Find the indicated variables

Luke has 48 books. He puts 7 books in a box. How many boxes can he fill? Explain how you interpreted the remainder

Damm [24]

He can fill 6 boxes. 48 / 7 = 6R6.

I interpreted the remainder by removing the remainder to get the answer.

3 0

3 years ago

Read 2 more answers

If you answer it correctly then I will give you brainliest 5 stars and a thank you

shepuryov [24]

Step-by-step explanation:

L H J because they are all on the same line.

8 0

3 years ago

Read 2 more answers

−5.5x + 0.46 = −3.94

aliina [53]

Answer:

x= 0.78 (rounded to the hundredth)

Step-by-step explanation:

-5.5x + 0.46 = -3.94

You need to isolate x so the easiest thing to do is subtract 0.46 and move it to the other side of the equal sign.

-5.5x= -3.84 - 0.46

-5.5x = -4.3

divide -5.5 to get x alone

x= -4.3/-5.5

x= 0.78

7 0

3 years ago

7) PG & E have 12 linemen working Tuesdays in Placer County. They work in groups of 8. How many

BabaBlast [244]

Part A

Since order matters, we use the nPr permutation formula

We use n = 12 and r = 8

$_{n}P_{r} = \frac{n!}{(n-r)!}\\\\_{12}P_{8} = \frac{12!}{(12-8)!}\\\\_{12}P_{8} = \frac{12!}{4!}\\\\_{12}P_{8} = \frac{12*11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1}\\\\_{12}P_{8} = \frac{479,001,600}{24}\\\\_{12}P_{8} = 19,958,400\\\\$

There are a little under 20 million different permutations.

<h3>Answer: 19,958,400</h3>

Side note: your teacher may not want you to type in the commas

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Part B

In this case, order doesn't matter. We could use the nCr combination formula like so.

$_{n}C_{r} = \frac{n!}{r!(n-r)!}\\\\_{12}C_{8} = \frac{12!}{8!(12-8)!}\\\\_{12}C_{8} = \frac{12!}{4!}\\\\_{12}C_{8} = \frac{12*11*10*9*8!}{8!*4!}\\\\_{12}C_{8} = \frac{12*11*10*9}{4!} \ \text{ ... pair of 8! terms cancel}\\\\_{12}C_{8} = \frac{12*11*10*9}{4*3*2*1}\\\\_{12}C_{8} = \frac{11880}{24}\\\\_{12}C_{8} = 495\\\\$

We have a much smaller number compared to last time because order isn't important. Consider a group of 3 people {A,B,C} and this group is identical to {C,B,A}. This idea applies to groups of any number.

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Another way we can compute the answer is to use the result from part A.

Recall that:

nCr = (nPr)/(r!)

If we know the permutation value, we simply divide by r! to get the combination value. In this case, we divide by r! = 8! = 8*7*6*5*4*3*2*1 = 40,320

So,

$_{n}C_{r} = \frac{_{n}P_{r}}{r!}\\\\_{12}C_{8} = \frac{_{12}P_{8}}{8!}\\\\_{12}C_{8} = \frac{19,958,400}{40,320}\\\\_{12}C_{8} = 495\\\\$

Not only is this shortcut fairly handy, but it's also interesting to see how the concepts of combinations and permutations connect to one another.

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<h3>Answer: 495</h3>

5 0

2 years ago

Fill in the blank to complete the following sentence.

Romashka-Z-Leto [24]

Answer:

but there is not any blank

6 0

2 years ago