find the shadow cast by a 10 foot lamp post when the angle of elevation of the sun is 58 degrees. find the length to the nearest
tenth of a foot.
1 answer:
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Answer:
Null hypothesis:
Alternative hypothesis:
So the p value is a very low value and using any significance level for example always
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significantly different from proportion 2.
Step-by-step explanation:
1) Data given and notation
represent the number of people with a characteristic in 1
represent the number of people with a characteristic in 2
sample of 1 selected
sample of 2 selected
represent the proportion of people with a characteristic in 1
represent the proportion of people with a characteristic in 2
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if the proportion 1 is different from proportion 2 , the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
3) Calculate the statistic
Replacing in formula (1) the values obtained we got this:
4) Statistical decision
For this case we don't have a significance level provided , but we can calculate the p value for this test.
Since is a two sided test the p value would be:
So the p value is a very low value and using any significance level for example always
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significantly different from proportion 2.
Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.
1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.
According to this theorem,
Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then
Take positive value x. You get
2. According to the previous theorem,
Then
Answer:
This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then
This means that you cannot find solutions of this equation. Then CD≠2 cm.