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So you use the formula?

Total  number  =

120 [  1-  r^n]  / [ 1 - 1.10]    where  r  =1.10    and n  = 7

120   [  1 - 1.10^7  ] /  [ 1  -1.10]   ≈   1138  people

b) four members are running for president in a society with 50 members. how many different vote counts are possible, if each of the members vote for one of the four candidates, or can choose to abstain?

Just count abstain as a 5th candidate.

I am not claiming to be positive but I think 

a) four members are running for president in a society with 50 members. how many different vote counts are possible, if each of the members vote for one of the four candidates?

50 stars, 3bars (to seperate into 4 bundles)        53C3 =23426

Find an inequality that relates the sength of the altitudes in a triangle (you may have to consider area and side lengths.

Be careful because if Alonzo doesn't get the ball on the seventh throw, then he may or may not get it on the sixth throw and so on. 

[100 / 73]^(1 /5) = 6.4965 % - Growth rate per year compounded yearly.

Yes, It's correct!

Guest- 

Can you at least try to make it easy for us to read????

For how many positive integers $n\geq 2$ is $1001_n$ a prime number? 

What does n/geq even mean?????

If you fix your question, I will help you out.

P    Q     R    S       T 

QS   = 10

PS  = 19

So

PS - QS  =  PQ

19   -10   =   9  =  PQ

So   QR    =   9

So

PQ + QR  =  PR  =  1/2  of PT

9 +  9   =   18  =  PR  = 1/2 of PT

So PT  =36

PS - PR   = RS

19  - 18  =  1  = RS

So

PQ  + QR  + RS  +  ST   =  PT

PS  +  ST   =   36

19 + ST  = 36

17  =  ST

We have that

(n - 1)^2  + n^2 +  ( n + 1)^2   = 29

n^2  - 2n  + 1  +  n^2  + n^2 +2n +1   =  29      simplify

3n^2  +  2   = 29

3n^2  = 27

n^2 =  9

n = 3

So....the three integers are    2, 3 and 4

And their sum  =   9

You are correct guest....I miscalculated the  number of integers from 10-99  in my first answer

My corrected answer agrees with yours....!!!!

Sorry Cphill: My short computer code says it is "3" of the beginning of 370:
n=1234567891011..........3603613623633643653663673683693;s=0;p=0;cycle: s=s+(n%10);p=p+1;n=int(n/10);if(n!=0, goto cycle,0);print"Total Sum =",s;print"Total Num =",p
OUTPUT:
1234567891011........603613623633643653663673683693

Total Sum = 3738
Total Num = 1000

If we can limit the cables that we must try, then the question becomes much easier. Think of a way to limit the values that we must try and better relate the 'unknown' properties (an equation).

To have infinite solutions ...... let the first equation  be a multiple of 2  of the second equation

So   2  [ 2x + y  =  b]    =   4x   +  2y   = 2b 

a =  2     and    2b = -8   so    b  = -4

So

(a,b)   =  (2, -4)

First, fix the orientation of the two reds in order to not overcount (this is because rotations come into play when the one color isn't fixed. Then, consider how to place the last three pairs of colors.

Call the roots  A, B, C, D

A + B + C + D =   7

BCD +  ACD  +  ABD  +  ABC   =   -7

ABCD   =  -2

So....we have....

1                1                1                1

___  +    _____    +   _____    +   _____   =

 A              B                 C                D

BCD  +  ACD   +   ABD    +   ABC

______________________________   =   

             ABCD

              -7

          _____  =        3.5

              -2

 If PAD is  is an  equilateral triangle with side length 6, then  each edge of the pyramid must have a length of 6

So....the sum of the lengths of the edges  =   6 * 6  =  36 units

There are 4^8 ways of passing the ball, without any restrictions.  After 7 passes, there are 3*4^6 ways the ball could go back to Alonzo (which is not allowed for 8 passes, because the people must be different), so for 8 passes, the number of ways is 4^8 - 3*4^6 = 53248.

1 - 9  =   puts us at the 9th digit

10- 99  = two digits for each integer * 90  integers   =  90*2  =  180 digits

This puts us at  189  digits

So....we need to solve this  where n is the number of integers after 99

189  +  3n   =  1000

3n  = 1000 - 189

3n   =  811

n = 270 + 1/3

So  the  integer  we  are   looking for is the  1st digit of  the 271st integer after  99  =

99  + 271  =   370

So....the 1000th digit is    3

Also consider that that Alonzo couldn't have had the ball at the seventh pass (based on the second to last sentence).

thank you! how did you get the answer so fast though? i was unsucessfully guessing and checking for a long time :'(

thank you! :)

Draw a circle of the people and label around the circle the letters A,B,C,D, and E (to easily keep track).

We also know that eight passes were completed, and that each person has 6 choices. Find the total.

Hint: What makes the question seem hard is the big numbers. Try a few examples that are smaller like gcd(2!+1,3!), gcd(3!+1,4!), gcd(4!+1,5!), etc.

Then, try to find a way to generalize this.

When you see such a problem, think about your how relate the factors of the numbers and the definitions of the numbers.