Write the following expressions in terms of base e: $\text {(a) } \log _{2}\left(x^{2}-1\right) \text { (b) } \log _{3}(5 x+1) \text { (c) } \log (x+2) \text { (d) } \log _{2}\left(2 x^{2}-1\right)$

Assume that $13.5 \mathrm{~g}$ of $\mathrm{Al}$ react with $\mathrm{HCl}$ according to the following equation, at STP: $\mathrm{Al}(s)+\mathrm{HCl}(a q) \longrightarrow \mathrm{AlCl}_3(a q)+\mathrm{H}_2(g)$
Remember to balance the equation first.
a. How many moles of $\mathrm{Al}$ react?
b. How many moles of $\mathrm{H}_2$ are produced?
c. How many liters of $\mathrm{H}_2$ at STP are produced?

Match the following terms with the definition.

$$\begin{array}{llll} \text { anorchidism } & \text { cryptorchidism } & \text { hesitancy } & \text { prostatitis } \\ \text { balanitis } & \text { cystitis } & \text { hypospadias } & \text { sterility } \\ \text { chancre } & \text { epispadias } & \text { leukorrhea } & \text { testicular torsion } \\ \text { chlamydia } & \text { genital herpes } & \text { phimosis } & \text { trichomoniasis } \\ \text { condylomas } & \text { gynecomastio } & \text { priapism } & \text { varicocele } \end{array}$$

failure of the testicles to descend into the scrotum before birth ________.

A nozzle receives $0.1 \mathrm{~kg} / \mathrm{s}$ of steam at $1\ \mathrm{MPa}, 400^{\circ} \mathrm{C}$ with negligible kinetic energy. The exit is at $500$ $\mathrm{kPa}, 350^{\circ} \mathrm{C}$, and the flow is adiabatic. Find the nozzle exit velocity and the exit area.

The North Carolina State study described in Exercise 13.13 also looked at the relationship between student goals and success in getting a C or better in the course. The study report says: "The probability of passing CHE 205 was different for students who would be satisfied with a grade of C or better (36% of 14 students), B or better (64% of 64), A (90% of 30), creative work beyond an A (82% of 11).

Use the information given to make a 4 x 2 table of goal by success or failure for the 119 students.

A force of 13 N is needed to keep a spring with a 2-kg mass stretched 0.25 m beyond its natural length. The damping constant of the spring is c=8. Graph the position function of the mass.

The article “Expectation Analysis of the Probability of Failure for Water Supply Pipes” (J. of Pipeline Systems Engr. and Practice, May 2012: 36–46) proposed using the Poisson distribution to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number of failures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson distribution with $\mu=1$. Determine $P(X = 2)$ first from the pmf formula.

A hollow conducting spherical shell has an inner radius of $8.00 \mathrm{~cm}$ and an outer radius of $10.0 \mathrm{~cm}$. The electric field at the inner surface of the shell, $E_{\mathrm{i}}$, has a magnitude of $80.0 \mathrm{~N} / \mathrm{C}$ and points toward the center of the sphere, and the electric field at the outer surface, $E_o$, has a magnitude of $80.0 \mathrm{~N} / \mathrm{C}$ and points away from the center of the sphere (see the figure). Determine the magnitude of the charge on the inner surface and the outer surface of the spherical shell.

Air flows from a reservoir, maintained at $20^{\circ} \mathrm{C}$ and $2 \mathrm{~MPa}$ absolute, and exits from a nozzle with $\mathrm{M}_{e}=4$. The receiver pressure is then raised until the flow is just subsonic throughout the entire nozzle. Calculate this receiver pressure.

Solve. See the first Concept Check in this section.

In general, what points can have coordinates reversed and still have the same location?

Calculate the change in Gibbs free energy for the following reaction. Indicate whether the reaction is spontaneous under standard conditions.

$$2 \mathrm{NH}_3(\mathrm{~g}) \longrightarrow \mathrm{N}_2 \mathrm{H}_4(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g})$$

Create a variable pounds to store a weight in pounds. Convert this to kilograms and assign the result to a variable kilos. The conversion factor is 1 kg = 2.2 lb.

The vertices of a figure are given. Find the coordinates of the figure after the transformations given.

$$P ( - 2,2 ) , Q ( 4,2 ) , R ( 2 , - 6 ) , S ( - 4 , - 6 )$$

Diate with respect to the origin using a scale factor of 5. Then dilate with respect to the origin using a scale factor of 0.5

Calculate the change in Gibbs free energy for the following reaction. Indicate whether the reaction is spontaneous under standard conditions.

$$\mathrm{H}_2(\mathrm{~g})+\mathrm{Cl}_2(\mathrm{~g}) \longrightarrow 2 \mathrm{HCl}(g)$$