Melody

thanks Shockfish,

I alwasy like playing with these, I hope you don't mind.

Jack rolls 5 fair six-sided dice. What is the probability that at least two dice show the same number?

What is the prob that they are all different

1*5/6*4/6*3/6*2/6 = 5! / 6^4 = 120 / 1296 = 5/54

So the prob that they are NOT all different is     1 - 5/54  =    49/54

\(\frac{(2x^2 + 3x - 5)}{x(x^2 - 1)}= \frac{A}{x} + \frac{B}{(x - 1)} + \frac{C}{(x + 1)}\\ \frac{(2x^2 + 3x - 5)}{x(x^2 - 1)}= \frac{A(x - 1)(x + 1)}{x(x - 1)(x + 1)} + \frac{Bx(x + 1)}{(x - 1)(x + 1)x} + \frac{C(x - 1)x}{(x + 1)(x - 1)x}\\ \frac{2x^2 + 3x - 5}{x(x^2 - 1)}= \frac{A(x - 1)(x + 1)+Bx(x + 1)+C(x - 1)x}{x(x - 1)(x + 1)} \\ \)

Now expand and equate coefficients

LaTex:

\frac{(2x^2 + 3x - 5)}{x(x^2 - 1)}= \frac{A}{x} + \frac{B}{(x - 1)} + \frac{C}{(x + 1)}\\
\frac{(2x^2 + 3x - 5)}{x(x^2 - 1)}= \frac{A(x - 1)(x + 1)}{x(x - 1)(x + 1)} + \frac{Bx(x + 1)}{(x - 1)(x + 1)x} + \frac{C(x - 1)x}{(x + 1)(x - 1)x}\\
\frac{2x^2 + 3x - 5}{x(x^2 - 1)}= \frac{A(x - 1)(x + 1)+Bx(x + 1)+C(x - 1)x}{x(x - 1)(x + 1)} \\

Are you for real?

\(123_7=1*7^2+2*7^1+3*1\)

Use this knowledge to answer your own question.

Is this what you mean?

Sorry BuilderBoi.  :)

oh if you have a free geogebra account you can save you pics online.

For posting all of my pics I used Gyazo.  It is like an onle version of 'Snip'

Gyazo has a free and a paid version.  They are the same except the paid version lets you store as many pics as you want but the free one stores only the most recent few.  I am not sure how many becasue I have the paid version.

I do not think Gyazo is the best online storage of pics, I expect there are many to chose from. This forum saves in Tinypics I think if you use the provided one.  But i used to find the link to tinypics was often broken, so Gyazo has been a better for me.  

Hi BilderBoi,

Thanks!

I use a free program called GeoGebra.  It takes a while to get the hang of, just do simple things to start and your knowledge will build. 

Here is a download page.  I didn't know that there were all these ones to choose from.  I just use Classic 6.

I don't think there used to be so many when i dowloaded mine.  ://

ABCDE is NOT a regular pentagon so your logic is incorrect.

Equal chords are subtended from equal angles. at the centre

We have 4 equilateral triangles.  

together that make an angles at the centre of  4*60 = 240degrees

The angle at the centre remaining for the last tirangle is 120 degrees.

The Apothem for the 4 congruent trianlges is   sqrt3

So their total area is  4sqrt3

The last triangle is isosceles with angles 120, 30,30

The length of the base is 2sqrt3 and the height is 1 so ther area is    sqrt3

So the total area is  5sqrt3 units     (which agrees with asin's answer.)

Here is the pic