Three of these expressions are equal to the volume of the barn shown. Which expression is not?
2 answers:
The statement that does not match the others is the one at lower right.
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The barn's volume can be decomposed into a rectangular prism and a triangular one. Thus the <em>upper right</em> expression is a true represenation of the barn's volume:
... Volume of triangular prism + Volume of rectangular prism
The volume of a <em>rectangular prism</em> is the product of its dimensions. The dimensions of the rectangular prism portion of the barn's volume are a, b, c, so the volume of that portion is ...
... Volume of rectangular prism = a·b·c
The volume of a <em>triangular prism</em> is the area of the triangular base multiplied by the length of the prism. Here, the triangular base has base dimension b and height (d-c), so its area is ...
... Area of triangular barn end = (1/2)b(d-c)
Since the length of the barn is "a", the volume of the triangular prism is ...
... Volume of triangular prism = (1/2)b(d-c)a = (1/2)·a·b·(d-c)
The <em>total volume</em> is the sum of the volumes of the parts ...
... a·b·c + (1/2)·a·b·(d-c) . . . . . . matches the <em>upper right</em> selection
This can be factored by removing a·b to outside parentheses:
... a·b·((1/2)·(d-c) + c) . . . . . . . . . matches the <em>lower left</em> selection
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Since the two left selections match the one at upper right, the odd one is the one at lower left.
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Answer:
The traveler can plan such a tour in 3003 ways.
Step-by-step explanation:
The order that the cities are chosen is not important, since it is chosen by the company and not by the traveler. So we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this problem, we have that:
Combinations of 5 cities from a set of 15. So
The traveler can plan such a tour in 3003 ways.