Question

depending on the day of the week, a local gas station charges greater than $25 and up to $55 for a full tank of gas. these charges can be represented by the compound inequality 25 < w ≤ 55. which graph represents the charges? four number line graphs are shown, with the first having closed circles at 25 and 55, the second open circles at 25 and 55, the third closed at 25 and open at 55, the fourth open at 25 and closed at 55

Explanation:

Step1: Analyze the inequality symbols

For \(25 < w\), we use an open - circle at \(25\) (because \(25\) is not included). For \(w\leq55\), we use a closed - circle at \(55\) (because \(55\) is included).

Step2: Determine the direction of the line

Since \(w\) is greater than \(25\) and less than or equal to \(55\), the line should be between \(25\) and \(55\) on the number line.

Answer:

The graph with an open - circle at \(25\) and a closed - circle at \(55\) with a line connecting them (the last graph in the sequence of options provided in the problem, assuming the order of graphs is as described in the problem statement where the last one has an open - circle at \(25\) and a closed - circle at \(55\)) represents the charges.