All Answers 359195 Answers

$$\\F=\frac{G*M_1*M_2}{d^2}\\\\
$Make G the subject$\\\\
G=\frac{F*d^2}{M_1*M_2}\\\\$$

Zac is correct but if you are a little kid it might be confusing.

83 - [59 - (22 - 18)]

Just do the brackets on the inside and work outwards from there.

22-18=4    so it becomes

83 - [59 - 4]

59-4=55    so it becomes

83-55

and you can finish it :)

I understand it now, thanks a lot Alan =)

Let b =initial number of blue tiles and w = initial number of white tiles.

Initially

b/w = 5/9  or b = 5w/9   (1)

After

(b+9)/(w-9) = 13/15  or 15(b+9) = 13(w-9)    (2)

Using (1) in (2)

15(5w/9 + 9) = 13(w - 9)

15*5*w/9 + 15*9 = 13*w - 13*9

25w/3 + 135 = 13w - 117

Multiply through by 3

25w + 405 = 39w - 351

39w - 25w = 405 + 351

14w = 756

w = 756/14 = 54

Put this back into (1)

b = 5*54/9 = 30

Hence total number of tiles: b + w = 30 + 54 = 84

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The state of the Markov chain after a time t depends on the initial state.  The occupancy of state 0 after time t is its initial occupancy (1/3) multiplied by the sum of the probabilities of the transitions to and from that state from the other states (the first column of P(t)).

Notice that the sum of the terms in the first column of P(t) given in the answer to part 4 is divided by 3 (i.e. multiplied by 1/3).

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Yeah it does thanks Alan. What's still causing some confusion for me is what is the point of mentioning that the initial distribution for the markov chain is (1/3 , 1/3, 1/3)?

Does this help?

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These are the answers provided by my lecturer but yes I also think it's a typo and should be -3 rather than 3, forgot to mention that! 

My problem is just the fundamentals, how does the calculation for P(0.1) look like? Once I see it I can make sense of it (I hope)

Are you sure the answer given for part 1 is correct?  Looks to me like the 3 on the bottom line of Q should be -3.

If you then calculate P(0.1) you get the numbers in the first column in part 4 the same as given in the answer.

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What kind of hatred do you have towards anons, Titanium?

A loonie is a Canadian one-dollar coin.

A toonie is a Canadian two-dollar coin.

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Let the cursor hover over the log button.  You will see a mini menu appear on which is ln (log to the base e).

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This is an example of applying the minus sign to everything enclosed in the respective brackets.

-(22 - 18) can also be written as -1*(22-18).

83 - [59 - (22 - 18)]

83 -59 +(22 - 18)

83 -59 +22 -18

I think you can do the rest :)

8(9s+15)=6(4s-4)

$$\small{\text{$
\begin{array}{rcl}
8(9s+15) &=& 6(4s-4) \\
8\cdot 9s+8\cdot 15 &=& 6\cdot 4s - 6\cdot 4 \\
72s + 120 &=& 24s - 24 \quad | \quad - 24s\\
72s-24s + 120 &=& -24 \\
48s +120 &=& - 24 \\
48s +120 &=& - 24 \quad | \quad - 120\\
48s &=& - 24- 120\\
48s &=& -144\\
48s &=& -144 \quad | \quad :48\\\\
s & =& -\dfrac{144}{48} \\\\
\mathbf{s} & \mathbf{=} &\mathbf{ - 3 }
\end{array}
$}}\\\\\\\\
\small{\text{$\mathbf{check:}
\begin{array}{rcl}
8\cdot [9(-3)+15] &=& 6\cdot [4(-3)-4]\\
8\cdot (-27+15) &=& 6\cdot (-12-4)\\
8\cdot (-12) &=& 6\cdot (-16) \\
-96 &=& -96 \qquad \mathrm{okay}
\end{array}
$}}$$

What is the slope of the line through the points (-2, -5) and (1, -7)

The formula of a line is y=mx+b

and m is the slop.

We have point 1 with x = -2 and y = -5 ... so we have   -5 = m*(-2) + b  or -5 = -2m+b

We have point 2 with x = 1 and y = -7... so we have      -7 = m*(1) + b   or -7= m+b

Now we subtract the equation 2 of the equation 1:        -7 -(-5) = m+b - (-2m+b)

so we have  -7+5 = m+b+2m-b

or  -2 = 3m

and the slope m  is $$\small{\text{$-\dfrac{2}{3}$}}$$ 

Hey, I’m your friendly neighborhood troll. I charge a fair fare to cross my bridge, (most cats and dogs cross tollfree). I rarely throw anyone in the river because they can’t pay the fair. I do throw them in if they have CDD. That’s to prevent them from contaminating the kingdom. I have responsibilities and I take them seriously. I even jump in myself when I have a flare up :)

i really need to start thinking which role anyone will play in a good vs evil situation

ok

maybe zegroes......hes always the serious one, especially serious about his hatred of roses

im not a spy, im the op man..........i even have back up proof in pixel gun 3d

I don't know about that.

Nauseated is funny but he is not ususally too friendly.  Do you think he is into infiltration?

I think he may be too caustic for that :/

a spy is more like Nauseated's job

my job isnt to be like james bond

my job is to be liam neeson

im just glad i finally beated my #1 enemy of the forums

ANOTHER SONIA MIRACLE!!!!!!

the next crowing achievement of Titanium Rome's career at web2.0calc.com is here!

whats next!?

YES befriend you enemy - Then you can know what he is up to and be one step in front of him.

That is what spies do.  But I don't really think that you should be a spy :)

i dont think he did

but if itll make you stop complaining, then ill thumbs it up