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liq [111]
3 years ago
7

What is the length of line segment KJ?

Mathematics
1 answer:
Karolina [17]3 years ago
5 0

Please consider the attached file.

We can see that triangle JKM is a right triangle, with right angle at M. Segment KM is 6 units and segment MJ is 3 units. We can also see that KJ is hypotenuse of right triangle.

We will use Pythagoras theorem to solve for KJ as:

KJ^2=KM^2+MJ^2

KJ^2=6^2+3^2

KJ^2=36+9

KJ^2=45

Now we will take positive square root on both sides:

\sqrt{KJ^2}=\sqrt{45}

KJ=\sqrt{9\cdot 5}

KJ=3\sqrt{5}

Therefore, the length of line segment KJ is 3\sqrt{5} and option D is the correct choice.

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|×|=×<br>is the absolute value of x always, sometimes, or never x​
il63 [147K]

Answer:

Sometimes

Step-by-step explanation:

I’ll give you an example so you can understand:

Let’s say x is 4. So plug 4 into the problem:

|4|=4  →  This is a very true statement, where the absolute value of 4 is equal to 4.

Now, let’s say x is -7. So plug -7 into the problem:

|-7|=-7  →  This is a false statement because it’s saying that the absolute value of -7 is -7 which is very untrue.

So |x|=x only works for positive numbers, but not negative numbers. Therefore, |x|=x is the absolute value of x <u>sometimes.</u>

<u />

Hope this helps and answers your question! :)

6 0
3 years ago
A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selec
VMariaS [17]

Answer:

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}=

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

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]

5 0
3 years ago
What is 5.138 + 2.624 = ? (show ur work)
Mrac [35]

Answer:

7.762

Step-by-step explanation:

Brainliest!

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I don't understand what one
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Answer:

14y-13y² is the answer. sorry for dirty handwriting

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