6⁴A. 10 B. 24C. 4⁶D. 6•6•6•6
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<h2><u>Answer with explanation</u>:</h2>
Let be the distance traveled by deluxe tire .
As per given , we have
Null hypothesis :
Alternative hypothesis :
Since is left-tailed and population standard deviation is known, thus we should perform left-tailed z-test.
Test statistic :
where, n= sample size
= sample mean
= Population mean
=sample standard deviation
For , we have
By using z-value table,
P-value for left tailed test : P(z≤-2.23)=1-P(z<2.23) [∵P(Z≤-z)=1-P(Z≤z)]
=1-0.9871=0.0129
Decision : Since p value (0.0129) < significance level (0.05), so we reject the null hypothesis .
[We reject the null hypothesis when p-value is less than the significance level .]
Conclusion : We do not have enough evidence at 0.05 significance level to support the claim that t its deluxe tire averages at least 50,000 miles before it needs to be replaced.
The firts thig we are going to do is create tow triangles using the angles of elevation of Paul and Jose. Since the problem is not giving us their height we'll assume that the horizontal line of sight of both of them coincide with the base of the tree.
We know that Paul is 19m from the base of the tree and its elevation angle to the top of the tree is 59°. We also know that the elevation angle of Jose and the top of the tree is 43°, but we don't know the distance between Paul of Jose, so lets label that distance as
.
Now we can build a right triangle between Paul and the tree and another one between Jose and the tree as shown in the figure. Lets use cosine to find h in Paul's trianlge:
Now we can use the law of sines to find the distance between Paul and Jose:
Now that we know the distance between Paul and Jose, the only thing left is add that distance to the distance from Paul and the base of the tree:
We can conclude that Jose is 33.9m from the base of the tree.
We know that Paul is 19m from the base of the tree and its elevation angle to the top of the tree is 59°. We also know that the elevation angle of Jose and the top of the tree is 43°, but we don't know the distance between Paul of Jose, so lets label that distance as
Now we can build a right triangle between Paul and the tree and another one between Jose and the tree as shown in the figure. Lets use cosine to find h in Paul's trianlge:
Now we can use the law of sines to find the distance
Now that we know the distance between Paul and Jose, the only thing left is add that distance to the distance from Paul and the base of the tree:
We can conclude that Jose is 33.9m from the base of the tree.