To determine which option uses intercepts that have viable solutions, we need to evaluate each pair:
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Option #1: (number of quarters, number of dimes)
Both quarters and dimes are quantifiable in whole numbers (non-negative integers). The intercepts could represent situations where one of the variables is zero (e.g., all quarters and no dimes, or all dimes and no quarters), leading to viable solutions. -
Option #2: (human age, human weight)
While age and weight are also quantifiable, the relationship between them is not linear or directly dependent in a way that creates consistent intercepts. Age can be zero or a positive integer, but weight can vary widely and does not have a straightforward zero intercepts relationship with age. -
Option #3: (height, shoe size)
Height and shoe size can also be related, but again, they do not have a linear relationship with clear intercepts. For example, it's possible to have certain ranges of shoe sizes that don't correlate neatly with specific heights.
Based on this analysis, Option #1: (number of quarters, number of dimes) is the only one that uses intercepts with viable solutions.
Thus, the answer is:
Option #1 uses intercepts that have viable solutions.