Write a linear function $f$ with the values $f(0)=8$ and $\ f(4)=20$ .

f(x) = 3x + 8 is the required linear function.

Step-by-step explanation:

We know that the slope-intercept form of linear equation is

y  = mx+b

here

Given initial value

f(0) = 8

Thus, the y-intercept = b = 8

Also given

at x = 4, f(4) = 20

so

substituting the point (4, 20) and y-intercept b=8 in the slope-intercept form to determine the slope

y = mx+b                        

20 = m(4) + 8

20 = 4m + 8

4m = 20-8

4m = 12

Dividing both sides by 4

m = 3

Thus, the slope = m = 3

Now, substituting m = 3 and b = 8 in the slope-intercept of linear function

y = mx+b

y = 3x + 8

or

f(x) = 3x + 8

Thus,

f(x) = 3x + 8 is the required linear function.

VERIFICATION:

Given the linear function

f(x) = 3x + 8

plug in x = 0

f(0) = 3(0) + 8

f(0) = 8

plug in x = 4

f(x) = 3x + 8

f(4) = 3(4) + 8

f(4) = 12+8

f(4) = 20

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! )

over the argument its not good to fight.