Evaluate the algebraic expression at the indicated values of the variables. (Simplify your answer.) 4x2 - 2y - 5xy at x = 5 and y = -2The total U.S. personal income I [in billions of dollars] from 1970 and projected to 2024 can be approximated by I = 528.1(1.059)t where t is the number of years past 1970. A. What value of t corresponds to the year 2005? t: B. What did the formula estimate total U.S. personal income would be in the year 2005? [Round your answer to the nearest billion.) billion dollars \fA company makes portable heaters for outdoor dining. The company has total cost function C(a) = 40x + 1240 and the total revenue function R(a) = 70x, where a represents the number of heaters. (a) What is the company's profit function, P(@ )? (Simplify your expression.) P(x) (b) What is the company's profit if they sell 80 heaters? (Round to the nearest whole number if needed.)A company sells a package of face masks for $19.95. Assume the total costs {in dollars] to produce x packages of masks is 0(3) = 0.5511? -l- 550 . A+ What is the company's revenue function, Rm] ? Rm} :| | B. What is the company's revenue from selling 85 packages of face masks? S {Round your answer to two decimal places if needed.) C. What is the company's profit from selling 35 packages of face masks? 5 {Round your answer to two decimal places if needed.) A company has revenue function R(;c) = 650:6 .1132 ,where a? is the quantity of items sold. Find an expression for the price of each item. price = i A company has total cost function C(37) = 0.11122 + 403: + 2000 . {a} Express the average-cost function as a single fraction. {b} Express the average-cost function as a sum of simplified fractions. Average cost = Average cost = Dynamo Electric, Inc. makes and sells surge protectors. Their total cost function is C(22) = 5:6 l 966 and their revenue function is Rte) = 11:13 . How many surge protectors does Dynamo need to sell to break even? Select an answer v A company distributes college Logo sweatshirts. The total cost function is Linear, and the total cost for 45 sweatshirts is $4074, whereas the total cost for 249 sweatshirts is 53'134. [a] Find the sLope of the total cost function, C(59) . slope = {b} Write the equation for the total cost function, C(56). C(37) 2' Suppose that from 2020 to 2060, the number of females in the U.S. under the age of 18 (in millions} can be modeled by N = 0.14:1: + 37.1, where x is the number of years after 2020. Interpret the meaning of the slope, 0.14 , in the context of this problem. '33:? The slope 0.14 represents the number of females in the U.S. under age 18 (in millions.) '33:? The number of females in the U.S. under age 18 is predicted to increase by 0.14 million per year. '33:? The slope 0.14 represents the number of females in the U.S. under age 18 (in millions] 37.1 years after 2020. '13:} Every 0.14 years, the number of females in the U.S.under age 18 is predicted to increase by 32.1 million. '33:? Every 37.1 years, the number of females in the U.S.under age 18 is predicted to increase by 0.14 million. A company has the Linear total cost function C(59) = 173 -l 2026. [a] What is the company's marginal cost? marginal cost = (b) What does marginal cost mean in the context of this problem? '13:} If the number of items produced increases by one, total costs will increase by 17 dollars. '13:} If the number of items produced increases by 17, total costs will increase by 2026 dollars. '3' If the number of items produced increases by 2026, total costs will increase by 1? dollars. '3' If the number of items produced increases by one, total costs will be equal to 1? dollars. [c]: What are the company's fixed costs? A company has total profit function 13(3) production level.) :c2 + 3023: 22701, where x is the number of items {or B. Find the break-even production level[s]. items [Enter your answers separated by a comma if you have more than one.) C. What production level[s] maximize profit? items [Enter your answers separated by a comma if you have more than one.) D. What is the maximum profit? The maximum profit is dollars. E. Fill in the value for each letter on the graph of the profit function. [Graph is not to scale.) PM A. The monthly charge (in dollars) for water in a small town is given by 58 f(x) = 0 > 2,000 where a is the water usage (in gallons.) A. What is the smallest possible monthly charge? dollars B. What is the charge for using 3000 gallons? dollarsNotice that m223+1 _(m1)(:c1} 325m+4 (m1)($4]' Which side of the equation is in factored form? -"'2111- the Left side '33:? the right side '3' both sides are factored ""33 neither side is factored We can simpLif}.t the expression on the Left by '33:? canceLLing the 2:2 terms in the expression on the Left '33:? canceLLing the [:3 1) factors in the expression on the right '13:? neither of the above '13:? either of the above Find the equilibrium price and quantity for the foLlowing supply and demand functions. Demand: 3) = 336 1.4g SuppLy: p = 21 + 0.1:} equiLibrium quantity = equiLibrium price = S Suppose the profit from the sale of 3 items of a product is Pm) = $2 + 822: 381. What two production levels will yield a profit of $1200? [Enter your answers separated with a comma.) items \fB. Of(x) = -2x + 3 Of(ac) = ac2 - 4x Of(x) = -2x2 - 5x Of(x) = 2x3 - 3x + 1 Of (ac ) = - 1 4 4 3x2 4 1 Of(a) = - 3 - ac + 22 Of(ac) = = 5 2x + - a