To find the formula to find radius, solve for r using the formula for circumference.
to solve:
1. divide each side by 2
2. you get r = c/2
to solve:
1. divide each side by 2
2. you get r = c/2
Is this a direct variation problem
1 answer:
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Answer:
Critical values:
95% confidence interval would be given by (3.646;4.472)
Step-by-step explanation:
1) 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".
The data is:
4.65 3.89 2.73 4.35 3.80 4.86 4.33 4.37 4.76 4.05 3.05 3.87
2) Compute the sample mean and sample standard deviation.
In order to calculate the mean and the sample deviation we need to have on mind the following formulas:
=AVERAGE(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)
On this case the average is
=STDEV.S(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)
The sample standard deviation obtained was s=0.6503
3) Find the critical value t* Use the formula for a CI to find upper and lower endpoints
In order to find the critical value we need to take in count that our sample size n =12 <30 and on this case we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. The degrees of freedom are given by:
We can find the critical values in excel using the following formulas:
"=T.INV(0.025,11)" for
"=T.INV(1-0.025,11)" for
The confidence interval for the mean is given by the following formula:
And we can use Excel to calculate the limits for the interval
Lower interval : "=4.059 -2.201*(0.6503/SQRT(12))" =3.646
Upper interval : "=4.059 +2.201*(0.6503/SQRT(12))" =4.472
So the 95% confidence interval would be given by (3.646;4.472)
Answer:
35/37
Step-by-step explanation:
In this question, we are to calculate the ratio that represents the cosine of angle O
Firstly, please check attachment for diagram of the triangle.
Mathematically, the trigonometric term Cos means the ratio of the length of the adjacent to that of the hypotenuse
The hypotenuse is the longest length which is 37 which represents the length ON
The side adjacent to angle O is the side OP which is 35
Thus, the ratio representing the cosine of angle O is 35/37
