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.

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.

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

Angle PAN

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

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;   

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.

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

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

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?

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");

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.

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