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Ghella [55]
3 years ago
6

Pls help find shaded area

Mathematics
1 answer:
Pavlova-9 [17]3 years ago
6 0
<h3>Exact area = 12pi - 9*sqrt(3)  square inches</h3><h3>Approximate area = 22.1106545749577 square inches</h3>

==========================================================

Work Shown:

Assuming the chord is horizontal along with the diameter, then this means the two smallest minor arcs are both 30 degrees each. This leaves the northern most arc to be 180-30-30 = 120 degrees in measure

A = area of northern sector (you can think of it as a pizza slize)

A = (angle/360)*pi*r^2

A = (120/360)*pi*6^2

A = 12pi

B = area of triangle

B = (1/2)*side1*side2*sin(included angle)

B = (1/2)*6*6*sin(120)

B = 18*sqrt(3)/2

B = 9*sqrt(3)

C = area of shaded region

C = A - B

C = 12pi - 9*sqrt(3)  .... exact area

C = 22.1106545749577 ... use a calculator to get the approximate area

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Step-by-step explanation:

Data given and notation

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\hat p=0.021 estimated proportion of interest

p_o=0.012 is the value that we want to test

\alpha=0.01 represent the significance level

Confidence=99% or 0.99

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p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that true proportions is higher than 0.012.:  

Null hypothesis:p \leq 0.012  

Alternative hypothesis:p > 0.012  

When we conduct a proportion test we need to use the z statisitic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.021 -0.012}{\sqrt{\frac{0.012(1-0.012)}{1655}}}=3.363  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.01. The next step would be calculate the p value for this test.  

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

p_v =P(z>3.363)=0.00039  

So the p value obtained was a very low value and using the significance level given \alpha=0.01 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is significantly higher than 0.012 (1.2%)

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