A company makes concrete paving stones in different sizes. Each stone has a volume of 360 inches and a height of 3 inches. the s
2 answers:
Answer:
The answer is 6.
Step-by-step explanation:
Given is that the total volume is 360 cubic inches
The height is fixed at 3 inches
So, total area will be = square inches.
Let's assume the minimum size in any dimension to be 3 inches.
Now we have to find possible combinations of numbers greater than 2 that will make 120. So, we have
3 x 40
4 x 30
5 x 24
6 x 20
8 x 15
10 x 12
These have the same answer in reverse order as well. So we will consider these.
Therefore, there are 6 different paving stones with different base.
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<h3>Answer: 28</h3>
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Explanation:
Method 1
Imagine a table with 8 rows and 8 columns to represent all possible match-ups. You can actually draw out this table or just think of it as a thought experiment.
There are 8*8 = 64 entries in the table. Along the northwest diagonal, we have each team pair up with itself. This is of course silly and impossible. We cross off this entire diagonal so we drop to 64-8 = 56 entries.
Then notice that the lower left corner is a mirror copy of the upper right corner. A match-up like AB is the same as BA. So we must divide by 2 to get 56/2 = 28 different matches.
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Method 2
There are 8 selections for the first slot, and 8-1 = 7 selections for the second slot. We have 8*7 = 56 permutations and 56/2 = 28 combinations.
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Method 3
Use the nCr combination formula with n = 8 and r = 2
There are 28 combinations possible. Order doesn't matter (eg: match-up AB is the same as match-up BA).
Notice how the (8*7)/2 expression is part of the steps shown above in the nCr formula.