How to find the missing factor for binomials
1 answer:
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Answer:
Step-by-step explanation:
You can create a right triangle out of this information and then use right triangle trig to solve.
We are given the height of the triangle as the height of the tower which is 150m.
We are given the angle of inclination as the degree the tower makes with the ground which is 72.
From the angle of 72 degrees, which is also known as the reference angle, we have the side across from it (the height) and we are looking for the side adjacent to it (how far from the base of the tower the keys will land). Side opposite the reference angle over side adjacent to the reference angle is the tangent ratio:
and, solving for x,
Make sure your calculator is in degree mode to solve this. Divide 150 by the tan(72) and find that
x = 48.7 m
Answer:
We can therefore conclude that the geographical distribution of hotline callers could be the same as the U.S population distribution.
Step-by-step explanation:
The null Hypothesis: Geographical distribution of hotline callers could be the same as the U.S. population distribution
Alternative hypothesis: Geographical distribution of hotline callers could not be the same as the U.S. population distribution
The populations considered are the Midwest, South, Northeast, and west.
The number of categories, k = 4
Number of recent calls = 200
Let the number of estimated parameters that must be estimated, m = 0
The degree of freedom is given by the formula:
df = k - 1-m
df = 4 -1 - 0 = 3
Let the significance level be, α = 5% = 0.05
For α = 0.05, and df = 3,
from the chi square distribution table, the critical value = 7.815
<u>Observed and expected frequencies of calls for each of the region:</u>
<u>Northeast</u>
Observed frequency = 39
It contains 18.1% of the US Population
The probability = 0.181
Expected frequency of call = 0.181 * 200 = 36.2
<u>Midwest</u>
Observed frequency = 55
It contains 21.9% of the US Population
The probability = 0.219
Expected frequency of call = 0.219 * 200 =43.8
<u>South</u>
Observed frequency = 60
It contains 36.7% of the US Population
The probability = 0.367
Expected frequency of call = 0.367 * 200 = 73.4
<u>West</u>
Observed frequency = 46
It contains 23.3% of the US Population
The probability = 0.233
Expected frequency of call = 0.233 * 200 = 46
Where observed frequency
Expected frequency
Calculate the test statistic value, x²
Since the test statistic value, x²= 5.535 is less than the critical value = 7.815, the null hypothesis will not be rejected, i.e. it will be accepted. We can therefore conclude that the geographical distribution of hotline callers could be the same as the U.S population distribution.