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4 years ago

Given: m

Mathematics

1 answer:

Nutka1998 [239]4 years ago

7 0

Answer:

$m\angle MEJ=25^{\circ}.$

Step-by-step explanation:

The arcs LY, KM, KL and MJ together form the full revolution angle, thus

$4x+50^{\circ}+6x+x+10^{\circ}+4x=360^{\circ},\\ \\15x=300^{\circ},\\ \\x=20^{\circ}.$

Note that

$m\angle MOJ=4x=80^{\circ},$

then

$m\angle MLJ=\dfrac{1}{2}\cdot 80^{\circ}=40^{\circ}.$

So,

$m\angle ELM=180^{\circ}-40^{\circ}=140^{\circ}.$

Also

$m\angle LOK=30^{\circ},$

$m\angle KML=\dfrac{1}{2}\cdot 30^{\circ}=15^{\circ}.$

In triangle EML,

$m\angle MEL+m\angle EML+m\angle ELM=180^{\circ},\\ \\m\angle MEL=180^{\circ}-15^{\circ}-140^{\circ}=25^{\circ}.$

Thus, $m\angle MEJ=25^{\circ}.$

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Examine the required sample size needed to be able to

Xelga [282]

Answer:

$n=(\frac{2.33(500)}{10})^2 =13572.25 \approx 13573$

And if we use a sample level of n =2000 the margin of error would be higher as we can see here:

$ME=2.33\frac{500}{\sqrt{2000}}=26.05$

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".

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

$\mu$ population mean (variable of interest)

$\sigma=500$ represent the population standard deviation assumed

n represent the sample size (variable of interest)

Confidence =98% or 0.98

ME = 10 represent the margin of error desired

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =10 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 98% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.01;0;1)", and we got $z_{\alpha/2}=2.33$ , replacing into formula (b) we got:

$n=(\frac{2.33(500)}{10})^2 =13572.25 \approx 13573$

So the answer for this case would be n=13573 rounded up to the nearest integer

And if we use a sample level of n =2000 the margin of error would be higher as we can see here:

$ME=2.33\frac{500}{\sqrt{2000}}=26.05$

3 0

4 years ago

The sum of 42 and a number x is 51

n200080 [17]

Answer:

x = 9

Step-by-step explanation:

"The sum of 42 and a number x is 51" in "mathy" words:

42 + x = 51

Then, subtract both sides by 42:

42 + x - 42 = 51 - 42

x = 9

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3 years ago

Identify which of the following tables shows the number of triangles and the total perimeter for the following pattern. Use the

belka [17]

Answer:

Step-by-step explanation:

Identify which of the following tables shows the number of triangles and the total perimeter for the following pattern. Use the table to predict the perimeter for 5 triangles.

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3 years ago

Un número multiplicado que me 343

irina1246 [14]

7 multiplicado por 49 =343

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3 years ago

There are 22456 pine trees in the park the park workers are going to plant 6478 more trees this year how many trees will there b

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Step-by-step explanation:

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3 years ago