Dillion has 4 blue marbles and 12 red marbles
And max has 96 red marbles
Answer:
5in x 10in
Step-by-step explanation:
Solution:
1. You have to assume that the ring will land on the board and as a result, just focus on one rectangle of the board since they are all the same size.
2. For the ring to land entirely inside the rectangle, the center of the ring needs to be 1.5 inches inside the border (radius is 1.5 inches), so the "winning rectangle" will have dimensions:
L = (x - 2(1.5)) = x - 3
w = (2x - 2(1.5)) = 2x-3.
3. Now, we will set up and solve our geometric probability equation. The winning rectangle's area of (x-3)*(2x-3) divided by the total rectangle's area of x*(2x) = 28%
(2x-3)*(x-3)/(2x^2) = .28
2x^2 - 9x + 9 = .56x^2
1.44x^2 - 9x + 9 = 0
4 . Now you can plug that in the quadratic formula and get the solutions x = 1.25 or 5. However, it cannot by 1.25 because that is too small of a dimension for the the circle with diameter of 3 to fit in, the answers has to be 5.
5. As a result, the dimensions of the rectangles are 5in x 10in.
Graph is accurate enuf so that you can determine immed that the vertex / minimum is at (3,-4) and that the y-intercept is at (0,5).
If by "solutions" you mean "roots," the roots are {1, 5} (where y=0).
Area = width * length
if width = 3/8 length ⇒ length = 8/3 width
area = width * 8/3 width = 8/3 width² = 6
width² =
width =
