To determine the number of hours \( h \) that Maria still needs to spend to complete her community service program, you want to consider the total hours required and the hours she has already completed.
Maria needs to complete a total of \( 5 \frac{1}{2} \) hours (which is \( 5.5 \) hours), and she has already completed \( 3 \frac{3}{4} \) hours (which is \( 3.75 \) hours).
To find the remaining hours, you would set up the equation:
\[ 5 \frac{1}{2} - 3 \frac{3}{4} = h \]
Alternatively, to express it in terms of the hours she still needs to spend, an equation can be written as:
\[ h = 5 \frac{1}{2} - 3 \frac{3}{4} \]
However, if we manipulate this to solve for \( h \) directly, we would rearrange it like this:
\[ h + 3 \frac{3}{4} = 5 \frac{1}{2} \]
This means:
\[ h = 5 \frac{1}{2} - 3 \frac{3}{4} \]
So the corresponding equation that can be used to determine the number of hours \( h \) that Maria still needs to spend is:
\[ h + 3 \frac{3}{4} = 5 \frac{1}{2} \]
From the options given in your question, it appears there is a slightly incorrect representation. None directly match the correct setup above. If we had to select from what was given, the correct interpretation closest to the scenario is:
\[ h - 3 \frac{3}{4} = 5 \frac{1}{2} \]
But it should be noted that this option has been duplicated and isn't a direct reflection of the right logical setup based on the context. The accurate relationship is:
\[ h = 5 \frac{1}{2} - 3 \frac{3}{4} \]
Hence, none of the options appear fully correct, but you'd want to represent it in the form where you add or subtract correctly based on the need for the remaining hours.