Answer:
Event A. P(A) = 1/28
Event B. P(B) = 1/56
Step-by-step explanation:
Event A. We have 3! ways of arranging the juggler, acrobat and pianist and ⁶P₁ ways of arranging the rest of the performers. We ave ⁹P₁ ways of arranging all the performers.
So, P(A) = 3!⁶P₁/⁹P₁ = 3!6!/9! = 3!6!/(9 × 8 × 7 × 6!) = 6/(3 × 8 × 7) = 1/28
Event B. We have ³C₁ ways of combining the violinist, acrobat and comedian in any order and ⁶P₁ ways of arranging the rest of the performers. We ave ⁹P₁ ways of arranging all the performers.
So, P(B) = ³C₁ × ⁶P₁/⁹P₁ = 3!6!/9! = 3 × 6!/(9 × 8 × 7 × 6!) = 3/(3 × 8 × 7) = 1/56
The y intercept occurs when x = 0. Therefore it is -180.
The x-intercepts are the roots of the equation.
x1 = 9
x2 = 4
x3 = 5
The shape of the graph would look approximately like the attached graphic.
Answer:
A. 6x^3 - 24x^2 + 6x + 36.
Step-by-step explanation:
(2x - 6)(3x^2 - 3x - 6)
= 2x(3x^2 - 3x - 6) - 6(3x^2-3x-6)
= 6x^3 - 6x^2 - 12x - 18x^2 + 18x + 36
Simplifying like terms:
= 6x^3 - 24x^2 + 6x + 36 (answer).
