Question

which relationships could have a negative correlation? select three options.
□ number of hours worked and free time
□ speed of a car and minimum stopping distance
□ the speed of a train and the length of time to reach the destination
□ adult’s head circumference and age
□ a tadpole’s age and the length of it’s tail

Explanation:

1. Number of hours worked and free time: As hours worked increase, free time (total time - work hours) decreases, so negative correlation.
2. Speed of a train and time to destination: Using \( \text{time}=\frac{\text{distance}}{\text{speed}} \), if speed increases, time (for fixed distance) decreases, negative correlation.
3. Tadpole’s age and tail length: As tadpoles mature (age increases), their tails shorten (metamorphosis), so tail length decreases with age, negative correlation.

• "Speed of car and stopping distance" has positive correlation (higher speed → longer stopping distance).
• "Adult’s head circumference and age" has no correlation (adult head size is stable with age).

Answer:

• number of hours worked and free time
• the speed of a train and the length of time to reach the destination
• a tadpole’s age and the length of it’s tail