<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.
The first one would be C and the 2nd is A.
Let p be the proportion. Let c be the given confidence level , n be the sample size.
Given: p=0.3, n=1180, c=0.99
The formula to find the Margin of error is
ME = 
Where z (α/2) is critical value of z.
P(Z < z) = α/2
where α/2 = (1- 0.99) /2 = 0.005
P(Z < z) = 0.005
So in z score table look for probability exactly or close to 0.005 . There is no exact 0.005 probability value in z score table. However there two close values 0.0051 and 0.0049 . It means our required 0.005 value lies between these two probability values.
The z score corresponding to 0.0051 is -2.57 and 0.0049 is -2.58. So the required z score will be average of -2.57 and -2.58
(-2.57) + (-2.58) = -5.15
-5.15/2 = -2.575
For computing margin of error consider positive z score value which is 2.575
The margin of error will be
ME = 
=
= 2.575 * 0.0133
ME = 0.0342
The margin of error is 0.0342
Answer:

Step-by-step explanation:

hope this helps
brainliest appreciated
good luck! have a nice day!
Probability is the measurement of the likelihood of something happening
So, looking through the different questions, whether they have a graph or picture, you look at the numbers and divide by the total to determine the probablility.
Hope this helps