Answer:
The probability that an uses drugs given that the result was negative is 0.0224.
Step-by-step explanation:
Let's denote the events as follows:
<em>D</em> = an intern uses drugs.
<em>X</em> = the test result was positive.
The information provided is:
![P(X|D)=0.80\\P(X|D^{c})=0.03\\P(D)=0.10](https://tex.z-dn.net/?f=P%28X%7CD%29%3D0.80%5C%5CP%28X%7CD%5E%7Bc%7D%29%3D0.03%5C%5CP%28D%29%3D0.10)
Compute the probability that the test result of an intern is positive as follows:
![P(X)=P(X|D)P(D)+P(X|D^{c})P(D^{c})\\=P(X|D)P(D)+P(X|D^{c})[1-P(D^{c})]\\=(0.80\times0.10)+(0.03\times(1-0.10))\\=0.107](https://tex.z-dn.net/?f=P%28X%29%3DP%28X%7CD%29P%28D%29%2BP%28X%7CD%5E%7Bc%7D%29P%28D%5E%7Bc%7D%29%5C%5C%3DP%28X%7CD%29P%28D%29%2BP%28X%7CD%5E%7Bc%7D%29%5B1-P%28D%5E%7Bc%7D%29%5D%5C%5C%3D%280.80%5Ctimes0.10%29%2B%280.03%5Ctimes%281-0.10%29%29%5C%5C%3D0.107)
The probability that the test result of an intern is positive is <em>P (X) = 0.107</em>.
Compute the probability that the result is negative given that he/she uses drugs as follows:
![P(X^{c}|D)=1-P(X|D)=1-0.80=0.20](https://tex.z-dn.net/?f=P%28X%5E%7Bc%7D%7CD%29%3D1-P%28X%7CD%29%3D1-0.80%3D0.20)
Compute the probability that an uses drugs given that the result was negative as follows:
![P(D|X^{c})=\frac{P(X^{c}|D)P(D)}{P(X^{c})}=\frac{P(X^{c}|D)P(D)}{1-P(X)} =\frac{0.20\times0.10}{1-0.107} =0.0224](https://tex.z-dn.net/?f=P%28D%7CX%5E%7Bc%7D%29%3D%5Cfrac%7BP%28X%5E%7Bc%7D%7CD%29P%28D%29%7D%7BP%28X%5E%7Bc%7D%29%7D%3D%5Cfrac%7BP%28X%5E%7Bc%7D%7CD%29P%28D%29%7D%7B1-P%28X%29%7D%20%3D%5Cfrac%7B0.20%5Ctimes0.10%7D%7B1-0.107%7D%20%3D0.0224)
Thus, the probability that an uses drugs given that the result was negative is 0.0224.
Answer:
49
Step-by-step explanation:
y = -x² - 10x + 24
For a parabola ax² + bx + c, the vertex is at x = -b/(2a).
In this case, a = -1 and b = -10. So:
x = -(-10) / (2 * -1)
x = -5
The y coordinate is:
y = -(-5)² - 10(-5) + 24
y = -25 + 50 + 24
y = 49
Answer:
23
Step-by-step explanation:
The sides opposite equal angles of a triangle have equal length:
KJ = IJ
9x -11 = 6x -5
3x = 6 . . . . . . . . add 11-6x
x = 2
__
Perimeter = (7x-5) +(6x -5) +(9x -11) = 22x -21 = 22(2) -21 = 23
The perimeter of triangle JIK is 23 units.
Answer:
<em>17 inches </em>
Step-by-step explanation:
c² = a² + b²
c = √(225 + 64) = √289 = <em>17 inches</em>