Midterm Review CE Math 1030

Transcription

1 Midterm Review CE Math 030 Please show all of your work for full credit on each problem. Circle your final answer and write it on the blank to the right of the problem. Partial credit will be awarded where work is shown, easy to follow and relevant to the problem. Name: School: Instructor/Period:. Smoothie Palace has a total of 5 ingredients. Five of the ingredients are vegetables and the other ten ingredients are fruits. You may pick three different ingredients from which to make a smoothie. In other words, an orange, orange, apple smoothie is not allowed. a) How many possible different 3-ingredient smoothies would contain only fruit? This area reserved for grading. Please do not write in this area. b) How many possible different 3-ingredient smoothies that can be made from these 5 ingredients. Answer: possible earned c) What is the probability of randomly choosing a smoothie with only fruit? Answer: total Answer: Math 030 Sample Midterm Page of 8

2 2. Assume that today the probability of rain is 0.5, the probability of fog is 0.4 and the probability of rain and fog is a) Illustrate this information in a Venn diagram b) Explain what the overlap in the circles means in terms of the current problem. c) What is the probability of rain or fog today? d) What is the probability of neither rain nor fog today? 3. The final exam for your math class is written by one of three professors A, B or C. There is a 50% chance the exam will be written by A, 20% by B and 30% by C. A will ask a geometry question 0% of the time, B will ask a geometry questions 80% of the time and C will ask a geometry question 50% of the time. a) Draw a tree diagram to illustrate the given information. b) What is the probability A did NOT write the exam? c) What is the probability there is a geometry problem on the exam given that C or B wrote the exam? d) Given that there is NO geometry question on the exam, what is the probability A or C wrote the exam? 4. Two fair six-sided die are rolled three different times. Consider the event: E = we get a sum of 5 exactly two times a) Give an example of an outcome that favors the event E. b) Give an example of an outcome that does NOT favor the event E c) What is the probability of getting a sum of 5 on a single roll of a pair of dice? d) What is the probability of E? 2 of 8

3 5. Identify which of the following situations is answered by the equation: y = 5.49x For the incorrect model, explain why it is wrong. a) Richard needs ingredients for a desert. He buys some pecans from the bulk bins at $5.49 per pound and a bag of sugar for $2.50. Circle the appropriate choice: Model is correct for the situation Model is NOT correct for the situation If the situation is incorrect, explain why in a sentence. b) Richard needs ingredients for a desert. He buys some pecans from the bulk bin at $5.49 per pound and some bags of sugar for $2.50. Circle the appropriate choice: Model is correct for the situation Model is NOT correct for the situation If the situation is incorrect, explain why in a sentence. c) Richard needs ingredients for a desert. He buys some bags of sugar for $2.50 and a pound of pecans for $5.49. Circle the appropriate choice: Model is correct for the situation Model is NOT correct for the situation If the situation is incorrect, explain why in a sentence. 6. Use set notation to list the elements of each set. Set A: Transportation Ship Bus Strawberry Tiger a) B C b) (A C) c) A B d) (A B) (C B) Shoe Airplane Boat Canoe Car Camel Carnation Desk Set B: Manmade Items Computer Crayon Cat Set C: Starts with C 3 of 8

4 7. An ice cream store offers five different flavors of frozen yogurt: chocolate, vanilla, birthday cake, cheesecake and mocha. a) Alex wants to build an ice cream cone with one scoop of each possible flavor. How many ways can he order the ice cream scoops? b) Alex realizes he isn t hungry enough to eat five scoops of ice cream, but he does have room for three scoops. He wants each scoop to be a different flavor. How many unique combinations of three different flavors can he make if order doesn t matter? c) If Alex chooses his three unique flavors at random, what is the probability that he chooses one scoop each of chocolate, vanilla and mocha in any order? 8. In the Fall, the practice field at a small high school is shared between three different groups: football, marching band, and color guard. Each group needs to reserve the field for hour per week. Due to scheduling issues, the various groups are available to use the field at the following times: Football: Monday at 9:00, Wednesday at :00, Friday at 2:00 Marching Band: Monday at 9:00, Wednesday at 0:00 Color Guard: Monday at 0:00, Wednesday at :00, Friday at 2:00 a) Create a tree diagram illustrating all possible schedules for the practice field. b) Make a list of all possible scheduling options. 4 of 8

5 9. The spinner below is used at a carnival. There are two options for betting: Option A You pay $5 If the spinner lands on A, you get paid $6. If the spinner lands on B, you get paid $.50 If the spinner lands on C, you get paid $5 If the spinner lands on D, you get paid $0 Option B You pay $0 If the spinner lands on A, you get paid $2. If the spinner lands on B, you get paid $3 If the spinner lands on C, you get paid $0 If the spinner lands on D, you get paid $20 a) What is the expected value for Option A? Show your work and interpret your answer in a sentence. Work: Interpret your answer: b) Is Option B fair? Use mathematics and a sentence to explain your answer. Work: Sentence explaining if Option B is fair: c) From the perspective of the carnival owner, which option is better for business? Circle your answer and explain. Circle one choice: Option A Option B Explain: 5 of 8

6 0. Budget rents 6 moving trucks for $29.99 per day with an additional $0.69 per mile. Enterprise rents a 6 truck for $70 per day with an additional $0.49 per mile. a) Write an equation for the total cost to rent a truck from Budget if you drive m miles. y = b) Which line on the graph to the left represents the cost to rent from Budget if you drive m miles? Explain how you know. Cost (Dollars) Please circle the correct choice: The dashed solid line represents the cost to rent from Distance (Miles) c) In a sentence, describe the meaning of the slope if you choose to rent from Budget. d) Using the graph to determine when it s less expensive to rent from Budget. Explain how you found your answer. In a survey of 00 investors in the stock market * 50 owned shares in IBM * 40 owned shares in AT&T * 45 owned shares in GE * 20 owned shares in both IBM and AT&T * 5 owned shares in both AT&T and GE * 20 owned shares in both IBM and AT&T * 5 owned shares in all three a) Organize the data in a Venn diagram b) How many investors owned neither IBM nor GE? c) How many investors owned just IBM shares? d) How many investors owned either IBM or GE, but not AT&T? 6 of 8

7 2. Direct satellite receiver sales decreased from 6.3 million in 2004 to 2 million in a) What is the average change in sales per year from 2004 to 2009? b) If the change in sales is constant over time, how many direct satellite receivers should we anticipate being sold in the year 204? c) Let 2004 be the start (or year 0). How many direct satellite receivers should we anticipate being sold x years after 2004 if we assume the trend continues. d) If the trend continues, in what year will there be 0 direct satellite receivers sold? e) Do you think that the change in receiver sales will be constant for all years after 2004? 3. Josie is considering a job that pays on commission. The company hands her a brochure with the following table showing how much other associates have made per day in their first month on the job. Number of Associates Commission a) How much do associates make on average per day in their first month with the company? b) Josie knows her living expenses are $4550 per month and she plans to work 26 days in her first month. How much does she have to earn per work day to cover her expenses? c) Should Josie expect to make enough to cover her living expenses the first month she s employed with this company? Show your work, then write a sentence explaining your answer. d) How many days should Josie plan on working during her first month to cover her expenses? e) Given the data on the brochure is representative of Josie s earning potential, what is the probability that she will earn enough to cover her living expenses? 7 of 8

8 4. Consider the outcome of a single roll of a 20-sided die. Let A = {,2,3,4,5}, let B = {2,4,6,8,0,2,4,6,8,20} and C = {5,0,5,20} a) Write set A in set builder notation b) Write set B in set builder notation c) Is the cardinality of Set B less than, greater than or equal to the cardinality of Set C? Please circle the correct choice: The cardinality of Set B is greater than less than equal to the cardinality of Set c Explain. d) Find A B. e) Find A C. f) Find B. 5. Below is a contingency table showing the number of people aboard the Titanic, what class of ticket they held and the number of people who survived and died for each class of ticket. Survival Class of Ticket First Second Third Crew Total Alive Dead Total a) If we randomly pick a person aboard the ship, what is the probability that person was a member of the crew? b) What is the probability of surviving the sinking of the Titanic? c) If someone held a first-class ticket, what is the probability they survived? d) What is the probability a random chosen person held a third class ticket and survived? e) What can you conclude, using your answers from parts c) and d) about the impact of Class of Ticket on Survival? 8 of 8