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]
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]
