<h2>
Answer with explanation:</h2>
We are asked to prove by the method of mathematical induction that:
where n is a positive integer.
then we have:
Hence, the result is true for n=1.
- Let us assume that the result is true for n=k
i.e.
- Now, we have to prove the result for n=k+1
i.e.
<u>To prove:</u> 
Let us take n=k+1
Hence, we have:
( Since, the result was true for n=k )
Hence, we have:
Also, we know that:
(
Since, for n=k+1 being a positive integer we have:
)
Hence, we have finally,
Hence, the result holds true for n=k+1
Hence, we may infer that the result is true for all n belonging to positive integer.
i.e.
where n is a positive integer.
In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.
The number of independent ways by which a dynamic system can move, without violating any constraint imposed on it, is called number of degrees of freedom.
In other words, the number of degrees of freedom can be defined as the
minimum number of independent coordinates that can specify the position
of the system completely.
<span>
The degree of freedom represents the number of ways in which the expected classes are free to vary in the chi-square goodness-of-fit test.</span>
Answer:
Sam had 80 dollars in his pocket. He was feeling generous, so he handed out equal amount of money to each of his friends. After he handed out the money, he had 53 dollars left. How much did Sam give out to each one of his friends?
Step-by-step explanation:
In this real-world problem, the money he had at the beginning resembles the 80 in the equation. The -3x is the money he gives out to each of his friends. The 53 on the right-hand side is the money he has left after he gives the money away.
I dont see anything u have to post on here whats the question you need help on ?
X+x-17+39=180
2x+22=180
Subtract 22 from both sides
2x=158
X= 79
