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4 is ur answerrrrrrr

Starting at 1 there is probability 1/2 that it moves to 0 in 1 step.  There is probability 1/2² that it moves to 0 in 3 steps (1 → 2 → 1 → 0).  There is probability 1/ 2³ that it moves to 0 in 5 steps (1 → 2 → 1 → 2 → 1 → 0), etc.  

The expected number of steps is therefore t₁ = 1/2 + 3/2² +  5/2³ + ...  or 

$$t_1=\sum_{k=1}^\infty\frac{2k-1}{2^k}=3$$

Starting at 2 it takes 1 step to 1 from where the expected number of steps is 3 as obtained above, so t₂ = 1+3 or t₂ = 4

So the ordered pair is (t₁, t₂) =  (3, 4)

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ok thanks Alan :)

I do not understand what i am being asked to do :/

The circumference is just pi*diameter, so if the diameter is 20ft the circumference is 20pi ft.

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What you got is a rip-off.

$${\mathtt{20}}{\mathtt{\,\small\textbf+\,}}{\mathtt{20}}{\mathtt{\,\small\textbf+\,}}{\mathtt{40}}{\mathtt{\,\small\textbf+\,}}{\mathtt{10}}{\mathtt{\,\small\textbf+\,}}{\mathtt{30}}{\mathtt{\,\small\textbf+\,}}{\mathtt{30}}{\mathtt{\,\small\textbf+\,}}{\mathtt{20}}{\mathtt{\,\small\textbf+\,}}{\mathtt{20}}{\mathtt{\,\small\textbf+\,}}{\mathtt{30}}{\mathtt{\,\small\textbf+\,}}{\mathtt{10}}{\mathtt{\,\small\textbf+\,}}{\mathtt{20}} = {\mathtt{250}}$$

$${\frac{{\mathtt{100\,000}}}{{\mathtt{3}}}} = {\mathtt{33\,333.333\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

You can't take the square root of a negative value (not while dealing with real numbers, anyway), so what is the first integer bigger than pi?

Here's a picture to help:

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^ They explain it all...

Yeah, it's so relieving and you feel so good once you've solved and incredibly hard maths question (of course one that is appropriate). Gets rid of all the stress.

agreed. math is fun. i may not get it some topics, but i enjoy it 2!

claps 2 u, MathsGod... claps 2 u

The answer is

=x^2 - 2x - 8x +16

=x^2 - 10x + 16

Hah, yay!?

Well Melody, they should. lol

Yes it's me ... Ros.....al.a?

I just used MathCad to work out your expression Melody.  

Well you could read the old posts I guess.

I put one or two of them in the wrap I think :)

omg that is wht im stressing about

A point  is chosen at random in the interior of equilateral triangle . What is the probability that  has a greater area than each of  and ?

Thanks Alan that makes sense.   

How did you work out my expression?

There is 1 ace of spades and there are 12 face cards.  The other 39 cards are irrelevant!  So this reduces to the probability of choosing the ace of spades first out of a pack of 13.  This probability is just 1/13.

As it happens, Melody, your complicated expression evaluates to 1/13.

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I got it, it is 1/13. i lost the solution.

There are 22 possible ways of ending up where he started after 6 steps.  11 of them where his first step is in a clockwise direction and another 11 where his first step is in an anti-clockwise direction.  The direction of each step is chosen with probability 1/2, so overall probability = 22*(1/2)⁶ ≈ 0.34375

If we number the vertices as 0 1 2 3 4 5, where 0 is the initial vertex, then the following list shows the 11 routes from 0 back to 0 in which the first step goes to vertex 1 (the other 11 are obtained by interchanging the 1s and 5s and interchanging the 2s and 4s).

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