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2 years ago

What is completely factored form or this expression?

Mathematics

2 answers:

sweet-ann [11.9K]2 years ago

6 0

<h2><u>Answer</u><u> </u>:)</h2>

$\sf{y^{2}-12y+32 }$

$\sf{y^{2}-(8+4)y+32 }$

$\sf{y^{2}-8y-4y+32 }$

$\sf{ y(y-8)-4(y-8) }$

$\sf{(y-8)(y-4) }$

$\sf{(y-4)(y-8) }$

$\\\\\\$

<h3><u>Therefore</u><u> </u></h3>

$\sf{option~ B~ is ~correct }$

$\sf{ }$ $\sf{ }$ $\sf{ }$

Irina18 [472]2 years ago

5 0

Answer:

(y-4) (y-8)

Step-by-step explanation:

y^2-12y+32

What two numbers multiply to 32 and add to -12

-8*-4 = 32

-8+-4 = -12

(y-4) (y-8)

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In the past, 21% of all homes with a stay-at-home parent, the father is the stay-at-home parent. An independent research firm ha

Afina-wow [57]

Answer:

A sample size of 79 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

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

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$\pi = 0.21$

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.09?

A sample size of n is needed.

n is found when M = 0.09. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.09 = 1.96\sqrt{\frac{0.21*0.79}{n}}$