There are 6! = 720 ways of arranging the lamps.
If the leftmost lamp is red, there are 3 choices of lamp in the leftmost position, and the remaining 5 can be placed in any order, so there are 3×5! = 360 ways of arranging the lamps and the leftmost is red.
Hence there is a 360/720 = 1/2 probability that the leftmost lamp is red.
Ignoring lamp color for the moment, the probability of arranging 3 lit lamps and 3 unlit lamps is the same, 1/2.
Since Ryan arranges the lamps randomly by color, then turns 3 of them on randomly, the two events are independent. So
P(leftmost red AND leftmost lit) = P(red) × P(lit) = 1/2² = 1/4
An obtuse triangle must have an angle greater than 90degrees (cannot equal 90). Therefore, A. would be the correct answer. This is because A. is the only set of angles that includes an angle greater than 90. Also, all angle measures add up to equal 180degrees.
The sum (for all polygons) of the exterior angles are 360. So, 360/11 is 32.72
hope this helps!
Answer:
2155.13
Step-by-step explanation:
Pi * r(squared)*h