Question stringlengths 28 1.07k | Answer stringlengths 1 54 | Answer_type stringclasses 6
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A company has 8 employees, including 3 managers and 5 engineers. How many different ways are there to form a team of 4 employees that includes at least 1 manager and at least 2 engineers? | 60 | integer | Not supported with pagination yet |
The mass of one of the small spheres of a Cavendish balance is 0.0100 kg, the mass of the nearest large sphere is 0.500 kg, and the center-to-center distance between them is 0.0500 m. Assuming the gravitational force on each sphere due to the other is $X * 10^{-10}$ N, what is X? | 1.33 | float | Not supported with pagination yet |
The image produced by a concave mirror is at -16.2m, and the magnification is 1.79. What is the object distance in terms of meter? | 9.05 | float | Not supported with pagination yet |
How many ways are there to partition a set of 5 elements into 3 non-empty cycles? | 35 | integer | Not supported with pagination yet |
Calculate the required memory size in Mebibytes (MiB) (in 3 sig.fig.) for storing a frame in 720p if the sampling scheme Y'CbCr 4:2:0 is used. Note that There are 1280 × 720 pixels in one 720p frame. Each pixel contains three primary-colour components. Each primary-colour component requires 1 byte of memory for storage... | 1.32 | float | Not supported with pagination yet |
Find all positive integers $n<2^{250}$ for which simultaneously $n$ divides $2^n$, $n-1$ divides $2^n-1$, and $n-2$ divides $2^n - 2$. Return all positive integers as an ascending list. | [4, 16, 65536] | list of integer | Not supported with pagination yet |
What is \lim_{x o 9} ((x - 9)/(\sqrt{x} - 3))? | 6 | integer | Not supported with pagination yet |
Using n=8 approximate the value of $\int_{0}^4 cos(1 + \sqrt{x}) dx$ using the Simpson's rule. | -2.47160136 | float | Not supported with pagination yet |
Compute $\int_{|z| = 2} (5z - 2) / (z * (z - 1)) dz$. The answer is Ai with i denoting the imaginary unit, what is A? | 31.4 | float | Not supported with pagination yet |
Consider the following graph, with links costs listed, and assume we are using shortest-path (or lowest-cost) routing, and that routing has equilibrated to a constant set of routing tables. The routing algorithm uses poisoned reverse, advertising an infinite weight for the poisoned paths. is the distance that B adverti... | True | bool | |
What is the value of the inflection point of f(x) =(10 ln(x))/(x^2)? | 2.301 | float | Not supported with pagination yet |
suppose $x=\sqrt{17}/17$. what is the value of $\frac{2}{\pi} \int_0^{+\infty} \frac{\sin ^2 t}{t^2} cos(2xt) dt$? Rounding it to the hundredths place and return the value. | 0.757 | float | Not supported with pagination yet |
Let $X_1, X_2, \ldots$ be a sequence of independent indetically distributed random variables drawn according to the probability mass function $p(x) = N(0,1)$. Let $q(x)=N(1,1)$ be another probability mass function. Use natural logarithm to evaluate $\lim -\frac{1}{n}\log{q(X_1,X_2,\ldots,X_n)}$ as $n \to \infty$. | 1.4 | float | Not supported with pagination yet |
If a,b,c,d > 0 and c^2 + d^2 = (a^2 + b^2)^3, is a^3/c + b^3/d < 1? | False | bool | Not supported with pagination yet |
Phased Solutions Inc. has paid the following dividends per share from 2011 to 2020:
2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020
$0.70 | $0.80 | $0.925 | $1.095 | $1.275 | $1.455 | $1.590 | $1.795 | $1.930 | $2.110
If you plan to hold this stock for 10 years, believe Phased Solutions will continu... | 60.23 | float | Not supported with pagination yet |
Let $P(r,t,T)$ denote the price at time $t$ of $1 to be paid with certainty at time $T, t\leT$, if the short rate at time $t$ is equal to $r$. For a Vasicek model you are given: $P(0.04, 0, 2)=0.9445$, $P(0.05, 1, 3)=0.9321$, $P(r^*, 2, 4)=0.8960$. What is $r^*$? | 0.08 | float | Not supported with pagination yet |
Is 10 a quadratic residue modulo 19? Use Gauss's Lemma to answer it. | False | bool | Not supported with pagination yet |
Solve the following linear programming problems: maximize 3x + y subject to (1) -x + y <= 1, (2) 2x + y <= 4, (3) x>= 0 and y >= 0. What's [x, y] for the optimal solution? | [2, 0] | list of integer | Not supported with pagination yet |
For the following functions, which are bounded entire functions? 1. f(x)=0; 2. f(x)= 1+i; 3. f(x)=sin(x); 4. f(x)=min{|cos(x)|,1}. Here i=\sqrt{-1} and $|\cdot|$ is the norm of a complex number. Return the numbers of the answers as a list. | [1, 2] | list of integer | Not supported with pagination yet |
Incompressible oil of density 850 kg/m^3 is pumped through a cylindrical pipe at a rate of 9.5 liters per second. The second section of the pipe has a diameter of 4.0 cm. What are the flow speed in that section? (Unit: m/s) | 7.6 | float | Not supported with pagination yet |
Suppose a convex 3d-object has k pentagonal faces and m hexagonal faces. All faces are regular. What is k? | 12 | integer | Not supported with pagination yet |
If r(t) = (6t+2)i + 5t^2j - 8tk, find the Binormal vector as [xi, yj, zk]. What are x, y, z? Return them as a list. | [0.8, 0.0, 0.6] | list of float | Not supported with pagination yet |
Consider the matrix of A=[[1, -1], [-1, 4]], is this a positive definite matrix? | True | bool | Not supported with pagination yet |
What is 3^(3^(3^3)) mod 100? | 87 | integer | Not supported with pagination yet |
which n <= 20 can be constructed a regular n-gonwith compass and straightedge? return all the possible numbers in a list | [3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20] | list of integer | Not supported with pagination yet |
Let a undirected graph G with edges E = {<2,1>,<2,0>,<2,3>,<1,4>,<4,3>}, which <A,B> represent Node A is connected to Node B. What is the minimum vertex cover of G? Represent the vertex cover in a list of ascending order. | [2, 4] | list of integer | Not supported with pagination yet |
What is the number of labelled rooted forests on 6 vertices | 16807 | integer | Not supported with pagination yet |
A group of 7 people is to be divided into 3 committees. Within each committee, people are ranked in a certain order. In how many ways can this be done? | 12600 | integer | Not supported with pagination yet |
Are the circuits shown in Fig. Qla and Fig. Q1b are identical? (Hint: Compare the Tranfer functions) | True | bool | |
Suppose f is analytic on the closed unit disk, f(0) = 0, and |f(z)| $\leq$ |e^z| whenever |z| = 1. How big can f((1 + i)/2) be? Return a numerical number. | 1.9221 | float | Not supported with pagination yet |
In triangle ABC, AB = 9x-1, CB = 5x-0.5, AC = 4x+1, and AC = CB. Find the measure of AB. | 12.5 | float | Not supported with pagination yet |
In how many ways can a convex polygon with 8 sides be divided into triangles by connecting its vertices, with no intersecting lines? | 132 | integer | Not supported with pagination yet |
For a $1,000 investment, what is the future value of the investment if the interest rate is 8% compounded annually for 3 years? | 1259.71 | float | Not supported with pagination yet |
What's phi(29791) where phi is Euler's Totient Function? | 28830 | integer | Not supported with pagination yet |
Let m and n be the roots of the equation 2x^2 + 15x + 16 = 0. What is the value of 1/m + 1/n? | -0.9375 | float | Not supported with pagination yet |
Let a undirected graph G with edges E = {<0,2>,<1,4>,<9,6>,<8,12>,<2,4>,<1,3>,<1,5>,<12,1>,<8,1>,<5,9>,<0,10>,<5,2>,<0,8>,<3,4>,<3,11>,<7,1>,<2,1>,<0,12>,<1,0>,<7,8>}, which <A,B> represent Node A is connected to Node B. What is the minimum vertex cover of G? Represent the vertex cover in a list of ascending order. | [0, 1, 2, 3, 8, 9] | list of integer | Not supported with pagination yet |
Define f(x)=(4x+5)/(9-3x), is the function continuous at x=-1? | True | bool | Not supported with pagination yet |
assume you are Indonesian. In 2010, the rupiah exchange rate was around IDR15,000/USD, and the consumer price index in Indonesia and the United States was at 100. In 2019, the exchange rate changed to IDR14,000/USD. Simultaneously, Indonesia’s inflation rose 5% due to the consumer price index rising to 105. Meanwhile, ... | 14666.67 | float | Not supported with pagination yet |
Calculate the minimum kinetic energy of an electron that is localized within a typical nuclear radius of 6 x 10^-15 m in MeV. | 15.9 | float | Not supported with pagination yet |
Apply the Graeffe's root squaring method to find the roots of the following equation x^3 + 3x^2 - 4 = 0 correct to two decimals. What's the sum of these roots? | -3 | integer | Not supported with pagination yet |
If $X(k)$ is the N-point DFT of a sequence $x(n)$, then circular time shift property is that N-point DFT of $x((n-I))_N$ is $X(k) e^{-j 2 \pi k \mid / N}$. Is it true? | True | bool | Not supported with pagination yet |
While a person is walking, his arms swing through approximately a 45° angle in 0.5s.As a reasonable approximation, we can assume that the arm moves with constant speed during each swing. A typical arm is 70.0 cm long, measured from the shoulder joint. What is the acceleration (in metre per second squared) of a 1.0 g dr... | 1.73 | float | Not supported with pagination yet |
In the process of searching circles in an image, object O is detected. The contour of the object O is represented with the Fourier Descriptors (80,40,0,0,-1,0,0,1). Given that the Fourier Descriptors of a circle are (0,40,0,0,0,0,0,0). Is the object O a circle-like polygon in the image? Bear in mind that there is some ... | True | bool | Not supported with pagination yet |
Consider a group of 10 people {A,B,C,D,E,F,G,H,I,J} and we are to choose a committee of 4 people from them. Given that (1) A and B should not be chosen together, and that (2) A, C, F should not be chosen together, then how many ways are there to choose such a committee? | 176 | integer | Not supported with pagination yet |
what is the limit of (2n)!!/(2n+1)!! as n goes to infinity? | 0.0 | float | Not supported with pagination yet |
You are given: (i) The current exchange rate is 0.011$/¥. (ii) A four-year dollar-denominated European put option on yen with a strike price of $0.008 sells for $0.0005. (iii) The continuously compounded risk-free interest rate on dollars is 3%. (iv) The continuously compounded risk-free interest rate on yen is 1.5%. C... | 42.77325 | float | Not supported with pagination yet |
Let f be a bounded entire function, z_1,z_2 be two points in the ball B(0,r). What is the value of the integral $\int_{|z|=r} f(z)/(z-z_1)(z-z_2) dz$? | 0.0 | float | Not supported with pagination yet |
One end of a 2.00-kg rope is tied to a support at the top of a mine shaft 80.0 m deep. The rope is stretched taut by a 20.0-kg box of rocks attached at the bottom. If a point on the rope is in transverse SHM with f = 2.00 Hz, how many cycles of the wave are there in the rope’s length? | 1.81 | float | Not supported with pagination yet |
You have a coin and you would like to check whether it is fair or biased. More specifically, let $\theta$ be the probability of heads, $\theta = P(H)$. Suppose that you need to choose between the following hypotheses: H_0 (null hypothesis): The coin is fair, i.e. $\theta = \theta_0 = 1 / 2$. H_1 (the alternative hypoth... | 0.023 | float | Not supported with pagination yet |
An ordinary deck of cards containing 26 red cards and 26 black cards is shuffled and dealt out one card at a time without replacement. Let $X_i$ be the color of the $i$th card. Compute $H(X_1,X_2,\ldots,X_{52})$ in bits. | 48.8 | float | Not supported with pagination yet |
Each day Paul, who is in third grade, eats lunch at school. He likes only Twinkies (t) and soda (s), and these provide him a utility of utility = U(t,s) = \sqrt{ts}. If Twinkies cost $0.10 each and soda costs $0.25 per cup, Paul's mom gives him $1, how many Twinkies should Paul buy to maximize utility? | 5 | integer | Not supported with pagination yet |
In the process of searching circles in an image, object O is detected. The contour of the object O is represented with the Fourier Descriptors (-20,60,-20,20,-20,21,-20,20). Given that the Fourier Descriptors of a circle are (0,40,0,0,0,0,0,0). Is the object O a circle-like polygon in the image? Bear in mind that there... | False | bool | Not supported with pagination yet |
Find acceleration in m/(min^2) at time t = 5 min of a helicopter whose height is s(t) = 300t - 4t^3 m. | -120 | integer | Not supported with pagination yet |
A network with one primary and four secondary stations uses polling. The size of a data frame is 1000 bytes. The size of the poll, ACK, and NAK frames are 32 bytes each. Each station has 5 frames to send. How many total bytes are exchanged if each station can send only one frame in response to a poll? | 21536 | integer | Not supported with pagination yet |
What are the real eigenvalues of the matrix [[3, -2, 5], [1, 0, 7], [0, 0, 2]]? | [1, 2, 2] | list of integer | Not supported with pagination yet |
Suppose there are 10 independent random variables $X_1, X_2, \cdots, X_10$. Each of the $X_i$ lies within the range of [10, 11] with a mean value of 10.5. If we take the mean of the 10 random variables as $\hat{X_n}$. What is the upper bound of the probability that $\hat{X_n}$ is either smaller than 10.2 or larger than... | 0.3305 | float | Not supported with pagination yet |
What is \lim_{x \to 0} (csc(x) - cot(x))? | 0 | integer | Not supported with pagination yet |
Let’s assume Mutual Fund A has an annualized return of 15% and a downside deviation of 8%. Mutual Fund B has an annualized return of 12% and a downside deviation of 5%. The risk-free rate is 2.5%. What is the Sortino ratio for Fund A? | 1.56 | float | Not supported with pagination yet |
True or false: there exists a graph with score (1, 1, 2, 2, 3, 3, 4, 4). | True | bool | Not supported with pagination yet |
The electric flux through a spherical surface is $4.0\times 10^4 N \cdot m^2/C$. What is the net charge enclosed by the surface? | 3.54e-07 | float | Not supported with pagination yet |
Compute the integral $\iint_D xy^2 dA$, where $D$ is the rectangle defined by 0 <= x <= 2 and 0 <= y <= 1. | 0.66667 | float | Not supported with pagination yet |
Let $X \sim N(0,1)$ and let the distortion measure be squared error. Here we do not allow block descriptions. Compute the minimum expected distortion for one bit quantization of $X$ using a squared error distortion measure. | 0.363 | float | Not supported with pagination yet |
A uniform plank of length L = 6.0 m and mass M = 90 kg rests on sawhorses separated by D = 1.5 m and equidistant from the center of the plank. Cousin Throckmorton wants to stand on the right-hand end of the plank. If the plank is to remain at rest, how massive can Throckmorton be? (Unit: kg) | 30 | integer | Not supported with pagination yet |
Let L^1[0,2] be the space of all the Lebesgue integrable functions on the interval [0,2], and C[0,2] be the space of all the continuous functions on the interval [0,2]. Suppose H=L^1[0,2], and X=C[0,2]. For any f\in L^1[0,2], define operator T as $(Tf)(x)=\int_0^x f(t)dt$. For the linear operator T from H to X, what is... | [1, 2] | list of integer | Not supported with pagination yet |
For matrix A = [[2, 4, 3], [3, 0, 1], [1, 2, 5]], what is its determinant? | -42 | integer | Not supported with pagination yet |
Suppose that:
The 1-year spot rate is 3%;
The 2-year spot rate is 4%; and
The 3-year spot rate is 5%. What is the price of a 100-par value 3-year bond paying 6% annual coupon payment? | 102.95 | float | Not supported with pagination yet |
Passing to polar coordinates, calculate the double integral $\iint_S ydxdy$ with $y$ > 0, where S is a semicircle of a diameter 1 with center at point C(1/2, 0) above the X axis. | 0.0833 | float | Not supported with pagination yet |
In how many ways can 8 people be seated at 5 identical round tables? Each table must have at least 1 person seated. | 1960 | integer | Not supported with pagination yet |
Given a network in the figure, From Interface m1 of router R2 it can reach how many destinations? | 4 | integer | |
Please solve the equation sin(4*x) + x = 54 and provide all the roots using newton-raphson method. | [53.52, 54.25, 54.76] | list of float | Not supported with pagination yet |
Find the interval in which the smallest positive root of the following equations lies: x^3 - x - 4 = 0. Determine the roots correct to two decimal places using the bisection method | 1.8 | float | Not supported with pagination yet |
The product of two of the four roots of the quartic equation x^4 - 18x^3 +kx2 + 200x - 1984 = 0 is -32. Determine the value of k. | 86 | integer | Not supported with pagination yet |
Is the set of 3 * 3 matrices in reduced row-echelon form a subspace of R^{3 * 3}? | False | bool | Not supported with pagination yet |
A linear learning machine based on the kernel $k(x,x')=f(x)f(x')$ will always find a solution proportional to $f(x)$. True or false? | True | bool | Not supported with pagination yet |
Suppose 100 cars will be offered on the used-car market. Let 50 of them be good cars, each worth $10,000 to a buyer, and let 50 be lemons, each worth only $2,000. Suppose that there are enough buyers relative to sellers that competition among them leads cars to be sold at their maximum willingness to pay. What would th... | 6000 | integer | Not supported with pagination yet |
True or false: there exists a graph with score (1, 1, 1, 2, 2, 3, 4, 5, 5). | True | bool | Not supported with pagination yet |
For any poitie integer $n$, let $\langle n\rangle$ denote the closest integer to $\sqrt{n}$. Evaluate $\sum_{n=1}^{\infty} \frac{2^{\langle n \rangle}+2^{-\langle n \rangle}}{2^n}$. | 3.0 | float | Not supported with pagination yet |
What is the total number of colors in RGB color space? | 16777216 | integer | Not supported with pagination yet |
Can we use the method of compass and straightedge construction to construct the edge length of a cube, such that the volume of the cube is equal to X time the volume of a given cube, where X belongs to the set {3,17,8,27,343,1331}? Return the answer list for the respective values of X with 1 for yes and 0 for no. | [0, 0, 1, 1, 1, 1] | list of integer | Not supported with pagination yet |
Calculate the Hamming pairwise distances and determine the minimum Hamming distance among the following codewords: 00000,10101,01010 | 2 | integer | Not supported with pagination yet |
Find the smallest positive integer that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 5, and a remainder of 1 when divided by 7. | 8 | integer | Not supported with pagination yet |
The mass of Earth is 5.97x10^24 kg, the mass of the Moon is 7.35x10^22 kg, and the mean distance of the Moon from the center of Earth is 3.84x105 km. The magnitude of the gravitational force exerted by Earth on the Moon is X * 10^20 N. What is X? Return a numeric value. | 1.99 | float | Not supported with pagination yet |
Suppose that feedback is used on a binary symmetric channel with parameter $p=0.5$. Each time a $Y$ is received, it becomes the next transmission. Thus $X_1$ is Bern(1/2), $X_2=Y_1$, $X_3=Y_2$, \ldots, X_n=Y_{n-1}. Find $\lim_{n\to\infty} \frac{1}{n} I(X_n;Y_n)$ in bits. | 0.0 | float | Not supported with pagination yet |
ABC is a right triangle. AM is perpendicular to BC. The size of angle ABC is equal to 55 degrees. Find the size of angle MAC. | 55 | integer | |
Consider the 7.0-TeV protons that are produced in the LHC collider at CERN. Find the available center-of-mass energy if these protons collide with other protons in a fixed-target experiment in GeV. | 114.5 | float | Not supported with pagination yet |
suppose F(x,y,z)=0. What is $\frac{\partial x}{\partial y} \frac{\partial y}{\partial z} \frac{\partial z}{\partial x}$? | -1.0 | float | Not supported with pagination yet |
In a sinusoidal sound wave of moderate loudness, the maximum pressure variations are about $3.0 \times 10 ^ {-2}$ Pa above and below atmospheric pressure. Find the corresponding maximum displacement if the frequency is 1000 Hz. In air at normal atmospheric pressure and density, the speed of sound is 344 m/s and the bul... | 1.2 | float | Not supported with pagination yet |
For the equation x^4 + 2*x^3 + x = 10, there are four roots. What is the sum of the roots using newton-raphson method. | -2.0 | float | Not supported with pagination yet |
Portfolio | Portfolio 1 | Portfolio 2 | Portfolio 3
Expected Portfolio Return | 5.3% | 6.5% | 7.2%
Portfolio Standard Deviation | 8.2% | 9.1% | 10.1%
If we use Roy's safety-first criterion to decide with portfolio is optimal, with a threshold return of 5%. Is portfolio 2 the optimal one? Answer True or False. | False | bool | Not supported with pagination yet |
Suppose there are 8,000 hours in a year (actually there are 8,760) and that an individual has a potential market wage of $5 per hour. Suppose a rich uncle dies and leaves the individual an annual income of $4,000 per year. If he or she devotes 75 percent of full income to leisure, how many hours will be worked? | 1400 | integer | Not supported with pagination yet |
Suppose we are given the following information. Use this information to calculate abnormal return. Rf: 4%
Rm: 12%
Beta of the Portfolio: 1.8
Beginning Value of Portfolio: $50,000
Ending Value of Portfolio: $60,000
What is the abnormal return? | 0.016 | float | Not supported with pagination yet |
Consider an m * n matrix A and an n * m matrix B (with n != m) such that AB = I_m. Are the columns of A linearly independent? | False | bool | Not supported with pagination yet |
Finding all the real roots of the equation $\sqrt{x^2+x+1}+\sqrt{2 x^2+x+5}=\sqrt{x^2-3 x+13}$. Return the answer as a list with ascending order. | [-1.7807764064, 0.2807764064] | list of float | Not supported with pagination yet |
Suppose a student who was farsighted wears glasses that allows him to read at a distance of 20cm from his eyes to the book. His near-point distance is 63cm. If his glasses are 1.5cm from his eyes, what is the refractive power of his glasses lenses? | 3.846 | float | Not supported with pagination yet |
Traders in major financial institutions use the Black-Scholes formula in a backward fashion to infer other traders' estimation of $\sigma$ from option prices. In fact, traders frequently quote sigmas to each other, rather than prices, to arrange trades. Suppose a call option on a stock that pays no dividend for 6 month... | 0.251 | float | Not supported with pagination yet |
In 1985 the space shuttle Challenger flew a cesium clock and compared its time with a fixed clock left on Earth. The shuttle orbited at approximately 330 km above Earth with a speed of 7712 m/s. Calculate the expected time lost per second (in picoseconds) for the moving clock and compare with the measured result of $-2... | 330.76 | float | Not supported with pagination yet |
An Aston Martin V8 Vantage sports car has a lateral acceleration of $0.96g = (0.96)(9.8 m / s^2) = 9.4 m / s^2$. This is the maximum centripetal acceleration the car can sustain without skidding out of a curved path. If the car is traveling at a constant 40m/s on level ground, what is the radius R of the tightest unban... | 170 | integer | Not supported with pagination yet |
You have a coin and you would like to check whether it is fair or biased. More specifically, let $\theta$ be the probability of heads, $\theta = P(H)$. Suppose that you need to choose between the following hypotheses: H_0 (null hypothesis): The coin is fair, i.e. $\theta = \theta_0 = 1 / 2$. H_1 (the alternative hypoth... | True | bool | Not supported with pagination yet |
If the quartic x^4 + 3x^3 + 11x^2 + 9x + A has roots k, l, m, and n such that kl = mn, find A. | 9 | integer | Not supported with pagination yet |
Each of the four jet engines on an Airbus A380 airliner develops athrust (a forward force on the airliner) of 322,000 N (72,000 lb).When the airplane is flying at 250 m/s, what horsepower does each engine develop? (Unit: hp) | 108000 | integer | Not supported with pagination yet |
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