instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Suppose 0 = -3*r - 4*y, -y - 35 = -5*r + 4*y. Let x = -32 - -54. Solve 2*o - r*v = -x, -v = o - 0*o - 1 for o.\n | -3\n | ibivibiv/math_instruct | |
Let c = -268 + 286. Let u = -3 - -5. Suppose u*v = c + 128. List the prime factors of v.\n | 73\n | ibivibiv/math_instruct | |
What is the highest common divisor of 4 and 12?\n | 4\n | ibivibiv/math_instruct | |
How many minutes are there between 6:48 AM and 1:15 PM?\n | 387\n | ibivibiv/math_instruct | |
Rearrange 19483*w**2 - 19486*w**2 + 483 + 319 to p*w**2 + l*w + y and give y.\n | 802\n | ibivibiv/math_instruct | |
Calculate (-15 - 7 - -2) + 7 - (-27 + -32).\n | 46\n | ibivibiv/math_instruct | |
What is -295 divided by -2717?\n | 295/2717\n | ibivibiv/math_instruct | |
Let q = 375 + -281. Suppose -2*r - 3*r + 25 = 0, 4*r - 47 = -3*d. Calculate the remainder when q is divided by d.\n | 4\n | ibivibiv/math_instruct | |
Simplify (i*i**(-6)/i*i**(-5/4)*(i/(i*i**(2/5)))**(6/13))**(7/9) assuming i is positive.\n | i**(-13531/2340)\n | ibivibiv/math_instruct | |
What is 2727445335 to the power of 1/3, to the nearest integer?\n | 1397\n | ibivibiv/math_instruct | |
Simplify (sqrt(612))**2 + -5 + (sqrt(17) - 3*(sqrt(102)/sqrt(6) + sqrt(17))).\n | -5*sqrt(17) + 607\n | ibivibiv/math_instruct | |
Suppose -4*d - 5*o + 31 = 0, -3*d = 5*o - 8 - 19. Suppose -3*b - 5*f = -10*f - 9, d*b = 5*f + 12. Solve 4*l = 7*l + h - b, 4*l + h = 3 for l.\n | 0\n | ibivibiv/math_instruct | |
Suppose -26*q + 536775000 = -11*q. What is q rounded to the nearest one million?\n | 36000000\n | ibivibiv/math_instruct | |
1*4/(-12)*7/21\n | -1/9\n | ibivibiv/math_instruct | |
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"Whats new
# Joint vs conditional probability
#### ABSMOGHE
##### New Member
Subscriber
Hi I was trying to understand the difference between Joint Probability and Conditional Probability
I came across this post of yours.
... | Sure, let me help clarify the distinction between joint and conditional probabilities using some detailed explanations and examples.
Joint probability refers to the likelihood of two events occurring together. It is denoted as P(A and B), or sometimes as P(AB). This represents the simultaneous occurrence of event A a... | ibivibiv/math_instruct | |
What is 498 to the power of 1/2, to the nearest integer?\n | 22\n | ibivibiv/math_instruct | |
Expand (-6*n + 0*n + 3*n)*(2 - n - 2) + (-4 + 4 + 2*n)*(10*n + n - n).\n | 23*n**2\n | ibivibiv/math_instruct | |
How many minutes are there between 12:51 AM and 12:07 PM?\n | 676\n | ibivibiv/math_instruct | |
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"cartesian coordinates converter. The coordinates describe a point in the plane uniquely. How do you convert (6210^circ) from polar to cartesian coordinates?. It is an odd omission that GH includes a native component to conver... | Let's begin by discussing Cartesian coordinates and their significance in mathematics and science. A two-dimensional Cartesian coordinate system consists of two perpendicular lines, known as axes: the horizontal x-axis and the vertical y-axis. Any point P in the plane can be described using an ordered pair (x, y), whe... | ibivibiv/math_instruct | |
Find the second derivative of 4*o**5 - 2*o**3 - 195604*o**2 - 9520973*o - 2.\n | 80*o**3 - 12*o - 391208\n | ibivibiv/math_instruct | |
-3 (base 8) to base 16\n | -3\n | ibivibiv/math_instruct | |
b"What is the vth term of -52, -41, -30?\n" | 11*v - 63\n | ibivibiv/math_instruct | |
What is the highest common factor of 319 and 29?\n | 29\n | ibivibiv/math_instruct | |
Let m = -31.04 + 31. What is the third smallest value in -4/3, m, 5?\n | 5\n | ibivibiv/math_instruct | |
List the prime factors of 2137553.\n | 11, 194323\n | ibivibiv/math_instruct | |
Let g = 0.1 - -0.14. Let i = -0.04 + g. Which is the second biggest value? (a) 0.3 (b) 2/5 (c) i\n | a\n | ibivibiv/math_instruct | |
Evaluate ((-1300)/(-125))/(-13)*(-5 + 4).\n | 4/5\n | ibivibiv/math_instruct | |
Sort 0, -5, -4, 2, -263.\n | -263, -5, -4, 0, 2\n | ibivibiv/math_instruct | |
Suppose 2*r - 90 = 4*x, -2*x = 4*r - 3*x - 180. Calculate the remainder when r is divided by 16.\n | 13\n | ibivibiv/math_instruct | |
Suppose 4*b - 31238 - 24398 = 0. Is b prime?\n | False\n | ibivibiv/math_instruct | |
Sort -2, 2, 6 in ascending order.\n | -2, 2, 6\n | ibivibiv/math_instruct | |
Calculate prob of sequence grd when three letters picked without replacement from {d: 1, u: 2, z: 3, g: 1, r: 12}.\n | 2/969\n | ibivibiv/math_instruct | |
List the prime factors of 27259532.\n | 2, 1567, 4349\n | ibivibiv/math_instruct | |
What are the prime factors of 22422?\n | 2, 3, 37, 101\n | ibivibiv/math_instruct | |
Let z be 27/(-18) + 1*(-3)/(-2). Suppose 2*b = -5*l - 6, 3*b + 5*l = -z - 4. Sort 0, b, 1, -3.\n | -3, 0, 1, b\n | ibivibiv/math_instruct | |
Let f = 0.31 - -0.69. Which is the second smallest value? (a) 0.06 (b) -0.3 (c) f\n | a\n | ibivibiv/math_instruct | |
Suppose 3*a = 3*j + 38 - 11, 2*a = j + 13. Suppose f + 5*z + 16 = 0, 2*f + 8 = -0*f - a*z. Find the third derivative of 4*k**4 - f*k**4 - k**4 - k**2 wrt k.\n | -24*k\n | ibivibiv/math_instruct | |
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"# Compensating for bullet drop
1. Dec 18, 2013
### Dux
I'm hoping that someone on this board can tell me where I'm going wrong here.
Basically, I'm trying to calculate the upward angle at which one would need to aim a gun... | The problem presented by Dux is an application of physics principles, specifically those concerning motion and projectile trajectories. To address his question, let's first review some fundamental concepts and then delve into the calculations he has attempted. This will enable us to identify any errors and provide a c... | ibivibiv/math_instruct | |
Let p = -934 - -265. Let n = 673 + p. Which is the nearest to 0? (a) n (b) 3.1 (c) 0.4\n | c\n | ibivibiv/math_instruct | |
What is the units digit of 252?\n | 2\n | ibivibiv/math_instruct | |
Suppose -h = -4*y + 1072, -5*y - h = 4*h - 1340. Suppose -110 = 6*l + y. Let d = -26 - l. Is d a composite number?\n | False\n | ibivibiv/math_instruct | |
Suppose 2*m = 3*q - 1, -185*q + 183*q - 11 = m. Put 3, 17, m in decreasing order.\n | 17, 3, m\n | ibivibiv/math_instruct | |
What is the seventh root of 2830788 to the nearest integer?\n | 8\n | ibivibiv/math_instruct | |
Which is the second smallest value? (a) -0.025 (b) 0.5 (c) 19701\n | b\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 z and 1 s when two letters picked without replacement from {z: 1, r: 4, s: 2, b: 2}.\n | 1/18\n | ibivibiv/math_instruct | |
Calculate the remainder when 3647 is divided by 82.\n | 39\n | ibivibiv/math_instruct | |
What are the prime factors of 1994?\n | 2, 997\n | ibivibiv/math_instruct | |
Let d = -25903/10 - -12959/5. Suppose w + 5 = 1. Let z = -0.46 - -0.06. Which is the closest to -0.1? (a) d (b) w (c) z\n | c\n | ibivibiv/math_instruct | |
What is -0.4 times -477.024?\n | 190.8096\n | ibivibiv/math_instruct | |
Differentiate 417 - 297*a**2 - 1212173*a + 1212173*a wrt a.\n | -594*a\n | ibivibiv/math_instruct | |
Let a(b) be the third derivative of -b**6/180 + b**4/8 + b**3/2 - 3*b**2. Let i(g) be the first derivative of a(g). Find the first derivative of i(p) wrt p.\n | -4*p\n | ibivibiv/math_instruct | |
Let g = 16397.5 + -16398. Which is the smallest value? (a) -3/4 (b) g (c) 712\n | a\n | ibivibiv/math_instruct | |
What is 298 minutes after 5:22 AM?\n | 10:20 AM\n | ibivibiv/math_instruct | |
Calculate (-8)/(-60)*57/(30780/100).\n | 2/81\n | ibivibiv/math_instruct | |
Calculate (-16 + -2 - (-11 - 0 - 0)) + 7.\n | 0\n | ibivibiv/math_instruct | |
Let l be (-32)/(-3) - 2/3. Suppose 4*m = -m + l. What are the prime factors of m?\n | 2\n | ibivibiv/math_instruct | |
Let k = -0.19834 - -42361.19834. Which is smaller: 0.1 or k?\n | 0.1\n | ibivibiv/math_instruct | |
What are the prime factors of 8953?\n | 7, 1279\n | ibivibiv/math_instruct | |
Simplify (q**19)**42/(q**(3/8))**(1/22) assuming q is positive.\n | q**(140445/176)\n | ibivibiv/math_instruct | |
Total of 4 and -0.4679722.\n | 3.5320278\n | ibivibiv/math_instruct | |
Suppose 10 - 475 = -5*f. Does 31 divide f?\n | True\n | ibivibiv/math_instruct | |
What is (((-8)/(-7))/4)/(90/(-42))?\n | -2/15\n | ibivibiv/math_instruct | |
Expand -2*y**5 + 0*y**5 + 6*y**5 + (-3*y + 4*y + y)*(39*y**2 + 3*y**4 - 39*y**2) + 0*y**5 + 2*y**5 - 3*y**5.\n | 9*y**5\n | ibivibiv/math_instruct | |
b"What is the ith term of -2705, -2707, -2709, -2711, -2713, -2715?\n" | -2*i - 2703\n | ibivibiv/math_instruct | |
Sort -2, 1, -94, -1 in ascending order.\n | -94, -2, -1, 1\n | ibivibiv/math_instruct | |
Factor -12*r**2 + 7988*r + 190072.\n | -4*(r + 23)*(3*r - 2066)\n | ibivibiv/math_instruct | |
What is 104013648 to the power of 1/2, to the nearest integer?\n | 10199\n | ibivibiv/math_instruct | |
What is the cube root of 3470288150 to the nearest integer?\n | 1514\n | ibivibiv/math_instruct | |
Calculate prob of picking 1 d and 1 c when two letters picked without replacement from {z: 2, d: 2, c: 1}.\n | 1/5\n | ibivibiv/math_instruct | |
Convert 13 (base 6) to base 5.\n | 14\n | ibivibiv/math_instruct | |
Let r(j) be the first derivative of 2/3*j**3 + 0*j + 3 + 0*j**2 - 3/4*j**4. Find the third derivative of r(m) wrt m.\n | -18\n | ibivibiv/math_instruct | |
Solve -23*r = 153 - 544 for r.\n | 17\n | ibivibiv/math_instruct | |
Suppose 465 = 26*w - 7231. Suppose 297*l - 1 = w*l. Let k(m) = -1. Let a(i) = -2*i + 7. Determine l*a(s) + 3*k(s).\n | -2*s + 4\n | ibivibiv/math_instruct | |
Two letters picked without replacement from znkkyggzggfnfggffgg. What is prob of sequence kz?\n | 2/171\n | ibivibiv/math_instruct | |
How many minutes are there between 9:08 PM and 12:12 AM?\n | 184\n | ibivibiv/math_instruct | |
Suppose h - 2*w - 2*w + 283 = 0, 0 = 4*h - 3*w + 1171. Let f = -198 - h. Is f prime?\n | True\n | ibivibiv/math_instruct | |
What is the value of (6/(-4)*38)/((-66)/(-77)*7/(-2))?\n | 19\n | ibivibiv/math_instruct | |
Suppose -42*q = -36*q - 6. Sort -5, q, 5, -1.\n | -5, -1, q, 5\n | ibivibiv/math_instruct | |
What is the highest common divisor of 81 and 2943?\n | 27\n | ibivibiv/math_instruct | |
Let f(q) = -q**3 + 13*q**2 - 59*q + 125. Let j be f(7). Find a such that -1/6*a**2 - j + 2*a = 0.\n | 6\n | ibivibiv/math_instruct | |
Calculate 10.013193 + 0.2.\n | 10.213193\n | ibivibiv/math_instruct | |
What is 5*(-12)/(-30) - 15/9?\n | 1/3\n | ibivibiv/math_instruct | |
Convert 209.22894ns to minutes.\n | 0.000000003487149\n | ibivibiv/math_instruct | |
What is the common denominator of 35/181604 and -33/9868?\n | 448017068\n | ibivibiv/math_instruct | |
What is prob of sequence el when two letters picked without replacement from feeelefeeeel?\n | 4/33\n | ibivibiv/math_instruct | |
Work out -1.63 * -913.\n | 1488.19\n | ibivibiv/math_instruct | |
Suppose -2*y - 3*y + 20 = 0. Suppose 232 = y*u - 24. Is u/1 - 0/(-2) a multiple of 19?\n | False\n | ibivibiv/math_instruct | |
What is the remainder when 82582197 is divided by 70886?\n | 7\n | ibivibiv/math_instruct | |
Let s(q) = -q. Let x(c) = -373*c - 3. Calculate s(x(r)).\n | 373*r + 3\n | ibivibiv/math_instruct | |
Let g(s) = -s**2 - 3. Let w(l) = 7*l + 17 + 0 + 14 - 10 - l**2. Let i be w(0). Suppose 0 = 2*o - 3*v - 11, 5*o - v = -0*o + i. Determine g(o).\n | -19\n | ibivibiv/math_instruct | |
What is the third biggest value in 5448, -2/15, 0.2, 2, 1, -5?\n | 1\n | ibivibiv/math_instruct | |
Let f(d) = 7*d**2 - 9*d - 7. Let x be f(4). Find the second derivative of -131 + 0*q**3 + q**4 - 2*q + 67 + 0*q**3 - 11*q**2 + x wrt q.\n | 12*q**2 - 22\n | ibivibiv/math_instruct | |
Is 6840011 a composite number?\n | True\n | ibivibiv/math_instruct | |
Let p = 2540 + -2544. Sort -3, -1/8, p, 8, -0.2 in decreasing order.\n | 8, -1/8, -0.2, -3, p\n | ibivibiv/math_instruct | |
Let r(j) = j + 34. Let o(b) = -14*b**2 - b - 1. Let l be o(-1). Let c be r(l). Suppose -25 = -7*k + 2*k. Calculate the greatest common factor of c and k.\n | 5\n | ibivibiv/math_instruct | |
Let c(m) = -4*m + 7. Suppose -1455*q = -1448*q - 84. Suppose 43*r - 40*r = -q, -4*r - 31 = 3*p. Let x(v) = -6*v + 10. Give p*x(w) + 7*c(w).\n | 2*w - 1\n | ibivibiv/math_instruct | |
Calculate prob of picking 2 v and 1 q when three letters picked without replacement from mmvnqv.\n | 1/20\n | ibivibiv/math_instruct | |
What is the square root of 1525032958 to the nearest integer?\n | 39052\n | ibivibiv/math_instruct | |
Let s be -3*(-3)/(-27)*-6. Let x(m) be the first derivative of 2/45*m**5 + 0*m + 1/18*m**4 + s - 1/9*m**2 - 2/27*m**3. Factor x(i).\n | 2*i*(i - 1)*(i + 1)**2/9\n | ibivibiv/math_instruct | |
Solve 28*h - 38*h = 30 for h.\n | -3\n | ibivibiv/math_instruct |
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