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Mathematics

1 answer:

cluponka [151]2 years ago

5 0

They would be similar triangles because they cannot be congruent due to the fact that the side lengths are different. They are dilutions of each other which again proves that they are similar, not congruent.

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Write the following using algebraic notation, using the letter x for any unknown numbers:

Maru [420]

Answer:

$4(x-3)$

Step-by-step explanation:

$(x-3)\times 4$

$4(x-3)$

$4x-12$

5 0

2 years ago

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In an effort to estimate the mean dollars spent per visit by customers of a food store, the manager has selected a random sample

Galina-37 [17]

Answer:

$45.67-1.66\frac{12.30}{\sqrt{100}}=43.63$

$45.67+1.66\frac{12.30}{\sqrt{100}}=47.69$

And the best answer for this case would be:

About $47.69

Step-by-step explanation:

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".

$\bar X=45.67$ represent the sample mean

$\mu$ population mean (variable of interest)

s=12.3 represent the sample standard deviation

n=100 represent the sample size

Solution to the problem

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:

$df=n-1=100-1=99$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,99)".And we see that $t_{\alpha/2}=1.66$