The expression provided is:

$p(x) = \left\lfloor \frac{60}{x} \right\rfloor$

where $\left\lfloor \cdot \right\rfloor$ denotes the floor function, which rounds down to the nearest integer. We are asked to evaluate $p(7)$.

Substituting $x = 7$ into the function:

$p(7) = \left\lfloor \frac{60}{7} \right\rfloor$

First, calculate $\frac{60}{7}$:

$\frac{60}{7} \approx 8.5714$

Now, applying the floor function to 8.5714, we round down to the nearest integer:

$p(7) = \left\lfloor 8.5714 \right\rfloor = 8$

Thus, $p(7) = 8$.

Would you like more details on this, or do you have any questions?

Here are 5 related questions to expand on this topic:

1. How does the floor function differ from the ceiling function?
2. Can you evaluate $p(5)$ for the same function?
3. What is the difference between the floor and the round function?
4. How does the function behave as $x$ approaches infinity?
5. What happens to $p(x)$ when $x = 1$?

Tip: The floor function always rounds down, so even if the result is very close to the next integer, it will still go to the lower one.