To determine which options could use both intercepts to produce viable solutions, we need to understand the context of "intercepts" in relation to the variables given in each pair. The two intercepts usually refer to the x-intercept and y-intercept in a coordinate graph, typically when analyzing relationships between two quantitative variables.
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(age, weight): While age and weight are both quantitative, the relationship between them can be complex, making it difficult to use intercepts effectively in a straightforward linear equation. The intercepts may not provide viable solutions for understanding their relationship.
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(years of experience, starting salary): This pair typically has a linear relationship where more years of experience can correlate to a higher starting salary. You could use intercepts here effectively, especially in a regression analysis where you might find a starting salary (y-intercept) when years of experience is zero.
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(temperature, number of car rentals): There's likely a relationship where temperature affects the number of car rentals (e.g., more rentals in warmer weather). This relationship might be modeled with intercepts, as they can provide insights into baseline rentals (at a theoretical temperature) and temperature effects.
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(number of nominations, number of awards): This relationship can also be said to have linear characteristics, where more nominations could translate into more awards. This could allow for viable interpretation using intercepts.
Considering these analyses, the options where both intercepts can be used to create viable solutions are:
- (years of experience, starting salary)
- (temperature, number of car rentals)
- (number of nominations, number of awards)
Of these, the most straightforwardly interpretable for its linearity and clear causation would be (years of experience, starting salary). However, all three of these pairs can yield viable solutions when analyzed accordingly, depending on the exact context and data at hand.