A large spinning wheel has 20 pie slices of different colors. There are 7 green slices, 4 red slices, and the rest are black. If you spin the wheel and the pointer stops at green you win $2, stops at red you win $5, stops at black you win nothing. If you are charged $3 to play this game then how much is the expected value if you played 10 times?

Expected value is $13

Step-by-step explanation:

It is given that number of slices in spinning wheels =20

Number of green slice = 7

Number of red slice = 4

It is given that when green and red slice comes there is a win

Probability of outcome of green slice

Probability of outcome of red slice

It is given that when green slice comes win price is $2 and when red slice come price $5

So winning price

Charge of each play is $3

So expected value if he plays one times =$1.7 - $3 = -$1.3

He plays 10 times

Therefore total expected values = 10×-$1.3= $13

equal to

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is