Your company, Sonic Video, Inc., has conducted research that shows the following probability distribution, where X is the number of video arcades in a randomly chosen city with more than 500,000 inhabitants:

$$\begin{matrix} \text{x} & \text{0} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6} & \text{7} & \text{8} & \text{9}\\ \text{P(X=x)} & \text{.07} & \text{.09} & \text{.35} & \text{.25} & \text{.15} & \text{.03} & \text{.02} & \text{.02} & \text{.01} & \text{.01}\\ \end{matrix}$$

a. Compute the mean, variance, and standard deviation (accurate to one decimal place). b. As CEO of Startrooper Video Unlimited, you wish to install a chain of video arcades in Sleepy City, U.S.A. The city council regulations require that the number of arcades be within the range shared by at least 75% of all cities. What is this range? What is the largest number of video arcades you should install so as to comply with this regulation?

Use the Change of Base Formula to rewrite each expression using common logarithms. $\log _{7} 8$

List as many words as you can think of that contain the root, mart, voc, or vok.

Find the domain, vertical asymptote, and x-intercept of the logarithmic function, and sketch its graph by hand. $y=2+\log _{10}(x+1)$

Sketch a graph of the parabola with the given vertex through the given point. vertex (1,5), point (2,11)

Graph each equation. Describe each graph and its lines of symmetry. Give the domain and range for each graph. $x^{2}-y^{2}=25$

Solve each system.

$$\left\{\begin{aligned} x+y-z &=1 \\ 3 x+3 y+z &=3 \\ 2 x+2 y-2 z &=2 \end{aligned}\right.$$

Find the opposite and the reciprocal of each number. $\sqrt{3}$

Simplify the expression.

$$\left(-5 t^{2}\right)\left(6 t^{-9}\right)$$

Use synthetic division to show that x is a solution of the thirddegree polynomial equation, and use the result to factor the polynomial completely. List all the real solutions of the equation. Polynomial Equation $2 x^{3}-17 x^{2}+12 x+63=0$ Value of x $x=-\frac{3}{2}$

Subtract. Use models if needed. (9x - 12) - (5x - 7).

Each pair of figures is similar. Find the length of x.

Negate the following sentences. If f is a polynomial and its degree is greater than 2, then $f^{\prime}$ is not constant.

Nosotros estabamos peleando cuando yo (me estaba rompiendo / me rompi) el dedo.