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melisa1 [442]
3 years ago
7

The students in the service club are mixing paint to make a mural. The table below shows the different parts of paint that the s

tudents mix together.
Two mixture of paint will be the same shade if the red and white paint are in the same ratio. how many shades of paint did the students make? Explain

Mathematics
1 answer:
Novay_Z [31]3 years ago
6 0

There are really only two different shades of what I think is pink.

1/3 is equal to 2/6 which is equal to 3/9

1/2 is equal to 2/4 which is equal to 4/8

The bolded ones are the original mixtures given.

Start with 1/3 Multiply top and bottom by 2 and you get 2/6

When you multiply top and bottom of 1/3 by by 3 you get 3/9

Use the same idea for 1/2

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The coffee Lily likes is composed of 97.3% water and 2.7% cocoa. The coffee John likes is composed of 96% water and 4% cocoa. Ho
mestny [16]

30 ounces of the coffee John likes consists of

  • 0.96\cdot30=28.8 ounces of water
  • 0.04\cdot30=1.2 ounces of cocoa

To this mixture we're adding x ounces of water, so that the new mix has a total volume of 30+x ounces and matches the composition of the coffee Lily likes. This means it would consist of

  • 0.973\cdot(30+x)=28.8+x ounces of water
  • 0.027\cdot(30+x)=1.2 ounces of cocoa (same amount of cocoa as before because pure water is being added)

Solve for x:

0.973(30+x)=28.8+x\implies29.12+0.973x=28.8+x

\implies0.39=0.027x

\implies x\approx14.4

###

Just to confirm: the new mixture consists of

  • 28.8+14.4=43.2 ounces of water
  • 1.2+0=1.2 ounces of cocoa

giving a total volume of 43.2+1.2=44.4 ounces of coffee, and \dfrac{43.2}{44.4}\approx0.973, as required.

4 0
3 years ago
Suppose that a group of 10 students are to be assigned to four dorm rooms: a single, a double, a triple and a quad. How many way
Nesterboy [21]

Answer:

Total number of ways to select all sstudent to make assignment = 10×36×70×1 = 25200

Step-by-step explanation:

We have given number of students = 10

These 10 students are assigned to four dorm rooms a single, a double, a triple and a quad

So number of ways to assigned single student =^{10}C_1=\frac{10!}{1!9!}=10\\

Now left student = 10 -1 = 9

So number of ways to assigned double student =^{9}C_2=\frac{9!}{2!7!}=36

Now left student = 9-2 = 7

So number of ways to assigned triple student =^{7}C_3=\frac{7!}{2!4!}==70

Now left student = 7 - 3 = 4

So number of ways to assigned quad student =^{4}C_4=\frac{4!}{4!0!}=1

So total number of ways to select all sstudent to make assignment = 10×36×70×1 = 25200

6 0
3 years ago
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