Question

fill in the blank 1 point label the following as true if they show causation or false if they do not show causation. choose your answer... the length of a rectangle affects the width of the rectangle. choose your answer... the amount of time a cell phone is used affects the charge of its battery. choose your answer... the number of ice - cream bars sold affects the number of milkshakes sold. choose your answer... the number of soccer balls a team owns affects the number of games the team wins during the soccer season.

Explanation:

Causation means one variable directly influences another.

• The length of a rectangle and its width are related by the formula for the area of a rectangle \(A = l\times w\). If the area is fixed, changing the length will change the width (inverse - proportion). If the area is not fixed, in a general sense (for a given rectangle), the length and width are two independent variables that together determine the area. But if we consider the relationship in terms of the formula \(w=\frac{A}{l}\) (assuming \(A\) is non - zero), there is a functional relationship which implies causation in a mathematical sense.
• The amount of time a cell phone is used and its battery charge: As the phone is used (time increases), the battery charge (assuming no charging) will decrease. So, the time of use affects (causes a change in) the battery charge.
• The number of ice - cream bars sold and milkshakes sold: There could be an external factor (e.g., temperature) that affects both. But there is no direct causation (one does not directly cause the other).
• The number of soccer balls a team owns and the number of games won: There is no direct causal link. A team could have many balls but still lose games due to other factors like player skill, strategy, etc.

Answer:

1. False (The number of soccer balls a team owns affects the number of games the team wins during the soccer season)
2. False (The number of ice - cream bars sold affects the number of milkshakes sold)
3. True (The amount of time a cell phone is used affects the charge of its battery)
4. True (The length of a rectangle affects the width of the rectangle)