Each open sentence defines a relation, and x and y are real numbers. Graph each relation and tell whether it is a function. {(x, y): y=-|x|}

A relation contains the point (-3, 10). The _____ contains the point (10, -3).

Scientists found that the number of ant species in Clark Canyon, Nevada, increases at a rate of 0.0037 species per meter of elevation. There are approximately 3 ant species at sea level. a. Write an equation that gives the number of ant species as a function of the elevation (in meters). b. Identify the dependent and independent variables in this situation. c. Explain how you can use the equation from part (a) to approximate the number of ant species at an elevation of 2 meters.

a. What is the first-shift scheme? b. What is an example of positive group polarization? c. What is the relationship between diffusion of responsibility and risky shift?

For each of the following pairs of firms, explain which firm would be more likely to engage in advertising.

a family-owned farm or a family-owned restaurant

Use the sinking fund formula

$$p = \frac { A \left( \frac { r } { n } \right) } { \left( 1 + \frac { r } { n } \right) ^ { ( n \cdot t ) } - 1 }$$

to determine the payment needed to reach the accumulated amount. To ensure that enough is invested each period, round each answer up to the next cent. Quarterly payments with a 10% interest rate compounded quarterly for 40 years to accumulate $1,000,000

Identify whether a scatterplot would or would not be an appropriate visual summary of the relationship between the following variables. In each case, explain on your reasoning. Blood pressure and age. Region of country and opinion about stronger gun control laws.

Round all answers up to the next cent. The city of St. Louis wishes to repay a debt of $25,000,000 in 50 years. How much should the city invest semiannually in a sinking fund paying a 7.5% interest rate compounded semiannually to accumulate$25,000,000 in 50 years?

Evaluate the expression.

$$729 ^ { t / 6 }$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation

$$x + \frac { 1 } { 3 } = \frac { 1 } { 2 }$$

is equivalent to

$$x + 2 = 3.$$

The Telephone Consumer Protection Act (TCPA) allows consumers to put themselves on a do-not-call registry. If a number is on the registry, commercial telemarketers are not allowed to call you. Do you believe this has affected the ability of surveyors to obtain accurate polling results? If so, how?

A sequence is defined recursively. Find the first seven terms of the sequence. $a_{n}=\sqrt{3 a_{n-1}}, \quad a_{1}=\sqrt{3}$

Let

$$Y _ { 1 } , Y _ { 2 } , \ldots , Y _ { n }$$

denote a random sample of size n from a population whose density is given by

$$f ( y ) = \left\{ \begin{array} { l l } { \alpha y ^ { \alpha - 1 } / \theta ^ { \alpha } , } & { 0 \leq y \leq \theta } \\ { 0 , } & { \text { elsewhere, } } \end{array} \right.$$

where α > 0 is a known, fixed value, but

$$\theta$$

is unknown. Consider the estimator

$$\hat { \theta } = \max \left( Y _ { 1 } , Y _ { 2 } , \ldots , Y _ { n } \right)$$

. Show that

$$\hat { \theta }$$

is a biased estimator for

$$\theta$$

.

Find the real solutions, if any, of each system. You may wish to check your answers visually on a computer or a graphing calculator.

$$\left. \begin{array} { l } { x ^ { 2 } - y ^ { 2 } = 15 } \\ { x + y = 1 } \end{array} \right.$$