an observer on a cliff 1200 feet above sea level sights two ships due East. The angle of depression to the shops are 48° and 33°
. What is the distance between the ships?
1 answer:
See the attached figure to better understand the problem
we know that
in the triangle ABC
tan 48°=AB/AC--------> AC=AB/tan48°------> 1200/tan 48°------> 1080.48 ft
in the triangle ABD
tan 33°=AB/AD---------> AD=AB/tan 33°-----> 1200/tan 33°------> 1847.88 ft
<span>the distance between the ships is AD-AC---> 1847.88-1080.48----> 767.4 ft
the answer is
</span>the distance between the ships is 767.4 ft<span>
</span>
we know that
in the triangle ABC
tan 48°=AB/AC--------> AC=AB/tan48°------> 1200/tan 48°------> 1080.48 ft
in the triangle ABD
tan 33°=AB/AD---------> AD=AB/tan 33°-----> 1200/tan 33°------> 1847.88 ft
<span>the distance between the ships is AD-AC---> 1847.88-1080.48----> 767.4 ft
the answer is
</span>the distance between the ships is 767.4 ft<span>
</span>
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Answer:
We conclude that there is no difference in potential mean sales per market in Region 1 and 2.
Step-by-step explanation:
We are given that a random sample of 12 supermarkets from Region 1 had mean sales of 84 with a standard deviation of 6.6.
A random sample of 17 supermarkets from Region 2 had a mean sales of 78.3 with a standard deviation of 8.5.
Let = mean sales per market in Region 1.
= mean sales per market in Region 2.
So, Null Hypothesis, :
= 0 {means that there is no difference in potential mean sales per market in Region 1 and 2}
Alternate Hypothesis, : >
0 {means that there is a difference in potential mean sales per market in Region 1 and 2}
The test statistics that will be used here is <u>Two-sample t-test statistics</u> because we don't know about population standard deviations;
T.S. = ~
where, = sample mean sales in Region 1 = 84
= sample mean sales in Region 2 = 78.3
= sample standard deviation of sales in Region 1 = 6.6
= sample standard deviation of sales in Region 2 = 8.5
= sample of supermarkets from Region 1 = 12
= sample of supermarkets from Region 2 = 17
Also, =
= 7.782
So, <u><em>the test statistics</em></u> = ~
= 1.943
The value of t-test statistics is 1.943.
Now, at a 0.02 level of significance, the t table gives a critical value of -2.472 and 2.473 at 27 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have<u><em> insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.
Therefore, we conclude that there is no difference in potential mean sales per market in Region 1 and 2.