Answer: 
Work Shown:
Note that (h,k) = (2,-3) is the center and r = 6 is the radius. The last line is not expanded out using the FOIL rule because its common practice to leave it in 
form. This form allows the reader to quickly determine the center and radius (rather than have to do a lot of algebraic steps before hand).
Answer:
Stated below:
Step-by-step explanation:
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The probability from 1.5 ≤ x ≤ 3 can be calculated by dividing the Area from x=1.5 to x=3 by the total Area of the distribution.
The given distribution is rectangular shaped, so its Area will be = Length x Width = 1 x 3 = 3 square units
From x = 1.5 to x = 3, the length is 1.5 and width is 1. So the area between these two intervals = 1.5 square units.
Thus, <span>P(1.5 ≤ X ≤ 3) = 1.5/3 = 0.5
</span>
Answer:
The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.
Step-by-step explanation:
We have that to find our 
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of 
.
So it is z with a pvalue of 
, so 
Now, find the margin of error M as such
In which 
is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 5.4 - 0.04 = 5.36 years.
The upper end of the interval is the sample mean added to M. So it is 5.4 + 0.04 = 5.44 years.
The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.
Mixed number: 2 3/4
improper fraction: 11/4
