CPhill

In 2007  ....... "t".would equal 22 in your formula.....so we have

P = .56.61*1.1^22  = about 461 thousand performances in 2007

The percent drop is given by :

 ( [22 - 9.3] / 22  * 100 ) %  = about 57.72 %

(a) 

N  = N₀ (1.014)^t    where N₀  is the initial population, t is in years and N is the population after t years

(b)

2N₀  =N₀ (1.014)^t     divide through by N₀

2  = (1.014)^t        take the log of both sides

log 2  = log (1.014)^t    and by a log property we can write

log 2  = t * log (1.014)     divide both sides by log(1.014)

log 2 / log 1.014    = t  = about 49.85 yrs = 50 yrs

(c)  If it doubles again, it is 4 times the original number, i.e., 4N₀....and we can solve this :

log 4 / log 1.014  = t = about 99.71 yrs = 100 yrs

So......it takes about 50 years to double again

Part (c) was edited for an original mistake......!!!!!!

The perimeter is given by  :

2(30 - 10) + (3/4)pi(30 + 10)   =  about 134.25 in

The area is given by

(1/2)(3/4)(pi) (30^2  - 10^2)  = about 942.48 in²

We first need to find the number in the intersection of the Venn Diagram [ the number owning both].....this is given by

(Number owning H and C)  =   (Number owning H) + (Number owning C) - (Number owning H or C)

(Number owning H and C)  =          150                   +       180                    -        230

=  100

Here's the Diagram.......

b.  P(H but not C) =  50 / 250   = 1/5 = 20%       [ remember that 20 people fall "outside" the circles ]

c.  P( H and C)  = 100 / 250   = 2/5   = 40%

d. P (Neither)  = 20 / 250   = 2/25  = 8%

e. P(H but not C) =   same as b     ....... P(C but not H) = 80 / 250  = 8/25  = 32%

Hang in there.....this is a little difficult to grasp.....!!!!!

Rosala.....you know that I always love your funny posts......!!!!

Go ahead and post some more pics......they are always good.....!!!!!

Look at my revised first answer......I realize that I made a mistake with the Venn Diagram....!!!

To answer your other questions, we have

P (Humanities  but not Economics)  = 10%   [ this is just the "10" in the left circle]

P (Neither)  = [100 - (10 + 20 + 28)] / 100  =  [100 - 58] /100  =    42/ 100 = 42%  [this would be everyone falling "outside" the circles and their intersection ]

P (Exactly one of the courses)  = [ 10 + 28] / 100   =  38 / 100   = 38%   [this is the sum of the two values  in the circles, but not in the intersection]

Could you post some particular problems that are giving you trouble ????

Let's just say that there are 100 students.........it won't make any difference in the end.......

1. Here's the Venn Diagram : 

2.  P(H or E)  = P(H) + P(E)  - P(H and E)   =  30 + 48  - 20   =  58%  [ 58 students out of 100 ]

Agree with Guest.......you start off with z and x, but then, you have the equation  z = cyⁿ

(?????)