In circle T, what is the value of x?
2 answers:
Answer:
x = 19°
Step-by-step explanation:
Refer the attached figure
Given : ∠ACB = 71°
∠BAC = x°
Thales' theorem : If A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle ∠ABC is a right angle.
So, by Thale's theorem ∠ABC is a right angle in the given figure
i.e.∠ABC = 90°
In ΔABC ,
To find x we will use angle sum property of triangle
Angle sum property of triangle : Sum of all angles is 180°
⇒∠BAC+∠ABC+∠ACB = 180°
⇒x°+90°+71° = 180°
⇒x°+161° = 180°
⇒x° = 180°-161°
⇒x° =19°
∠BAC = x° =19°
Thus x = 19°
Hence Option 1 is correct .
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Answer:
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).
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 .
For this problem, we have that:
Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. So 1537 - 1184 = 353 read at or below this level. Then
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:
The upper limit of this interval is:
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).