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Autumn would be 9 months ago.  It's autumn right now.

Yes nauseated is correct.   If one is wrong another one has to be wrong.

There you go Happy, you are in good company - we are all  'stupid'  

OH except for nauseated of course - he is just nauseating.    LOL 

The probability that he gets exactly one incorrect?

IT IS ZERO he can't get just one incorrect. If one wrong check is in an envelope then the other envelope has a wrong check too. 

Happy7's dumbness is contagious!

There are 24 possiible arrangements.......

Let's look at the possible arrangements with  cheque 1 going into envelope 1.

So we have

1 2 3 4

1 2 4 3

1 3 2 4

1 3 4 2

1 4 2 3

1 4 3 2

Note that only 2 of these have cheque 1 going into  envelope 1 and all the others the wrong ones. These would be 1 3 4 2  and 1 4 2 3. So, that is 1/3 of the possible arrangements where  cheque 1 goes into envelope 1.

And every other arrangement (2nd check in 2nd envelope, etc.) would have the sme probabilty.

So, the answer - I think - is 1/3.......

4*1/4*2/3*1/2*1=1/3  Maybe 

I said the prob that the first one is right is 1/4

The prob that the 2nd is wrong is 2/3

The prob that the 3rd is wrong is 1/2

The prob  that the last one is wrong is 1

BUT

it could be the 1st or 2nd or 3rd or 4th that is right so i multiplied by 4

I won't guarantee that it is correct but it sounds ok to me. :)

Look here

0.007 rounded.

There is a calc on the home page. 

1/30?  My brain just isn't working.  I need to eat

This one seems difficult...but it's not that hard.....

If we unroll the cylinder we have a rectangle that is 48cm high and 16cm wide. And the string would extend from one bottom edge of the rectangle to the opposite top corner. Thus, the string is the hypoteneuse of a right triangle with legs of 48 and 16. And the string's length is given by.....

√(48^2 + 16^2) = √2560 ≈ 50.6 cm

I think that's it ......???

Sorry that's wrong. Think about it more carefully.

I believe that would be 1/16.  I just woke up, so don't blame me if I'm wrong.

If you key in a decimal...it will give you a fraction.....

20-3x=2(4x-2)+7x   OK...let's simplify this...so we have....

20 - 3x = 8x - 4 + 7x      combine like terms

20 - 3x  = 15x - 4           the idea is to get all the x's on one side amd everything else on the other

Add 3x to both sides and add 4 to both sides.....this gives...

24 = 18x       divide both sides by 18

24/18  =    reduce the fraction

4/3 = x

Does that help???

Post an example that might be giving you trouble.....

When I evaluated (9  + √80)^(1/3) and (9 - √80)^(1/3), I immediately saw that these were related to Phi and phi.....

....but note.....(9 + √80)^(1/3) = (Phi)2  where Phi = (1 + √5)/2 

Christ Chris, What archive did you dig that out of !

This one is tricky.....but note.....(9 + 4√5)^(1/3) = (Phi)²  where Phi = (1 + √5)/2

And (9 -4√5)^(1/3) = phi² = Phi ^-2 where Phi ^-1  = phi = 2/(1 + √5)

So we have

Phi ² + Phi ^-2   =

Phi ² + phi ²       and by a property of Phi and phi......Phi² = 1 + Phi   and phi² = 1 - phi ... so we have

(1 + Phi)  + (1 - phi) =

2 + Phi - phi            and by another property of Phi and phi.....Phi - phi = 1    so we have

2 + 1 = 3

Look here