To determine which pairs of variables could use both intercepts to produce viable solutions, we need to consider the characteristics of the relationships represented by the points.
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(temperature, number of car rentals): This could indicate a relationship where temperature influences car rentals. The intercepts here could correspond to scenarios of zero temperature or zero rentals.
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(years of experience, starting salary): Generally, this shows a relationship where more experience leads to higher starting salaries. Possible intercepts might not be as meaningful since a starting salary of $0 with several years of experience is less practical.
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(age, weight): This can involve a direct relationship; however, the intercept may not produce meaningful biological insights (like a weight of 0 for age).
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(number of nominations, number of awards): Here, we might interpret this as a relationship that could make sense, as it could represent an increasing trend with appropriate intercepts.
Given this analysis, the best candidates for producing viable interpretations from both intercepts are (temperature, number of car rentals) and (number of nominations, number of awards).
However, if the question asks for only one answer based on viable solutions in terms of common practical interpretations, the best option would be:
(number of nominations, number of awards).
This is because both intercepts (zero nominations leading to zero awards) represent a direct correlation in a more practical context.