To find the actual distance \( d \) between Samantha's school and the park using the map scale, we can set up a proportion based on the information provided.
The map scale states that 0.5 inches corresponds to 2 miles. Therefore, to relate the distance on the map (2.75 inches) to the actual distance \( d \), we can write the proportion as follows:
\[ \frac{0.5 \text{ in}}{2 \text{ miles}} = \frac{2.75 \text{ in}}{d \text{ miles}} \]
From this proportion, we can use the equivalent fraction representation. This leads us to the following proportion:
\[ 0.5 \cdot d = 2 \cdot 2.75 \]
Simplifying this gives us:
\[ d = \frac{2 \cdot 2.75}{0.5} \]
Thus, the correct proportion that Samantha can use to determine the distance \( d \) is:
\[ 0.5d = 2 \cdot 2.75 \]
So the correct response from the options provided is:
0.5d = 2 * 2.75