Elena would like to know the average height of seventh graders in her school district. She measures the heights of everyone in a random sample of 20 students. The mean height of Elena's sample is 61 inches, and the MAD (mean absolute deviation) is 2 inches.

Complete question is;

Elena would like to know the average height of seventh graders in her school district. She measures the heights of everyone in a random sample of 20 students. The mean height of Elena's sample is 61 inches, and the MAD (mean absolute deviation) is 2 inches.

Select all the true statements. Make your selections bold.

A. The median height of the sample must be between 59 and 63 inches.

B. Another random sample of 20 students is likely to have a mean between 57 and 65 inches.

C. The mean height of these 20 students is likely to be the same as the mean height of all students in the district.

D. The mean height of these 20 students is likely to be the same as the mean height of a second random sample of 20 students.

E. Elena would be more likely to get an accurate estimate of the mean height of the population by sampling 40 people instead of sampling 20 people.

Options A, B & E are true.

Step-by-step explanation:

We are told that Elena's mean absolute deviation is 2 inches.

This means that the distance between each data point and the mean is equal to 2. This value gives us a good idea about the variability present in the dataset.

This is calculated from the difference between the mean of the absolute value of the initial mean and each data set.

Now, looking at the options. In option A, since mean height of the 20 students is given as 61, it means the median will be close to that figure too. Thus, between 59 and 63 inches given is appropriate.

In option B, if another random sample is taken, the mean would likely be close to 61 too since the MAD is 2.

Thus range given is okay.

In options C & D, there is no evidence to prove that the new mean would be the same as the district or the second random sample. This, both options are not appropriate.

In option E, if she uses a Sample of 40, she will obviously get a more accurate figure because the more the sample the more accurate the average result that represents the population.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.