Question

which situation could be represented by the graph?

students in the children’s 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:

1. Analyze the number line: The closed dot at 8 means \( x \geq 8 \), and the open dot at 11 means \( x < 11 \). So the inequality is \( 8 \leq x < 11 \).
2. Check each option:

• First option: "At least 8, no more than 11" would be \( 8 \leq x \leq 11 \) (closed dot at 11), which doesn't match.
• Second option: "Between $8 and $11" would be \( 8 < x < 11 \) (open dots at both), which doesn't match.
• Third option: "No fewer than 8 ( \( x \geq 8 \)) and less than 11 ( \( x < 11 \))" matches \( 8 \leq x < 11 \).
• Fourth option: Describes two separate intervals (\( x \leq 8 \) or \( x > 11 \)), which doesn't match the number line's single interval.

Answer:

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