Answer:
The answer is: 7
Step-by-step explanation:
\frac{\frac{21}{4}}{\frac{3}{4}} = 7
Answer:
(- 4, - 2 )
Step-by-step explanation:
Under a rotation about the origin of 90°
a point (x, y ) → (- y, x ) , then
(- 2, 4 ) → (- 4, - 2 )
Answer:
-15
Step-by-step explanation:
-3+8-5. 5x3=15 and because it is -p it would be -15.
Answer:
a
![P(X = 0) = 0.6065](https://tex.z-dn.net/?f=%20P%28X%20%3D%200%29%20%3D%20%200.6065%20)
b
![P(x < 25 ) = 1.18 *10^{-33}](https://tex.z-dn.net/?f=P%28x%20%3C%20%2025%20%29%20%3D%20%20%201.18%20%2A10%5E%7B-33%7D%20)
c
Step-by-step explanation:
From the question we are told that
The rate is
= 0.5 / hr
Generally Poisson distribution formula is mathematically represented as
![P(X = x) = \frac{(\lambda t) ^x e^{-\lambda t }}{x!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%20%5Cfrac%7B%28%5Clambda%20t%29%20%5Ex%20e%5E%7B-%5Clambda%20t%20%7D%7D%7Bx%21%7D)
Generally the probability that no error occurred during a day is mathematically represented as
Here t = 1 hour according to question a
So
![P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%20%5Cfrac%7B%5Clambda%5Ex%20e%5E%7B-%5Clambda%7D%7D%7Bx%21%7D)
Hence
![[tex]P(X = 0) = \frac{\frac{1}{2} ^0 e^{-\frac{1}{2}}}{0!}](https://tex.z-dn.net/?f=%5Btex%5DP%28X%20%3D%200%29%20%3D%20%20%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%20%5E0%20e%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%7D%7B0%21%7D)
=> ![P(X = 0) = 0.6065](https://tex.z-dn.net/?f=%20P%28X%20%3D%200%29%20%3D%20%200.6065%20)
Generally the probability that a critical error occurs since the start of a day is mathematically represented as
Here t = 1 hour according to question a
So
![P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%20%5Cfrac%7B%5Clambda%5Ex%20e%5E%7B-%5Clambda%7D%7D%7Bx%21%7D)
Hence
![P(x \ge 25 ) = 1 - P(x < 25 )](https://tex.z-dn.net/?f=P%28x%20%5Cge%2025%20%29%20%3D%20%201%20-%20P%28x%20%3C%20%2025%20%29)
Here
![P(x < 25 ) = \sum_{x=0}^{24} \frac{e^{-\lambda} * \lambda^{x}}{x!}](https://tex.z-dn.net/?f=P%28x%20%3C%20%2025%20%29%20%3D%20%5Csum_%7Bx%3D0%7D%5E%7B24%7D%20%5Cfrac%7Be%5E%7B-%5Clambda%7D%20%2A%20%5Clambda%5E%7Bx%7D%7D%7Bx%21%7D)
=> ![P(x < 25 ) = \frac{e^{-0.5} *0.5^{0}}{0!} + \cdots + \frac{e^{-0.5} *0.5^{24}}{24!}](https://tex.z-dn.net/?f=P%28x%20%3C%20%2025%20%29%20%3D%20%20%5Cfrac%7Be%5E%7B-0.5%7D%20%2A0.5%5E%7B0%7D%7D%7B0%21%7D%20%2B%20%5Ccdots%20%2B%20%5Cfrac%7Be%5E%7B-0.5%7D%20%2A0.5%5E%7B24%7D%7D%7B24%21%7D)
![P(x < 25 ) = 0.6065 + \cdots + \frac{e^{-0.5} *0.5^{24}}{6.204484 * 10^{23}}](https://tex.z-dn.net/?f=P%28x%20%3C%20%2025%20%29%20%3D%20%200.6065%20%2B%20%5Ccdots%20%2B%20%5Cfrac%7Be%5E%7B-0.5%7D%20%2A0.5%5E%7B24%7D%7D%7B6.204484%20%2A%2010%5E%7B23%7D%7D)
![P(x < 25 ) = 0.6065 + \cdots + 6.0*10^{-32}](https://tex.z-dn.net/?f=P%28x%20%3C%20%2025%20%29%20%3D%20%200.6065%20%2B%20%5Ccdots%20%2B%206.0%2A10%5E%7B-32%7D)
![P(x < 25 ) = 1.18 *10^{-33}](https://tex.z-dn.net/?f=P%28x%20%3C%20%2025%20%29%20%3D%20%20%201.18%20%2A10%5E%7B-33%7D%20)
Considering question c
Here t = 2
Gnerally given that the system just started up and an error occurred the probability the next reset will occur within 2 hours
![P(x \le 5 ) = \sum_{n=0}^{5} \frac{(\lambda t) ^x e^{-\lambda t }}{x!}](https://tex.z-dn.net/?f=P%28x%20%5Cle%205%20%29%20%3D%20%20%5Csum_%7Bn%3D0%7D%5E%7B5%7D%20%20%5Cfrac%7B%28%5Clambda%20t%29%20%5Ex%20e%5E%7B-%5Clambda%20t%20%7D%7D%7Bx%21%7D)
=> ![P(x \le 5 ) = \frac{(0.5 * 2) ^ 0 e^{- 0.5 * 2 }}{0!} + \cdots + \frac{(0.5 * 2) ^ 5 e^{- 0.5 * 2 }}{5!}](https://tex.z-dn.net/?f=P%28x%20%5Cle%205%20%29%20%3D%20%20%20%5Cfrac%7B%280.5%20%2A%20%202%29%20%5E%200%20e%5E%7B-%200.5%20%20%2A%202%20%7D%7D%7B0%21%7D%20%2B%20%5Ccdots%20%20%2B%20%20%20%5Cfrac%7B%280.5%20%2A%20%202%29%20%5E%205%20%20e%5E%7B-%200.5%20%20%2A%202%20%7D%7D%7B5%21%7D)
=> ![P(x \le 5 ) = \frac{1* 2.7183 }{1 } + \cdots + \frac{1 *2.7183 }{120}](https://tex.z-dn.net/?f=P%28x%20%5Cle%205%20%29%20%3D%20%20%20%5Cfrac%7B1%2A%202.7183%20%7D%7B1%20%7D%20%2B%20%5Ccdots%20%20%2B%20%20%20%5Cfrac%7B1%20%20%2A2.7183%20%7D%7B120%7D)
=>
Answer:
(See explanation for further details)
Step-by-step explanation:
Classification based on sides:
Equilateral - Three sides with same length.
Isosceles - Two sides with same length.
Scalene - No sides with same length.
Classification based on sides:
Acute-Angled - All angles are acute. ![(0^{\circ} < \theta < 90^{\circ}, 0^{\circ} < \alpha < 90^{\circ}, 0^{\circ} < \beta < 90^{\circ}, \theta + \alpha + \beta = 180^{\circ})](https://tex.z-dn.net/?f=%280%5E%7B%5Ccirc%7D%20%3C%20%5Ctheta%20%3C%2090%5E%7B%5Ccirc%7D%2C%200%5E%7B%5Ccirc%7D%20%3C%20%5Calpha%20%3C%2090%5E%7B%5Ccirc%7D%2C%200%5E%7B%5Ccirc%7D%20%3C%20%5Cbeta%20%3C%2090%5E%7B%5Ccirc%7D%2C%20%5Ctheta%20%2B%20%5Calpha%20%2B%20%5Cbeta%20%3D%20180%5E%7B%5Ccirc%7D%29)
Right-Angled - One angle is right. ![(0^{\circ} < \theta < 90^{\circ};\alpha = 90^{\circ}, 0^{\circ} < \beta < 90^{\circ}, \theta + \alpha + \beta = 180^{\circ})](https://tex.z-dn.net/?f=%280%5E%7B%5Ccirc%7D%20%3C%20%5Ctheta%20%3C%2090%5E%7B%5Ccirc%7D%3B%5Calpha%20%3D%2090%5E%7B%5Ccirc%7D%2C%200%5E%7B%5Ccirc%7D%20%3C%20%5Cbeta%20%3C%2090%5E%7B%5Ccirc%7D%2C%20%5Ctheta%20%2B%20%5Calpha%20%2B%20%5Cbeta%20%3D%20180%5E%7B%5Ccirc%7D%29)
Obtuse-Angled - One angle is obtuse. ![(0^{\circ} < \theta < 90^{\circ},90^{\circ}](https://tex.z-dn.net/?f=%280%5E%7B%5Ccirc%7D%20%3C%20%5Ctheta%20%3C%2090%5E%7B%5Ccirc%7D%2C90%5E%7B%5Ccirc%7D%3C%5Calpha%20%3C%20180%5E%7B%5Ccirc%7D%2C%200%5E%7B%5Ccirc%7D%20%3C%20%5Cbeta%20%3C%2090%5E%7B%5Ccirc%7D%2C%20%5Ctheta%20%2B%20%5Calpha%20%2B%20%5Cbeta%20%3D%20180%5E%7B%5Ccirc%7D%29)