Answer:
Accept the null hypothesis if it is two tailed test.
Step-by-step explanation:
The null hypotheses can only be accepted if it is a two tailed test and calculated chi square must be less than the critical value of chi square.
Then the difference between the the observed and expected frequencies will be zero.
where
H0 : σ²-σ²= 0 Ha: σ²-σ²≠0
For this the critical region would be greater than the calculated value of chi square. If so we will accept the null hypothesis and reject the alternative hypothesis.
Answer:
98.7 cm
Step-by-step explanation:
The length in centimeters will always be 1/10 of the length in millimeters.
Answer:
Matrix transformation = ![\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
Vertices of the new image: P'= (5,-2), Q'= (6,-3), R'= (2,-3)
Step-by-step explanation:
Transformation by reflection will produce a new congruent object in different coordinate. Reflection to y-axis made by multiplying the x coordinate with -1 and keep the y coordinate unchanged. The matrix transformation for reflection across y-axis should be: .
To find the coordinate of the vertices after transformation, you have to multiply the vertices with the matrix. The calculation of the each vertice will be:
P'= ![\left[\begin{array}{ccc}-5\\-2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%5C%5C-2%5Cend%7Barray%7D%5Cright%5D)
= (5,-2)
Q'= ![\left[\begin{array}{ccc}-6\\-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-6%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
= (6,-3)
R'= ![\left[\begin{array}{ccc}-2\\-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
= (2,-3)
In order to form a triangle, the third side must be at least greater than the difference of the other two sides
4 - 3 = 1 So the third side must be greater than 1 foot and the third side must be less than the sum of the other two sides
4 + 3 = 7 So, the third side must be less than 7
1 < third side < 7
