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A container contains 20 lollies of 3 types (5 black, 5 white and 10 clear). Ben Bob and Peter decides to choose 5 lollies each, Ben would only choose the lollies that has an opposite colour to what peter chooses ( i.e. Ben would only choose white if Peter chooses black and vice versa ) unless...

7c) Prove that for any positive integer m, [2m+1]/[2m+4] <= sqr.root [(3m-2)/(3m+1)] Hence deduce that (1/2)(5/8)(7/10).....(2n+1/2n+4) <= 1/sqrroot(3n+1) also 8bi) Show that r+1/r-1 = 1 + 2/r + 2/r^2 + 2/r^3 + ..... + 2/r^n + 2/r^(n+1) ii) show that sum of...

1997 4u maths 6a) The serues 1-x^2+x^4-.....+x^4n has 2n+1 terms i) Explain why 1-x^2+x^4-.....+x^4n = [1+x^(4n+2)]/[1+x^2] ii) Hence show that 1/[1+x^2] <= 1-x^2+x^4-......+x^4n <= 1/[1+x^2] + x^(4n+2) iii) Hence show that, if 0<=y<=1, then inv.tan y <= y - (y^3)/3 +...

Further questions 8 1.Show that (lx+my+nz)²≤(l²+m²+n²)(x²+y²+z²) Deduce that (a) (a+b+c)²≤3(a²+b²+c²) (b) (a³+b³+c³)≤(a²+b²+c²)(a^4+b^4+c^4) 2. If a>0, b>0, c>0 and d>0, show that 16/(a+b+c+d)≤3/(b+c+d) + 3/(a+c+d) + 3/(a+b+d) + 3/(a+b+c)≤1/a + 1/b +1/c + 1/d if any1 can post...

A fair coin is to be tossed repeatedly. For integers r and s, not both zero, let P(r,s) be the probability that a total of r heads are tossed before a total of s tails are tossedso that P(0,1) = 1 and P(1,0) = 0. (i) Explain why, for r, s≥1, P(r,s)=½P(r-1,s)+½P(r,s-1). (ii)Find...

The probability that n accidents occur at a given intersection during a year is P(n)= e^(-2.6) x [(2.6)^n]/n! (i) Find the probability that no accidents occur at the intersection in a given year. Give your answer correct to three dec. places. (ii) What is the probability...

In a game, two players take turns at drawing, and immediately replacing, a marble from a bag containing two green and three red marbles. The game is won by player A drawing a green marble, or player B drawing a red marble. Player A draws first. Find the probability that: (i) A wins on her...

one of the bio pracs ask u to demonstrate the effect of ph, temp and substrate on an enzyme......does any1 kno wat a junket tablet does?.....i forgot wat effect it has on milk. Thx

2003 HSC Q7cii) ok i need help on this question....here it goes.... 7(c) Suppse that α is a real number with 0 < α < pi. Let P(n)= cos(α/2) cos(α/4) cos(α/8)...cos(α/2^n) (i) Show that P(n) sin(α/2^n) = 1/2 P(n-1) sin(α/2^n-1) (ok i did this part)...