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nika2105 [10]
2 years ago
12

Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -8x^2 + 8x + 5.

Mathematics
1 answer:
sertanlavr [38]2 years ago
6 0
f(x)=-8x^2+8x+5\\\\f(x)=0\iff-8x^2+8x+5=0\\\\a=-8;\ b=8;\ c=5\\\\\Delta=b^2-4ac\\\\\Delta=8^2-4\cdot(-8)\cdot5=64+160=224\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{224}\approx\sqrt{225}=15\\\\x_1\approx\frac{-8-15}{2\cdot(-8)}=\frac{-23}{-16}=1\frac{7}{16}\approx1.5\\\\x_2\approx\frac{-8+15}{2\cdot(-8)}=\frac{7}{-16}=-\frac{7}{16}\approx-0.5
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Pete is a politician. He claims that 32% of the households in his district have total household incomes below the poverty level.
victus00 [196]

Answer:

z=\frac{0.3867 -0.32}{\sqrt{\frac{0.32(1-0.32)}{225}}}=2.145  

For a bilateral test the p value would be:  

p_v =2*P(z>2.145)=0.0320  

Step-by-step explanation:

Information given

n=225 represent the sample selected

X=87 represent the households with incomes below the poverty level

\hat p=\frac{87}{225}=0.3867 estimated proportion of households with incomes below the poverty level

p_o=0.32 is the value that we want to test

z would represent the statistic

p_v represent the p value

System of hypothesis

We want to check if the true proportion is equal to 0.32 or not.:  

Null hypothesis:p=0.32  

Alternative hypothesis:p \neq 0.32  

The statistic is given bY:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Replacing we got:

z=\frac{0.3867 -0.32}{\sqrt{\frac{0.32(1-0.32)}{225}}}=2.145  

For a bilateral test the p value would be:  

p_v =2*P(z>2.145)=0.0320  

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Step-by-step explanation:

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Alenkasestr [34]
<h3>Given</h3>

tan(x)²·sin(x) = tan(x)²

<h3>Find</h3>

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Subtract the right side and factor. Then make use of the zero-product rule.

... tan(x)²·sin(x) -tan(x)² = 0

... tan(x)²·(sin(x) -1) = 0

This is an indeterminate form at x = π/2 and undefined at x = 3π/2. We can resolve the indeterminate form by using an identity for tan(x)²:

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