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Fofino [41]
2 years ago
11

A man wants to test for diabetes. His family history shows that the probability of getting diabetes is 0.6. He decides to do a h

ome test to check whether he has the disease. The test has an 85% accuracy rate. What is the probability before the test is taken that the patient has diabetes? 0.08 0.09 0.51 0.60
Mathematics
1 answer:
lesantik [10]2 years ago
8 0
So,

The probability of the man having diabetes is 0.6 or 60%.  Because we are figuring the probability BEFORE the test is taken that he has the disease, we can disregard the test and its accuracy rate.  That rate is 60%, the probability of him having diabetes.

The correct option is D.
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Step-by-step explanation:

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Suppose cos(x)= -1/3, where π/2 ≤ x ≤ π. What is the value of tan(2x). EDGE
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Answer:

D

Step-by-step explanation:

We are given that:

\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi

And we want to find the value of tan(2<em>x</em>).

Note that since <em>x</em> is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

\displaystyle \tan(2x)=\frac{\sin(2x)}{\cos(2x)}

Using double angle identities:

\displaystyle  \tan(2x)=\frac{2\sin x\cos x}{\cos^2 x-\sin^2 x}

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(<em>x</em>) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since <em>x</em> is in QII, cosine and tangent will be negative while sine will be positive. Hence:

<h2>\displaystyle  \tan(2x)=\frac{2(2\sqrt{2}/3)(-1/3)}{(-1/3)^2-(2\sqrt{2}/3)^2}</h2>

Simplify:

\displaystyle  \tan(2x)=\frac{-4\sqrt{2}/9}{(1/9)-(8/9)}

Evaluate:

\displaystyle  \tan(2x)=\frac{-4\sqrt{2}/9}{-7/9} = \frac{4\sqrt{2}}{7}

The final answer is positive, so we can eliminate A and B.

We can simplify D to:

\displaystyle \frac{2\sqrt{8}}{7}=\frac{2(2\sqrt{2}}{7}=\frac{4\sqrt{2}}{7}

So, our answer is D.

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Step-by-step explanation:

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