Answer:
Step-by-step explanation:
Given the following probabilities for events A and B
We want to find P(A ∪ B ∪ C).
Using the inclusion/exclusion formula for the union of three events:
P(A ∪ B ∪ C) = P(A) + P(B) + P(C) − P(A ∩ B) − P(A ∩ C)−P(B∩C)+P(A∩B∩C).
Therefore, P(A or B or C) = 0.48
Answer:
4(12x + 32) = 48x + 128
Step-by-step explanation:
2 hours and 35 minutes is the travel time.
Answer:
x = 1 +√5
Step-by-step explanation:
There are different formulas for the area of a triangle available, depending on the given information.
<h3>Formulas</h3>
When two sides and the angle between them are given, the relevant area formula is ...
Area = 1/2(ab)sin(C)
When the base and height of a triangle are given, the relevant area formula is ...
Area = 1/2bh
<h3>Equal Areas</h3>
The problem statement tells us the two triangles shown have equal areas. That means the two formulas will give the same result.
Area from angle = Area from base/height
1/2(x·x)sin(30°) = 1/2(x-2)(x+1)
x² = 2(x² -x -2) . . . . . . . . . . . use sin(30°) = 1/2, multiply by 4
x² -2x -4 = 0 . . . . . . . . subtract x², eliminate parentheses
(x -1)² = 5 . . . . . . . . . add 4+1 to complete the square
<h3>Value of x</h3>
x = 1 ± √5 . . . . . . take the square root, add 1
The value of x must be greater than 2 in order for the triangle side lengths to be positive. (x-2 > 0) This means x = 1-√5 is an extraneous solution.
The value of x is 1 +√5.
