Point D is on line segment \overline{CE}

Mathematics

1 answer:

ANTONII [103]3 years ago

5 0

Answer:

DE = 18

Step-by-step explanation:

Given that,

Point D is on line segment CE.

DE = x+10, CD=6 and CE=3x

We need to find the length of DE.

ATQ,

CE = CD + DE

Putting all the values,

3x = 6 + x+10

Taking like terms together

3x-x = 16

2x = 16

x = 8

DE = x+10

= 8+10

= 18

Hence, the length of DE is 18.

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The hourly wages earned by 20 employees are shown in the first box and whisker plot below. The person earning $15 per hour quits

serg [7]

I added the plots in the attachments.

Answer:

The mean will decrease

The median will remain the same

Explanation:

1- checking the mean:

Mean of the salaries is calculated as follows:

$Mean = \frac{sum-of-salaries}{number-of-employees}$

Now, we can note that two parameters affect the mean, let's consider each:

a. Number of employees:

We are given that one employee is replaced with another. This means that the number of employees did not change

b. Sum of salaries:

We are given that a person earning $15 left and the new person earns $7. This means that:

New sum of salaries = old sum of salaries - 15 + 7 = old sum of salaries - 8

This means that the sum of salaries decreased by 8

Now, for the mean:

We can conclude that since the numerator decreased while the denominator stayed the same, the mean will decrease

2- checking the median:

In the whisker plots, the median is represented by the vertical line inside the plot.

In the first plot, we can note that the vertical line is nearly half the distance between 9 and 10. This means that, for the first plot, the median is approximately 9.5

In the second plot, the place of the median is unchanged. It is still approximately midway between 9 and 10 which means that the median in the second plot is approximately 9.5

Therefore, the median of the data remains unchanged.

Hope this helps :)