Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
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]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
