Math Answers

The marketing research department for a company that manufactures and sells laptop computers

established the following price-demand and cost functions, respectively:

p (x) = 1,000 - 25x

C(x) = 2,150 + 250x

where p() is the wholesale price in United States dollars at which y thousand laptops can be sold and

C(x) is in thousands of dollars. The domain of both functions is, 1 < x < 10.

formulate a revenue and a profit function

Suppose the production cost is R293 250, computing cost is R1 035, labour cost is R4 140 and the saving on reusable material is R1 725, determine the number of devices produced

When preparing a bouquet, a florist can choose from seven roses, six carnations, and four chrysanthemums. How many bouquets can the florist make if the bouquet must have at least one flower?

Solve the recurrence relation A(n) = 6A(n - 1) - 11A(n - 2) + 6A(n - 3) subject to initial values A(1) = 2, A(2) = 6, A(3) = 20.

2. Use set builder notation to give a description of each of

these sets.

a) {0, 3, 6, 9, 12}

b) {−3, −2, −1, 0, 1, 2, 3}

c) {m, n, o, p}

Suppose three coins are tossed. Let S be the random variable representing

the number of heads that occur. Determine the sample space and the values of a

random variable

Consider the following sets.

U = { 1, 2, …. 10 }

A = { 3, 4, 5, 6, 8, 10 } ` C = { 2, 4, 6, 7, 8 }

B = { 1, 3, 5 }

Perform the following set operations by writing the resulting sets using the roster method. Moreover, sketch the Venn diagram.

1. A’ = ________________________________________________

2.B’ = ________________________________________________

3. A U B = _____________________________________________

4. A ∩ B = _____________________________________________

5. A' ∩ B = _____________________________________________

6. (A ∩ B) U C = _________________________________________

7. A ∩ (B U C’) = _________________________________________

A committee of 6 can be formed from a group of 5 sophomores, 7 juniors, and 8 senior. In how many ways can these be done if:

A. there are 2 members from each class on the committees

B. there shall be exactly 3 seniors, 2 juniors, and 1 sophomore on the committee

Using a Venn diagram, show the following:

1. A U B

2. (A U B)’

3. A ∩ B’

4. A’ U B’

5. A ∩ B ∩ C

Simplify (A ∩ B) U (A ∩ B’) U (A’ ∩ B) U (A’ ∩ B’)