Maria has purchased a basic stained glass kit for $100. She plans to make stained glass suncatchers and sell them. She estimates that the materials for making each suncatcher will cost $13. Model this situation
with a rational function that gives the average cost of a stained glass suncatcher when the cost of the kit
is included in the calculation. Use the graph of the function to determine the minimum number of
suncatchers that brings the average cost below $22.50.
The minimum number of suncatchers that brings the average cost below
$22.50 is

Step-by-step explanation:

fixed cost = 100

variable cost = 13

soooo....

cost =  (13x + 100)/x

the questions wants to know  when cost  < 22.50

22.5 > (13x+100)/x

look at graph attached ;)

it looks to me like it's at 11

22.5 > (13(11) + 100) / 11

22.5 > 22.09

try 10

22.5 > (13(10) +100)/10

22.5  > 23   not true  so yes.. 11 is when the cost goes below 22.50

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )