Answer:
The conditions for carrying out a significance test are:
1. It must be a Random sampling
2. It should be a Normal distribution
3. It should be Independent
Step-by-step explanation:
SRS means simple random sample; it is a sampling technique in which individuals can be chosen from the population in such a way that every individual stands an equal chance to be selected as the sample.
The conditions needed or required to carry out a significance test of the teacher's suspicion are:
1. It must be a Random sampling
2. It should be a Normal distribution
3. It should be Independent
All of these conditions are met; the sampling is random as indicated by SRS, it is a normal distribution because one popular rule states that a sample size of at least 30 is enough and here we have a sample size of 45, it is independent because the sample size of 45 is less than 10% of the population
Answer:
![\large\boxed{A^2=\left[\begin{array}{ccc}1&-12\\6&-8\end{array}\right] }](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7BA%5E2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-12%5C%5C6%26-8%5Cend%7Barray%7D%5Cright%5D%20%7D)
Step-by-step explanation:
![A=\left[\begin{array}{ccc}-3&4\\-2&0\end{array}\right]\\\\A^2=\left[\begin{array}{ccc}-3&4\\-2&0\end{array}\right] \cdot\left[\begin{array}{ccc}-3&4\\-2&0\end{array}\right] =\left[\begin{array}{ccc}(-3)(-3)+(4)(-2)&(-3)(4)+(4)(0)\\(-2)(-3)+(0)(-2)&(-2)(4)+(0)(0)\end{array}\right]\\\\A^2=\left[\begin{array}{ccc}1&-12\\6&-8\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3%264%5C%5C-2%260%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5CA%5E2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3%264%5C%5C-2%260%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3%264%5C%5C-2%260%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%28-3%29%28-3%29%2B%284%29%28-2%29%26%28-3%29%284%29%2B%284%29%280%29%5C%5C%28-2%29%28-3%29%2B%280%29%28-2%29%26%28-2%29%284%29%2B%280%29%280%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5CA%5E2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-12%5C%5C6%26-8%5Cend%7Barray%7D%5Cright%5D)
The ratio is 10:14 or 5:7 which is the ratio of boys to girls!
The missing angle is 130 degrees.
The sum of all the angles of a hexagon equal 720 degrees. So, you'd add all the known angles together (this gives you 590), then subtract that from 720. Thus getting 130 degrees as a final answer.
I hope this helps!
