The differential equation below models the temperature of an 89°C cup of coffee in a 23°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 73°C. Solve the differential equation to find an expression for the temperature of the coffee at time t. (Let y be the temperature of the cup of coffee in °C, and let t be the time in minutes, with t = 0 corresponding to the time when the temperature was 89°C.)

Consider an economy where government expenditures are 10 and total tax revenues are 10. the supply of labor is fixed at 125 and the supply of capital is fixed at 8. the economy is described by the following equations. y k to the power of 1 divided by 3 end exponent l to the power of 2 divided by 3 end exponent c 2.5 + 0.75 ( y - t ) i 10 - 0.5 r the level of private savings is

Given the following information, calculate the savings ratio: liabilities = $25,000 liquid assets = $5,000 monthly credit payments = $800 monthly savings = $760 net worth = $75,000 current liabilities = $2,000 take-home pay = $2,300 gross income = $3,500 monthly expenses = $2,050 multiple choice 2.40% 3.06% 34.78% 33.79% 21.71%

An allergy products superstore buys 6000 of their most popular model of air filters each year. the price of the air filters is $18. the cost of ordering and receiving shipments is $12 per order. accounting estimates annual carrying costs are 20% of the price. the supplier lead time is 2 days. the store operates 240 days per year. each order is received from the supplier in a single delivery. there are no quantity discounts. what is the store’s minimum total annual cost of placing orders & carrying inventory?