Aspinner of a board game can land on any one of three regions labeled: a, b, and c. if the probability the spinner lands on b is five times that offive times that of a, and the probability the spinner lands on c is three times that ofthree times that of a, find the probability the spinner lands on a.

1/9

Step-by-step explanation:

Let's call x the probability of landing in A

So, probability of landing on B is 5x and probability of landing on C is 3x.

As we only have this options, the probabilities A + B + C = 1. So,

x + 5x + 3x = 1

9x = 1

x = 1/9

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)