Radius OB measures x units. Which expression represents
1 answer:
Answer:
Circumference of the smaller circle = 2.1x units
Step-by-step explanation:
Given question is incomplete; here is the complete question.
Two similar circles are shown. The circumference of the larger circle, with radius OB, is 3 times the circumference of the smaller circle, with radius OA. Radius OB measures x units. Which expression represents the circumference of the smaller circle with radius OA ?
Radius of the larger circle OB = x units
Radius of the smaller circle OA = y units
Circumference of larger circle = 2πx units
Circumference of smaller circle = 2πy units
Since circumference of larger circle is 3 times the circumference of smaller circle,
2πx = 3(2πy)
2πx = 6πy
x = 3y
y =
Therefore, circumference of the smaller circle = units
= units
= 2.094x
≈ 2.1x
Circumference of the smaller circle circle = 2.1x units
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Answer:
a)
And the margin of error is given by:
The confidence level is 0.96 and the significance level is and the value of
and the margin of error is given by:
We can calculate the critical value and we got:
And if we solve for the deviation like this:
And replacing we got:
b)
And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor
Step-by-step explanation:
Previous concepts
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 sample mean
population mean (variable of interest)
represent the population standard deviation
n=80 represent the sample size
Solution to the problem
Part a
The confidence interval for the mean is given by the following formula:
(1)
For this case we can calculate the mean like this:
And the margin of error is given by:
The confidence level is 0.96 and the significance level is and the value of
and the margin of error is given by:
We can calculate the critical value and we got:
And if we solve for the deviation like this:
And replacing we got:
Part b
For this case is the sample size is doubled the margin of error would be:
And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor