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3 years ago

M is the midpoint of LN. what is LM?

Mathematics

2 answers:

Serjik [45]3 years ago

7 0

Given,

M is the midpoint of LN.

Thus,

LM = MN

3x = 2x + 2

3x - 2x = 2

x = 2

Hence,

LM = 3x = 3 * 2 = 6

Hence, LM is 6 units.

kherson [118]3 years ago

4 0

Answer: LM = 6 units.

Step-by-step explanation: Given that the point M is the mid-point of the line segment LN shown in the figure.

We are to find the length of LM.

From the figure, we note that

LM = 3x and MN = 2x + 2.

Since M is the mid-point of LN, so it will divide LN in two equal parts.

That is, we must have

$LM=MN\\\\\Rightarrow 3x=2x+2\\\\\Rightarrow 3x-2x=2\\\\\Rightarrow x=2.$

Therefore, we get

$LM=3\times2=6~\textup{units}.$

Thus, LM = 6 units.

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And rounded up we have that n=1681

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".

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$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

If solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by: