Factor <img src="https://tex.z-dn.net/?f=x%5E2-2x%2B3" id="TexFormula1" title="x^2-2x+3" alt="x^2-2x+3" align="absmiddle" class=

A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 90% of the time if the

Ahat [919]

Answer:Given:

P(A)=1/400

P(B|A)=9/10

P(B|~A)=1/10

By the law of complements,

P(~A)=1-P(A)=399/400

By the law of total probability,

P(B)=P(B|A)*P(A)+P(B|A)*P(~A)

=(9/10)*(1/400)+(1/10)*(399/400)

=51/500

Note: get used to working in fraction when doing probability.

(a) Find P(A|B):

By Baye's Theorem,

P(A|B)

=P(B|A)*P(A)/P(B)

=(9/10)*(1/400)/(51/500)

=3/136

(b) Find P(~A|~B)

We know that

P(~A)=1-P(A)=399/400

P(~B)=1-P(B)=133/136

P(A∩B)

=P(B|A)*P(A) [def. of cond. prob.]

=9/10*(1/400)

=9/4000

P(A∪B)

=P(A)+P(B)-P(A∩B)

=1/400+51/500-9/4000

=409/4000

P(~A|~B)

=P(~A∩~B)/P(~B)

=P(~A∪B)/P(~B)

=(1-P(A∪B)/(1-P(B)) [ law of complements ]

=(3591/4000) ÷ (449/500)

=3591/3592

The results can be easily verified using a contingency table for a random sample of 4000 persons (assuming outcomes correspond exactly to probability):

===....B...~B...TOT

..A . 9 . . 1 . . 10

.~A .399 .3591 . 3990

Tot .408 .3592 . 4000

So P(A|B)=9/408=3/136

P(~A|~B)=3591/3592

As before.

Step-by-step explanation: its were the answer is

5 0

3 years ago

PLEASE HELP. I WILL MARK BRAINLIEAST!!

emmainna [20.7K]

There’s technically two answers, you could put Angles 3 and 6, or Angles 7 and 2

3 0

3 years ago

Read 2 more answers

Identify the slope and the y-intercept in the equation y = -3/4x + 3. Please make sure to say which is the slope and which is th

Liula [17]

Answer:

the y -intercpt is the 3

the slope is -3/4

Step-by-step explanation:

this is because the 3 is the starting point on the y-axis and the slope is -3/4 because you are going down 3 to the right 4 ---hope this helps

5 0

3 years ago

Read 2 more answers

Given the function ƒ(x) = x 2 - 4x - 5 Identify the zeros using factorization. Draw a graph of the function. Its vertex is at (2

s344n2d4d5 [400]

The zeroes of the equation are 5, -1

6 0

2 years ago

Will Mark Brainiest!!! Simplify the following:

xz_007 [3.2K]

Answer:

1.B

2.A

3. B

Step-by-step explanation:

1. $\frac{x+5}{x^{2} + 6x +5 }$

We have the denominator of the fraction as following:

$x^{2} + 6x + 5 \\= x^{2} + (1 + 5)x + 5\\= x*x + 1x + 5x + 5*1\\= x ( x + 1) + 5(x + 1)\\= (x + 1) (x + 5)$

As the initial one is a fraction, so that its denominator has to be different from 0.

=> ( $x^{2} +6x+5$ ) ≠ 0

⇔ (x +1) (x +5) ≠ 0

⇔ (x + 1) ≠ 0; (x +5) ≠ 0

⇔ x ≠ -1; x ≠ -5

Replace it into the initial equation, we have:

$\frac{x+5}{x^{2} + 6x +5 } = \frac{x+5}{(x+1)(x+5)}$

As (x+5) ≠ 0; we divide both numerator and denominator of the fraction by (x +5)

=> $\frac{x+5}{x^{2} + 6x +5 } = \frac{x+5}{(x+1)(x+5)} = \frac{1}{x+1}$

So that $\frac{x+5}{x^{2} + 6x +5 } = \frac{1}{x+1}$ with x ≠ 1; x ≠ -5

So that the answer is B.

2. $\frac{(\frac{x^{2} -16 }{x-1} )}{x+4}$

As the initial one is a fraction, so that its denominator has to be different from 0

=> x + 4 ≠ 0

=> x ≠ -4

As $\frac{x^{2}-16 }{x-1}$ is also a fraction, so that its denominator (x-1) has to be different from 0

=> x - 1 ≠ 0

=> x ≠ 1

We have an equation: $x^{2} - y^{2} = (x - y ) (x+y)$

=> $x^{2} - 16 = x^{2} - 4^{2} = (x -4) (x +4)$

Replace it into the initial equation, we have:

$\frac{(\frac{x^{2} -16 }{x-1} )}{x+4} \\= \frac{x^{2} -16 }{x-1} . \frac{1}{x + 4}\\= \frac{(x-4)(x+4)}{x-1}. \frac{1}{x + 4}$

As (x + 4) ≠ 0 (proven above), we can divide both numerator and the denominator of the fraction by (x +4)

=> $\frac{(x-4)(x+4)}{x-1} .\frac{1}{x+4} =\frac{x-4}{x-1}$

So that the initial equation is equal to $\frac{x-4}{x-1}$ with x ≠-4; x ≠1

=> So that the correct answer is A

3. $\frac{x}{4x + x^{2} }$

As the initial one is a fraction, so that its denominator (4x + x^2) has to be different from 0

We have:

(4x + x^2) = 4x + x.x = x ( x + 4)

So that: (4x + x^2) ≠ 0 ⇔ x ( x + 4 ) ≠ 0

⇔ $\left \{ {{x\neq 0} \atop {(x+4)\neq0 }} \right.$ ⇔ $\left \{ {{x\neq 0} \atop {x \neq -4 }} \right.$

As (4x + x^2) = x ( x + 4) , we replace this into the initial fraction and have:

$\frac{x}{4x + x^{2} } = \frac{x}{x(x+4)}$

As x ≠ 0, we can divide both numerator and denominator of the fraction by x and have:

$\frac{x}{x(x+4)} =\frac{x/x}{x(x+4)/x} = \frac{1}{x+4}$

So that $\frac{x}{4x+x^{2} } = \frac{1}{x+4}$ with x ≠ 0; x ≠ -4

=> The correct answer is B

3 0

3 years ago