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masha68 [24]
2 years ago
12

The graph shown compares the number of pages of the same book read by Emily and Serena over time.

Mathematics
1 answer:
iragen [17]2 years ago
7 0

Using linear equations, the number of minutes that both would read for them to read equal number of pages is: 30 minutes.

<h3>What is the Equation of a Linear Graph?</h3>

Equation of a linear graph is given as, y = mx + b, where m and b are the slope and y-intercept of the graph respectively.

Equation for Emily's graph:

Slope (m) = rise/run = 1/3

y-intercept (b) = 2

Substitute m = 1/3 and b = 2 into y = mx + b

y = 1/3x + 2

Equation for Serena's graph:

Slope (m) = rise/run = 2/5

y-intercept (b) = 0

Substitute m = 2/5 and b = 0 into y = mx + b

y = 2/5x + 0

y = 2/5x

To find how many minutes for both of them to read the same number of pages, make both equations equal to each other.

2/5x = 1/3x + 2

2/5x - 1/3x = 2

1/15x = 2

Multiply both sides by 15

x = (2)(15)

x = 30

The answer is 30 minutes for both to read the same number of pages.

Learn more about linear equations on:

brainly.com/question/14323743

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

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(c) P(X = −2) = 1/9

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Step-by-step explanation:

Given:

- Two 3-sided fair die.

- Random Variable X_1 denotes the number you get for rolling 1st die.

- Random Variable X_2 denotes the number you get for rolling 2nd die.

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

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

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

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

       

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

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

                                 : ( 2 / 9 )

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

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

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

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                          P(Y=0) = 0

                          P(Y=1) =  1/3

                          P(Y=2) = 1/ 3

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