1. [-/1 Points] DETAILS HARMATHAP12 1.1.002. MY NOTES ASK YOUR TEACHER Solve the equation. 2x + 29 = 8x + 5 X = Need Help? Read It Submit Answer 2. [-/1 Points] DETAILS HARMATHAP12 1.1.003. MY NOTES ASK YOUR TEACHER Solve the equation. x + 5 = 5(x + 1) Need Help? Read It Submit Answer 3. [-/1 Points] DETAILS HARMATHAP12 1.1.009. MY NOTES ASK YOUR TEACHER Solve the equation. (Give an exact answer. Do not round.) 5 (x - 9) = 8(x + 7) - x X = Need Help? Read It Submit Answer 4. [-/1 Points] DETAILS HARMATHAP12 1.1.023. MY NOTES ASK YOUR TEACHER Use a calculator to solve the equation. Round your answer to three decimal places. 3.254x - 8.639 = -3.6(8.626x + 4.915) X = Need Help? Read It Submit Answer5. [-/1 Points] DETAILS HARMATHAP12 1.1.045. MY NOTES ASK YOUR TEACHER A $649,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by y = 649,000 - 1800x dollars. After how many months will the value of the building be $425,800? X = months Need Help? Read It Watch It Submit Answer 6. [-/1 Points] DETAILS HARMATHAP12 1.1.047.MI. MY NOTES ASK YOUR TEACHER High interest rates make it difficult for people to pay off credit card debt in a reasonable period of time. The interest / (in dollars) paid on a $10,000 debt over 3 years when the interest rate is % can be approximated by the equation shown below.+ 175.393 + 0.663 = r If the credit card interest rate is 19.4%, find the amount of interest paid during the 3 years. I = $ Need Help? Read it Master it Submit Answer 7. [-/1 Points] DETAILS HARMATHAP12 1.1.049. MY NOTES ASK YOUR TEACHER Burnem Inc. manufactures thumb drives and sells them to a distributor. Burnem's total cost and total revenue (in dollars) for x thumb drives are given by the following equations. Total cost = 3x + 4041 and Total revenue = 12x How many thumb drives must Burnem sell to break even? X = thumb drives Need Help? Read it Watch It Submit Answer 8. [-/2 Points] DETAILS HARMATHAP12 1.1.053. MY NOTES ASK YOUR TEACHER Using data from 2010 and projected to 2020, the population of the United Kingdom (y, in millions) can be approximated by the equation 10.0y - 4.55x = 581 where x is the number of years after 2000. t (a) What is the projected population in 2024? (b) In what year is the population predicted to be 71.75 million? Need Help? Read It Submit Answer9. [-/3 Points] DETAILS HARMATHAP12 1.1.066. MY NOTES ASK YOUR TEACHER Disposable income, the amount left after taxes have been paid, is one measure of the health of the economy. Using U.S. Energy Information Administration data for selected years from 2015 and projected to 2040, the U.S. real disposable income per capita (in dollars) can be approximated by the equation I = 707.6t + 39,090 where t is the number of years after 2015. (a) What t-value corresponds to 2028? t = (b) Find the predicted U.S. per capita real disposable income (to the nearest $10) in 2028. (c) In what year is the U.S. per capita real disposable income expected to exceed $53,000? Need Help? Read It Submit Answer 10. [-/5 Points] DETAILS HARMATHAP 12 1.6.007. MY NOTES ASK YOUR TEACHER A linear revenue function is R = 68x. (Assume R is measured in dollars.) (a) What is the slope m? m= (b) What is the marginal revenue MR? MR = What does the marginal revenue mean? O Each additional unit sold yields this many dollars in revenue. O If the number of units sold is increased by this amount, the revenue increases by $1. Each additional unit sold decreases the revenue by this many dollars. O If the number of units sold is increased by this amount, the revenue decreases by $1. (c) What is the revenue received from selling one more item if 50 are currently being sold? What is the revenue received from selling one more item if 100 are being sold? $ Need Help? Read It Submit Answer11. [-/5 Points] DETAILS HARMATHAP12 1.6.008. MY NOTES ASK YOUR TEACHER A linear revenue function is R = 38.96X. (a) What is the slope m? m = (b) What is the marginal revenue MR? MR = What does the marginal revenue mean? O If the number of units sold is increased by this amount, the revenue increases by $1. Each additional unit sold decreases the revenue by this many dollars. If the number of units sold is increased by this amount, the revenue decreases by $1. O Each additional unit sold yields this many dollars in revenue. (c) What is the revenue received from selling one more item if 49 are currently being sold? $ What is the revenue received from selling one more item if 91 are being sold? Need Help? Read It Submit Answer 12. [-/4 Points] DETAILS HARMATHAP12 1.6.009. MY NOTES ASK YOUR TEACHER Let C(x) = 6x + 250 and R(x) = 29x. (a) Write the profit function P(x). P(x) = (b) What is the slope m of the profit function? m= (c) What is the marginal profit MP? MP = d) Interpret the marginal profit. O Each additional unit sold increases the profit by this much. This is the smallest number of units that can be sold in order to make a profit. Each additional unit sold decreases the profit by this much. The profit is maximized when this many units are sold. Need Help? Read It Submit Answer13. [-/17 Points] DETAILS HARMATHAP12 1.6.013. MY NOTES ASK YOUR TEACHER Extreme Protection, Inc. manufactures helmets for skiing and snowboarding. The fixed costs for one model of helmet are $6800 per month. Materials and labor for each helmet of this model are $50, and the company sells this helmet to dealers for $75 each. (Let x represent the number of helmets sold. Let C, R, and P be measured in dollars.) (a) For this helmet, write the function for monthly total costs C(x). C ( x ) (b) Write the function for total revenue R(x). R (X ): (c) Write the function for profit P(x). P ( X ) = (d) Find C(200). C(200) = Interpret C(200). For each $1 increase in cost this many more helmets can be produced. For every additional helmet produced the cost increases by this much. O When this many helmets are produced the cost is $200. This is the cost (in dollars) of producing 200 helmets. Find R(200). R(200) = Interpret R(200). O For every additional helmet produced the revenue generated increases by this much. O When this many helmets are produced the revenue gen generated is $200. This is the revenue (in dollars) generated from the sale of 200 helmets. For each $1 increase in revenue this many more helmets can be produced. Find P(200). P(200) = Interpret P(200). O This is the profit (in dollars) when 200 helmets are sold, but since it is negative it means that the company loses money when 200 helmets are sold. O This is the profit (in dollars) when 200 helmets are sold, and since it is positive it means that the company makes money when 200 helmets are sold. For each additional helmet sold the profit (in dollars) increases by this much, but since it is negative it means that the company needs to decrease the number of helmets sold in order to make a profit. O For each additional helmet sold the profit (in dollars) increases by this much, but since it is positive it means that the company is producing too many helmets. (e) Find C(300). C(300) = Interpret C(300). O This is the cost (in dollars) of producing 300 helmets. O For every additional helmet produced the cost increases by this much. O When this many helmets are produced the cost is $300. O For each $1 increase in cost this many more helmets can be produced. Find R(300). R(300) =Interpret R(300). O This is the revenue (in dollars) generated from the sale of 300 helmets. O For every additional helmet produced the revenue generated increases by this much. When this many helmets are produced the revenue generated is $300. O For each $1 increase in revenue this many more helmets can be produced. Find P(300). P(300) = Interpret P(300). O This is the profit (in dollars) when 300 helmets are sold, and since it is positive it means that the company makes money when 300 helmets are sold. This is the profit (in dollars) when 300 helmets are sold, but since it is negative it means that the company loses money when 300 helmets are sold. For each additional helmet sold the profit (in dollars) increases by this much, but since it is negative it means that the company needs to decrease the number of helmets sold in order to make a profit. O For each additional helmet sold the profit (in dollars) increases by this much, but since it is positive it means that the company is producing too many helmets. (f) Find the marginal profit MP. MP = Write a sentence that explains its meaning. When revenue is increased by this much the profit is increased by $1. O Each additional helmet sold increases the profit by this many dollars. For each $1 increase in profit this many more helmets can be produced. O When costs are decreased by this much the profit is increased by $1. Need Help? Read It Submit Answer14. [-/1 Points] DETAILS HARMATHAP12 1.6.017.MI. MY NOTES ASK YOUR TEACHER A jewelry maker incurs costs for a necklace according to C(x) = 25x + 1650. If the revenue function for the necklaces is R(X) = 55x how many necklaces must be sold to break even? necklaces Need Help? Read It Watch It Master It Submit Answer 15. [-/3 Points] DETAILS HARMATHAP12 1.6.019. MY NOTES ASK YOUR TEACHER A manufacturer sells belts for $12 per unit. The fixed costs are $2000 per month, and the variable cost per unit is $8. (a) Write the equations of the revenue R(x) and cost C(x) functions. R (X ) = C( x) = (b) Find the break-even point. It takes units to break even. Need Help? Read It Submit Answer 16. [-/4 Points] DETAILS HARMATHAP 12 1.6.023. MY NOTES ASK YOUR TEACHER Electronic equipment manufacturer Dynamo Electric, Inc. makes several types of surge protectors. Their base model surge protector has monthly fixed costs of $825. This particular model wholesales for $12 each and costs $6.50 per unit to manufacture. (a) Write the function for Dynamo's monthly total costs. C(x ) = (b) Write the function for Dynamo's monthly total revenue. R ( X ) = (c) Write the function for Dynamo's monthly profit. P ( x ) = (d) Find the number of this type of surge protector that Dynamo must produce and sell each month to break even. surge protectors Need Help? Read It Submit