A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 52.0 minutes. Find the probability that a given class period runs between 50.25 and 50.75 minutes.

The probability that a given class period runs between 50.25 and 50.75 minutes = 0.25

Step-by-step explanation:

Length of the class = 52 - 50 = 2

The probability density is

The probability that a given class period runs between 50.25 and 50.75 minutes. is calculated by multiplying range with the probability density.

Range = 50.75 - 50.25 = 0.5

Now the probability P (50.25<x<50.75) = 0.5 × 0.5 = 0.25

This is the probability that a given class period runs between 50.25 and 50.75 minutes.

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 .

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)