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

Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. $x^{2}+4 x y+y^{2}-3=0$

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.

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.

(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?

A picture-framing company sells two types of glass: regular and nonglare. For a piece of nonglare glass, the charge is equal to the length of the longest side in inches multiplied by the rate $0.75 per inch. For what length will the charge for nonglare glass be the same as the charge for regular glass? What will the charge be? Explain your answers.

For the equation, solve for $y$ and identify the new coefficient of $x$ and new constant term.

$\frac{5}{6} x+\frac{1}{7} y=-\frac{4}{7}$

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

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

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;

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.

a) Construct a regular hexagon with sides of length 3 cm. b) Calculate its area, showing your method clearly.

What would be the output if line $16$ of Listing $12.9$ is replaced by the following line?

throw new Exception("New info from method1");

Refer to Appendix page discussed before, to find data about the average number of days with precipitation of $0.01$ in. or more for selected cities in the United States. Using a calculator or computer, enter the data for the annual number of days with precipitation.

Find the mean, range, standard deviation, and variance for this data.