Assume 3 in every 1000 students at a local community college have quit due to serious health issues. an insurance company offers them an $8000 policy for $50 a year. what is the amount the insurance company should expect to make on average on every student that pays?

if 3 for every 1000 students quit due serious health issues, then you can see the proportion doing the quotient between this numbers. This is:

3/1000 = 0.003

Then if you choose a random student, you have a 0.003 probability of choosing one who can have a health issue.

and a 0.997 probability to choose a student with no health issues.

Now, the company wins  $50 for the healthy students, and lose ($50 - $8000)  = -$7950 for each student that is sick (because they initially pay the 50$ and latter get the $8000).

Then the insurance company should expect to make in average:

0.997*$50 - 0.003*($7950) = $26

So the company should expect to make 26 dollars per student in a year.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this