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Well Alan, at least you have some reasoning.  I think that beats my guess     LOL.  

Area = (pi/4)*diameter^2

Ok.Thanks

cos(x + y) = cos(x)*cos(y) - sin(x)*sin(y)

so  cos(pi/3  + A) = cos(pi/3)*cos(A) - sin(pi/3)*sin(A)

cos(pi/3) = 1/2  and sin(pi/3) = sqrt(3)/2      These are standard values that are worth remembering.

Hence cos(pi/3 + A)  = (1/2)cos(A) - (sqrt(3)/2)sin(A)

Multiply by the 2 to get 2cos(pi/3 + A) = cos(A) - sqrt(3)sin(A)

Yes,ALAN you are right.

Please prove it

I think you must mean 2*cos(pi/3 + A) which is cos(A) - sqrt(3)*sin(A)

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My reasoning is as follows:

However, since it's a question of probabilities, I don't guarantee that my reasoning is correct!!

why 50% ? :D

Note that the result of  (3.538^1)/3 is as guest #1 specified.  

Technically, guest #1 is correct; however, I suspect that this interpretation is not what the questioner meant!

According to the calculator on the home page it is:

.

Can't see an analytical solution. Numerical result is seen below:

.

Rounded: 

1.18

Not Rounded:

1.1793333333333

Solveit asked me to look at this question.

I saw it when it was first posted and I wasn't really sure.   I am still not sure.

I'd guess the answer is 50%    That seems logical to me .......

Would anyone like to comment?  

\(A_{circle}=\pi r^2\\ d_{circle}=2r\)

\(d_{circle}=2r\\ r=\frac d2\\ A_{circle}=\pi \times (\frac{d}{2})^2\\ A_{circle}=\pi \times \frac{d^2}{4} \)

Thnx Emily, c u 2 tomorrow!   And goodnight! 

MMM       CM             XC                    IX               -

M                       CC                XXX               IV

-------------------------------------------------------------

MM       (M-CCC)    (C-XXXX)         (X-I) -(IIII)

MM     ( DD-CCC)     (LL-XXXX)           V

MM         DCC                LX                   V

MMDCCLXV

LOL, HSC     !!!!!!!

I'm going to assume that the growth function is p(x) =  3(2)^x    and that the predatory function is

s(x) = 2^x + 4

The population after three weeks  is just p(3) - s(3)  =

3(2)^3  - [2^3 + 4]  =

24 - [ 12]  =   

12

MMM       CM             XC                    IX               +

M                       CC                XXX               IV

-------------------------------------------------------------

MMMM    CM    CC   XC        XXX     IX      IV                  

MMMM      M       C     C           XX     iX       IIII

MMMMM                CC              XX      X       III

MMMMMCCXXXIII

\(\bar VCCXXXIII\)

I just lined them up and did it a bit like algebra then I took the minus units away from the plus units etc.  

It was an interesting exercise that I had not done before. 

The square root of two is already in its simplest form, if you need an approxmation just punch it into your calculator.

Don't know what you mean by this table of probability. 

Precalculus is a form of torture developed and honed for decades to be used by cruel men and women who enjoy to see those they teach squirm having to radicalize and other obnoxious things that will end in Calculus. Push on my friend!

Just so you would have to learn to spell another word in addition to the word "calculus"

WollframAlpha actually is capable of performing these operations.....I suppose there are some algorithms that one could learn, but....I'm not sure it would be worth the trouble to remember them !!!

Just for fun...here is the answer to the third one :

B TW...the last one can't be represented by a Roman Numeral....it produces a decimal approximation