(a) A lamp has two bulbs of a type with an average lifetime of 1800 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean μ = 1800, find the probability that both of the lamp's bulbs fail within 2000 hours. (b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1000 hours.

Sally is buying a home and the closing date is set for april 20th. the annual property taxes are $1,234.00 and have not been paid yet. using actual days, how much will the buyer be credited and the seller be debited

Suppose that two firms produce differentiated products and compete in prices. as in class, the two firms are located at two ends of a line one mile apart. consumers are evenly distributed along the line. the firms have identical marginal cost, $60. firm b produces a product with value $110 to consumers.firm a (located at 0 on the unit line) produces a higher quality product with value $120 to consumers. the cost of travel are directly related to the distance a consumer travels to purchase a good. if a consumerhas to travel a mile to purchase a good, the incur a cost of $20. if they have to travel x fraction of a mile, they incur a cost of $20x. (a) write down the expressions for how much a consumer at location d would value the products sold by firms a and b, if they set prices p_{a} and p_{b} ? (b) based on your expressions in (a), how much will be demanded from each firm if prices p_{a} and p_{b} are set? (c) what are the nash equilibrium prices?

Bayside coatings company purchased waterproofing equipment on january 2, 20y4, for $190,000. the equipment was expected to have a useful life of four years and a residual value of $9,000. instructions: determine the amount of depreciation expense for the years ended december 31, 20y4, 20y5, 20y6, and 20y7, by (a) the straight-line method and (b) the double-declining-balance method. also determine the total depreciation expense for the four years by each method. depreciation expense year straight-line method double-declining-balance method 20y4 $ $ 20y5 20y6 20y7 total $