PLEASE HELP!!!!!

Mathematics

2 answers:

Debora [2.8K]3 years ago

8 0

The correct answer is; "△DEF is not a right triangle because no two sides are perpendicular." - I took the test.

Alenkasestr [34]3 years ago

7 0

<span>â–łDEF is not a right triangle because no two sides are perpendicular. There are two ways to determine if DEF is a right triangle. You can use the pythagorean theorem to see of a^2 + b^2 = c^2, or you can calculate the slope of each pair of lines to see if their product is -1. I'll demonstrate both methods, but given the available options, I suspect that the product of the slopes is the one you need. Slope method. Slope of DE = (1-(-1))/(-4-3) = 2/-7 = -2/7 Slope of EF = (-1-(-4))/(3-(-1)) = 3/4 Slope of DF = (1-(-4))/(-4-(-1)) = 5/-3 = -5/3 Since we're looking for -1 as a product and we have 2 negative slopes and 1 positive slope, we only need to check DE against EF and EF against DF. So -2/7 * 3/4 = -6/28 = -3/14. This isn't -1, so not perpendicular. 3/4 * -5/3 = -15/12 = -5/4. Still not -1, so not perpendicular. Since no sides of perpendicular to any other sides, DEF is not a right triangle. Now for the pythagorean theorem method. First, let's take a look at the length of the 3 sides of DEF. Actually, we just need to look at the square of the lengths of each side. So square of length DE = (-4 - 3)^2 + (1 - (-1))^2 = -7^2 + 2^2 = 49 + 4 = 53. square of length EF = (3-(-1))^2 + (-1-(-4))^2 = 4^2 + 3^2 = 16+9 = 25 square of length DF = (-4-(-1))^2 + (1-(-4))^2 = -3^2 + 5^2 = 9 + 25 = 34 The longest side is DE, so lets add up the squares of the other 2 sides to see if they equal the square of DE. 25 + 34 = 59. And 59 is not equal to 53. So we know that triangle DEF is NOT a right triangle. Now let's look at the options and see what's correct. â–łDEF is not a right triangle because no two sides are perpendicular. * This is a true statement. So it's the correct answer. The remaining 3 other options all claim that one side is perpendicular to another and as such are incorrect.</span>

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$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

$19.1+3.355\frac{1.5}{\sqrt{9}}=20.78$

And the best option would be:

C. [17.42,20.78]

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".

$\bar X=19.1$ represent the sample mean

$\mu$ population mean (variable of interest)

s=1.5 represent the sample standard deviation

n=9 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:

$df=n-1=9-1=8$

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(0.005,8)".And we see that $t_{\alpha/2}=$