Point R is midpoint of segment GL. GR = 6x - 3 RL = 2x + 9 GR =? RL =? GL =?

1 answer:

4 0

Because R is the midpoint, both segments are equal to each other. set sides equal to each other to solve for R.

6x-3 = 2x+9 x=3

plug x value into each equation

GR= 15

RL= 15

GL= 30

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Passengers using New York's MetroCard system must swipe the card at a rate between 10 and 40 inches per second, or else the card

zepelin [54]

Answer:

E(X) = 27.5 in/s

s.d (X) = 13.28 in/s

1st quartile = 16.25 in/s

3rd quartile = 38.75 in/s

33.33%

Step-by-step explanation:

Solution:-

- The Research shows that actual swipe rates by subway riders are uniformly distributed between 5 and 50 inches per second.

- The uniform distribution of the swipe rate can be expressed by the limits of swipe rates as [ a , b ] as follows:

- The random variable X follows a uniform distribution for the rate of card swiped expressed by parameters [ 5 , 50 ].

X ~ U ( 5 , 50 )

a) The mean value E(X) for the distribution is:

E(X) = ( b - a ) / 2

E(X) = (50-5) / 2

E(X) = 27.5 in/s

b) The standard deviation s.d for the distribution is as follows:

s.d (X) = sqrt ( { [ (b-a) + 1 ]^2 -1 } / 12 )

s.d (X) = sqrt ( { [ (5-5) + 1 ]^2 -1 } / 12 )

s.d (X) = 13.28 in/s\

c) The first quartile is given by the 25% of the swipe rates lie under:

1st quartile = a + 0.25*(b-a)

1st quartile = 5 + 0.25*(50 - 5)

1st quartile = 5 + 11.25 = 16.25 in/s

d) The third quartile is given by the 75% of the swipe rates lie under:

3rd quartile = a + 0.75*(b-a)

3rd quartile = 5 + 0.75*(50 - 5)

3rd quartile = 5 + 33.75 = 38.75 in/s

e) what percentage of subway riders must re-swipe the card because they were outside the acceptable range?

1 - P(10<= x <=40) =

1 - (30/45) = 1 - 2/3 = 1/3 = 33.33%

4 0

4 years ago

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