Alice, Bob, and Charlotte are looking for butterflies. They look in three separate parts of a field, so that their probabilities of success do not affect each other. Alice finds 1 butterfly with probability 17%, and otherwise does not find one. Bob fines 1 butterfly with probability 25%, and otherwise does not find one. Charlotte finds 1 butterfly with probability 45%, and otherwise does not find one. Let X be the number of butterflies that they find together. What is the expected value of X?

The expected number of butterflies that they find together is 0.87.

Step-by-step explanation:

Let A = number of butterflies caught by Alice, B = number of butterflies caught by Bob and C = number of butterflies caught by Charlotte.

The probability function of A is:

The probability function of B is:

The probability function of C is:

The random variable X is denoted as the number of butterflies that they find together.

Compute the expected value of X as follows:

E (X) = E (A + B + C)

        = E (A) + E (B) + E (C)

Thus, the expected number of butterflies that they find together is 0.87.

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

2.56 is the width of the garden

step-by-step explanation: