Answer:
The theoretical probability of obtaining exactly four heads when flipping six coins is also 23.4%.
Step-by-step explanation:
Getting x successes out of n trials is a binomial distribution and is given by:
p(x) = 
Here, n = 6
x = 2
p = probability of one head = 
q = 1 - p
= 
=
Substitute these values, we get,
p(2) = 
= 
= 
= 0.234
= 23.4%
We know that 
Now,
p(4) = 
=
= p(2)
Hence, the theoretical probability of obtaining exactly four heads when flipping six coins is also 23.4%.
20/100= x/0.4 then cross multiply 20/250=x which 0.08 the answer is 0.08
Answer:
7.5 liters
Step-by-step explanation:
Here what we need to know is the liters of the first solution, that we will call x. We know that the 40% of x plus the 60% of 30 MUST be equal to the 56% of total liters. The total liters are the sum of both substances, i.e, the x liters of the 1st sugar solution and the 30 liters of the second, which is 30+x liters. So, we have that:
0.4*x + 0.6*30 = 0.56(30+x)
Using distributive and the fact that 0.6*30 = 18 and 0.56*30=16.8
0.4x + 18 = 16.8 + 0.56x
Subtract 16.8 in both sides:
0.4x + 18 - 16.8 = 0.56x
0.4x + 1.2 = 0.56 x
Subtract now 0.4x in both sides:
1.2 = 0.56 x - 0.4x
1.2 = 0.16x
Divide both sides by 0.16
1.2/0.16 = 0.16/0.16 x
7.5 = x
So, the first solution must be of 7.5 liters in order to have a 56% in the mixture.
Well first take 1 die the chance of getting odd is 1/2 now the 2nd die is also 1/2 so what you do from now is multiply them 1/2*1/2=1/4
You have a 1/4 chance of both dice showing an odd number
Perpendicular slope: flip sign and reciprocal = 2
Y = 2x + b
Plug in point (8,5)
5 = 2(8) + b
5 = 16 + b
b = -11
Equation: y= 2x - 11
