A circle has a radius of 40 centimeters. Find the length of the arc intercepted by a central angle of 5π/3. Express the answer i
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Answer:
The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of .
Of the 533 randomly selected Americans surveyed, 351 were in favor of the initiative.
This means that
90% confidence level
So , z is the value of Z that has a p-value of
, so
.
The lower limit of this interval is:
The upper limit of this interval is:
The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).
Check the picture below.
Hey there, hope I can help!
Assuming you know how to simplify this, I will not show the steps but can add them later on upon request
Lets use the quadratic formula now
Multiply the numbers 2 * 1 = 2
![\mathrm{Apply\:radical\:rule}: \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b} \ \textgreater \ \sqrt{47}\sqrt{2^2}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aradical%5C%3Arule%7D%3A%20%5Csqrt%5Bn%5D%7Bab%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5Csqrt%5Bn%5D%7Bb%7D%20%5C%20%5Ctextgreater%20%5C%20%20%5Csqrt%7B47%7D%5Csqrt%7B2%5E2%7D%20)
![\mathrm{Apply\:radical\:rule}: \sqrt[n]{a^n}=a \ \textgreater \ \sqrt{2^2}=2 \ \textgreater \ 2\sqrt{47} \ \textgreater \ \frac{2+2\sqrt{47}}{2}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aradical%5C%3Arule%7D%3A%20%5Csqrt%5Bn%5D%7Ba%5En%7D%3Da%20%5C%20%5Ctextgreater%20%5C%20%20%5Csqrt%7B2%5E2%7D%3D2%20%5C%20%5Ctextgreater%20%5C%20%202%5Csqrt%7B47%7D%20%5C%20%5Ctextgreater%20%5C%20%20%5Cfrac%7B2%2B2%5Csqrt%7B47%7D%7D%7B2%7D)
Moving on, I will do the second part excluding the extra details that I had shown previously as from the first portion of the quadratic you can easily see what to do for the second part.
Therefore our final solutions are
Hope this helps!
Assuming you know how to simplify this, I will not show the steps but can add them later on upon request
Lets use the quadratic formula now
Multiply the numbers 2 * 1 = 2
Moving on, I will do the second part excluding the extra details that I had shown previously as from the first portion of the quadratic you can easily see what to do for the second part.
Therefore our final solutions are
Hope this helps!