Step-by-step explanation:
We will prove by mathematical induction that, for every natural 
,
We will prove our base case, when n=4, to be true.
Base case:
Inductive hypothesis:
Given a natural ,
Now, we will assume the induction hypothesis and then use this assumption, involving n, to prove the statement for n + 1.
Inductive step:
With this we have proved our statement to be true for n+1.
In conlusion, for every natural 
.
Answer: b. H0: μ ≥ 5; Ha: μ < 5
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean.
While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
The mean is 5 years and they claim it will perform for more than 5 years.
Therefore, for the case above;
H0: μ ≥ 5; Ha: μ < 5
Note: a null hypothesis must always include an equal to sign.
If its division the answer is 1/15
if its multiplication it is 27/5
addition 48/5
subtraction -42/5
