What is the area of the rectangle with points of (-5,5) (-1,7) (0,-5) (4,-3)
1 answer:
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Prove:
Using mathemetical induction:
P(n) =
for n=1
P(n) = = 6
It is divisible by 2 and 3
Now, for n=k,
P(k) =
Assuming P(k) is divisible by 2 and 3:
Now, for n=k+1:
P(k+1) =
P(k+1) =
P(k+1) =
Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also
divisible by 2 and 3.
Hence, by mathematical induction, P(n) = is divisible by 2 and 3 for all positive integer n.
Using the z-distribution and the formula for the margin of error, it is found that:
a) A sample size of 54 is needed.
b) A sample size of 752 is needed.
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which z is the z-score that has a p-value of .
The margin of error is of:
90% confidence level, hence, z is the value of Z that has a p-value of
, so
.
Item a:
The estimate is .
The sample size is <u>n for which M = 0.03</u>, hence:
Rounding up, a sample size of 54 is needed.
Item b:
No prior estimate, hence
Rounding up, a sample of 752 should be taken.
A similar problem is given at brainly.com/question/25694087