A triangle has the following two angle measures:
1 answer:
Answer:
62°
Step-by-step explanation:
Given that the triangle has two angle measures of 41° and 77°.
All the angles in a triangle must add up to 180° (e.g. 20° + 60° + 100°). So we write a simple equation to solve for the mystery angle measure:
Let x = the missing measure
Now that we have our equation, let's start solving it. First, we need to add 41 and 77 together which simplifies the equation:
Then we subtract 118 from both sides to isolate x - this will give us the value of this variable:
Therefore, the third angle must have a measure of 62°.
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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.
then use the common difference "d", to get the 2nd and 3rd terms
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