If there are 12 people sitting at a round table , how many different pairs of people can have conversations during dinner, assum
2 answers:
Answer:
Step-by-step explanation:
Given that there are 12 people sitting around at a table.
We see that any two persons can have conversations. If we count A with B as one conversation this is the same as B with A
i.e. order does not matter
So here we have to use combinations.
2 people out of 12 where order does not matter can be done in 12C2 ways
No of conversations =
If we use a dodedecon as a geometrical figure with 12 vertices representing 12 persons the conversation between pairs can be associated with all diagonals and sides connecting two vertices.
Sides are 12 and diagonals are 54 totalling 66.
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Answer:
Step-by-step explanation:
The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.
The volume of the square prism is given by , where
is the base length and
is the height. Substituting given values, we have:
The volume of a trapezoidal prism is given by , where
and
are bases of the trapezoid,
is the length of the height of the trapezoid and
is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases (
) multiplied by the trapezoid's height (
).
Substituting given values, we get:
Therefore, the total volume of the composite figure is (ah, perfect)
Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer: