Using the z-distribution, as we are working with a proportion, it is found that the margin of error for the 90% confidence interval is of 0.0524 = 5.24%.
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:

In which:
is the sample proportion.
The margin of error is given by:

In this problem, the critical value is given as z = 1.645, and since 26 out of 80 students said they would be willing to pay extra:

Then, the <em>margin of error</em> is of:

More can be learned about the z-distribution at brainly.com/question/25890103
Answer:

And if we use the normal standard distribution or excel we got:

Step-by-step explanation:
For this case we have the following info given:
represent the mean
represent the standard deviation
represent the sample size
The distribution for the sample size if we use the central limit theorem (n>30) is given by:

And for this case we want to find the following probability:

And for this case we can use the z score formula given by:

And replacing we got:

And if we use the normal standard distribution or excel we got:

Answer:
4r-7
Step-by-step explanation:
-14+7-9r+13r
combine like terms
4r-14+7
combine like terms
4r-7
hope this helped :)
General Idea:
When a point or figure on a coordinate plane is moved by sliding it to the right or left or up or down, the movement is called a translation.
Say a point P(x, y) moves up or down ' k ' units, then we can represent that transformation by adding or subtracting respectively 'k' unit to the y-coordinate of the point P.
In the same way if P(x, y) moves right or left ' h ' units, then we can represent that transformation by adding or subtracting respectively 'h' units to the x-coordinate.
P(x, y) becomes
. We need to use ' + ' sign for 'up' or 'right' translation and use ' - ' sign for ' down' or 'left' translation.
Applying the concept:
The point A of Pre-image is (0, 0). And the point A' of image after translation is (5, 2). We can notice that all the points from the pre-image moves 'UP' 2 units and 'RIGHT' 5 units.
Conclusion:
The transformation that maps ABCD onto its image is translation given by (x + 5, y + 2),
In other words, we can say ABCD is translated 5 units RIGHT and 2 units UP to get to A'B'C'D'.