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Butoxors [25]
3 years ago
8

A shade of green paint is made by mixing yellow paint and blue paint in the ratio 5:2. Mel has 30 litres of yellow paint and 9 l

itres of blue paint.what is the maximum amount of green paint she can make?
Mathematics
1 answer:
vodomira [7]3 years ago
4 0

Answer:

31.5 litres

Step-by-step explanation:

If Mel uses all 30 litres of yellow paint, then:

5 / 2 = 30 / x

5x = 60

x = 12

Mel would need 12 litres of blue paint, but she only has 9 litres.  So the amount of yellow paint she needs is:

5 / 2 = x / 9

2x = 45

x = 22.5

Mel will use 22.5 litres of yellow paint with 9 litres of blue paint to make a total of 31.5 litres of green paint.

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bulgar [2K]

We need to find out how many adults must the brand manager survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage.

From the given data we know that our confidence level is 90%. From Standard Normal Table we know that the critical level at 90% confidence level is 1.645. In other words, Z_{Critical}=1.645.

We also know that E=5% or E=0.05

Also, since, \hat{p} is not given, we will assume that \hat{p}=0.5. This is because, the formula that we use will have \hat{p}(1-\hat{p}) in the expression and that will be maximum only when \hat{p}=0.5. (For any other value of \hat{p}, we will get a value less than 0.25. For example if, \hat{p} is 0.4, then 1-\hat{p}=0.6 and thus, \hat{p}(1-\hat{p})=0.24.).

We will now use the formula

n=(\frac{Z_{Critical}}{E})^2\hat{p}(1-\hat{p})

We will now substitute all the data that we have and we will get

n=(\frac{1.645}{0.05})^2\times0.5(1-0.5)

n=(32.9)^2\times0.25

n=270.6025

which can approximated to n=271.

So, the brand manager needs a sample size of 271

3 0
3 years ago
Need help quick please. Find the area of the sector use 3.14 for pi
olga55 [171]

\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=9\\ \theta =120 \end{cases}\implies \begin{array}{llll} A=\cfrac{(120)\pi (9)^2}{360}\implies A=27\pi \\\\\\ \stackrel{using~\pi =3.14}{A\approx 84.8} \end{array}

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2 years ago
Solve the following system of equations by substitution
WITCHER [35]

Answer:

(-1, 1)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

  • Terms/Coefficients
  • Coordinates (x, y)
  • Solving systems of equations using substitution/elimination

Step-by-step explanation:

<u>Step 1: Define Systems</u>

y = 2x + 3

y = x + 2

<u>Step 2: Solve for </u><em><u>x</u></em>

<em>Substitution</em>

  1. Substitute in <em>y</em>:                                                                                                  2x + 3 = x + 2
  2. [Subtraction Property of Equality] Subtract <em>x</em> on both sides:                         x + 3 = 2
  3. [Subtraction Property of Equality] Subtract 3 on both sides:                        x = -1

<u>Step 3: Solve for </u><em><u>y</u></em>

  1. Substitute in <em>x</em> [Original Equation]:                                                                  y = -1 + 2
  2. Add:                                                                                                                    y = 1
3 0
3 years ago
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It cost a farmer 43.60 pre acre to harvest corn. How much does it cost to harvest 1325.5 acres
KATRIN_1 [288]

Answer:

$57,791.8

Step-by-step explanation:

Each acre cost $43.60.

If the famer wants to harvest 1325.5 acres he has to pay 43.6 per acre

43.60×1325.5= 57,791.8

4 0
3 years ago
The length of a rectangle is 5 in longer than its width.
NeTakaya

Answer:

Length = 21

Width = 16

Step-by-step explanation:

We know that the formula for perimeter is:

P=2W+2L

And we also know that:

L=W+5

So then we put all that we know in the formula:

74=2W+2(W+5)

Now we expand the brackets and do some algebra:

74=4W+10 (-10)

64=4W (÷4)

16=W

Now that we know the width we can pop that into the length equation:

L=16+5

L=21

5 0
3 years ago
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