An apartment building has a total of 120 apartments. The equation $$ m(p)=5 p $$ gives the amount of money made, in hundreds of dollars, when $$ p $$ apartments are rented. What is the domain for this situation? $$ \{m(p) \mid m(p) \leq 600\} $$ $$ \left\{\begin{array}{|l|}\hline \square\{0,1,2,3, \ldots 120\}\end{array}\right. $$ $$ \{0,5,10,15,20, \ldots, 600\} $$

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To determine the **domain** for the function $$ m(p) = 5p $$, where $$ p $$ represents the number of apartments rented in a building with a total of 120 apartments, consider the following:

1. **Possible Values of $$ p $$:**
   - $$ p $$ must be an integer because you can't rent a fraction of an apartment.
   - $$ p $$ can range from 0 (no apartments rented) to 120 (all apartments rented).

2. **Interpreting the Options:**
   - **Option 1:** $$ \{m(p) \mid m(p) \leq 600\} $$  
     This describes the **range** of the function (possible values of $$ m(p) $$), not the domain.
     
   - **Option 2:** $$ \{0, 1, 2, 3, \ldots, 120\} $$  
     This correctly represents the **domain** of $$ p $$, specifying all possible integer values from 0 to 120.
     
   - **Option 3:** $$ \{0, 5, 10, 15, 20, \ldots, 600\} $$  
     This also describes the **range** of the function $$ m(p) $$, as it lists the possible outputs based on the domain.

**Conclusion:**
The correct domain is the set of integers from 0 to 120, which is represented by the second option.

**Answer:**  
$$ \{0,1,2,3, \ldots, 120\} $$
The domain is all integers from 0 to 120. **Answer:** $$ \{0,1,2,3, \ldots, 120\} $$

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