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Category: Calculus and Above
Satisfied Customers: 8993
Experience:  B.S. in Civil Engineering
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# 1. A recent survey discovered 315 people like Honda and 218

### Customer Question

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: A∩C'∪B A∪(C^'∪B) c. (A'∪B)'∩(B∪C∩B^') 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(B∩A). The cell in row B and column Totals represents n(B). n(∩) A A’ Totals B B’ Totals
Submitted: 1 year ago.
Category: Calculus and Above
Expert:  Ryan replied 1 year ago.

Hi,

Thank you for using the site. I'll be happy to help you with these problems.

Please let me know if there is a specific deadline for completion.

Thanks,

Ryan

Customer: replied 1 year ago.
I would like to get it back by tomorrow evening
Expert:  Ryan replied 1 year ago.

Ok, no problem. I'll let you know if I need any additional information or clarification.

Thanks,

Ryan

Customer: replied 1 year ago.
Sounds good
Expert:  Ryan replied 1 year ago.

Here are the solutions:

Solutions

Thanks,

Ryan

Customer: replied 1 year ago.
On question #8, you have C(6, 5) = 6! / (6! * (6 – 5)!) = 6. When I do the calculations, I get C(6, 5) = 6! / (6! * (6 – 5)!) = 1/(6-5)1=1/1!=1/1=1Is the correct answer 6 or 1? If it is 6, can you show me how you got that?
Expert:  Ryan replied 1 year ago.

I'm sorry about that. The correct result is 6. It's the preceding notation that is incorrect. It should have been:

C(6, 5) = 6! / (5! * (6 - 5)!) = 6

Ryan

Customer: replied 1 year ago.
Thanks
Expert:  Ryan replied 1 year ago.

You're welcome. Please don't hesitate to ask if you discover anything that doesn't seem right or is confusing.

Customer: replied 1 year ago.
Question #9 - How did you know to multiply 4 to the power of 10 and 3 to the power or 10 in a & b?
Expert:  Ryan replied 1 year ago.

In part a there are 4 possible choices that the student can select from for each of the 10 questions. The total number of ways that the student can list the answers is then 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 4^10.

In part b, the only combinations to be counted are the ones where the student selected an incorrect answer. Since only 1 of the 4 answers is correct, there are 3 "incorrect" choices that the student can select from. Like the above explanation, in this case the student then has (3 choices for the first answer)*(3 choices for the second answer)*(3 choices for the third answer)... The total number of ways that 10 incorrect answers can be listed is then 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 = 3^10.

Customer: replied 1 year ago.
makes sense. thanks
Expert:  Ryan replied 1 year ago.

You're quite welcome.