Write a paragraph explaining President Woodrow Willson's goals for the League of Nations. What were some of its weaknesses? What was significant about its establishment?

a) Only a vertical translation has been applied to the graph of $y=\log _{3} x$ so that the graph of the transformed image passes through the point (9, -4). Determine the equation of the transformed image. b) Only a horizontal stretch has been applied to the graph of $y=\log _{2} x$ so that the graph of the transformed image passes through the point (8, 1). Determine the equation of the transformed image.

Standard automobile license plates in California display a nonzero digit, followed by three letters, followed by three digits. How many different standard plates are possible in this system?

Given figure shows a scatter plot of the number of units sold, y, of 20 varieties of a canned soup versus the amount of shelf space, x, allocated to each variety. Do you think that sales are affected by the amount of allocated shelf space, or vice versa?

Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list its terms and state its degree.

$$\begin{array}{rrr} \hline \quad \footnotesize \text{Polynomial} & \ \quad \footnotesize \text{Type} & \quad \footnotesize \text{Terms} & \quad \footnotesize \text{Degree} \\ \hline -8 & \quad \gray{\rule{8mm}{4mm}} &\quad\gray{\rule{10mm}{4mm}} & \quad\gray{\rule{8mm}{4mm}} \end{array}$$

A survey of cars on a certain stretch of highway during morning commute hours showed that 70% had only one occupant, 15% had 2, 10% had 3, 3% had 4, and 2% had 5. Let X represent the number of occupants in a randomly chosen car. a. Find the probability mass function of X. b. Find $P(X \leq 2).$ c. Find P(X > 3). d. Find $\mu_{x}$ e. Find $\sigma_{x}.$

(a) find an equation of the tangent line to the graph of f at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the derivative feature of a graphing utility to confirm your results. f(x) = ½x ln x², (-1, 0)

In this exercise, find the slope of the graph of the function at the indicated point. Use the derivative feature of a graphing utility to confirm your results.

Function: $f(t)=\frac{3}{4} e^t$, Point: $\left(0, \frac{3}{4}\right)$

Graph $y_1=x^2-2x, y_2=x$, and $y_3=y_1 \div y_2$ in the same $[-10,10,1]$ by $[-10,10,1]$ viewing rectangle. Then use the $\boxed{\text{TRACE}}$ feature to trace along $y_3$. What happens at $x=0$ ? Explain why this occurs.

Fill in the blanks: If $f(x)=3^x$ and $g(x)=\log _3 x$, then funetions f and g are ____ functions, and their graphs are _____ with respect to the line with equation _____ The domain of f is the ____ of $g$ and vice versa.

Evaluate the expression for the given value of the variable.

z/2 when z = 8

Fill in the blank with the appropriate response, (Remember that the vertical stretch or shrink factor is positive.)

The graph of $y=-\frac{1}{4}|x+2|-3$ can be obtained from the graph of $y=|x|$ by shifting horizontally $\underline{\qquad\qquad}$ units to the $\underline{\qquad\qquad}$ vertically shrinking by applying a factor of $\underline{\qquad\qquad}$ , reflecting across the $\underline{\qquad\qquad}$ -axis, and shifting vertically $\underline{\qquad\qquad}$ units in the $\underline{\qquad\qquad}$ direction.

Multiply or divide mentally by first converting to scientific notation (if necessary) and rounding to one significant digit.\

$$\frac{7.76 \times 10^{13}}{3.1 \times 10^5}$$

The captain of a Navy gunboat orders a volley of twenty-five missiles to be fired at random along a five-hundred-foot stretch of shoreline that he hopes to establish as a beachhead. Dug into the beach is a thirty foot-long bunker serving as the enemy's first line of defense. The captain has reason to believe that the bunker will be destroyed if at least three of the missiles are on target. What is the probability of that happening?