Calculate the pH of a 0.2 M solution of LiHCO3

• Let P ( A ) = 0.5, P ( A ∩ B ) = 0.2 and P ( A | B ) = 0.5. Determine P ( B ) =  (as a decimal) and P ( A ∪ B ) =  (as a decimal)
• Three identical light bulbs are connect in parallel. If the probability of the system to operate normally is 99.2%, determine the probability of each light bulb to fail p =  (as a decimal).

In the US, fluoride is added to drinking water. In 2015, the US Department of Health [12] lowered the recommended amount of fluoride in drinking water. Fluoride is added to drinking water to help prevent tooth decay, but too much fluoride can lead to fluorosis (white stains in the enamel of the teeth). A particular city wants to check whether their drinking water meets the specifications made by the department of health. The department of health recommends that there should be 0.7 milligrams of fluoride per liter of water. Suppose we collect a random sample of 40 different liters of water and find the the average amount of fluoride per liter of water is 0.775 milligrams with standard deviation 0.2 milligrams. Conduct a hypothesis test using α = .01. Make sure to state the null and alternative hypotheses, state the appropriate test statistic, set up the rejection region, find the P-value for this test, make your conclusion using both the rejection region method and the P-value, and state your conclusion in the context of the problem. Also, find a 99% confidence interval for the true average amount of fluoride per liter of water and use this interval to make a conclusion about the test of hypothesis.

There are three different potential states of the economy next year. The chart below shows you the returns for stocks Green and Wave under each potential economic situation, along with the probability of each situation occurring (note that the probabilities are not all the same). These are the only two stocks in the economy.

Green and Wave can be combined on a 50/50 basis to form portfolio Green Wave. Consider Portfolio Green Wave to be the market portfolio. Based on the information above, calculate the following: Please use the specified units. To help you out, the standard deviation of Green is 5.05569% and Green’s covariance with portfolio Green Wave is .00207. Be certain to show your work and carry answer to 3 decimal places for B and G; and 6 decimal places for C and D.

1. Expected return of wave (percent)?
2. Standard Deviation of wave (percent)?
3. Covariance between Green and Wave (decimal)?
4. Correlation Coefficient between Green and Wave (decimal)?
5. Expected return of portfolio Green Wave (percent)?
6. Standard Deviation of portfolio Green Wave (percent)?
7. Beta of Green (decimal)?

Chuck Stout is the RM for the Holiday Inn Express. His 220-room property normally sells 85 percent of its rooms on Tuesday nights at an ADR of $141.50. All variable costs related to selling his rooms are $55.00 per room. The DOSM at his Holiday Inn Express is proposing to place a bid to sell 125 rooms for a Tuesday night next month at a rate of $109.00 per room. Chuck believes that if the hotel wins this group rooms bid, the transient room sales for that day will ensure a sell-out at the rate of $141.50.

What would be the total amount of after-variable costs rooms’ revenue the hotel will achieve if it wins the group rooms contract?

What would be the after-variable room’s income if the hotel does not win the contract?

BUS201 - Business Law

Question 6

John Fogarty was staying at the Homelike Hotel and took a bath in the tub provided with his room. When he was ready to get out of the tub, he pulled on a device in the wall of the tub called a “Soap & Grab,” which was designed to be used for the purpose of helping people pull themselves out of the tub. Instead of performing that function, however, the “Soap & Grab” pulled out of the wall and hit John in the face, breaking his nose and giving him severe cuts. John would like to sue the Homelike Hotel for negligence but has no direct evidence of what they did or did not do concerning the “Soap & Grab.” Identify the legal doctrine under which John might establish a duty against the hotel in a negligence lawsuit and explain whether John’s situation meets the requirements of that legal doctrine.

An amusement park, whose customer set is made up of two markets, adults and children, has developed demand schedules as follows: Price ($) Quantity Adults Children 5 15 20 6 14 18 7 13 16 8 12 14 9 11 12 10 10 10 11 9 8 12 8 6 13 7 4 14 6 2 The marginal operating cost of each unit of quantity is $5. Because marginal cost is a constant, so is average variable cost. Ignore fixed costs. The owners of the amusement part want to maximize profits. Calculate the price, quantity, and profit if: The amusement park charges a different price in each market. The amusement park charges the same price in the two markets combined. Explain the difference in the profit realized under the two situations.

Alexandra Marcus, manager of the Sky Club Hotel, has requested your assistance on a queuing issue to improve the guest service at the hotel. Alexandra Marcus is considering how to restructure the front desk to reach an optimal level of staff efficiency and guest service. Observation of arrivals during the peak check-in time of 3:00PM to 5:00PM shows that an average of 80 guests arrive each hour. It takes an average of 3 minutes for the front-desk clerk to register each guest. At present, the hotel has five clerks on duty, each with a separate waiting line.

PLEASE SHOW CALCULATIONS!!

a. Average utilization rate of a server (p)

b. The probability of no. customers in the system (Po)

c. Average number of customers in the system (L)

d. Average time in the system (W)

e. Average waiting in line (Wq)

f. Average number of customers in line waiting Lq

Use the information in the chart to answer the questions that follow

Given the above information on two investments A and B, calculate the following statistics:

1. Calculate the Expected Return for A. Give your answer in decimal form to 3 decimals places. For example, 9% is 0.09.

2. Calculate the standard deviation for A. Give your answer in decimal form to 3 decimals places. For example, 9% is 0.09.

3. Calculate the Expected Return for B. Give your answer in decimal form to 3 decimals places. For example, 9% is 0.09.

4. Calculate the standard deviation for B. Give your answer in decimal form to 3 decimals places. For example, 9% is 0.09.

5. Assume that the expected return for A is 10% and the expected return for B is 5.5%. Calculate the expected return on a portfolio consisting of 60% A and 40% B. Give your answer in decimal form to 3 decimals places. For example, 9% is 0.09.

2. A company that manufactures auto parts is weighing the possibility of investing in an FMC (Flexible Manufacturing Cell). This is a separate investment and not a replacement of any existing facilities. Management desires a good estimate of the distribution characteristics of the AW. There are 3 random variables. An economic analyst is hired to estimate the desired parameter, AW. She concludes that the scenario presented to her is suitable for Monte Carlo simulation because of the uncertainties and a direct approach is virtually impossible. The company has done a preliminary economic study and provided the analyst with the following estimates:

• Investment – Normally distributed with mean of $200,000 and SD of $10,000

• Life – Uniformly distributed with minimum of 5 years and maximum of 15 years

• Market Value at End of Life – $20,000 (single outcome, no uncertainty)

• Annual Net Cash Flow – $32,000 (0.5 probability) $40,000 (0.3 probability) $44,000 (0.2 probability)

• MARR – 10% All the elements subject to variation vary independently.

Use Monte Carlo simulation to compute E(AW). Start with 200 trials and increase in increments of 200 until you feel confident that a stable (steady state) value is reached. What is that value?PLEASE SHOW IN EXCEL WITH FORMULAS