For less than twice a number K
2 answers:
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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.
Answer:
Step-by-step explanation:
Given
Solving (a):
We have:
Express f(x) as y
Swap x and y
Add 8 to
Square both sides
Rewrite as:
Express y as:
To determine the domain, we have:
The original function is
The range of this is:
The of the
function is the
of the
function.
<em>Hence, the domain is:</em>