reinout-g

It is common for the letter i to be used for the complex part.

This means $$i^2 = -1$$

If you enter i in the calculator, it will act like the complex variable.

Depends... what would he have had for lunch? 

Okay let me rephrase this to

$$A = P(1+r)^n$$

where A = 9750, r = 0.05 and n = 7

Then we can rewrite this to $$P = \frac{A}{(1+r)^n}$$

filling in the variables gives $${\mathtt{P}} = {\frac{{\mathtt{9\,750}}}{\left({{\mathtt{1.05}}}^{{\mathtt{7}}}\right)}} \Rightarrow {\mathtt{P}} = {\mathtt{6\,929.142\: \!968\: \!768\: \!685\: \!314\: \!7}}$$

I think you mean $$\frac{(4x)^3}{(-4x)^3}$$ instead of $$\frac{(4x)^3}{(-4x)3 }$$

This gives;

$$\frac{(4x)^3}{(-1*4x)^3 } = \frac{(4x)^3}{(-1)^3 (4x)^3 } = \frac{1}{-1} = -1$$ for $$x \neq 0$$

It is time for a new logic puzzle!!

It took me a while to solve this one, but eventually I found the answer.

There's a street with 5 houses with 5 different colors in a row. Each house has a owner with a different nationality, each owner drinks a certain type of beverage, smokes a certain brand of cigar and has a certain pet. All owners have a different pet, type of cigar or drink. There are 15 hints given:

1. The Brit lives in the red house. 
2. The Swede keeps dogs as pets. 
3. The Dane drinks tea. 
4. The green house is on the immediate left of the white house. 
5. The green house's owner drinks coffee. 
6. The owner who smokes Pall Mall rears birds. 
7. The owner of the yellow house smokes Dunhill. 
8. The owner living in the center house drinks milk. 
9. The Norwegian lives in the first house. 
10. The owner who smokes Blends lives next to the one who keeps cats. 
11. The owner who keeps the horse lives next to the one who smokes Dunhill. 
12. The owner who smokes Bluemasters drinks beer. 
13. The German smokes Prince. 
14. The Norwegian lives next to the blue house. 
15. The owner who smokes Blends lives next to the one who drinks water. 

Find out who owns the fish...

Reinout

Nice job Anonymous!

You are the very first one to correctly answer the coaches, athletes problem!

Why don't you sign up so we can identify your inner genius more often!

Reinout

Here is an update on the probability puzzles!
-------------------------------------------------------------------------------------------------------------------------------------- 
Easier one: 

The fabulous game host Steve offer you a bag with 5001 pearls of which 2501 are white and 2500 are black. He asks you to draw as many pearls from the bag as you desire without looking. Steve then tells you how many black and white pearls you drew. If there are equally as much white as black pearls in the draw you gain €10 for each pearl you drew. How many pearls should you draw?

-------------------------------------------------------------------------------------------------------------------------------------- 
Hard one (still unanswered): 

You and your best friend have been arrested for several white collar crimes. (Or something else which is more classy than stealing a candy bar) 
Your attorney has told you the police has only got enough evidence to put you and your friend behind bars for 3 years. 
However, the both of you are given the option to confess. If both of you confess you will both serve 10 years, 
if one of you confesses and the other does not, the one who did not confess will serve 20 years. 
Obviously, if you both remain silent you will both serve 3 years. 
You are not allowed to have any communication with your friend. 
Suppose your main priority is to keep yourself out of jail, and your secondary priority is to keep your partner out of jail. 
You have decided that you find it twice as important to keep yourself out of jail as you find it important to keep your partner out of jail. 
(So for example, in your opinion him serving 10 years is equal to you serving 5). 
You estimate the chance of your partner confessing p. 
For which values of p will you choose to confess and for which values will you keep silent? 

HINT: make a formula for the amount of suffering you expect, also taking the suffering for your friends jailtime into account.

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

Reinout-g 

No really, I have no idea what you want me to do.

There is no way you can expand this other than writing out the number e, which makes no sense.

2.707785173e+34 

2 . 7 0 7 7 8 5 1 7 3 e + 3 4 

2  .  7  0  7  7  8  5  1  7  3  e  +  3  4  

2   .   7   0   7   7   8   5   1   7   3   e   +   3   4  

2    .    7    0    7    7    8    5    1    7    3    e    +    3    4   

2     .     7     0     7     7     8     5     1     7     3     e     +     3     4   

2      .      7      0      7      7      8      5      1      7      3      e      +      3      4  

http://web2.0calc.com/questions/tgx-cosx-1-sinx_1