To determine the best estimate for the wind speed during a strong gale near Beth's house in miles per hour, we can follow these steps:
1. Identify the Wind Speed Range for Strong Gale in Knots:
According to the given table, the wind speed range for a strong gale (category 9) is 41-47 knots.
2. Convert the Wind Speeds from Knots to Miles per Hour:
One knot is approximately equal to 1.15 miles per hour. Thus, to convert the wind speed range from knots to miles per hour, we multiply each bound by 1.15.
- For the lower bound:
[tex]\( 41 \, \text{knots} \times 1.15 \, \left( \frac{\text{miles}}{\text{hour \cdot knot}} \right) = 47.15 \, \text{miles/hour} \)[/tex]
- For the upper bound:
[tex]\( 47 \, \text{knots} \times 1.15 \, \left( \frac{\text{miles}}{\text{hour \cdot knot}} \right) = 54.05 \, \text{miles/hour} \)[/tex]
3. Calculate the Best Estimate for the Wind Speed:
The best estimate for the wind speed in miles per hour will be the average of the lower and upper bounds.
[tex]\[
\text{Best Estimate} = \frac{47.15 \, \text{miles/hour} + 54.05 \, \text{miles/hour}}{2}
\][/tex]
[tex]\[
\text{Best Estimate} = \frac{101.2 \, \text{miles/hour}}{2} = 50.6 \, \text{miles/hour}
\][/tex]
Therefore, the best estimate for the wind speed during the strong gale near Beth's house is [tex]\( 50.6 \)[/tex] miles per hour.
