\begin{tabular}{|l|l|}
\hline
Hours (h) & Miles (m) \\
\hline
3 & 45 \\
\hline
3 & 60 \\
\hline
5 & 75 \\
\hline
\end{tabular}

Which statements are correct? Check all that apply.

A. The variable [tex]$m$[/tex] is the independent variable.
B. The number of miles increases as time increases.
C. The number of hours causes a change in the number of miles ridden.
D. The variable [tex]$h$[/tex] is the independent variable.
E. The variable [tex]$h$[/tex] is the dependent variable.
F. The farther Mason rides, the less time it takes.
G. The variable [tex]$m$[/tex] is the dependent variable.



Answer :

To solve this problem, we need to carefully analyze the relationship between the given variables, time (hours, [tex]\( h \)[/tex]) and distance (miles, [tex]\( m \)[/tex]), to determine which statements are correct.

Based on the solution provided for a similar problem, we can verify the following points step-by-step:

1. The variable [tex]\( m \)[/tex] is the independent variable.
- An independent variable is one that is manipulated or controlled in an experiment or scenario. Here, [tex]\( m \)[/tex] (miles) depends on [tex]\( h \)[/tex] (hours), not the other way around. Therefore, this statement is incorrect.

2. The number of miles increases as time increases.
- Given the table:

[tex]\[ \begin{tabular}{|l|l|} \hline h (hours) & m (miles) \\ \hline 3 & 45 \\ \hline 3 & 60 \\ \hline 5 & 75 \\ \hline \end{tabular} \][/tex]

- By observing the table, as the hours increase from 3 to 5, miles ridden also increase (from 45, 60 to 75). Thus, this statement is correct.

3. The number of hours causes a change in the number of miles ridden.
- When analyzing the impact of hours on miles, it shows that the longer Mason rides (more hours), the more miles he covers. So, hours indeed cause a change in miles ridden. This statement is correct.

4. The variable [tex]\( h \)[/tex] is the independent variable.
- Hours ([tex]\( h \)[/tex]) are the independent variable because they influence the number of miles ridden ([tex]\( m \)[/tex]). This statement is correct.

5. The variable [tex]\( h \)[/tex] is the dependent variable.
- The dependent variable is typically the one that changes in response to the independent variable. Here, [tex]\( m \)[/tex] (miles) depends on [tex]\( h \)[/tex] (hours). Hence, this statement is incorrect.

6. The farther Mason rides, the less time it takes.
- This statement does not follow logically from the table. Typically, the farther you ride, the more time it takes. This statement is incorrect.

7. The variable [tex]\( m \)[/tex] is the dependent variable.
- The dependent variable is the one affected by the independent variable. Here, [tex]\( m \)[/tex] (miles) is affected by [tex]\( h \)[/tex] (hours), making miles the dependent variable. This statement is correct.

Based on the step-by-step analysis, the correct statements are:

- The number of miles increases as time increases.
- The number of hours causes a change in the number of miles ridden.
- The variable [tex]\( h \)[/tex] is the independent variable.
- The variable [tex]\( m \)[/tex] is the dependent variable.

Thus, the correct statements are:

[tex]\[ \text{[4, 7, 2, 3]} \][/tex]