Transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. $r \cos \theta=4$

Selected operating data for two divisions of Outback Brewing, Ltd., of Australia are given below:

$$\begin{matrix} \text{Division}\\ \text{ } & \text{Queensland} & \text{New South Wales}\\ \text{Sales} & \text{\$ 4.000.000} & \text{\$ 7.000.000}\\ \text{Average operating assets} & \text{\$ 2.000.000} & \text{\$ 2.000.000}\\ \text{Net operating income} & \text{\$ 360.000} & \text{\$ 420.000}\\ \text{Property, plant, and equipment (net)} & \text{\$ 950.000} & \text{\$ 800.000}\\ \end{matrix}$$

1. Compute the rate of return for each division using the return on investment (ROI) formula stated in terms of margin and turnover. 2. Which divisional manager seems to be doing the better job? Why?

Check Understanding Explain why peer groups have a significant impact on individuals' political opinions.

How have changes in population growth affected demographics in Italy?

Explain why giving away personal things might be a sign of someone considering suicide.

What different systems of government did Sparta and Athens have?

Find the matrix product. Note that each product can be found mentally, without the use of a calculator or pencil-and-paper calculations.

$$\left[\begin{array}{ll}{0} & {0} \\ {1} & {0}\end{array}\right]\left[\begin{array}{ll}{2} & {4} \\ {6} & {8}\end{array}\right]$$

Find the normal form of each polynomial. a. $(1 + x + x^2)(1 + x^3)$ b. $(1 + x + x^2 + x^3)(1 + x^4)$ c. $(1 + x + x^2 + x^3 + x^4)(1 + x^5)$ d. Describe a pattern.

Construct truth tables for this compound statement. Determine whether the statement is a. a tautology b. a contradiction c. neither. $(p \wedge q) \vee(p \wedge \neg r)$ $$ \begin{array}{|c|c|c|c|c|c|c|}\hline p & {q} & {r} & {\neg r} & {p \wedge q} & {p \wedge \neg r} & {(p \wedge q) \vee(p \wedge \neg r)} \\ &&&& \hline \\ &&&& \hline \\ &&&& \hline \\ &&&& \hline \\ &&&& \hline \\ &&&& \hline \\ &&&& \hline \\ &&&& \hline \\ \hline\end{array} $$

Write an equation in point-slope form of the line that passes through the given point and with the given slope m. (4, 0); m = -1

Complete each statement by writing the correct word or words. A group of genes that are regulated together is called a(n) ____.

1. En el futuro, ¿nos darán los robots más tiempo para dedicarlo al ____ y al descanso? a. uso b. ocio c. avance

Find the values of x for which $\frac{\mathrm{d} y}{\mathrm{d} x}=0$. Verify your answers by using your GDC. $y=2 x^{3}-9 x^{2}+12 x-7$

Do the systems

$$\left( \begin{array}{rrr}{1} & {0} & {3} \\ {-1} & {1} & {-1} \\ {0} & {2} & {4}\end{array}\right) \left( \begin{array}{l}{x_{1}} \\ {x_{2}} \\ {x_{3}}\end{array}\right)=\left( \begin{array}{l}{1} \\ {1} \\ {1}\end{array}\right)$$

                                 have unique solution?