Graph each hyperbola. $\frac{y^{2}}{9}-\frac{x^{2}}{9}=1$

Solve the equation, if possible. If an equation is an identity or a contradiction, state this.

$$\frac { 3 } { 4 } x + 1.5 = - 19.5$$

A wire is strung tightly between two immovable posts. Discuss how an increase in temperature affects the speed of a transverse wave on this wire. Give your reasoning, ignoring any change in the mass per unit length of the wire.

An experiment involves tossing a single die. These are some events: A: Observe a 2 B: Observe an even number C: Observe a number greater than 2 D: Observe both A and B E: Observe A or B or both F: Observe both A and C

a. List the simple events in the sample space. b. List the simple events in each of the events A through F. c. What probabilities should you assign to the simple events? f. Calculate the probabilities of the six events A through F by adding the appropriate simple-event probabilities.

Find the angle between the diagonal of a cube and an adjacent side.

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.

$$\left\{\begin{aligned} 2 x-2 y-2 z &=2 \\ 2 x+3 y+z &=2 \\ 3 x+2 y &=0 \end{aligned}\right.$$

A measurement is given. Find the minimum and maximum possible measurements. A bag of apples weighs 4 lbs to the nearest lb.

The mathematics department has 30 teaching assistants to be divided among three courses, according to their respective enrollments. The table shows the courses and the number of students enrolled in each course.

$$\begin{matrix} \text{Course} & \text{College Algebra} & \text{Statistics} & \text{Liberal Arts Math} & \text{Total}\\ \text{Enrollment} & \text{978} & \text{500} & \text{322} & \text{1800}\\ \end{matrix}$$

a. Apportion the teaching assistants using Hamilton’s method. b. Use Hamilton’s method to determine if the Alabama paradox occurs if the number of teaching assistants is increased from 30 to 31. Explain your answer.

An airline advertisement states, "To get the special fare you must purchase your tickets between January 1 and February 15 and fly round trip between March l and April 1. You must depart on a Monday, Tuesday, or Wednesday, and return on a Tuesday, Wednesday, or Thursday , and stay over at least one Saturday." (a) Determine which of the following individuals will qualify for the special fare. (b) If the person does not qualify for the special fare, explain why. Xavier plans to purchase his ticket on January 15, depart on Monday, March 3, and return on Tuesday, March 18. Gina plans to purchase her ticket on February 1, depart on Wednesday, March 12, and return on Thursday, April 3. Kara plans to purchase her ticket on February 14, depart on Tuesday, March 4, and return on Monday, March 19. Christos plans to purchase his ticket on January 4, depart on Monday, March I 0, and return on Thursday, March 13. Chang plans to purchase his ticket on January 1, depart on Monday, March 3, and return on Monday, March 10.

Graph using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals. $y=\ln |x|$

Design a clamp circuit to clamp the negative extreme of a periodic input waveform to -5 V. Use diodes, Zener diodes, and resistors of any values required. Assume a 0.6-V forward drop for all diodes and that the Zener diodes have an ideal characteristic in the breakdown region. Power-supply voltages of $\pm 15 \mathrm{V}$ are available.

Which risk has the highest probability of death in the United States? (a) Motor vehicle accident, (b) Drowning, (c) Fire, (d) Firearm assault, (e) Earthquake.

What is the most likely mode of decay for each?

$$^{238} _{92} U$$

Let $Q$ be a nonzero divisible $\mathbb{Z}$ -module. Prove that $Q$ is not a projective Z-module. Deduce that the rational numbers $\mathbb{Q}$ is not a projective $\mathbb{Z}$ -module. [Show first that if $F$ is any free module then $\cap_{n=1}^{\infty} n F=0$ (use a basis of $F$ to prove this). Now suppose to the contrary that $Q$ is projective and derive a contradiction from Proposition 30$(4) . ]$