Consider a game in which a player rules a number cube to determine the number of points earned. if a player rolls a number greater than or equal to 4 the number of roll is added to the total points. any other roll is deducted from the players total. what is the expected value of the points earned on a single roll in this game?

Expected value is the sum of probabilities for all outcomes...

4*(1/6)+5*(1/6)+6*(1/6)-3*(1/6)-2*(1/6)-1*(1/6)

(4+5+6)/6-(3+2+1)/6

15/6-6/6

9/6

1.5

So the expected value for a single roll in this game is 1.5 points.

There is something missing in the given model equation. I think the correct equation is y= -1/4 x^2 + 5x. You maybe forgot to type the '+' sign. I checked it initially, and I got an answer that's in the choices. So, hopefully, this is correct.

To find the maximum height, you must solve this equation through differential calculus. To find the maxima or minima, you differentiate the equation y in terms of x and equate it to zero. 

y' = 2(-1/4)x + 5 = -1/2*x + 5 = 0

By doing this, you would solve the value of x or the horizontal distance.

-1/2*x = -5
x =-5*-2
x = 10 inches

Finally, we substitute this x to the original equation to determine the maximum height y.

y = -1/4*10 + 5(10)
y = 25 inches

The answer is C.