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2 years ago

A trellis consists of overlapping wooden slats.

Mathematics

1 answer:

Alex73 [517]2 years ago

8 0

The position of the angles are corresponding angles.

The value of x should be 6 for the slats to be parallel.

The theorem use to prove the parallel slat is the corresponding angle theorem.

The measure of the indicated angles are 42 degrees.

<h3>How to know a corresponding angles?</h3>

Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal.

Therefore, the position of the angles are corresponding angles

Since the angles are corresponding angles, they are congruent.

Therefore,

3x + 24 = 7x

24 = 7x - 3x

24 = 4x

x = 6

The theorem use to prove the postulate is the corresponding angle theorem.

The measure of the indicated angle can be calculated as follows:

7(6) = 42 degrees.

learn more on corresponding angles here:brainly.com/question/26251987

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The 99% confidence interval would be given by (196.2;283.8)

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We need to assume that the data comes from a random sample and we need to assume that the distribution of the data is normal.

Step-by-step explanation:

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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".

$\bar X=240$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=15 represent the sample standard deviation

n=4 represent the sample size

Part a

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

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=4-1=3$

Since the Confidence is 0.99 or 99%, 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: "=-T.INV(0.005,3)".And we see that $t_{\alpha/2}=5.84$

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

$240-5.84\frac{15}{\sqrt{4}}=196.2$

$240+5.84\frac{15}{\sqrt{4}}=283.8$

So on this case the 99% confidence interval would be given by (196.2;283.8)

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What assumption about the data is necessary for the inference derived from the analysis to be valid?

We need to assume that the data comes from a random sample and we need to assume that the distribution of the data is normal.

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