The probability that a randomly selected carton has a puncture or a smashed corner is 12.6%.
In this problem, the events are:
Event A: Puncture.
Event B: Smashed corner.
The "or" probability is given by:
∩
5% have a puncture, hence 
8% have a smashed corner, hence 
0.4% have both a puncture and a smashed corner, hence
Then:
Therefore, The probability that a randomly selected carton has a puncture or a smashed corner is 12.6%.
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For this case we must solve the following expression:
÷ 
According to the PEMDAS algebraic order method, we have the following order:
P: Parenthesis
E: Exponents
MD: Multiplication and division
AS: Addition and subtraction
So, we have:
Answer:
Answer:
a) The distance of the light's base from the bottom of the building is approximately: 5.2 ft
b) The length of the beam is approximately: 10.4 ft
Step-by-step explanation:
First, we have to recognize that we may draw a right triangle to picture our problem. Then, in order to find out the distance of the light's base from the bottom of the building, we need to use the tangent trigonometric function:
tan(angle) = opposite side / adjacent side
We know the angle and the opposite side and we want to find the adjacent side:
adjacent side = opposite side / tan(angle) = 9 ft / tan(60°) = 9 ft / = 9 ft / 1.73 = 5.2 ft
In order to find the length of the light beam, we use Pythagoras Theorem:
leg1²+leg2² = hyp²
Since the length of the beam corresponds to the hypotenuse and since we already know the length of the two legs, it is just a matter of substituting the values:
hyp = square_root(leg1²+leg2²) = square_root(9² + 5.2²) ft = square_root(108.4) ft = 10.4 ft
