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# xcvxv - Name Math 110 Final Exam SHOW ALL WORK(1 1 1 An ice...

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Unformatted text preview: Name Math 110, Final Exam SHOW ALL WORK! (1 1) 1. An ice cream stand bought Popsicles for \$.15 each and Fudgesicles for \$.20 mch for a total of \$41.00. They sold all the Popsicles for 131.55 each and all the Fudgesicles for \$1.80 each and received a total of \$391 .40. How many Popsicles and how many Fudgesicles did they sell? (Deﬁne variable(s), set up equation(s), and solve.) 2.The following table represents the percentage of our Gross Domestic Product (GDP) that was spent on education for several years. Year 1950 1955 1960 1970 1980 1990 1995 Percentage 6.4 6.7 7.7 9.3 12 15.2 19.5 (4) a. Using Ordinary Least Squares Regression ﬁnd the best ﬁt line for this data. (Let x =# of years after 1950; for example, 1950 would give x = 0, 1955 would give x = 5, etc. and let y = percentage of GDP spent on education.) Line (5) b. According to the model found in part (a), how much would you expect the percentage of GDP spent on education to increase (decrease) each year? (5) c. In what year would you expect the percentage of GDP spent on education to be 25%? (3)3. Find the slope of the line passing through (-22,9) and (-5, -l3). (4) 4. Find the intercepts ofthe line -l3x + 41y = 117. x-intercept y-intercept (4) 5. Find the equation of a line parallel to x = 2 and passing through the point (-3,1). 6. Paula’s pies has found that it costs \$2.50 to make each pie and \$1750 per week in ﬁxed costs to keep the shop open. Paula sells her pics for \$12.50 per pie. (4) a. Write the cost equation for Paula’s Pies. (Let C = total weekly cost, x = the number of pics produced each week.) (2) b. Write the revenue equation for Paula’s Pies. (Let R = weekly revenue, x = the number of pics sold each week.) (4) c. What is Paula’s proﬁt if she produces and sells 225 pies this week? (5) d. How many pies must Paula produce and sell each week to break even? (l7) 7. Model the following situation, but DO NOT SOLVE. Clearly identify the variables, objective function and constraints. Mary’s Monogram’s designs and sells two types of monogrammed picture frames: modern and ornate. They can produce up to a total of 58 picture frames each day using up to a total of 3 10 man-hours of labor. It takes 6 man-hours to malte each modem frame and 8 man-hours to make each ornate ﬁ‘ame. Because of demand, they must produce at least twice as many modern as ornate ﬁames. If the proﬁt for each modem frame is \$18 and the proﬁt for each ornate ﬁame is \$25, how many frames of each type should be made each day in order to maximize the company’s proﬁt? (l3)8. Along a stretch of highway near theUniversity, there are three traffic lights. The possibilities for sequences of red and green lights are listed below: {006, GGR, GRG, RGG, RGR, RRG, GRR, RRR} Using this uniform sample space (assxime the events are equally likely), answer these questions. a. What is the probability of stopping exactly once? b. What is the probability of not st0pping at the ﬁrst light and stopping at exactly one light? c. What is the probability of a red on the ﬁrst light or a green on the second light? 1 d. What is the probability of not stopping at the second light given that you did stop at the ﬁrst light? m'—_—mw'—“"T—mm7 Part Time Student l7l0 One person is selected at random from this group. a. Find the probability that the person is a non-student. b. Find the probability that the person is a man. c. What is the probability that the person is not a full time student and is a woman? (1. What is the probability that the person is a part time student or is a man? e. What is the probability that the person is a full time student, given that the person is a woman? f. Let M be the event of selecting a man and N be the event of selecting a non-student. Are the events M and N independent events? (Show computations to Justify your answer.) (1 l) 10. Five thousand tickets are given away as door prizes at a charity dinner. Tickets are to be drawn at random and prizes awarded as follows: 1 prize of\$500, 3 prizes of \$50, 6 prizes of \$10, and 15 prizes of \$5. ‘ a. Set up a probability distribution; table for this game. b. What is the expected value of this raffle? For the following questions state the formula needed to solve the problem, identify the value of the variables and solve. All interest rates are annual unless otherwise stated. (7) ll. Mary invested \$1500 in a 130 day that had a simple interest rate of 4.2%. How much was her investment worth at the end of the 130 days? (7) 12. Stan took out a \$l0,500 loan. When he repaid it 8 months later, he owed \$750 interest. What was the simple interest rate on his loan? mt m INT: “Wot W=?V(\*rt). Fv a1‘1’VC his“) Q: (\ JUL») ~\ (12) 13. Karen invested some money at 5.7% interest, compounded semi-annually, for 5 years. At the end of that time her balance was \$3725. How much was her initial investment worth? b) How much interest did she receive; over the 5 years? (8) 14. Inﬂation has been running at 4.2% ber year. A car now costs \$25,000. How much would it have cost 7 years ago? (6) 15. Find the eﬂ‘ective annual interest rate of an annual rate of 6.25%, compounded daily. Round your answer to the nearest .01%. 1 E ...
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