Let x be the amount of time (in minutes) that a particular San Francisco commuter must wait for a BART train. Suppose that the density curve is as pictured below (a uniform distribution): A horizontal line segment is graphed on the coordinate plane. The horizontal x axis is labeled "Minutes" and has two tick marks at 0 and 20. The vertical axis is labeled "Density" and has one tick mark at 0.05. The line enters the viewing window at (0, 0.05) and stops at (20, 0.05). (a) What is the probability that x is less than 8 min? more than 14 min? P (x is less than 8 minutes) = P (x is more than 14 minutes) = (b) What is the probability that x is between 7 and 11 min? P (x is between 7 and 11 minutes) = (c) Find the value c for which P(x < c) = .9. c = mins

a)

b)

c) We want to find a value c who satisfy this condition:

And using the cumulative distribution function we have this:

And solving for c we got:

Step-by-step explanation:

For this case we define the random variable X as he amount of time (in minutes) that a particular San Francisco commuter must wait for a BART train, and we know that the distribution for X is given by:

Part a

We want this probability:

And for this case we can use the cumulative distribution function given by:

And using the cumulative distribution function we got:

For the probability if we use the cumulative distribution function and the complement rule we got:

Part b

We want this probability:

And using the cdf we got:

Part c

We want to find a value c who satisfy this condition:

And using the cumulative distribution function we have this:

And solving for c we got:

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .