<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.
<h3>
Answer: 0.98976</h3>
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Explanation:
60% of the people have been vaccinated, so 40% have not.
The probability of getting five people in a row that aren't vaccinated is (0.40)^5 = 0.01024
Subtract this from 1 to get the probability of at least one vaccinated person in the sample of five.
1-0.01024 = 0.98976
This works because the events "at least one vaccinated" and "none vaccinated" are complementary. One or the other must happen, which means the two probabilities add to 1.
Answer:
the first one is x=-3(16+y/2
secone one is x=11+2y
Step-by-step explanation:
Answer:
28.27 in²
Step-by-step explanation:
The area of a circle is dependent on only one variable: the radius:
A = πr²
If the radius is 3 inches, as you seem to indicate, then:
A = π(3 in)² = 9π in² = 28.27 in²