Math Answers

Your statement date is every 4^th day of the month. You made a purchase on April 3. When is the statement date for the said purchase?

The following data represents the number of packages of 5 popular brands of cigarettes sold by a supermarket on 8 randomly selected days:

Brand

A

B

C

D

E

21

35

32

28

14

47

25

38

35

12

27

41

19

23

31

20

45

60

33

36

31

40

43

48

32

53

29

42

40

23

35

42

45

29

31

22

36

29

42

30

Perform an analysis of variance, at 0.05 level of significance, and determine whether or not the 5 brands sell, on the average, the same number of cigarettes at this supermarket. (15 points)

Consider two sets A and B such that A ⊆ B. Find the possible values of x if A = {2, 4, 6, x} and B = {2, 3, 5, 6, x+1}. Ans: x = 3. Please explain.

State the number of subsets of {p, q, r, s}. Explain the answer please as I don't understand how to do this.

5. Let S = {1, 2} and T = {1, 2, 3}.

a. List all the subsets of S and T

C. What fraction of the subsets of T are also subsets of S

5. Let S = {1, 2} and T = {1, 2, 3}.

a. List all the subsets of S and T

C. What fraction of the subsets of T are also subsets of S

The overhead read distances of adult females are normally distributed with a mean of 195 cm any standard deviation of 8.6 cm. Find the probability that the individual distance is greater than 204.30 cm. Find the probability that the mean of 15 randomly selected distances is greater than 193.50 cm. Why can’t the normal distribution be used in part B even though the sample size does not exceed 30?

[A] A company calculates its expected profits as a function of the quantity of the items it can sell. How much are their expected profits if the company’s profit function is P(q)=q³−2000q+500 and their current sales quantity, q, is 60?

[C] The marketing department of Spager Ltd estimated that if the selling price of product is set at $15 per unit then the sales will be 50 units per week, while, if the selling price is set at $20 per unit, the sales will be 30 units per week. Assume that the graph of this function is linear. The production department estimates that the variable cost will be $5 per unit and that the fixed cost will be $50 per week, and special cost are estimated as $0.125x2, where x is the quantity of output. All production is sold.

(a) Show that the relationship between price (Pr) and quantity sold (x) , are given by the equation Pr = 27.5 - 0.25x.

(b) Find the revenue function, R.

(c) Find the total cost function (C).

(d) Advise the company on production and pricing policy if it wishes to maximize profits, and find the maximum profit.

[DE] Find the Wronskian of the following functions and determine whether it is linearly dependent or linearly independent on (-∞,∞).

1. {x², x+1, x-3}               ans, W=8, linearly independent
2. {3e^2x, e^2x}                     ans, W=0, linearly dependent
3. {x², x³, x⁴}                    ans, W=2x^6, linearly independent

[LA] 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.