Suppose that a company needs new equipment, and that the machinery in question earns the company revenue at a continuous rate of 66000t 38000 dollars per year during the first six months of operation, and at the continuous rate of $71000 per year after the first six months. The cost of the machine is $160000. The interest rate is 5% per year, compounded continuously. a) Find the present value of the revenue earned by the machine during the first year of operation. Round your answer to the nearest cent. Value: $ equation editorEquation Editor b) Determine how long it will take for the machine to pay for itself; that is, how long until the present value of the revenue is equal to the cost of the machine. Round your answer to the nearest hundredth. Years: equation editorEquation Editor

What are the period and vertical shift of the cosecant function below? period: ; vertical shift: 1 unit up period: ; vertical shift: 2 units up period: ; vertical shift: 1 unit up period: ; vertical shift: 2 units up?

Horace society is planning its annual western fair raceway gala. the gala committee has assembled the following expected costs for the event: dinner (per person) $10 gaming token and program (per person) $2 prize payouts $4,300 tickets and advertising $800 private box suite rental $1,700 lottery licenses $200 the committee members would like to charge $40 per person for the evening’s activities.required: 1. what is the break-even point for the dinner-dance (in terms of the number of persons who must attend)? 2. assume that last year only 200 persons attended the dinner-dance. if the same number attend this year, what price per ticket must be charged in order to break even? 3. refer to the original data ($40 ticket price per person). prepare a cvp graph for the dinner- dance from zero tickets up to 600 tickets sold.

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