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Degger [83]
3 years ago
8

There are 17 portable mini suites (a.k.a. cages) in a row at the paws and claws holiday pet resort. they are neatly labeled with

their guests' names. there are 8 poodles and 9 tabbies. how many ways can the "suites" be arranged if:
Mathematics
1 answer:
DiKsa [7]3 years ago
4 0
Given that there are 17 portable mini suites (a.k.a. cages) in a row at the Paws and Claws Holiday Pet Resort. They are neatly labeled with their guests' names. There are 8 poodles and 9 tabbies. How many ways can the "suites" be arranged if: a) there are no restrictions.

b) cats and dogs must alternate.

c) dogs must be next to each other.

d) dogs must be next to each other and cats must be next to each other.


Part A:

If there are no restrictions, then the number of ways the "suites" can be arranged is given by:

17!=17\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1=355,687,428,096,000 \ ways



Part B:

If cats and dogs must alternate, then the number of ways the "suites" can be arranged is given by:

9!\times8!=9\times8\times7\times6\times5\times4\times3\times2\times1\times8\times7\times6\times5\times4\times3\times2\times1=14,631,321,600 \ ways



Part C:

If dogs must be next to each other, then the group of dogs are taken as 1 object and there are now 10 objects to arrange. The number of ways to arrange 10 objects is given by:

10!=10\times9\times8\times7\times6\times5\times4\times3\times2\times1=3,628,800
 \ ways

Also, the group of dogs can be arranged in:

8!=8\times7\times6\times5\times4\times3\times2\times1=40,320
 \ ways

Therefore, the total number of ways the "suites" can be arranged is given by:

10!\times8!=3,628,800\times40,320=146,313,216,000 \ ways



Part D:

If dogs must be next to each other and cats must be next to each other, then the group of dogs are taken as 1 object and the group of cats are taken as 1 object, then there are now 2 objects to arrange.

The number of ways to arrange two objects is given by:

2!=2\times1=2

The number of ways the 9 dogs are to be arranged is given by:

9!=9\times8\times7\times6\times5\times4\times3\times2\times1=362,880

The number of ways the 8 cats are to be arranged is given by:
8!=8\times7\times6\times5\times4\times3\times2\times1=40,320

Therefore, the total number of ways the "suites" can be arranged is given by:

2!\times9!\times8!=2\times362,880\times40,320=29,262,643,200 \ ways
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Find The T value for point that splits segment EF in half if point E is located at (5,-2) and point F is located at (-1,3).
Tanzania [10]

The formula of a midpoint between two points:

M\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)

We have:

(5,\ -2)\to x_1=5,\ y_1=-2\\\\(-1,\ 3)\to x_2=-1,\ y_2=3

Substitute:

\dfrac{5+(-1)}{2}=\dfrac{4}{2}=2\\\\\dfrac{-2+3}{2}=\dfrac{1}{2}

Answer: T\left(2,\ \dfrac{1}{2}\right)

4 0
2 years ago
Which of the following describes the sum in terms of p and q?(1 point)
snow_tiger [21]

The description of the summation expression given as p + (-q) is the sum, p + (-q), is the number located a distance, |p|, from , q, in the negative direction.

<h3>How to describe the sum in terms of p and q?</h3>

The summation expression is given as:

p + (-q)

In the above summation expression, we assume that:

p ⇒ Positive number

- q ⇒ Negative number

Having said that:

The expression -q would go in the negative direction if plotted on a number line

This means that the description of the summation expression given as p + (-q) is the sum, p + (-q), is the number located a distance, |p|, from , q, in the negative direction.

Hence, the description of the summation expression given as p + (-q) is the sum, p + (-q), is the number located a distance, |p|, from , q, in the negative direction.

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6 0
1 year ago
The system of equations is solved using the linear combination method.
Alborosie

The interpretation of 0 = -12 is (a) There are no solutions to the system because the equations represent parallel lines.

<h3>How to interpret the result?</h3>

The result is given as:

0 = -12

By comparison 0 and -12 do not have the same value

i.e. 0 ≠ - 12

This means that the system of equation has no solution

Hence, the interpretation of 0 = -12 is (a)

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4 0
1 year ago
Please help me answer this I don't understand, I would really appreciate how you solved it as well.
abruzzese [7]

Answer: Parallel

Step-by-step explanation:

Set your -2x+10y=5 equation equal to y

-2x+10y=5

<u>      -10y -10y</u>

-2x=5-10y

<u>-5      -5       </u>

<u>-2x-5</u>+<u>-10y</u>

-10 -10 -10

-1/5x-1/2=y

Now you can put your equations into your graphing calculator and examine the lines made

(if you dont have one search up <em>online graphing calculator</em> on google or your app store)

5 0
3 years ago
Solve 5c − c + 10 = 34. <br> −6 <br> 6 <br> 11 <br> −11
natima [27]

Subtract 10 and collect terms to get the variable term by itself on the left.

... 4c = 24

Divide by the coefficient of the variable, 4.

... c = 6

The appropriate choice is the second one:

... 6

_____

You don't actually have to sove the equation to find the right answer. You just need to see which answer works.

-6: 5(-6) -(-6) +10 = -14 ≠ 34

6: 5(6) -(6) +10 = 34 . . . . . . . this answer works (you can stop here)

11: 5(11) -(11) +10 = 54 ≠ 34

-11: 5(-11) -(-11) +10 = -34 ≠ 34

7 0
3 years ago
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