instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Simplify ((((h*h**(3/5))/h)/h)/h**(-2/5))**29/((h/(h*h**1))**36)**(-3/10) assuming h is positive.\n | h**(-54/5)\n | ibivibiv/math_instruct | |
In base 14, what is 55ac5 + -138?\n | 5598b\n | ibivibiv/math_instruct | |
Suppose 0 = -l - 1 - 3. Let w = 3 + l. Let h(j) = j**3 - 2*j**2 - 4*j + 2. Let i be h(3). Is w bigger than i?\n | False\n | ibivibiv/math_instruct | |
What is the closest to 0 in 4.5557, 2/21, 0.1, -1, 0?\n | 0\n | ibivibiv/math_instruct | |
Three letters picked without replacement from xxxxlxxxxxxxxxxxlx. Give prob of picking 3 x.\n | 35/51\n | ibivibiv/math_instruct | |
Suppose -5*k + 3*k = 0. Suppose k*x - 8163 = -9*x. Is x a composite number?\n | False\n | ibivibiv/math_instruct | |
Let i be ((-1)/(-1) + 0)/(-1). Calculate the least common multiple of 8 and (i/(-1))/((-7)/(-14)).\n | 8\n | ibivibiv/math_instruct | |
726112 divided by -4\n | -181528\n | ibivibiv/math_instruct | |
In base 12, what is 5 - -70?\n | 75\n | ibivibiv/math_instruct | |
What is 55/3 of a minute in seconds?\n | 1100\n | ibivibiv/math_instruct | |
Let j be 1/((-21)/(-96)) + (-6)/(-14). Suppose -j*b + 16*b = -880. Let s = -77 - b. Solve l = 5*l - 3*p - 31, -s*l + 5*p + 37 = 0 for l.\n | 4\n | ibivibiv/math_instruct | |
Find s, given that -2*s**2/7 + 13808*s/7 - 23832608/7 = 0.\n | 3452\n | ibivibiv/math_instruct | |
Solve -6*v - 9 - 7 = 4*y, -4 = 4*y for v.\n | -2\n | ibivibiv/math_instruct | |
Sort -2, -4, 1, 6 in increasing order.\n | -4, -2, 1, 6\n | ibivibiv/math_instruct | |
What is the greatest common factor of 131515 and 2095?\n | 5\n | ibivibiv/math_instruct | |
Solve 11*v + 3*a = 10*v + 5, -4*v + 20 = -5*a for v.\n | 5\n | ibivibiv/math_instruct | |
Simplify m**0*m*m*m**(1/21)/m assuming m is positive.\n | m**(22/21)\n | ibivibiv/math_instruct | |
What is the fourth biggest value in 1/2, -12, -17, -0.8, -1, 1?\n | -1\n | ibivibiv/math_instruct | |
Suppose 9*h = 4*h + 3*x + 6, 6 = 3*h - 3*x. Let l(u) = -5*u**2 + u - 5. Let c be l(h). Let a(d) = -15*d - 11. What are the prime factors of a(c)?\n | 2\n | ibivibiv/math_instruct | |
Which is the closest to 0.2? (a) -30 (b) -182/9 (c) 2 (d) -0.05\n | d\n | ibivibiv/math_instruct | |
Suppose -2*s + p - 7 = -2*p, 2*p - 11 = -5*s. What is the nearest to s in -2/17, 0.4, -3/5?\n | 0.4\n | ibivibiv/math_instruct | |
Let q be (-5)/((-3)/(-2 - -5)). Suppose x - 4*c = 5, 5 = -10*x + 11*x + 4*c. Solve -2*m = 2*m - x*l - 22, l + q = m for m.\n | 3\n | ibivibiv/math_instruct | |
What is 1161 - -55078?\n | 56239\n | ibivibiv/math_instruct | |
Let r(h) be the second derivative of 487*h**4/6 + 365*h**3/6 + 123*h. Find the second derivative of r(z) wrt z.\n | 1948\n | ibivibiv/math_instruct | |
Evaluate -2 - (-4 + -1) - (13 + (-21 - -7)).\n | 4\n | ibivibiv/math_instruct | |
Let d(h) = 2*h - 2. Let s be d(2). Suppose 2 = y - s. Calculate the least common multiple of 2 and y.\n | 4\n | ibivibiv/math_instruct | |
Let n(j) = 2*j**2 + 2. Suppose 5*o - 159 = 3*o - 5*a, 0 = -3*o - a + 245. Suppose 0 = 2*s + o - 8. Let b = s + 35. Calculate n(b).\n | 10\n | ibivibiv/math_instruct | |
What is 627 minutes after 2:19 PM?\n | 12:46 AM\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 30 and 3863085.\n | 15\n | ibivibiv/math_instruct | |
Evaluate (1/14)/((-103)/(-17304)*-180).\n | -1/15\n | ibivibiv/math_instruct | |
(0 + 1)*(-29 + 24)\n | -5\n | ibivibiv/math_instruct | |
Let y = 124 - 114. Let j(a) = -a**3 + 13*a**2 - 28*a - 14. Let z be j(y). Solve 5 = z*q - 1 for q.\n | 1\n | ibivibiv/math_instruct | |
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"# Quaternions Group Homomorphic to Klein Group
I'm currently studying some stuff about group theory and I came to problem of showing that $$\displaystyle\frac{Q_8}{\langle-1\rangle}\cong V_4,$$ so I checked on this link: Qua... | The given text snippet discusses a problem from group theory, specifically demonstrating that the quaternion group modulo its center is isomorphic to the Klein four-group (also known as the viergruppe) using the First Isomorphism Theorem. To understand this, let us review the necessary definitions and theorems. We wil... | ibivibiv/math_instruct | |
What is 341278188 to the power of 1/3, to the nearest integer?\n | 699\n | ibivibiv/math_instruct | |
What is the tenth root of 1695993951 to the nearest integer?\n | 8\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(77.5583 * 17.1767) - (38.6079 + 63.8924) | 1229.6954 | ibivibiv/math_instruct | |
Convert 569579.3ml to litres.\n | 569.5793\n | ibivibiv/math_instruct | |
Simplify (w**(-1/2)*w*w**(-1/3))/((w*(w**1/w)/w)/w)**(-16/7)*((w**(-1))**(-46))**(-2) assuming w is positive.\n | w**(-3953/42)\n | ibivibiv/math_instruct | |
What is the hundreds digit of 373?\n | 3\n | ibivibiv/math_instruct | |
Solve -92*t - 13 = -79*t for t.\n | -1\n | ibivibiv/math_instruct | |
Suppose 3*a**3 + 1544982*a**2 - 4634973*a = 0. What is a?\n | -514997, 0, 3\n | ibivibiv/math_instruct | |
What is the common denominator of 57/3015530 and 36/53?\n | 159823090\n | ibivibiv/math_instruct | |
Let g(h) = -6*h - 290 + 145 + 3*h + 145. Let p = -6 - -8. Let c(l) = 3*l**p - 1 - 9*l**2 + 1. Calculate g(c(a)).\n | 18*a**2\n | ibivibiv/math_instruct | |
Calculate (5/((-300)/24))/(7/5).\n | -2/7\n | ibivibiv/math_instruct | |
Let a be (2 + -2 + 1)*(-24)/(-5). Factor -114/5*w**2 - a*w**4 - 24/5 + 84/5*w + 15*w**3 + 3/5*w**5.\n | 3*(w - 2)**3*(w - 1)**2/5\n | ibivibiv/math_instruct | |
b"What is the fth term of 2065, 4153, 6291, 8503, 10813?\n" | 4*f**3 + f**2 + 2057*f + 3\n | ibivibiv/math_instruct | |
Sort -15, -5, 0 in descending order.\n | 0, -5, -15\n | ibivibiv/math_instruct | |
Let m = -235 - -230. What is the closest to -0.1 in -4, m, -0.07?\n | -0.07\n | ibivibiv/math_instruct | |
Let c(b) = -46*b**3 + b**2 + 2. Let z(v) = -v**3 - v**2 - 2. Calculate 2*c(x) + 2*z(x).\n | -94*x**3\n | ibivibiv/math_instruct | |
What is the distance between 26.04 and 0.9?\n | 25.14\n | ibivibiv/math_instruct | |
What is prob of sequence sss when three letters picked without replacement from xxxxxxxsxxxsxsx?\n | 1/455\n | ibivibiv/math_instruct | |
26243 (base 9) to base 5\n | 1031242\n | ibivibiv/math_instruct | |
Solve 2*u + 8 = -2*s, -5*s - 25702*u = -25709*u - 4 for s.\n | -2\n | ibivibiv/math_instruct | |
Let p(s) = -2*s**3 - 3*s**2 - 4*s + 2. Suppose 1161*a + 36 = 1143*a. Calculate p(a).\n | 14\n | ibivibiv/math_instruct | |
Let u = -374 + 1348. Is u prime?\n | False\n | ibivibiv/math_instruct | |
Find the first derivative of c**4 - 208*c**3 - 261 wrt c.\n | 4*c**3 - 624*c**2\n | ibivibiv/math_instruct | |
Let s = -12685.756 - -12777. Let k = -91 + s. Let z = -0.124 - k. Round z to two dps.\n | -0.37\n | ibivibiv/math_instruct | |
What is the third derivative of -12*i**3*s**5 - 13*i**3*s**3 + 3*i**3 + 43*i*s**2 + 4 wrt s?\n | -720*i**3*s**2 - 78*i**3\n | ibivibiv/math_instruct | |
What is the highest common factor of 180 and 1020?\n | 60\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 78 and 156.\n | 78\n | ibivibiv/math_instruct | |
Let g = 51.85 + -57. Let c = -1.15 - g. What is the fourth biggest value in -0.4, c, -4, -74?\n | -74\n | ibivibiv/math_instruct | |
Find the common denominator of 47/36590169 and -46/104643.\n | 109770507\n | ibivibiv/math_instruct | |
What is -12232930 divided by 1223293?\n | -10\n | ibivibiv/math_instruct | |
Let b = 222 - 176. Is b a multiple of 3?\n | False\n | ibivibiv/math_instruct | |
What is the first derivative of -6*q**3 + 626*q**2 + 2381?\n | -18*q**2 + 1252*q\n | ibivibiv/math_instruct | |
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"## on operator commutation
Hi, I have a question,
As it is said in QM, if two operators commute, they have so many common eigenstates that they form a basis. And the inverse is right.
Now there is the question,
if A,B,C are ... | In quantum mechanics (QM), the concept of operator commutation plays a crucial role in determining whether operators share common eigenstates. The commutator of two operators, denoted by $[A, B]$, represents their difference in order of operation. Specifically, for any pair of operators $A$ and $B$, their commutator i... | ibivibiv/math_instruct | |
Which is the closest to 1? (a) 1.2 (b) -1/7 (c) 4/3\n | a\n | ibivibiv/math_instruct | |
-8829 * 2\n | -17658\n | ibivibiv/math_instruct | |
How many minutes are there between 12:12 AM and 4:37 AM?\n | 265\n | ibivibiv/math_instruct | |
What is the smallest value in 4/5, -7.3, -38/3?\n | -38/3\n | ibivibiv/math_instruct | |
What is 3/16 of a kilometer in centimeters?\n | 18750\n | ibivibiv/math_instruct | |
Rearrange -1 + 2*j + 18921027*j**2 - 18927536*j**2 + 0 to the form x*j + v*j**2 + h and give h.\n | -1\n | ibivibiv/math_instruct | |
Solve -2955*q + 3 = -2*o - 2954*q, 5*o = -4*q - 14 for o.\n | -2\n | ibivibiv/math_instruct | |
What is the value of 6 + 33 - (6 + 3 + (-1 + -6 - -2))?\n | 35\n | ibivibiv/math_instruct | |
Let x be (-6)/8 - (-9)/504*26. Put 5, -0.3, 0.5, x in decreasing order.\n | 5, 0.5, x, -0.3\n | ibivibiv/math_instruct | |
Let s(o) be the second derivative of 221*o**4/12 + 2*o**3/3 + 5*o**2/2 - o. Let j be s(10). Let w = j + -15745. Round w to the nearest one thousand.\n | 6000\n | ibivibiv/math_instruct | |
Suppose 12*a = 14*a - 4*u - 3656, -7344 = -4*a + 4*u. What is the remainder when a is divided by 25?\n | 19\n | ibivibiv/math_instruct | |
Let d(z) = 248*z + 863. What are the prime factors of d(2)?\n | 3, 151\n | ibivibiv/math_instruct | |
What is -0.4 - -0.0009567?\n | -0.3990433\n | ibivibiv/math_instruct | |
3 (base 11) to base 6\n | 3\n | ibivibiv/math_instruct | |
What comes next: 1370, 1367, 1362, 1355?\n | 1346\n | ibivibiv/math_instruct | |
Let u(w) = -22*w. Let d(q) = -q**2. Calculate u(d(y)).\n | 22*y**2\n | ibivibiv/math_instruct | |
Expand n**3 + 0*n**3 + 0*n**3 - 3*n**3 - 4 + 4 + (3*n**2 - 5*n**2 + 0*n**2)*(-2*n + 2*n + 3*n) - 7*n**3 + 0*n**3 - 4*n**3.\n | -19*n**3\n | ibivibiv/math_instruct | |
What is the tens digit of 901?\n | 0\n | ibivibiv/math_instruct | |
Multiply 109 and 676.\n | 73684\n | ibivibiv/math_instruct | |
Express 199 - 402 + 362*g + 203 as v + c*g and give c.\n | 362\n | ibivibiv/math_instruct | |
Let b = -24 - -40. Let y = -8 + b. List the prime factors of y.\n | 2\n | ibivibiv/math_instruct | |
What is ((378/(-60))/21)/(2/(-20))*(-14)/(-35)?\n | 6/5\n | ibivibiv/math_instruct | |
In base 10, what is -11722 + -4906?\n | -16628\n | ibivibiv/math_instruct | |
Put -1, 0, 7, -5 in decreasing order.\n | 7, 0, -1, -5\n | ibivibiv/math_instruct | |
List the prime factors of 18392198.\n | 2, 11, 17, 49177\n | ibivibiv/math_instruct | |
Let i be (-3 - (-23)/1) + 3. Suppose -10 = -2*p, -3*y - 6*p = -2*p - 572. Suppose -3*h + 7*h = y. Calculate the highest common divisor of h and i.\n | 23\n | ibivibiv/math_instruct | |
What is 0.3725489 litres in millilitres?\n | 372.5489\n | ibivibiv/math_instruct | |
Suppose 0 = 4*p + 5*q, -3*p - 2*q + 4*q = 0. Let o be -1 + (p - 16)/(-1). Suppose -13 = -x + o. Round x to the nearest ten.\n | 30\n | ibivibiv/math_instruct | |
Let d = 47 - 47. Solve d*h + 3*h = 0 for h.\n | 0\n | ibivibiv/math_instruct | |
Let p(i) = -107*i + 5671. Let k be p(53). Put -1, 2, k, 3/8, -0.8 in increasing order.\n | -1, -0.8, k, 3/8, 2\n | ibivibiv/math_instruct | |
Suppose 3*o - 23 = -8. Suppose -v - o*d - 1 = 5, -5*v = -d + 4. Let b be 4/((-1)/(1/v)). Solve -4*m - 4 = 3*i + 2, -8 = b*i - 3*m for i.\n | -2\n | ibivibiv/math_instruct | |
Solve -1 + 0 = 5*a + 4*m, 0 = a + 3*m - 2 for a.\n | -1\n | ibivibiv/math_instruct | |
Calculate the common denominator of -21/10 and 23/32049.\n | 320490\n | ibivibiv/math_instruct | |
Simplify (sqrt(77) + 5*(-2*sqrt(77) + sqrt(77)))/(sqrt(112) + sqrt(112)*-2 + sqrt(112) + sqrt(112) + sqrt(112) + sqrt(112)).\n | -sqrt(11)/3\n | ibivibiv/math_instruct |
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