Question

1. a volleyball team played five games. in those games, the team won by 7 points, lost by 3, lost by 2, won by 4, and won by 9. what was the mean difference in scores over the five games?
2. use the expression - 8(-2.5 - 7).

a. simplify the expression by applying the distributive property.
b. evaluate the expression.

1. the water level of a lake fell by 1 1/2 inches during a 1 2/3 - week - long dry spell. find the average rate at which the water level changed every week.
2. simplify the expression 2(2/5)+2(-1/5).
3. the temperature of a pot of water was 180.3°f and cools at a rate of - 2.5°f per minute.

a. what is the temperature after 20 minutes?
b. look for relationships how many minutes will it take to cool from 180.3°f to 100.3°f?

1. look for relationships an elevator descends at a constant speed. what is the change in elevation after 19 seconds?
2. the quiz scores for 6 students who studied together in a math class are in the table.

a. what is the mean quiz score?
b. what is the median quiz score?
elevator descent

time (sec.)	change in elevation (meters)
6	- 13.5
10	- 22.5
12	- 27

quiz scores

score

3

4.5

6.5

8

8.5

10

Explanation:

1.

Step1: Define the data set

The differences in scores are \(7, - 3,-2,4,9\).

Step2: Calculate the sum

Sum \(S=7+( - 3)+(-2)+4 + 9=15\).

Step3: Calculate the mean

The number of data - points \(n = 5\). Mean \(\bar{x}=\frac{S}{n}=\frac{15}{5}=3\).

Step1: Apply the distributive property \(a(b + c)=ab+ac\)

Here \(a=-8\), \(b=-2.5\), \(c = - 7\). So \(-8(-2.5-7)=(-8)\times(-2.5)+(-8)\times(-7)\).

Step2: Simplify each product

\((-8)\times(-2.5)=20\) and \((-8)\times(-7)=56\). Then \((-8)\times(-2.5)+(-8)\times(-7)=20 + 56=76\).

We already simplified the expression in part a to 76.

Answer:

3

2.

a.