A curve of radius 30 m is banked so that a 950 kg car travelling
at
40 km/h can go round it even if the road is so icy that the
coefficient of static friction is approximately zero. You are
commissioned to tell the local police the range of speeds at which
a car can travel around this curve without skidding. Neglect the
effects of air drag and rolling friction. If the coefficient of
static friction is 0.3, what is the range of speeds you tell
them?
In: Physics
1. Approximately 25% of the adult population is allergic to pets with fur or feathers, but only 4% of the adult population has a food allergy. A quarter of those with food allergies also have pet allergies.What is the probability a person has food allergies but is not allergic to pets?
A. 0.01
B. 0.03
C. 0.04
D. 0.0625
E. 0.24
2. Suppose the probability there are children in a car involved in an auto accident is 0.3. Further suppose that if there are children in a car that is involved in an auto accident, there is a 0.1 probability the driver was 55 years or older. However, if there no children in a car that is involve in an auto accident, suppose there is a 0.25 probability that driver was 55 years or older.What is the probability there were children in a car involved in an auto accident if the driver was not 55 years or older?
A. 0.66
B. 0.34
C. 0.333
D. 0.27
E. 0.01
3. Suppose the probability there are children in a car involved in an auto accident is 0.3. Further suppose that if there are children in a car that is involved in an auto accident, there is a 0.1 probability the driver was 55 years or older. However, if there no children in a car that is involve in an auto accident, suppose there is a 0.25 probability that driver was 55 years or older.What is the probability there were no children in a car involved in an auto accident if the driver was not 55 years or older?
A. 0.933
B. 0.66
C. 0.525
D. 0.34
E. 0.25
In: Statistics and Probability
1- Most real estate offers are conditional on the buyer obtaining the necessary financing to complete the purchase. Based on past experience, one ofCanada's largest real estate agencies believes that 4% of the sales fail because the buyer is unable to obtain the financing approval from their mortgage broker or lender. The real estate agency has recently submitted 60 different offers, all of which are conditional on financing.
What is the sampling distribution model of the proportion of clients in this group who may not receive the necessary funding to purchase the house? Round to one decimal.
A. Mean = 4.0%; standard deviation = 0.3%
B. Mean = 4.0%; standard deviation = 2.5%
C. Mean = 96.0%; standard deviation = 2.5%
D. Mean = 96.0%; standard deviation = 0.3%
2- The director of admission of a large university is interested in determining the proportion of students who would like to live on campus in the coming academic year. Rather than examine the records for all students, the director randomly selects 150 students and finds that 108 of them would like to live on campus. Using a 90% confidence interval, what is the estimated true proportion of students who would like to live on campus in the coming academic year?
A.0.72 ± 0.04457
B.0.72 ± 0.060301
C.0.72 ± 0.089582
D.0.72 ± 0.028135
In: Statistics and Probability
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The average risk of transmission of the human immunodeficiency virus (HIV) to a health care worker after percutaneous exposure to HIV-infected blood has been estimated as 0.3 percent. However, the factors that influence this risk have not been determined, and the efficacy of postexposure prophylaxis with antiretroviral drugs have not been clinically evaluated. If postexposure prophylaxis is effective, it would offer an entirely new strategy for preventing HIV transmission in nonoccupational settings as a supplement to the preferred strategy of preventing exposure. Study of occupational exposure to HIV presents an important opportunity to evaluate postexposure prophylaxis, because the source, time, and many details of the exposure are known. A nationwide, prospective, placebo-controlled trial of prophylaxis with zidovudine after percutaneous exposure to HIV among health care workers was discontinued when only 84 health care workers enrolled after one year since many thousands would be needed to assess the reduction of a 0.3 percent risk of transmission. Nevertheless, occupational exposure to HIV and infection continue to occur, and there is a compelling public health need for data on the efficacy of postexposure prophylaxis.
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In: Nursing
Consider the following information regarding the performance of a money manager in a recent month. The table represents the actual return of each sector of the manager’s portfolio in column 1, the fraction of the portfolio allocated to each sector in column 2, the benchmark or neutral sector allocations in column 3, and the returns of sector indices in column 4.
| Actual Return | Actual Weight | Benchmark Weight | Index Return | |||||||||
| Equity | 2.5 | % | 0.6 | 0.6 | 3% (S&P 500) | |||||||
| Bonds | 1.5 | 0.1 | 0.1 | 1.7 (Barclay’s Aggregate) | ||||||||
| Cash | 0.5 | 0.3 | 0.3 | 0.5 | ||||||||
a-1. What was the manager’s return in the month? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.)
a-2. What was her overperformance or underperformance? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.)
b. What was the contribution of security selection to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)
c. What was the contribution of asset allocation to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)
In: Finance
The current risk-free rate is 4 percent and the market risk premium is 6 percent. You are trying to value ABC company and it has an equity beta of 0.7. The company earned $3.00 per share in the year that just ended. You expect the company's earnings to grow 4 percent per year. The company has an ROE of 12 percent.
What is the value of the stock? Do not round intermediate calculations. Round your answer to the nearest cent.
$
What is the present value of the growth opportunity? Do not round intermediate calculations. Round your answer to the nearest cent.
$
In: Finance
Epson has one bond outstanding with a yield to maturity of 5% and a coupon rate of 8%. The company has no preferred stock. Epson's beta is 0.9, the risk-free rate is 0.6% and the expected market risk premium is 6%.
Epson has a target debt/equity ratio of 0.7 and a marginal tax rate of 34%.
1. What is Epson's (pre-tax) cost of debt?
2. What is Epson's cost of equity?
3. What is Epson's capital structure weight for equity, i.e., the fraction of long-term capital provided by equity?
4. What is Epson's weighted average cost of capital?
In: Finance
Value at Risk (VaR) is an attempt to provide a single number for
senor management summarizing the total risk in a portfolio of
financial assets. It has become widely used by corporate treasurers
and fund managers as well as by financial institutions.
A company currently has $5 million invested in commodity X and $3 million invested in commodity Y. The daily sigma of commodity X is 1 percent, the daily sigma of commodity Y is 1.5 percent, and the coefficient of correlation between returns from the two commodities is 0.7. What is the total investment’s VaR for the next 10 days with a 99 percent confidence level?
In: Finance
4. Consider two competing first order reactions A->B and A->C. One (B) has a preexponential factor of 1010 units, the other (C) of 1013 units. At 144 deg F, both reactions proceed at a rate of 0.001 mol/(l s) in a 0.7 mol/l solution of A.
a. (4) What are the activation energies of each of the reactions
b. (4) At which temperature is the production of B twice as fast as that of C? At which temperature is the production of C twice as fast as that of B? If B is the desired product and C is not, would you rather run the reaction at low or high temperatures
In: Chemistry
A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years):
| 2.0 | 1.4 | 6.0 | 1.6 | 5.1 | 0.4 | 1.0 | 5.3 |
| 15.7 | 0.7 | 4.8 | 0.9 | 12.3 | 5.3 | 0.6 |
Assume that the lifetime distribution is exponential and use an argument parallel to that of this example to obtain a 95% CI for expected (true average) lifetime. (Round your answers to two decimal places.)
( , ) years
What is a 95% CI for the standard deviation of the lifetime distribution? [Hint: What is the standard deviation of an exponential random variable?] (Round your answers to two decimal places.)
( , ) years
In: Statistics and Probability