Simplify: 8 + 14 – 5 - 7 + 3 - 7

9. A band director wants to form a committee of 4 parents from a list of 45 band parents.

Alex73 [517]

Answer:

Part (A): The number of ways to select 12 jurors are 86493225.

Part (B): The number of ways to select 2 alternates are 306.

Part (C): Part (a) is an example of combination and Part (a) is an example of permutation

Step-by-step explanation:

Consider the provided information.

A band director wants to form a committee of 4 parents from a list of 45 band parents.

Part (A): How many different groups of 4 parents can the band director select?

Since order doesn't matter so we will use combination.

Use the formula for combination $^{n}C_{r}=\frac{n!}{r!(n-r)!}$

Substitute n=45 and r=4 in above formula.

$^{45}C_{4}=\frac{45!}{4!(45-4)!}$

$^{45}C_{4}=\frac{45!}{4!41!}$

$^{45}C_{4}=148995$

Hence, the number of ways are 148995.

Part (B) How many different ways can the band director select 4 parents to serve in the band parents’ association as president, vice president, treasurer, and secretary?

Since the order matter so we will use permutation:

The formula for permutation is: $^{n}P_{r}=\frac{n!}{(n-r)!}$

Substitute n=45 and r=4 in above formula.

$^{45}P_{4}=\frac{45!}{(45-4)!}$

$^{45}P_{4}=\frac{45!}{41!}$

$^{45}P_{4}=3575880$

Hence, the number of ways are 3575880.

Part (C) . Explain the difference between parts (a) and (b) in terms of how you decided to solve each part.

Part (A) is an example of number of combination where order doesn't matter.

Part (B) is an example of permutation where order matter.

7 0

3 years ago

A rectangle prism has a volume of 144 cm. The base is a square with a length of 4 cm. What is the height of the prism?

Andre45 [30]

The height would be 36 because you have to divide 144 by 4

4 0

3 years ago

58.(A) (5pts)A certain type of bacteria, given favorable growth medium, quadruples in population every 6 hours. Given that there

Jet001 [13]

Answer:

157286400 bacteria

Step-by-step explanation:

We are given the following in the question:

The bacteria increases 4 times every 6 hours.

Initially there are 150 bacteria.

Thus, we can write the function for number of bacteria after x hours,

$f(x) = 150(4)^{\frac{x}{6}}$

We have to find the number of bacteria in 2.5 days.

1 day = 24 hours

Thus,

$2.5\text{ days} = 24\times 2.5 = 60\text{ hours}$

Putting x = 60 in the above equation, we get,

$f(60) = 150(4)^{\frac{60}{6}} = 150(4)^{10} = 157286400$

Thus, there will be 157286400 bacteria in two and a half days.

5 0

4 years ago

When you divide a fraction less than 1 by a whole number greater than 1 how dose the quotient compare to the dividend

mihalych1998 [28]

A is the correct answer

4 0

3 years ago

Read 2 more answers

Solve for x: <br>5x - 3y = 22<br> 10x - 4y = 46

Alik [6]

Answer:

x=5, y=1

Step-by-step explanation:

Isolate x for 5x-3y=22

5x-3y=22

Add 3y to both sides

5x-3y+3y=22+3y

Simplify

5x=22+3y

Divide both sides by 5

5x/5=22/5+3y/5

Simplify

x=22+3y/5

Substitute x=22+3y/5

10*22+3y/5-4y=46

Simplify 10*22+3y/5-4y

10*22+3y/5=2(3y+22)

=2(3y+22)-4y

Expand 2(3y+22)

=6y+44-4y

Simplify 6y+44-4y

=2y+44

Isolate y for 2y+44=46

2y+44=46

Subtract 44 from both sides:

2y+44-44=46-44

Simplify

2y=2

Divide both sides by 2;

2y/2=2/2

Simplify;

y=1

For x=22+3*1/5 substitute y=1

y=22+3*1/5

22+3*1=25

=25/5

Divide the numbers;25/5=5

=5

x=5

The solutions to the system of equations are;

x=5, y=1

8 0

3 years ago

Simplify: 8 + 14 – 5 - 7 + 3 - 7 - 4