Can someone please explain how to solve this problem(31)
1 answer:
Answer:
(-1.92, 1.08)
Step-by-step explanation:
The <em>incenter</em> is the center of the largest circle that can be inscribed in the triangle. That circle is called the <em>incircle</em>. The incenter is at the point of intersection of the angle bisectors. For a right triangle, the <em>inradius</em> (the radius of the incircle), is found from a simple formula:
r = (a + b - c)/2 . . . . . where c is the hypotenuse, and a and b are the legs
In your triangle, the inradius is ...
r = (5 + 3 -√(5² +3²))/2 = 4 -√8.5 ≈ 1.08452
Among other things, this means the coordinates of the incenter are about (1.08, 1.08) from the right angle vertex, so are about ...
incenter ≈ (-1.92, 1.08)
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Answer:
Events E and F are independent.
Step-by-step explanation:
E = {multiple of 3} = {3, 6, 9, 12}
P(E) = 4/12
F = {even number} = {2, 4, 6, 8. 10, 12}
P(F) = 6/12
E and F = {even and multiple of 3} = {6, 12}
P(E∩F) = 2/12
In order for two events to be independent the following relationship must be true:
Testing this property:
The relationship holds true, thus events E and F are independent.