Answer: 90% confidence interval is (25.8,30.2).
Step-by-step explanation:
Since we have given that
n = 5
Mean = 28
Standard deviation = 3
It is a 90% confidence interval , so, z = 1.64
We need to find the interval.
so, it would be
![x\pm z(\dfrac{\sigma}{\sqrt{n}})\\\\=28\pm 1.64\times (\dfrac{3}{\sqrt{5}})\\\\=28\pm 2.2\\\\=(28+2.2,28-2.2)\\\\=(25.8,30.2)](https://tex.z-dn.net/?f=x%5Cpm%20z%28%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%29%5C%5C%5C%5C%3D28%5Cpm%201.64%5Ctimes%20%28%5Cdfrac%7B3%7D%7B%5Csqrt%7B5%7D%7D%29%5C%5C%5C%5C%3D28%5Cpm%202.2%5C%5C%5C%5C%3D%2828%2B2.2%2C28-2.2%29%5C%5C%5C%5C%3D%2825.8%2C30.2%29)
Hence, 90% confidence interval is (25.8,30.2).
Theorem: If a function y = f(x) has a real root of b, then (x – b) is a factor of f(x).
As given in the problem, there are two roots: –2 and 1/2. The multiplicity of 1/2 is 2 meaning that the root 1/2 repeats twice. So the function f(x) can be written like this.
f(x) = k• (x – (–2))(x – 1/2)^2 = k•(x + 2)(x – 1/2)^2
We're supposed to find the coefficient k to complete the function.
Given that f(–3) = 5, we can plug –3 in for x and 5 in for f(x).
So 5 = k •(–3 + 2)(–3 – 1/2)^2
5 = k(–1)(–7/2)^2
5 = -k•49/4
Then 5 • 4/49 = -k
Or k = –20/49
So the function with the least degree is
f(x) = –20/49 (x + 2)(x – 1/2)^2.
Answer:
4/10
Step-by-step explanation:
4/10 is equal to 2/5, and 4+6=10
By using the distance formula which is attached
Answer:
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Step-by-step explanation:
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