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A sports mortgage is the brainchild of Stadium Cap- ital Financing Group, a company headquartered in Chicago, Illinois. It is an innovative way to finance cash-strapped sports programs by allowing fans to sign up to pay a "mortgage" over a certain number of years for the right to buy good seats at football games for several decades with season ticket prices locked in at current prices. In California, the locked-in price period is 50 years. Assume UCLA fan X' purchases a $130,000 mortgage and pays for it now to get season tickets for $290 each for 50 years, while fan Y' buys season tickets at $290 in year 1, with prices increase ing by $20 per year for 50 years. (a) Which fan made the better deal if the interest rate is 8% per year? (b) What should fan X be willing to pay up front for the mortgage to make the two plans exactly equiva- lent economically? (Assume he has no reason to give extra money to UCLA at this point.)An assistant to Stacy gave her the PW values for four alternatives they are comparing for the devel- opment of a remote control vibration control sys- tem for offshore platform application. The results in the table use a MARR of 14% per year. Deter- mine which alternative(s) should be selected (a) if the alternatives are exclusive, and (b) if the projects are independent. K Life n, years 3 12 6 PW over a years, $ 16/08 31.12 -257.46 140.46 PW over 6 years, $ 26.94 15.78 -653.29 140.46 PW over 12 years, $ 39.21 60.45 -257.46 204.46 Future Worth ComparisonA plane layer of coal of thickness & = I'm experiences uniform volumetric generation at a mic of q = 20 W/m due to slow oxidation of the coal particles. Averaged over a daily period, the top surface of the layer trans- fers heat by convection to ambient air for which h =3 W/m'-K and T. = 25 C, while receiving solar irradiation in the amount G, = 400 Wm'. Irradiation from the atmosphere may be neglected. The solar absorptivity and emissivity of the surface are each = =095. Ambient air TA (a) Write the steady-state form of the heat diffusion equation for the layer of coal. Verify that this equa- tion is satisfied by a temperature distribution of the form m=I From this distribution, what can you say about condi- tions at the bottom surface (x = Q? Sketch the temper- ature distribution and label key features. (b) Obmin an expression for the rate of heat transfer by conduction per unit area at .= L. Applying am energy balance to a control surface about the top surface of the layer, obtain an expression for Evaluate T, and TQU) for the prescribed conditions. (cl Daily average values of Gy and & depend on & num- ber of factors, such as time of year, cloud cover, and wind conditions. For A = $ Win' - K, compute and plot 7, and TOO) as a function of G, for 50 8 G 5 500 Wim'. For G. = 400 W/m , compute and plot 7, and 710) as a function of h for 5 5 Am 50 Win-KThe probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width, is given by 1 2 3 I(x) 0.41 0.37 0.16 0.05 0.01 Construct the cumulative distribution function of X. Let X denote the diameter of an armored electric cable and Y denote the diameter of the ceramic mold that makes the cable. Both X and Y are scaled so that they range between 0 and 1. Suppose that X and Y have the joint density f (z, y) = - 01/2).The total number of hours, measured in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a continuous random variable X that has the density function 0<: f o elsewhere. find the probability that over a period of one year family runs their vacuum cleaner less than hours between and>