The measure of an exterior angle of a regular polygon is given. Find the measure of an interior angle. Then find the number of sides. 72

Let G be an r-regular graph with n vertices and m edges. Find (and prove) a simple algebraic relation between r, n, and m.

Identify Point of View How did the work of New Deal era artists and writers contribute to our appreciation today of the New Deal?

Lo-bed Company produced 4,000 units of product that required four standard hours per unit. The standard fixed overhead cost per units is $1.20 per hour at 16,400 hours, which is 100% of normal capacity. Determine the fixed factory overhead volume variance.

A regular heptagon (7 sides) has perimeter 126 and area A. Express the apothem a of the heptagon algebraically in terms of the area A.

Your pay as a lifeguard is $\$14.50$ an hour for a regular 40-hour week. Your overtime rate is $1\frac{1}{2}$ times your regular hourly rate. During this past week, you earned $\$712.50$ in total pay. How many hours of overtime did you work in that week?

A card is drawn at random from a regular deck of 52 cards. Find the probability of each event. A spade is drawn.

A homeowner buys a new refrigerator and a new air conditioner. Which one of these devices would you expect to have a higher COP? Why?

(a) Explain how to find the nth state matrix of a Markov chain. (b) Explain how to find the steady state matrix of a Markov chain. (c) What is a regular Markov chain? (d) What is an absorbing Markov chain? (e) How is an absorb ing Markov chain different than a regular Markov chain?

Many traffic experts argue that the most important factor in accidents is not the average speed of cars but the amount of variation. Suppose that the speeds of a sample of 200 cars were taken over a stretch of highway that has seen numerous accidents. Compute the variance and standard deviation of the speeds, and interpret the results.

The base of the isosceles triangle is also a side of regular pentagon PENTA. Find the measure of each angle.

Angle PAN

Assume a normal distribution with known population variance. Calculate the LCL and UCL for each of the following.

a. $\bar{x}=50 ; n=64 ; \sigma=40 ; \alpha=0.05$

b. $\bar{x}=85 ; n=225 ; \sigma^2=400 ; \alpha=0.01$

c. $\bar{x}=510 ; n=485 ; \sigma=50 ; \alpha=0.10$

When you ride a bicycle at full speed and the bike stops suddenly, why do you have to push hard on the handlebars to keep from flying forward?

Solve. The length of a side of the base of a regular square pyramid is 6 in. and the height of the pyramid is 10 in. Find the volume of the pyramid.