All Answers 358105 Answers

I don't know but I will just start an answer thread here.  ( the calc puts the zeros in but the are not needed)

How about

$${{\mathtt{22}}}^{{\mathtt{0.22}}} = {\mathtt{1.973\: \!935\: \!646\: \!137\: \!177\: \!9}}$$

$${{\mathtt{2}}}^{{\mathtt{0.222}}} = {\mathtt{1.166\: \!349\: \!369\: \!788\: \!467\: \!3}}$$

$${{\mathtt{2}}}^{\left({\mathtt{0.2}}{\mathtt{\,\times\,}}\left({\mathtt{0.2}}{\mathtt{\,\times\,}}\left({\mathtt{0.2}}\right)\right)\right)} = {\mathtt{1.005\: \!560\: \!580\: \!398\: \!468\: \!2}}$$

$${{\mathtt{0.2}}}^{\left({\mathtt{0.2}}{\mathtt{\,\times\,}}\left({\mathtt{0.2}}{\mathtt{\,\times\,}}\left({\mathtt{0.2}}\right)\right)\right)} = {\mathtt{0.987\: \!207\: \!031\: \!388\: \!177\: \!8}}$$

$${{\left({\left({\mathtt{0.2}}{\mathtt{\,\times\,}}\left({\mathtt{0.2}}\right)\right)}^{{\mathtt{0.2}}}\right)}}^{{\mathtt{0.2}}} = {\mathtt{0.879\: \!189\: \!311\: \!540\: \!889\: \!8}}$$

Well my answers are getting smaller     

$$\\4(a+6)\ge 5(a+3)\\
4a+24\ge 5a+15\\
4a+24-5a\ge 5a+15-5a\\
24-1a\ge 15\\
24-1a-24\ge 15-24\\
-a\ge -9\\
a\le9\qquad $I multiplied both sides by -1 so I had to turn the inequality around$$$

Thank you!

I am sorry Awsomeee, what I was telling you before was not quite right  

29/289z<16/161z

$$\\\frac{29z}{289}<\frac{16z}{161}\\\\
\frac{29z}{289}-\frac{16z}{161}<0\\\\
z\left(\frac{29}{289}-\frac{16}{161}\right)<0\\\\
z\left(\frac{45}{46529}\right)<0\\\\
$This will only be true if $
z<0$$

Turn 2 1/3 into an improper fraction.  It becomes 7/3.   

Turn 4 1/3 into an improper fraction.  It becomes 13/3.

The ratio of the two numbers is (2 1/3) divided by (4 1/3).  This ratio is the same if we multiply top and bottom by 3, to get 3*(2 1/3) divided by 3*(4 1/3).  

This is 3*(7/3) divided by 3*(13/3). 

The 3's cancel on the top, leaving 7,  and they cancel on the bottom, leaving 13. So the ratio is 7/13.  

The missing number at the start is therefore 13.

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Thanks Heureka   

Here is a vey interesting you tube clip on FRACTALS

You can do them on any calculator.  A fraction sign is the same as  divide. :)

sorry but can you show me in more depth I still don't get it

$$2\frac{1}{3} \text{ is to }4\frac{1}{3}\text{ as }7 \text{ is to x}\\\\
\text{Multiply the first two numbers by 3 to get}\\\\
7 \text{ is to } 13 \text{ as } 7 \text{ is to x}\\\\
\text{So it's now clear what x is!}$$

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Okay I get the same answer too but my explanation is a little different again.

I'm going to put spy1 in row 1 that is 4 ways

spy2 i row 2 that is 3 ways

spy3 in row 3 that is 2 ways

spy 4 in row 4 that is 1 way       so so far I have  4*3*2*1 = 4!   Just like CPhill.

Now there are 4P4 or 4! permutations for the order that the spys can be chosen in.

So the number of ways is 4!*4! = 576       

I would not have thought to do it that way.  Thanks Alan  

If you want the volume of the pyramid it is given by (1/3)*area of base*height = (1/3)*10^2*5 mm³ ≈ 166.7 mm³

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it is not possible to do so . sorry i can;t make it larger more

Your image is very small kes! Can you replace it with one a little larger?

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1. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you. Example: Calculate the square root of 10 ( ) to 2 decimal places. 1. Find the two perfect squarenumbers it lies between.

Use the key that looks like √x  or type in sqrt and put your number in the parentheses (then press Enter of the = key).

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If sin(angle) = 0.857 then angle = sin^-1(0.857).  This can be done on the calculator using asin(0.857) as asin is the same thing as sin^-1

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Wilson's theorem says that, if p is a prime number, then (p-1)! = -1mod(p)

However, I haven't been able to see how to use it to prove that 36*27! + 25 is divisible by 31.

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Put it diagonally in a 1mx1m package?

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I get the same answer as Alan....but with a slightly different explanation...

The first spy can sit in any of the first four "vertical" benches . The next spy has three vertical benches to choose from. The third spy has two and the last one has one. That's 4 x 3 x 2 x 1 = 4! ways = 24 ways. But, once seated, we can also arrange these vertical columns in 4! ways.....so....4! x 4!  = 24 x 24 = 576.