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

(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 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;

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");

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

A dynamometer is a device used to measure torque and speed and to vary the load on rotating devices. The dynamometer operates as follows to control the amount of torque: A hydraulic actuator attached to the axle presses a tire against a rotating flywheel. The greater the displacement of the actuator, the greater the force that is applied to the rotating flywheel. A strain gage load cell senses the force. The displacement of the actuator is controlled by an electrically operated valve whose displacement regulates fluid flowing into the actuator. Draw a functional block diagram of a closed-loop system that uses the described dynamometer to regulate the force against the tire during testing. Show all signals and systems. Include amplifiers that power the valve, the valve, the actuator and load, and the tire.

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.

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

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?

Predict the Output:

ListNode *p = new ListNode(56.4, new ListNode(31.5));
ListNode *q = p;
while (q->next->next != NULL)
q = q->next;
cout << q->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.