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2 answers:
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Answer:
<u>(a) x = 2</u>
Step-by-step explanation:
x - 12 = -8x + 6
First, move all the like terms to one side of the equation. We will move all the x's to the left, and the rest to the right in this equation. (Don't forget to pay attention to the signs of the numbers as you move them over the equal sign.)
x - 12 + 8x = 6
x + 8x = 6 + 12
9x = 18
Next, solve for x by isolating it to one side of the equation. Here, we'll have to divide 18 by 9 (do the opposite of what 9 is doing with x; instead of multiplying it with 18 like it currently is with x, divide 18 by it.)
x =
x = 2
Therefore, your answer is (a), since x = 2.
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Answer:
The probability that the diagnosis is correct is 0.95249.
Step-by-step explanation:
We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.
Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.
Let the probability that people in the United States have diabetes = P(D) = 0.083.
So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917
Also, let A = <u><em>event that the diagnostic test is accurate</em></u>
So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98
And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95
<u>Now, the probability that the diagnosis is correct is given by; </u>
Probability = P(D) P(A/D) + P(D')
P(A/D')
= (0.083 0.98) + (0.917
0.95)
= 0.08134 + 0.87115
= 0.95249
Hence, the probability that the diagnosis is correct is 0.95249.