Answer:
The required amount of mice is 11.82 gram.
Step-by-step explanation:
Given : Assuming that it is known from previous studies that σ = 4.5 grams. If we wish to be 95% confident that the mean weight of the sample will be within 3 grams of the population mean for all mice subjected to this protein diet.
To find : How many mice should be included in our sample?
Solution :
The formula used in the situation is
![z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
Where, z value at 95% confidence interval is z=1.96
gram is the mean of the population
gram is the standard deviation of the sample
Substituting the value, to find x sample mean
![1.96=\frac{x-3}{4.5}](https://tex.z-dn.net/?f=1.96%3D%5Cfrac%7Bx-3%7D%7B4.5%7D)
![1.96\times 4.5=x-3](https://tex.z-dn.net/?f=1.96%5Ctimes%204.5%3Dx-3)
![8.82=x-3](https://tex.z-dn.net/?f=8.82%3Dx-3)
![x=8.82+3](https://tex.z-dn.net/?f=x%3D8.82%2B3)
![x=11.82](https://tex.z-dn.net/?f=x%3D11.82)
Therefore, The required amount of mice is 11.82 gram.
Answer:
Step-by-step explanation:
Yes they are similar. You have no angles given at all. But if you multiply the sides of the small triangle by 3/2 you get the lengths of the sides of the larger triangle.
So they are similar by SSS
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Answer:
The area of the triangle with the given vertices is 10 square units
Step-by-step explanation:
x y
D 3 3
E 3 -1
F -2 -5
D 3 3
Area: A=Abs [(xd ye + xe yf + xf yd) - (yd xe + ye xf + yf xd)] /2
Absolute value: Abs
A = Abs { [(3)(-1)+(3)(-5)+(-2)(3)] - [(3)(3)+(-1)(-2)+(-5)(3)] } / 2
A = Abs [ (-3-15-6)-(9+2-15) ] / 2
A = Abs [ (-24)-(-4) ] / 2
A = Abs ( -24+4) / 2
A = Abs (-20) / 2
A = 20 / 2
A = 10 square units