Answer:
rotation about the origin
The answer would be 6 and 2
F(x) = <span>3x/(8+x) = y
f^(-1) is the inverse function. As its name suggests if f(x) = y that we need to find a g(x) such that g(y) = x
In order to find f^(-1) switch x with y and solve for y
3y/(8+y) = x
x(8+y) = 3y
8x+xy = 3y
8x=3y-xy
8x = y(3-x)
y = 8x/(3-x)
f^(-1) = y = </span>8x/(3-x)
Answer:
The probability of testing positive for one is 0.20.
The probability of testing negative for one sample is (1-0.2)=0.8.
We only save time when all five are negative, which has a probability of 0.8^5=0.32768.
This means that the expected number of tests is
combined sample tests negative = 1 with probability 0.32768
combined sample tests positive = 1+5 retests = 6 with probability 0.67232
Expected number of tests
=Σ nipi / n
=(1*0.32768+6*0.67232)/5 [divide by 5 because we tested 5 samples]
= 0.87232 < 1
So yes, there is a saving.
Note: In practice, all medical tests are not absolute, i.e. they give false-positives(α) and false-negatives (β). The ratios 1-α and 1-β are respectively measures of specificity and sensitivity.
These two parameters complicate the simplistic evaluation above.
Answer:
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