To pass inspection, a new basketball should bounce between 68% and 75% of the starting height. A new ball is dropped from 6 feet and bounces back 4 feet 1 inch. Does the ball pass inspection?

Answer 1

To determine if the basketball passes inspection, we need to calculate the percentage height of the bounce compared to the starting height.

1. Convert the bounce height to feet: The ball bounces back to 4 feet 1 inch. Since there are 12 inches in a foot: \[ 1 \text{ inch} = \frac{1}{12} \text{ feet} \] Therefore, 4 feet 1 inch is: \[ 4 + \frac{1}{12} = \frac{48}{12} + \frac{1}{12} = \frac{49}{12} \text{ feet} \]

2. Calculate the starting height: The starting height is 6 feet.

3. Calculate the bounce percentage: \[ \text{Bounce Percentage} = \left(\frac{\text{Bounce Height}}{\text{Starting Height}}\right) \times 100 \] Plugging in the values: \[ \text{Bounce Percentage} = \left(\frac{\frac{49}{12}}{6}\right) \times 100 \] Simplifying the fraction: \[ = \left(\frac{49}{12} \div 6\right) \times 100 = \left(\frac{49}{12} \times \frac{1}{6}\right) \times 100 = \left(\frac{49}{72}\right) \times 100 \]

   Now, we calculate \( \frac{49}{72} \): \[ \frac{49}{72} \approx 0.6806 \] Multiplying by 100: \[ 0.6806 \times 100 \approx 68.06% \]

4. Check if the percentage is within the acceptable range: The acceptable range is between 68% and 75%.

   Since \( 68.06% \) is slightly above 68% but below 75%, we can conclude:

The ball does pass inspection as its bounce height percentage (68.06%) is within the required range of 68% to 75%.