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4 years ago

15

If the equation y = 1/6(x + 12) were graphed in the xy-plane, which of the following statements would be true of the graphed lin

e?
A. It would be perpendicular to the graph of y = 1/6x + 3.

B. It would be parallel to the graph of 12y = 2x + 3.

C. It would have the same slope as the graph of x + 6y = 18.

D. It would have the same y‑intercept as the graph of y = 1/6x + 12.

1 answer:

oksano4ka [1.4K]4 years ago

3 0

The answer would be B it would be parallel to the graph of 12y = 2x + 3

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In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain or nervous system (based on data from

Maksim231197 [3]

Answer:

$z=\frac{0.0003214 -0.00034}{\sqrt{\frac{0.00034(1-0.00034)}{420095}}}=-0.654$

$p_v =2*P(Z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.005$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that the true proportion not differs significantly from the specified value of 0.00034 or 0.034%.

Step-by-step explanation:

1) Data given and notation

n=420095 represent the random sample taken

X=135 represent the subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today)

$\hat p=\frac{135}{420095}=0.0003214$ estimated proportion of subjects developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute as reported in USA Today)

$p_o=0.00034$ is the value that we want to test

$\alpha=0.005$ represent the significance level

Confidence=99.5% or 0.995

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the brain or nervous system at a rate that is different from the rate of 0.0340% :

Null hypothesis: $p=0.00034$

Alternative hypothesis: $p \neq 0.00034$

When we conduct a proportion test we need to use the z statistic, and the is given by:

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

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.0003214 -0.00034}{\sqrt{\frac{0.00034(1-0.00034)}{420095}}}=-0.654$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.005$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z$

So the p value obtained was a very high value and using the significance level given $\alpha=0.005$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that the true proportion not differs significantly from the specified value of 0.00034 or 0.034%.

4 0

3 years ago

You recently sent out a survey to determine if the percentage of adults who use social media has changed from 66%, which was the

il63 [147K]

Answer:

The 98% confidence interval estimate of the proportion of adults who use social media is (0.56, 0.6034).

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 $1 - \frac{\alpha}{2}$ .

Of the 2809 people who responded to survey, 1634 stated that they currently use social media.

This means that $n = 2809, \pi = \frac{1634}{2809} = 0.5817$

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a pvalue of $1 - \frac{0.02}{2} = 0.99$ , so $Z = 2.327$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5817 - 2.327\sqrt{\frac{0.5817*4183}{2809}} = 0.56$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5817 + 2.327\sqrt{\frac{0.5817*4183}{2809}} = 0.6034$

The 98% confidence interval estimate of the proportion of adults who use social media is (0.56, 0.6034).

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3 years ago

Determine the equations of the vertical and horizontal asymptotes, if any, for y=x^3/(x-2)^4

djverab [1.8K]

Answer:

Option a)

Step-by-step explanation:

To get the vertical asymptotes of the function f(x) you must find the limit when x tends k of f(x). If this limit tends to infinity then x = k is a vertical asymptote of the function.

$\lim_{x\to\\2}\frac{x^3}{(x-2)^4} \\\\\\lim_{x\to\\2}\frac{2^3}{(2-2)^4}\\\\\lim_{x\to\\2}\frac{2^3}{(0)^4} = \infty$

Then. x = 2 it's a vertical asintota.

To obtain the horizontal asymptote of the function take the following limit:

$\lim_{x \to \infty}\frac{x^3}{(x-2)^4}$

if $\lim_{x \to \infty}\frac{x^3}{(x-2)^4} = b$ then y = b is horizontal asymptote

Then:

$\lim_{x \to \infty}\frac{x^3}{(x-2)^4} \\\\\\lim_{x \to \infty}\frac{1}{(\infty)} = 0$

Therefore y = 0 is a horizontal asymptote of f(x).

Then the correct answer is the option a) x = 2, y = 0

3 0

3 years ago

Read 2 more answers

Are these lines parallel perpendicular or neither

Natasha_Volkova [10]

Answer:

perpendicular

Step-by-step explanation:

start but putting each line into the standard line format

2x-y=-5

-y=-2x-5

y=2x+5

x+2y=-6

2y=-x-6

y=-(1/2)x-3

if lines are parallel the slopes would be the same. 2 is not equal to -1/2

if lines are perpendicular the slope of one would be the opposite inverse of the other.

negative inverse of 2 = - (1/2)

so the lines are perpendicular

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3 years ago

Gaby deposited $200 in a savings account earning 4% simple interest over 7 years. What was the total interest Gaby earned?

Yuki888 [10]

I=prt. I= $200 X 4% X 7. I= 8 X 7. I= 56. Her total interest earned was $56 :)

5 0

3 years ago