Please write neatly on this document, showing all calculations, and boxing calculated answers.

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1 Math 083 Review for Exam 4 Name Please write neatly on this document, showing all calculations, and boxing calculated answers. 1) We will compare these two options for flying to Las Vegas and parking a car at the airport: Long Beach airport has a fare available of $ with parking for $12 per day John Wayne airport has a fare of $ with economy parking for $7 per day. a) Let d = Let c = b) Write a formula of the cost for using Long Beach airport: c) Write a formula of the cost for using John Wayne airport: d) We wish to see how many days you d need to park for it to make sense to pay the higher airfare. After solving the system, answer this question in a sentence. 2) A bottle of vitamins at a local retailer sells for $8.99. If one buys online the cost is $6.99 plus $4.95 for shipping and handling. a) Let n = b) Let c = c) Write a formula for the cost for buying at a local retailer: d) Write a formula for the cost for buying online: e) We wish to know how many bottles we must buy for it to make sense to pay the shipping and handling costs. After solving the system, answer the question in a sentence. 3) (From Desmos) Find the vertex yy = 4xx 2 + 3xx 5. Interpret in terms of what is minimized or maximize. 4) (FROM Desmos) Find the vertex yy = 3xx 2 + 5xx 2. Interpret in terms of what is minimized or maximize.

2 5) Determine the interval(s) on which the function (f(x)) is strictly decreasing and strictly increasing. Write your answer as an interval or union of intervals. a) Decreasing: b) Increasing: c) Using the graph of f(x) above, find values of x for which f(x) = 2. d) Find f(-7), f(0), and f(3). 6) From years of experience, a bagel shop has determined that at a price of p = $2.50, they will sell x = 450 bagels each week. If they lower the price to p = $2.00, they will sell 550 bagels each week. The costs of doing business for a company can be found by adding fixed costs (such as rent, insurance, and wages) and variable costs (which are the costs to produce the product you are selling). The portion of the bagel shop s fixed weekly costs allotted to bagels is $200, and the supplies to produce each bagel cost $0.75. a) Revenue for this bagel shop can be modeled by R(x) = x x. How much revenue do they make if the sell 300 bagels? b) If their goal is to make at least $1100 in revenue, how many bagels should they sell? c) Write an equation for the total cost of x bagels: C = d) Last, write the profit equation: P =

7) This graph shows an auto parts maker s daily profit in y dollars for x parts sold. a) Give the coordinates of the y-intercept. b) Explain what it means.

e) Use what you know about the factored form of a polynomial to find the equation of this parabola: y = - ( ) ( ) f) What is the maximum profit this business

Verify in the equation from (e). 8) The stopping distance of a car depends on the reaction time of the driver and the speed of the car.

We will also assume that the pavement is dry. Thus the stopping distance is made up of the reaction distance and the braking distance.

3 7) This graph shows an auto parts maker s daily profit in y dollars for x parts sold. a) Give the coordinates of the y-intercept. b) Explain what it means. c) Give the values of the two roots. d) For each root, give the factor. e) Use what you know about the factored form of a polynomial to find the equation of this parabola: y = - ( ) ( ) f) What is the maximum profit this business can generate in a day and how many parts do they need to sell to achieve this amount of profit? First use the graph to obtain the approximate values. Verify in the equation from (e). 8) The stopping distance of a car depends on the reaction time of the driver and the speed of the car. If we use an assumed reaction time, we can calculate this stopping distance based solely upon the speed of the car when the brakes were applied. We will also assume that the pavement is dry. Thus the stopping distance is made up of the reaction distance and the braking distance. It is given by the equation: D(r) = r r. (Source: Virginia DMV Learner s Manual) a) What does r represent and what are the units? b) What does D represent and what are the units? c) What does the point (30, 75) represent? d) Give the coordinates of the x and y intercepts and describe what they mean.

10) Translate the percent increase decrease problems into an algebraic expression and solve in context. a) Studymore College is expected to grow 3% in enrollment to 25,750 students.

4 9) A video game company collected the following data: a) We wish to write a profit function: P(x) Begin with the factors from the roots/zeros. P(x) = a ( ) ( ) b) Determine the value for a by using one of the other points. # of games profit c) Check P(x) with any point you have not yet used. 10) Translate the percent increase decrease problems into an algebraic expression and solve in context. a) Studymore College is expected to grow 3% in enrollment to 25,750 students. How many students do they currently have? b) The Buzzjob Hair Salon currently charges $50 for a haircut. If they have a sale and reduce their prices by 15%, what will a haircut cost? c) The Slapitogether Construction Company has sold 25 out of the 85 homes they will be building in Santa Ana. What percent have they sold? d) Costs of electric bills are expected to increase by 7%. If you currently pay $60 per month, how much will you pay? e) The Flybynight Delivery Service wishes to increase its number of trucks by 20%. If they add 14 trucks, how many do they currently have? f) If a class of 40 decreases to a class of 25, by what percent has the class decreased in size?

5 11) Find the diagonal of this rectangle. x 8 cm 15 cm 12) Find the missing side of this right triangle, rounding to 2 decimal places. 10 cm 17 cm x 13) A ladder is leaning against a house. The top of the ladder is placed so you can get into a window that is 20 feet off the ground. The bottom of the ladder is 8 feet from the house. How tall must the ladder be? Make a drawing with all the specifics. Round your answer to the nearest foot. 14) You deposit $5000 in an account earning 5% annual interest a) How much would be in your account if you earned simple interest for 10 years? b) How much would be in your account if you earned compound interest for 10 years, compounded annually? c.) How much would be in your account if you earned compound interest for 10 years, compounded monthly?

6 15) Miscellaneous a) Find the product: (x - 3) (x + 8) b) Find the product: (x + 8) (x + 8) c) Factor: d) Factor: e) F(x) = (x + 5) (x - 8); What is F(10)? f) G(x) = ; What is G(-3)? g) Find the zeros for g(x): STUDY YOUR QUIZZES and BOARD PROBLEMS!!!

Please show work for all calculated answers. Show work in a neat and organized manner.

Math 083 Review for Final Exam Name Please show work for all calculated answers. Show work in a neat and organized manner. 1) Using the frequency table for a monthly budget, find all of the relative frequencies