Answer:
Angle RNQ is equal in measure to arc PR.
Step-by-step explanation:
Consider the complete question is,
Points N, P, and R all lie on circle O. Arc PR measures 120° How does the measure of angle RNQ relate to the measure of arc PR?
A.Angle RNQ is equal in measure to arc PR.
B.Angle RNQ is half the measure of arc PR.
C.Angle RNQ is twice the measure of arc PR.
D.Angle RNQ is four times the measure of arc PR.
By the below attached diagram,
In triangle PRN,
O∈PN,
Such that, RO = RN,
⇒ m∠RON = m∠RNO ......(1),
Also, m∠ROP+m∠RON = 180° ( linear pairs ),
⇒ 120° + m∠RON = 180°
⇒ m∠RON = 180° - 120° = 60°,
From equation (1),
m∠RNO = 60°,
Again,
m∠RNO + m∠RNQ = 180° ( linear pairs )
⇒ 60° + m∠RNQ = 180°
⇒ m∠RNQ = 180° - 60° = 120°,
But, Arc PR measures 120°
Hence, Angle RNQ is equal in measure to arc PR.
Answer:
A sample size of at least 1,353,733 is required.
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 zscore that has a pvalue of .
The margin of error is:
98% confidence level
So , z is the value of Z that has a pvalue of
, so
.
You would like to be 98% confident that you esimate is within 0.1% of the true population proportion. How large of a sample size is required?
We need a sample size of at least n.
n is found when M = 0.001.
Since we don't have an estimate for the proportion, we use the worst case scenario, that is
So
Rounding up
A sample size of at least 1,353,733 is required.