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Varvara68 [4.7K]
2 years ago
6

Which triangle is similar to ΔJKL? ΔJKM, ΔMKL, ΔKML, ΔLJK.

Mathematics
2 answers:
kirill [66]2 years ago
7 0
The answer would be ΔKML because the right angle of ΔKML is in the same place as <span>ΔJKL</span>
nadezda [96]2 years ago
4 0

Answer:

Triangle \triangle KML is similar to the given triangle \triangle JKL.

Step-by-step explanation:

Let us analyze the given options one by one.

\triangle JKM is not similar to the triangle \triangle JKL because it is not written in correct order. The way we write the triangle (order of vertices) is very important. Since angles K of both the triangles are not equal, therefore, order is messed up. If the order had been \triangle JMK then this would have been correct.

\triangle MKL is not similar to triangle \triangle JKL because the corresponding angles are not equal. Again the order it not right. If the order had been \triangle KML, then this option would have been correct.

\triangle KML is similar to the given triangle \triangle JKL because corresponding angles of both the triangles are equal.

\triangle LJK is not similar to the given triangle \triangle JKL because the corresponding angles of the two triangles are not equal.

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Complete question is;

In a certain community, 8% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all person with diabetes as having the disease, and incorrectly diagnoses 10% of all person without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having diabetes actually has the disease.

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P(has diabetes | positive) = 0.442

Step-by-step explanation:

Probability of having diabetes and being positive is;

P(positive & has diabetes) = P(has diabetes) × P(positive | has diabetes)

We are told 8% or 0.08 have diabetes and there's a correct diagnosis of 95% of all the persons with diabetes having the disease.

Thus;

P(positive & has diabetes) = 0.08 × 0.95 = 0.076

P(negative & has diabetes) = P(has diabetes) × (1 –P(positive | has diabetes)) = 0.08 × (1 - 0.95)

P(negative & has diabetes) = 0.004

P(positive & no diabetes) = P(no diabetes) × P(positive | no diabetes)

We are told that there is an incorrect diagnoses of 10% of all persons without diabetes as having the disease

Thus;

P(positive & no diabetes) = 0.92 × 0.1 = 0.092

P(negative &no diabetes) =P(no diabetes) × (1 –P(positive | no diabetes)) = 0.92 × (1 - 0.1)

P(negative &no diabetes) = 0.828

Probability that a person selected having diabetes actually has the disease is;

P(has diabetes | positive) =P(positive & has diabetes) / P(positive)

P(positive) = 0.08 + P(positive & no diabetes)

P(positive) = 0.08 + 0.092 = 0.172

P(has diabetes | positive) = 0.076/0.172 = 0.442

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2 years ago
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