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Mrrafil [7]
3 years ago
6

there is a pile of 8 blocks: 4 are white, 3 are yellow, and 1 is purple. By placing the blocks side by side in a straight line,

how many different color patterns could you make
Mathematics
2 answers:
Ainat [17]3 years ago
7 0
Ways to arrange 1 block: 1! = 1
Ways to arrange 3 blocks: 3! = 6
Ways to arrange 4 blocks: 4! = 24
Ways to arrange 8 blocks: 8! = 40320

The answer is 8! / (1! × 3! × 4!)

Explaination: Pretend you have the sequence WYWWWYYP. See where the 4 white blocks are? Pretend we took 2 white blocks and swapped their places. The sequence would still be WYWWWYYP. It turns out, any of the white blocks can swap places with any other white blocks and the sequence will still be the same. We know there are 4! ways to "scramble" the white blocks with only each other. So we divide by 4! In our answer. The process is the same with the yellow blocks - we divide by 3! to account for the fact that "scrambling" them produces the same sequence. And you probably saw there's only one purple block, so you can't swap it with anything and still have the same sequence - that makes sense because dividing by 1 doesn't change the answer.
kkurt [141]3 years ago
4 0

Answer:

I could make 280 different color patterns.

Step-by-step explanation:

Let's suppose that we want to arrange in a straight line N objects.

Let's also suppose that in this N objects there are N1 objects of a certain class (this N1 objects are equal between them), N2 objects of a certain class (this N2 objects are also equal between them), ... , Nn objects of a certain class.

Mathematically :

N=N1+N2+...+Nn

This is a condition to apply the following equation

The total ways to arrange them are :

\frac{N!}{N1!N2!...Nn!}

Where ''!'' is the factorial number.

For example :

4! = 4 x 3 x 2 x 1

3! = 3 x 2 x 1

1! = 1

0! is defined as 1

In this exercise we only need to apply this equation to answer the question.

There are 8 blocks.

4 are white

3 are yellow

1 is purple

8=4+3+1=8

The first condition is satisfied. Now, we can apply the equation to find the arrangements.

\frac{8!}{4!3!1!}=280

There are 280 different color patterns.

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Sergio [31]

Answer:

m = 9

Step-by-step explanation:

-2m + 8 + m + 1 = 0

-m + 9 = 0

9 = m

3 0
3 years ago
What's the steps used to solve modeling problems in the correct order​
Stolb23 [73]

Answer:

see below

Step-by-step explanation:

The first step is to read the problem

Then you need to make a plan

Implement the plan

Then evaluate the answer to see if it makes sense

6 0
3 years ago
A pair of skis was discounted 20%. How many percent will the discounted price have to be increased to return to the original pri
denis-greek [22]

Answer:

25%

Step-by-step explanation:

Let the original price of A pair of skis be $100

discount given on A pair of skis = 20% on original price

discount value of A pair of skis in $ = 20% * $100

                   =  (20 * 100)/100 = $20

discounted price of A pair of skis =  original price - discount = 100 -20 = $80

in order to increase discounted price to original price of $100

there must be increase of $20 to discounted price which is $80

percentage increase on discounted price   to return to the original price =

(increased \ amount / discounted \ price) * 100 \\=>( 20/80) * 100 =  25\\

therefore 25% must be increase on discounted price to return to the original price

6 0
3 years ago
surveyor stands 100 m from the base of a tower on which an antenna stands. He measures the angles of elevation to the top and bo
balu736 [363]

Answer: 36.3m

Step-by-step explanation:

To solve this, we can draw two triangle rectangles, where the distance between the man and the base of the tower is one of the cathetus, the adjacent one, the height will be the opposite cathetus.

The triangle where the elevation angle is 58° is associated with the height of the tower without the aerial

The other triangle, where the elevation angle is 63° is associated with the height of the tower with the aerial.

Then we can calculate those two heights, then compute the difference, and the difference will be equal to the height of the aerial.

In both cases we want to calculate the opposite cathetus, then we should use the relation:

Tan(θ) = (Op. cath)/(Adj. cath)

The height without the aerial is h1, let's find it:

Tan(58°) = h1/100m

Tan(58°)*100m = h1 = 160m.

The height with the aerial is h2, let's find it:

Tan(63°) = h2/100m

Tan(63°)*100m = h2 = 196.3m

Then the height of the aerial will be:

h2 - h1 =  196.3m -  160m = 36.3m

6 0
3 years ago
6x + 3 (2x) - 7 - 2³ Please include th steps to solving it.
Alchen [17]

Answer:

24x-15

Step-by-step explanation:

Let's do this together with a step-by-step explanation!

First we need to make sure we remember that there are appropriate ways on how to solve these. LIKE PEMDAS.

6x + 3 (2x) - 7 - 2³

Let's multiply the 3 and 2x together.

6x + 6x - 7 - 2³

Now let's do the exponent

6x + 6x - 7 - 8

Now let's add everything together! But remember only common variables can be added together.

24x - 15 is the answer.

You can no longer break anything down.

I really hope this helped you!

4 0
3 years ago
Read 2 more answers
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