Answer:

The general formula for the margin of error is given by:

And for this case the width is:

And if we decrease the confidence level from 95% to 90% then the critical value
would decrease and in effect the width for this new confidence interval decreases.
As confidence level decreases, the interval width decreases
Step-by-step explanation:
For this cae we know that the sample size selected is n =41
And we have a confidence interva for the true mean of foot length for students at a college selected.
The confidence interval is given by this formula:

And for this case the 95% confidence interval is given by: (21.71,25.09)
A point of etimate for the true mean is given by:

And the margin of error would be:

The general formula for the margin of error is given by:

And for this case the width is:

And if we decrease the confidence level from 95% to 90% then the critical value
would decrease and in effect the width for this new confidence interval decreases.
As confidence level decreases, the interval width decreases
Classwork:
Given
and
, we have
(1) 
Using the composition found in (1), we have
(2) 
(3) 
Using the composition found in (3),
(4) 
Homework:
Now if
, we would have
(1) 
For (2), we could explicitly find
then evaluate it at <em>x</em> = -1 like we did in the classwork section, but we don't need to.
(2) 
(3) We can demonstrate that both methods work here:
• by using the result from (1),

• by evaluating the inner function at <em>x</em> = 2 first,

not sure how the first two pictures apply here, since they're just a single circle.
check the picture below.
the one on the left can have 3 common tangent lines, the one on the right, only two common ones.
Answer18:
The quadrilateral ABCD is not a parallelogram
Answer19:
The quadrilateral ABCD is a parallelogram
Step-by-step explanation:
For question 18:
Given that vertices of a quadrilateral are A(-4,-1), B(-4,6), C(2,6) and D(2,-4)
The slope of a line is given m=
Now,
The slope of a line AB:
m=
m=
m=
The slope is 90 degree
The slope of a line BC:
m=
m=
m=
The slope is zero degree
The slope of a line CD:
m=
m=
m=
The slope is 90 degree
The slope of a line DA:
m=
m=
m=
m=
The slope of the only line AB and CD are the same.
Thus, The quadrilateral ABCD is not a parallelogram
For question 19:
Given that vertices of a quadrilateral are A(-2,3), B(3,2), C(2,-1) and D(-3,0)
The slope of a line is given m=
Now,
The slope of a line AB:
m=
m=
m=
The slope of a line BC:
m=
m=
m=
m=3
The slope of a line CD:
m=
m=
m=
The slope of a line DA:
m=
m=
m=3
The slope of the line AB and CD are the same
The slope of the line BC and DA are the same
Thus, The quadrilateral ABCD is a parallelogram