Question

which situation could be represented by the graph?
5 6 7 8 10 11 12 13 14 15
students in the childrens choir are at least 8 years old but no more than 11 years old.
babysitters earn between $8 and $11 per hour.
a program at a community college can be completed in no fewer than 8 months, but must be completed in less than 11 months.
the dogs at a veterinary clinic are all 8 years old or under or are older than 11 years.

Explanation:

First, analyze the number line: it has a closed dot at 8 (meaning 8 is included) and an open dot at 11 (meaning 11 is not included), with the segment between them shaded. This represents the inequality $8 \leq x < 11$. Now match this to each option:

1. First option: "at least 8, no more than 11" is $8 \leq x \leq 11$ (includes 11, does not match).
2. Second option: "between $8 and $11" typically means $8 < x < 11$ (excludes 8, does not match).
3. Third option: "no fewer than 8, less than 11" is $8 \leq x < 11$, which matches the number line exactly.
4. Fourth option: represents $x \leq 8$ or $x > 11$, which is the opposite of the shaded segment, so it does not match.

Answer:

A program at a community college can be completed in no fewer than 8 months, but must be completed in less than 11 months.