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solong [7]
3 years ago
7

There are 11 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 5 poodles and 6 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.
Mathematics
1 answer:
BigorU [14]3 years ago
3 0

Step-by-step explanation:

a) 7!

If there are no restrictions, answer is 7! as it is the permutation of all animals.

b) 4! x 3!

As cats are 6 and Dogs are 5, thus 1st and last must be cats in order to have alternate arrangements. Therefore the only choices are the order of the cats among  themselves and the order of the dogs among themselves. There are 4! permutations of the cats and 3! permutations of the dogs, so there are a total of 4! x 3! possible arrangements of the suites.

c) 3! x 5!

There are 3! possible arrangements of  the dogs among themselves. Now, if we consider the dogs as  one ”object” together, then we can think of arranging the 4 cats  together with this 1 additional object. There are 5! such arrangements possible, so there are a total of 3! · 5! possible arrangements of the suites.

d) 2 x 4! x 3!

As required that all the cats must be together and all the dogs must be together, either the cats are all  before the dogs or the dogs are all before the cats. There are two possible arrangements thus two times of both possibilities is the answer i.e.  2 x 4! x 3!

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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
KengaRu [80]

Answer:

Using the ratio and proportion method, we find that on an average 1.875 rooms can be painted per gallon.

Step-by-step explanation:

Concept: Use the method of ratio and proportion. Given that for 2/5 gallons of paint, we can paint 3/4 of rooms. So, for one gallon of paint, divide 2/5 by 3/4.

2/5 gallons of paint = 3/4 rooms

1 gallon of paint = \frac{\frac{3}{4} }{\frac{2}{5} } = \frac{15}{8} =1.875 rooms

So, on an average they can paint 1.875 rooms per gallon.

For more explanation, refer the following link

brainly.com/question/11243787

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8 0
2 years ago
I’m not sure how to solve “system of equations”
natka813 [3]

Hey there! :)

Answer:

(2, -2)

Step-by-step explanation:

-2x + y = -6

4x + 3y = 2

We can begin by setting the first equation equal to y:

-2x + y = -6

Add 2x to both sides:

y = 2x - 6

Plug this equation for y into the second equation:

4x + 3(2x - 6) = 2

Distribute:

4x + 6x - 18 = 2

Combine like terms:

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Plug the value of 'x' into an equation to solve for 'y':

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7 0
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Solnce55 [7]

Answers:

  • a) Mean = 20.4
  • b) New mean = 20

==================================================

Explanation:

To get the mean, we add up the scores and divide by 10 (because there are 10 scores at first)

28+13+4+12+32+22+13+22+26+32 = 204

204/10 = 20.4

The mean is 20.4

------------

For part b), we redo those steps shown above, but tack 16 onto the list. So we'll add up all the values (including that 16 at the end) and divide by 11 this time.

28+13+4+12+32+22+13+22+26+32+16 = 220

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The new mean is 20.

The new mean is slightly smaller than the old mean. Notice how 16 is smaller than 20.4, so this new score pulls down the mean just a little bit.

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