9. Write your own situation in which speed, 5 , is an independent variable. 11. Critique Reasoning you spend \( d \) dollars for \( g \) identical pairs of glasses. A friend claims that because \( d \) increases if you increase \( g \). and \( g \) increases if you increase \( d \), either \( d \) or \( g \) could be the independent variable. is your friend correct? Explain. 10. Name at least two independent variables that could result in a change in a monthly cell phone bill. 12. The cost, \( c \), of supplies for school depends on other factors. List at ieast two independent variables that could affect the cost of school supplies.

Below are responses to each item: 9. Situation with Speed as an Independent Variable:  Imagine you’re testing a remote‐controlled car on a track. You decide to vary the car’s speed (your independent variable) by setting different speed levels, and then measure how long it takes (the time, which is the dependent variable) to complete a fixed distance. In this scenario, you control the speed and observe its effect on the finish time. 11. Critique of the Friend’s Reasoning:  Your friend’s claim is flawed. Although the total dollars spent, d, increases as the number of pairs of glasses, g, increases (if each pair costs the same), the relationship between them is a dependent one (typically d = (price per pair) × g). That is, you usually decide how many pairs (g) you want, and then the total cost (d) is determined by that choice. The fact that increasing one causes an increase in the other does not make both independent; it only shows correlation. In a mathematical model like this, one of the variables must be chosen as the independent variable (for example, g as the number bought), and the other (d) is computed from it. 10. Independent Variables Affecting a Monthly Cell Phone Bill:  Two examples of independent variables include:  • The number of minutes used (talk time)  • The amount of data consumed (in gigabytes)  Other independent factors might include the number of texts sent or any extra charges (like international calls) that you decide to incur. 12. Independent Variables Affecting the Cost of School Supplies:  Two independent variables that could affect the cost, c, of school supplies might be:  • The number of students (more students generally mean more supplies are needed)  • The quality or type of supplies required (for instance, premium supplies cost more than standard ones)  Other factors could include the prices of individual items and regional price variations, but the above are two clear examples. These answers clarify the roles of independent variables in each scenario, showing how they are chosen or varied to see the effect on the dependent outcomes.