I really need help with this ... I've been stuck for ages even though I thought I was doing it right. Can someone please go through and explain to me (there's a link)...

Step-by-step explanation:

height of water in cylinder (h) =3/4 x 30cm =22.5 cm

diameter (d)  = 12cm            radius = d/2 =12cm /2 =6cm

Volume (V1)=r^2h= 22/7 x (6cm)^2 x 22.5cm =22/7 x 36cm^2 x 22.5cm

                                                                      =2545 cm^3

Diameter = d = 8cm                           radius = r = 8cm/2 =4cm

π =22/7

Volume (V2 )=(4/3) πr^3 = (4/3) π(4cm)^3 = (4/3) x 22/7 x64cm^3 =268cm^3

total volume after the sphere entered =V1 +V2 =(2545 +268)cm^3

                                                                             =2813cm^3

now yoy use the volume formula but make height the subject

V=πr^2h                     h=V/πr^2h =2813cm^3 /(22/7) x (6cm)^2

                                                    =2813cm^3 x 7 /22 x36cm^2

                                                    =19691cm^3  /  792cm^2

                                                    =24.9 cm

therefore the height of the water in the container is 24.9 cm

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! )