A surgical procedure requires choosing among 4 alternative methodologies. The first can result in 6 possible outcomes, the second in 5 possible outcomes, and the remaining methodologies can each result in 3 possible outcomes. What is the total number of outcomes possible?

There are total 17 different outcomes possible of the surgical procedure.

Step-by-step explanation:

A surgical procedure is to be performed.

The procedure can be performed by selecting 4 alternative methodologies.

Each of these 4 alternative methodologies have various outcomes.

The first methodology can result in 6 different outcomes.

The second methodology can result in 5 different outcomes.

The third methodology can result in 3 different outcomes.

The fourth methodology can result in 3 different outcomes.

The total number of outcomes of the surgical procedure is:

Total number of outcomes =

                                             = 6 + 5 + 3 + 3

                                             = 17

Thus, there are total 17 different outcomes possible of the surgical procedure.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

answer would be 8.64 or s = 11π/4 inches

step-by-step explanation:

s = r θ  

where s = arc length  

r = radius = 3 inches  

θ = central angle in radians = ( π /180)*165  

s = 3(π/180)*165  

= 8.64 inches