Exam 2: Linear Models, Equations, and Inequalities

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. The linear model for this data is $y = 67.3 + 1.07 x$ , where $x$ is number of hours studied and $y$ is score on the test. Use this model to predict the score on the test of a student who studies 13 hours. Hours 5 10 4 6 10 9 Score 64 86 69 86 59 87

Solve the equation for y. - $y - 2 x ^ { 2 } + 5 = 0$

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. -Jim wants to plan a meal with 150 grams of carbohydrates and 1400 calories. If green beans have 7 grams of carbohydrates and 30 calories per half-cup serving and french fried shrimp have 9 grams of carbohydrates and 190 calories per three-ounce serving, how many servings of green beans and shrimp should he use?

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. -Walt made an extra $5000 by working a second job. He invested part of this money at 7% and the rest at 10%. If his annual return totaled $470, how much must he have invested at 10%?

Solve the equation. - $- 11.2 q = - 116.4 - 1.5 q$

Solve the formula for the specified variable. - $\mathrm { A } = \mathrm { P } ( 1 + \mathrm { nr } )$ for $\mathrm { r }$

Does the system have a unique solution, no solution, or many solutions? - $\left\{ \begin{array} { l } 2 x + 3 y = 6 \\4 x + 6 y = 12\end{array} \right.$

Solve the equation. - $4 ( y + 4 ) = 5 ( y - 6 )$

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. -Suppose that the number of inhabitants of Country A is given by $y = - 7.26 x + 949.26$ million, and the number of inhabitants of Country B is given by $y = 4.14 x + 790.8$ million, where $x$ is the number of years since 2010 . When the number of inhabitants of Country A equals the number of inhabitants of Country B, how many people inhabit each country?

Solve the equation for y. - $3 x - 10 y = - 6$

The table below gives the quantity of a product demanded and the quantity supplied for various prices. Solve the problem. -Find the linear equation that gives the price as a function of the quantity supplied. Price (dollars) Quantity Demanded Quantity Supplied 100 700 0 120 660 80 140 620 160 160 580 240 180 540 320

Solve the system of equations by elimination, if a solution exists. - $\left\{ \begin{array} { l } 8 x + 8 y = 64 \\3 x - 5 y = - 40\end{array} \right.$

Solve the inequality graphically. Give the solution in interval notation. -Use the $x$ -intercept method to solve $9 ( 2 x - 4 ) > 27 ( x + 2 )$

Find the linear function that is the best fit for the given data. Round decimal values to the nearest hundredth, if necessary. - 1 2 3 4 5 6 17 20 19 22 21 24

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 certain product has supply and demand functions given b $\text { by } p = 3 q + 21 \text { and } p = 164 - 8 q$ , respectively, where p is the price in dollars and q is the quantity supplied or demanded at price p. What price gives market Equilibrium?

Use the data shown in the scatter plot to determine whether the data should be modeled by a linear function. -

Translate the sentence to an algebraic inequality. -Jon has 791 points in his math class. He must have 72% of the 1200 points possible by the end of the term to receive credit for the class. What is the minimum number of additional points he must earn by the end of the Term to receive credit for the class?

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate. - $\frac { x - 8 } { 4 } + \frac { x + 5 } { 5 } = x + 7$

Does the system have a unique solution, no solution, or many solutions? - $\left\{ \begin{array} { l } 2 x - 4 y = 2 \\y = \frac { 1 } { 2 } x - \frac { 1 } { 2 }\end{array} \right.$

Solve the system of equations by substitution, if a solution exists. - $\left\{ \begin{array} { l } x + 9 y = 49 \\- 6 x + 8 y = 16\end{array} \right.$