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2 years ago

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The circumference of a circle is 11 inches. What is the area, in square inches, of the circle? Express your answer in terms of p

i

2 answers:

kakasveta [241]2 years ago

7 0

Answer

A = 30.25pi. PLS GIVE BRAINLIEST

Step-by-step explanation:

so if circumference is 11, and formula for circumference is 2pi*r, we can work backwards to find the radius.

Radius: 11pi/2 = 5.5pi = 5.5 is radius

Area = pi * r^2

so Area = pi*5.5^2

so A = 30.25pi left in terms of pi

forsale [732]2 years ago

5 0

Answer: 11/4pi

Step-by-step explanation:

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Write the exact value solution and an approximation for 10^4x=25

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Answer:

exact value: $x= \frac{log25}{4}$

approximate: x=0.349485

Step-by-step explanation:

Exact Value:

$10^{4x} = 25$

$log (10^{4x})= log 25$

$4x = log 25$

$x= \frac{log25}{4}$

Approximate:

$x= \frac{log25}{4}$

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Answer:

a) $29.4-1.96\frac{7}{\sqrt{10}}=25.06$

$29.4+1.96\frac{7}{\sqrt{10}}=33.74$

So on this case the 95% confidence interval would be given by (25.06;33.74)

b) $z=\frac{29,4-25}{\frac{7}{\sqrt{10}}}=1.988$

$p_v =P(z>1.988)=0.0234$

If we compare the p value and the significance level given $\alpha=Step-by-step explanation:Previous conceptsA confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval". 
The margin of error is the range of values below and above the sample statistic in a confidence interval. 
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean". 
Part a
Data given: 30 30 42 35 22 33 31 29 19 23
We can calculate the sample mean with the following formula:[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}= 29.4$ the sample mean

$\mu$ population mean (variable of interest)

$\sigma=7$ represent the population standard deviation

n=10 represent the sample size

95% confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$29.4-1.96\frac{7}{\sqrt{10}}=25.06$

$29.4+1.96\frac{7}{\sqrt{10}}=33.74$

So on this case the 95% confidence interval would be given by (25.06;33.74)

Part b

What are H0 and Ha for this study?

Null hypothesis: $\mu \leq 25$

Alternative hypothesis : $\mu>25$

Compute the test statistic

The statistic for this case 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:

$z=\frac{29,4-25}{\frac{7}{\sqrt{10}}}=1.988$

Give the appropriate conclusion for the test

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

$p_v =P(z>1.988)=0.0234$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

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