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3 years ago

Solve this quadratic equation by completing the square. (2x^2 = -8x + 45)

1 answer:

8 0

$(2x^2 = -8x + 45) \\ \\ 2x^2 + 8x - 45 = 0 \\ \\ x = \frac{-8+2 \sqrt{106} }{4} , \frac{-8-2 \sqrt{106} }{4} \\ \\ x = - \frac{4- \sqrt{106} }{2} , - \frac{4+ \sqrt{106} }{2} \\ \\ Answer: x = - \frac{4- \sqrt{106} }{2} , - \frac{4+ \sqrt{106} }{2}$

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Colt1911 [192]

The answer is D Explanation: since the the slope is negative the x should be negative and D is the only one that has a negative X.

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2 years ago

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A) 40
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3 years ago

In 2002, the mean age of an inmate on death row was 40.7 years with a standard deviation of 9.6 years according to the U.S. Depa

marissa [1.9K]

Answer:

The 95% confidence interval for the current mean age of death-row inmates is between 42.23 years and 35.57 years.

Step-by-step explanation:

The confidence interval of the mean is given by the next formula:

$\\ \overline{x} \pm z_{1-\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$ [1]

We already know (according to the U.S. Department of Justice):

The (population) standard deviation for this case (mean age of an inmate on death row) has a standard deviation of 9.6 years ( $\\ \sigma = 9.6$ years).
The number of observations for the sample taken is $\\ n = 32$ .
The sample mean, $\\ \overline{x} = 38.9$ years.

For $\\ z_{1-\frac{\alpha}{2}}$ , we have that $\\ \alpha = 0.05$ . That is, the level of significance $\\ \alpha$ is 1 - 0.95 = 0.05. In this case, then, we have that the z-score corresponding to this case is:

$\\ z_{1-\frac{\alpha}{2}} = z_{1-\frac{0.05}{2}} = z_{1-0.025} = z_{0.975}$

Consulting a cumulative standard normal table, available on the Internet or in Statistics books, to find the z-score associated to the probability of, $\\ P(z$ , we have that $\\ z = 1.96$ .

Notice that we supposed that the sample is from a population that follows a normal distribution. However, we also have a value for n > 30, and we already know that for this result the sampling distribution for the sample means follows, approximately, a normal distribution with mean, $\\ \mu$ , and standard deviation, $\\ \sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}}$ .

Having all this information, we can proceed to answer the question.

Constructing the 95% confidence interval for the current mean age of death-row inmates

To construct the 95% confidence interval, we already know that this interval is given by [1]:

$\\ \overline{x} \pm z_{1-\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$

That is, we have:

$\\ \overline{x} = 38.9$ years.

$\\ z_{1-\frac{\alpha}{2}} = 1.96$

$\\ \sigma = 9.6$ years.

$\\ n = 32$

Then

$\\ 38.9 \pm 1.96*\frac{9.6}{\sqrt{32}}$

$\\ 38.9 \pm 1.96*\frac{9.6}{5.656854}$

$\\ 38.9 \pm 1.96*1.697056$

$\\ 38.9 \pm 3.326229$

Therefore, the Upper and Lower limits of the interval are:

Upper limit:

$\\ 38.9 + 3.326229$

$\\ 42.226229 \approx 42.23$ years.

Lower limit:

$\\ 38.9 - 3.326229$

$\\ 35.573771 \approx 35.57$ years.

In sum, the 95% confidence interval for the current mean age of death-row inmates is between 42.23 years and 35.57 years.

Notice that the "mean age of an inmate on death row was 40.7 years in 2002", and this value is between the limits of the 95% confidence interval obtained. So, according to the random sample under study, it seems that this mean age has not changed.

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3 years ago

Which set of points lies on the the graph of the function.

meriva

Answer:

(0,0), (-1, 1), and (1,-1)

Step-by-step explanation:

If you were to plot all the points they would all end up being on the green line

I hope this helped?

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2 years ago

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HELP PLEASE Determine the missing statements and reasons for the following proof.

lilavasa [31]

Reasons:
Reason 3: Congruent supplements theorem

Statements:
Statement 4: Angle 1 is congruent with angle 2

Answer: Option D:
Reason 3: Congruent supplements theorem.
Statement 4: Angle 1 is congruent with angle 2

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3 years ago

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