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The tensile strength of silicone rubber is thought to be a function of curing temperature. A study was carried out in which samples of 12 specimens of the rubber were prepared using curing temperatures of 20 C and 45 C. The data below show the tensile strength values in megapascals. 20 C: 2.07 2.14 2.22 2.03 2.21 2.03 2.05 2.18 2.09 2.14 2.11 2.02 45"C: 2.52 2.15 2.49 2.03 2.37 2.05 1.99 2.42 2.08 2.42 2.29 2.01 (a) Show a dot plot of the data with both low and high temperature tensile strength values. (b) Compute sample mean tensile strength for both samples. (c) Does it appear as if curing temperature has an influence on tensile strength, based on the plot? Comment further. (d) Does anything else appear to be influenced by an increase in curing temperature? Explain.Tom, the owner of Burger Palace, determined that his weighted average cost of capital is 8%. He ex- pects a return of 4% per year on all of his invest- ments. A proposal presented by the owner of the Dairy Choice next door seems quite risky to Tom, but is an intriguing partnership opportunity. Tom has determined that the proposal's "risk factor" will require an additional 3% per year return for him to accept it. (a) Use the recommended approach to determine the MARR that Tom should use, and explain how the 3% risk factor is compensated for in this MARK. (b) Determine the effective MARR for his busi- ness if Tom turns down the proposal. Mix and WACC Electrical generators produce not only electricity, but also heat from conductor resistance and from friction losses in bearings. A company that manu- factures generator coolers for nuclear and gas tur- bine power plants undertook a plant expansion through financing that had a debt-equity mix of 45-55. If $18 million came from mortgages and bond sales, what was the total amount of the financing? Determine the debt-to-equity mix when Applied Technology bought out Southwest Semiconductor using financing as follows: $12 million from mort- gages, $5 million from retained earnings, $10 mil- lion from cash on hand, and $20 million from bonds.Fairmont Industries primarily relies on 100% eq- uity financing to fund projects. A good opportunity is available that will require $250,000 in capital. The Fairmont owner can supply the money from personal investments that currently earn an aver- age of 7.5% per year. The annual net cash flow from the project is estimated at $30,000 for the next 15 years. Alternatively, 60% of the required amount can be borrowed for 15 years at 7% per year. If the MARR is the WACC, determine which plan, if either, should be undertaken. This is a before-tax analysis. Omega Engineering Inc. has an opportunity to in- vest $10,000,000 in a new engineering remote control system for offshore drilling platforms. Fi- nancing will be split between common stock sales ($5,000,000) and a loan with an 8% per year inter- est rate. Omega's share of the annual net cash flow is estimated to be $1.35 million for each of the next 5 years. Omega is about to initiate CAPM as its common stock evaluation model. Recent analy- sis shows that it has a volatility rating of 1.22 and is paying a premium of 5% on its common stock dividend. The U.S. Treasury bills are currently paying 4% per year. Is the venture financially at- tractive if the MARR equals (a) the cost of equity capital and (b) the WACC?1. Ten attributes were rank-ordered in terms of in- creasing importance and were identified as A, B, C, . . ., and J. Determine the weight of (a) attri- bute C and (b) attribute J. A team of three people submitted the following statements about the attributes to be used in a weighted attribute evaluation. Use the statements to determine the normalized weights if assigned scores are between 0 and 100. Attribute Comment 1. Flexibility (F) The most important factor 2. Safety (S) 70% as important as uptime 3. Uptime (U) One-half as important as flexibility 4. Rate of retum (R) Twice as important as safety Different types and capacities of crawler hoes are being considered for use in a major excavation on a pipe-laying project. Several supervisors who served on similar projects in the past have identi- fied some of the attributes and their view of rela- tive importance. For the information that follows, determine the weighted rank order, using a 0-to-10 scale and the normalized weights.The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function 20.000 f(x) = (x+100) I>0, 0 , elsewhere. Find the probability that a bottle of this medicine will have a shell life of (a) at least 200 days; (b) anywhere from 80 to 120 days.Magnetron tubes are produced on an automated assembly line. A sampling plan is used periodically to assess quality of the lengths of the tubes. This measurement is subject to uncertainty. It is thought that the probability that a random tube meets length specification is 0.99. A sampling plan is used in which the lengths of 5 random tubes are measured. (a) Show that the probability function of Y , the number out of 5 that meet length specification, is given by the following discrete probability function: 5! f(y) = y!(5 - y)! (0.99)"(0.01)5-". (b) Suppose random selections are made off the line and 3 are outside specifications. Use fly) above either to support or to refute the conjecture that the probability is 0.99 that a single tube meets specifications.The proportion of the budget for a certain type of industrial company that is allotted to environmental and pollution control is coming under scrutiny. A data collection project determines that the distribution of these proportions is given by f(y) = 5(1-V)'. OSys1. elsewhere. (a) Verify that the above is a valid density function. (b) What is the probability that a company chosen at random expends less than 10% of its budget on environmental and pollution controls? (c) What is the probability that a company selected at random spends more than 50% of its budget on environmental and pollution controls?\fThe following scores represent the final examination grades for an elementary statistics course: 60 32 57 74 70 54 64 89 76 48 67 17 69 74 80 85 (a) Construct a stem-and-leaf plot for the examination grades in which the stems are 1, 2, 3, 9 (b) Construct a relative frequency histogram, draw an estimate of the graph of the distribution, and discuss the skewness of the distribution. (c) Compute the sample mean, sample median, and sample standard deviation