instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Expand (6*r + r - r)*(6 - 15 - 5)*(-1 + 2 - 3).\n | 168*r\n | ibivibiv/math_instruct | |
Let c be 1 - 8930/1872 - -2. Let i = 11/72 - c. Calculate the common denominator of (-97)/22 - (-2)/4 and i.\n | 143\n | ibivibiv/math_instruct | |
Expand 3 - 3 + 2*a**3 + (a**2 - 1 + 1)*(-4 - 2*a + 4) + 8*a**2 - 2*a**3 - 8*a**2 + 7*a**3 - 4*a**3 + 0*a**3 + (-1 + 2*a + 1)*(-6*a + 2*a + 0*a)*(0*a - a + 0*a).\n | 9*a**3\n | ibivibiv/math_instruct | |
Suppose -4*b = -b - 3489. Is b a composite number?\n | False\n | ibivibiv/math_instruct | |
Let r = 758.3 + -758. Which is the closest to 0.1? (a) r (b) -2/17 (c) -5\n | a\n | ibivibiv/math_instruct | |
Let d(r) = -3*r**3 + 2*r**2 - 4*r - 3. Let u be d(-3). Let j = -48 + u. What is the tens digit of j?\n | 6\n | ibivibiv/math_instruct | |
Is 5317.58 not equal to 179?\n | True\n | ibivibiv/math_instruct | |
What is -23.082 - 0.17936601587?\n | -23.26136601587\n | ibivibiv/math_instruct | |
Calculate the remainder when 2678 is divided by 270.\n | 248\n | ibivibiv/math_instruct | |
Round -0.000074147731 to 7 dps.\n | -0.0000741\n | ibivibiv/math_instruct | |
What is the next term in 894, 1277, 1916, 2811?\n | 3962\n | ibivibiv/math_instruct | |
How many minutes are there between 2:19 PM and 10:56 PM?\n | 517\n | ibivibiv/math_instruct | |
Let n(i) = -6*i**2 - 22. Let t(v) = 81*v - 221*v + 70*v + 73*v. Calculate n(t(q)).\n | -54*q**2 - 22\n | ibivibiv/math_instruct | |
In base 15, what is 1121 + 0?\n | 1121\n | ibivibiv/math_instruct | |
Suppose 0 = -5*x - 49 + 119. Let q be (-24)/((x/(-56))/(2/12)). Let s(n) = -n**2 + n + 2. Let a be s(2). Solve 4*c - 4*p - q = -a*c, c - 4*p = 4 for c.\n | 4\n | ibivibiv/math_instruct | |
Let a be (-2)/(-11) - 80/(-44). Let x be ((-8)/(0 + a))/(-2). Solve x*n = -n - 9 for n.\n | -3\n | ibivibiv/math_instruct | |
Does 68 divide 1273640?\n | True\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 28514 and 106?\n | 106\n | ibivibiv/math_instruct | |
How many minutes are there between 8:23 PM and 6:22 AM?\n | 599\n | ibivibiv/math_instruct | |
Let v(b) = 13*b**2 + 144*b + 181. Determine v(-11).\n | 170\n | ibivibiv/math_instruct | |
What is the ten millions digit of 41886876?\n | 4\n | ibivibiv/math_instruct | |
Suppose -z = 5*y - 101, 360 = 20*z - 15*z - 4*y. Differentiate -z*c**3 + 13 + 9 - 2 + 3 with respect to c.\n | -228*c**2\n | ibivibiv/math_instruct | |
b"What is the wth term of -45, -83, -183, -375, -689, -1155, -1803, -2663?\n" | -5*w**3 - w**2 - 39\n | ibivibiv/math_instruct | |
Let u be 6/21 + 5/7. Suppose u = 2*p - p. Let m = p - -6. What is the units digit of m?\n | 7\n | ibivibiv/math_instruct | |
Suppose -3*k + 9*w - 4*w = -4399, -2*k + 3*w + 2933 = 0. Suppose 4*f + 4*p - 12 = 0, -5*f + f = p - 9. Is (f - 2) + (k - -5) composite?\n | True\n | ibivibiv/math_instruct | |
Let s(v) = -145*v**2 - 2*v + 8. Let p(d) = -144*d**2 - d + 9. Let u(y) = 3*p(y) - 4*s(y). Is u(2) a composite number?\n | True\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 24 and 6.\n | 24\n | ibivibiv/math_instruct | |
Let k(v) = 80*v**2 + 35. Let q be k(-6). Suppose 10*p - 1995 - q = 0. Is p a multiple of 14?\n | False\n | ibivibiv/math_instruct | |
Let a(i) = i**2 - 9*i + 1. Let p be a(10). Let m be p/1*(0 + 76/2). What is the highest common divisor of m and 38?\n | 38\n | ibivibiv/math_instruct | |
Let f be 34/102*(-12)/(-10). Which is the third smallest value? (a) 0.2 (b) f (c) 3 (d) 4\n | c\n | ibivibiv/math_instruct | |
Let s = 333 + -82. Is s composite?\n | False\n | ibivibiv/math_instruct | |
Calculate 13 + (-25*(-60)/375 - (-1 - 1)).\n | 19\n | ibivibiv/math_instruct | |
Expand (2*k - 2*k + 2*k**3 + (-2*k + 2*k - 2*k**2)*(0*k + k - 3*k) - 2*k**3 - k + k)*(-3*k**2 - 4*k**2 + 56*k**2).\n | 196*k**5\n | ibivibiv/math_instruct | |
What is 274336 to the power of 1/7, to the nearest integer?\n | 6\n | ibivibiv/math_instruct | |
Convert 2 (base 11) to base 13.\n | 2\n | ibivibiv/math_instruct | |
Put -2, 16107, 0.3 in descending order.\n | 16107, 0.3, -2\n | ibivibiv/math_instruct | |
Simplify ((i*i*i**0*i*i)/i*(i/(i/(i*i*i**(1/11)*i))*i)/i)/(i*i**(-1/2))**(-50) assuming i is positive.\n | i**(342/11)\n | ibivibiv/math_instruct | |
Simplify ((-3*sqrt(114)*-2)/(sqrt(6)*2*3))**2 + -4.\n | 15\n | ibivibiv/math_instruct | |
Express (8*p + 2*p - 6*p)*(-4 + 1 + 2) in the form h + v*p and give v.\n | -4\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {v: 1, p: 1, f: 2}. Give prob of sequence vpff.\n | 1/12\n | ibivibiv/math_instruct | |
Suppose -q - 2*q + 18 = 0. Let f(x) = 2*x**2 + 9 + x - x**2 + q*x. List the prime factors of f(-6).\n | 3\n | ibivibiv/math_instruct | |
Let x be (7 - 6)*(0 + 0). Suppose 18*u - 21*u + 36 = x. Suppose u = 8*w - 4*w. Solve 2*o - 15 = -w*a - o, 4*o = -a + 8 for a.\n | 4\n | ibivibiv/math_instruct | |
Add together -0.1182 and 47845559917.\n | 47845559916.8818\n | ibivibiv/math_instruct | |
What is eleven tenths of a litre in millilitres?\n | 1100\n | ibivibiv/math_instruct | |
Let v(i) be the first derivative of -3*i**4/4 - 4*i**3/3 + 2*i**2 - 3*i + 2184. Let g(t) = -9*t**3 - 12*t**2 + 11*t - 8. Determine -3*g(y) + 8*v(y).\n | 3*y**3 + 4*y**2 - y\n | ibivibiv/math_instruct | |
Let f = -1/6 + 1/78. Which is the nearest to -2? (a) f (b) -0.4 (c) -3\n | c\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 1594184 and 2391276.\n | 4782552\n | ibivibiv/math_instruct | |
Let z(k) = k + 2. Let v be -5*-2*1/(-5). Let p be z(v). Is 5 + (p/2 - -1) composite?\n | True\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {h: 1, i: 8, k: 4, t: 2}. Give prob of picking 1 k and 1 t.\n | 8/105\n | ibivibiv/math_instruct | |
What is -56458 divided by -2?\n | 28229\n | ibivibiv/math_instruct | |
What is 3448.843ug in kilograms?\n | 0.000003448843\n | ibivibiv/math_instruct | |
Which is the biggest value? (a) -0.5 (b) -8.96 (c) -2 (d) 4/5\n | d\n | ibivibiv/math_instruct | |
Let v = -36/11 - -224/55. Let f = 0.4 + -0.4. Let j = 78 + -77. Which is the nearest to -1? (a) v (b) f (c) j\n | b\n | ibivibiv/math_instruct | |
What is prob of picking 1 i and 3 g when four letters picked without replacement from {i: 4, f: 1, g: 3, n: 2, r: 1, w: 1}?\n | 4/495\n | ibivibiv/math_instruct | |
What is the closest to -4/9 in 1814, -5, -493?\n | -5\n | ibivibiv/math_instruct | |
Simplify 3 + 1 + ((sqrt(396) + 0 + sqrt(396))**2 - sqrt(11)) + (sqrt(704) - (0 + sqrt(704) + -5))**2.\n | -sqrt(11) + 1613\n | ibivibiv/math_instruct | |
Which is smaller: 3542 or 11854?\n | 3542\n | ibivibiv/math_instruct | |
Let b(d) = -7*d**2. Let x(y) = 10*y + 26. Let o(t) = t + 3. Let q(n) = -52*o(n) + 6*x(n). What is b(q(i))?\n | -448*i**2\n | ibivibiv/math_instruct | |
Let z(h) = -6520*h + 984487. What is z(151)?\n | -33\n | ibivibiv/math_instruct | |
-5 (base 7) to base 4\n | -11\n | ibivibiv/math_instruct | |
Let c = -18.4 - -17.9. Let k = 32 - 129/4. What is the second biggest value in c, -2, k?\n | c\n | ibivibiv/math_instruct | |
Sort 3, -402666, -4 in descending order.\n | 3, -4, -402666\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 1 and 2.\n | 1\n | ibivibiv/math_instruct | |
Let z = -0.026 - 2.074. Let k = -4.7 - z. Round k to the nearest integer.\n | -3\n | ibivibiv/math_instruct | |
Put -66, 3, -3, 2, 0.5, 9 in decreasing order.\n | 9, 3, 2, 0.5, -3, -66\n | ibivibiv/math_instruct | |
228971 divided by 6\n | 228971/6\n | ibivibiv/math_instruct | |
Let g(m) be the first derivative of m**3/3 + m**2 - 2*m - 2. Let u(f) = f**2 - 8 + 11*f + 4*f**2 + f**2 - 3. What is -11*g(r) + 2*u(r)?\n | r**2\n | ibivibiv/math_instruct | |
Let p(m) be the second derivative of -31*m**3/6 - 3*m**2/2 + 5*m. Let n be p(-3). Suppose -3*f + 117 = -n. Is f a composite number?\n | True\n | ibivibiv/math_instruct | |
Suppose -10 = 2*r + 4*i, -3*r - 9 = -4*r + 5*i. Let f be (-44)/(-12) - r/3. Suppose 11*y - 13*y + 6 = 0. Sort 2, f, y in increasing order.\n | 2, y, f\n | ibivibiv/math_instruct | |
Round -21433.38555 to the nearest 10.\n | -21430\n | ibivibiv/math_instruct | |
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# 7.3: Solving Linear Systems by Elimination
Difficulty Level: At Grade Created by: CK-12
## Learning Objectives
• Solve a linear system of equations using elimi... | The HTML code you've provided, "<meta http-equiv="refresh" content="1; url=/nojavascript/"", is not directly related to the lesson on "Solving Linear Systems by Elimination". However, I will provide an explanation of the given topic while trying to connect it briefly to the HTML code at the end.
When dealing with sys... | ibivibiv/math_instruct | |
Let f = 9.99 - -0.01. Let z = f + -7. What is the nearest to 1/2 in z, 0.1, 0?\n | 0.1\n | ibivibiv/math_instruct | |
Is -1026917 greater than -1026944?\n | True\n | ibivibiv/math_instruct | |
What is the remainder when (725/(-50))/((-2)/4) is divided by 5?\n | 4\n | ibivibiv/math_instruct | |
Let h(l) = 192124 + 4*l - 384242 + 192122. Let u(j) = -5*j - 5. Calculate -4*h(q) - 3*u(q).\n | -q - 1\n | ibivibiv/math_instruct | |
Suppose 2*o - 8 = -0*o. Suppose -o*h + 4 = -k - k, -h = 5*k - 12. Suppose k*f - 4*f = -14. Is f even?\n | False\n | ibivibiv/math_instruct | |
Convert 1300332221 (base 5) to base 15.\n | 41e541\n | ibivibiv/math_instruct | |
Suppose 0 = -8*x + 4*x. Let f(y) = -y**3 + 7*y**2 - 2*y + 11. Let o be f(7). Which is the closest to -0.1? (a) o (b) x (c) -0.03\n | c\n | ibivibiv/math_instruct | |
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"# Between every two MST's there's a series of “nearby” MST's
Given undirected connected graph $G=(V,E)$ and a weight function $w:E\to\mathbb{R}$, two MST's $T_1, T_2$ are nearby if there exists $e\in T, e'\in T'$ such that $... | To begin, let us reiterate the definition of "nearby" Minimum Spanning Trees (MSTs). Two MSTs, $T\_1$ and $T\_2$, of an undirected connected graph $G = (V, E)$ with a weight function $w: E -> \mathbb{R}$ are considered nearby if there exist edges $e\_{1} o T\_1$ and $e\'_{1} o T\_2$ such that $(T\_1 - {e\_1}) o (T\... | ibivibiv/math_instruct | |
Simplify (j**(-1/19)*(j/(j*(j*j**(-6))/j))/j)**(-47)*(j**2*j/j**(2/9))/(j**(-2/5)/j**4) assuming j is positive.\n | j**(-192673/855)\n | ibivibiv/math_instruct | |
Collect the terms in 46785*u**3 - 23393*u**3 - 23390*u**3.\n | 2*u**3\n | ibivibiv/math_instruct | |
Suppose -o**4 + 14183*o**3 - 184210*o**2 = 0. Calculate o.\n | 0, 13, 14170\n | ibivibiv/math_instruct | |
What is the tens digit of 1036?\n | 3\n | ibivibiv/math_instruct | |
Solve -3*l + 11 = i, i + 1 = -l + 2*l for i.\n | 2\n | ibivibiv/math_instruct | |
Find the second derivative of -8*j + j**3 - j**3 + 9*j**4 wrt j.\n | 108*j**2\n | ibivibiv/math_instruct | |
Let l = -21.28 + 0.28. Let h = 15.8 + l. Let a = -6.08 - h. Round a to one dp.\n | -0.9\n | ibivibiv/math_instruct | |
Simplify (((sqrt(180) + 1*sqrt(180))*-4)/(sqrt(3) - sqrt(363)*-1))/((-2*sqrt(72)*-2)/(sqrt(18)/(sqrt(3) - sqrt(3)*-1) + sqrt(6))).\n | -sqrt(5)/4\n | ibivibiv/math_instruct | |
What is the hundreds digit of 994641?\n | 6\n | ibivibiv/math_instruct | |
What is 258.674 rounded to the nearest ten?\n | 260\n | ibivibiv/math_instruct | |
Let p = -166.985 + -11.015. What is the nearest to -1 in 3, -0.2, -4, p?\n | -0.2\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 37300 and 225.\n | 335700\n | ibivibiv/math_instruct | |
Simplify -5 + sqrt(242)*2.\n | -5 + 22*sqrt(2)\n | ibivibiv/math_instruct | |
What is the hundred millions digit of 852725936?\n | 8\n | ibivibiv/math_instruct | |
Is 1732844295 a multiple of 3731?\n | True\n | ibivibiv/math_instruct | |
What is -38433 (base 15) in base 10?\n | -179823\n | ibivibiv/math_instruct | |
Let h(k) = 2*k**3 - 55*k**2 - 30*k + 37. Determine h(28).\n | -19\n | ibivibiv/math_instruct | |
Let 2*z**5/3 - 24484*z**4/3 + 26533798*z**3 - 28573513552*z**2/3 + 2723908705568*z/3 = 0. Calculate z.\n | 0, 197, 5924\n | ibivibiv/math_instruct | |
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"# Why does $\pm$ mean two different things in statistics?
In statistics, why do we sometimes use the symbol $$\pm$$ to mean interval of numbers, for example in confidence intervals, and sometimes to mean two numbers, for exa... | In statistics, the symbol ± is often encountered and might appear to have multiple meanings depending on the context. However, upon closer examination, it becomes clear that the symbol retains its fundamental meaning while adapting to various applications within statistical theory and practice. At its core, the symbol... | ibivibiv/math_instruct | |
Let g(o) = -o**2 - o - 32. Let n(t) = -4*t**2 - 3*t - 98. Let i(p) = 7*g(p) - 2*n(p). Calculate i(0).\n | -28\n | ibivibiv/math_instruct | |
Let d = 0.062 + -0.022. What is the second biggest value in 2/7, d, 2?\n | 2/7\n | ibivibiv/math_instruct |
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