Solve the equation by the zero factor property x^2+6x-16=0
1 answer:
The expression
can be factored into
..............(1)
The zero factor property says that if p*q=0, then either p=0, or q=0, or both, i.e. x=y=0.
Therefore, using the zero factor property, we see from (1) that
either (x+8)=0, or (x-2)=0, or (x+8)=0 AND (x-2)=0.
Thus solving previous equations,
x=-8, or x=2
can be factored into
The zero factor property says that if p*q=0, then either p=0, or q=0, or both, i.e. x=y=0.
Therefore, using the zero factor property, we see from (1) that
either (x+8)=0, or (x-2)=0, or (x+8)=0 AND (x-2)=0.
Thus solving previous equations,
x=-8, or 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.