For the elastic body defined in Question 1 (below), define the boundary conditions in terms of displacement, assuming the boundary surface at the point in question has direction cosines with respect to x and y and z equal to l=0.8 and m=0.6 and n=0 . Consider the case when the change in volume is negligible.

Are all the compatibility equations satisfied for the Plane Stress conditions? If not, which equations are not satisfied? Explain the case for the Plane Strain conditions?

Question 1:

Write down the equilibrium equations for a three-dimensional isotropic material in terms of displacements. Assume that the material modulus of elasticity, Poisson ratio and density are, and that the body forces are due to the material weigh and the constant gravitational accelerations applied in z-direction.

The data below are comparing two different methods of measuring blood alcohol concentration. Test the hypothesis that these two methods differ, with the assumption that these data are not normally distributed, with an α = 0.01. Which test would be most appropriate? Provide critical value and calculated test statistic, and then state your conclusion.

1

x is a binomial random variable. (Give your answers correct to three decimal places.)

(a) Calculate the probability of x for:     n = 7,    x = 3,    p = 0.9
P(x) =   

(b) Calculate the probability of x for:     n = 5,    x = 4,    p = 0.25
P(x) =  

(c) Calculate the probability of x for:     n = 8,    x = 2,    p = 0.6
P(x) =   

(d) Calculate the probability of x for:     n = 6,    x = 5,    p = 0.45
P(x) =   

(e) Calculate the probability of x for:     n = 10,    x = 8,    p = 0.8
P(x) =   

(f) Calculate the probability of x for:     n = 8,    x = 7,    p = 0.45
P(x) =  

Answer the following questions. Remember that you can only enter numbers in the boxes given and that decimal places are separated with a dot (not with a comma). Do not leave empty boxes, otherwise partial marks will not be given. Also, enter at least 4 decimals in your answers whenever possible.

Suppose you have the following AD and AS equations:

• ?=82−0.8?Y=82−0.8π (AD equation)
• ?=−7+1.8?Y=−7+1.8π (Short Run AS equation)
• ?=49.15Y=49.15 trillions (Long Run output)

a) The real GDP in equilibrium the short run is equal to Answer for coordinate ..... trillions.

b) The inflation rate in equilibrium in the short run is equal to .

c) The expected inflation in the long run is ... %.

A stock is currently at $50. Over each of the next two 6-month periods, the stock may move up to a factor 1.2 or down by a factor of 0.8 in each period. A European put option with strike price of $48 and maturity of one year is available. The current risk-free rate is 4.0% per year.

a. Is the put option in the money or out the money? Explain

b. What is the current value of this European put option?

c. Find the time value for this put option.

d. What is the price of a European call option with the same strike price and maturity?

e. Is the call option in the money or out of the money? Explain f. Find the time value for this call option.

A stock is currently at $50. Over each of the next two 6-month periods, the stock may move up to a factor 1.2 or down by a factor of 0.8 in each period. A European put option with strike price of $48 and maturity of one year is available. The current risk-free rate is 4.0% per year .

a. Is the put option in the money or out the money? Explain

b. What is the current value of this European put option?

c. Find the time value for this put option.

d. What is the price of a European call option with the same strike price and maturity?

e. Is the call option in the money or out of the money? Explain f. Find the time value for this call option.

According to a summary of the payroll of Mountain Streaming Co., $643,000 was subject to the 6.0% social security tax and the 1.5% Medicare tax. Also, $21,000 was subject to state and federal unemployment taxes.

a. Calculate the employer's payroll taxes, using the following rates: state unemployment, 4.2%; federal unemployment, 0.8%.
$fill in the blank 262f0002cffe034_1

b. Journalize the entry to record the accrual of payroll taxes. If an amount box does not require an entry, leave it blank.

In the following problems answer is given in bracket, I just want the steps how to get them:

(a). Calculate the % of each DRY product when coal is burned stoichiometrically in air. The mass analysis of the coal is: 80% C; 10% H₂; 5% S; and 5% ash.(76.7%N, 22.5%CO₂; 0.8% SO₂)

(b). Find the air fuel ratio for stoichiometric combustion of Butane by volume. Calculate the percentage of carbon dioxide present in the DRY flue gas if 30% excess air is used. (30.95/1; 10.6%)

Make sure you cover both parts as Chegg Question allows at max 4 sub-parts. I want all the steps to get the correct answer.

Problem 2.2 Consider a production system consisting of three Bernoulli
machines and a controller, which also obeys the Bernoulli reliability model. This
production system is considered up if the controller and at least two machines are
up. During each cycle, the controller is up with probability 0.8 and each machine
is up with probability 0.9. The controller and the machines fail independently.
(a) Calculate the probability that the production system is up.
(b) Assume that a second controller, identical to the first one, is added to the
system, and the re-designed system is up if at least one controller and two
machines are up. Calculate the probability that the re-designed production
system is up.
(c) Explain the reason for the difference between the two numbers you calculated.