instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
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|---|---|---|---|
Suppose -2*y - 3*t + 9 = y, 0 = 3*t. Suppose 5*l - 28 = -3, 5*r + 4*l = 35. What is the second derivative of x**y - 2*x - r*x**3 + 0*x wrt x?\n | -12*x\n | ibivibiv/math_instruct | |
What is 5754 + 792573?\n | 798327\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 1121 and 4189.\n | 59\n | ibivibiv/math_instruct | |
What is ((-36)/(-21))/((-9144)/(-3810))?\n | 5/7\n | ibivibiv/math_instruct | |
Let i = -18 - -18. Suppose -2*d + i*d = 0. Let k be ((-7)/2)/(-7)*d. Solve -4*c + c - 12 = k for c.\n | -4\n | ibivibiv/math_instruct | |
Expand (-2 + 2 - 2)*(-12 + 12 + 18*j)*(-2*j**3 - 1 + 1)*(1 - 1 - 3*j + (-4 + 2 + 1)*(-3*j - 3*j + 4*j)).\n | -72*j**5\n | ibivibiv/math_instruct | |
Let w = 0.053 + -22.653. Let k = w - -20. What is the closest to -1/2 in 4, -4, k?\n | k\n | ibivibiv/math_instruct | |
Let t(k) = 3*k. Let x(g) = -g**2 + 13*g - 10. Suppose 2*u - 38 = -14. Let q be x(u). Let r(i) = -2*i**q - 31*i + 31*i. What is t(r(z))?\n | -6*z**2\n | ibivibiv/math_instruct | |
Let d(u) = -2*u**2 - u + 7. Let o be d(-5). Let n = 95 + o. Let c be (-169)/(-9) + 2/9. What is the highest common factor of c and n?\n | 19\n | ibivibiv/math_instruct | |
Is 761723 prime?\n | False\n | ibivibiv/math_instruct | |
Let w = 4 + -12. Let q = -18 + 11. Let r = 6 + q. Is r greater than w?\n | True\n | ibivibiv/math_instruct | |
Is 981900 a multiple of 45?\n | True\n | ibivibiv/math_instruct | |
Let b = 39 - 39.000076. Round b to five dps.\n | -0.00008\n | ibivibiv/math_instruct | |
55517490 divided by -11103498\n | -5\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 5121348 and 72.\n | 12\n | ibivibiv/math_instruct | |
Let w = -82072 + 153191. Is w composite?\n | False\n | ibivibiv/math_instruct | |
Let r be 6*(-6)/20 + 64/32. What is the closest to 1 in -2/13, r, -2/7?\n | r\n | ibivibiv/math_instruct | |
Calculate (-790)/1659*24/5.\n | -16/7\n | ibivibiv/math_instruct | |
Let r = 1422535 - 274316. Is r prime?\n | True\n | ibivibiv/math_instruct | |
What is 477296 to the power of 1/8, to the nearest integer?\n | 5\n | ibivibiv/math_instruct | |
Which is the fourth smallest value? (a) -1/2 (b) -2/5 (c) 0.04261 (d) -7 (e) 0.4\n | c\n | ibivibiv/math_instruct | |
What is 893624 divided by 893624?\n | 1\n | ibivibiv/math_instruct | |
Suppose -z + 14 = -2*l, -3*z + 5*z - 28 = -l. Calculate the greatest common divisor of z and 154.\n | 14\n | ibivibiv/math_instruct | |
Calculate the common denominator of -3/61142 and -69/418.\n | 672562\n | ibivibiv/math_instruct | |
Round -0.000072924755 to 4 decimal places.\n | -0.0001\n | ibivibiv/math_instruct | |
Let a(n) = 9*n**2 + 1. Let t be a(1). Suppose 5*x = -3*q - 4 + 57, 5*x = -t. What is the remainder when q is divided by 8?\n | 5\n | ibivibiv/math_instruct | |
What is the square root of 3155585182 to the nearest integer?\n | 56175\n | ibivibiv/math_instruct | |
Suppose 5*o**5/2 - 97155*o**4 + 485680*o**3 + 1262835*o**2 + 1359995*o/2 = 0. Calculate o.\n | -1, 0, 7, 38857\n | ibivibiv/math_instruct | |
17 + 18 + -4 + -29\n | 2\n | ibivibiv/math_instruct | |
Let w(h) = 2*h**3 - 20*h**2 + 45*h + 159. Let m(d) = 20*d**2 - 46*d - 154. Let z(o) = -3*m(o) - 2*w(o). Find t, given that z(t) = 0.\n | -6, -2, 3\n | ibivibiv/math_instruct | |
Let r be 170 + 15 + 378/(-22) + (-2)/(-11). Solve -24*m = r - 24 for m.\n | -6\n | ibivibiv/math_instruct | |
List the prime factors of 23282438.\n | 2, 11641219\n | ibivibiv/math_instruct | |
What is the value of -5 + -3 - -7 - -7 - 10?\n | -4\n | ibivibiv/math_instruct | |
Which is greater: 3625959 or 3625958?\n | 3625959\n | ibivibiv/math_instruct | |
What is 25/4 of a decade in months?\n | 750\n | ibivibiv/math_instruct | |
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"# [SOLVED]Prove √a+√b+√c+√d≤10
#### anemone
##### MHB POTW Director
Staff member
Prove that if $a,\,b,\,c,\,d>0$ and $a\le 1,\,a+b\le 5,\,a+b+c\le 14,\,a+b+c+d\le 30$, then $\sqrt{a}+\sqrt{b}+\sqrt{c}+\sqrt{d}\le 10$.
####... | The problem at hand involves proving that a certain inequality holds true given a set of constraints on variables a, b, c, and d. This type of problem falls under the broader category of mathematical inequalities, which deal with the comparison of two expressions involving unknown quantities. Inequalities are crucial ... | ibivibiv/math_instruct | |
How many weeks are there in 5598.73188 seconds?\n | 0.0092571625\n | ibivibiv/math_instruct | |
How many seconds are there in 6/5 of a hour?\n | 4320\n | ibivibiv/math_instruct | |
What is 74 (base 8) in base 7?\n | 114\n | ibivibiv/math_instruct | |
Expand (b**2 - b**2 + b**2)*(1 - 3 + 1) + 0*b**2 - 2*b**2 + b**2 - 2*b**2 + b - b + 4*b**2 - b**2 - 4*b**2 - 6*b**2 + 74*b - 74*b - 12*b**2 - 19*b + 19*b.\n | -23*b**2\n | ibivibiv/math_instruct | |
What is 0.0076618703 rounded to six decimal places?\n | 0.007662\n | ibivibiv/math_instruct | |
Let c(v) = 51*v**2 - 57*v + 5. Let x(a) = 229*a + 2 - 227*a + 2*a**2 - 1. Let q(b) = -c(b) + 5*x(b). What is the second derivative of q(d) wrt d?\n | -82\n | ibivibiv/math_instruct | |
Let b(a) = 181*a - 1758. Determine b(9).\n | -129\n | ibivibiv/math_instruct | |
Solve -65*a - 161 = -80*a + 94 for a.\n | 17\n | ibivibiv/math_instruct | |
What is -4.804289601 rounded to three dps?\n | -4.804\n | ibivibiv/math_instruct | |
Suppose -5*d = -0*d - 5*y - 5, 4*y = 3*d. Find the third derivative of -2*t**3 + 0*t**2 + d*t**3 - t**3 - 10*t**2 wrt t.\n | 6\n | ibivibiv/math_instruct | |
Expand (-5*c + 0 + 0 + 1 - 1 + 2*c + (2 + 2 - 5)*(2*c - 4*c + 3*c) + 2*c - 4*c + c + 4*c + 0 + 0)*(0 + 1 + 1 + (2 - 1 + 0)*(-4 + 6 - 3)).\n | -c\n | ibivibiv/math_instruct | |
-0.1*11\n | -1.1\n | ibivibiv/math_instruct | |
What is the highest common factor of 4971 and 3376795329?\n | 4971\n | ibivibiv/math_instruct | |
Work out -153814896 - -5067.\n | -153809829\n | ibivibiv/math_instruct | |
Let n(z) = -5*z**3 + 2*z**2 + 106*z + 104. Determine n(-1).\n | 5\n | ibivibiv/math_instruct | |
-35846 divided by 1\n | -35846\n | ibivibiv/math_instruct | |
What is the product of -0.4 and 926?\n | -370.4\n | ibivibiv/math_instruct | |
12 + (4 - (3 - (-4 + 10)))\n | 19\n | ibivibiv/math_instruct | |
Expand (2*q + 2*q - 7*q)*(5*q - 4*q - 3*q)*(0*q - 1 + 4*q - 2*q).\n | 12*q**3 - 6*q**2\n | ibivibiv/math_instruct | |
Let q = -107.2 - 1915.8. Let g = -2112.15 - q. Let z = g - -89. Which is the biggest value? (a) z (b) -1/6 (c) 2/13 (d) -2/3\n | c\n | ibivibiv/math_instruct | |
-280 divided by -5\n | 56\n | ibivibiv/math_instruct | |
Collect the terms in 38*s + s + 18*s + 38*s.\n | 95*s\n | ibivibiv/math_instruct | |
What is the nearest to -9/142 in 2/5, -1, 2/7?\n | 2/7\n | ibivibiv/math_instruct | |
0.5 times 0.1269\n | 0.06345\n | ibivibiv/math_instruct | |
Let h(q) = q**3 + 17*q**2 + 7*q + 23. Calculate h(-17).\n | -96\n | ibivibiv/math_instruct | |
Let p be 6 - (3 - (6 - 5)). Suppose -3*g = -8*g. Solve 4*w + 11 = m, 0 = p*w + 12 - g for m.\n | -1\n | ibivibiv/math_instruct | |
Factor -1585*n**2/2 - 2171*n/2 - 293.\n | -(n + 1)*(1585*n + 586)/2\n | ibivibiv/math_instruct | |
Work out -0.3 - 2.55542.\n | -2.85542\n | ibivibiv/math_instruct | |
How many minutes are there between 8:41 PM and 5:40 AM?\n | 539\n | ibivibiv/math_instruct | |
Simplify ((((m**(-11)*m)/m)/m*m/((m*m**(-10)*m)/m)*(m**(-1/7))**(7/6))**(3/16))**37 assuming m is positive.\n | m**(-481/32)\n | ibivibiv/math_instruct | |
What is 553 minutes before 7:28 PM?\n | 10:15 AM\n | ibivibiv/math_instruct | |
Sort 15, -2, 2/3, 0.3, -1 in increasing order.\n | -2, -1, 0.3, 2/3, 15\n | ibivibiv/math_instruct | |
Let g be (-6)/(-15)*(-5)/(-2). Let f(k) = 2*k**2 + k. Let i be f(g). Which is the nearest to -1? (a) 2/3 (b) i (c) 4/9\n | c\n | ibivibiv/math_instruct | |
Expand 6 - 328*c**3 - 33*c**4 + 328*c**3 + (-6*c**2 + 0*c**2 - 3*c**2)*(-4*c**2 + 2*c**2 + 3*c**2).\n | -42*c**4 + 6\n | ibivibiv/math_instruct | |
Calculate 78 divided by -14.\n | -39/7\n | ibivibiv/math_instruct | |
Do 0 and -150/157 have different values?\n | True\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {l: 1, k: 1, m: 3}. Give prob of sequence mmm.\n | 1/10\n | ibivibiv/math_instruct | |
Simplify (m**(-5)*(m/(m**(-2)/m))/m)**(-18)/(m*m/m**(2/9)*m**1)**(2/43) assuming m is positive.\n | m**(13882/387)\n | ibivibiv/math_instruct | |
What is the least common multiple of 6 and 310?\n | 930\n | ibivibiv/math_instruct | |
Let j(v) = 2*v + 23. Let f(a) = -4*a - 46. Let q(p) = -3*f(p) - 5*j(p). What are the prime factors of q(0)?\n | 23\n | ibivibiv/math_instruct | |
Let u(l) be the first derivative of 3*l**3 - l**2/2 + l - 13. Is 9 a factor of u(1)?\n | True\n | ibivibiv/math_instruct | |
Suppose -13*q + 1156 = -9*q. Is q a prime number?\n | False\n | ibivibiv/math_instruct | |
Rearrange (-486*n - 376*n - 178*n + 145*n)*(19 - 5 - 3) to the form p + u*n and give u.\n | -9845\n | ibivibiv/math_instruct | |
What is the nearest to -6 in 1, 0.4, 0.1, -3?\n | -3\n | ibivibiv/math_instruct | |
In base 16, what is 35fbc + 2?\n | 35fbe\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 144 and 644160.\n | 1932480\n | ibivibiv/math_instruct | |
Let q = 74 - 72. Suppose 2*i = -l + 216, i - q*l = 3*l + 108. Does 32 divide i?\n | False\n | ibivibiv/math_instruct | |
Let f be ((-22)/12 - -2) + (-1475)/2478. Let z = 1 + -1. Let m = 0.4 + z. Which is the closest to -1? (a) m (b) -5 (c) f\n | c\n | ibivibiv/math_instruct | |
Simplify ((sqrt(84) - 3*((sqrt(84)*1 - sqrt(84) - sqrt(84)) + sqrt(84)) - sqrt(84)) + sqrt(84))/((-2*sqrt(60))/sqrt(5) + sqrt(12)).\n | -sqrt(7)\n | ibivibiv/math_instruct | |
Let y be (-1 - -5)*4*1. Suppose -2*w = -y + 2. What is the remainder when 12 is divided by w?\n | 5\n | ibivibiv/math_instruct | |
Let u(t) = -t**3 + t**2 - 8*t - 4. Give u(-5).\n | 186\n | ibivibiv/math_instruct | |
Expand (-9*d - 17*d + 4 + 21*d - 22)*(18*d - 13*d - 10*d).\n | 25*d**2 + 90*d\n | ibivibiv/math_instruct | |
List the prime factors of 184779.\n | 3, 7, 419\n | ibivibiv/math_instruct | |
What is 1506/(-36) + (-404 - -447)?\n | 7/6\n | ibivibiv/math_instruct | |
Let s = -70 + 181. Calculate the remainder when s is divided by 28.\n | 27\n | ibivibiv/math_instruct | |
What is the highest common divisor of 493 and 69629?\n | 29\n | ibivibiv/math_instruct | |
Let i = -18 + 18.4. Let h(n) = 7*n**3 - n**2 - 3*n - 2. Let l be h(-2). Let o = 223/4 + l. Put 0, o, i in increasing order.\n | o, 0, i\n | ibivibiv/math_instruct | |
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"### Two Trees
Two trees 20 metres and 30 metres long, lean across a passageway between two vertical walls. They cross at a point 8 metres above the ground. What is the distance between the foot of the trees?
### Golden Tria... | ### Problem One: Two Trees
This problem requires knowledge of geometry, specifically right triangles and the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of ... | ibivibiv/math_instruct | |
What is the third derivative of d**4 + 7*d**5 + 6*d**5 - 10031*d**2 + 24*d**3 + 10399*d**2 + 6*d + 0 + 0 wrt d?\n | 780*d**2 + 24*d + 144\n | ibivibiv/math_instruct | |
Sort 0, 0.23, 1/2, 0.39, 2/15 in ascending order.\n | 0, 2/15, 0.23, 0.39, 1/2\n | ibivibiv/math_instruct | |
What comes next: -47, -110, -189, -284, -395, -522, -665?\n | -824\n | ibivibiv/math_instruct | |
In base 15, what is -68e - 2?\n | -691\n | ibivibiv/math_instruct | |
Three letters picked without replacement from bbvvvbbbbbbbbbbb. Give prob of picking 3 b.\n | 143/280\n | ibivibiv/math_instruct | |
((-72)/(-108)*-3)/((-2)/(-12))\n | -12\n | ibivibiv/math_instruct |
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