Aprofessor rolls a fair, six-sided die. using the classical method of probability, what is the probability that at least three spots will be showing up on the die

The required probability is 2/3.

Step-by-step explanation:

It is given that a professor rolls a fair, six-sided die.

We need to find the probability that at least three spots will be showing up on the die.

Total possible outcomes = {1,2,3,4,5,6}

Number of total outcomes = 6

At least three spots will be showing up on the die.

Favorable outcomes = {3,4,5,6}

Number of favorable outcomes = 4

Formula for probability:

Therefore, the required probability is 2/3.

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 .

i got 10.28 but that rounds up to 10.3