Math Answers

In a survey of meals taken by 104 students during lunch, the following data were obtained: 88 students eat at least Sandwich, Salad or Salmon; 45 students eat Sandwich; 37 students eat Salad; 45 students eat Salmon; 13 students eat Sandwich and Salad; 13 students eat Salad and Salmon ; 20 students eat Sandwich and Salmon. Based on the survey, calculate the number of students who:

1. do not eat any of Sandwich, Salad or Salmon for lunch?

2. eat all Sandwich, Salad and Salmon for lunch?

3. eat Salad or Salmon?

4. do not eat Sandwich for lunch?

5. do not eat Sandwich and Salad for lunch?

6. do not eat Sandwich or Salad for lunch?

7. eat Salmon but do not eat Sandwich or Salad for lunch?

8. only eat one meal either Sandwich only, or Salad only or Salmon only for lunch?r

9. do not eat Salmon but eat Sandwich and Salad for lunch?

10. eat at least two meals for lunch?

From a total of 125 employees, 102 employees are assigned to perform ONLY ONE programming job, either system programming or application programming. And 10 employees are not assigned to perform any of those programming jobs. Overall, 52 employees are assigned to perform ONLY system programming jobs.

a. How many employees are assigned to perform both system programming jobs and application programming jobs?

b. How many employees are assigned to perform system programming jobs or application programming jobs?

c. How many employees are assigned to perform system programming jobs?

d. How many employees are NOT assigned to perform system programming jobs?

 Suppose someone e-mails you 10 different files you need to save one-by-one to your computer. Suppose that in total you have 6 different empty folders on your computer.

(i) How many ways can you save the files into the 6 folders if the temporal order in which you save the individual files does not matter.

(ii) How many ways can you save the files into the 6 folders if the temporal order in which you save the individual files matters.

An influenza vaccine is produced by two different companies. It is known that a vaccine produced by company 1 is effective with probability 0.89, while a vaccine produced by company 2 is effective with probability 0.93. We also know that company 1 supplies 40% of the vaccines, while company 2 supplies 60% of the vaccines ordered by the government.

(i) What is the probability that a vaccine is effective, given that it was produced by company 2?

(ii) What is the probability that a randomly chosen vaccine from the government’s order is not effective?

(iii) What is the probability that given a vaccine is not effective that it was produced by company 1?

You have a deck of 52 playing cards (check online for the full composition of a 52 card deck if you are unsure).

(i) How many different 8 card hands can be dealt?

(ii) What is the probability that a hand of 8 dealt randomly contains (exactly) 2 aces?

(iii) What is the probability that a hand of 7 dealt randomly will have 7 cards of the same suit? 

You have a deck of 52 playing cards

(i) How many different 8 card hands can be dealt?

(ii) What is the probability that a hand of 8 dealt randomly contains (exactly) 2 aces?

(iii) What is the probability that a hand of 7 dealt randomly will have 7 cards of the same

suit?

Check that {1,(x+1),(x+1)^2} is a basis of the vector space of polynomial over R of degree at most 2. Find the coordinate of 3+x+2x^2 with respect to the basis.

Construct a K-map for F(x, y, z) = xz + yz + xyz. Use this K-map to find the implicants, prime implicants, and essential prime implicants of F(x, y, z).

Find the volume in the first octant bounded by x+y+z=9, and the inside cylinder 3y=27-x^3

The average hospitality girls working in a certain area is 19 years old. A civic oriented group made a recent survey on the age of the hospitality girls working in the same locality. A random sample of 20 respondents showed an average of 15.4 years old with a standard deviation of 2.14 years old. Using a 0.05 level of significance, has the hospitality girls gone lower?