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Marina86 [1]
2 years 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:
skad [1K]2 years ago
3 0

Answer:

3876

Step-by-step explanation:

Given the following :

Fraternity members = 20

They are to attend 5 different parties in groups of 4

Meaning a group = 4 persons

Atleast one brother will attend exactly one of the parties. (the brothers are indistinguishable).

Then, exactly one brother at a party (20 - 1) = 19, since they are indistinguishable.

Group members are in 4's

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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You mix 1-3 teaspoon of baking soda with 3 teaspoon of salt.what is the value of the ratio of baking soda to salt?
erastova [34]

Answer:1-3:3

Step-by-step explanation:

8 0
2 years ago
Alan says that two lines in the coordinate plane are perpendicular if and only if the slopes of the lines are m and 1m. Identify
mart [117]

Answer:

First, two lines are perpendicular if one has slope m, and the other has slope -1/m (Not 1m as Alan says)

That is the first error of Alan.

Now, there is another error.

If m = 0, then -1/m tends to minus infinity (in this case we would have a vertical line).

But we can not really divide by zero, so we should state that:

m can not be zero, if a line is horizontal, the perpendicular line must be vertical.

7 0
2 years ago
Jane wishes to bake an apple pie for dessert. The baking instructions say that she should bake the pie in an oven at a constant
Viktor [21]

Answer:

Therefore k= \frac{ln2 }{18}, A=184

Step-by-step explanation:

Given function is

T(t)=230 -e^{-kt}

where T(t) is the temperature in °C and t is time in minute and A and k are constants.

She noticed that after 18 minutes the temperature of the pie is 138°C

Putting T(t) =138°C and t= 18 minutes

138=230 -Ae^{-k\times 18}

\Rightarrow  -Ae^{-18k}=138-230

\Rightarrow  Ae^{-18k}=92 .....(1)

Again after 36 minutes it is 184°C

Putting T(t) =184°C and t= 36 minutes

184=230-Ae^{-k\times 36}

\Rightarrow Ae^{-36k}=230-184

\Rightarrow Ae^{-36k}=46.......(2)

Dividing (2) by (1)

\frac{Ae^{-36k}}{Ae^{-18k}}=\frac{46}{92}

\Rightarrow e^{-18k}=\frac{46}{92}

Taking ln both sides

ln e^{-18k}=ln\frac{46}{92}

\Rightarrow -18k =ln (\frac12)

\Rightarrow -18k= ln1-ln2

\Rightarrow k= \frac{ln2 }{18}

Putting the value k in equation (1)

Ae^{-18\frac{ln2}{18}}=92

\Rightarrow A e^{ln2^{-1}}=92

\Rightarrow A.2^{-1}=92

\Rightarrow \frac{A}{2}=92

\Rightarrow A= 92 \times 2

⇒A= 184.

Therefore k= \frac{ln2 }{18}, A=184

7 0
2 years ago
This line plot shows something about trails in a state park. What is true about the data in this line plot?
Zepler [3.9K]

Answer:

The total length of the Dogwood Trail is 24 kilometers

The difference between the lengths of the trails is 6 kilometers

Step-by-step explanation:

<u><em>The complete and correct question is</em></u>

The diagram shows two different nature trails in a state park. The solid line shows the Dogwood Trail. The dashed line shows the Elm Trail.

Which of the following statements are true about the lengths of the trails? Check all that apply.

1.The total length of the Dogwood Trail is 16 kilometers.

2.The total length of the Dogwood Trail is 24 kilometers.

3.The Elm Trail is longer than the Dogwood Trail.

4.The difference between the lengths of the trails is 2 kilometers.

5.The difference between the lengths of the trails is 6 kilometers.    

<u><em>The picture in the attached figure</em></u>

step 1

Find the value of a

Applying the Pythagorean Theorem in the right triangle ABC

13^2=a^2+5^2\\a^2=169-25\\a^2=144\\a=12\ km

step 2

Find the value of b

Applying the Pythagorean Theorem in the right triangle CDE

5^2=b^2+3^2\\b^2=25-9\\b^2=16\\b=4\ km

step 3

Find the total length of the Dogwood Trail (solid blue line)

The total length is equal to

AD=AB+BC+CE+ED ---> by segment addition postulate

substitute the given values

AD=a+5+b+3=(a+b+8)\ km

substitute the value of a and b

AD=(12+4+8)=24\ km

step 4

Find the total length of the Elm Trail  (dashed red line)

The total length is equal to

AD=AC+CD ---> by segment addition postulate

substitute the given values

AD=13+5=18\ km

<u><em>Verify the following statements</em></u>

Part 1) The total length of the Dogwood Trail is 16 kilometers

The statement is false

Because

The total length of the Dogwood Trail is 24 kilometers (see the explanation)

Part 2) The total length of the Dogwood Trail is 24 kilometers

The statement is true (see the explanation)

Part 3) The Elm Trail is longer than the Dogwood Trail

The statement is false

Because

The Elm Trail is smaller than the Dogwood Trail

18\ km < 24\ km

Part 4) The difference between the lengths of the trails is 2 kilometers

The statement is false

Because

The difference is equal to

24-18=6\ km

Part 5) The difference between the lengths of the trails is 6 kilometers

The statement is true

Because

The difference is equal to

24-18=6\ km

4 0
2 years ago
Read 2 more answers
What is the measure of Angle J K L? Triangle J K L . The exterior angle to angle K has a measure of 83 degrees. 83 degrees 97 de
nasty-shy [4]

Answer:

The measure of angle JKL is 97 degrees.

Step-by-step explanation:

Given:

A triangle JKL .

Measure of exterior angle K = 83 degrees

We have to find the measure of \angle JKL .

In (\triangle\ JKL) we see that the exterior angle is in linear pair with \angle JKL .

Note:

Linear pair angles sum is 180 degree.

Let \angle JKL be 'x' degrees .

So,

⇒ x+83=180

⇒ <em>Subtracting 83 from both sides.</em>

⇒ x+83-83=180-83

⇒ x=180-83

⇒ x=97 degrees

The measure of angle JKL in the triangle is of 97 degrees.

5 0
2 years ago
Read 2 more answers
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