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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. Is the contrast of the image is poor? Judge it based on the histogram of the image.

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True

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Given that the spacing between vibrational energy levels of the HCl molecule is 0.36 eV, calculate the effective force constant in N/m.

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490.0

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What is the number of labelled forests on 8 vertices with 5 connected components, such that vertices 1, 2, 3, 4, 5 all belong to different connected components?

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320

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Suppose ${X_n:n\geq 1}$ be independent and exponentially distributed with parameter 1. what is the probability $P(\limsup _{n \rightarrow infty} X_n/\log(n)=1)? Return a numeric value.

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1.0

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Find the measure of angle A in the figure below. Return the numeric value.

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87

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In triangle RST, X is located on the side RS, Y is located on the side RT, Z is located on the side ST, and XY and XZ are midsegments of △RST. If the length of side XY is 7, the length of side RT is 13, and the measure of angle YXZ is 124°, what is the measure of ange RYX?

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124

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How many triangles are there whose sides are all integers and whose maximum side length equals 11?

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36

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An object 11cm tall is 9cm from a mirror. If the image distance is -3cm from the mirror, what is the image height in terms of cm?

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3.67

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What is (sin(2x) / x)^(1+x) when x is approaching 0?

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2.0

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An ultrasonic transducer used for medical diagnosis oscillates at 6.7 Mhz.How long does each oscillation take, and what is the angular frequency? (Unit: 10^7 rad/s)

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4.2

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Given an image $$ \begin{array}{llllllll} 6 & 5 & 6 & 7 & 7 & 7 & 7 & 7 \\ 7 & 7 & 7 & 7 & 6 & 7 & 7 & 7 \\ 8 & 8 & 8 & 6 & 5 & 5 & 6 & 7 \\ 8 & 8 & 8 & 6 & 4 & 3 & 5 & 7 \\ 7 & 8 & 8 & 6 & 3 & 3 & 4 & 6 \\ 7 & 8 & 8 & 6 & 4 & 3 & 4 & 6 \\ 8 & 8 & 8 & 7 & 5 & 5 & 5 & 5 \\ 8 & 9 & 9 & 8 & 7 & 6 & 6 & 4 \end{array} $$ . Find an appropriate threshold for thresholding the following image into 2 regions using the histogram.

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6.25

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What is the number of labelled forests on 10 vertices with 5 connected components, such that vertices 1, 2, 3, 4, 5 all belong to different connected components?

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50000

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In Image processing, opening is a process in which first dilation operation is performed and then erosion operation is performed. Is it true?

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False

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Does cos(x) = x^k have a solution for k = 2023?

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True

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Is the set of 3 * 3 matrices in reduced row-echelon form a subspace of R^{3 * 3}?

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False

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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 unbanked curve it can negotiate? (Unit: m))

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170

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Determine the AC power gain for the common-emitter amplifier in the figure. Assume that $\beta_{ac} = 100$, the internal emitter resistance $r_e = 12.3 \Omega$.

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33540

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In triangle RST, X is located on the side RS, Y is located on the side RT, Z is located on the side ST, and XY and XZ are midsegments of △RST. If the length of side XY is 7, the length of side RT is 13, and the measure of angle YXZ is 124°, what is the length of side ST?

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14

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Suppose the codeword that we use to describe a random variable X always starts with a symbol chosen from the set {7, 8, 9} , followed by binary digits {0, 1}. Thus we have a ternary code for the first symbol and binary thereafter. Give the optimal uniquely decodeable code (minimum expected number of symbols) for the probability distribution $p = (16/69, 15/69, 12/69, 10/69, 8/69, 8/69)$.

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[7, 8, 9, 70, 80, 90]

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If a preferred share of stock pays dividends of $1.90 per year, and the required rate of return for the stock is 9%, then what is its intrinsic value?

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22.11

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Find which digit is at 1001th place after the decimal point in the decimal expansion of the fraction 9/28.

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2

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The two-step Adams-Bashforth method of approximation uses the approximation scheme $y_{i+2}=y_{i+1} - 1/2 * hf(t_i,y_i)+ 3/2 * hf(t_{i+1},y_{i+1})$. Given that y(0)=1 and y(1)=2, use the Adams-Bashforth method to approximate y(3) for y=-y^2 with a step size of h=1.

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-19.875

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Compute covariance of x=(1,2,3,4), y=(2,3,4,5)

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1.67

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Given a network in the figure, From Interface m1 of router R2 it can reach how many destinations?

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4

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Find the size of angle x in the figure.

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24

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Given $V_s = 5V$, $R_1 = 480 \Omega$, $R_2 = 320 \Omega$, and $R_3 = 200 \Omega$, find the power dissipated by the 3 resistors $P_1, P_2, P_3$ in the figure. Represent your answer as a list [$P_1, P_2, P_3$] in the unit of mW.

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[51.2, 78.15, 125.0]

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An 8% bond with 18 years to maturity has a yield of 9%. What is the price of this bond?

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91.17

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In Chord, assume the size of the identifier space is 16. The active nodes are N3, N6, N8 and N12. Show all the target key (in ascending order, ignore the node's identifier itself) for N6.

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[7, 8, 10, 14]

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the monotone function f on [0,1] is differentiable almost everywhere. This can be proved by: (a) Fubini Theorem; (b) Tonelli Theorem; (c) Vitali Cover Theorem; (d) None of the above. Which option is correct?

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(c)

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How many integers between 1 (included) and 100 (included) are divisible by either 2, 3, or 5?

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74

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Calculate the Gross Domestic Product using the total expenditure approach: Consumption Expenditures | $500 billion Wages and salaries | $400 billion (Gross Private) Investments Expenditures | $80 billion Government Expenditures | $100 billion Taxes | $70 billion Imports | $50 billion Exports | $30 billion What is the GDP (in billions)?

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660

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If the annual earnings per share has mean $8.6 and standard deviation $3.4, what is the chance that an observed EPS less than $5.5?

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0.1814

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In a group of 1000 people, at least how many people have to share the same birthday?

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3

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Let m and n be the roots of the equation 2x^2 + 15x + 16 = 0. What is the value of 1/m + 1/n?

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-0.9375

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Let $a_0=5/2$ and $a_k=(a_{k-1})^2-2$ for $k\geq 1$. Compute $\prod_{k=0}^{\infty}(1-1/a_k)$ in closed form.

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0.42857

output

In the figure,At what rate is thermal energy generated in the $20 \Omega$ resistor? Answer in unit of W (3 sig.fig.).

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1.63

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True or false: there exists a graph with score (1, 1, 2, 2, 3, 3, 4, 4).

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True

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An object of height 5cm is placed 10 cm in front of a convex mirror that has a radius of curvature of 45.0 cm. Determine the magnification of the image.

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1.8

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The dependence between adjacent n-blocks of a stationary process grows linearly with n. True or False?

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False

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Find the rms(Root Mean Square) voltage value (in V) of the waveform in figure (3 sig fig.).

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3.45

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In triangle RST, X is located on the side RS, Y is located on the side RT, Z is located on the side ST, and XY and XZ are midsegments of △RST. If the length of side XY is 7, the length of side RT is 13, and the measure of angle YXZ is 124°, what is the length of side XZ?

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6.5

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The Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Laboratory collides gold ions onto other gold ions head on. The energy of the gold ions is 100 GeV per nucleon. What is the speed of the gold ions as a fraction of the speed of light?

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0.99996

output

Let W(t) be the standard Brownian motion. Find P(W(1) + W(2) > 2).

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0.186

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Use Stoke's Theorem to evaluate $\int_C \vec{F} \cdot d \vec{r}$ where $\vec{F} = z^2 \vec{i} + y^2 \vec{j} + x \vec{k}$ and $C$ is the triangle with vertices (1,0,0), (0,1,0) and (0,0,1) with counter-clockwise rotation.

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-0.166

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A spring is mounted horizontally, with its left end fixed. A spring balance attached to the free end and pulled toward the right indicates that the stretching force is proportional to the displacement, and a force of 6.0 N causes a displacement of 0.030 m. We replace the spring balance with a 0.50-kg glider, pull it 0.020 m to the right along a frictionless air track, and release it from rest. Find the period T of the resulting oscillation. (Unit: s)

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0.31

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What is \int_{-3}^1 (7x^2 + x +1)dx?

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65.333

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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 would be the total size of the flattened output vector from each filter?

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25

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What is \lim_{x \to (\pi)/2} (cos(x)cos(tan(x)))?

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0

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G = Q, and G is under the operation a * b = a + b + 3. Is G a group?

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True

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Perform 2 iterations with the Müller method for the following equation: x^3 - 1/2 = 0, x_0 = 0, x_1 = 1, x_2 = 1/2. What's the decimal value of x_3?

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0.7929

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