3. what is the net amount that a contestant should expect to win per game if the game were to be played many
times?

0.55

Missing Statement:

At a carnival, one game costs $1 to play. The contestant gets one shot in an attempt to bust a balloon. Each balloon

contains a slip of paper with one of the following messages:

If the contestant does not bust a balloon, then the $1 cost is forfeited. The table below displays the probability

distribution of the discrete random variable, or net winnings for this game

Net Winnings −1         0        1          4            9

Probability      0.25     ?      0.3     0.08     0.02

Step-by-step explanation:

First we find of the missing probability for net winnings of 0, in which case:

When you receive the message, “Sorry, you do not win, but you get your dollar back,” then your net winnings is 0$.

The  probability of winning 0$ is = 1 - 0.25 - 0.3 - 0.08 -0.02 = 0.35

So now we have the complete details:

Net Winnings −1         0        1          4            9

Probability     0.25    0.35    0.3     0.08     0.02

Now we need to find ,the net amount that a contestant should expect to win is the expected value of the probability distribution.

Expected value of probability distribution = −1(0.25 ) +0 (0.35 ) + 1(0.3 ) +4 (0.08 ) + 9(0.02 )

Expected value of probability distribution = 0.55

The net amount that a contestant should expect to win per game if the game were to be played many  times is 0.55

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

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕