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TIGER-Lab 109

Use Green's Theorem to evaluate $\oint_{C} xy dx + x^2y^3dy$ where $C$ is the triangle with vertices (0,0), (1,0), (1,2) with positive orientation

0.6667

float

Find the fraction of the standard solar flux reaching the Earth (about 1000 W/m^22) available to a solar collector lying flat on the Earth’s surface at Regina, Saskatchewan (latitude 50°N) at noon on the summer solstice.

0.891

float

suppose $lim_{n \rightarrow \infty}a_n=1$, what is the limit of (a_1+2a_2+...+na_n)/n^2?

0.5

float

How many ways are there to arrange the letters in the word *BANANA* up to the symmetries of the word?

30

integer

What's the maximum number of edges in a simple triangle free planar graph with 30 vertices?

56

integer

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.

51.0

float

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 $\hat{x} = g(\hat{y})$.

True

bool

Find the largest integer for which (x+11)/(x+7) is an integer.

-3

integer

Assuming we are underground, and the only thing we can observe is whether a person brings an umbrella or not. The weather could be either rainy or sunny. Assuming the P(rain)=0.6 and P(sunny)=0.4. Assuming the weather on day $k$ is dependent on the weather on day $k-1$. We can write the transition probability as P(sunny $\mid$ sunny) = P(rain $\mid$ rain) = 0.7. The person has 60\% chance to bring an umbrella when the weather is rainy, and 40\% chance to bring an umbrella when the weather is sunny, i.e. P(umbrella $\mid$ rain) = 0.6 and P(umbrella $\mid$ sunny) = 0.4. If we observe that the person (1) brought an umbrella on day 1, (2) did not bring an umbrella on day 2, (3) brought an umbrella on day 3. What are the most likely weather from day 1 to day 3? Return the answer as a list of binary values, where 1 represents rain and 0 represents sunny.

[1, 1, 1]

list of integer

A camper pours 0.300 kg of coffee, initially in a pot at 70.0°C into a 0.120-kg aluminum cup initially at 20.0°C. What is the equilibrium temperature? Assume that coffee has the same specific heat as water and that no heat is exchanged with the surroundings. (Unit: °C)

66.0

float

For the two linear equations $2 * x + 3 * y + z = 8$ and $4 * x + 4 * y + 4z = 12$ and $x + y + 8z = 10$ with variables x, y and z. Use cramer's rule to solve these three variables.

[-1, 3, 1]

list of integer

Suppose that $X_1,X_2,...$ are real numbers between 0 and 1 that are chosen independently and uniformly at random. Let $S=\sum_{i=1}^k X_i/2^i$, where $k$ is the least positive integer such that $X_k<X_{k+1}$, or $k=\infty$ if there is no such integer. Find the expected value of S.

0.29744254

float

Given a color image of size 28 x 28 x 3 pixels, how many convolutional filters in the first layer of a Convolutional Neural Network if the first layer's output tensor has size 26 x 26 x 64?

64

integer

Consider $x(t)$ to be given as, $$ x(t)=\cos (1000 \pi t) $$ . Let the sampling frequency be $2000 \mathrm{~Hz}$. Does aliasing occur?

False

bool

30 students from 5 classes solved 40 math problems. Each student must answer at least one question. Every two students in the same class solved the same number of questions. The number of questions answered by any two students in different classes is also different. Question: What's maximum possible number of students who only answered one question?

26

integer

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.

-19.875

float

Let $P_5(x)$ be the fifth-degree Taylor polynomial approximation for f(x)=sin(x), centered at x=0. What is the Lagrange error of the polynomial approximation to sin(1)?.

0.000198

float

suppose the sequence a_n satisfies 0<a_n<1, and $(1-a_n)a_{n+1}>1/4$ for all n, what is the limit of a_n as n goes to infinity?

0.5

float

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 hypothesis): The coin is not fair, i.e. $\theta > 1 / 2$. We toss 100 times and observe 60 heads. Can we reject H_0 at significance level $\alpha = 0.01$?

False

bool

What is the number of equivalent parameter settings due to interchange symmetries in a mixture model with 10 components?

3628800

integer

What is $(\frac{1 + cos(2x) + i*sin(2x)}{1 + cos(2x) - i*sin(2x)})^30$ with $x = \pi / 60$?

-1.0

float

Suppose a European call option on a barrel of crude oil with a strike price of $50 and a maturity of one-month, trades for $5. What is the price of the put premium with identical strike price and time until expiration, if the one-month risk-free rate is 2% and the spot price of the underlying asset is $52?

2.92

float

The current price of gold is $412 per ounce. The storage cost is $2 per ounce per year, payable quaterly in advance. Assuming a constant intrest rate of 9% compounded quarterly, what is the theoretial forward price of gold for delivery in 9 months?

442.02

float

Let a undirected graph G with edges E = {<0,2>, <2,4>, <3,4>, <1,4>}, which <A,B> represent Node A is connected to Node B. What is the minimum vertex cover of G if 0 is one of vertex cover? Represent the vertex cover in a list of ascending order.

[0, 4]

list of integer

Let $R(D)$ be the rate distortion function for an i.i.d. process with probability mass function $p(x)$ and distortion function $d(x, \hat{x})$ , $x \in \mathcal{X}$ , $\hat{x} \in \hat{\mathcal{X}}$. If we add a new reproduction symbol $\hat{x}_0$ to $\hat{\mathcal{X}}$ with associated distortion $d(x, \hat{x}_0)$, $x \in \mathcal{X}$, $R(D)$ will decrease. True or False?

True

bool

Does the function $y=xe^{-x^2/2}$, does it satisfy the equation $xy' = (1 - x^2)y$

True

bool

What is the Fisher information for the Gaussian distribution family $f_\theta(x)=N(0,\theta)$? (a) $2\theta$. (b) $2\theta^2$. (c) $0.5\theta^{-1}$. (d) $0.5\theta^{-2}$. Which option is correct?

(d)

option

Consider the discrete memoryless channel $Y=XZ$ where $X$ and $Z$ are independent binary random variables that take on values 0 and 1. Let $P(Z=1)=0.5$. Find the capacity of this channel in bits.

0.322

float

Consider a source $X$ uniformly distributed on the set $\{1, 2, \dots, m\}$. The rate distortion function for this source with Hamming distortion is $R(D) = \log{m}-H(D)-D\log{(m-1)}$ for $0\leq D\leq 1-\frac{1}{m}$, and $R(D) = 0$ otherwise. True or False?

True

bool

The 4 8x8 images shown below are encoded with JPEG coding. Based on their expected DCT (Discrete Cosine Transform) coefficients, Sort the images according to the magnitude of their DC coefficients. Provide your answer in a list of ascending order.

[0, 1, 2, 3]

list of integer

Assuming $x$ and $y$ are both 2-d random variable. The covariance matrix of $x=((1,2),(2,3),(3,5),(4,4))$, $y=((3,4),(1,5),(5,3),(3,3))$ is $Cov$. What is the trace of $Cov$?

-0.166

float

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

3.45

float

Let $X$ be uniformly distributed over $\{1, 2, \ldots, m\}$. Assume $m=2^n$ . We ask random questions: Is $X\in S_1$? Is $X\in S_2$? ... until only one integer remains. All $2^m$ subsets of $\{1, 2, \ldots, m\}$ are equally likely. Suppose we ask $n+\sqrt{n}$ random questions. Use Markov's inequality to find the probability of error (one or more wrong objects remaining) when $n$ goes to infinity?

0.0

float

what is the value of \sum_{n=0}^{\infty}(-1)^n \frac{1}{3 n+1}? Round the answer to the thousands decimal.

0.8356488482647211

float

Let I=[0,1]\times[0,1]. Suppose $E={(x, y) \in I: sin(x)<\frac{1}{2}, cos(x+y) is irrational}$, what is the Lebesgue measure of E?

0.5235987667

float

A court is investigating the possible occurrence of an unlikely event T. The reliability of two independent witnesses called Alf and Bob is known to the court: Alf tells the truth with probability \alpha and Bob with probability \beta, and there is no collusion between the two of them. Let A and B be the events that Alf and Bob assert (respectively) that T occurred, and let \tau=P(T). What is the probability that T occurred given that both Alf and Bob declare that T occurred? Suppose \alpha=\beta=9/10 and \tau=1/1000. Return the answer up to the thousands decimal.

0.075

float

is 1/4 belongs to Cantor set? Is 1/13 belongs to Cantor set? Return the two answers as a list with 1 for yes and 0 for no. For example, if you think both belong to Cantor set, return [1,1]

[1, 1]

list of integer

Sir Lancelot, who weighs 800 N, is assaulting a castle by climbing a uniform ladder that is 5.0 m long and weighs 180 N. The bottom of the ladder rests on a ledge and leans across the moat in equilibrium against a frictionless, vertical castle wall. The ladder makes an angle of with the horizontal. Lancelot pauses onethird of the way up the ladder. Find the magnitude of the contact force on the base of the ladder. (Unit: N)

1020

integer

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

0

integer

Find the arc length of y = (1/4)x^4 over the interval [1,2] using the Trapezoidal Rule T_5.

3.958

float

In how many ways can we form a 7-digit number using the digits 1, 2, 2, 3, 3, 3, 3?

105

integer

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?

124

integer

Let G_n(s) be the probability generating function of the size Z_n of the n-th generation of a branching process, where Z_0=1 and var(Z_1)>0. Let H_n be the inverse function of the function G_n, viewed as a function on the interval [0, 1]. Is M_n= {H_n(s)}^{Z_n} defines a martingale with respect to the sequence Z? Return 1 for yes and 0 for no.

1.0

float

Does the utility function U(x,y) = xy/(x+y) has a convex indifference curve?

True

bool

suppose sequence x_n satisfies x_n*x_{n+1}=n for all n>=1, and $\lim_{n\rightarrow\infty}\frac{x_n}{x_{n+1}}=1$. What's the value of $\pi*x_1^2$?

2.0

float

For a two-period binomial model for stock prices, you are given: (i) Each period is 6 months. (ii) The current price for a nondividend-paying stock is $70.00. (iii) u =1.181, where u is one plus the rate of capital gain on the stock per period if the price goes up. (iv) d = 0.890 , where d is one plus the rate of capital loss on the stock per period if the price goes down. (v) The continuously compounded risk-free interest rate is 5%. What is the current price of a one-year American put option on the stock with a strike price of $80.00.

10.75

float

Determine the time constant (i.e. τ ) of the circuit in the figure. Answer in unit of seconds (3 sig.fig.).

3.93

float

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 (0,113,0,0,1,0,0,1). 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 high frequency noise in the image. You should take this into account when you make your judgment.

True

bool

For the function $f(x)=|x|−1$ defined on $[-1,1]$. Does it meet the criteria of Rolle's Theorem? Answer true or false.

False

bool

In how many ways can a committee of 2 men and 3 women be selected from a group of 6 men and 8 women?

840

integer

Suppose the demand curve for oPads is given by $p=\frac{500-x}{10}, What is the elasticity value of this demand function.

-1.5

float

The perfectly competitive videotape-copying industry is composed of many firms that can copy five tapes per day at an average cost of $10 per tape. Each firm must also pay a royalty to film studios, and the per-film royalty rate (r) is an increasing function of total industry output (Q): r = 0.002Q. Demand is given by Q = D(P) = 1,050 - 50P. Assuming the industry is in long-run equilibrium, what will be the equilibrium price of copied tapes?

11

integer

A monopolist can produce at constant average and marginal costs of AC = MC = 5. The firm faces a market demand curve given by Q = 53 - P. Calculate the consumer surplus obtained by consumers under perfect competition (where price = marginal cost)?

1152

integer

Your company has just written one million units of a one-year European asset-or-nothing put option on an equity index fund. The equity index fund is currently trading at 1000. It pays dividends continuously at a rate proportional to its price; the dividend yield is 2%. It has a volatility of 20%. The option’s payoff will be made only if the equity index fund is down by more than 40% at the end of one year. The continuously compounded risk-free interest rate is 2.5% Using the Black-Scholes model, determine the price of the asset-or-nothing put options. Give the answer in millions.

3.6

float

Consider a forward contract on a 4-year bond with maturity 1 year. The current value of the bond is $1018.86, it has a face value of $1000 and a coupon rate of 10% per annum. A coupon has just been paid on the bond and further coupons will be paid after 6 months and after 1 year, just prior to delivery. Interest rates for 1 year out are flat at 8%. Compute the forward price of the bond.

999.998976

float

for the matrix $A=(\begin{array}{rrrrr} 1 & 2 & 3 & 4 & -3 \1 & 2 & 0 & -5 & 1 \2 & 4 & -3 & -19 & 6 \3 & 6 & -3 & -24 & 7\end{array})$, what is its row rank and column rank? return the two numbers as a list.

[2, 2]

list of integer

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].

[8, 4]

list of integer

A distribution represented by a directed tree can be written as an equivalent distribution over the corresponding undirected tree. True or false?

True

bool

Given the following equation: x^4 - x - 10 = 0. determine the initial approximations for finding the smallest positive root. Use these to find the root correct to three decimal places with Secant method.

1.856

float

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.

2.99

float

Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly $10^14$ times as great as that of ordinary solid matter. Suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. The star's initial radius was $7 \tims 10^5$ km (comparable to our sun); its final radius is 16 km. If the original star rotated once in 30 days, find the angular speed (in rad/s) of the neutron star.

4600.0

float

CheckMate forecasts that its dividend will grow at 20% per year for the next four years before settling down at a constant 8% forever. Dividend (current year,2016) = $12; expected rate of return = 15%. What is the fair value of the stock now?

273.0

float

Light of wavelength 400 nm is incident upon lithium (phi = 2.93 eV). Calculate the stopping potential in V.

0.17

float

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)

0.31

float

A QCIF (176x144) image sequence is encoded using the MPEG video coding algorithm with the following Group Of Pictures (GOP). When a single bit error occurs in the 5th picture of a GOP, which pictures could possibly be affected by this error? Represent the answer in a list sorted in ascending order.

[4, 6, 7, 8, 9, 10, 11, 12]

list of integer

Coloring the edges of a complete graph with n vertices in 2 colors (red and blue), what is the smallest n that guarantees there is either a triangle in red or a 6-clique in blue?

18

integer

determine the ratio of the radius of a uranium-238 nucleus to the radius of a helium-4 nucleus.

3.9

float

Find the sum of $\sum_{n=1}^{\infty} (cost(1/n^2) - cost(1/(n+1)^2))$

-0.459

float

As shown in ./mingyin/integral1.png line $y=c$, $x=0$, and parabola $y=2x-3x^3$ splits the plane into the two shaded regions. Suppose two regions have the same areas. What is the value $c$?

0.444444

float

For a one-period binomial model for the price of a stock, you are given: (i) The period is one year. (ii) The stock pays no dividends. (iii) u =1.433, where u is one plus the rate of capital gain on the stock if the price goes up. (iv) d = 0.756 , where d is one plus the rate of capital loss on the stock if the price goes down. (v) The continuously compounded annual expected return on the stock is 10%. What is the true probability of the stock price going up.

0.52

float

For $p(x)=f(x)g(x)$, if $f(2)=3$, $f'(2)=-4$, $g(2)=1$, and $g'(2)=6$, what is $p'(2)$?

14

integer

Consider a probability density $p_x(x)$ defined over a continuous variable x, and suppose that we make a nonlinear change of variable using $x = g(y)$. In the case of a linear transformation, the location of the maximum density transforms in the same way as the variable itself.

True

bool

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?

3.67

float

Find the volume of a solid bounded by the elliptical paraboloid $z=2x^2 + y^2 + 1$, the plane x+y=1, and the coordinate planes.

0.75

float

A perceptual audio codec is used to compress an audio signal. The codec groups every 4 barks into a subband and then allocates bits to different subbands according to the result of a spectrum analysis based on a psychoacoustic model. All samples in the same subband are quantized with the same quantizer, and the bit resolution of which is allocated by the codec. (The Bark scale is a psychoacoustical scale proposed by Eberhard Zwicker in 1961.) Fig. Q1a shows the frequency spectrum of a windowed segment of audio signal. The psychoacoustic model shown in Fig. Q1b is used in the audio codec to derive the masking threshold for the audio segment. How many potential maskers in Fig. Q1a?

7

integer

Assuming we are underground, and the only thing we can observe is whether a person brings an umbrella or not. The weather could be either rain or sunny. Assuming the P(rain)=0.6 and P(sunny)=0.4. Assuming the weather on day $k$ is dependent on the weather on day $k-1$. We can write the transition probability as P(sunny $\mid$ sunny) = P(rain $\mid$ rain) = 0.7. The person has 60% chance to bring an umbrella when the weather is rain, and 40% chance to bring an umbrella when the weather is sunny, i.e. P(umbrella $\mid$ rain) = 0.6 and P(umbrella $\mid$ sunny) = 0.4. If we observe that the person (1) brought an umbrella on day 1, (2) did not bring an umbrella on day 2, (3) brought an umbrella on day 3. What is the probability that day 2 is raining?

0.5167

float

Find the solutions to the second order boundary-value problem. y''-2y'+2y=0, y(0)=0, y(\pi/2) = 1. What is y(\pi/4)?

0.322

float

An investor who is bullish about a stock may wish to construct a bull spread for that stock. One way to construct such a spread is to buy a call with strke price $K_1$ and sell a call with the same expiration date but with a strike price of $K_2 > K_1$. If we draw the payoff curve for that a spread, the initial cost of the spread would be negative is this True? Answer True or False.

False

bool

Use divergence therem to evaluate $\iint_S \vec{F} \cdot d \vec{S}$ where $\vec{F} = yx^2 \vec{i} + (xy^2 - 3z^4)\vec{j} + (x^3+y^3)\vec{k}$ and the surface $S$ consists of the sphere of radius 4 with $z \le 0$ and $y \le 0$. Note all three surfaces of this solid are included in $S$.

0.0

float

Consider a resistor made from a hollow cylinder of carbon as shown below. The inner radius of the cylinder is $R_i=0.2$mm and the outer radius is $R_o=0.3$mm. The length of the resistor is $L=0.9$mm. The resistivity of the carbon is $\rho=3.5 * 10^{-5} \Omega \cdot m$. What is the resistance in $\Omega \cdot m$?

2.5

float

Use the Birge-Vieta method to find a real root correct to three decimals of the following equation: x^3 - 11x^2 + 32x - 22 = 0, p = 0.5

1

integer

A survey shows that a mayoral candidate is gaining votes at a rate of 2000t + 1000 votes per day, where t is the number of days since she announced her candidacy. How many supporters will the candidate have after 60 days, assuming that she had no supporters at t = 0?

3660000

integer

In the figure, at what rate is thermal energy being generated in the 2R-resistor when $V_s = 12V$ and $R = 3.0\Omega$? Answer in unit of W.

6

integer

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

1.570796

float

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.

0.42857

float

Is 7 a quadratic residue modulo 19? Use Gauss's Lemma to answer it.

True

bool

Assume a temperature of 300 K and find the wavelength of the photon necessary to cause an electron to jump from the valence to the conduction band in silicon in nm.

1130.0

float

What is the order of the group S_3 * Z_2?

12

integer

Let's assume that the 10-year annual return for the S&P 500 (market portfolio) is 10%, while the average annual return on Treasury bills (a good proxy for the risk-free rate) is 5%. Whats the market Treynor Ratio? Return the numeric value between 0 and 1.

0.05

float

For equation x^2*y^2-3y+2x^3=0, and suppose y=f(x). Then what is the derivate f'(1) near the point (1,1) and the point (1,2)? return the answer in a list.

[8, -14]

list of integer

Both A, B are n-by-n matrices with rank(A)=n, rank(A*B)=0. What is rank(B)?

0.0

float

Which of these codes cannot be Huffman codes for any probability assignment? (a) {0, 10, 11}. (b) {00, 01, 10, 110}. (c) {0, 1}.

(b)

option

A door 1.00 m wide, of mass 15 kg, can rotate freely about a vertical axis through its hinges. A bullet with a mass of 10 g and a speed of 400 m/s strikes the center of the door, in a direction perpendicular to the plane of the door, and embeds itself there. Find the door's angular speed. (Unit: rad/s)

0.4

float

Estimate the PE ratio for a firm that has the following characteristics: Length of high growth = five years Growth rate in first five years = 25% Payout ratio in first five years = 20% Growth rate after five years = 8% Payout ratio after five years = 50% Beta = 1.0 Risk-free rate = T-bond rate = 6% Cost of equity = 6% + 1(5.5%) = 11.5% Risk premium = 5.5% What is the estimated PE ratio for this firm?

28.75

float

The difference equation of a causal system is $y[n]+0.5 y[n-1]=x[n]-x[n-2]$, where $y[n]$ is its output and $x[n]$ is its input. Is the system a FIR filter?

False

bool

Mr. Jackson bought his house in 1995, and financed the loan for 30 years at an interest rate of 7.8%. His monthly payment was $1260. In 2015, Mr. Jackson decides to pay off the loan. Find the balance of the loan he still owes.

104761.48

float

Given 3 Colors whose RGB representations are given as follows: Color 1: (0.5, 0.5, 0.5), Color 2: (0.4, 0.6, 0.5), Color 3: (0.3, 0.7, 0.5), Which Color does not carry chrominance (Color) Information? Answer with 1 or 2 or 3.

1

integer

Calculate the interest rate (between 0 and 1) for an account that started with $5,000 and now has $13,000 and has been compounded annually for the past 12 years. Answer with the numeric value.

0.0828

float

Given that the Hue-Saturation subspace shown in Fig. Q2 is a perfect circle and that colors A, B and C can be represented as the 3 points shown in the subspace. Which color has the smallest saturation coefficient?

(b)

option

In how many ways can a group of 10 people be divided into 3 non-empty subsets?

9330

integer