instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Calculate 7*(-4)/(-120)*-6.\n | -7/5\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 227171805?\n | 1\n | ibivibiv/math_instruct | |
What is the next term in 204, 1609, 5418, 12831, 25048, 43269?\n | 68694\n | ibivibiv/math_instruct | |
Calculate the remainder when 57598 is divided by 976.\n | 14\n | ibivibiv/math_instruct | |
Solve 8 = 5*n - 2*v - 0, n = -4*v - 16 for n.\n | 0\n | ibivibiv/math_instruct | |
What is the hundreds digit of 62410075?\n | 0\n | ibivibiv/math_instruct | |
Suppose -4*u + 5*a = -0*u - 30, u = 5*a + 15. Suppose -5*l - u*y - 140 = -9*l, 5*l - 4*y - 184 = 0. Calculate the remainder when 217 is divided by l.\n | 17\n | ibivibiv/math_instruct | |
Factor 27*w**2 + 1/2*w**4 + 6*w**3 + 81/2 + 54*w.\n | (w + 3)**4/2\n | ibivibiv/math_instruct | |
Let k(x) = -2*x**2 - 2*x + 4. Let q(y) = 1. Suppose -4*t - 1621*n + 1625*n = 0, -3*n = t - 12. Determine t*q(s) - k(s).\n | 2*s**2 + 2*s - 1\n | ibivibiv/math_instruct | |
Let g = 648.2 - 648. Which is the nearest to g? (a) 7 (b) 2 (c) 5\n | b\n | ibivibiv/math_instruct | |
Rearrange (7*t**2 - 65*t**2 - 19*t**2)*(17*t - 18*t + 9*t)*(3 + 0 - 4) to a*t**3 + i*t + s*t**2 + d and give a.\n | 616\n | ibivibiv/math_instruct | |
List the prime factors of 391335.\n | 3, 5, 7, 3727\n | ibivibiv/math_instruct | |
What is 20730.2 plus -1207.0852?\n | 19523.1148\n | ibivibiv/math_instruct | |
Differentiate 7824*o**3*w**3 - 2*o*w**3 - 2*w**3 - 16*w**2 - w wrt o.\n | 23472*o**2*w**3 - 2*w**3\n | ibivibiv/math_instruct | |
Evaluate (-1 - (16 - 0)) + (-75 - (292 + -275)).\n | -109\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 747 and 18.\n | 9\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(12.288 * 10.116) - (52.99 - 23.202) | 94.5174 | ibivibiv/math_instruct | |
Suppose s = 3*s - 4*z - 390, 3*s + 5*z - 585 = 0. Suppose 24 = t - 4*v, 5*t - 6*v + v - s = 0. Let g = t - -41. What is the tens digit of g?\n | 8\n | ibivibiv/math_instruct | |
Let k = 45.1 + -44.8. Let h = 20 + -16. Let n = h + -3. Which is smaller: n or k?\n | k\n | ibivibiv/math_instruct | |
Let x = 51 - 11. Let l be 2*(-45)/x*-4. Suppose n - 45 = -4*n. Calculate the greatest common divisor of n and l.\n | 9\n | ibivibiv/math_instruct | |
Which is the second biggest value? (a) 1/2 (b) -0.3 (c) -45172\n | b\n | ibivibiv/math_instruct | |
What is the hundreds digit of 4797?\n | 7\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 11 and 8679956.\n | 1\n | ibivibiv/math_instruct | |
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"Home » » Two angles of a pentagon are in the ratio 2:3. The others are 60o each. Calculat...
Two angles of a pentagon are in the ratio 2:3. The others are 60o each. Calculat...
Question
Two angles of a pentagon are in the ... | A pentagon is a five-sided polygon, and it is a fundamental concept in geometry. When discussing the angles of a pentagon, it's important to understand the properties of regular and irregular pentagons. A regular pentagon has all sides and interior angles equal, while an irregular pentagon does not share this property... | ibivibiv/math_instruct | |
Let w(y) = -80*y + 157. Let u be w(2). Let f = -14 - -26. Sort f, u, -2, -7 in ascending order.\n | -7, u, -2, f\n | ibivibiv/math_instruct | |
Calculate -2*(-4)/(-8) - 2.\n | -3\n | ibivibiv/math_instruct | |
Solve -28 = -29*z + 32*z - 73 for z.\n | 15\n | ibivibiv/math_instruct | |
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"# The Newton-Raphson Method
amath
The Newton-Raphson Method is an iterative algorithm for finding a zero of a function given the estimate of the zero. The method uses the derivative of the function and iterates the current ... | The Newton-Raphson Method is a potent mathematical tool used to find roots or zeros of differentiable functions. This technique was developed independently by Isaac Newton and Joseph Raphson in the late 17th century. It belongs to a broader class of methods called "root-finding algorithms." These methods aim at determ... | ibivibiv/math_instruct | |
Evaluate (46 - (3 - -11)) + -18.\n | 14\n | ibivibiv/math_instruct | |
Suppose -56 = -0*h - 2*h. Let r = 46 - h. Calculate the lowest common multiple of 14 and r.\n | 126\n | ibivibiv/math_instruct | |
What is (-1)/28 + (-112)/448?\n | -2/7\n | ibivibiv/math_instruct | |
What is the tens digit of -6 + ((-124935)/(-21) - 2/7) + -1?\n | 4\n | ibivibiv/math_instruct | |
Suppose 0 = 3*z - 2*r - 32, -4*r + 136 = -z + 150. Suppose -349 + 115 = -6*q. Calculate the remainder when q is divided by z.\n | 9\n | ibivibiv/math_instruct | |
What are the prime factors of 1436?\n | 2, 359\n | ibivibiv/math_instruct | |
Let s be 2/7 - (-2)/((-42)/69). Let m be s - (-11)/((-55)/(-540)). Calculate the greatest common divisor of 15 and m.\n | 15\n | ibivibiv/math_instruct | |
What is the tens digit of ((-121)/22 + 34)*983*2?\n | 3\n | ibivibiv/math_instruct | |
Solve 29*g - 422 + 509 = 0 for g.\n | -3\n | ibivibiv/math_instruct | |
What is 100d (base 15) in base 8?\n | 6474\n | ibivibiv/math_instruct | |
Suppose 0 = s - 4 + 1. Suppose 2*c - 5*c = 42. Let o = c + 27. Solve -s*h - 31 = 5*b, -4*b + 5*b + o = -4*h for h.\n | -2\n | ibivibiv/math_instruct | |
Which is smaller: 1003 or -233?\n | -233\n | ibivibiv/math_instruct | |
What is 397/4 - (-1284477)/(-84228)?\n | 84\n | ibivibiv/math_instruct | |
What is the highest common divisor of 88251 and 20969205?\n | 3837\n | ibivibiv/math_instruct | |
Simplify (sqrt(110)/((sqrt(30)*-2)/sqrt(3)))**2 - (sqrt(33) - (sqrt(33) + 6*(sqrt(132)/sqrt(4) + sqrt(33))))/sqrt(3).\n | 11/4 + 12*sqrt(11)\n | ibivibiv/math_instruct | |
Rearrange 120*p - 91*p + 126*p + 158*p + 85*p to the form s + k*p and give k.\n | 398\n | ibivibiv/math_instruct | |
-60 - 61867957\n | -61868017\n | ibivibiv/math_instruct | |
Convert 3136 (base 10) to base 14.\n | 1200\n | ibivibiv/math_instruct | |
Put 3, 50, 4 in increasing order.\n | 3, 4, 50\n | ibivibiv/math_instruct | |
Convert 0.3722885l to millilitres.\n | 372.2885\n | ibivibiv/math_instruct | |
What is -9908 + 9878 - (0 - 71)?\n | 41\n | ibivibiv/math_instruct | |
Let x(q) = -q**3 - 3*q**2 + 6*q + 13. Let d be x(-4). Solve -2*t = h + 5, 0 = d*t - 4*h + 13 + 6 for t.\n | -3\n | ibivibiv/math_instruct | |
What are the prime factors of 25355853?\n | 3, 43, 65519\n | ibivibiv/math_instruct | |
(208/(-2))/(-2)*79/(-158)\n | -26\n | ibivibiv/math_instruct | |
Is 318476153 a prime number?\n | True\n | ibivibiv/math_instruct | |
How many minutes are there between 10:43 PM and 12:27 AM?\n | 104\n | ibivibiv/math_instruct | |
Let q = -0.1593 - 0.4797. Let l = -0.639 - q. Which is the fourth biggest value? (a) 5 (b) 1 (c) l (d) -2\n | d\n | ibivibiv/math_instruct | |
Suppose 20 = -4*b + l + 81, 0 = -2*b - 2*l + 18. Suppose -28*u + 19*u = -45. Suppose -u*g - 16 - b = 0. Let k(s) = s**2 + 7*s - 5. Calculate k(g).\n | -11\n | ibivibiv/math_instruct | |
Let g = -10 + -1. Let f = 11.0000048 + g. Round f to 6 decimal places.\n | 0.000005\n | ibivibiv/math_instruct | |
Solve -2113*d - 53772 = 5392 for d.\n | -28\n | ibivibiv/math_instruct | |
Expand (-7 + 2 + 3)*(-g + g + 2*g) + 0*g - 2*g + g + 0*g - 2*g + 0*g - g - 5*g + 3*g - 29 - 18*g + 29 - 11*g + 11*g + 17*g.\n | -11*g\n | ibivibiv/math_instruct | |
Evaluate (-7 - -5)/((-56)/98).\n | 7/2\n | ibivibiv/math_instruct | |
Simplify (w*w**(2/31)*w)**(-5/7)*(w/(w*w*w**19))/w**(7/6) assuming w is positive.\n | w**(-29479/1302)\n | ibivibiv/math_instruct | |
Let u be 2/7 + 2021/7. Let s = -36 + u. Calculate the greatest common divisor of 23 and s.\n | 23\n | ibivibiv/math_instruct | |
What is the units digit of 4/(-32) + 21525/40?\n | 8\n | ibivibiv/math_instruct | |
Let w = -92.74 - -96.74. What is the second biggest value in w, 3, -2?\n | 3\n | ibivibiv/math_instruct | |
Let s be ((-21)/14)/((-3)/8). Suppose 0*z = -s*z + 8. Find the first derivative of -23 + 22*q**2 + 41 - 50*q**z wrt q.\n | -56*q\n | ibivibiv/math_instruct | |
Let i(a) = 3124*a**2 + 5*a - 4. Let v = 4 + 0. Let t be i(v). What is t rounded to the nearest ten thousand?\n | 50000\n | ibivibiv/math_instruct | |
Round -0.00000719921 to six dps.\n | -0.000007\n | ibivibiv/math_instruct | |
What is the integer value of n, where 0 ≤ n ≤ 180, such that cos n degrees = cos 259 degrees? | Since the cosine function has a period of $360$ degrees, we can write $\cos 259^\circ = \cos (259^\circ - 360^\circ) = \cos (-101^\circ)$.
Using the identity $\cos (-\theta) = \cos \theta$, we have $\cos (-101^\circ) = \cos 101^\circ$.
Since the cosine function has a range of $[-1,1]$, the values of $\cos n^\circ$ and ... | ibivibiv/math_instruct | |
Evaluate (0/((-13)/(39/(-6))))/(-2).\n | 0\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 609 and 8903?\n | 29\n | ibivibiv/math_instruct | |
What is the greatest common factor of 2140 and 80?\n | 20\n | ibivibiv/math_instruct | |
Let w be 10/45 + (-11)/9. Let f(m) = -m**2 - 12*m - 1. Let d be f(-6). Let i be w/21 - 10/d. Is -1 at most i?\n | True\n | ibivibiv/math_instruct | |
Calculate prob of picking 2 p when two letters picked without replacement from ppphphhphhhphphhhpp.\n | 4/19\n | ibivibiv/math_instruct | |
Rearrange (2 + 1 - 1)*(-1 - 12 - 4)*(-4*r + 95*r + 37*r) to n + d*r and give d.\n | -4352\n | ibivibiv/math_instruct | |
What is -11.88 rounded to the nearest integer?\n | -12\n | ibivibiv/math_instruct | |
Suppose 2*z - 156 + 148 = 0. Suppose z*n = 9*n - 1760. List the prime factors of n.\n | 2, 11\n | ibivibiv/math_instruct | |
Calculate the common denominator of -25/1294419 and 83/42.\n | 2588838\n | ibivibiv/math_instruct | |
Let h = 79 - 77. Suppose -7*i + 117 = 2*i. Which is the fourth smallest value? (a) 5 (b) h (c) i (d) 2/9\n | c\n | ibivibiv/math_instruct | |
Let r(b) = 5*b**3 + 2*b + 2. What is r(-1)?\n | -5\n | ibivibiv/math_instruct | |
Is (-572)/(-99) + 4/18 a multiple of 5?\n | False\n | ibivibiv/math_instruct | |
Let u(p) be the third derivative of -p**6/210 + 2*p**5/7 - 6*p**4 + 112*p**3/3 - 52*p**2 - 1. Factor u(m).\n | -4*(m - 14)**2*(m - 2)/7\n | ibivibiv/math_instruct | |
Solve -3*t - 2*k - 3*k + 17 = 0, -6*k + 19 = 5*t for t.\n | -1\n | ibivibiv/math_instruct | |
Calculate the least common multiple of (-1)/(2 - 17/8) and 4.\n | 8\n | ibivibiv/math_instruct | |
What is the second biggest value in -7.4, 9.7659, -2?\n | -2\n | ibivibiv/math_instruct | |
Simplify (m**(-2/43)/((m*m/(m*m**(-20)))/m*m))/(m*m*m*m**7)**(-35/3) assuming m is positive.\n | m**(12335/129)\n | ibivibiv/math_instruct | |
-3 (base 13) to base 10\n | -3\n | ibivibiv/math_instruct | |
b"What is the lth term of -1719, -1750, -1831, -1986, -2239?\n" | -4*l**3 - l**2 - 1714\n | ibivibiv/math_instruct | |
Solve -7*m = -4*m + 12 for m.\n | -4\n | ibivibiv/math_instruct | |
Expand (-2 - 1 + p**2 + 0)*(0*p**2 + 3*p**2 - 2*p**2).\n | p**4 - 3*p**2\n | ibivibiv/math_instruct | |
Factor -4*h**2/3 - 1892*h/3 + 196024.\n | -4*(h - 214)*(h + 687)/3\n | ibivibiv/math_instruct | |
What is the thousands digit of 2425031519?\n | 1\n | ibivibiv/math_instruct | |
What is 385 minutes after 8:50 AM?\n | 3:15 PM\n | ibivibiv/math_instruct | |
What is the product of 411 and 5?\n | 2055\n | ibivibiv/math_instruct | |
Three letters picked without replacement from nmkmmntmmkmk. Give prob of sequence ntn.\n | 1/660\n | ibivibiv/math_instruct | |
What is the closest to 22 in 1, 0.279, 5?\n | 5\n | ibivibiv/math_instruct | |
Suppose p - 3 = 0, -4*m - 222 = -3*p + 3. Let q = m - -129. Let y = q - 52. List the prime factors of y.\n | 23\n | ibivibiv/math_instruct | |
Suppose y - 2*t - 3 = 3, 30 = y + 4*t. Let d be (-7)/y*28/(-2). Solve -3*b - 18 = u, -d*u = 4*b - 3*u + 32 for b.\n | -5\n | ibivibiv/math_instruct | |
Suppose 33 = 3*y - 3*l, l - 13 - 36 = -5*y. Suppose 377 - 161 = 72*h. Solve 2*k = -0*k + 4*n + y, -17 = h*k + 2*n for k.\n | -3\n | ibivibiv/math_instruct | |
Let v(f) be the second derivative of -f**6/360 + f**5/120 + 13*f**4/24 + f**3 + 6*f. Let k(w) be the second derivative of v(w). Is k(0) a prime number?\n | True\n | ibivibiv/math_instruct | |
Let p(h) = -298*h + 180. Let b(z) = 199*z - 120. Let d(t) = 7*b(t) + 5*p(t). Let m be d(2). Is -137 less than m?\n | True\n | ibivibiv/math_instruct |
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