Answer:
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- <u><em>Event A: 1/35</em></u>
- <u><em>Event B: 1/840</em></u>
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Explanation:
<u>Event A</u>
For the event A, the order of the first 4 acts does not matter.
The number of different four acts taken from a set of seven acts, when the order does not matter, is calculated using the concept of combinations.
Thus, the number of ways that the first <em>four acts</em> can be scheduled is:


And<em> the number of ways that four acts is the singer, the juggler, the guitarist, and the violinist, in any order</em>, is 1: C(4,4).
Therefore the<em> probability of Event A</em> is:

Event B
Now the order matters. The difference between combinations and permutations is ordering. When the order matters you need to use permutations.
The number of ways in which <em>four acts </em>can be scheculed when the order matters is:


The number of ways <em>the comedian is first, the guitarist is second, the dancer is third, and the juggler is fourth</em> is 1: P(4,4)
Therefore, <em>the probability of Event B</em> is:

Answer:
18
Step-by-step explanation:
6 x 3 = 18
pretty sure it’s 108 because each angle of a pentagon is 108
Well, luckily it is apparent that (x-1) is a root because when x=1 the equation is equal to zero. So we can divide the equation by that factor to find the other roots.
(2x^3+9x^2+4x-15)/(x-1)
2x^2 r 11x^2+4x-15
11x r 15x-15
15 r 0
(x-1)(2x^2+11x+15)=0
(x-1)(2x^2+6x+5x+15)=0
(x-1)(2x(x+3)+5(x+3))=0
(x-1)(2x+5)(x+3)=0
So the roots are x= -3, -2.5, 1