Final answer:
The paired data likely to show a nonlinear association are B (Age and weight of puppies) and E (Height of a bouncing ball and time). The other options are linear, show no correlation, or the relationship isn't typically measured to assess correlation.
Step-by-step explanation:
The question asks which paired data will show a nonlinear association. Nonlinear associations occur when the relationship between two variables cannot be described using a straight line. Here are the paired data from the options provided, along with an explanation for which ones could show a nonlinear association:
- Area and side length of a square (A): This is a linear relationship because the area (A) is equal to the side length (s) squared (A = s^2). As the side length increases, the area increases proportionally to the square of the side length.
- Age and weight of puppies (B): This could show a nonlinear relationship because as puppies grow (increase in age), their weight doesn't increase at a constant rate but accelerates and then levels off as they reach adulthood.
- Amount of money earned and length of hair (C): This is likely to show no correlation as there's no logical or biological reason to expect that the length of one's hair would affect their earnings, thus the relationship, if any, would likely be nonlinear or non-existent.
- Age and number of siblings (D): This would also likely have no correlation since the number of siblings a person has is not affected by their age.
- Height of a bouncing ball and time (E): This is an example of a nonlinear relationship because the height of a bouncing ball changes in cycles due to gravity and loss of energy through bounciness, not in a constant, linear fashion with respect to time.
In summary, the paired data that are more likely to show a nonlinear association are options B (Age and weight of puppies) and E (Height of a bouncing ball and time).