In a popular online role playing game, players can create detailed designs for their

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

1) Fred Flint is paid $11.95 an hour with time-and-a-half pay for all hours he works over 40

allsm [11]

Fred's overtime rate and pay is $17.925 and $98.5875 respectively

<h3>Total payment</h3>

Amount paid per hour = $11.95

Amount paid overtime per hour = $11.95 × 1.5

= $17.925

Total hours worked last week = 45 1/2 hours

Overwork time = 45 1/2 hours - 40 hours

= 5 1/2 hours

Fred's overtime pay = 5 1/2 hours × $17.925

= 11/2 × 17.925

= $98.5875

Normal work rate = 40 hours × $11.95

= $478

Fred's total pay = Fred's overtime pay + Normal work rate

= $98.5875 + $478

= $576.5875

Therefore, Fred's total pay is $576.5875

Learn more about total pay:

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5 0

2 years ago

Find the values of x and y given that ABCD is congruent to EFGH.

Kazeer [188]

Answer:

x=7 , y = 8.

Step-by-step explanation:

10x+65 = 135

or, 10x = 70

so, x = 7

Now,

4y-4=28

or, 4y = 32

so, y = 8

7 0

3 years ago

George found he blinked 85 times in 15mts at this rate how many seconds passed during 51 blinks?

Irina18 [472]

9 seconds

i did this to solve: I crossed multiplied this $\frac{85}{15}$ with $\frac{51}{x}$

so 15 x 51=765 divided by 85 = 9

6 0

3 years ago

Which function is a horizontal compression of its parent function f(x)=x^7 by a factor of 4?

nasty-shy [4]

Note that what we want is to compress any point (a, b) in the parent function, to (a, b/4).

(a, b) is a point of the graph of the function $f(x)=x^7$ , thus we can rewrite the point as:
$(a, a^7)$ .

This point is compressed to

$\displaystyle{ (a, \frac{a^7}{4} )$ .

This means that the function we are looking for is $\displaystyle{ t(x)= \frac{x^7}{4}$ .

Answer: <span>t(x)=1/4x^7
</span>

6 0

3 years ago

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