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Eduardwww [97]
2 years ago
13

Triangle J K L is shown. Point N is the midpoint of side J L and point M is the midpoint of side K L. The length of J K is 19.6

meters. The lengths of J N and N L are 7.4 meters. The lengths of K M and M L are 10.7 meters.
What is the distance between points M and N?

meters
Mathematics
1 answer:
Kruka [31]2 years ago
7 0

The distance between points M and N according to the task content is; 9.8 meters.

<h3>What is the distance between points M and N?</h3>

From observation of the task content information; it can be deduced for a fact that the line segment MN which joins points M and N is parallel to the line JK. This follows from the fact that M and N are midpoints KL and JL respectively.

Hence, it follows that triangles NLM and JLK are congruent and by the ratio of corresponding sides equality;

NM/19.6 = 7.4/(2×7.4)

NM = 19.6/2 = 9.8 meters.

This follows from congruence theorems in which case, the ratio of corresponding sides of congruent triangles are equal.

Read more on congruent triangles;

brainly.com/question/1675117

#SPJ1

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Step-by-step explanation:

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The SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36 scores is selected. a) What is the probab
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Answer:

a) 0.0082

b) 0.9987

c) 0.9192

d) 0.5000

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Step-by-step explanation:

The question is concerned with the mean of a sample.  

From the central limit theorem we have the formula:

z=\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }

a) z=\frac{1224-1200}{\frac{60}{\sqrt{36} } }=2.40

The area to the left of z=2.40 is 0.9918

The area to the right of z=2.40 is 1-0.9918=0.0082

\therefore P(\bar X\:>\:1224)=0.0082

b) z=\frac{1230-1200}{\frac{60}{\sqrt{36} } }=3.00

The area to the left of z=3.00 is 0.9987

\therefore P(\bar X\:

c) The z-value of 1200 is 0

The area to the left of 0 is 0.5

z=\frac{1214-1200}{\frac{60}{\sqrt{36} } }=1.40

The area to the left of z=1.40 is 0.9192

The probability that the sample mean is between 1200 and 1214 is

P(1200\:

d) From c) the probability that the sample mean will be greater than 1200 is 1-0.5000=0.5000

e) z=\frac{73.46-1200}{\frac{60}{\sqrt{36} } }=-112.65

The area to the left of z=-112.65 is 0.

The area to the right of z=-112.65 is 1-0=1

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The total cost of the dinner is $176.20.

<h3>What is the total cost of the dinner?</h3>

The total cost of the dinner is the sum of the bill for the dinner, the tax and the tip.

Total cost = tip + bill of the dinner + tip

Tax = 0.08 x 140 = $11.20

Total cost = $140 + $25 + $11.20 = $176.20

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Step-by-step explanation:

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