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nikdorinn [45]
3 years ago
15

In order to make a specific shade of green paint, a painter mixes 1 and 1/2 quarts of blue paint, 2 cups of green paint, and 1/2

gallon of white paint. How much of each color is needed to make 100 cups of this shade of green paint?
Mathematics
1 answer:
Svetlanka [38]3 years ago
6 0

<u>Answer</u>:

To make 100 cups of the required shade of green the amount of blue, green and white paint required is 150 cups, 200 cups and 50 gallons respectively.

<u>Step-by-step explanation:</u>

We have been given that in order to make a specific shade of green paint, a painter mixes 1 and 1/2 quarts of blue paint, 2 cups of green paint, and 1/2 gallon of white paint.  

We need to find out how much of each colour is needed to make 100 cups of this shade of green paint.

Assuming that the given data is to make 1 cup of the required shade of green, we now need to find the amount of colours needed to make 100 cups of this shade of green paint.

For 1 cup of the required green paint 1.5 cups of blue paint is used, hence for 100 cups the amount of blue paint required is:

=100 x 1.5=150

For 1 cup of the required green paint 2 cups of green paint is used, hence for 100 cups the amount of green paint required is:

=100 x 2=200

Similarly, for 1 cup of the required green paint 0.5 gallons of white paint is used, hence for 100 cups the amount of white paint required is:

=100  x 0.5=50

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<h3>What are the hypotheses tested?</h3>

At the null hypotheses, it i tested if the mean difference remains the same, that is:

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At the alternative hypotheses, it is tested if it has decreased, hence:

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Step-by-step explanation:

Trying to factor as a Difference of Squares :

1.1      Factoring:  r2-96

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 96 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step  1  :

 r2 - 96  = 0

Step  2  :

Solving a Single Variable Equation :

2.1      Solve  :    r2-96 = 0

Add  96  to both sides of the equation :

                     r2 = 96

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     r  =  ± √ 96  

Can  √ 96 be simplified ?

Yes!   The prime factorization of  96   is

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To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 96   =  √ 2•2•2•2•2•3   =2•2•√ 6   =

               ±  4 • √ 6

The equation has two real solutions  

These solutions are  r = 4 • ± √6 = ± 9.7980  

Two solutions were found :

                  r = 4 • ± √6 = ± 9.7980

Processing ends successfully

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