Question

which situation could be represented by the graph?
5 6 7 8 9 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:

1. Analyze the number line: The closed circle at 8 means \( x \geq 8 \), and the open circle at 11 means \( x < 11 \).
2. Evaluate each option:

• First option: "At least 8, no more than 11" would be \( 8 \leq x \leq 11 \) (closed at 11), which doesn't match.
• Second option: "Between $8 and $11" would be \( 8 < x < 11 \) (open at 8), which doesn't match.
• Third option: "No fewer than 8 months, less than 11 months" is \( 8 \leq x < 11 \), which matches the number line.
• Fourth option: "8 or under or older than 11" is \( x \leq 8 \) or \( x > 11 \), which doesn't match.

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.