What system of inequalities is shown in the graph?

Mathematics

1 answer:

nikitadnepr [17]2 years ago

4 0

Answer:

Step-by-step explanation:

x ≤ −1 and y ≤ −0.4x + 2

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Subtract from 1: 1-0.95 = 0.05
Divide by 2: 0.05/2 = 0.025
Subtract from 1: 1-0.025 = 0.975

Using a z-table (http://www.z-table.com) we see that this is associated with a z-score of 1.96.

The margin of error, ME, is given by:
$ME=z*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

We want ME to be 4%; 4% = 4/100 = 0.04. Substituting this into our equation, as well as our proportion and z-score,
$0.04=1.96\sqrt{\frac{0.63(1-0.63)}{n}}
\\
\\\text{Dividing both sides by 1.96,}
\\
\\\frac{0.04}{1.96}=\sqrt{\frac{0.63(0.37)}{n}}
\\
\\\text{Squaring both sides,}
\\
\\(\frac{0.04}{1.96})^2=\frac{0.63(0.37)}{n}
\\
\\\text{Multiplying both sides by n,}
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\\n(\frac{0.04}{1.96})^2=0.63(0.37)
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\\n(\frac{0.04}{1.96})^2=0.2331
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\\\text{Isolating n,}
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\\n=\frac{0.2331}{(\frac{0.04}{1.96})^2}=559.67\approx560$

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