Question

a) 0 1 2 3 4 5 6 7 8 9 10 b) 0 1 2 3 4 5 6 7 8 9 10 c) 0 1 2 3 4 5 6 7 8 9 10 d) 0 1 2 3 4 5 6 7 8 9 10

Explanation:

To determine the correct number line, we analyze the endpoints: a closed dot (filled circle) represents inclusion (≤ or ≥), and an open dot (hollow circle) represents exclusion (< or >). In option B, the left endpoint (at 4) is open (excluding 4) and the right endpoint (at 5) is closed (including 5), which matches the typical representation for an interval like \(4 < x \leq 5\). Other options have inconsistent or incorrect endpoint types (e.g., A has closed at 4 and open at 5, C has both closed, D has both open).

Answer:

B) The number line with an open dot at 4 and a closed dot at 5, with a blue segment connecting them.