Math Answers

Two boxes, 1 and 2 are given. Suppose box 1 contains 6 black and 7 white balls. Box 2 contains 9 black and 8 white balls. Three balls are selected at random from box 1 and put into box 2. Then two balls are selected at random from box 2.

1) what is the probability that these two balls have the same color

2) what is the probability that these two balls have the different colors

An elevator starts with 4 passengers and stops at 4 floors. Find the probability of the following events:

1) all passengers leave at the same floor (Event A)

2) all passengers leave at the two floors (Event B)

3) all passengers leave at the three floors (Event C)

4) all passengers leave at different floors (Event D)

Let W be the set of all 3×3 real diagonal matrices. Prove that W is a subspace of M33.

1, In how many ways each 5 boys and 3 girls be seated around a table if:

i) There is no restriction?

ii, Boy Bi and girl Gi are not adjacent?

ji, No girls are adjacent?

2. Each user on a computer system has a password, which is six to eight characters

long. where each character is an upper case letter or a digit Fach password must

contain at least one digit. How many possible passwords are there?

3.how many ways are there to distribute 10 identical bones to 4 dogs if each dog must

stat least | bone and Fifi may not receive more than 3 bones’?

2.1. The following is a recipe for making 18 scones: 1 cup white sugar, cup butter, 2 teaspoons vanilla essence, 1 cups flour, 2 eggs, 1 teaspoons baking powder, cup of milk. On your birthday you decide to use this recipe to make scones for the staff at your school. How would you adjust the recipe so that you can make 60 scones?                                      

A Biotech company produces enzymes at a rate that can be described by the Poisson process.

Their lipase enzyme from a genetically modified bacteria produces glycerol at an average rate of

3 mg/L per minute.

4.1 Find the probability that the enzyme will produce exactly 5 mg/L in a given minute. (2)

4.2 What is the likelihood that the enzyme will produce four or more mg/L in a given minute? (7)

4.3 What chance is there that no product will be produced in a given minute?

The manager of a local gym has determined that the length of time patrons spend at the gym is a

normally distributed variable with a mean of 80 minutes and a standard deviation of 20 minutes.

5.1 What proportion of patrons spends more than 2 hours at the gym? (3)

5.2 What proportion of patrons spend less than 1 hour at the gym? (3)

5.3 What is the least amount of time spent by 60% of patrons at the gym?

Calculate the average price paid per kilogram of sodium hydroxide in a lab storeroom consisting

of 40 kilograms bought for R15 each; 10 kilograms bought for R20 each; 5 kilograms bought for

R40 each; and 50 kilograms bought for R10 each.

1.     True or false: (~p∧q) ∨ (~p∨q)≡ (~p∨q)

How does the graph of y=3x^2 differ from the graph of y= -x^2?A: The graph of y= 3x^2 opens upward and is narrower.B: The graph of y= 3x^2 opens upward and is winder.C: The graph of y= 3x^2 opens downward and is narrower.D: The graph of y= 3x^2 opens downward and is wider.