Answer:
What type of problem are you asking? Math, English, Computer, etc.
Step-by-step explanation:
Answer:
The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).
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 z-score that has a p-value of
.
Of the 533 randomly selected Americans surveyed, 351 were in favor of the initiative.
This means that 
90% confidence level
So
, z is the value of Z that has a p-value of
, so
.
The lower limit of this interval is:

The upper limit of this interval is:

The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).
Answer:
The flight was 137.45 miles farther than the direct path.
(make slight changes if directions were given on how to round. This is to the nearest hundredth)
Step-by-step explanation:
Use the Law of Cosines.
c^2=
a^2+b^2-2abcosC
You know two sides and the angle in between. The Law of Cosines will give us the third side.
The third side is the direct path of the airplane. We'll add the two other given sides to find the detour route that they took instead.
Then subtract the smaller number (direct route) from the actual route. See image.
There's no way to do that without seeing the drawing or hearing a lot more information. For one thing, we don't even know the size of the circle yet.
Unlike the previous problem, this one requires application of the Law of Cosines. You want to find angle Q when you know the lengths of all 3 sides of the triangle.
Law of Cosines: a^2 = b^2 + c^2 - 2bc cos A
Applying that here:
40^2 = 32^2 + 64^2 - 2(32)(64)cos Q
Do the math. Solve for cos Q, and then find Q in degrees and Q in radians.