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In a Gigabit Ethernet LAN, the average size of a frame is 1000 bytes. If a noise of 2ms occurs on the LAN, how many frames are destroyed?

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250

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A certain underlying state graph is a tree where each node has three successor nodes, indexed $a$, $b$, $c$. There are two assets defined on this tree which pay no dividends except at the terminal time $T$. At a certain period it is known that the prices of the two accets are multiplied by factors, depending on the successor node. These factors are shown in the table below: | | a | b | c security | 1 | 1.2 | 1.0 | 0.8 | 2 | 1.2 | 1.3 | 1.4 Is there a short-tem riskless asset for this period? Answer True or False.

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True

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Aisha graduates college and starts a job. She saves $1000 each quarter, depositing it into a retirement savings account. Suppose that Aisha saves for 30 years and then retires. At retirement she wants to withdraw money as an annuity that pays a constant amount every month for 25 years. During the savings phase, the retirement account earns 6% interest compounded quarterly. During the annuity payout phase, the retirement account earns 4.8% interest compounded monthly. Calculate Aisha’s monthly retirement annuity payout.

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1898.27

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compute the integral $\iint_V \frac{d x d y d z}{(1+x+y+z)^3}$, where V={(x, y, z): x, y, z \geq 0, x+y+z\leq 1}.

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0.034

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x=0.3168. what is the value of $x*\prod_{n=1}^\infty(1-\frac{x^2}{n^2 \pi^2})/sin(x)$?

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1.0

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What is the determinant of matrix [[0, 1, 2], [7, 8, 3], [6, 5, 4]]?

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-36

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consider a forward contract on a non-dividend paying stock that matures in 6 months. The current stock price is $50 and the 6-month interest rate is 4% per annum. What is the forward price, F.

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51.0

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Consider the set S:= {2^{-m} + n^{-1}: m, n \in N}. What is the maximum of S?

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False

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Evaluate $\int_c z^2 / (z - 5) dz$, where c is the circle that $|z| = 2$.

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0

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If polygon ACDF is similar to polygon VWYZ, AF = 12, CD = 9, YZ = 10, YW = 6, and ZV = 3y-1, find the length of FD.

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15

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Suppose there are three routers between a source host and a destination host. Ignoring fragmentation, an IP datagram sent from the source host to the destination host will travel over how many interfaces? How many forwarding tables will be indexed to move the datagram from the source to the destination? Answer in [Interfaces, Tables].

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[8, 4]

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A bird is lost in a 3 by 3 by 3 cubical maze. The bird flies from room to room going to adjoining rooms with equal probability through each of the walls. To be specific, the corner rooms have 3 exits. What is the entropy rate of this random walk? Use base 2 logarithm and return the entropy rate in bits.

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2.03

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How many labeled graphs with a score of (6, 2, 2, 2, 2, 2, 2) are there?

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15

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Compute the are of that part of the helicoid z = arctan(y/x) which lies in the first octant between the cylinder $x^2+y^2 = 1^2$ and $x^2+y^2 = 2^2$.

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2.843

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For a matrix A, is the function F(A) = det A from the linear space R^{3*3} to R a linear transformation?

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False

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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?

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1.33

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Use the Trapezoidal Rule with to approximate $\int_0^{\pi} sin^2(x)dx$. Return the approximated demical value.

instruction

1.570796

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The difference equation of a digital system is given by $$ y[n]=8 x[n]+2 x[n-1]-x[n-2], $$ where $x[n]$ and $y[n]$ are, respectively the current samples of the input and the output signals of the system. Determine if the system is a FIR.

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True

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Find the curvature for f(x) = \sqrt{4x - x^2}, x = 2.

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0.5

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Across what potential difference in V does an electron have to be accelerated to reach the speed v = 1.8 x 10^7 m/s? Calculate this relativistically.

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924.0

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For which 2 * 2 matrices A does there exist a nonzero matrix M such that AM = MD, where D = [[2, 0], [0, 3]]? Give your answer in terms of eigenvalues of A.

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[2, 3]

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Find the size of angle MBD in the figure below.

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72

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Arbitrarily place 19 points in a unit square and cover as many of these points as possible with a circle of diameter $\frac{\sqrt 2}{3}$. Question: At least how many points can be guaranteed to be covered?

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3

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Suppose g(x) is the horizontal asymptote of function f(x) = (3^x)/(1+3^{-x}). What are possible values of g(2023)?

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0

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A group of 9 people is split into 3 committees of 3 people. Committees are identical besides of members. In how many ways can this be done?

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280

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Carl the clothier owns a large garment factory on an isolated island. Carl's factory is the only source of employment for most of the islanders, and thus Carl acts as a monopsonist. The supply curve for garment workers is given by l = 80w, where l is the number of workers hired and w is their hourly wage. Assume also that Carl's labor demand (marginal revenue product) curve is given by l = 400 - 40MRP_l. How many workers will Carl hire to maximize his profits?

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200

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compute the integral \int_{\Gamma} \frac{x*dy-y*dx}{x^2+y^2}, where $\Gamma$ is any piecewise smooth, closed curve that encloses the origin but does not pass through it.

instruction

6.2831852

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Given image \begin{tabular}{|llll|} \hline 7 & 1 & 6 & 0 \\ 3 & 3 & 7 & 6 \\ 6 & 6 & 5 & 7 \\ \hline \end{tabular} , and the bit-depth of the image is 4. Suppose you want to use the thresholding technique to segment the image. What is the appropriate threshold value based on the histogram of the image? Follow the following rule when you do thresholding or grouping: pixel $(i, j) \in$ Group A pixels if $g(i, j) \leq$ current threshold $\mathrm{T}$; pixel $(i, j) \in$ Group B pixels otherwise, where $g(i, j)$ is the intensity value of pixel $(i, j)$.

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4

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Find the x value of the solutions to the linear system: 7x - y = 15x, -6x + 8y = 15y.

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0

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Is the Taylor Series for $f$ at x=5 where $f(x)=\sum_{n=0}^{\infty}\frac{x^n}{n!} absolutely converging?

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1.0

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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, the United States’ inflation rate rose 10% due to the consumer price index rising to 110. Whats the real exchange rate?

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14666.67

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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?

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3.846

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How many ways are there to color the vertices of a cube with two colors, up to rotation?

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23

output

In a certain nuclear reaction initiated by 5.5-MeV alpha particles, the outgoing particles are measured to have kinetic energies of 1.1 MeV and 8.4 MeV. What is the Q value of the reaction in MeV?

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4.0

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Is the transformation [[-1, 0], [0, -1]] invertible?

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True

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Consider Convolutional Neural Network D2 which takes input images of size 32x32 with 1 colour channels. The first layer of D2 uses 4 filters of size 5x5, a stride of 2, and zero-padding of width 1. Consider CNN D2 which takes input images of size 32x32 with 1 colour channels. The first layer of D2 uses 4 filters of size 5x5, a stride of 2, and zero-padding of width 1. What is the total number of weights defined for the entire activation output of this first layer? (ie. If you flattened all filters and channels into a single vector)

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900

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While riding a multispeed bicycle, the rider can select the radius of the rear sprocket that is fixed to the rear axle. The front sprocket of a bicycle has radius 12.0 cm. If the angular speed of the front sprocket is 0.6 rev/s, what is the radius (in cm) of the rear sprocket for which the tangential speed of a point on the rim of the rear wheel will be 5 m/s? The rear wheel has radius 0.330 m.

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2.99

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For matrix A = [[5, 4], [1, 2]], what are its eigen values?

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[1, 6]

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Is the cumulative distribution function of the standard gaussian distribution $F(x)=1/\sqrt{2 \pi} \int_{-\infty}^x e^{-t^2/2} dt$ is log-concave? Return 1 for yes and 0 for no.

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1.0

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Is there exist a holomorphic function $f$ on the unit disk $B(0,1)$ (boundary excluded) such that $f(B(0,1))=C$? Here C is the complex space. Return 1 for yes and 0 for no.

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1.0

output

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 advertise to C infinity?

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True

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Consider the matrix of A=[[1, 4], [4, 1]], is this a positive definite matrix?

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False

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An image has the gray level PDF $p_r(r)$ shown in Fig. Q1a. One wants to do histogram specification SO that the processed image will have the specified $p_z(z)$ shown in Fig. Q1b. Can we use intensity mapping function $T: z=1-r$ to achieve the goal?

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False

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Suppose the graph of a polynomial f(t) = a + bt + ct^2 passes through points (1, -1), (2, 3), and (3, 13). What is f(-1)?

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9

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What is 3^(3^(3^3)) mod 100?

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87

output

Assume that half of the mass of a 62-kg person consists of protons. If the half-life of the proton is 10^33 years, calculate the number of proton decays per day from the body.

instruction

3.5e-08

output

Calculate the future value of an ordinary annuity of $800 per year for 4 years at 5% rate of return.

instruction

3448.1

output

Titan, the largest moon of Saturn, has a mean orbital radius of 1.22x10^9 m. The orbital period of Titan is 15.95 days. Hyperion, another moon of Saturn, orbits at a mean radius of 1.48x10^9 m. Use Kepler's third law of planetary motion to predict the orbital period of Hyperion in days.

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21.3

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Calculate the required memory size in Mebibytes (MiB) (in 3 sig.fig.) for storing a frame in 1080p if the sampling scheme R'G'B' 4:4:4 is used. Note that there are 1920 × 1080 pixels in one 1080p frame. Each pixel contains three primary-colour components. Each primary-colour component requires 1 byte of memory for storage. 1 Mebibyte has 1024^2 bytes.

instruction

5.93

output

Consider a probability density $p_x(x)$ defined over a continuous variable x, and suppose that we make a nonlinear change of variable using $x = g(y)$. The location $\hat{y}$ of the maximum of the density in $y$ is not in general related to the location $\hat{x}$ of the maximum of the density over x by the simple functional relation $\hat{x} = g(\hat{y})$.

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True

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