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zmey [24]
3 years ago
15

Tell whether x and y show direct variation. Explain your reasoning. x=y+2

Mathematics
1 answer:
Mashutka [201]3 years ago
6 0

Answer:

It does not show variation

Step-by-step explanation:

Given

x = y + 2

Required

Determine if there's direct variation between x and y

The general form of direct variation is:

y = kx

Make y the subject of formula in the given parameters;

x = y + 2

y = x - 2

Compare y = x - 2 to y = kx

<em>Since they are not of the same form, then the given equation do not show direct variation</em>

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Bob Nale is the owner of Nale’s Quick Fill. Bob would like to estimate the mean number of gallons of gasoline sold to his custom
ira [324]

Answer:

a) The best estimator for the population mean is given by the sample mean \hat \mu = \bar X = 5.70

b) The 99% confidence interval would be given by (4.969;6.431)    

c) We are 99% confident that the true mean for th number of gallons of gasoline  sold to his customers is between 4.969 and 6.431.

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=1.9 represent the population standard deviation

n=45 represent the sample size  

2) Part a

The best estimator for the population mean is given by the sample mean \hat \mu = \bar X = 5.70

3) Part b. Develop a 99 percent confidence interval for the population mean.

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.95 or 95%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=2.58

Now we have everything in order to replace into formula (1):

5.7-2.58\frac{1.9}{\sqrt{45}}=4.969    

5.7+2.58\frac{1.9}{\sqrt{45}}=6.431

So on this case the 99% confidence interval would be given by (4.969;6.431)    

4) Part c. Interpret the meaning of part (b).

On this case we can say this: We are 99% confident that the true mean for th number of gallons of gasoline  sold to his customers is between 4.969 and 6.431.

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Step-by-step explanation6 divided by 9

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Please help me (30 points) 1. A recipe calls for 2 1/3 cups of flour, 3/4 cups of white sugar, and 1/3 cups of brown sugar. The
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Lets find how much flour we need for just one serving.

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Best of Luck!

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