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 5181 and 264.\n | 33\n | ibivibiv/math_instruct | |
Let f(b) = 0*b - 4*b + 8*b - 4*b**3 + 3. List the prime factors of f(-2).\n | 3\n | ibivibiv/math_instruct | |
Round 0.00000577425414 to 7 decimal places.\n | 0.0000058\n | ibivibiv/math_instruct | |
Express -249*u**2 + 1 + 10*u + 2*u - 12*u as r*u**2 + v + w*u and give v.\n | 1\n | ibivibiv/math_instruct | |
Let n = -78 + 83. Let o(v) = -2*v**2 + 16*v - 27. Let f be o(n). Let g = 4 - f. Solve 4*i + 5*a - 7 + g = 0, -2 = -3*i - 5*a for i.\n | 4\n | ibivibiv/math_instruct | |
What is the value of (-4)/((-56)/35)*2?\n | 5\n | ibivibiv/math_instruct | |
Is 1563093269 a prime number?\n | True\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 572 and 104.\n | 52\n | ibivibiv/math_instruct | |
Evaluate (-336)/40*(-5030)/306327.\n | 4/29\n | ibivibiv/math_instruct | |
Let j = -51/5 + 143/15. What is the nearest to 0 in 3, j, -1/2, 0.1?\n | 0.1\n | ibivibiv/math_instruct | |
What is the remainder when 106 is divided by (-234)/(-6) - (-1 + 4 - 1)?\n | 32\n | ibivibiv/math_instruct | |
Divide -7874 by -1210.\n | 3937/605\n | ibivibiv/math_instruct | |
What is the common denominator of 115/254496 and -91/11568?\n | 254496\n | ibivibiv/math_instruct | |
Let q = 17/24 + -3/8. Let l(x) be the first derivative of -2*x + q*x**3 + 2*x**2 - 1. What is l(-4)?\n | -2\n | ibivibiv/math_instruct | |
Is -2215 less than 1?\n | True\n | ibivibiv/math_instruct | |
Suppose n = 6*n - 25. Suppose 0 = -0*y + n*y - 20. Which is greater: 6 or y?\n | 6\n | ibivibiv/math_instruct | |
Let f be (-42)/(-21) + 1 + 2. Let m(i) = 14*i**2 - 16*i + 57. Is 29 a factor of m(f)?\n | False\n | ibivibiv/math_instruct | |
Let v = -1 - 1. Let g be 54/(-3)*v/3. Suppose 0 = -0*p - 2*p - 2*q + 218, 3*q - 3 = 0. What is the highest common factor of g and p?\n | 12\n | ibivibiv/math_instruct | |
What is prob of picking 2 g, 1 c, and 1 d when four letters picked without replacement from {c: 6, y: 2, e: 1, g: 2, d: 5}?\n | 3/182\n | ibivibiv/math_instruct | |
Determine b so that 735*b**4 + 1002*b**3 + 330 + 66*b**2 - 522 - 798*b**2 - 686*b - 202*b + 75*b**5 = 0.\n | -8, -2, -2/5, 1\n | ibivibiv/math_instruct | |
Solve -210 = 43*u - 73*u for u.\n | 7\n | ibivibiv/math_instruct | |
Let l be 14/((462/12)/11). Let s(x) = -4*x**2 + 4*x. Let u(b) = 9*b**2 - 7*b. Calculate l*u(j) + 7*s(j).\n | 8*j**2\n | ibivibiv/math_instruct | |
1 divided by 1022\n | 1/1022\n | ibivibiv/math_instruct | |
Collect the terms in 24*i**2 + 21*i**2 - 86*i**2 + 22*i**2 + 18*i**2.\n | -i**2\n | ibivibiv/math_instruct | |
Let x(k) = -9*k + 83. Let y be x(12). Let v = 2382 - y. Is v composite?\n | True\n | ibivibiv/math_instruct | |
Let b = -229.4555 + -0.7345. Round b to zero decimal places.\n | -230\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-67.472 % -19.243) - 32.383 | -42.1260 | ibivibiv/math_instruct | |
Is 854875093 composite?\n | True\n | ibivibiv/math_instruct | |
Let s = -13 - -13.3. Let k = -1.7 - s. Which is the nearest to k? (a) 2/5 (b) -1 (c) -0.3\n | b\n | ibivibiv/math_instruct | |
Round -1665.035197 to the nearest ten.\n | -1670\n | ibivibiv/math_instruct | |
Sort -19, -5, -5862/7, -0.056.\n | -5862/7, -19, -5, -0.056\n | ibivibiv/math_instruct | |
Expand (-104*l + 212*l + 256*l**4 - 108*l)*(-26 + 2*l + 26).\n | 512*l**5\n | ibivibiv/math_instruct | |
Collect the terms in 178204 - 534601 + 178196 - 444*z + 178201.\n | -444*z\n | ibivibiv/math_instruct | |
Is 515 a multiple of 149?\n | False\n | ibivibiv/math_instruct | |
Let d = 8 + -6. Suppose f = -2, 5*v + 222*f - 221*f = 13. Solve 1 = v*u - d*u for u.\n | 1\n | ibivibiv/math_instruct | |
Sort -4, 0, -29, 1304 in decreasing order.\n | 1304, 0, -4, -29\n | ibivibiv/math_instruct | |
Solve 33*y - 152 = 104*y - 5*h + 477, 0*h = 4*y + 2*h + 40 for y.\n | -9\n | ibivibiv/math_instruct | |
Round 0.00003298042 to 7 dps.\n | 0.000033\n | ibivibiv/math_instruct | |
Simplify ((d/(d/d**(-1/7))*d/(((d/(d**(-13/4)*d))/d)/d))/(d**10/d**(1/7)))**(-4/23) assuming d is positive.\n | d**(41/23)\n | ibivibiv/math_instruct | |
Let v(s) = s**3 + 9*s**2 + 9*s + 12. Let l be v(-8). Suppose l*n = -n - 25, 10 = -p - 4*n. Calculate the greatest common divisor of p and 25.\n | 5\n | ibivibiv/math_instruct | |
Is 7666673 a composite number?\n | True\n | ibivibiv/math_instruct | |
Rearrange 13799*h**2 - 14122*h**2 + 0*h**3 + 12*h**3 - 4*h**3 - 2*h**3 to the form a + b*h**2 + v*h + z*h**3 and give z.\n | 6\n | ibivibiv/math_instruct | |
Does 4762 divide 518622903?\n | False\n | ibivibiv/math_instruct | |
Factor 2*v**2/15 - 206*v/15 + 176.\n | 2*(v - 88)*(v - 15)/15\n | ibivibiv/math_instruct | |
Let p(d) be the second derivative of d**3/3 + 4*d. Let w(q) = -3*q. Calculate w(p(s)).\n | -6*s\n | ibivibiv/math_instruct | |
211341 (base 5) to base 4\n | 1232320\n | ibivibiv/math_instruct | |
What is the next term in -35143, -140397, -315821, -561415, -877179, -1263113?\n | -1719217\n | ibivibiv/math_instruct | |
Which is the nearest to 1? (a) -60/17 (b) 3 (c) 28 (d) 3/7 (e) -0.38 (f) 1/6\n | d\n | ibivibiv/math_instruct | |
Let g(u) = -u - 1. Let k(v) be the first derivative of -9*v**2/2 - 8*v + 4770. Let h be 2/7 - 834/(-21). Give h*g(i) - 5*k(i).\n | 5*i\n | ibivibiv/math_instruct | |
Sort 177, 1/3, 2 in decreasing order.\n | 177, 2, 1/3\n | ibivibiv/math_instruct | |
Let o = 2/18461 + 295366/92305. Factor -o*d**3 + 48/5*d**2 + 32/5 - 64/5*d + 2/5*d**4.\n | 2*(d - 2)**4/5\n | ibivibiv/math_instruct | |
If $a \text{ Y } b$ is defined as $a \text{ Y } b = a^2 - 2ab + b^2$, what is the value of $3 \text{ Y } 2$? | Substituting $a=3$ and $b=2$ into the definition, we have $3 \text{ Y } 2 = 3^2 - 2(3)(2) + 2^2 = 9 - 12 + 4 = \boxed{1}$.
The answer is: 1 | ibivibiv/math_instruct | |
Express 3669 + 2*t**2 - 20783 + 2015 + 4*t - 4*t - 2*t**2 + (-2 + 0 + 0)*(3 + t**2 - 3) in the form c*t + d*t**2 + f and give f.\n | -15099\n | ibivibiv/math_instruct | |
Let b = -2609 + 4944. What is the tens digit of b?\n | 3\n | ibivibiv/math_instruct | |
What is 120 minutes before 2:23 AM?\n | 12:23 AM\n | ibivibiv/math_instruct | |
What is -4*(-450)/840*-1*7?\n | -15\n | ibivibiv/math_instruct | |
Let h be 1 - (24/(-284) + 1). Let j = -100/497 - h. Sort j, -0.1, 5 in ascending order.\n | j, -0.1, 5\n | ibivibiv/math_instruct | |
Let z(b) = b**3 - 14*b**2 + 12*b + 9. Let s be z(13). Let u(w) = -w**2 - 5*w + 2. What is the remainder when 22 is divided by u(s)?\n | 4\n | ibivibiv/math_instruct | |
Suppose 4*d - 7 = 13. Suppose -36 = -4*r + 4*a, -a + d*a + 23 = 3*r. Is r a multiple of 13?\n | True\n | ibivibiv/math_instruct | |
Express -178*s**3 - 5*s**2 - 81*s**3 + 38*s**4 - 8*s + 3*s**2 + 256*s**3 in the form q*s + f*s**3 + b*s**4 + t*s**2 + o and give f.\n | -3\n | ibivibiv/math_instruct | |
Collect the terms in 1288 - 698 + 14*x**2 - 29*x**2 - 590 + 10*x**2.\n | -5*x**2\n | ibivibiv/math_instruct | |
Solve 46229 = -197*y + 41304 for y.\n | -25\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"×
$$PQR$$ is an isosceles triangle where $$PQ = PR$$. $$X$$ is a point on the circumcircle of $$\triangle PQR$$, such that it being in the opposite region of $$P$$ with respect to $$QR$$. The normal drawn from the point $$P$... | To solve the problem presented, we need to understand and apply several geometric principles. We will break down the problem into smaller parts, tackle each one, and then integrate the solutions to arrive at our final answer.
First, let's define our terms and symbols:
* $$\triangle PQR$$ is an isosceles triangle wit... | ibivibiv/math_instruct | |
What is next in -130, -252, -384, -532, -702?\n | -900\n | ibivibiv/math_instruct | |
List the prime factors of 2109658.\n | 2, 397, 2657\n | ibivibiv/math_instruct | |
Simplify (-4*sqrt(175)/(2*sqrt(5)))/(sqrt(28)/(-4*sqrt(8)/sqrt(2) - sqrt(4))) + 0.\n | 10*sqrt(5)\n | ibivibiv/math_instruct | |
Suppose 24 = 8*p - 12*p. Let h(c) = -c**2 - 10*c - 13. What is the units digit of h(p)?\n | 1\n | ibivibiv/math_instruct | |
Let a = -98.6 + 99. What is the second biggest value in -2/3, 0.2, 4, a?\n | a\n | ibivibiv/math_instruct | |
Two letters picked without replacement from vcc. Give prob of sequence cv.\n | 1/3\n | ibivibiv/math_instruct | |
What is 470 minutes after 4:14 AM?\n | 12:04 PM\n | ibivibiv/math_instruct | |
Let q = -2382 + 2382. Let c(w) = -2*w + 7 + 4*w + w**2 - w. Calculate c(q).\n | 7\n | ibivibiv/math_instruct | |
Let t(z) = 48*z**2 - 43*z - 1. Determine t(3).\n | 302\n | ibivibiv/math_instruct | |
Let o(u) = u**3 + 54*u**2 + 73*u - 1. What is the tens digit of o(-51)?\n | 7\n | ibivibiv/math_instruct | |
List the prime factors of (-12)/12 + 7 - -5719.\n | 5, 229\n | ibivibiv/math_instruct | |
Solve 2 = 2*r + 4*g, -2 = 3*r - g - 19 for r.\n | 5\n | ibivibiv/math_instruct | |
Calculate -20415 divided by 6.\n | -6805/2\n | ibivibiv/math_instruct | |
Let c = 14 + 82. Let o be c/160 + 1 + (-517186)/(-90). Let y = -5755 + o. What is the common denominator of -53/3 and y?\n | 9\n | ibivibiv/math_instruct | |
What is the derivative of -1256*b**4 + 24*b**3 + 22851?\n | -5024*b**3 + 72*b**2\n | ibivibiv/math_instruct | |
Let l(m) = m**3 + m - 12. Suppose 0 = 3*g + 5*d - 25, -7*g + d - 5 = -6*g. Give l(g).\n | -12\n | ibivibiv/math_instruct | |
(-20)/(-12 - -2) + (-16 - 17 - 2)\n | -33\n | ibivibiv/math_instruct | |
Which is smaller: -12607 or -12606?\n | -12607\n | ibivibiv/math_instruct | |
What comes next: -1208, -1211, -1216, -1223, -1232?\n | -1243\n | ibivibiv/math_instruct | |
Sort -1, 0.018, -0.0059, 10, 3 in decreasing order.\n | 10, 3, 0.018, -0.0059, -1\n | ibivibiv/math_instruct | |
Let m be ((-4)/6)/((-1)/3). Suppose 0 = -k + 5 + 1. Let u be (k/(-2))/(3/(-4)). Solve 2*p - u = -m for p.\n | 1\n | ibivibiv/math_instruct | |
Suppose 9 = 5*x - 8*x + g, 2*x - 4 = 4*g. Let t(b) = -5*b**3 - 1. Let u be t(-1). Sort u, x, 3.\n | x, 3, u\n | ibivibiv/math_instruct | |
Let g(r) = 11*r**2 + 178*r - 14. Determine g(-18).\n | 346\n | ibivibiv/math_instruct | |
Let h be 13 - -5 - 8/2. Suppose -a = -3*a + 2*q + h, 3*a + 2*q - 46 = 0. Solve a = -3*l, 4*l + 22 = i + 8 for i.\n | -2\n | ibivibiv/math_instruct | |
Let n(g) = 9*g**3 - 3*g**2 - 6*g + 3. Let l(m) = 18*m**3 - 5*m**2 - 12*m + 5. What is 3*l(i) - 5*n(i)?\n | 9*i**3 - 6*i\n | ibivibiv/math_instruct | |
Let v(h) = -5*h - 197. Calculate v(-40).\n | 3\n | ibivibiv/math_instruct | |
Simplify (((t**(2/3))**(-6/11))**(-29))**(-39) assuming t is positive.\n | t**(-4524/11)\n | ibivibiv/math_instruct | |
Put 20/81, 3, 4, -0.2 in descending order.\n | 4, 3, 20/81, -0.2\n | ibivibiv/math_instruct | |
Suppose 7*b - 3*v - 33 = 3*b, -4*v - 12 = 0. What is the remainder when 13 is divided by b?\n | 1\n | ibivibiv/math_instruct | |
Let r(w) = w**2 - 1 + 5*w - 2*w**2 - 8 - w**3 - 6*w. Suppose 0 = 2*x - 3*v + 15, -2*x + 2*v - 10 = -5*x. Give r(x).\n | -9\n | ibivibiv/math_instruct | |
What is next in 190416, 190418, 190420, 190422, 190424, 190426?\n | 190428\n | ibivibiv/math_instruct | |
Find X + 120 \div 60 - 173$. 1102. What is the value of unknown variable X? | To solve this problem, we need to determine the value of x, which represents the unknown variable in the equation.
The equation is: X + 120 ÷ 60 - 173 = 1102
Lets simplify the equation:
X + 2 - 173 = 1102
X - 171 = 1102
To isolate x, we add 171 to both sides of the equation:
X - 171 + 171 = 1102 + 171
X = 1273
The valu... | ibivibiv/math_instruct | |
Work out -304 + 21072685.\n | 21072381\n | ibivibiv/math_instruct | |
Let t = -8.3 - -8. Let h = -1.7 + t. Let s = h + 1.8. What is the smallest value in 2/11, s, -2?\n | -2\n | ibivibiv/math_instruct | |
Let u(f) be the first derivative of f**2 - 4*f + 1. Suppose 2*i = -40 - 60. Let a = i + 47. Give u(a).\n | -10\n | ibivibiv/math_instruct | |
What is the biggest value in 8, 1/4, -0.9, 4, 2?\n | 8\n | ibivibiv/math_instruct | |
Express 6 + 167*y + 4*y - 1202*y - 6 as f*y + g and give f.\n | -1031\n | ibivibiv/math_instruct |
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