Question

jacqueline practiced drums four times last week for sessions of 40 minutes, 35 minutes, 45 minutes, and 30 minutes. cassie practiced five times last week for sessions of 15 minutes, 30 minutes, 15 minutes, 15 minutes, and 50 minutes. which statement is true based on the data above? o the two girls practiced for the same total amount of time last week. o the average length of time cassie spent practicing is greater than the average length of time jacqueline spent practicing. o the difference in length between cassies longest and shortest practice sessions was greater than the difference between jacquelines longest and shortest sessions. o the greatest amount of time either girl spent practicing was one of jacquelines practice sessions.

Explanation:

1. First, calculate the total practice - time for each girl.

• For Jacqueline, who practiced 4 times with session - lengths 40, 35, 45, 30 minutes. The total time is \(40 + 35+45 + 30=150\) minutes, and the average time per session is \(\frac{150}{4}=37.5\) minutes. The difference between the longest (45 minutes) and shortest (30 minutes) session is \(45 - 30 = 15\) minutes.
• For Cassie, who practiced 5 times with session - lengths 15, 30, 15, 15, 50 minutes. The total time is \(15+30 + 15+15+50 = 125\) minutes, and the average time per session is \(\frac{125}{5}=25\) minutes. The difference between the longest (50 minutes) and shortest (15 minutes) session is \(50 - 15 = 35\) minutes.

1. Analyze each statement:

• The average length of time Cassie spent practicing (\(25\) minutes) is less than the average length of time Jacqueline spent practicing (\(37.5\) minutes), so the statement "The average length of time Cassie spent practicing is greater than the average length of time Jacqueline spent practicing" is false.
• The difference in length between Cassie's longest (\(50\) minutes) and shortest (\(15\) minutes) practice sessions is \(35\) minutes. The difference between Jacqueline's longest (\(45\) minutes) and shortest (\(30\) minutes) practice sessions is \(15\) minutes. So, the difference in length between Cassie's longest and shortest practice sessions is greater than the difference between Jacqueline's longest and shortest sessions.
• The greatest amount of time either girl spent practicing was 50 minutes (Cassie's longest session), which is Cassie's practice - time, not Jacqueline's.

Answer:

The difference in length between Cassie's longest and shortest practice sessions was greater than the difference between Jacqueline's longest and shortest sessions.