The transformation of this shape was rotation, it was rotated 180 degrees clockwise around the axis.
Answer:
Decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence that indicate that there is a significant difference between the two treatments
Step-by-step explanation:
From the question we are told that
The sample size is n = 12
The first mean is ![M_1 = 55](https://tex.z-dn.net/?f=M_1%20%20%3D%20%2055)
The variance is ![s^2_1 = 8](https://tex.z-dn.net/?f=s%5E2_1%20%3D%20%208)
The second mean is
The second variance is ![s^2_2 = 4](https://tex.z-dn.net/?f=s%5E2_2%20%3D%20%204)
Let the level of significance be ![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%200.05)
The null hypothesis is ![H_o : M_1 = M_2](https://tex.z-dn.net/?f=H_o%20%20%3A%20%20M_1%20%3D%20M_2)
The alternative hypothesis is ![H_a : M_1 \ne M_2](https://tex.z-dn.net/?f=H_a%20%20%3A%20%20M_1%20%5Cne%20M_2)
Generally the test statistics is mathematically
![t = \frac{M_1 - M_2 }{ \sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2}} }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7BM_1%20-%20M_2%20%7D%7B%20%5Csqrt%7B%5Cfrac%7Bs_1%5E2%7D%7Bn_1%7D%20%2B%5Cfrac%7Bs_2%5E2%7D%7Bn_2%7D%7D%20%7D)
=> ![t = \frac{55 - 52 }{ \sqrt{\frac{8}{12} +\frac{4}{12 }} }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B55%20-%2052%20%7D%7B%20%5Csqrt%7B%5Cfrac%7B8%7D%7B12%7D%20%2B%5Cfrac%7B4%7D%7B12%20%7D%7D%20%7D)
=>
Generally the degree of freedom is mathematically represented as
![df = 12 -1](https://tex.z-dn.net/?f=df%20%3D%2012%20-1)
=>
Generally from the t- distriibution table the critical value of
at a degree of freedom of
is
![t_{0.05 , 11} = 2.20098516](https://tex.z-dn.net/?f=t_%7B0.05%20%2C%2011%7D%20%3D%20%202.20098516)
Here given that the critical value is greater than the t statistics value the
Decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence that indicate that there is a significant difference between the two treatments
1 is a and 2 is b hope its right
20000 ÷(1+4,75%)^20
=20000 ÷ 1,0475^20
=7905,86
You have to deposit $790586 today.
Answer:
She should use the formula
to find a diameter of 16 inches.
Step-by-step explanation:
The circunference of a circle is given by:
![C = 2\pi r](https://tex.z-dn.net/?f=C%20%3D%202%5Cpi%20r)
In which r is the radius, which is half the diameter. So, it can also be given by the following formula:
![C = 2\pi \frac{d}{2} = \pi d](https://tex.z-dn.net/?f=C%20%3D%202%5Cpi%20%5Cfrac%7Bd%7D%7B2%7D%20%3D%20%5Cpi%20d)
In which d is the diameter.
Which formula should Maria use to help her find the diameter of the rug?
She should use this formula:
![C = \pi d](https://tex.z-dn.net/?f=C%20%3D%20%5Cpi%20d)
Since the circunference is 50.24 inches, the diameter will be of:
![d = \frac{C}{\pi} = \frac{50.24}{\pi} = 16](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7BC%7D%7B%5Cpi%7D%20%3D%20%5Cfrac%7B50.24%7D%7B%5Cpi%7D%20%3D%2016)