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
Answer:
54 seconds
Step-by-step explanation:
Answer:
Step-by-step explanation:
A dilation is something that enlarges or shrinks an existing figure, retaining all angle measures. The two figures will be similar, not congruent.
A dilation of 1/2 (which is less than one) will make a figure smaller. You divide each coordinate point by two
(x, y) → (
)
Infinitely many solutions.
This is a modulus inequality.
First part: when (6x + 2) is positive
6x + 2 < 10
6x < 10 - 2
6x < 8
x < 8/6
x < 4/3
Second part: when (6x + 2) is negative.
-(6x + 2) < 10 Divide both sides of inequality by -1 and change the sign.
(6x + 2) > -10
6x + 2 > -10
6x > -10 - 2
6x > -12 Divide both sides by 6.
x > -12/6
x > -2.
Combined solution: x < 4/3 and x > -2
-2 < x < 4/3.
Graph is a line on the number line between -2 and 4/3.
-2 and 4/3 are excluded from solution.
