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2 answers:
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The appropriate method to use in solving the given question is permutation. Then, the numbers of ways to arrange the buttons is 1320 ways.
In the given question, the order of arrangement is important, so that the number of ways that Fiona could order the buttons can be determined by permutation method.
i.e =
Red 6
Green 3
Yellow 3
Total 12
Since no two neighbouring buttons of the same colour is allowed, then 3 buttons would be arranged at a time.
Thus, n = 12 and r = 3;
=
=
=
= 12 x 11 x 10
= 1320
Therefore the buttons can be arranged in 1320 ways without two neighbors having the same colour.
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Answer:
The dimensions of the work area are 16 ft by 36 ft
Step-by-step explanation:
Let
x ----> the length of the work area in feet
y-----> the width of the work area in feet
we know that
The perimeter of the work area is equal to
simplify
----> equation A
The area of the work area is equal to
---> equation B
substitute equation A in equation B
solve the quadratic equation by graphing
using a graphing tool
The solutions are
x=16 ft, y=36 ft
or
x=36 ft, y=16 ft
see the attached figure
therefore
The dimensions of the work area are 16 ft by 36 ft
