Answer:
n = 30....................
90^2-54^2=5184
root 5184=72
pr=72
P(x) to P(x+2), you need to graph the same but shift 2 units to the left.
New function :
Max = 4 ,coordinate points (-5, 0) and (5,0)
The adjoint of the matrix
is ![\left[\begin{array}{cc}-1&0\\-2&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%260%5C%5C-2%261%5Cend%7Barray%7D%5Cright%5D)
<h3>How to determine the adjoint?</h3>
The matrix is given as:
![\left[\begin{array}{cc}1&0\\2&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C2%26-1%5Cend%7Barray%7D%5Cright%5D)
For a matrix A be represented as:
![A = \left[\begin{array}{cc}a&b\\c&d\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D)
The adjoint is:
![Adj = \left[\begin{array}{cc}d&-b\\-c&a\end{array}\right]](https://tex.z-dn.net/?f=Adj%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dd%26-b%5C%5C-c%26a%5Cend%7Barray%7D%5Cright%5D)
Using the above format, we have:
![Adj = \left[\begin{array}{cc}-1&0\\-2&1\end{array}\right]](https://tex.z-dn.net/?f=Adj%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%260%5C%5C-2%261%5Cend%7Barray%7D%5Cright%5D)
Hence, the adjoint of the matrix
is ![\left[\begin{array}{cc}-1&0\\-2&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%260%5C%5C-2%261%5Cend%7Barray%7D%5Cright%5D)
Read more about matrix at:
brainly.com/question/11989522
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Answer:
The null and alternative hypotheses are:


Under the null hypothesis, the test statistic is:




Therefore, the test-statistic is 
Now the F critical value at 0.02 significance level for df1 = 10- 1 =9 and df2 = 16 - 1 =15 is:

Since F statistic is greater than the F critical value, we therefore, reject the null hypothesis and conclude that there is sufficient evidence to support the claim that there is a difference in the variation in the listening times for men and women.