1 A recent survey discovered 315 people like Honda and 218 l

1. A recent survey discovered 315 people like Honda and 218 like Toyota. Of those surveyed, 103 stated they liked both. How many total people were surveyed? Be sure to state/show how you solved.

2. Let Universal Set = U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 7}, and C = {5, 6, 7}. List the members of the following sets: AC\'B A(C^\'B) c. (A\'B)\'(BCB^\')

3. A company manufacturers three sizes of shovels (small, medium, and large). The company has manufacturing plants overseas and in the United States. The overseas plant can produce 30 small, 10 medium, and 10 large shovels daily. The stateside plant can produce 10 small, 20 medium, and 10 large shovels daily. The company has an order for at least 900 small, at least 800 medium, and at least 600 large shovels. Overseas production costs are $160 per day and stateside is $185. Determine the number of days each plant should operate to minimize production costs to complete this order. a. Define variables. b. Objective Function. c. Constraints. d. Critical points (check each and show solutions). e. Final answer.

4. Mary manages a crew that builds two types of storage racks. Rack 1 will yield a profit of $60 per rack and Rack 2 will yield a profit of $80 per rack. However, to build a Rack 1 unit requires 6 labor hours and has an overhead cost of $25. Each Rack 2 unit needs 20 labor hours and has an overhead cost of $40. Mary’s total budget to build storage racks is 1000 labor hours and $3000. How many racks of each should Mary’s crew build to maximize profit? a. Define variables. b. Objective Function. c. Constraints. d. Critical points (check each and show solutions). e. Final answer.

5. A high school class is considering 12 students to run for student council. The student council has five positions available: President, Vice President, Secretary, Treasurer, and Planner. How many ways cans the class fill the five positions?

6. An organization wants to create a team to organize their holiday party. The team will consist of six people. There are 12 potential team members to select from, 7 men and 5 women. a. How many total ways can six people be selected for the team? b. How many total ways can six people be selected for the team where there are more men than women? How many total ways can six people be selected for the team where there will be an equal number of men and women?

7. Evaluate the following expressions and simplify when possible. Be sure to show your work. 7!/3!(7-3)! (6!(-1+a)!)/4!(1+a)!

8. A zoo is planning to have a lion exhibit consisting of 5 lions. Determine how many ways the following are possible if the zoo can select from six female and three male lions (and show your work). All female lions. 2 males and 3 females. 3 males and 2 females.

9. A student is getting ready to take a multiple-choice quiz with 10 questions. Each question has four possible answers, labeled a, b, c, d. There is only one correct answer per question. Since the student did not prepare for the quiz, he will simply guess. a. How many different submissions could the student submit? b. How many different ways can the student submit a quiz with all 10 questions answered incorrectly? c. How many different ways can the student submit a quiz and get exactly 90% correct?

10. If n(A\')=75, n(B\')=85, n(A\'B\')=145, n(U)=200 , complete the following table and show your work. The cell in row B and column A represents n(BA). The cell in row B and column Totals represents n(B). n() A A’ Totals B B’ Totals

Solution

1. A : people liking honda

    B: people liking toyota

n(A U B) : number of people surveyed.

n(A U B) = n(A) + n(B) - n(A intersection B)

              = 315 + 218 - 103

              = 430