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3 years ago

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A certain disease has an incidence rate of 0.2%. If the false negative rate is 8% and the false positive rate is 4%, compute the

probability that a person who tests positive actually has the disease.

1 answer:

alexira [117]3 years ago

7 0

Answer:

32%

Step-by-step explanation:

Imagine 100000 people are tested.

<u>Of these 100000:</u>

10000080.02= 2000 will have the disease

<u>8% of them:</u>

2000*0.08= or 160, will test negative and the remaining
1840 will test positive.

<u>Of the 98000 who do not have the disease, 4% will test positive:</u>

98000*0.04= 3920 will test positive

<u>So of the:</u>

1840+3920= 5760 total people who test positive,

1840 will have the disease

<u>Thus, the probability is: </u>

1840/5760 ≈0.3194 = 32%

So, out of people who test positive actually 32% has the disease.

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3 years ago

Multiplying Powers with the Same Base

Luda [366]

Applying the product rule of exponents, each product of powers are matched with its simplified expression as:

1. $5 \times 5^3 = 5^4$

2. $5 \times 5^3 = 5^4$

3. $5^{-3} \times 5^{-3} = \frac{1}{5^6}$

4. $5^{-4} \times 5^{4} \times 5^0 = 5^0$

5. $5^{7} \times 5^{3} = 5^{10}$

To multiply the powers having the same base, we will apply the product rule for exponents.

<h3>What is the Product Rule for Exponents?</h3>

Base on the product rule for exponents, we have, $a^m \times a^n = a^{m + n} = a^{mn}$ .
In order to find the products of two given numbers that have the same base, the exponents would be added together.

1. $5^6 \times 5^{-4$

Add the exponents together

$5^6 \times 5^{-4} = 5^{(6) + (-4)}$

$5^6 \times 5^{-4} = 5^2$

2. $5 \times 5^3$

Add the exponents together

$5 \times 5^3 = 5^{(1 + 3)}$

$5 \times 5^3 = 5^4$

3. $5^{-3} \times 5^{-3}$

Add the exponents together

$5^{-3} \times 5^{-3} = 5^{(-3) + (-3)$

$5^{-3} \times 5^{-3} = 5^{-6$

$5^{-3} \times 5^{-3} = \frac{1}{5^6}$

4. $5^{-4} \times 5^{4} \times 5^0$

Add the exponents together

$5^{-4} \times 5^{4} \times 5^0 = 5^{(-4) + (4) + (0)$

$5^{-4} \times 5^{4} \times 5^0 = 5^0$

5. $5^{7} \times 5^{3}$

Add the exponents together

$5^{7} \times 5^{3} = 5^{10}$

In summary, applying the product rule of exponents, each product of powers are matched with its simplified expression as:

1. $5 \times 5^3 = 5^4$

2. $5 \times 5^3 = 5^4$

3. $5^{-3} \times 5^{-3} = \frac{1}{5^6}$

4. $5^{-4} \times 5^{4} \times 5^0 = 5^0$

5. $5^{7} \times 5^{3} = 5^{10}$

Learn more about product rule of exponents on:

brainly.com/question/847241

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