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A target is made of a yellow square inside of a green square. What is the theoretical probability that a dart will hit the green square if the side length of the yellow square is 4, and the side length of the green square is 8?

A.

0.25

B.

0.5

C.

0.75

D.

0.8

NotSoSmart Dec 23, 2018

#1**+2 **

The side length of the yellow square is 4, so the area of the yellow square is 16 (units^2).

The total area of the green is the [Area of Green Square] - [Area of Yellow Square]. The side length of the green square is 8, so with the yellow square inside, the area is 64 (units^2). 64 - 16 = 48 (units^2).

The probability of the dart hitting the green area is (Green Area) / (Total Area), which is \(\dfrac{48}{64} = \boxed{0.75}\). The answer is C) 0.75.

- PM

PartialMathematician Dec 23, 2018

#1**+2 **

Best Answer

The side length of the yellow square is 4, so the area of the yellow square is 16 (units^2).

The total area of the green is the [Area of Green Square] - [Area of Yellow Square]. The side length of the green square is 8, so with the yellow square inside, the area is 64 (units^2). 64 - 16 = 48 (units^2).

The probability of the dart hitting the green area is (Green Area) / (Total Area), which is \(\dfrac{48}{64} = \boxed{0.75}\). The answer is C) 0.75.

- PM

PartialMathematician Dec 23, 2018

#3**+1 **

_____________________

| |

| 48 units^2 |

| __________ |

| | | |

| | 16 units^2 | |

| | | |

| |________ __| |

| ____________________|

48/(48+16) = 0.75

PartialMathematician
Dec 23, 2018