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Nana76 [90]
3 years ago
10

What is the area of an equilateral triangle with the base of 8 cm? Round your answer to the hundredths place. ​

Mathematics
2 answers:
Lady_Fox [76]3 years ago
5 0

Step-by-step explanation:

\frac{{x}^{2} \times  \sqrt{3}}{4}

for x=8, area=16*root(3)

Contact [7]3 years ago
5 0

Answer:

Let's find the height:

Half of 8 is 4.

4^2 + 8^2 = 80

80(lets find the square root of 80): 8.944 ^2 = 79.995136 close enough to 80

Your new height is 8.944.

8 x 8.944 = 71.552, 71.552 x 1/2 (basically just dividing by 2) = 35.776 rounded would be = 35.78 cm^2

Formula of area of a triangle:

B(base)H(height) x 1/2(basically just dividing by 2)

In this case 8 is your base and 8.944 is your height.

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(a) Null Hypothesis, H_0 : \mu \leq 41  

    Alternate Hypothesis, H_A : \mu > 41

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We are given that in a random sample of 40 such periods from Spanish colonial times, the sample mean is x¯ = 47.0. Previous studies of sunspot activity during this period indicate that σ = 35.

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Alternate Hypothesis, H_A : \mu > 41     {means that the mean sunspot activity during the Spanish colonial period was higher than 41}

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                            T.S. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

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            n = sample of periods from Spanish colonial times = 40

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                P-value = P(Z > 1.08) = 1 - P(Z < 1.08)

                              = 1 - 0.8599 = <u>0.1401</u>

Since, the P-value of the test statistics is higher than the level of significance as 0.1401 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.

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