What are three problems the have the sum of 4
1 answer:
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Check the picture below.
the radius, so-called because if we circumscribe the triangle in a circle, that'd be the radius of the circumcircle, is 3 inches, as you see there in the picture in red.
now, bear in mind that the triangle is an equilateral one, and therefore, 180/3 = 60, meaning all its interior angles are congruently 60°.
if we run the radius of the triangle, like there, it will cut one of those interior angles in half, namely the radius is an angle bisector, and if we run a perpendicular line to the bottom side, like the dashed one there, we end up with a 30-60-90 triangle, to which we can apply the 30-60-90 rule, as you see it there.
since we know what half of a side of the triangle is, as you see it there in blue, then we can use that and plug it in at
the radius, so-called because if we circumscribe the triangle in a circle, that'd be the radius of the circumcircle, is 3 inches, as you see there in the picture in red.
now, bear in mind that the triangle is an equilateral one, and therefore, 180/3 = 60, meaning all its interior angles are congruently 60°.
if we run the radius of the triangle, like there, it will cut one of those interior angles in half, namely the radius is an angle bisector, and if we run a perpendicular line to the bottom side, like the dashed one there, we end up with a 30-60-90 triangle, to which we can apply the 30-60-90 rule, as you see it there.
since we know what half of a side of the triangle is, as you see it there in blue, then we can use that and plug it in at
Answer:
n=269 residents should be sample required to be sure that a 90% confidence interval for the proportion who favor the construction will have a margin of error no greater than 0.05
Step-by-step explanation:
A 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".
represent the real population proportion of interest
represent the estimated proportion for the sample
n is the sample size required (variable of interest)
represent the critical value for the margin of error
The population proportion have the following distribution
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can assume that the estimates proportion is 0.5 since we don't have other info provided to assume a different value. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=269