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3 years ago

Use the discriminant to describe the roots of each equation. Then select the best description,

1 answer:

6 0

$\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{6}x^2\stackrel{\stackrel{b}{\downarrow }}{+13}x\stackrel{\stackrel{c}{\downarrow }}{+6}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ \underline{positive}&\textit{two solutions}\qquad \textit{\Large \checkmark}\\ negative&\textit{no solution} \end{cases} \\\\\\ 13^2-4(6)(6)\implies 169-144\implies 25$

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The graph of the function f(x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply.

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Answer:

Explained below.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

$\mu_{\hat p}= p$

The standard deviation of this sampling distribution of sample proportion is:

$\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}$

(a)

The sample selected is of size n = 450 > 30.

Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.

The mean and standard deviation are:

$\mu_{\hat p}=p=0.75\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.75(1-0.75)}{450}}=0.0204$

So, the sampling distribution of sample proportion is $\hat p\sim N(0.75,0.0204^{2})$ .

(b)

Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:

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Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.95.

(c)

The sample selected is of size n = 200 > 30.

Then according to the central limit theorem the sampling distribution of sample proportion is normally distributed.

The mean and standard deviation are:

$\mu_{\hat p}=p=0.75\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.75(1-0.75)}{200}}=0.0306$

So, the sampling distribution of sample proportion is $\hat p\sim N(0.75,0.0306^{2})$ .

(d)

Compute the probability that the sample proportion will be within 0.04 of the population proportion as follows:

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$=P(-1.31$

Thus, the probability that the sample proportion will be within 0.04 of the population proportion is 0.81.

(e)

The probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 450 is 0.95.

And the probability that the sample proportion will be within 0.04 of the population proportion if the sample size is 200 is 0.81.

So, there is a gain in precision on increasing the sample size.

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3 years ago

QUESTION: 12+ 15 = 3x6 - 4

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Answer:

Step-by-step explanation:

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Answer:

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Remark

If you just want the way this would be written out the answer is

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4 years ago