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Right on, Bertie.....

The people who say that maths is boring are usually the people who don't understand/can't do maths.

The boring response is a defense mechanism. They don't want to say that they don't understand the subject, so rather than admit that, they either try to belittle it or say that it's boring.  

Just come in on this conversation, here's my take on it.

First method: First ball can go into any of the three boxes, second ball can go into any of the three boxes etc, total number of arrangements is 3*3*3*3*3*3 = 729.

Second method: All six b***s could go into a single box, or they could be split five in one box and one in another, or they could be split 4 - 2 - 0, or 4 -1 -1 and so on, seven possible splits.

The number of possibilities for each split as follows.

6 - 0 - 0: 3 ways of doing this, (the 6 can be in any one of the three boxes).

5 - 1 - 0: 36 ways. There are 6 possible orders for the 5-1-0, and 6 possible choices for the odd ball.

4 - 2 - 0: 90 ways. Again 6 possible orders and 6C2=15 choices for the 2.

4 - 1 - 1: 90 ways. 6 possible orders, (3 possibilities for the 4, but double this because the two 1's are different), then 6C4=15 choices for the 4.

3 - 3 - 0: 60 ways. 3 possible orders (positions for the 0), and 6C3=20 choices for either 3.

3 - 2 - 1: 360 ways. 6 possible orders, 6 choices for the 1 and 5C2=10 coices for the 2 or 3.

2 - 2 - 2: 90 ways. 6C2=15 choices for the first 2, 4C2=6 choices for the second 2.

Total = 3 + 36 + 90 + 90 + 60 + 360 + 90 = 729. 

2 pints  = 1 quart

4 quarts = 1 gallon

Therefore

8 pints = 1 gallon

4 is a factor of 8, so......8 is the LCM

well, does 3^2+5^2 equal 6^2 ?

Annaliese has a mutual fund that compounds annually at 3.5% per annum. Her principal was $750 and her current balance is $954.21. How many years has she had this fund?

r=0.035,         FV=954.21,       P=750       n=?

$$\\FV=P(1+r)^n\\\\
954.21=750(1.035)^n\\\\
\frac{954.21}{750}=1.035^n\\\\
log\;\frac{954.21}{750}=log\;1.035^n\\\\
log\;\frac{954.21}{750}=n\;log\;1.035\\\\
n=\frac{log\;\frac{954.21}{750}}{log\;1.035}\\\\$$

n= $${\frac{{log}_{10}\left({\frac{{\mathtt{954.21}}}{{\mathtt{750}}}}\right)}{{log}_{10}\left({\mathtt{1.035}}\right)}} = {\mathtt{7.000\: \!016\: \!844\: \!029\: \!362\: \!8}}$$

7 years.

NOTE:   If you have not done logs yet then perhaps you were supposed to just keep multiplying $750 by 1.035 and see how many times you had to do that before you got a total of $954.21

It should be 7 times.  :)

That is because   1-2m    would have to equal 0.

They are almost all anon questions and most are answered.

If you think members get a better deal, and they certainly should do, you can become a member.

AND

If you think this is the best way to get your question answered then you must be a totally illogical person an hence you will never acheive at mathematics anyway.

Hi Nauseated,

If all 6 b***s are different and all 3 boxes are different   3^6=729  certainly sounds correct.

this is the answer that I had given for this scenario

The solutions to this quadratic may be expressed as:

$$\\x_+=\frac{1-2m+\sqrt{6m^2+m+4}}{2m+3}\\\\x_-=\frac{1-2m-\sqrt{6m^2+m+4}}{2m+3}$$

There are an infinite number of values of m that have one root negative and one root positive.  However, if you are looking for the value of m that makes one root the negative of the other, then that is clearly m = 1/2.

.

@@ End of Day Wrap    Mon 23/3/15   Sydney, Australia    Time 8:50 pm   ♪ ♫

Hi everyone,

Great answers from Alan, CPhill, gibsonj338, Geno3141, Mathrulz, Heureka and Hipbanana.  Thanks you :)

Interest posts:

Translation from Turkish

Tues 24/3/15

kar gördüm kaydım kaymaz olaydım

sana bir söz vermiştim ley ben o sözden caydım

If you're talking about visible stars.......there seems to be no consensus.....

Here's an article that might be of interest......

Thanks Alan, I will really have to think about this one.  

$$\\(Z-\frac{7}{3})(-z-\frac{5}{12})=(2z-\frac{27}{15})\\\\
$I'm going to multiply both sides by 180$\\\\
3(Z-\frac{7}{3})*60(-z-\frac{5}{12})=180(2z-\frac{27}{15})\\\\
(3z-7)(-60z-25)=360z-324\\\\
(3z-7)(60z+25)=324-360z\\\\
180z^2+75z-420z-175=324-360z\\\\
180z^2-345z+360z-175-324=0\\\\
180z^2+15z-499=0\\\\$$

Now finish it with the quadratic formula.

$${\mathtt{180}}{\mathtt{\,\times\,}}{{\mathtt{z}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{z}}{\mathtt{\,-\,}}{\mathtt{499}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{z}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{39\,945}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}}\right)}{{\mathtt{120}}}}\\
{\mathtt{z}} = {\frac{\left({\sqrt{{\mathtt{39\,945}}}}{\mathtt{\,-\,}}{\mathtt{5}}\right)}{{\mathtt{120}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{z}} = -{\mathtt{1.707\: \!187\: \!105\: \!848\: \!766\: \!1}}\\
{\mathtt{z}} = {\mathtt{1.623\: \!853\: \!772\: \!515\: \!432\: \!8}}\\
\end{array} \right\}$$

Rough explanation of where the expression in b comes from:

I should have noted that w_k goes to w(x)dx in passing from the discrete to the continuous (so "mass" goes to "mass per unit length"*"(infinitesimal) length"; with "mass per unit length" being "density").

.

thanx  

thanx heureka

If I completely factored -4x^3+24x^2-36x would the answer be -4x(x-3)^2   ?

$$-4x^3+24x^2-36x \\
= -4x \cdot (x^2-6x+9) \\
= -4x \cdot (x-3)\cdot (x-3) \\
= -4x \cdot (x-3)^2 \\
= (-4)\cdot x \cdot (x-3)\cdot (x-3)$$

How about putting the middle step in. 

I want to just check it in my head and i don't want to make any mistakes.