To determine which options could use both intercepts to produce viable solutions, we need to consider whether the pairs of variables can both logically intersect at meaningful points.
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(number of nominations, number of awards): This pair is potentially viable. Both variables can realistically intersect at (0,0). The more nominations you have, the more awards you could expect, but it's not a 1:1 relationship.
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(years of experience, starting salary): This pair is also viable. You can have a starting salary of 0 when years of experience is 0, and the relationship often tends to increase with more years of experience.
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(age, weight): This might not yield a meaningful solution using intercepts. While there is a relationship, the specific intersection points might not provide valuable insights.
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(temperature, number of car rentals): This pair can also yield viable solutions. Depending on the temperature, there can be a logical point where car rentals could be 0, and you can analyze the relationship based on that.
Based on the analysis, the viable pairs using both intercepts would be:
- (number of nominations, number of awards)
- (years of experience, starting salary)
- (temperature, number of car rentals)
The simplest way to answer your question in a multiple-choice scenario is that both (number of nominations, number of awards) and (years of experience, starting salary) are the best options for using both intercepts to produce viable solutions.