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The gamma function is a sort of continuous version of the factorial function.  

When n is an integer then Γ(n) = (n-1)!

But Γ(n) is also defined for non-integer values of n.

.

0+50*1-60-60*0+10

=0+50-60-0+10

=50-60+10

=0

Ok thanks Alan.

That gamma function.  I know I have seen it before but could you refresh my memory please?

Π is the Greek upper case letter, pi, and stands for the product (analogous to Σ for the sum).

. 

Thanks,

I don't know that symbol Alan, I thought that there must be one to do that job.

What is the symbol called?   :/ [I am talking about the first formula]

Gamma function ?  mmm.....

Possibly as:

$$\prod_{n=2}^K(2n-1)$$

or as:

$$\frac{2^{K+1}\Gamma(K+\frac{1}{2})}{2\sqrt{\pi}}$$

where Γ() is the Gamma function

$$\Gamma (t)=\int_0^{\infty}x^{t-1}e^{-x}dx$$

.

a + 9 = 8[a - (2 - a)]

a + 9 = 8[a - 2 + a]

a + 9 = 8[2a - 2]

a + 9 = 16a - 16

25 = 15a

a = 25/15 → 5/3 → 1.666...

.

Now I have a new question.  

2K people can be paired off in   3*5*7*......*(2K-1)   ways

How can I write this as a formula?

Look Bertie, Alan and Chris, I did it my way and I got the same answer as Bertie and Chris!      WOW!!

I know my way is no where near as sensible as Chris's way but I learned heaps doing it this way

4 people

There are 3 ways to pair up 4 people, if the order of the pairs counts then this would be 3*2*2 = 12 ways

For instance   AB CD could also be AB DC, BA CD, or BA CD      

They can then be put in a circle 12*(2-1) = 12 ways

So 4 people can be paired off and THEN placed in a circle 12 ways

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

6 people

There are 3*5 ways to pair up 6 people, if the order of the pairs counts then this would be 15*2^3 = 120 ways

Now they can be placed in a circle   120*2! = 240

So 6 people can be paired off and THEN placed in a circle 240 ways

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

8 people

There are 3*5*7=105 ways to pair up 8 people, if the order of the pairs counts then this would be 105*2^4 = 1680 ways

Now they can be placed in a circle   1680*3! = 240

So 8 people can be paired off and THEN placed in a circle 10080 ways         @@  BINGO  @@

Okay I am just starting to get somewhere.

I am looking at how many ways even numbers of people can be paired off

This post is NOT directly related to the question above.

4 people   ABC and D

AB CD

AC BD

AD BC

that is 4 people can be paired off in 3 ways

Now, before I wanted to do it as 4C2 which is 6

This would give the 6 above but each time you get one pair you automatically get the another pair so it can be seen that this will be too big by a factor of 2   so it is   4C2/2 = 6/2=3

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6 People

Now I am going to look at 6 people  A B C D E and  F

AB    there  are four more so they can be paired up 3 ways

AC    3 ways

AD    3 ways

AE     3 ways

AF     3 ways

Total = 3*5 =15

So 6 people can be paired off  15 ways.   This is  (6-1)(4C2)/2  = 15

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

8 People

Now I am going to look at 8 people  A B C D E F G and H

AB   then 6 more =  15 ways

AC   then 6 more =  15 ways

AD   then 6 more =  15 ways

AE   then 6 more =  15 ways

AF   then 6 more =  15 ways

AG   then 6 more =  15 ways

AH  then 6 more =  15 ways

That is a total of  7*15=105    (8-1)(6-1)4C2/2 = 7*5*3

that is 8 people can be paired off in 105 ways

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So   2K people can be paired off in   3*5*7*......*(2K-1)   ways

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So   4 people are paired (and the pairs are then considered as 1)

they are then put clockwise into a cirlce (or anticlockwise)  rotations are considered the same.

The number of ways this could be done is  4*1=4 ways

6 people - it could  be done   5*3*2! = 30 ways

8 people - it could be done  7*5*3*3! = 1050 ways

2K people - it could be done  (2k-1)(2k-3)....5*3*(k-1)!

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I made an error is my first post so I have done it again

$$\\\frac{(x+1)}{(2x-2)}-\frac{(x-1)}{(2x+2)}-\frac{(4x)}{(x^2-1)}+\frac{(x^2+1)}{(x^2-1)}=\frac{x-1}{x+1}$$

$$\\LHS=\frac{(x+1)}{2(x-1)}-\frac{(x-1)}{2(x+1)}+\frac{(x^2+1)}{(x^2-1)}-\frac{(4x)}{(x^2-1)}\\\\
LHS=\frac{(x+1)^2}{2(x-1)(x+1)}-\frac{(x-1)^2}{2(x+1)(x-1)}+\frac{(x^2+1)-4x}{(x^2-1)}\\\\
LHS=\frac{(x+1)^2-(x-1)^2}{2(x-1)(x+1)}+\frac{x^2+1-4x}{(x-1)(x+1)}\\\\
LHS=\frac{(x^2+2x+1)-(x^2-2x+1)}{2(x-1)(x+1)}+\frac{x^2-4x+1}{(x-1)(x+1)}\\\\
LHS=\frac{4x}{2(x-1)(x+1)}+\frac{x^2-4x+1}{(x-1)(x+1)}\\\\
LHS=\frac{2x}{(x-1)(x+1)}+\frac{x^2-4x+1}{(x-1)(x+1)}\\\\
LHS=\frac{2x+x^2-4x+1}{(x-1)(x+1)}\\\\
LHS=\frac{x^2-2x+1}{(x-1)(x+1)}\\\\
LHS=\frac{(x-1)(x-1)}{(x-1)(x+1)}\\\\
LHS=\frac{x-1}{x+1}\\\\
LHS =RHS$$

incorrect answer of xxx1xxx2xxx0xxxs

the correct answer is 0

x=0

y=2

you guys are incorrectives as pneumonoultramicroscopicsilicvolcanoconiosisincorrectivemaker

the perfect answer is

cos(2a-1)-cos(a+1)=0

x^2-9x-36=0 is the answer people.

the only thing that you guys do is make up answers and get them incorrectly as a duphus gubers

incorrect answers you got there.

its 60 miles per hour is how much miles there is in 300 miles in 5 hours

25

this is the right answer for the easiest question ever

and i can think any math questions in my brain

////////////////////////////////////////

How many digits?

From the numbers from 1 through 9, there are 9 digits.

From the numbers from 10 through 99, there are 90 numbers of 2 digits each = 180 digits.

From the numbers from 100 through 999, there are 900 numbers of 3 digits each = 2700 digits.

Total number of digits:  9 + 180 + 2700  =  2889 digits.

How many 7s?

From 000 to 099 there are 10 7s in the one's place and 10 7s in the ten's place = 20 sevens.

There will be 20 sevens in each of the regions 100-199, 200-299, ... 900-999 = 20 x 9 = 180 sevens.

But, in the region 700 - 799, there are 100 7s in the hundred's place.

Total of 300 7s. 

So, the probability of getting a 7:  300/2889

If all the digits from 000 through 999 were used (this includes more zeros than actually printed but won't change the sum), there would be 300 1s, 300 2s, 300 3s, ..., 300 9s.

300(0) + 300(1) + 300(2) + 300(3) + 300(4) + 300(5) + 300(6) + 300(7) + 300(8) + 300(9)  =  13,500

HELLO???? 

IT'S SOOO EMPTY 

I HAVE NOOOOOOO IDEA!!!!!

SORRY I CAN'T HELP

Let x be the number.

"twelve decreased by twice a number"   --->   12 - 2x

"8 times the sum of number and 4"   --->   8(x + 4)

12 - 2x  =  8(x + 4)

12 - 2x  =  8x + 32                    (distributive property)

12        =  10x + 32                   (add 2x to both sides)

-20       =  10x                           (subtract 32 from both sides)

x  =  -2                                      (divide both sides by 10)

8,000,000 / 20,000,000,000  =  0.0004

To turn 0.0004 into a percentage, multiply by 100   --->   0.04%

3cot(x) + 1  =  4

--->   3cot(x)  =  3

--->     cot(x)  =  1

If cot(x) = a/b, then tan(x) = b/a

--->   tan(x) = 1

--->         x  =  tan^-1(1)

--->         x  =  45^o ± n·180°