For which pair of related quantities would time be the independent variable?
Question 2 options:
a)
length of race, finish time
b)
distance to work, commute time
c)
flight time, rainfall
d)
grade, time spent on project
d) grade, time spent on project
Time spent on a project can vary depending on the grade you want to achieve. So, in this case, time would be the independent variable. It's like trying to cook the perfect meal - you adjust the time you spend in the kitchen depending on how tasty you want it to be!
The pair of related quantities for which time is the independent variable is option d) grade and time spent on the project. In this scenario, the grade that a student receives on a project depends on the amount of time that they spend working on it. The time spent on the project is considered the independent variable, as it is the factor that the grade depends on. The grade, on the other hand, is considered the dependent variable, as it is the result or outcome of the time spent on the project.
To determine which pair of related quantities has time as the independent variable, we need to understand the concept of independent and dependent variables.
In any scientific experiment or observation, variables are used to represent quantities that can change. The independent variable is the one that the researcher or observer deliberately manipulates or controls. It is typically represented on the x-axis of a graph. The dependent variable, on the other hand, is the variable that is being measured or observed and changes in response to the independent variable. It is represented on the y-axis of a graph.
Let's examine each option:
a) Length of race, finish time: In a race, the length of the race is typically predetermined, and the finish time depends on the length of the race. Therefore, the length of the race is the independent variable, and finish time is the dependent variable.
b) Distance to work, commute time: The distance to work is something that the individual chooses or has control over, and the commute time depends on the distance. Hence, distance to work is the independent variable, and commute time is the dependent variable.
c) Flight time, rainfall: In this pair, flight time and rainfall do not have a clear cause-and-effect relationship. Flight time does not directly influence rainfall, nor does rainfall impact the duration of a flight. Therefore, neither can be considered the independent or dependent variable.
d) Grade, time spent on project: The grade received on a project is typically determined by the quality and effort put into it. The time spent on the project is controlled by the individual, and the grade depends on the quality of the project. Hence, the time spent on the project is the independent variable, and the grade received is the dependent variable.
Based on this analysis, the pair with time as the independent variable is option d) grade, time spent on the project.