Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week, h, to the cumulative grade-point average, G, of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.

$$\begin{matrix} \text{Hours of} & \text{Grade-Point}\\ \text{Video Games} & \text{Average, G}\\ \text{per Week, h} & \text{ }\\ \text{0} & \text{3.49}\\ \text{0} & \text{3.05}\\ \text{2} & \text{3.24}\\ \text{3} & \text{2.82}\\ \text{3} & \text{3.19}\\ \text{5} & \text{2.78}\\ \text{8} & \text{2.31}\\ \text{8} & \text{2.54}\\ \text{10} & \text{2.03}\\ \text{12} & \text{2.51}\\ \end{matrix}$$

Predict the grade-point average of a student who plays video games for 8 hours each week.

Find the extreme values of $f$ subject to both constraints.

$$\begin{array}{l} f(x, y, z)=3 x-y-3 z \\ x+y-z=0, \quad x^{2}+2 z^{2}=1 \end{array}$$

Express the equation in exponential form. $\log _{7}(3 y)=2$

Sketch the region determined by the indicated constraints. Then find the minimum and maximum values of the objective function and where they occur, subject to the constraints.

Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week, h, to the cumulative grade-point average, G, of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.

$$\begin{matrix} \text{Hours of} & \text{Grade-Point}\\ \text{Video Games} & \text{Average, G}\\ \text{per Week, h} & \text{ }\\ \text{0} & \text{3.49}\\ \text{0} & \text{3.05}\\ \text{2} & \text{3.24}\\ \text{3} & \text{2.82}\\ \text{3} & \text{3.19}\\ \text{5} & \text{2.78}\\ \text{8} & \text{2.31}\\ \text{8} & \text{2.54}\\ \text{10} & \text{2.03}\\ \text{12} & \text{2.51}\\ \end{matrix}$$

Explain why the number of hours spent playing video games is the independent variable and cumulative grade-point average is the dependent variable.

Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week, h, to the cumulative grade-point average, G, of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.

$$\begin{matrix} \text{Hours of} & \text{Grade-point}\\ \text{Video Games} & \text{Average, $G$}\\ \text{per Week, $h$} & \text{ }\\ \hline \text{0} & \text{3.49}\\ \text{0} & \text{3.05}\\ \text{2} & \text{3.24}\\ \text{3} & \text{2.82}\\ \text{3} & \text{3.19}\\ \text{5} & \text{2.78}\\ \text{8} & \text{2.31}\\ \text{8} & \text{2.54}\\ \text{10} & \text{2.03}\\ \text{12} & \text{2.51}\\ \end{matrix}$$

Interpret the slope.

_____ controls a plant's response to day length.

Let $h=(b-a) / 3, x_{0}=a, x_{1}=a+h, \text { and } x_{2}=b.$ Find the degree of precision of the quadrature formula $\int_{a}^{b} f(x) d x=\frac{9}{4} h f\left(x_{1}\right)+\frac{3}{4} h f\left(x_{2}\right)$

Professor Grant Alexander wanted to find a linear model that relates the number of hours a student plays video games each week, h, to the cumulative grade-point average, G, of the student. He obtained a random sample of 10 full-time students at his college and asked each student to disclose the number of hours spent playing video games and the student’s cumulative grade-point average.

$$\begin{matrix} \text{Hours of} & \text{Grade-Point}\\ \text{Video Games} & \text{Average, G}\\ \text{per Week, h} & \text{ }\\ \text{0} & \text{3.49}\\ \text{0} & \text{3.05}\\ \text{2} & \text{3.24}\\ \text{3} & \text{2.82}\\ \text{3} & \text{3.19}\\ \text{5} & \text{2.78}\\ \text{8} & \text{2.31}\\ \text{8} & \text{2.54}\\ \text{10} & \text{2.03}\\ \text{12} & \text{2.51}\\ \end{matrix}$$

Use a graphing utility to find the line of best fit that models the relation between number of hours of video game playing each week and grade-point average. Express the model using function notation.

Over a period of several hours, observe the motion of the stars in the vicinity of Polaris. Write a brief summary of the motion of the stars in the vicinity of Polaris.

In a twenty-minute period, a surfer catches 3 waves and wipes out twice. What is the ratio of waves caught to wipeouts?

Some types of sponges and cnidarians reproduce asexually. Why is this beneficial to them?

Both a father and his child drink water that has flowed through lead pipes. There is also lead-based paint on the walls of their home. Over time, the child shows the effects of lead poisoning. The father does not. Explain how this could be possible.

A point P(x, y) is given. Suppose that P is the terminal point determined by t. Find sin t, cos t, and tan t. $P\left(\frac{3}{5},-\frac{4}{5}\right)$