Perform each of the following conversions, being sure to set up clearly the appropriate conversion factor in each case.

e. $125 \mathrm{~mL}$ to pints

if they are compressed the same distance?

The function in this exercise is given as the sum or difference of two terms. First graph the term (with the same set of axes). Then, using the graph as a guide, sketch the graph of the function.

$y=\tan x+\frac{1}{x^2}, \quad-\frac{\pi}{2}<x<\frac{\pi}{2}$

Ya sabes lo que hacen Luis, Susana y David. Luego contesta la pregunta sobre lo que haces tú.

¿Qué piensas hacer este fin de semana?

Give the location of the vertical asymptote(s) if they exist, and state whether function values will change sign (positive to negative or negative to positive) from one side of the asymptote to the other.

$$\mathrm{Y}_2=\frac{-2 x}{x^3+x^2-x-1}$$

The random variable X has probability density function

$$f ( x ) = C e ^ { x } \quad 0 < x < 1$$

(a) Find the value of the constant C. (b) Give a method for simulating such a random variable.

A company's stock does not have to be listed on one of the major stock exchanges in order to trade. It can be traded on _____________.

A. Over-the-counter market
B. NYSE Euronext
C. NASDAQ
D. AMEX

Normally, rates of diffusion vary inversely with molecular weights; so smaller molecules diffuse faster than do larger ones. In cells, however, calcium ion diffuses more slowly than does cAMP. Propose a possible explanation.

The solid cylindrical steel rod $BC$ of length $L=24$ $\mathrm{in}$. is attached to the rigid lever $AB$ of length $a=15$ $\mathrm{in}$. and to the support at $C$. Design specifications require that the displacement of $A$ not exceed $1 \mathrm{~in}$. when a $100-\mathrm{lb}$ force $\mathbf{P}$ is applied at $A$. Determine the required diameter of the rod. $G=11.2 \times 10^{6} \mathrm{psi}$ and $\tau_{\text {all }}=15 \mathrm{~ksi}$.

Suppose a random variable $X$ has the Poisson distribution with $a=3.5$. Find each of the following.\

$$P(X \leq 3)$$

The distance Train A travels is represented by d=70 t, where d is the distance in kilometers and t is the time in hours. The distance Train B travels at various times is shown in the table. What is the unit rate of each train? Which train is going faster?

Laquesha bought a 24-inch diameter wheel for her bicycle and measured it carefully. Arrange these measures in order from least to greatest: circumference, radius, diameter

Distance In Exercises $75-80$, find the distance between the point and line, or between the lines, using the formula for the distance between the point $\left(x_1, y_1\right)$ and the line $A x+B y+$ $C=0$

$$\text { Distance }=\frac{\left|A x_1+B y_1+C\right|}{\sqrt{A^2+B^2}}$$

Point: $(2,3)$ Line: $4 x+3 y=10$

Perform the following for the function

$$f(x)=3 x^4+5 x^3-35 x^2-55 x+22 .$$

(a) List all possible rational zeros. (b) Find all rational zeros. (c) Use the intermediate value theorem to show that there must be a zero between $3$ and $4$. (d) Use Descartes' rule of signs to determine the possible number of positive zeros and negative zeros. (e) Use the boundedness theorem to show that there is no zero less than $-5$ and no zero greater than $4$.