A random sample of 84 students at a university showed an average age of 22 years and a sample standard deviation of 3 years. Fin
1 answer:
Answer:
The margin of error for the 94% confidence interval is 0.6154.
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for population mean is:
The margin of error of this interval is:
The critical value of <em>z</em> for 94% confidence level is, <em>z</em> = 1.88.
Compute the margin of error for the 94% confidence interval as follows:
Thus, the margin of error for the 94% confidence interval is 0.6154.
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Answer:
The length of AC is 222 units.
Step-by-step explanation:
Given AC and AE are common external tangents of G and D.
BC= 123 , GB=20 and AG=101.
We have to find the measure of AC.
As, a straight line joined from the center i.e radius is perpendicular to tangent drawn. Therefore,
In ΔABG, by Pythagoras theorem
⇒
⇒
⇒ AB=99 units.
Hence, AC=AB+BC=99+123=222 units.
The length of AC is 222 units.
For a better understanding of the solution given here please find the attached file which has the relevant diagram.
To answer this question we will have to make use of <u>the Isosceles Triangle Theorem</u> which states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. Thus, as a corollary we know that is EF is the angle bisector of the vertex angle ∠E, then, EF is the perpendicular bisector of the of the base DK.
Please follow the diagram of a complete understanding of the logic and the solution.
As EF is the angle bisector as given in the question, thus we will have:
.
Also, from the Theorem we know that KF will be half of DK and thus, KF will be: centimeters.
Likewise, from the same theorem we have:
