To determine which options could use both intercepts to produce viable solutions, we need to consider the nature of the variables involved in each pair. The goal is to see if both variables can logically intercept and produce meaningful results.
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(number of nominations, number of awards): This pair logically makes sense. The number of nominations (independent variable) could impact the number of awards (dependent variable). If we consider a linear relationship, both intercepts can be significant: if there are zero nominations, typically, there would be zero awards (the intercept with the awards axis).
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(years of experience, starting salary): This pair also logically makes sense. Generally, as years of experience increase (independent variable), starting salary (dependent variable) may also increase. Again, depending on the context, both intercepts could yield meaningful insights.
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(age, weight): The relationship here could be more variable and context-dependent. While age and weight can be related in certain populations, it might not yield meaningful intercepts in a general sense—particularly because weight does not necessarily start from zero consistently as age starts from zero.
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(temperature, number of car rentals): This situation could produce relevant data, as temperature might affect the number of car rentals seasonally. However, both intercepts might not yield meaningful insights, since a negative temperature might not realistically correlate to car rentals in certain contexts.
Based on this analysis, the options that could likely use both intercepts to produce viable solutions are:
- (number of nominations, number of awards)
- (years of experience, starting salary)
These two pairs provide a clearer context for deriving meaningful data from both intercepts.