1.A hospital spokesperson reported that 4 births had taken place at the RG Hospital during the last 24 hours. Find the following probabilities:

a.P(A) = that 2 boys and 2 girls are born.

b.P(B) = no boys are born.

c.P(C) = at least one boy is born.

2.The odds that a team will win in the finals is 4:3. What is their chance of winning?

3.The probability that a patient entering RG Hospital will consult a physician is 0.7, that he/she will consult a dentist is 0.5 and that he/she will consult a physician or a dentist or both is 0.9. What is the probability that a patient entering the hospital will consult both a physician and a dentist?

Sally and Mike are playing frisbee at the beach. When Sally throws the frisbee the probability is 0.14 that it comes back to Sally, the probability is 0.7 that it goes to Mike, and the probability is 0.16 that the dog runs away with the frisbee. When Mike throws the frisbee there is a 0.66 probability that Sally gets it, a 0.28 probability that it comes back to Mike, and a 0.06 probability that the dog runs away with the frisbee. Treat this as a 3--state Markov Chain with the dog being an absorbing state. If Mike has the frisbee, what is the expected value for the number of times Mike will throw the frisbee before the dog gets it? (Give your answer correct to 2 decimal places.)

The investor decides to diversify by investing $3,000 in Gryphon stock and $5,000 in Royal stock, which Grypon stock has an expected return of 9.4% and a standard deviation of 5.24%, and which Royal stock has an expected return of 10% and a standard deviation of 13.5%. The correlation coefficient for the two stocks' returns is 0.7. Calculate the expected return and standard deviation of the portfolio.

And I calculated that the expected return of the portfolio is 9.78%, and STDEV of the portfolio is 9.91%.

My question is: Suppose the investor decides to invest an additional $3,000 in a treasury bill yielding 3.5%. What will be the expected return and standard deviation of this portfolio.

(ps. need details solutions.. )

Suppose that the fuel price at a specific gas station consists of :

A fixed government fuel excise of $0.416/L

Wholesale costs for supplier, which average $0.712/L, with a variance of 0.10.

Retail costs (including profit margin) at an average of $0.212/L, with a variance of 0.0012.

a) Find the average total fuel cost on any given day

b) Given that wholesale and retail costs have a correlation of 0.7, find the variance in total fuel price

c) Assuming that the total fuel price is normally distributed, what is the probability of fuel being priced at less than $1/L on any given day?

A filtration component consists of a rectangular channel having dimensions H = 10 cm, W = 50 cm, and L = 100 cm, containing carbon pellets of diameter 5 mm, is modelled using the Ergun equation. Develop the pressure drop versus mass flowrate (for ?̇ in the range of 1 – 50 kg/s) characteristic for the following porosities (due to packing arrangement): ? = 0.5, 0.7, and 0.9. The fluid properties may be taken to be ρ = 1000 kg/m3 , μ = 1.0 × 10-3 Pa⸱s. What is the pressure drop when ?̇ = 50 kg/s? Is it better to operate three filters in series or in parallel? Why?

note-please attach diagram with answer, do with easy method so I can understand question..
Q:34.6An earth canal in good condition is 17 m wide at the bottom and has side slope of 2 horizontal to
1 vertical. One side slope extends to a height of 7.8 m above the bottom level and the other side
extends to an elevation of 1.8 m, then extends flat to a distance of 150 m and rises vertically. If
the slope of the canal is 0.7 m per 1379 m, estimate the discharge in (m3/s) when the depth of water is
2.5 m. Assume Chezy's constant C = 39.

1.Answer the following questions.

a)A solid shaft transmits 75kW power at 200rpm.Determine the diameter of the shaft if the twist in the shaft is not exceeded 1⁰ in 1m length of the shaft, and shear stress is limited to 50N/mm^2.

Take rigidity modulus, G=100kN/mm^2

b)A hollow shaft with a diameter ratio of 0.7(internal outside) is required to transmit 500kW at 300 rpm with a uniform twisting moment. Allowable shear stress in the material is 70N/mm^2 and twist in a length of 2.5m is not to exceed 1⁰.Determine the maximum external diameter of the shaft satisfying these conditions. Take modulus of rigidity G= 80KN/mm^2

The solid rod shown here has a radius of ?. If it is subjected to the force of ?? at B point, answer the following questions.

Use ??=700 ??; ???=11 ??; ???=15 ??; ???=8 ??; ?=0.7 ??

1. (a) Determine the internal loadings, T, M and V on the sectioned area; see the free body diagram (ii) (5 pts)
2. (b) Determine the shear stress developed by the shear force (V) at A point (5 pts)
3. (c) Determine the normal stress developed by the bending moment (M) at A point (5 pts)
4. (d) Determine the shear stress developed by the torque (T) at A point (5 pts)
5. (e) Determine the stress components at A, ??,?? (5 pts)

A cart loaded with bricks has a total mass of 10.1 kg and is pulled at constant speed by a rope. The rope is inclined at 29.9 ◦ above the horizontal and the cart moves 8 m on a horizontal floor. The coefficient of kinetic friction between ground and cart is 0.7 .

The acceleration of gravity is 9.8 m/s2 .

1. What is the normal force exerted on the cart by the floor?

Answer in units of N.

2. How much work is done on the cart by the rope?

Answer in units of kJ.

3. Note: The energy change due to friction is a loss of energy.

What is the energy change Wf due to fric- tion?

Answer in units of kJ.

Alpha is deciding whether to invest $1 million in a project. There is a 70% chance that the project will be successful, yielding a return of 20% on investment. However, there is a 30% chance that the project will fail, in which case Alpha will only recover 80% of his investment. 1. What is the expected value of investing in the project? 2. Suppose Alpha evaluates the project in accordance with prospect theory. Specifically, v(x) = ( (x − r) 0.8 if x ≥ r −λ(r − x) 0.8 if r > x, where λ > 1, r = $1 million is the reference point, and x is the amount of money received by Alpha at the end of the project. The corresponding probability weighting functions are such that γ = δ = 0.6. (a) Argue (mathematically) that Alpha is loss averse. (b) What is Alpha’s value of investing in the project if λ = 2? (c) Find the value of λ such that Alpha is indifferent between investing and not investing in the project. Beta’s boss assigns him a task on Monday which must be completed before Wednesday. The task takes a total of 10 hours. If Beta works on the task for xt hours on day t, then he suffers a disutility of x 2 t on day t. Throughout the problem t ∈ {1, 2, 3}, where 1 stands for Monday, 2 for Tuesday, and 3 for Wednesday. Beta’s time preferences are given by exponential discounting with the discount factor of δ = 0.8 per day. 1. What is the present value (as measured on Monday) of Beta’s disutility if he works for 6 hours on Monday and 4 hours on Tuesday? 2. Beta’s problem is to complete the task before Wednesday in such a way to minimize the present value of his distuility (as measured on Monday). Write down the mathematical version of Beta’s problem (that is, minimize some function subject to some constraint) 3. How many hours does Beta choose to work the task on Monday? 4. Now suppose that the boss wants to assign a new task to Beta on Tuesday and would therefore like Beta to have more time on Tuesday. She incentivizes Beta by offering him a reward of r3 = 10x1 on Wednesday if Beta works on Monday for x1 hours on the first task. How many hours does Beta choose to work on Monday?