Answer:
Step-by-step explanation:
From the way the answers are presented, it can be seen that x refers to the radius of the base of the cone
radius:
and we are told that the height is twice the radius, so:
height:
and now we use the formula to calculate the volume of a cone:
where is volume,
is radius, and
is the height. and
is a constant
in this case
so we substitute thisvalues in the formula for the volume:
Rearranging the terms
which is option A.
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.