A recent article in a university newspaper claimed that the proportion of students who commute more than miles to school is no m
1 answer:
Answer:
The null hypothesis is , in which x is the proportion tested.
The alternative hypothesis is
Step-by-step explanation:
A recent article in a university newspaper claimed that the proportion of students who commute more than miles to school is no more than x.
This means that at the null hypothesis, we test if the proportion is of at most x, that is:
Suppose that we suspect otherwise and carry out a hypothesis test.
The opposite of at most x is more than x, so the alternative hypothesis is:
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Answer:
88.7°
Step-by-step explanation:
First, visualize. Assuming that the tower is at a perfectly 90° angle to the ground, you have a right triangle. We will call this triangle ΔABC where A is where you are, B is the top of the tower, and C is the base of the tower. Now we know the following:
∠A = ?
∠B = ?
∠C = 90
a = 346346
b = 7777
c = ?
Note: Triangles are labeled with three pairs of letters: a, b and c and A, B and C. The lower case letters, a, b and c represent the sides, and the upper case letters are the angles that are directly opposite of those sides. (see attached reference)
c is easy, c is the hypotenuse, so you can use the following equation to find the hypotenuse:
a² + b² = c²
Rearranged:
c = ±
Substitute a and b:
c = ±
Comes out to ~346433.3 meters.
Now if we use the Law of Sines:
=
=
We can use c and a, since we're trying to find what angle A is, so the ratio is set up as:
=
Well we know that C = 90, and so sin(90) in degrees (as opposed to radians) is 1. So then the set of equations is now:
=
Cross Multiply to get rid of the fractions:
346346 = 346433.3 * sin(A)
Divide:
= sin(A)
Using a calculator, if you take the arcsin of that fraction, you will get what angle A is supposed to be:
arcsin( ) = ∠A = 88.7°
