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Factorials come into play only when repetition is not allowed, hence the 'reduce by one before multiplying' effect. Putting the first coin into box A doesn't prevent you from also putting the second coin into that box, so repetition is definitely allowed. In any case, the first choice is 'which...

Yes the question was for you. y=f(x^2) has the same symmetry properties as y=f(|x|). However it is squashed unevenly in the horizontal direction. Points that were originally at x=4 are now at x=2 and x=-2. Points that were originally at x=25 are now at x=5 and x=-5.

Re: HSC 2015 4U Marathon So kind of like series and parallel electric circuits? I'm getting (1-p)² - (1-p)⁵.

Nup, there are no factorials or perms/combs here. If the coins and the boxes are both distinguishable, then each coin has 4 possibilities, each leading to a different result. So the number of cases if we allow a box to be empty is 4¹⁰. If we want at least one coin in each box, we have to...

Toss a coin into each box, as each box must have at least one coin. That leaves 6 coins to distribute amongst 4 boxes, where we are now free to place no coins in a box. Place the 6 coins in a line, and place 3 dividers somewhere in the line. Possibilities are: 00|00|0|0 meaning the first 2...

The answer is 9C3. Not sure at the moment what it would be if the boxes were identical, but definitely not 9P3 - it has to be LESS than 9C3.

Re: HSC 2015 4U Marathon So what's the difference between three connected roads and one long road made up of three segments? I'm still missing something here.

I still have only ten fingers and one head, so I guess I'm a pre-mutation.

Re: Plane travels at a speed of 240km/h when there's no wind. Today there's wind velo You asked this before, and it was moved because it doesn't belong in this thread. Same answer as before: You mean the initial VELOCITY vector, not position vector. Edit: Looks like they've merged the...

Re: HSC 2015 4U Marathon I'm afraid I can't picture what you are describing. Surely if three roads start from here, then each 'connect' again at the destination, then you only need one road to get there. And these roads that aren't connected ... do they just end in a cul-de-sac? I don't know...

From the stats that are published after every HSC. These particular numbers are from the 2011 stats, but the larger subjects are pretty much the same every year.

So ... testing your understanding ... if f(x) = √x, what does the graph of y=f(-|x|) look like?

Re: HSC 2015 4U Marathon Connected to what?

You don't have to do well in it (compared to others) in order to get a good ATAR. Here is the (approximate) percentage of the state you must beat in each of the courses you mentioned, in order to get a mark equivalent to a 99 ATAR. In brackets is the percentage of the state you must beat in...

Schools do NOT submit ranks. They submit MARKS.

How do teachers detect plagarism? In the same way a hacker is the best person to write anti-virus software ... they've been there done that.

Don't you mean 'find the initial VELOCITY vector' ?

Re: HSC 2015 3U Marathon I answered the wrong question for (IV). It should be 1-(1/2)⁵ = 31/32. But again ... I don't know why people insist on using perms and combs for a straightforward 2 unit question. The only way of getting an odd product is if every number is odd. That is 1/2 for each...

Re: HSC 2015 3U Marathon (I) 5/6 × 4/6 × 3/6 × 2/6 = 5/54 (II) They have to be different, where the missing number is 1 or 6, ie. 1/3 of previous answer = 5/162 (III) P(1,1,1,2,3) = (1/6)⁵ [for getting precisely those numbers in that order] × 5C2 ways of picking the position of 2 and 3...

Re: HSC 2015 3U Marathon I've been trying to generalise this to n² matches and n boxes, with the same restriction, but I can't get a finite form. Any suggestions?