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I think

the number of ways that n identical votes can be distibuted to k people (assuming that each person gets at least one vote =  $$\binom{n+k-1}{n}$$

1.  4 students are running for club president in a club with 50 members. How many different vote counts are possible, if all 50 members are required to vote?

I am going to assume that everyone gets at least 1 vote.

(50+4-1)C50 = 53C50

$${\left({\frac{{\mathtt{53}}{!}}{{\mathtt{50}}{!}{\mathtt{\,\times\,}}({\mathtt{53}}{\mathtt{\,-\,}}{\mathtt{50}}){!}}}\right)} = {\mathtt{23\,426}}$$

2.  4 students are running for club president in a club with 50 members. How many different vote counts are possible, if members may choose not to vote?

I think this assumes that they all get at least 1 vote and at least 1 does not vote at all

(50+5-1)C50 = 54C50

$${\left({\frac{{\mathtt{54}}{!}}{{\mathtt{50}}{!}{\mathtt{\,\times\,}}({\mathtt{54}}{\mathtt{\,-\,}}{\mathtt{50}}){!}}}\right)} = {\mathtt{316\,251}}$$

If some people get no votes it would be higher - does it need to be worked out that way?

Ref:

5x-7=13x+17     subtract 5x, 17 from both sides

-24  = 8x            divide by 8 on both sides

-3 = x

So  ...  6(x - 4) = 6(-3 - 4)  =  6 (-7)  = -42

that was me btw

oopsies

; \definecolor{aopsblue}{rgb}{0,0,0.8}\textcolor{aopsblue}{ \definecolor{aopsblue}{rgb}{0,0,0.8}\textcolor{aopsblue}{\definecolor{aopsblue}{rgb}{1,0,0}\textcolor{aopsblue}{simple, the square root of 25 is 5.}}}

4x-24 is 24 divided by 4=x which is 6

Like Bandinage said there is millions (including decimals)

But if you want to know the difference between them you should've said that.

64 - 99 

64 - 100

100 - 64 =36 - 1 = 35 I think....

Hmmm. I'm not sure why it's still wrong.

Melody could you give me a question similar to this question please? And could you write it in text. So I don't have the urge to copy and paste.  

:D

I was trying a new way.

But in just remembered that $ doesn't effect nothing else words. :)

\sqrt{25}=5.  Is the easier way.

Hold on, I'll work on it for you.   . . . . 

Taking sean1w0ii's answer a little further we see sin(2a) = 10 which is impossible!  sin has to be between the limits of -1 to +1.

This means you don't get "a"!

.

Mellie,  Do you know what the correct answer is?

No anon, i guess you made a mistake   

Hi MG,

Why did you put those dollars signs in your code for?

LOL!!!.....I didn't misprint anything......I just can't see........!!!!

10.851 is correct......

Yeah, MG1.....that makes more sense.....

2cosasina=sin2a 

Yeah, I know you didn't ask a question, it's just that I don't know what other procedures we could follow to get the correct answer

Yes, but only when I get the whole question wrong three times, will I be able to get it OR if I get the question right. I don't know what to do, because if I get it wrong, my report for the week will be very bad :(

d = √[ (5 - 3)^2 + ( -6 - -2)^2 ] =

 √[ (5 - 3)^2 + ( -6 + 2)^2 ]  =

 √[ (2)^2 + ( -4) ^2]  =

√ [ 4 + 16 ]  =

√20 =

√(4 * 5) =

2√5

$$$\sqrt{25}=5$$$

V_cone = (1/3)*pi*r^2*h

Where r is the radius and h is the height.........

Ok then.

$$\\y=8\times \left(\frac{2}{4}-\frac{\frac{6^3}{2}}{15}\right)\\(2 \div 4 =0.5)\\y=8\times \left(0.5-\frac{\frac{6^3}{2}}{15}\right)\\6^3=(6\times6\times\66)=216\\216 \div 2= 108\\y=8\times \left(0.5-7.2\right)\\0.5-7.2=-6.7\\y=8\times-6.7=-41.6\\y=-53.6$$

 Keeping doing dumb mistakes... Meant 53.6 after 8*-6.7

What did i do wrong..?!  I don't know...