Solve the following quadratic by completing the square. y = x2 - 6x +2

Mathematics

1 answer:

Nana76 [90]2 years ago

4 0

Answer: $3 \pm \sqrt{7}$

Step-by-step explanation:

$1) \text{ } x^{2}-6x+2=0\\\\2) \text{ } x^{2}-6x=-2\\\\3) \text{ } x^{2}-6x+\left(\frac{-6}{2} \right)^{2}=-2+\left(\frac{-6}{2} \right)^{2}=7\\\\4) \text{ } (x-3)^{2}=7\\\\5) \text{ } x-3 =\pm \sqrt{7} \longrightarrow \boxed{3 \pm \sqrt{7}}$

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Step-by-step explanation:

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Answer:

We are 95% confident that the percent of executives who prefer trucks is between 19.43% and 33.06%

Step-by-step explanation:

We are given that in a group of randomly selected adults, 160 identified themselves as executives.

n = 160

Also we are given that 42 of executives preferred trucks.

So the proportion of executives who prefer trucks is given by

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We are asked to find the 95% confidence interval for the percent of executives who prefer trucks.

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n×p ≥ 10

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42 ≥ 10 (satisfied)

n×(1 - p) ≥ 10

160×(1 - 0.2625) ≥ 10

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The required confidence interval is given by

$p \pm z\times \sqrt{\frac{p(1-p)}{n} }$

Where p is the proportion of executives who prefer trucks, n is the number of executives and z is the z-score corresponding to the confidence level of 95%.

Form the z-table, the z-score corresponding to the confidence level of 95% is 1.96

$p \pm z\times \sqrt{\frac{p(1-p)}{n} }$

$0.2625 \pm 1.96\times \sqrt{\frac{0.2625(1-0.2625)}{160} }$