You are challenged to a lucky draw game. If you draw a face card (K. O. J) from a standard deck of cards, you earn 10 points. If
you draw any other card, you lose 2 points. What is the expected value of a draw?
0.77
1.69
1.85
2.31

There are 52 cards in a standard deck. There are 4 suits, and there are 3 different types of face cards, so 4*3=12 face cards in a 52 card deck.

So the probability of drawing one of those cards is 12/52 or 3/13. The probability of drawing other cards is 40/52 or 10/13. So the right choice is A.

Hope this helped!

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x