instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Suppose 5*u + 3*t - 347 = 0, -2*t - 60 = -u + 12. What is the tens digit of u?\n | 7\n | ibivibiv/math_instruct | |
Round 1.162932 to 2 decimal places.\n | 1.16\n | ibivibiv/math_instruct | |
What are the prime factors of 415802/58 - 10*(-2)/4?\n | 2, 17, 211\n | ibivibiv/math_instruct | |
Simplify ((u*u**(-1))/u*u*u)**18*(u*(u*u*u**(-1)/u)/u*u)**(-1/2)*(u**1/(u/(u**(2/5)/u)))**(-21) assuming u is positive.\n | u**(301/10)\n | ibivibiv/math_instruct | |
Two competing gas stations are located on opposite sides of a highway, each deciding independently of the other their gas prices for the day. The price each station sets is denoted by a positive number. If they both set the same gas price, they will split the customers equally. But, if one station lowers its price, mor... | To find the Nash Equilibrium, we need to find the gas prices for station A and station B such that neither station has an incentive to change its price, given the other station's price.
First, let's find the best response for station A, given station B's price y. To do this, we need to maximize station A's profit func... | ibivibiv/math_instruct | |
Let i(x) = -x - 5. Let o(d) = d + 1. Suppose 2*k - 4*n - 10 = 0, 5*k + 4*n + 11 = 8. Calculate k*i(v) + 2*o(v).\n | v - 3\n | ibivibiv/math_instruct | |
Calculate the remainder when 332022 is divided by 10983.\n | 2532\n | ibivibiv/math_instruct | |
What is the next term in -38475894, -38475878, -38475862, -38475846, -38475830?\n | -38475814\n | ibivibiv/math_instruct | |
Solve -3663*f + 3660*f = -24 for f.\n | 8\n | ibivibiv/math_instruct | |
Evaluate (-324)/14 - (-352 - -328).\n | 6/7\n | ibivibiv/math_instruct | |
Suppose 6*u = -9*u + 22*u. Let x be 10 - ((-5)/(-1) + -2). Solve -2*z - x*z = u for z.\n | 0\n | ibivibiv/math_instruct | |
Let j = 1863.7 - 1864. What is the nearest to -3/10 in 4, 5/3, -4, j?\n | j\n | ibivibiv/math_instruct | |
Find the third derivative of -2*q**3*u**2 + 1618*q**3*u - 6*q**3 - q**2*u**2 + 263*q - 7*u**2 wrt q.\n | -12*u**2 + 9708*u - 36\n | ibivibiv/math_instruct | |
Calculate -5 - (-3 + -5 + 2 - -7).\n | -6\n | ibivibiv/math_instruct | |
In base 9, what is -371 - 32?\n | -413\n | ibivibiv/math_instruct | |
What is the nearest to 3 in -0.4, -17/18, -4?\n | -0.4\n | ibivibiv/math_instruct | |
What is the square root of 1553999 to the nearest integer?\n | 1247\n | ibivibiv/math_instruct | |
What is the tens digit of (-7 - (-2 + 0))*69/(-5)?\n | 6\n | ibivibiv/math_instruct | |
Evaluate -11 - 8 - -15 - (-5 + (-1 - -2)).\n | 0\n | ibivibiv/math_instruct | |
Work out 0.03 + -5162367.\n | -5162366.97\n | ibivibiv/math_instruct | |
Suppose -3*u - u - 10 = 2*r, 4*u + 25 = -5*r. Which is the second biggest value? (a) -0.2 (b) 4 (c) r\n | a\n | ibivibiv/math_instruct | |
Let z(t) = t**2 + 38*t + 148. Let s be z(-34). Suppose 1 = -q, x + s*q - 46 = 10*q. Suppose 0 = -2*k + 105 - 9. What is the highest common factor of x and k?\n | 48\n | ibivibiv/math_instruct | |
Suppose 50 + 75 = 25*g. Let q be 5 + -361 - (0 - g). What is q rounded to the nearest 100?\n | -400\n | ibivibiv/math_instruct | |
What is prob of picking 3 q when three letters picked without replacement from {r: 2, q: 10, j: 6}?\n | 5/34\n | ibivibiv/math_instruct | |
Suppose -c - 7 = -3*h, 3*h = -2*h + 20. Suppose 5*i + 15 = -2*l, -c*i + 0*i = 25. Suppose 11*y - 360 = l*y. What is the units digit of y?\n | 0\n | ibivibiv/math_instruct | |
Let f be 116/(-30) - (-2)/(-15). Let b(j) = -2*j - 5. Let h be b(f). Suppose 6*g - 5 = g + 4*o, h*g = -2*o + 3. Is -1/4 bigger than g?\n | False\n | ibivibiv/math_instruct | |
Let j = -1/184 + -5243/184. Let b = j - -28. What is the closest to 3 in -3, 4, b?\n | 4\n | ibivibiv/math_instruct | |
Calculate (-56)/(-10) + -2 - 3.\n | 3/5\n | ibivibiv/math_instruct | |
Sort 3, 68, 37 in increasing order.\n | 3, 37, 68\n | ibivibiv/math_instruct | |
List the prime factors of 77080341.\n | 3, 13, 1976419\n | ibivibiv/math_instruct | |
Find the common denominator of 8/1441 and -8/1179.\n | 12969\n | ibivibiv/math_instruct | |
Suppose -19*o = -15*o + 4. Let u(f) = -5*f**2 + 4*f + 2. Let l(h) = -h**2 + h. Calculate o*u(a) + 2*l(a).\n | 3*a**2 - 2*a - 2\n | ibivibiv/math_instruct | |
b"What is the nth term of 1419, 1414, 1411, 1410?\n" | n**2 - 8*n + 1426\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Groups of Order 30/C 5 x D 3
## Theorem
Let $G$ be a group of order $30$.
Let $G$ have the group presentation:
$\gen {x, y: x^{15} = e = y^2, y x y^{-1} = x^{11} }$
Then $G$ is isomorphic to the group direct product of... | We will begin by discussing groups and their properties, focusing on the concept of a group presentation and the group direct product. Afterward, we'll delve into the theorem provided, which pertains to a particular group of order 30. The proof of this theorem utilizes various aspects of group theory, including conjug... | ibivibiv/math_instruct | |
-0.3*44.51131\n | -13.353393\n | ibivibiv/math_instruct | |
What are the prime factors of 36984785?\n | 5, 797, 9281\n | ibivibiv/math_instruct | |
Expand (-3 + 3 - k)*((-1 + 3 + 0)*(3*k + 0*k - k) - 3*k + 4*k - 2*k + k - 2 + 2 - k - 4*k + 2*k)*(2*k**2 + 4 - 4).\n | -2*k**4\n | ibivibiv/math_instruct | |
What is the greatest common factor of 4020 and 2280?\n | 60\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {n: 1, s: 2, o: 2, d: 1, v: 1, x: 1}. What is prob of sequence osx?\n | 1/84\n | ibivibiv/math_instruct | |
Rearrange 18*q**3 - 5*q**3 + 10*q - 3124 - 12*q**3 + 3067 to z*q**2 + h*q**3 + j*q + i and give j.\n | 10\n | ibivibiv/math_instruct | |
Suppose -4*s + 0 + 7 = -v, 4*s = 12. Let f be 1*-9 - (6 + -6). Let u be (2/(-3))/(3/f). Solve 0*l + 4*l - u = v*q, 10 = 4*l - q for l.\n | 3\n | ibivibiv/math_instruct | |
Let v be -3 + 3 - (-3 - -5). Let w be 0/(1 + 0/1). Let t = v - w. Which is smaller: t or -1?\n | t\n | ibivibiv/math_instruct | |
Simplify -1 + -4 + (sqrt(147)*1 - sqrt(147)).\n | -5\n | ibivibiv/math_instruct | |
What is 8208.778mm in micrometers?\n | 8208778\n | ibivibiv/math_instruct | |
What is prob of picking 1 f, 1 s, and 1 p when three letters picked without replacement from sirifiprisfiisrsdsf?\n | 5/323\n | ibivibiv/math_instruct | |
Calculate the remainder when 739 is divided by ((-513)/(-6))/9*6.\n | 55\n | ibivibiv/math_instruct | |
Let k(o) = -4*o**3 + 20*o**2 + 3. Let r(p) = -11*p**3 + 59*p**2 + 10. Let q(t) = -8*k(t) + 3*r(t). Let u be q(17). Let n = 136 + u. Is n a multiple of 32?\n | False\n | ibivibiv/math_instruct | |
Let q be 52/5 + 2 + (-27)/(-45). Suppose -1684 = q*t - 17*t. What are the prime factors of t?\n | 421\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 e, 1 t, and 2 y when four letters picked without replacement from nyyrnryetererrrryyy.\n | 15/1292\n | ibivibiv/math_instruct | |
Let n = -23 + 48. Suppose 4*k - 5*i = -2*i + 27, -n = 5*i. What is the greatest common divisor of 9 and k?\n | 3\n | ibivibiv/math_instruct | |
Let z = -3 + 6. Is (z - -1) + 1/(-1) even?\n | False\n | ibivibiv/math_instruct | |
Is 72022417 composite?\n | False\n | ibivibiv/math_instruct | |
Let c = -103 + 326. List the prime factors of c.\n | 223\n | ibivibiv/math_instruct | |
Is 23798276 a multiple of 158?\n | True\n | ibivibiv/math_instruct | |
What is the square root of 4466724953 to the nearest integer?\n | 66834\n | ibivibiv/math_instruct | |
Let b = 24.9 + -24.6. What is the nearest to -0.1 in -0.13, -0.1, b?\n | -0.1\n | ibivibiv/math_instruct | |
Let i(y) = -y**2 + 9*y + 6. Let s be (0 - -15)*(-8)/(-12). Let g be i(s). Which is smaller: g or 0.2?\n | g\n | ibivibiv/math_instruct | |
Work out 403 + 10283.\n | 10686\n | ibivibiv/math_instruct | |
Is 8288499 a prime number?\n | False\n | ibivibiv/math_instruct | |
Evaluate 111/(-74)*(-4)/18.\n | 1/3\n | ibivibiv/math_instruct | |
What is the third root of 3806513 to the nearest integer?\n | 156\n | ibivibiv/math_instruct | |
Solve -q + 6 = -3*f, -3*q + 5*f = -23 + 13 for q.\n | 0\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Second partial derivative test question
Im looking at the solution for finding maximum and minimum of
$f(x,y) = xye^{-x² -y^2}$
To do so, it first finds the critical points using the second derivative, and these points a... | The second partial derivative test is a method used in multivariable calculus to determine whether a critical point of a function is a local maximum, local minimum, or a saddle point. This test involves the computation of several partial derivatives and the evaluation of their signs at the critical points. Moreover, i... | ibivibiv/math_instruct | |
Let m = 3.313 - -124.687. Which is the second biggest value? (a) m (b) 0.3 (c) 0.1\n | b\n | ibivibiv/math_instruct | |
Let d be 2/6 + 14/(-24). Let u be (-4 - 4) + (10 - (-80)/(-36)). What is the closest to d in u, -0.1, -2?\n | u\n | ibivibiv/math_instruct | |
Collect the terms in 14*j - 11*j - 5*j.\n | -2*j\n | ibivibiv/math_instruct | |
Round 5.1787078 to two decimal places.\n | 5.18\n | ibivibiv/math_instruct | |
What is -0.327 plus -1482595949?\n | -1482595949.327\n | ibivibiv/math_instruct | |
In base 12, what is -16 - -9bb92?\n | 9bb78\n | ibivibiv/math_instruct | |
What is the thousands digit of 1270?\n | 1\n | ibivibiv/math_instruct | |
How many nanoseconds are there in five quarters of a microsecond?\n | 1250\n | ibivibiv/math_instruct | |
Let b = 111253/6 - 18542. Put -17/46, b, -2 in ascending order.\n | -2, -17/46, b\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {o: 2, b: 3, d: 2, c: 2, w: 4, p: 2}. What is prob of picking 1 w and 1 c?\n | 8/105\n | ibivibiv/math_instruct | |
How many minutes are there between 10:07 PM and 3:44 AM?\n | 337\n | ibivibiv/math_instruct | |
Let i(y) = 81503*y**3 - 3*y**2 - 2*y - 1. Let k be i(3). Let f = -17632619/8 + k. Let h = 3535 + f. Find the common denominator of -19/4 and h.\n | 8\n | ibivibiv/math_instruct | |
Sort 1, 16, -2, -1, 5, -33509.\n | -33509, -2, -1, 1, 5, 16\n | ibivibiv/math_instruct | |
Suppose -12 = -5*g - 2*n, 0 = -3*g - 0*n - 4*n + 10. Suppose 2*a + 18 + g = 4*z, 0 = a - z + 5. Let u = 0.03 - -3.97. Are u and a nonequal?\n | True\n | ibivibiv/math_instruct | |
Suppose -18 = -288*l + 283*l + 22. Solve l*k - 29 = 11 for k.\n | 5\n | ibivibiv/math_instruct | |
Let s(d) = d**3 + 12*d**2 + 22*d + 79. Let o be s(-10). Is -1 at most as big as o?\n | True\n | ibivibiv/math_instruct | |
Suppose -12*j - 1433 = 3619. Let y = 433 + j. Solve y*w = 10*w - 2 for w.\n | -1\n | ibivibiv/math_instruct | |
Factor 3*c**2 + 18408*c + 28237872.\n | 3*(c + 3068)**2\n | ibivibiv/math_instruct | |
What is -37.81636 rounded to 2 dps?\n | -37.82\n | ibivibiv/math_instruct | |
Solve -p**2/7 - 2*p/7 + 3/7 = 0 for p.\n | -3, 1\n | ibivibiv/math_instruct | |
What is the common denominator of 71/12 and ((-276)/648)/(4/(-6))?\n | 36\n | ibivibiv/math_instruct | |
What is the third derivative of -1481*o**4 + 9*o**2 - 7*o wrt o?\n | -35544*o\n | ibivibiv/math_instruct | |
Let f = 6803/729 - -1/729. What is the closest to f in -1, -3, -1/10?\n | -1/10\n | ibivibiv/math_instruct | |
Let a be (2 - 12/8)*10. Suppose -5*j + 135 = -a*m + 15, 4*j - 2*m = 88. List the prime factors of j.\n | 2, 5\n | ibivibiv/math_instruct | |
Calculate prob of sequence qpj when three letters picked without replacement from {p: 1, s: 1, z: 1, h: 1, j: 1, q: 2}.\n | 1/105\n | ibivibiv/math_instruct | |
Let c = -0.08 - -48.08. Let l = c - 124. Let y = -80.3 - l. What is y rounded to the nearest integer?\n | -4\n | ibivibiv/math_instruct | |
What is five quarters of a litre in millilitres?\n | 1250\n | ibivibiv/math_instruct | |
Sort 1, -1, 40598, 5 in increasing order.\n | -1, 1, 5, 40598\n | ibivibiv/math_instruct | |
Let h(a) = 2*a**2 - 3*a - 19. List the prime factors of h(8).\n | 5, 17\n | ibivibiv/math_instruct | |
Suppose 0 = -5*u - 20 + 50. Suppose 4*q + 18 = 6, -4*y - q - 23 = 0. Put 0, y, -4, u in decreasing order.\n | u, 0, -4, y\n | ibivibiv/math_instruct | |
(-4)/(28/5)*30/150\n | -1/7\n | ibivibiv/math_instruct | |
Is 99331 prime?\n | False\n | ibivibiv/math_instruct | |
Suppose 2*z - 490 = -5*z. Let x(u) = -14*u - 22. Calculate the least common multiple of z and x(-8).\n | 630\n | ibivibiv/math_instruct | |
Let x be 2 - 5 - -6 - 4. Which is the closest to x? (a) 0.1 (b) 4 (c) -0.3\n | c\n | ibivibiv/math_instruct | |
Let v(d) = -d**3 - 8*d**2 + 2*d - 1. What is v(-8)?\n | -17\n | ibivibiv/math_instruct | |
Find b such that -2*b**2 + 12667432*b - 20057979184328 = 0.\n | 3166858\n | ibivibiv/math_instruct | |
Let m(d) be the second derivative of d**4/6 + 7*d**3/3 + 6*d**2 + 3*d + 3. Find f such that m(f) = 0.\n | -6, -1\n | ibivibiv/math_instruct |
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