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Rina8888 [55]
3 years ago
6

Center ( 9,-8 ), passes through ( 19,22 )

Mathematics
1 answer:
katovenus [111]3 years ago
6 0
Center at (h,k) and radius r is
(x-h)²+(y-k)²=r²

so given
center at (9,-8)

(x-9)²+(y-(-8))²=r²
(x-9)²+(y+8)²=r²

input the point (19,22) to find r²
x=19 and y=22
(19-9)²+(22+8)²=r²
10²+30²=r²
100+900=r²
1000=r²
10√10=r

well, the equation is
(x-9)²+(y+8)²=1000
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We have two fair three-sided dice, indexed by i = 1, 2. Each die has sides labeled 1, 2, and 3. We roll the two dice independent
Nikitich [7]

Answer:

(a) P(X = 0) = 1/3

(b) P(X = 1) = 2/9

(c) P(X = −2) = 1/9

(d) P(X = 3) = 0

(a) P(Y = 0) = 0

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(c) P(Y = 2) = 1/3

Step-by-step explanation:

Given:

- Two 3-sided fair die.

- Random Variable X_1 : Result on 1st die.

- Random Variable X_2: Result on 2nd die.

- Random Variable X = X_2 - X_1.

Solution:

 

- Possible outcomes of X : { - 2 , -1 , 0 ,1 , 2 }

- The corresponding probabilities for each outcome are:

                 ( X = -2 ):  { X_2 = 1 , X_1 = 3 }  

                P ( X = -2 ):  P ( X_2 = 1 ) * P ( X_1 = 3 )  

                                :  ( 1 / 3 ) * ( 1 / 3 )  

                                : ( 1 / 9 )    

                ( X = -1 ):  { X_2 = 1 , X_1 = 2 } + { X_2 = 2 , X_1 = 3 }

                P ( X = -1 ):  P ( X_2 = 1 ) * P ( X_1 = 3 ) + P ( X_2 = 2 ) * P ( X_1 = 3)

                                :  ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

                                : ( 2 / 9 )        

 ( X = 0 ):  { X_2 = 1 , X_1 = 1 } + { X_2 = 2 , X_1 = 2 } +  { X_2 = 3 , X_1 = 3 }

               P ( X = -1 ):3*P ( X_2 = 1 )*P ( X_1 = 1 )

                                :  3*( 1 / 3 ) * ( 1 / 3 )

                                : ( 3 / 9 ) = ( 1 / 3 )        

                  ( X = 1 ):  { X_2 = 2 , X_1 = 1 } + { X_2 = 3 , X_1 = 2 }

               P ( X = 1 ): 2* P ( X_2 = 2 ) * P ( X_1 = 1 )

                                : 2* ( 1 / 3 ) * ( 1 / 3 )

                                : ( 2 / 9 )

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                 P ( X = 2 ):  P ( X_2 = 3 ) * P ( X_1 = 1 )  

                                   :  ( 1 / 3 ) * ( 1 / 3 )  

                                   : ( 1 / 9 )                  

- The distribution Y = X_2,

                         P(Y=0) = 0

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                         P(Y=2) = 1/ 3

- The probability for each number of 3 sided die is same = 1 / 3.

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