Question

assessment practice
use the scatter plot to answer 10 and 11.

1. ten athletes ran two races of the same length. the scatter plot shows their times. select all statements that are true.

• nine of the times for the first race were at least 16 seconds.
• eight of the times for the second race were less than 17 seconds.
• there were seven athletes who were faster in the second race than in the first.
• there were three athletes who had the same time in both races.
• there were three athletes whose times in the two races differed by exactly 1 second.

1. what was the greatest difference for a single runner in finishing times in the races?

(scatter plot titled race times with x-axis time for first race (seconds) from 0 to 16, y-axis time for second race (seconds) from 0 to 16+; points plotted.)

Explanation:

Step1: Analyze the first statement

For the first - race times (x - axis), count the number of points with \(x\geq16\). There are 9 points with \(x\geq16\). So, the statement "Nine of the times for the first race were at least 16 seconds" is true.

Step2: Analyze the second statement

For the second - race times (y - axis), count the number of points with \(y < 17\). There are 8 points with \(y<17\). So, the statement "Eight of the times for the second race were less than 17 seconds" is true.

Step3: Analyze the third statement

An athlete is faster in the second race than in the first if \(y

Step4: Analyze the fourth statement

An athlete has the same time in both races if \(x = y\). Count the number of points where \(x = y\). There are 0 points where \(x = y\). So, the statement "There were three athletes who had the same time in both races" is false.

Step5: Analyze the fifth statement

Calculate \(|x - y|\) for each point. Count the number of points where \(|x - y|=1\). There are 3 points where \(|x - y| = 1\). So, the statement "There were three athletes whose times in the two races differed by exactly 1 second" is true.

For question 11:

Step1: Calculate the time difference for each point

For each point \((x,y)\), calculate \(|x - y|\).
For the point \((13,20)\), \(|x - y|=|13 - 20| = 7\).
For other points, calculate \(|x - y|\) values:
If \((x = 14,y = 16)\), \(|x - y|=|14 - 16|=2\); if \((x = 15,y = 16)\), \(|x - y|=|15 - 16| = 1\); if \((x=16,y = 16)\), \(|x - y|=0\) etc.

Answer:

For question 10:

• The first statement: True
• The second statement: True
• The third statement: True
• The fourth statement: False
• The fifth statement: True

For question 11:
7