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

A regular polyhedron has axis symmetry of order 3, but does not have plane symmetry. What is the figure? Explain.

Find the area of each regular polygon with the given apothem a and side length s. decagon, a = 19 m, s = 12.3 m

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

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.

What is the relationship between the side length and the apothem in each figure? a. a square b. a regular hexagon c. an equilateral triangle

For the following program fragments, predict what the output will be.

ListNode *p = new ListNode(56.4);
p = new ListNode(34.2, p);
cout << (*p).value << endl << p−>value;   

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

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 measure of an exterior angle of a regular polygon is given. Find the measure of an interior angle. Then find the number of sides. 18

(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?

For a sample of eight apartment buildings in Chicago, the percentage-occupancy rates during a recent month were as shown below:

$$\begin{array}{llll}50.0 \% & 79.1 & 61.3 & 43.9 \\ 68.1 & 70.0 & 72.5 & 66.3\end{array}$$

For these sample data, determine:

c. The standard deviation and variance.

For the following program fragments, predict what the output will be.

ListNode *p = new ListNode(56.4);
p = new ListNode(34.2, p);
cout << (*p).value << endl << p−>value;