Answer:
Step-by-step explanation:
Data given and notation
represent the sampe size for A
represent the sample size for B
represent the sample deviation for A
represent the sample deviation for B
represent the significance level provided
F test is a statistical test that uses a F Statistic to compare two population variances, with the sample deviations s1 and s2. The F statistic is always positive number since the variance it's always higher than 0. The statistic is given by:
Solution to the problem
System of hypothesis
We want to test if we have the same variation, so the system of hypothesis are:
H0:
H1:
Calculate the statistic
Now we can calculate the statistic like this:
1. -20
2. 9
3. -25
Hope this helps
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
![g(h(x)) = \sqrt[4]{x^2 + x +5} + 3](https://tex.z-dn.net/?f=g%28h%28x%29%29%20%3D%20%5Csqrt%5B4%5D%7Bx%5E2%20%2B%20x%20%2B5%7D%20%2B%203)
b
![h(g(x)) = \sqrt{x} + 7\sqrt[4]{x} + 17](https://tex.z-dn.net/?f=h%28g%28x%29%29%20%20%3D%20%5Csqrt%7Bx%7D%20%20%2B%207%5Csqrt%5B4%5D%7Bx%7D%20%2B%2017)
c
![h(h(x)) = [x^2 + x + 5 ]^2 + x^2 + x + 10](https://tex.z-dn.net/?f=h%28h%28x%29%29%20%3D%20%20%5Bx%5E2%20%2B%20x%20%2B%205%20%5D%5E2%20%2B%20x%5E2%20%2B%20x%20%2B%2010)
Step-by-step explanation:
From the question we are told that

and
![g(x) = \sqrt[4]{x} + 3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Csqrt%5B4%5D%7Bx%7D%20%2B%203)
Considering first question
Now we are told g(h(x))
i.e
![g(h(x)) = [x^2 + x + 5 ]^{\frac{1}{4} } + 3](https://tex.z-dn.net/?f=g%28h%28x%29%29%20%3D%20%20%5Bx%5E2%20%2B%20x%20%2B%205%20%5D%5E%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%20%2B%203)
=> ![g(h(x)) = \sqrt[4]{x^2 + x +5} + 3](https://tex.z-dn.net/?f=g%28h%28x%29%29%20%3D%20%5Csqrt%5B4%5D%7Bx%5E2%20%2B%20x%20%2B5%7D%20%2B%203)
Considering second question
Now we are told h(g(x))
i.e
![h(g(x)) = [x^{\frac{1}{4} } + 3]^2 + x^{\frac{1}{4} } + 3 + 5](https://tex.z-dn.net/?f=h%28g%28x%29%29%20%3D%20%20%5Bx%5E%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%20%2B%203%5D%5E2%20%2B%20%20x%5E%7B%5Cfrac%7B1%7D%7B4%7D%20%7D%20%2B%203%20%2B%205)
=> 
=> 
=> ![h(g(x)) = \sqrt{x} + 7\sqrt[4]{x} + 17](https://tex.z-dn.net/?f=h%28g%28x%29%29%20%20%3D%20%5Csqrt%7Bx%7D%20%20%2B%207%5Csqrt%5B4%5D%7Bx%7D%20%2B%2017)
Considering third question
![h(h(x))= [x^2 + x + 5]^2 + [x^2 + x + 5 ] + 5](https://tex.z-dn.net/?f=h%28h%28x%29%29%3D%20%5Bx%5E2%20%2B%20x%20%2B%205%5D%5E2%20%2B%20%5Bx%5E2%20%2B%20x%20%2B%205%20%5D%20%2B%20%205)
=> ![h(h(x)) = [x^2 + x + 5 ]^2 + x^2 + x + 10](https://tex.z-dn.net/?f=h%28h%28x%29%29%20%3D%20%20%5Bx%5E2%20%2B%20x%20%2B%205%20%5D%5E2%20%2B%20x%5E2%20%2B%20x%20%2B%2010)
Compute 2²⁰¹⁷ modulo 100.
From the given table,
2²² ≡ 2⁴² ≡ 2⁶² ≡ 4 (mod 100)
and we have
2017 = 32 • 62 + 33
62 = 1 • 42 + 20
Then
2²⁰¹⁷ ≡ (2⁶²)³² • 2³³ (mod 100)
2²⁰¹⁷ ≡ 4³² • 2³³ (mod 100)
2²⁰¹⁷ ≡ (2²)³² • 2³³ (mod 100)
2²⁰¹⁷ ≡ 2⁶⁴ • 2³³ (mod 100)
2²⁰¹⁷ ≡ 2⁶² • 2²² • 2¹³ (mod 100)
2²⁰¹⁷ ≡ 4² • 2¹³ (mod 100)
2²⁰¹⁷ ≡ (2²)² • 2¹³ (mod 100)
2²⁰¹⁷ ≡ 2⁴ • 2¹³ (mod 100)
2²⁰¹⁷ ≡ 2¹⁷ (mod 100)
and from the table, we get
2²⁰¹⁷ ≡ 2¹⁷ ≡ 72 (mod 100)