k.\n | -5\n | ibivibiv/math_instruct | |
(15/75)/((-8)/(-5))\n | 1/8\n | ibivibiv/math_instruct | |
Calculate ((-3)/18)/(2/(-9)).\n | 3/4\n | ibivibiv/math_instruct | |
List the prime factors of 320658747.\n | 3, 2389, 44741\n | ibivibiv/math_instruct | |
Let f be 0/(0 + (-16)/4). Suppose -3*p - 5*v = 9, f = p + 4*v - 2*v + 4. Suppose -p*s + 78 = s. Is s a multiple of 13?\n | True\n | ibivibiv/math_instruct | |
Let f(t) = 169*t**2 + 25*t - 7. Is f(-12) prime?\n | True\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 3057 and 85169039.\n | 1019\n | ibivibiv/math_instruct | |
Divide 24 by 6.\n | 4\n | ibivibiv/math_instruct | |
Let o(b) = b**2 + 4*b + 19. Let x be o(-9). Solve -x*z + 70*z = 0 for z.\n | 0\n | ibivibiv/math_instruct | |
What is 305 minutes before 1:28 AM?\n | 8:23 PM\n | ibivibiv/math_instruct | |
Let u(s) be the third derivative of -s**10/75600 + s**6/360 - s**5/60 - 3*s**2. Let g(n) be the third derivative of u(n). Differentiate g(f) wrt f.\n | -8*f**3\n | ibivibiv/math_instruct | |
Express (l + 3*l - 2*l)*(-l + l - 4*l**2) + 2*l**3 - 2*l**3 + 2*l**3 - 10*l - 4*l**3 + 10*l as p*l**3 + v*l**2 + s*l + n and give p.\n | -10\n | ibivibiv/math_instruct | |
Suppose 5*h - 4*h + 1 = 0, 4*c = -4*h + 512. Is 3 a factor of c?\n | True\n | ibivibiv/math_instruct | |
What is the greatest common factor of 87 and 609?\n | 87\n | ibivibiv/math_instruct | |
Let i = 1 + 4. Suppose -i*q + 15 = -2*q. Solve -1 + q = 4*u for u.\n | 1\n | ibivibiv/math_instruct | |
Evaluate (0 - 3 - 0)*((-2664)/(-324) + -8).\n | -2/3\n | ibivibiv/math_instruct | |
List the prime factors of 445510040.\n | 2, 5, 131, 85021\n | ibivibiv/math_instruct | |
Suppose 6 = m + 3. Suppose -m - 33 = -4*r. Suppose -3*a = -0*a - 4*u - r, a + 3*u - 3 = 0. Does 3 divide a?\n | True\n | ibivibiv/math_instruct | |
Calculate prob of picking 3 t when three letters picked without replacement from {z: 3, t: 11}.\n | 165/364\n | ibivibiv/math_instruct | |
Suppose -5*t - 7*d + 4*d - 2 = 0, t - 3*d + 4 = 0. Let k(v) = -v + 6. Let w be k(7). What is the units digit of (w + t/(-2))/((-4)/136)?\n | 7\n | ibivibiv/math_instruct | |
What are the prime factors of 18678680?\n | 2, 5, 71, 6577\n | ibivibiv/math_instruct | |
b"What is the fth term of 11, 6, -9, -40, -93?\n" | -f**3 + f**2 - f + 12\n | ibivibiv/math_instruct | |
In base 9, what is -2 - 508116?\n | -508118\n | ibivibiv/math_instruct | |
Is 7280 a multiple of 13?\n | True\n | ibivibiv/math_instruct | |
What is 2114985191 to the power of 1/2, to the nearest integer?\n | 45989\n | ibivibiv/math_instruct | |
Let t(j) = -327*j - 37. List the prime factors of t(-3).\n | 2, 59\n | ibivibiv/math_instruct | |
A company adopts a Cournot model to decide how much output to produce. The inverse demand function for its product is given as P=150-3Q. The companys cost function is C(Q)=10Q+20. There is only one other firm in the market with identical cost structure. Determine the optimal quantity of output that the company should p... | To find the optimal quantity of output that the company should produce to maximize its profit, we need to first find the reaction functions for both firms. The Cournot model assumes that each firm chooses its output level, taking the output level of the other firm as given.
Let Q1 be the output of the first firm and Q... | ibivibiv/math_instruct | |
What is the units digit of -3 - -6 - (-250 + 5 + 0)?\n | 8\n | ibivibiv/math_instruct | |
Solve 37 = -4*a + 4*x + 9, a + 5*x - 5 = 0 for a.\n | -5\n | ibivibiv/math_instruct | |
What is the third derivative of -4*a**6 + 92*a**5 + 501*a**2 wrt a?\n | -480*a**3 + 5520*a**2\n | ibivibiv/math_instruct | |
Simplify (-6*(2 + -2*(0 + sqrt(153)) - (sqrt(153) + 0 + sqrt(153) + 4 + (3*(sqrt(153) - (-1 + sqrt(153) - sqrt(153))) - sqrt(153)))))**2.\n | 6480*sqrt(17) + 199188\n | ibivibiv/math_instruct | |
Solve -4*a = 64*y - 51*y + 60, -20 = 4*a + 3*y for a.\n | -2\n | ibivibiv/math_instruct | |
What is the smallest value in 0.2999, -9, -65?\n | -65\n | ibivibiv/math_instruct | |
What is the value of (((-20)/282)/(-10))/((119/204)/(21/6))?\n | 2/47\n | ibivibiv/math_instruct | |
Let r(d) = 3*d**2 - 20*d - 5. Let h(v) = 2*v**2 - 13*v - 3. Give -8*h(z) + 5*r(z).\n | -z**2 + 4*z - 1\n | ibivibiv/math_instruct |
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