Solve the question

Anion, an environmental engineering consulting firm, is trying to be eco-friendly in acquiring an au- tomobile for general office use. It is considering a gasoline-electric hybrid and a gasoline-free all- electric hatchback. The hybrid under consideration is GM's Volt, which will cost $35,000 and have a range of 40 miles on the electric battery and several hundred more miles when the gasoline engine kicks in. Nissan's Leaf, on the other hand, is a pure electric that will have a range of only 100 miles, after which its lithium-ion battery will have to be recharged. The Leaf's relatively limited range cre- ates a psychological effect known as range anxiety. This fact alone has caused the company to lean to- ward purchasing the Volt, which is assumed to have a salvage value of $15,000 in 5 years. The Leaf could be leased for $349 per month (end-of-month payments) for 5 years after an initial $1500 down payment for "account activation." If the consulting company plans to ignore the range anxiety effect in making its decision, which automobile is the better option on the basis of a present worth analysis at an interest rate of 0.75% per month? Assume the oper- ating cost will be the same for both vehicles.A pipeline engineer working in Kuwait for the oil giant BP wants to perform a present worth analysis on alternative pipeline routings-the first predominately by land and the second primarily undersea. The un- dersea route is more expensive initially due to extra corrosion protection and installation costs, but cheaper security and maintenance reduces annual costs. Per- form the analysis for the engineer at 15% per year.Suppose a certain type of small data processing firm is so specialized that some have difficulty making a profit in their first year of operation. The probability density function that characterizes the proportion Y that make a profit is given by 1(y) = [ky' (1 - y). OSys1, elsewhere. (a) What is the value of k that renders the above a valid density function? (b) Find the probability that at most 50% of the firms make a profit in the first year. (c) Find the probability that at least 80% of the firms make a profit in the first year.Based on extensive testing, it is determined by the manufacturer of a washing machine that the time Y (in years) before a major repair is required is characterized by the probability density function f(y) = 10 -#/4, 920, elsewhere. (a) Critics would certainly consider the product a bargain if it is unlikely to require a major repair before the sixth year. Comment on this by determining A(Y > 6). (b) What is the probability that a major repair occurs in the first year?Assume an engineering company borrows $100,000 at 10% per year compound interest and will pay the principal and all the interest after 3 years. Compute the annual interest and total amount due after 3 years. Graph the interest and total owed for each year, and compare with the previous example that involved simple interest