Answer: [tex]\ell \le 46.75[/tex] (fourth choice)
Graph has a closed endpoint at 46.75 and the ray pointing to the left (i.e. shading is to the left).
Check out the diagram below.
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Explanation:
The phrasing "at most" means that's the highest ceiling possible. The longest the cape can be is 46.75 inches. So it could be this length or shorter.
If [tex]\ell[/tex] is this length, then either [tex]\ell = 46.75[/tex] or [tex]\ell < 46.75[/tex]
We can combine those two statements into the final answer of [tex]\ell \le 46.75[/tex]
The graph involves a closed point at this marker to include the endpoint (in contrast an open hole would leave the endpoint out). The shading is to the left to include every value smaller than 46.75
Realistically the smallest [tex]\ell[/tex] can get is [tex]\ell = 0[/tex], but we don't have to worry too much about this. This is because zero isn't anywhere near these shown values on the number line.
