See the attached file for questioins

Calculus

1. (5 pts) Find the second derivative of

2. (5 pts)   Find the derivative of

3. (5 pts)   Find y″

4. (5 pts)   Find the derivative of

5. (5 pts)   Find the derivative of

6. (5 pts)   The size of a population of lions after t months is . Find the growth rate when .

Discrete Math

1. A club with 17 women and 21 men needs to form a committee of size 7:

A. How many committees are possible?

B. How many committees are possible if a committee must have 3 women and 4 men?

C. How many committees are possible if a committee must consist of all women or all men?

D. How many committees are possible if a committee must have at least 3 women?

E. How many committees are possible if a committee must have exactly one woman?

F. How many committees of seven different executive positions are possible? (e.g., chair, treasurer, secretary, etc.)

2. In the questions below, suppose a “word” is a string of 8 letters of the alphabet with repeated letters allowed:

A. How many words are there?

B. How many words end with the letter T?

C. How many words begin with R and end with T?

D. How many words start with A or B?

E. How many words begin with A or end with B?

3. Let A = {1, 2, 3} and B = {a, b}

How many relations are there between the set A and B? (Do not give just a number but explain how you would compute it)

4. A bowl contains 53 red balls, 48 blue balls, and 72 green balls. A woman selects balls
at random without looking at them. We assume that the woman does not replace the balls after drawing them. What is the least number of balls she must select to be sure of having at least 16 balls of the same color? Explain.