Answer:

Step-by-step explanation:
Let points D, E and F have coordinates
and 
1. Midpoint M of segment DF has coordinates

2. Midpoint N of segment EF has coordinates

3. By the triangle midline theorem, midline MN is parallel to the side DE of the triangle DEF, then points M and N are endpoints of the midsegment for DEF that is parallel to DE.
Answer:
e^-1.6094 = 0.2
Step-by-step explanation:
The inverse of In is e
If In 0.2 = -1.6094
Then e^-1.6094 = 0.2
Answer:
The 90% confidence interval for the mean score of all takers of this test is between 59.92 and 64.08. The lower end is 59.92, and the upper end is 64.08.
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 62 - 2.08 = 59.92
The upper end of the interval is the sample mean added to M. So it is 62 + 2.08 = 64.08.
The 90% confidence interval for the mean score of all takers of this test is between 59.92 and 64.08. The lower end is 59.92, and the upper end is 64.08.
Answer:
The profit function is:

The maximum value is 406, 300 occurring when x = 640.
Step-by-step explanation:
The revenue function is:

And the cost function is:

Then the total profit function will be:

This is a quadratic function.
Therefore, the maximum value of the total profit will occur at its vertex point.
The vertex of a quadratic is given by:

In this case, a = -1, b = 1280, and c = -3300.
Then the point at which the maximum profit occurs is at:

And the maximum profit will be:

Answer:
x=9
Step-by-step explanation:
10x - 11 -4x = 43
6x -11 =43
6x = 54
x=9