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Pie
3 years ago
14

Find the perimeter of the shape below:

Mathematics
2 answers:
Alexandra [31]3 years ago
7 0

Answer:

21.4

Step-by-step explanation:

PSYCHO15rus [73]3 years ago
4 0

The given points are:

A             -4            3

B             0              2

C             2              4

D             0              -3

 

We use the distance formula to calculate for the length of each segment.

D^2 = (x2 – x1)^2 + (y2 – y1)^2

 

For segment AB:

D^2 = (0 + 4)^2 + (2 – 3)^2 = 17

D = sqrt 17

 

For segment BC:

D^2 = (2 - 0)^2 + (4 - 2)^2 = 8

D = sqrt 8

 

For segment CD:

D^2 = (0 - 2)^2 + (-3 – 4)^2 = 53

D = sqrt 53

 

For segment DA:

D^2 = (-4 - 0)^2 + (3 + 3)^2 = 52

D = sqrt 52

 

Getting the sum of all the segments will give the perimeter.

Perimeter = sqrt 17 + sqrt 8 + sqrt 53 + sqrt 52

Perimeter = 21.44

 

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Step-by-step explanation:

Denote the events a follows:

P = a person passes the security system

H = a person is a security hazard

Given:

P (H) = 0.04,\ P(P^{c}|H^{c})=0.02\ and\ P(P|H)=0.01

Then,

P(H^{c})=1-P(H)=1-0.04=0.96\\P(P|H^{c})=1-P(P|H)=1-0.02=0.98\\

(a)

Compute the probability that a person passes the security system using the total probability rule as follows:

The total probability rule states that: P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})

The value of P (P) is:

P(P)=P(P|H)P(H)+P(P|H^{c})P(H^{c})\\=(0.01\times0.04)+(0.98\times0.96)\\=0.9412

Thus, the probability that a person passes the security system is 0.9412.

(b)

Compute the probability that a person who passes through the system is without any security problems as follows:

P(H^{c}|P)=\frac{P(P|H^{c})P(H^{c})}{P(P)} \\=\frac{0.98\times0.96}{0.9412} \\=0.9996\\\approx1

Thus, the probability that a person who passes through the system is without any security problems is approximately 1.

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