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Vesnalui
16 days ago
14

A 20-person fraternity is making their weekend plans around 5 different parties in IV. Each brother will attend exactly one of t

he parties. Fraternity rules state that the fraternity must have a representative at each party. Assume that only the number of brothers that show up at a party is important, i.e. the brothers are indistinguishable. (a) How many different arrangements of plans are possible
Mathematics
1 answer:
Leona [9.2K]16 days ago
3 0

Answer:

3876

Step-by-step explanation:

We have the following data:

Members of the fraternity = 20

Their attendance at five parties is organized into groups of four.

This indicates that each group consists of 4 individuals.

At least one brother will be present at exactly one of the gatherings. (The brothers are indistinguishable).

Thus, precisely one brother at a gathering leaves (20 - 1) = 19, due to their indistinct nature.

Group sizes are in fours.

Calculating 19C4:

From: nCr = n! /(n-r)! r!

19C4 = 19! / (19 - 4)! 4!

= 19! / 15! 4!

= (19 * 18 * 17 * 16) / (4 * 3 * 2)

= 93024 / 24

= 3876

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Patricia is ordering t-shirts for her business. Company A charges $10.50 for each t-shirt and a one-time design fee of $45. Comp
Leona [9271]

Response:

I believe the answer might be either the second or the fourth option.

Apologies if this isn't accurate.

Detailed explanation:

6 0
22 days ago
Robert was able to travel 292.0 miles in 4.000 hours and used 38 liters of gasoline. What was robert's speed in feet per second?
zzz [9080]

Robert covered a distance of 292 miles.

He took 4 hours to complete this journey.

Next, let's convert miles to feet.

1 mile equals 5280 feet.

Thus, 292 miles in feet equals 292 * 5280 = 1541760 feet.

Now, converting 4 hours into seconds.

1 hour translates to 3600 seconds.

Therefore, 4 hours equals 3600 * 4 = 14400 seconds.

The question asks for speed in feet per second.

speed = \frac{distance}{time}

Thus,

\frac{1541760}{14400}

is 107.067 feet per second.

8 0
1 month ago
Jenna saves $2,500 per year in an account that earns 10% interest per year, compounded annually. Jenna will have(A $411,234) (B
Leona [9271]

Response:

The result is $43623.50

Detailed explanation:

This query involves compound interest.

The formula for calculating compound interest is

A=P(1+r)^t

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Provided information

P= $2,500

r= 10/100= 0.1

t= 30 years

Inserting values into the compound interest formula and calculating A gives us

A=2500(1+0.1)^30

A=2500(1.1)^30

A=2500*17.449

A=$43623.50

The total amount is $43623.50

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3 0
2 days ago
Mrs Atkins is going to choose two students from her class to take part in a competition.
babunello [8412]

Given:
Total girls in class = 16.
Total boys in class = 14.
To determine:
The various combinations for selecting one girl and one boy.
Solution:
We have,
Total girls = 16
Total boys = 14
Thus,
The total combinations for selecting one girl from 16 girls = 16.
The total combinations for selecting one boy from 14 boys = 14.
Now, the various ways to select one girl and one boy amount to:
Therefore, the total number of combinations is 224.
6 0
9 days ago
Consider the function represented by the equation y-6x-9=0. Which answer shows the equation written in function notation with x
AnnZ [9099]

we possess

y-6x-9=0

Step 1

Eliminate the variable y

y-6x-9=0

Add (6x+9) to each side

y-6x-9+(6x+9)=0+(6x+9)

y=(6x+9)

Step 2

Change to function notation

Define

f(x)=y

f(x)=(6x+9)

thus

the result is

f(x)=(6x+9)


6 0
1 month ago
Read 2 more answers
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