H=205+2*d
(h=height of sunflower/d=number of days passed)
We need to leave m alone on the right hand side, so let's move everything else to the left hand side.
First of all, we can subtract b from both sides to get
![y-b = mc](https://tex.z-dn.net/?f=%20y-b%20%3D%20mc%20)
Now, we can divide both sides by c to get
![\dfrac{y-b}{c}=m](https://tex.z-dn.net/?f=%20%5Cdfrac%7By-b%7D%7Bc%7D%3Dm%20)
And so we solved the expression for m, because we have written an expression in the form
, where the right hand side doesn't depend on m.
One ratio is 30:40 since 15 times 2 is 30 and 20 times 2 is 40.
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:
![P (H) = 0.04,\ P(P^{c}|H^{c})=0.02\ and\ P(P|H)=0.01](https://tex.z-dn.net/?f=P%20%28H%29%20%3D%200.04%2C%5C%20P%28P%5E%7Bc%7D%7CH%5E%7Bc%7D%29%3D0.02%5C%20and%5C%20P%28P%7CH%29%3D0.01)
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\\](https://tex.z-dn.net/?f=P%28H%5E%7Bc%7D%29%3D1-P%28H%29%3D1-0.04%3D0.96%5C%5CP%28P%7CH%5E%7Bc%7D%29%3D1-P%28P%7CH%29%3D1-0.02%3D0.98%5C%5C)
(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})](https://tex.z-dn.net/?f=P%28A%29%3DP%28A%7CB%29P%28B%29%2BP%28A%7CB%5E%7Bc%7D%29P%28B%5E%7Bc%7D%29)
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](https://tex.z-dn.net/?f=P%28P%29%3DP%28P%7CH%29P%28H%29%2BP%28P%7CH%5E%7Bc%7D%29P%28H%5E%7Bc%7D%29%5C%5C%3D%280.01%5Ctimes0.04%29%2B%280.98%5Ctimes0.96%29%5C%5C%3D0.9412)
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](https://tex.z-dn.net/?f=P%28H%5E%7Bc%7D%7CP%29%3D%5Cfrac%7BP%28P%7CH%5E%7Bc%7D%29P%28H%5E%7Bc%7D%29%7D%7BP%28P%29%7D%20%5C%5C%3D%5Cfrac%7B0.98%5Ctimes0.96%7D%7B0.9412%7D%20%5C%5C%3D0.9996%5C%5C%5Capprox1)
Thus, the probability that a person who passes through the system is without any security problems is approximately 1.
Answer:
(2x + y)(2x - y - 1)
Step-by-step explanation:
4x² - y² - 2x - y
4x² - y² is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
4x² - y²
= (2x)² - y²
= (2x - y)(2x + y)
expression is now
(2x - y)(2x + y) - (2x + y) ← factor out (2x + y) from each term
= (2x + y)(2x - y - 1)