Aplayer rolls a die and receives the number of dollars equal to the number on the die except when the die shows a 6. if a 6 is rolled, the player loses $6. if the game is to be fair, what should be the cost to play?

We expect to win k dollars with probability 1/6 if k is between 1 and 5, and we lose 6 dollars with probability 1/6. So, the expected value for this random variable is

So, you win on average 1.5 dollars, and if that's the cost to play, the game is fair.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet