Answer:
x ≥ 4
Step-by-step explanation:
Start with: 5x - 9 ≥ 11
Add 9 to both sides: 5x - 9 + 9 ≥ 11 + 9
Divide both sides by 5:
Simplify: x ≥ 4
Since you are not dividing both sides by a negative number, the greater than or equal to sign faces the same direction.
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.
The equivalent expression is ~
