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vodomira [7]
3 years ago
6

What is the area of a regular nonagon with 10 cm side length and an apothem of 6 cm?

Mathematics
1 answer:
pickupchik [31]3 years ago
8 0

The area of the regular nonagon is 270 sq cm.

Step-by-step explanation:

Given,

Each side of a regular nonagon (b) = 10 cm

The length of apothem (h) = 6 cm.

To find the area of the nonagon.

Formula

The area of a nonagon with b as each side and h as apothem is  = 9(\frac{1}{2}bh)

Now,

Putting the value of h and b we get,

Area = 9(\frac{1}{2}×10×6) sq cm = 270 sq cm

Hence, the area is 270 sq cm.

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A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard devi
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Answer:

Null hypothesis:\mu \leq 3.3  

Alternative hypothesis:\mu > 3.3  

z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768  

Since is a one right tailed test the p value would be:  

p_v =P(z>1.768)=0.039  

Step-by-step explanation:

Data given and notation

\bar X=3.4 represent the sample mean  

\sigma=0.4 represent the population deviation for the sample

n=50 sample size  

\mu_o =3.3 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses to be tested  

We need to conduct a hypothesis in order to determine if the mean is higher than 3.3, the system of hypothesis would be:  

Null hypothesis:\mu \leq 3.3  

Alternative hypothesis:\mu > 3.3  

Compute the test statistic  

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

We can replace in formula (1) the info given like this:  

z=\frac{3.4-3.3}{\frac{0.4}{\sqrt{50}}}=1.768  

P value

Since is a one right tailed test the p value would be:  

p_v =P(z>1.768)=0.039  

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Step-by-step explanation:

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