instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Expand -3*k**2 + k**2 + 0*k**2 + (7*k**2 - 3*k**2 - k**2)*(0 + 5 - 3) + 3*k**2 - 34*k + 34*k + 3*k**2 - 2*k**2 + 0*k**2.\n | 8*k**2\n | ibivibiv/math_instruct | |
What is the tens digit of 2 - (881530/(-39) + (-20)/12 + 2)?\n | 0\n | ibivibiv/math_instruct | |
Let i(r) = -r**2 + 337047*r - 45819900. Calculate i(136).\n | -4\n | ibivibiv/math_instruct | |
Let x(g) = -g**3 - 16*g**2 - 15*g + 14. Let s be x(-15). Let u = -12 + s. What is the third derivative of -49*v**5 + 8*v**u - 8*v**6 + 49*v**5 wrt v?\n | -960*v**3\n | ibivibiv/math_instruct | |
What is the result of the following expression?
9.6929 + (9.8226 * -50.587) | -487.2030 | ibivibiv/math_instruct | |
Let z = -8 + -8. Let s be (-3)/((-2)/(z/(-12))). Factor -2*g**5 - 20*g**2 + s*g - 7*g**3 - 10*g**4 + 0*g**3 - 12*g - 2 - 13*g**3.\n | -2*(g + 1)**5\n | ibivibiv/math_instruct | |
Let i = 1721.58 - 1695. Let a = 247 + -270.6. Let g = a + i. What is g rounded to 1 decimal place?\n | 3\n | ibivibiv/math_instruct | |
Suppose -3*b + 24 = 3*p - 0*b, 0 = -5*p + 3*b. Suppose -5*f + p*f + 4 = 0. Suppose 5*v - 2*w = 299, f*v - w + 2*w - 116 = 0. Is v prime?\n | True\n | ibivibiv/math_instruct | |
How many minutes are there between 11:57 AM and 9:38 PM?\n | 581\n | ibivibiv/math_instruct | |
Calculate (3*(-8)/12)/2.\n | -1\n | ibivibiv/math_instruct | |
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"Lecture 4: more on functions
• reading: MCS 4.3-4.4
• basic function definitions
• jectivity (injectivity, bijectivity, surjectivity)
• composition
• image
• cardinality relations
Definitions
A function $$f : A → B$$ is
... | Functions are fundamental building blocks in mathematics, used to describe relationships between sets. We'll dive deeper into their properties and behaviors, focusing on injectivity, surjectivity, bijectivity, composition, and cardinality.
Let's begin with a refresher on basic function definitions: Given two sets $A$... | ibivibiv/math_instruct | |
-10852 + -0.35\n | -10852.35\n | ibivibiv/math_instruct | |
What is the nearest to 6 in 7238, -3, 1/37, 0.7, 0.3, 0.2?\n | 0.7\n | ibivibiv/math_instruct | |
In base 6, what is -35 + -1?\n | -40\n | ibivibiv/math_instruct | |
Rearrange (2 - 2 - 3*i)*(8 + 9 - 28) + 2 + 11 + 257*i - 258*i to the form v + w*i and give v.\n | 13\n | ibivibiv/math_instruct | |
What is 1993 to the power of 1/2, to the nearest integer?\n | 45\n | ibivibiv/math_instruct | |
Let p(h) = h**2 - h - 1. Let n(c) = 6*c**2 + c + 9. Let x(u) = -2*n(u) - 2*p(u). Differentiate x(q) wrt q.\n | -28*q\n | ibivibiv/math_instruct | |
Let d(a) = 2*a - 20. Let h be d(11). Let l(j) = -h*j**2 - 3 + 6 - 4 + 2. Let n(t) = -t**3 + 4*t**2 + 10*t + 14. Let y be n(6). Calculate l(y).\n | -7\n | ibivibiv/math_instruct | |
What is the product of -6.2881 and 0.44?\n | -2.766764\n | ibivibiv/math_instruct | |
Suppose 6*f - 2*f - 5*h = -105, -5*f - 115 = -3*h. Let d = f + 669. Is d prime?\n | False\n | ibivibiv/math_instruct | |
Expand (-58 + 948 + 434)*(-4*x**5 + 0*x**5 + 3*x**5 + (0*x**2 + 0*x**2 - x**2)*(2*x**3 - 3*x**3 - 5*x**3)).\n | 6620*x**5\n | ibivibiv/math_instruct | |
Let m = -347 - -431. Calculate the smallest common multiple of 12 and m.\n | 84\n | ibivibiv/math_instruct | |
Express -4*n**4 - 63*n**3 + 63*n**3 + (4*n**3 - 9*n**3 - 3*n**3)*(2*n - 3*n - 2*n) in the form x*n + p*n**4 + f*n**3 + h*n**2 + c and give p.\n | 20\n | ibivibiv/math_instruct | |
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"Find all School-related info fast with the new School-Specific MBA Forum
It is currently 05 Aug 2015, 03:20
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance an... | A quadrilateral is a four-sided polygon, and when it is inscribed in a circle, its vertices (corners) touch the circumference of the circle. This relationship between the quadrilateral and the circle allows us to apply certain properties that help us solve geometric problems. Let's explore these properties and how the... | ibivibiv/math_instruct | |
Let m(b) be the third derivative of 0 + 0*b**4 + 0*b - 1/210*b**7 + 3*b**2 + 0*b**6 - 1/20*b**5 + 0*b**3. Find the third derivative of m(q) wrt q.\n | -24*q\n | ibivibiv/math_instruct | |
Calculate (-45)/10*5/15*-2.\n | 3\n | ibivibiv/math_instruct | |
Let u = 1780 - 1780. Let l = -0.1 - 0.4. Let k = -0.3 - -0.2. What is the nearest to u in l, k, 1/4?\n | k\n | ibivibiv/math_instruct | |
Sort 209, -2/15, 0, -0.1.\n | -2/15, -0.1, 0, 209\n | ibivibiv/math_instruct | |
List the prime factors of 3287752.\n | 2, 13, 101, 313\n | ibivibiv/math_instruct | |
Let r be (-498)/(-102) + -5 - (-4)/34. Let v be (-1)/3*-1*(r - 9). Let x(j) = -2*j. What is x(v)?\n | 6\n | ibivibiv/math_instruct | |
Suppose -3*j = -j, 3*s - 30 = -4*j. Suppose -4*z - p + 9 = -3*z, s = 5*z - 2*p. Suppose 3*q**3 + 1 - q**z - q**3 - 3*q + q = 0. What is q?\n | -1, 1\n | ibivibiv/math_instruct | |
Expand (-4*z + 2*z + 5*z)*(0*z**3 + 0*z**3 + 2*z**4) + (-3*z - 4*z + 18*z)*(-6*z**4 - 6*z + 6*z) + (z**2 + z**3 - z**2)*(3*z - 2*z**2 - 3*z).\n | -62*z**5\n | ibivibiv/math_instruct | |
Determine s, given that -s**2 - 945*s - 10274 = 0.\n | -934, -11\n | ibivibiv/math_instruct | |
Let j = 16 - -20. Let i be (8/(-446))/1*(-18)/j. Let x = i + -456/1115. Which is the second biggest value? (a) 19 (b) x (c) 3/5\n | c\n | ibivibiv/math_instruct | |
Let i(r) be the second derivative of -11*r**4/12 - r**3/2 - 3*r**2/2 - 975*r + 2. Let u(m) = 32*m**2 + 8*m + 8. Determine -8*i(z) - 3*u(z).\n | -8*z**2\n | ibivibiv/math_instruct | |
Calculate (-3 - -5) + 42 + -62 + -19.\n | -37\n | ibivibiv/math_instruct | |
Let k be ((-245)/(-196))/(110/16). Which is the third smallest value? (a) -5/2 (b) 2/7 (c) k (d) -6\n | c\n | ibivibiv/math_instruct | |
-2836831 (base 10) to base 4\n | -22310211133\n | ibivibiv/math_instruct | |
Let u(h) = -24042 + 23913 - 19*h + 15*h. Determine u(-35).\n | 11\n | ibivibiv/math_instruct | |
Let c = -20 + 25. Solve 2*s = s + c for s.\n | 5\n | ibivibiv/math_instruct | |
What are the prime factors of 10923198?\n | 2, 3, 11, 13, 29, 439\n | ibivibiv/math_instruct | |
Let -2*x**4 + 68*x**3 - 246*x**2 - 1244*x - 928 = 0. Calculate x.\n | -2, -1, 8, 29\n | ibivibiv/math_instruct | |
Solve -12*k - 510 = -474 for k.\n | -3\n | ibivibiv/math_instruct | |
Simplify sqrt(1573) + (-1 + sqrt(1573) + 5 - sqrt(1573)).\n | 4 + 11*sqrt(13)\n | ibivibiv/math_instruct | |
Let t(y) = 5*y**2. Let s(g) = 2*g**2 - 8*g + 8. Let w = 18 + -13. Let q(j) = -3 + j**2 + 1 + w - 3*j. Let v(p) = -8*q(p) + 3*s(p). Determine t(v(d)).\n | 20*d**4\n | ibivibiv/math_instruct | |
Find the common denominator of -77/291 and 71/194.\n | 582\n | ibivibiv/math_instruct | |
Factor i**3 - 19*i**2/4 + 19*i/4 + 3/2.\n | (i - 3)*(i - 2)*(4*i + 1)/4\n | ibivibiv/math_instruct | |
What is 0.0021059 rounded to four decimal places?\n | 0.0021\n | ibivibiv/math_instruct | |
Suppose 0*h + 9/2*h**4 + 0 + 3/2*h**2 + 9/2*h**3 + 3/2*h**5 = 0. What is h?\n | -1, 0\n | ibivibiv/math_instruct | |
Let p(v) be the third derivative of -v**6/120 + 13*v**5/30 - 23*v**4/24 - v**3 + v**2. Suppose 51*w = 192 + 1083. List the prime factors of p(w).\n | 2, 11\n | ibivibiv/math_instruct | |
What is the least common multiple of 184 and 18?\n | 1656\n | ibivibiv/math_instruct | |
An infinite geometric series has common ratio $-1/5$ and sum $16.$ What is the first term of the series? | Let the first term be $a$. Because the sum of the series is $16$, we have $16= \frac{a}{1-(-1/5)} = \frac{a}{6/5} = \frac{5a}{6}$. Therefore, $a=\boxed{\frac{96}{5}}$. The answer is \frac{96}{5} | ibivibiv/math_instruct | |
Is 40/7 < -6268?\n | False\n | ibivibiv/math_instruct | |
Is -3/2 greater than or equal to 425/2663?\n | False\n | ibivibiv/math_instruct | |
Let q = -48 - -45. Is q bigger than -0.1?\n | False\n | ibivibiv/math_instruct | |
Round -0.002032108706 to 3 decimal places.\n | -0.002\n | ibivibiv/math_instruct | |
What is the next term in 181, 365, 547, 727, 905?\n | 1081\n | ibivibiv/math_instruct | |
Simplify -1 + (-2 + sqrt(153) - (sqrt(85)/sqrt(5) + 1)**2) + (sqrt(153) + -2*sqrt(153) + 5 - (-1 + sqrt(153) + 2))**2.\n | -47*sqrt(17) + 607\n | ibivibiv/math_instruct | |
Calculate ((12597/(-78))/(-19))/(6/4)*9.\n | 51\n | ibivibiv/math_instruct | |
Solve -13 - 1017 = -132*z - 74*z for z.\n | 5\n | ibivibiv/math_instruct | |
Let g = -2 - -1.8. Let m = -1/5293 - 10569/89981. Let c = 23/2 + -11. What is the third smallest value in g, m, c?\n | c\n | ibivibiv/math_instruct | |
Let o(r) = 2*r + 36. Let h be o(-16). Suppose -9 = -i - h*l, -2*i + 60 = 3*i + 5*l. Suppose 2*x - 8 = x. Calculate the remainder when i is divided by x.\n | 5\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 5329350 and 1755.\n | 15988050\n | ibivibiv/math_instruct | |
Suppose -2*r + 8 = -2*t, 3*r + 9 = -5*t - 3. Is r < 1/17?\n | False\n | ibivibiv/math_instruct | |
Let o(n) = n**3 + 4*n**2 - 13*n. Let z(t) = t**3 + 5*t**2 - 13*t. Determine -5*o(d) + 4*z(d).\n | -d**3 + 13*d\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 348941 and 20414.\n | 41175038\n | ibivibiv/math_instruct | |
Collect the terms in -825 - 815 - 824 + 3299 + 20*t**2 - 835.\n | 20*t**2\n | ibivibiv/math_instruct | |
Let l = 612 + -899. Let z = -287 - l. Which is greater: -22/39 or z?\n | z\n | ibivibiv/math_instruct | |
Let w(h) = -h**2 - 5*h + 2. Let n = -10 + 12. Let u = -2 - n. Calculate w(u).\n | 6\n | ibivibiv/math_instruct | |
Which is the closest to -5? (a) -1/3 (b) -3 (c) 4 (d) -15\n | b\n | ibivibiv/math_instruct | |
Simplify -3*sqrt(7)*2*4.\n | -24*sqrt(7)\n | ibivibiv/math_instruct | |
What is 162445 to the power of 1/7, to the nearest integer?\n | 6\n | ibivibiv/math_instruct | |
What is the highest common divisor of 191 and 34189?\n | 191\n | ibivibiv/math_instruct | |
Is -329 < -313?\n | True\n | ibivibiv/math_instruct | |
What is 254 minutes before 2:28 PM?\n | 10:14 AM\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 34 and 11458.\n | 34\n | ibivibiv/math_instruct | |
How many minutes are there between 8:34 PM and 10:05 PM?\n | 91\n | ibivibiv/math_instruct | |
Suppose -28739*v + 28967*v - 185 = 145 + 126. Find b such that -45/2*b**v + 10*b - 5/6 = 0.\n | 1/9, 1/3\n | ibivibiv/math_instruct | |
Let h(x) = x**2 + 15*x - 2. Let k(v) = 5*v**2 + 37*v - 363. Let m be k(-13). Let y(j) = -j**2 + j. Determine m*h(f) + 2*y(f).\n | -f**2 + 17*f - 2\n | ibivibiv/math_instruct | |
Let u(s) be the second derivative of s**4/12 + 4*s**3/3 + 5*s**2 + 4*s. What is the units digit of u(-10)?\n | 0\n | ibivibiv/math_instruct | |
What is the tens digit of 14950584?\n | 8\n | ibivibiv/math_instruct | |
Let o(j) be the third derivative of -j**5/30 - j**4/4 - j**3/3 + 20*j**2. What is o(-5)?\n | -22\n | ibivibiv/math_instruct | |
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"# pptest
Phillips-Perron test for one unit root
## Description
example
h = pptest(y) returns the rejection decision h from conducting the Phillips-Perron test for a unit root in the univariate time series y.
example
[h,... | The Phillips-Perron (PP) test is a statistical method used to determine whether a time series contains a unit root, which indicates non-stationarity. This test is particularly useful when dealing with data that may be affected by serial correlation, a common issue in econometric analyses where observations close toget... | ibivibiv/math_instruct | |
Does 6 divide (-35)/4*(-3 + (5 - 10))?\n | False\n | ibivibiv/math_instruct | |
Collect the terms in 2*w**2 + 0*w**2 - 95*w**3 - 2*w**2.\n | -95*w**3\n | ibivibiv/math_instruct | |
Is 163054597 a composite number?\n | True\n | ibivibiv/math_instruct | |
What are the prime factors of 42982?\n | 2, 21491\n | ibivibiv/math_instruct | |
What is the product of 4 and -6959?\n | -27836\n | ibivibiv/math_instruct | |
What are the prime factors of 81050?\n | 2, 5, 1621\n | ibivibiv/math_instruct | |
Let i = 114 - 108. Solve -4*x + i*x = 0 for x.\n | 0\n | ibivibiv/math_instruct | |
Is -969/23639 at most -1?\n | False\n | ibivibiv/math_instruct | |
What is the third smallest value in 2/5, 7, -4, -5501/4, 1/3?\n | 1/3\n | ibivibiv/math_instruct | |
(-3826 + 3839)/(52/(-368))\n | -92\n | ibivibiv/math_instruct | |
What is the value of (48/2112)/((-2)/4)*4?\n | -2/11\n | ibivibiv/math_instruct | |
Let u = 2314/4025 - 2/575. Sort -1/5, -2/9, u, -0.4 in decreasing order.\n | u, -1/5, -2/9, -0.4\n | ibivibiv/math_instruct | |
Which is the closest to 1? (a) 3/5 (b) -0.08 (c) -0.5 (d) 2\n | a\n | ibivibiv/math_instruct | |
What is -1 + 657.507?\n | 656.507\n | ibivibiv/math_instruct | |
What is the common denominator of 2/9321 and -39/10346549?\n | 403515411\n | ibivibiv/math_instruct | |
What is twenty-seven halves of a micrometer in nanometers?\n | 13500\n | ibivibiv/math_instruct | |
Simplify (((r/((r*r/(r*r**2))/r))/r)**(-45)/(r**(-1/3))**(5/7))/((r**(3/7)*(r/(r**(-7)*r))/r)/(r/r**(2/3)*r**(4/9)/r)) assuming r is positive.\n | r**(-6074/63)\n | ibivibiv/math_instruct |
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