instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Suppose -595 = -3*y - 14*y. What is the remainder when 123 is divided by y?\n | 18\n | ibivibiv/math_instruct | |
What is -0.021088 rounded to 4 decimal places?\n | -0.0211\n | ibivibiv/math_instruct | |
Let w(k) = 23*k**2 + k + 1. Let l be w(2). Suppose -2*x + 30 = -2*j + 2*x, l = -4*j + x. Let u = 35 + j. What is the remainder when 18 is divided by u?\n | 8\n | ibivibiv/math_instruct | |
What is the highest common divisor of 60233312 and 17?\n | 17\n | ibivibiv/math_instruct | |
Work out 1.34295 * 5.\n | 6.71475\n | ibivibiv/math_instruct | |
Let x = 5 + -1. Let l = 4 + 0. Find the first derivative of f**l + f**x + 5 - 6 wrt f.\n | 8*f**3\n | ibivibiv/math_instruct | |
Subtract -0.1 from -1.14896.\n | -1.04896\n | ibivibiv/math_instruct | |
Let w be 2 - ((-4 - -4) + (-14)/(-8)). What is the second smallest value in 5, 3, w?\n | 3\n | ibivibiv/math_instruct | |
Let z = 213 + 3876. Calculate the highest common factor of z and 261.\n | 87\n | ibivibiv/math_instruct | |
What is the value of -23 - ((-42)/(-6) - 13)?\n | -17\n | ibivibiv/math_instruct | |
Collect the terms in 1200001*d**3 - 2400147*d**3 + 1200009*d**3.\n | -137*d**3\n | ibivibiv/math_instruct | |
Let u be 6*((4 - 18/4) + 1). Let x(z) = 5*z + 37 - z + 8. Let h be x(-11). Which is the nearest to h? (a) -2/15 (b) u (c) -1/4\n | a\n | ibivibiv/math_instruct | |
Let j(a) be the first derivative of 0*a + 3*a**2 - 1/10*a**5 + 1/40*a**6 + 0*a**3 + 1 + 1/8*a**4. Let x(b) be the second derivative of j(b). Factor x(u).\n | 3*u*(u - 1)**2\n | ibivibiv/math_instruct | |
Let j(u) = -43*u - 1. Let g(w) = -27*w + 2. Let o be g(1). Let c be o/15 - (-4)/6. What is the tens digit of j(c)?\n | 4\n | ibivibiv/math_instruct | |
What is 596 minutes before 8:44 AM?\n | 10:48 PM\n | ibivibiv/math_instruct | |
Which is the third smallest value? (a) 2 (b) 0.47 (c) -2\n | a\n | ibivibiv/math_instruct | |
Collect the terms in 10536*s**2 - 6*s**3 - 10536*s**2.\n | -6*s**3\n | ibivibiv/math_instruct | |
Which is greater: 102 or 45?\n | 102\n | ibivibiv/math_instruct | |
Let b(g) = -4*g - 5. Let k(m) = -3*m - 6. Give -6*b(a) + 5*k(a).\n | 9*a\n | ibivibiv/math_instruct | |
Let b = -26.506617 - 27.493299. Let g = -54 - b. What is g rounded to five decimal places?\n | -0.00008\n | ibivibiv/math_instruct | |
What is the difference between 0.0754 and 1950564210?\n | 1950564209.9246\n | ibivibiv/math_instruct | |
Let d(s) = 2*s**2 - 125*s + 1787. Let u be d(22). Solve 5*o - 26 + 6 = 5*l, -u*l = -4*o + 15 for l.\n | 1\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-17.656 / (-72.055 - -8.315) | 0.2770 | ibivibiv/math_instruct | |
What are the prime factors of 5359?\n | 23, 233\n | ibivibiv/math_instruct | |
Calculate the remainder when 1200673 is divided by 275.\n | 23\n | ibivibiv/math_instruct | |
Let 2*p**4 + 11346*p**3 + 574264*p**2 + 4610040*p = 0. Calculate p.\n | -5622, -41, -10, 0\n | ibivibiv/math_instruct | |
What is the next term in -34776, -34784, -34790, -34794, -34796?\n | -34796\n | ibivibiv/math_instruct | |
Let x(j) = -j**3 - 23*j**2 + 5*j + 3. Let o(s) = -s**3 - 27*s**2 + 6*s + 4. Let z(p) = 4*o(p) - 5*x(p). Calculate z(-7).\n | 8\n | ibivibiv/math_instruct | |
Find the common denominator of 161/55704 and 143/116147904.\n | 1277626944\n | ibivibiv/math_instruct | |
Put 5, 0.043, 1/3, -3/5, -1 in descending order.\n | 5, 1/3, 0.043, -3/5, -1\n | ibivibiv/math_instruct | |
Which is bigger: 15359 or 15358?\n | 15359\n | ibivibiv/math_instruct | |
Let s(m) = 372647*m - 6243. Let c be s(-131). What is c rounded to the nearest 1000000?\n | -49000000\n | ibivibiv/math_instruct | |
Evaluate -7 - (7 - (7 + (4 - 7))).\n | -10\n | ibivibiv/math_instruct | |
Which is smaller: -5 or -22?\n | -22\n | ibivibiv/math_instruct | |
What is the thousands digit of 382365739?\n | 5\n | ibivibiv/math_instruct | |
Does 66 divide 972?\n | False\n | ibivibiv/math_instruct | |
What is the millions digit of 456994905?\n | 6\n | ibivibiv/math_instruct | |
Let v(j) = 7*j + 5. Let g(w) = 8*w + 6. Let f(x) = -5*g(x) + 6*v(x). Let q(i) = 3*i**2. Give q(f(o)).\n | 12*o**2\n | ibivibiv/math_instruct | |
What is the highest common factor of 306 and 34?\n | 34\n | ibivibiv/math_instruct | |
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"## Saturday, February 03, 2007
### Van Roomen's Problem: Solution Explained
In today's blog, I will provide the solution to Van Roomen's problem. Van Roomen's problem established François Viète as one of the most important ... | The 17th century marked a significant period in the development of mathematics, particularly in the relationship between algebra and geometry. One notable event during this time was the proposal of Van Roomen's problem by Adriaan van Roomen, a Flemish mathematician. This problem played a crucial role in establishing F... | ibivibiv/math_instruct | |
Simplify (((sqrt(468) - (0 + sqrt(468) - sqrt(468)))*-6 - sqrt(468))**2 + 6*((sqrt(468)*-2)**2 - sqrt(468)) - sqrt(520)/(sqrt(360) - sqrt(40)))*2.\n | -73*sqrt(13) + 68328\n | ibivibiv/math_instruct | |
Let b = 4 + 0. Suppose -5*f - 4*a + 13 = 0, b*f + 3*a = -a + 8. Let p = 107 - 102. What is the lowest common multiple of p and f?\n | 5\n | ibivibiv/math_instruct | |
Let p(s) = -9374*s + 35. Let d(i) = -28122*i + 111. Determine 6*d(q) - 19*p(q).\n | 9374*q + 1\n | ibivibiv/math_instruct | |
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"# How to Adequately Implement Phase I of Two-Phase Simplex Algorithm on a Computer with Floating Point Error
I'm currently trying to write some code that implements Phase I of the two-phase Simplex Algorithm described here: ... | When implementing numerical algorithms like the two-phase simplex method, floating point errors can arise due to finite precision arithmetic used by computers. These errors necessitate careful consideration during implementation and testing to ensure accurate results. This discussion focuses on addressing this challen... | ibivibiv/math_instruct | |
Let m be 4*(0/(4/(-4)) - -4). What is the highest common factor of m and 2?\n | 2\n | ibivibiv/math_instruct | |
Let k be (1 - 3) + 775/372. Let x(w) be the second derivative of -3/2*w**2 + 0 + k*w**5 + 4*w - 31/36*w**4 + 17/6*w**3. Suppose x(o) = 0. What is o?\n | 1/5, 3\n | ibivibiv/math_instruct | |
List the prime factors of 3562.\n | 2, 13, 137\n | ibivibiv/math_instruct | |
Is 396857 prime?\n | False\n | ibivibiv/math_instruct | |
Find the second derivative of -3*a**2*t**3 - a**2*t**2 - 2120*a**2 + a*t**3 + 15*a*t**2 + 309*t**2 wrt a.\n | -6*t**3 - 2*t**2 - 4240\n | ibivibiv/math_instruct | |
Let h(n) be the first derivative of n**4/14 - 754*n**3/7 + 426387*n**2/7 - 107165266*n/7 + 216. Determine w, given that h(w) = 0.\n | 377\n | ibivibiv/math_instruct | |
Let f be -6*(5 + -2)/(-6). What is the nearest to f in 4, -1, 0.06?\n | 4\n | ibivibiv/math_instruct | |
Let s be 4/(-10) + 51/15. Let a be (1 - (3 - s))/1. Suppose 2*u = 3 + a. What is the highest common factor of 16 and u?\n | 2\n | ibivibiv/math_instruct | |
Suppose -h - 5*d + 18 = 0, -18*h + 14*h = -2*d - 28. Suppose -f + 2*f - 4 = 0. What is the nearest to 2/7 in f, h, 2?\n | 2\n | ibivibiv/math_instruct | |
Let v(r) be the third derivative of -4*r**4/3 + 2*r**3 - 21*r**2. Let b be v(-6). Calculate the highest common divisor of 51 and b.\n | 51\n | ibivibiv/math_instruct | |
b"What is the cth term of 11, 20, 53, 116, 215, 356, 545, 788?\n" | c**3 + 6*c**2 - 16*c + 20\n | ibivibiv/math_instruct | |
Suppose g - 27 = -2*g. Let j = -2 + 2. Let d(p) = -4*p - 1. Let t be d(-1). Solve -3*q + g + t = j for q.\n | 4\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {c: 4, s: 10}. Give prob of picking 2 c.\n | 6/91\n | ibivibiv/math_instruct | |
Simplify (-2*1*sqrt(44) - sqrt(44))/(sqrt(36)/(sqrt(36)/sqrt(4))).\n | -3*sqrt(11)\n | ibivibiv/math_instruct | |
Simplify sqrt(56)/(sqrt(8) + (sqrt(8) - sqrt(64)/(sqrt(8) - (sqrt(8)*2 + sqrt(8))))) + 3 + (sqrt(35) + (sqrt(105)*1)/sqrt(3))/(1*(1*sqrt(5) + sqrt(5))).\n | 3 + 7*sqrt(7)/5\n | ibivibiv/math_instruct | |
Suppose -4*v + 120 = -5*o, 0 = 3*v - 6*v - o + 90. What is the units digit of v?\n | 0\n | ibivibiv/math_instruct | |
Solve 0 = -3*f + 5*v - 28*v + 22*v - 14, 2*f - 3*v - 97 = 0 for f.\n | 5\n | ibivibiv/math_instruct | |
Is 432869443 composite?\n | False\n | ibivibiv/math_instruct | |
What is prob of sequence tpg when three letters picked without replacement from {t: 1, g: 3, b: 1, p: 9}?\n | 9/728\n | ibivibiv/math_instruct | |
Simplify (v**(-1/5)/v*v)**(4/5)*v/(v*(v**2*v)/v*v*v)*v**(-1) assuming v is positive.\n | v**(-129/25)\n | ibivibiv/math_instruct | |
In base 13, what is 1c - 3c7a9?\n | -3c78a\n | ibivibiv/math_instruct | |
Let n(g) = g**3 - 30*g**2 + 98*g + 9. Suppose -300 = -10*a - 0*a. Is n(a) a composite number?\n | True\n | ibivibiv/math_instruct | |
What is the closest to 1 in -1/25, -5, -3, 3/4?\n | 3/4\n | ibivibiv/math_instruct | |
b"What is the cth term of 30, 30, 28, 24?\n" | -c**2 + 3*c + 28\n | ibivibiv/math_instruct | |
Let z = 3 - 3. Let s = z + 1. Let w(f) be the first derivative of -3*f**2 - f + 1. What is w(s)?\n | -7\n | ibivibiv/math_instruct | |
Calculate the remainder when 142118 is divided by 170.\n | 168\n | ibivibiv/math_instruct | |
Let i(y) = -11*y + 89. Let j be i(8). Solve -3*s + j - 7 = 0 for s.\n | -2\n | ibivibiv/math_instruct | |
What is the greatest common factor of 919401 and 21?\n | 21\n | ibivibiv/math_instruct | |
What is the third smallest value in 4, -2, 2/13, 0.3, 6/11, 1?\n | 0.3\n | ibivibiv/math_instruct | |
Rearrange 6 - 7*i**3 - 3 - 14*i**2 + i**2 + 8*i**3 - 121*i**2 to z*i + f*i**3 + m + q*i**2 and give f.\n | 1\n | ibivibiv/math_instruct | |
What is the common denominator of -107/3876 and -169/6120?\n | 116280\n | ibivibiv/math_instruct | |
Let s = -3084.7 + 3084.4. Which is the second smallest value? (a) 8/7 (b) s (c) 5 (d) 1 (e) -23\n | b\n | ibivibiv/math_instruct | |
Let h(g) = 3*g + 6. Let l(q) = -4*q - 6. Let c(t) = 7*h(t) + 6*l(t). Determine c(5).\n | -9\n | ibivibiv/math_instruct | |
Let n(c) = 3*c**2 - 27*c + 24. Let k be n(8). Suppose -58*j + 29*j + 27*j = k. Solve 4*h + 20 = j, d + 2*d - 5*h - 37 = 0 for d.\n | 4\n | ibivibiv/math_instruct | |
Suppose -62*h - 4*h + 1320 = 0. What is the least common multiple of h and 30?\n | 60\n | ibivibiv/math_instruct | |
Expand -z + 4 - 4 + (4 + 2 - 5)*(-z + 3*z + 0*z) + (-9 + 1 - 2)*((-4*z + z + z)*(-2 + 0 + 1) + 3*z + z - 3*z) - 4*z + 3*z + 2*z.\n | -28*z\n | ibivibiv/math_instruct | |
Solve -124*u + 253 - 2650 = 455 for u.\n | -23\n | ibivibiv/math_instruct | |
Let o = 34 + 32. What is the highest common divisor of o and 6?\n | 6\n | ibivibiv/math_instruct | |
Solve -169665 = -8260*a - 29245 for a.\n | 17\n | ibivibiv/math_instruct | |
What is the lowest common multiple of 17171 and 10?\n | 171710\n | ibivibiv/math_instruct | |
What comes next: -16022, -15772, -15346, -14738, -13942, -12952, -11762?\n | -10366\n | ibivibiv/math_instruct | |
Solve -3*x + q + 10 = 0, 15930*q - 15927*q + 13 = 5*x - 1 for x.\n | 4\n | ibivibiv/math_instruct | |
Factor 897*l**3/2 + 2693*l**2/3 + 2699*l/6 + 2/3.\n | (l + 1)**2*(2691*l + 4)/6\n | ibivibiv/math_instruct | |
Solve -9954 - 2476 = -444*c + 17762 for c.\n | 68\n | ibivibiv/math_instruct | |
Simplify (-4 + sqrt(2299) + -4*(sqrt(2299)*-1 - sqrt(2299)) + 3 - (1 + (sqrt(2299)*-1*3 - (sqrt(2299)*-1 + 5))))**2.\n | 726*sqrt(19) + 278188\n | ibivibiv/math_instruct | |
Let n be 504/(-49) + (-2)/(-7). Let b = -7 - n. What is the greatest common factor of 1 and b?\n | 1\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 110 and 363.\n | 3630\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 72 and 2952.\n | 72\n | ibivibiv/math_instruct | |
Suppose -30 - 75 = -3*u + 288. Calculate the remainder when 654 is divided by u.\n | 130\n | ibivibiv/math_instruct | |
What are the prime factors of (-29 + (43 - 16))/(3060/1531 - 2)?\n | 1531\n | ibivibiv/math_instruct | |
Let p(b) = b**3 - 7*b**2 + 41*b + 5. Is p(12) composite?\n | False\n | ibivibiv/math_instruct | |
Let c(z) be the second derivative of -26*z**6/3 - 82*z**2 - 98*z. What is the derivative of c(o) wrt o?\n | -1040*o**3\n | ibivibiv/math_instruct | |
Let l(z) be the second derivative of z**3/3 + 161*z**2/2 + 19*z + 1. Is l(45) prime?\n | True\n | ibivibiv/math_instruct | |
Factor -693 - 4*a - 74*a + 232*a**2 - 229*a**2.\n | 3*(a - 33)*(a + 7)\n | ibivibiv/math_instruct | |
Expand (-2 + 1 - 2)*(2331*k - 8031*k + 1988*k - 2365*k - 10815*k).\n | 50676*k\n | ibivibiv/math_instruct | |
b"What is the oth term of 2651, 2625, 2599, 2573, 2547, 2521?\n" | -26*o + 2677\n | ibivibiv/math_instruct |
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