Exam 2: Linear Models, Equations, and Inequalities

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. -There were 28,000 people at a ballgame in Los Angeles. The day's receipts were $203,000. How many people paid $11 for reserved seats and how many paid $6 for general admission?

Provide an appropriate response. -True or Fal $\text { If } x < 4 \text { then } - 3 x < - 12$

Solve the double inequality. - $- 20 < - 5 \mathrm { a } \leq 0$

Solve the equation. - $\frac { 6 x + 7 } { 7 } + \frac { 3 } { 7 } = - \frac { 4 x } { 7 }$

Write the best-fit linear model for the data. -A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. The linear model for this data is $\mathrm { y } = 88.6 - 1.86 \mathrm { x }$ , where $x$ is the number of hours spent in the lab and $y$ is grade on the test. Use this model to predict the grade of a student who spends 12 hours in the lab.

Find the linear function that is the best fit for the given data. Round decimal values to the nearest hundredth, if necessary. - x 2 3 7 8 10 y 2 4 4 6 6

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate. - $- 5 x + 9 = - 1 + 8 x$

Solve the equation. - $13 ( 7 c - 4 ) = 5 c - 8$

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). The linear model for this data is $\mathrm { y } = 14.6 + 0.211 \mathrm { x }$ , where $\mathrm { x }$ is temperature and $\mathrm { y }$ is growth in millimeters. Use this model to predict the growth of a plant if the temperature is $57 .$ Temp 62 76 50 51 71 46 51 44 79 Growth 36 39 50 13 33 33 17 6 16

Write the best-fit linear model for the data. -A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. Find a linear function that approximates a student's course grade As a function of the number of hours spent in lab. Number of hours spent in labrade (percent) 10 96 11 51 16 62 9 58 7 89 15 81 16 46 10 51

Provide an appropriate response. -True or Fal $\text { If } x > 3 \text { then } 9 x > 27$

Solve the inequality and draw a number line graph of the solution. - $\frac { 2 x + 5 } { 9 } < \frac { 13 } { 2 }$

Write the best-fit linear model for the data. -The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Find a linear function that approximates a student's score as a function of the number of hours he or she Studied. Hours 5 10 4 6 10 9 Score 64 86 69 86 59 87

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate. - $\frac { x + 6 } { 5 } - 7 = \frac { x + 8 } { 7 } - 7$

You are given a table showing input and output values for a given function $y _ { 1 } = f ( x )$ x). Use the table to answer the question. -What is the $y$ -intercept of the graph of $y = f ( x )$ ?

Does the system have a unique solution, no solution, or many solutions? - $\left\{ \begin{array} { l } 6 x - y = 18 \\x + 5 y = 34\end{array} \right.$

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. Find a linear function that approximates a student's current GPA as a function of his or her Entering GPA. 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

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 manufacturer has total revenue given by the function $\mathrm { R } = 70 \mathrm { x }$ and has total cost given by $\mathrm { C } = 50 \mathrm { x } + 145$ , 000 , where $\mathrm { x }$ is the number of units produced and sold.

Solve the double inequality. - $13 < \frac { 5 x - 11 } { 11 } < 15$

Solve the equation. - $24 x - 2 = 6$