Exam 2: Linear Models, Equations, and Inequalities

Write the best-fit linear model for the data. -Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between $3.5$ and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs. The linear model for this data is $y = 3.67 + 0.0313 x$ , where $x$ is entering GPA and $\mathrm { y }$ is current GPA. Use this model to predict current GPA of a student whose entering GPA is 3.1. \begin{tabular} { c c } Entering GPA Current GPA 3.5 3.6 3.8 3.7 3.6 3.9 3.6 3.6 3.5 3.9 3.9 3.8 4.0 3.7 3.9 3.9 3.5 3.8 3.7 4.0

Solve the formula for the specified variable. - $\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \text { for } \mathrm { C }$

Solve the system of equations by substitution, if a solution exists. - $\left\{ \begin{array} { l } x + 2 y = 16 \\2 x + 3 y = 24\end{array} \right.$

Solve the equation for y. -The future value of a simple interest investment is given by $\mathrm { S } = \mathrm { P } ( 1 + \mathrm { rt } )$ , where $\mathrm { P }$ is the principal invested at a simple interest rate $\mathrm { r }$ for $\mathrm { t }$ years. What principal $\mathrm { P }$ must be invested for $t = 4$ months at the simple interest rate $r = 11 \%$ so that the future value grows to $\$ 3600$ .

Solve the equation for y. -The mathematical model $C = 400 x + 60,000$ represents the cost in dollars a company has in manufacturing x items during a month. How many items were produced if costs reached $380,000?

Translate the sentence to an algebraic inequality. -An omelette costs $1.00 more than Mario's order of pancakes. After treating his family to breakfast, Mario is sure that 6 omelettes and 3 orders of pancakes cost more than $25 but not more than $40, including tax of 7% And a tip of $3.50. In what price range is an order of pancakes?

Translate the sentence to an algebraic inequality. -Using the formula to find Fahrenheit $( \mathrm { F } )$ in terms of Celsius $( \mathrm { C } ) , \mathrm { F } = \left( \frac { 9 } { 5 } \right) \mathrm { C } + 32$ , find the range (to the nearest tenth) of the Fahrenheit temperature when the range of the Celsius temperature is between $2 ^ { \circ } \mathrm { C }$ and $6 ^ { \circ } \mathrm { C }$ , inclusive.

To find the number of units that gives break-even for the product, solve the equation R $\mathbf { R } = \mathbf { C }$ ound your answer to the nearest whole unit. -A chemist has two solutions that contain different concentrations of a certain acid. One is a 4% concentration and the other is an 11% concentration. How many cubic centimeters of each should the chemist mix to obtain 50 Cm3 of a solution with an acid concentration of 7.64%?

Solve the equation. - $- 3 x + 4 ( - 2 x - 7 ) = - 31 - 8 x$

Without graphing, determine whether the following data set is exactly linear, approximately linear or nonlinear. - Age (years) 18 23 20 26 29 16 25 20 32 Grade Point Average 2.5 3.0 2.7 3.2 3.9 2.0 3.5 3.1 3.6

Write the best-fit linear model for the data. -The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters). Find a linear function that approximates a plant's growth as a function of temperature. Temp 62 76 50 51 71 46 51 44 79 Growth 36 39 50 13 33 33 17 6 16

Solve the system of equations by substitution, if a solution exists. - $\left\{ \begin{array} { l } - 6 x + 6 y = 66 \\- 3 x + 4 y = 42\end{array} \right.$

Solve the system of equations graphically, if a solution exists. - \[\begin{array} { c } 3 x + 2 y = 5 \\ - 6 x - 4 y = 5

Provide an appropriate response. -John has been a teacher at West Side High School for the past 12 years. His salary during that time can be modeled by the linear equation y $y = 800 x + 33,000$ 0 where x is the number of years since he began teaching at West Side and y is his salary in dollars. Explain what the slope, 800, represents in this context.

Solve the inequality and draw a number line graph of the solution. - $4 x - 6 \geq 3 x + 1$

Provide an appropriate response. -Sketch a scatter plot for a set of data points for which it would be appropriate to fit a linear function. Then sketch a second scatter plot for a set of data points for which it would not be appropriate to fit a linear function. For the second scatter plot, explain why it would not be reasonable to fit the data points to a linear function.

Translate the sentence to an algebraic inequality. -The number of people at a concert is not to exceed 2718.

Solve the formula for the specified variable. - $\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh }$ for $\mathrm { b }$

Solve the equation for y. -When going more than 38 miles per hour, the gas mileage of a certain car fits the model $y = 43.81 - 0.395 x$ where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what Speed will the car average 15 miles per gallon? (Round to nearest whole number.)

Provide an appropriate response. -The double inequality $a < x \leq b$ means "a is less than $x$ and $x$ is less than or equal to $b ^ { \prime \prime }$ . Which of these inequalitie: satisfied by any real number $x$ ? (a) $- 5 < x \leq - 11$ (b) $- 8 < x \leq - 7$ (c) $0 < x \leq 4$ (d) $- 2 < x \leq 6$ ot