<u>Given</u>:
Given that the regular decagon has sides that are 8 cm long.
We need to determine the area of the regular decagon.
<u>Area of the regular decagon:</u>
The area of the regular decagon can be determined using the formula,

where s is the length of the side and n is the number of sides.
Substituting s = 8 and n = 10, we get;

Simplifying, we get;




Rounding off to the nearest whole number, we get;

Thus, the area of the regular decagon is 642 cm²
Hence, Option B is the correct answer.
Answer:
0.8894 is the probability that the test result comes back negative if the disease is present
.
Step-by-step explanation:
We are given the following in the question:
P(Disco Fever) = P( Disease) =

Thus, we can write:
P(No Disease) =

P(Test Positive given the presence of the disease) = 0.99

P( false-positive) = 4%

We have to evaluate the probability that the test result comes back negative if the disease is present, that is
P(test result comes back negative if the disease is present)
By Bayes's theorem, we can write:

0.8894 is the probability that the test result comes back negative if the disease is present
.
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Answer: d)In repeated samples of the same size, approximately 95 percent of the intervals constructed from the samples will capture the population difference in means.
Step-by-step explanation:
Confidence interval is constructed to estimate a range of values that could possibly contain the population parameter. This could be the population mean or population proportion. A 95 percent confidence interval does not mean 95% probability. It tells how confident that we are that the confidence interval contains the population proportion. If we construct 100 of the given confidence interval, we are confident that 95% of them would contain the true population parameter. Therefore, the correct option is
d)In repeated samples of the same size, approximately 95 percent of the intervals constructed from the samples will capture the population difference in means.