The given matrix equation is,
.
Multiplying the matrices with the scalars, the given equation becomes,
![\left[\begin{array}{cc}1.5x&9\\12&6\end{array}\right] +\left[\begin{array}{cc}y&4y\\3y&2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right] \\](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1.5x%269%5C%5C12%266%5Cend%7Barray%7D%5Cright%5D%20%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dy%264y%5C%5C3y%262y%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dz%26z%5C%5C6z%262%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%20%20)
Adding the matrices,
![\left[\begin{array}{cc}1.5x+y&9+4y\\12+3y&6+2y\end{array}\right] =\left[\begin{array}{cc}z&z\\6z&2\end{array}\right] \\](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1.5x%2By%269%2B4y%5C%5C12%2B3y%266%2B2y%5Cend%7Barray%7D%5Cright%5D%20%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dz%26z%5C%5C6z%262%5Cend%7Barray%7D%5Cright%5D%20%20%5C%5C%20)
Matrix equality gives,

Solving the equations together,

We can see that the equations are not consistent.
There is no solution.
209 action figures on his wall
380/100 = 3.8
so there would be 3.8 action figures per 1%
then 3.8*55 =209
The best design for this experiment would be a repeated measures design. This is ideal to determine if eating an apple makes you healthy.
<h3>What is an experimental design?</h3>
An experimental design refers to the general structure of an experiment including how people are distributed into the control and experimental group to test a specific phenomenon.
<h3>What is a repeated measures design?</h3>
In a repeated measures design all participants are both parts of the control group, in this case, people who do not eat apples, and the experimental group, or people who eat apples.
<h3>What does this design imply?</h3>
In the case of determining if eating an apple every day, this design implies:
- All participants will be asked to not eat apples every day for a specific period such as one or two months, and health levels will be measured during this time.
- After the first step, all participants will be asked to eat an apple every day during the period, and their health will be measured.
- The researcher can compare the results of each participant, which is more accurate than comparing one participant to another.
Learn more about experiments in: brainly.com/question/1452319