Vehicles passing over a bridge have two options for paying their bridge toll: paying with a live cashier or using a Speed Pass device affixed to the dashboard. Data on a busy day for cars and trucks passing over the bridge are shown here.
To find the percentage of vehicles that are trucks, given that they use Speed Pass, follow these steps:
1. Identify the number of trucks using Speed Pass: Based on the provided data, 47 trucks use Speed Pass.
2. Identify the total number of vehicles using Speed Pass: From the data, a total of 114 vehicles use Speed Pass.
3. Calculate the percentage: The percentage of vehicles that are trucks, given that they use Speed Pass, is calculated by dividing the number of trucks using Speed Pass by the total number of vehicles using Speed Pass and then multiplying by 100 to convert the fraction to a percentage.
[tex]\[
\text{Percentage of trucks using Speed Pass} = \left( \frac{\text{Number of trucks using Speed Pass}}{\text{Total number of vehicles using Speed Pass}} \right) \times 100
\][/tex]
Plugging in the values:
[tex]\[
\text{Percentage of trucks using Speed Pass} = \left( \frac{47}{114} \right) \times 100 \approx 41.2 \%
\][/tex]
Therefore, the percentage of vehicles that are trucks, given that they use Speed Pass, is [tex]\(41.2\%\)[/tex].
