Answer:
Percentage of balls which are red = 80%.
Step-by-step explanation:
Let the probability of drawing a red ball be x then the probability of drawing a white ball is 1-x.
There are 5C3 = 10 ways of getting 3 reds in 5 draws so the probability of this is 10* x^3 * (1 - x)^2.
The probability of getting 1 red in 5 draws = 5C1 * x (1-x)^4.
The first probability is 32 times the last.
So we have the equation:
10x^3(1 - x)^2 / 5x(1 - x)^4 = 32
2x^2 / (1 - x)^2 = 32
2x^2 = 32(1 -x)^2
2x^2 = 32( 1 - 2x + x^2)
2x^2 = 32 - 64x + 32x^2
30x^2 - 64x + 32 = 0
15x^2 - 32x + 16 = 0
(5x - 4)(3x - 4) = 0
x = 0.8, 1.333...
The probability must be < 1 so x = 0.8 = 80%.
Answer:
The longest sides is 18 m long.
Step-by-step explanation:
Let x meters be the length of the first side.
The length of the second side = x+9 m.
The length of the third = 3x m.
Perimeter = x + 3x + x + 9 = 39
5x + 9 = 39
5x = 30
x = 6 m.
The other 2 sides are 6+9 = 15 m and 3*6 = 18 m.
Answer:
Step-by-step explanation:
The simple interest formula is
I = Prt, where I is the interest earned, P is the initial investment, r is the interest rate in decimal form, and t is the time in years. We have that after 2 years, 9000 has turned into 10440. That means that the total interest earned was 10440 - 9000 = 1440
I = 1440
P = 9000
r = ?
t = 2
Filling in we have
1440 = 9000(r)(2) and
1440 = 18000r so
r = .08
As an interest rate, we multiply this by 100 to get 8%
