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11Alexandr11 [23.1K]
3 years ago
10

the drama club is holding auditions for 5 different parts in a one-act play. if 9 people audition, how many ways can the roles b

e assigned?
Mathematics
1 answer:
makkiz [27]3 years ago
3 0

Answer:

The roles can be assigned in 15120 ways.

Step-by-step explanation:

The parts, which means that the order in which the people are selected is important. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

P_{(n,x)} = \frac{n!}{(n-x)!}

In this question:

5 people chosen from a set of 9. So

P_{(9,5)} = \frac{9!}{(9-5)!} = 15120

The roles can be assigned in 15120 ways.

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4
taurus [48]

Answer:

x^2 - 2x + 10, option B

Step-by-step explanation:

Complex numbers:

The most important relation that involves complex numbers is given by:

i^2 = -1

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this question:

The solutions are:

x_1 = 1 - 3i, x_2 = 1 + 3i

We have to find the polynomial. All option have a = 1. So

(x - (1 - 3i))(x - (1 + 3i)) = x^2 - x(1 + 3i) - x(1 - 3i) + (1 - 3i)(1 + 3i) = x^2 - x -3ix - x + 3ix + 1^2 - (3i^2) = x^2 - 2x + 1 - 9i^2 = x^2 - 2x + 1 - 9(-1) = x^2 - 2x + 10

The correct answer is given by option b.

6 0
3 years ago
At a surf shop in Malibu, California, a used blue surfboard is on sale for $100. According to the salesperson, the new price rep
Leokris [45]

Answer:

$125

Step-by-step explanation:

if there was a discount of 20%, the sales price is 100 - 20 = 80% of the original price

let a = original price

this equation can be used to represent the question

a x 0.8 = 100 ]]divide both sides by 0.8

a = 100 / 0.8 = 125

4 0
2 years ago
Can someone help me with this?
tatiyna
Yes because PROPORTIONAL means the lines start on the axis which is the zero and it also has to be in a even line so yes it is proportional
6 0
3 years ago
You are paid $7.25/hour. You work 40 hours/week for 2 weeks. Your involuntary deductions are FICA (7.65%), federal withholding (
Vedmedyk [2.9K]

Answer:

$413.83

Step-by-step explanation:

Your earnings for the two weeks are

7.25(40)(2) = 580

The deductions for FICA will be

0.0765(580) = 44.37

The deductions for federal withholding will be

0.14(580) = 81.2

The deductions for state withholding will be

0.07(580) = 40.6

This makes your realized income

580-(44.37+81.2+40.6) = 580-166.17 = 413.83

7 0
3 years ago
Read 2 more answers
I know the answer but I need to explain how to get the answer. Please help❤️
kondaur [170]

Answer:

730, 735, 740

Step-by-step explanation:

Let the three consecutive multiples of 5 be, x, x+5 and x+10

Given,

x + x+5 + x+10 = 2205

3x + 15 = 2205

Subtract 15 from both sides,

3x = 2205 - 15

3x = 2190

Divide both sides by 3,

x = 2190/3 = 730

So, x= 730

x+5 = 735

x+10 = 740

5 0
2 years ago
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