Using the z-distribution, the p-value would be given as follows:
b) 0.0086.
<h3>What are the hypothesis tested?</h3>
At the null hypothesis we test if the means are equal, hence:

At the alternative hypothesis, it is tested if they are different, hence:

<h3>What are the mean and the standard error for the distribution of differences?</h3>
For each sample, they are given as follows:
Hence, for the distribution of differences, they are given by:
.
<h3>What is the test statistic?</h3>
The test statistic is given by:

In which
is the value tested at the null hypothesis.
Hence:


z = -2.63.
Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.
Hence option B is correct.
More can be learned about the z-distribution at brainly.com/question/13873630
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Answer:
Yes if Angle 7 and angle 6 are linear pairs in angles created by a straight line that cuts through parallel lines.
Step-by-step explanation:
Remember that two parallel lines that are cut by a transveral will create 8 angles, which will be similar to each other. Making four pairs of congruent angles means that they will be exactly the same angle located in different parts of the system. So if angles 6 and 7 are congruent, and the lines are cut by a transversal, then the lines are parallel.
Answer:
The speed of the first train is 45 mph and the speed of the second train is 75 mph
Step-by-step explanation:
Let x represent the speed of the first train in mph. Since the second train, is 30 mph faster then the first, therefore the speed of the second train is (x + 30).
The first train leaves at 1:00 pm, therefore at 6:00 pm, the time taken is 5 hours. Therefore the distance covered by the first train at 6:00 pm = x mph * 5 hours = 5x miles
The second train leaves at 3:00 pm, therefore at 6:00 pm, the time taken is 3 hours. Therefore the distance covered by the second train at 6:00 pm = (x + 30) mph * 3 hours = (3x + 90) miles
Since the second train overtakes the first at 6:00 pm, hence:
3x + 90 = 5x
2x = 90
x = 45
Therefore the speed of the first train is 45 mph and the speed of the second train is 75 mph (45 mph + 30 mph).
Answer:
A. $3,984
Step-by-step explanation:
The amount of interest is computed from ...
I = Prt
For the given values, the interest is ...
I = $3600×0.08×(16/12) = $384
Then the total amount that needs to be repaid is ...
Principal + Interest = $3600 +384 = $3,984
_____
The time period is 16 months, so is 16/12 years.
The time periods of the interest rate and "t" in the formula must match. If the interest rate is an annual rate, then "t" is in years. If the interest rate is a monthly rate, then "t" is the number of months.