To determine which pairs of variables could use both intercepts to produce viable solutions, we need to consider their nature as they relate to graphical representation and the context of their intercepts.
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(age, weight): This pair is typically continuous data and can both have intercepts (e.g., at age 0 or weight 0), but interpreting these intercepts might not be meaningful, particularly since age 0 is not applicable in human terms.
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(temperature, number of car rentals): Temperature could theoretically be negative (in Fahrenheit, for example), but the number of car rentals can't be negative, making it tricky to interpret intercepts in a meaningful way.
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(years of experience, starting salary): Generally, having 0 years of experience means a starting salary can be defined (which could be 0), giving meaningful intercepts. As experience increases, so does salary. This is a viable set that uses both intercepts effectively.
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(number of nominations, number of awards): Both variables are countable and non-negative. The only meaningful coordinates where intercepts can be used is at (0, 0) which indicates no nominations and no awards.
Based on the analysis, the pair (years of experience, starting salary) would be the most likely to use both intercepts to produce viable solutions as it relates to a direct relationship of a person's salary based on their experience, making its intercepts interpretable and practical.
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