Answer:
The answer is
<h2>

</h2>
Step-by-step explanation:
The slope of a line given two points can be found by using the formula

where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-4, 2) and (6, 8)
The slope is

We have the final answer as

Hope this helps you
Answer:
Mean=50.
standard deviation=50.
Step-by-step explanation:
Let the perfect score be 100.
The mean(average) of a data is given by: 
Here the number of data points are 100. out of which 50 attains a value 100,and 50 attains value 0.
so, sum of data points=50×100+50×0=5000.

Mean=50.
"Now the standard deviation of data points are calculated by firstly subtracting mean from every entry and then square the number and take it as new entry and calculate the mean of the new data entry and lastly taking the square root of this new mean".
Here if 50 is subtracted from each entry the new entry will have 50 entries as '50' and 50 entries as '-50'.
next on squaring we will have all the 100 entries as '2500'.
now the mean of these entries is: 
=2500
taking it's squareroot we have 
Hence, standard deviation=50.
i. The Lagrangian is

with critical points whenever



- If
, then
. - If
, then
. - Either value of
found above requires that either
or
, so we get the same critical points as in the previous two cases.
We have
,
,
, and
, so
has a minimum value of 9 and a maximum value of 182.25.
ii. The Lagrangian is

with critical points whenever
(because we assume
)



- If
, then
. - If
, then
, and with
we have
.
We have
,
,
, and
. So
has a maximum value of 61 and a minimum value of -60.
Answer:
20 in²
Step-by-step explanation:
Assuming that the width of the sign is x, then from the question, we're told that the length is 5 times it's width, so
b = x inches
l = 5x inches
Again, we're told that the perimeter of the sign is 24 inches, and we know already that the perimeter of a rectangle is given as
Perimeter = 2(l + b), substituting this, we have
24 = 2(5x + x)
24 = 10x + 2x
24 = 12x
x = 24 / 12
x = 2 inches.
Since x is the width of the rectangle, and it's 2 inches, we use it to find the length of the sign.
l = 5 * 2
l = 10 inches.
Then, we are asked to find the area of the sign. Area of a rectangle is given as
A = l * b, so if we substitute, we have
Area = 10 * 2
Area = 20 square inches
Answer is I'm the attachment hope it helps!!