Question

the average length of a sports car is more than 13 and is less than or equal to 16.5 feet. this average can be represented by the compound inequality 13 < n ≤ 16.5. graph the solution set.

Explanation:

Step1: Analyze the inequality \(13 < n \leq 16.5\)

For the inequality \(13 < n\), the value \(n\) is greater than 13, so we use an open circle at 13 (since 13 is not included in the solution set). For the inequality \(n \leq 16.5\), the value \(n\) is less than or equal to 16.5, so we use a closed circle at 16.5 (since 16.5 is included in the solution set). Then we draw a line segment connecting the open circle at 13 and the closed circle at 16.5 to represent all the values of \(n\) that satisfy the compound inequality.

Looking at the two graphs:

• The first graph has an open circle at 13 and a closed circle at 16.5 (wait, no, the first graph's second circle is at 16.5? Wait, the first graph's second circle is at 16.5? Wait, the first graph's x - axis labels: 12, 12.5, 13, 13.5, 14, 14.5, 15, 15.5, 16, 16.5, 17, 17.5. The first graph has an open circle at 13 and an open circle at 16.5? No, wait, maybe I misread. Wait, the first graph: the first circle is open at 13, the second circle is open at 16.5? No, the second graph has closed circles at 13 and 16.5. But our inequality is \(13 < n \leq 16.5\), so 13 is not included (open circle) and 16.5 is included (closed circle). Wait, maybe the first graph was mis - drawn in my initial thought. Wait, let's re - examine:

Wait, the first graph: the first circle is open at 13, the second circle is open at 16.5? No, the x - axis has 16.5 as a label. Wait, maybe the first graph's second circle is at 16.5, but it's open? No, the correct graph should have an open circle at 13 (because \(n>13\), not \(n\geq13\)) and a closed circle at 16.5 (because \(n\leq16.5\)). So among the two graphs:

The first graph: open circle at 13, closed circle at 16.5? Wait, the user's first graph: the circles are at 13 (open) and 16.5 (open)? No, maybe the user made a typo in the graph labels. Wait, the second graph has closed circles at 13 and 16.5. But our inequality is \(13 < n\), so 13 is not included (open circle), and \(n\leq16.5\), so 16.5 is included (closed circle). So the correct graph should have an open circle at 13 and a closed circle at 16.5, with a line between them. So the first graph (the one with open circle at 13 and closed circle at 16.5? Wait, maybe the first graph's second circle is closed. Wait, the user's first graph: the x - axis is labeled 12, 12.5, 13, 13.5, 14, 14.5, 15, 15.5, 16, 16.5, 17, 17.5. The first graph has an open circle at 13 and a closed circle at 16.5? Or is the second circle open? Wait, the problem is to graph \(13 < n\leq16.5\). So:

• At \(n = 13\): since \(n>13\), we use an open circle (not filled) at 13.
• At \(n=16.5\): since \(n\leq16.5\), we use a closed circle (filled) at 16.5.
• Then we draw a line from the open circle at 13 to the closed circle at 16.5.

So among the two options, the first graph (the one with open circle at 13 and closed circle at 16.5) is correct. Wait, maybe the first graph's second circle is closed. Let's assume that the first graph has an open circle at 13 and a closed circle at 16.5, and the second graph has closed circles at both 13 and 16.5. So the correct graph is the first one (the top - most graph in the user's image) because:

• For \(13 < n\), the point 13 is not included, so open circle.
• For \(n\leq16.5\), the point 16.5 is included, so closed circle.
• The line between them represents all values of \(n\) that are greater than 13 and less than or equal to 16.5.

Answer:

The correct graph is the one with an open circle at 13, a closed circle at 16.5, and a line segment connecting them (the first graph in the given options).