Homework answers / question archive / 1)Recall the R, Z, N, Q represent the set of real numbers, the set of integers, the set of natural numbers, and the set of rational numbers respectively

1)Recall the R, Z, N, Q represent the set of real numbers, the set of integers, the set of natural numbers, and the set of rational numbers respectively

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1)Recall the R, Z, N, Q represent the set of real numbers, the set of

integers, the set of natural numbers, and the set of rational numbers respectively. Find or describe the following sets
(a) Z − N.
(b) N ∪ Z
(c) Q ∩ Z
(d) R − Q.

2) A gambler places a bet on a horse race. To win, she must pick the

top three finishers in order. Six horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win her bet?

3) A nature preserve has a population of seven black bears. They have

been tagged #1 through #7, so they can be observed over time. Two of them are randomly selected and captured for evaluation. What is the probability that bears #3 and #5 are captured for evaluation?

 

4) How many cell sites were there per 10,000 subscribers in 1995? in 2003? Has the number of cell sites per subscriber increased or decreased from 1995 to 2003? What does the number of cell sites per 10,000 subscribers infer (if anything)? Show your work.

5) Sparky has scores of 70, 67, and 73 on his first three sociology tests.

if he needs to keep an average of 70 to stay eligible for lacrosse, what score on the fourth exam will accomplish this

6) Use Gauss-Jordan row reduction to solve the given system of equations.

(If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer using the parameters x and/or y.)
9x − 3y = 245x − 15y = 10

7) Which of the following functions has an oblique asymptote when graphed? O A(x) - 2x2 + 4x - 6x x +x-2 A(x) = 2x + 4x - 6x x- + 2x - 3 all of the above ((x) = 2x - 4x7 - 6x

8) A rectangular transport box with a surface area of 625 ft2

 is designed to contain a maximum volume. What are its dimensions so that its volume is maximized.

9) Solve the first-order differential equation by separating variables. (Use Cy' 

 for the constant of integration. Remember to use absolute values where appropriate.)

 = 2y/x + 7

10) Water is pouring into a (right circular) conical tank at the rate

of 8 cubic feet per minute. If the height of the tank is 12 feet and the radius of its circular opening at the top is 6 feet, how fast is the water level rising when the water is 4 feet deep?

11)  A space X is 2nd countable if and only if X has a countable basis. Theorem 5.11. Every uncountable set in a 2nd countable space has a limit point.