<span>-|2x-10|-1=2 has ZERO solutions since the absolute value function cannot yield negative outcomes. It can equal 0 or be positive, but it can never be negative.
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Assuming that every material in their respective categories has an equal likelihood of selection.
Categories:
(a) Wood types for cabinets: birch, maple, cherry.
Each wood type has a selection probability of 1/3.
(b) Finish types: transparent, semi-transparent.
Each finish type has a 1/2 chance of being selected.
(c) Knob types: bronze, steel, wood.
Each knob material carries a probability of 1/3.
The selection of materials for the cabinet, finish, and knobs is independent of one another.
Consequently,
Probability(birch wood AND bronze knob) = (1/3)*(1/3) = 1/9
Probability(wood knob) = 1/3
Probability(transparent stain) = 1/2
Probability(cherry wood AND semi-transparent stain) = (1/3)*(1/2) = 1/6
