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Sholpan [36]
3 years ago
13

Consider the system of equations. y = 3x + 2       y = − 2 3 x − 4 Explain why these particular equations can be graphed immedia

tely.
Mathematics
1 answer:
inessss [21]3 years ago
3 0

Answer:

These equations are in slope-intercept form. I can use the y-intercept and slope to graph both lines. I plot the y-intercept and use rise over run to locate another point on the line. Then, I can draw a line through the two points.

Step-by-step explanation:

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an arc subtends a central angle measuring 2pi/3 radians. what fraction of the circumference is this arc?
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Answer:

1/3

Step-by-step explanation:

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3 years ago
. Imagine a game of 3 players where exactly one player wins in the end and all players have equal chances of being the winner. T
lbvjy [14]

Answer:

5/9

Step-by-step explanation:

Number of players = 3

number of times game is repeated = 4

P( any person wins a game ) = 1/3

P ( any person does not win a game ) = 1 - 1/3 = 2/3

P ( any person wins no game in 4 attempts ) = ( 2/3 )^4 = 16/81

<em>Note : each player has equal chance of winning </em>

<u>Find the probability that there is at least one person who wins no games </u>

lets represent the probability of each player not wining a game with alphabet A

A1 = player 1 wins no game

A2 = player 2 wins no game

A3 = players 3 wins no game

Applying the inclusion-exclusion formula

<em>P( A1 ∪ A2 U A3 )</em><em> = P(A1 ) + P(A2) + P(A3) - P( A1 ∩ A2 ) - P( A2 ∩ A3 ) - P( A1            ∩ A3 )  + P( A1 ∩ A2 ∩ A3 ) </em>

where

P( A1 ∩ A2 ) = P( A1 wins all games )

P ( A1 wins all games in 4 attempts ) = ( 1/3 )^4 = 1/81

P( A1 ∩ A2 ∩ A3 ) = P ( no players wins any game in 4 attempts ) = 0

Hence

P( A1 ∪ A2 U A3 ) = 16/81 + 16/81 + 16/81 - 1/81 - 1/81 - 1/81 - 0 = 5/9

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