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A hall has n doors. Suppose n people choose any door at random to enter the hall. What is the probability that at least one door will not be chosen by any of the people? My approach was: P(At least 1 door not chosen) =1 - P(All doors chosen) And P(All doors chosen) = n! / n^n (not sure if...

Is there a quick way to evaluate this: Integrate from 0 to pi/2 [ 1 / ( (cos x)^2 + 2(sin x)^2 ) ] otherwise the t formula will take 2 pages to write it all.....

Just wondering if anyone knows or heard from any HSC markers that would we be marked down by not writing converse theorems in the HSC exams. I know my school accepts it when students do not write these converse theorems but I'm not* sure what other schools do. For example, let's say we are...

A point lies on the curve whose equation is x^4 + y^4 = 1. Prove that the distance of P from the origin is at most 2^(1/4). Can anyone help me with this problem? Thanks.

Please help me with this problem =(.......... harder 3u isnt my forte.... p.s. it is attached.

Please help me with this hard finance QNS: A company buys machinery for $500 000 and pays it off by 20 equal 6monthly installments, the first payment being made 6 months after the loan is taken out. If the interest rate is 12% pa, compounded monthly, how much will each installment be? Cheers

An unbiased dice is thrown 6 times. Find the probability that the 6 scores obtained will: a) Have a product which is an even number. b) Consist of exactly two 6's and 4 odd numbers. c) Be such that a 6 occurs only on the last throw and exactly three of the first five throws result in odd...

Hello, I'm having trouble doing 3c)ii). I showed that y could be y = 0 or x^2+y^2 = 1, but I have no clue on how to prove |k|> or < 2. Likewise, for qns 3b).... how do u actually explain |z+2| or arg (z+2) is between those boundaries? Any help will be apprecipated, thx.

How do you do this problem without cylindrical shells: The region bounded between the curves y = x and y = 3x - x^2 is rotated about the y - axis. Find the volume generated by taking slices perpendicular to the axis of rotation (y-axis). Answer is : 8pie/3 units^3.

Find the general solution of the equation cosx + cos2x + cos3x = 0. Can this be done other then using the summation to product formula?

Q. The Region R in the first quadrant such that y < / 4x^2 - x^4 is rotated about the y axis to form a solid of revolution. Use the method of decomposition into cylindrical shells to show the volume is 32 pie /3. (< / = less than or equal to) Hmm, how do you do this question? I keep getting...