Answer:
942 ft²
Step-by-step explanation:
The diagram shows the area to be 3/4 of that of a circle of radius 20 ft. The area of a circle is given by ...
A = πr² = π(20 ft)² = 400π ft²
Then 3/4 of that area is ...
dog run = (3/4)(400π ft²) = 300π ft² ≈ 942.48 ft²
The area of the dog's run is about 942 ft².
Answer:
(a) 0.9412
(b) 0.9996 ≈ 1
Step-by-step explanation:
Denote the events a follows:
= a person passes the security system
= a person is a security hazard
Given:

Then,

(a)
Compute the probability that a person passes the security system using the total probability rule as follows:
The total probability rule states that: 
The value of P (P) is:

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:

Thus, the probability that a person who passes through the system is without any security problems is approximately 1.
Answer:
the given expression is equivalent to
Step-by-step explanation:
![\frac{ \sqrt[4]{200} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%5B4%5D%7B200%7D%20%7D%7B2%7D%20)
X^2 - 8x + 13 = 0
subtract 13 from both sides
x^2 - 8x = -13
-8/2 = -4, (-4)^2 = 16, add 16 to both sides
x^2 - 8x + 16 = -13 + 16
factor the left side
(x - 4)^2 = 3