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Keith_Richards [23]
4 years ago
15

Consider various ways of ordering the letters in the word TENNESSEE. TENENESES, EESSENNET, TNNEESSEE, and so on. (a) How many di

stinguishable orderings are there
Mathematics
1 answer:
scoundrel [369]4 years ago
5 0

Answer:

3780.  

Step-by-step explanation:

To solve this we will start by just considering the number of ways to arrange 9 objects. We can do this in  9!  ways.

However since we have 3 reoccurring letters in Tennessee namely n,s and e we need to remove the times these form the same arrangement. Let me give an example to show what this means. Lets say we have the arrangement:

ennetssee

Now what happens if we exchange the places of the letters n for example? Of course we get the same arrangement of letters. We don’t want to count these as 2 different arrangements since for our interests they are the same. We therefore divide  9!  by the number of times this type of double counting occurs.

Since the word has the letter n occurring twice we will start by diving by  2! .

The letter s occurs 2 times as well so we will have to divide by  2!  again.

Finally the letter e occurs 4 times and so we will have to divide by  4!  here.

Now we get the following result:

9/(2 x 2 x 4)=3780.  

So in conclusion there are 3780 different ways to arrange the letters in Tennessee.

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Answer:

0.0007264

Step-by-step explanation:

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3 years ago
Reasoning Solve the system of linear equations using substitution. Use pencil and paper. Which expression would be easier to sub
spin [16.1K]

Answer:

x = 5 /2 , y = 9 / 8

Step-by-step explanation:

x = 4y - 2 ....... (i)

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Substituting eqn  (i) into eqn (ii);

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4y - 2 + 4y = 7

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y = 9 / 8

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3 years ago
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The area of ABED is 49 square units. Given AGequals9 units and ACequals10 ​units, what fraction of the area of ACIG is represent
Mrac [35]

Answer:

The fraction of the area of ACIG represented by the shaped region is 7/18

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the square ABED find the length side of the square

we know that

AB=BE=ED=AD

The area of s square is

A=b^{2}

where b is the length side of the square

we have

A=49\ units^2

substitute

49=b^{2}

b=7\ units

therefore

AB=BE=ED=AD=7\ units

step 2

Find the area of ACIG

The area of rectangle ACIG is equal to

A=(AC)(AG)

substitute the given values

A=(9)(10)=90\ units^2

step 3

Find the area of shaded rectangle DEHG

The area of rectangle DEHG is equal to

A=(DE)(DG)

we have DE=7\ units

DG=AG-AD=9-7=2\ units

substituteA=(7)(2)=14\ units^2

step 4

Find the area of shaded rectangle BCFE

The area of rectangle BCFE is equal to

A=(EF)(CF)

we have

EF=AC-AB=10-7=3\ units

CF=BE=7\ units

substitute

A=(3)(7)=21\ units^2

step 5

sum the shaded areas

14+21=35\ units^2

step 6

Divide the area of  of the shaded region by the area of ACIG

\frac{35}{90}

Simplify

Divide by 5 both numerator and denominator

\frac{7}{18}

therefore

The fraction of the area of ACIG represented by the shaped region is 7/18

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Step-by-step explanation:

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