All Answers 358156 Answers

No, because the radius and circumference aren't the same thing.

You can usually put it in by putting paranthesis around the fraction. Use the division button as you bar between your denominator and numerator. For instance if you want to enter the fraction 1/3 then you would enter (1/3) into your calculator.

Yes of course - that did not occur to me.  Thanks Alan.

2+2=5

or just 4

Good point

"Divide 225 by 3 to get rid of the exponent. "

There is no exponent here.  An exponent is a power.

The rest of the answer is pretty good though.

Although, it better to leave the answer exact.

Divide 225 by 3 to get rid of the exponent.

W*F  dimension of math is this from?

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!
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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?

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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.

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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  

Nice use of the Math (input=result) GoldenLeaf

or better still, leave it as (this is exact - the other is an approximation) 

$$75\pi x$$

0.1 is the answer!

Examples:

$${{log}}_{{\mathtt{2}}}{\left({\mathtt{64}}\right)} = {\mathtt{6}}$$  because 2⁶ = 64

$${{log}}_{{\mathtt{2}}}{\left({\mathtt{10}}\right)} = {\mathtt{3.321\: \!928\: \!094\: \!887\: \!362\: \!6}}$$  because 2^3.321928... = 10

On the scientific calculator on the Home page here, if you hover the cursor over the log key, the lg2 key will appear.  In the Math(Input=Result) window type log(x,2) to get the log to the base 2 of x.

Use the Pythagoras theorem:

$$hypotenuse=\sqrt{adjacent^2+opposite^2}$$

4x²+40x+100 = 4(x² + 10x +25) = 4(x+5)², so for this to be zero x must be -5.

Ok CreeperCosmo, except that you should have used the word "volume" where you have "area".

It's also worth noting that, in general, you need to consider the shape of the individual blocks as well as their volume.  For example, suppose each block was 12" by 1" by (1/2)".  The individual volume is still 6 cubic inches, so the volume ratio would still suggest you could get 36 of them in the box.  However, because of their shape you wouldn't even get one in the box.  

The volume ratio tells you the maximum conceivable number that can go in the box, but you need to take into account the shape of the individual pieces to decide how many will actually fit.  

In the case of the original question here, the shapes stack nicely to fill the box completely.

Hmm! The notation used in the question suggests that the first term is a=6 and the geometric progression ratio is r=-3.

If this is the case then the sequence goes

a = 6

ar = -18

ar² = 54

ar³ = -162

GoldenLeaf's approach was almost right, but he should have had 5, 4, 3, 2 and 1 in the numerators.

There are 5 possible choices for the first number, so probability of this is 5/40.  For each of these

there are 4 possible choices for the 2nd number, so probability of both 1st and 2nd is (5/40)*(4/39).  For each of these ... etc. to get the overall probability as

$${\mathtt{p}} = \left({\frac{{\mathtt{5}}}{{\mathtt{40}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{4}}}{{\mathtt{39}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{3}}}{{\mathtt{38}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{2}}}{{\mathtt{37}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{36}}}}\right) \Rightarrow {\mathtt{p}} = {\mathtt{0.000\: \!001\: \!519\: \!738\: \!361\: \!8}}$$

or p≈1.52*10^-6  

1/p = 658008

This question is usually asked with two different nouns.

The first is: If a tree falls in the forest, and there is no one around to hear, does it make a sound?

The second is: If a tree falls in the forest, and there is no one around to hear, does it make a noise?

The questions have philosophical elements; but in this form, it is semantics.

The first is a physical process. Sound is a form of energy and the presents of an intelligent entity with auditory sensors are not required for a sound to occur. Doest light from a sun ceases to exist because no one is seeing it?

The second is an interpretation of sound. Noise is a subjective interpretation. What is noise to one may be music to another. Heavy metal is an example of this: to one it is music to another it is noise.

The Heavy metal sounds coming from a junk yard may be noise to local neighbors but metaphorical music to the owners because that noise represents profit.

The answer to the second question is NO. Without intelligence there cannot be an interpretation of the sound.

Just a semantically inspired thought while looking for a forest through the trees. Did you hear that?

@@ End of Day Wrap - Wed 7/5/14   Sydney, Australia Time 19:45

Hello everyone,

It is midweek and the questions came in thick and fast.  Some great answers were provided by GoldenLeaf,Foxtears, NothingLikeHmework, Rom, awesomeatmath, lebron, Alan, Bobtyford, CreeperCosmo, problem and reinout-g. Thank you everyone. 

I think all the member questions have been answered.  Not all answers have been checked and not all answerers have received the points to which I think they are entitled.  I will put more effort into this tonight.  Sorry.  Sometimes there just is not enough hours in the day.  

Many answerers put more effort into newer questions.  This may be a little unfair but the logic is that if your question has been sitting there for a long time you may well have figured it out by some other means, so it may be less relevant.   If your question has fallen off the first page you can repost if you want to.  Remember, members will always get priority and it is simple and free to become a member.

Reinout-g updated our puzzle pages last night.  Thankyou reinout-g.  I noticed that CreeperCosmo has already answered 2 of the puzzles.  This is great,  I don't think that I have given you credit (and points) for them yet but I will.  

Here is a difficult one that some people might be interested in;

http://web2.0calc.com/questions/solve-for-x_4#r104171

I think that is it.  Thankyou all.

Melody.  

The range for the first 6 days is 29-16=13   

If the seventh day has a 'score' of 2 then the new range is 29-2=27

27-13=14

12% of 4.115.267 is

493,832.04

Many Your welcomes.