Final answer:
In order to determine if the data sets show a direct variation, we need to analyze if they have a constant ratio. If the data points form a straight line when plotted on a graph, then they show a direct variation. If the data points do not form a straight line, then they do not show a direct variation.
This correct answer is none of the above.
Step-by-step explanation:
In order to determine if the data sets show a direct variation, we need to analyze if they have a constant ratio. If the data points form a straight line when plotted on a graph, then they show a direct variation. If the data points do not form a straight line, then they do not show a direct variation.
For example, if we have two sets of data where as one variable increases, the other variable also increases at a constant rate, then it would represent a direct variation. However, if the increase or decrease in one variable does not have a constant rate of change, then it would not represent a direct variation.
Using this information, we can now determine if the given data sets show a direct variation.
A. Yes - The data points form a straight line when plotted on a graph, indicating a direct variation.
B. No, and they are not mutually exclusive either - The data points do not form a straight line and do not show a direct variation. Additionally, they are not mutually exclusive, meaning that an increase in one variable does not necessarily result in an increase or decrease in the other variable.
C. No, but they are mutually exclusive - The data points do not form a straight line and do not show a direct variation. However, they are mutually exclusive, meaning that an increase in one variable results in a corresponding increase or decrease in the other variable.
D. Not enough information given to determine the answer - Without the data sets or any further information, we cannot determine if the data shows a direct variation or not.
This correct answer is none of the above.