A) 5 to be chosen among a Total : 10 Men + 8 Women
¹⁸C₅ = (18!)/(5!)(13!) = 8,568 groups of five
b) A must to have men and women. If so we have to deduct all groups of 5 that are all men and all group of 5 that are all women
Groups of 5 with only men: ¹⁰C₅ = 252
Groups of 5 with only women: ⁸C₅ = 56
So number of committees of 5 men and women mixed =
8568 - 252 - 56 = 8,260 committees
c) 3 Women and 2 Men:
⁸C₃ x ¹⁰C₂ = 2,520 groups of 3 W and 2 M
d) More women than men, it means:
3 W + 2 M OR (we have found it in c) = 2,520)
4 W + 1 M OR ⁸C₄ x ¹⁰C₁ →→→→ = 700
5 W + 0 M OR ⁸C₅ x ¹⁰C₀ →→→→ = 56
Total where W>M = 3,276 groups of 5 where women are at least 3
You have to complete the square to get it into vertex form. Do this by setting the function equal to zero and at the same time moving the constant over to the other side of the equals sign so you have this:
. Now we can complete the square on the polynomial by taking half the linear term, squaring it, and adding it to both sides. Our linear term is 4. Half of 4 is 2, and 2 squared is 4, so we add 4 to both sides:
and simplify to get
. In this process we have created a perfect square binomial on the left, which happens to be
. Now move the -6 back over by addition to get
. The vertex is found at (-2, 6), the third choice down.
Answer:
F(x) =-4(x+3)+5= - 4x-12+5= - 4x-7
Step-by-step explanation:
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Answer:
1/6
Step-by-step explanation:
Harry 1x1/2=1/2
Jacqueline 1/2x1/2=1/4
Stanley 1/3x1/4=1/12
1-1/2-1/4-1/12=
12/12-6/12-3/12-1/12=
2/12 or 1/6
