Answer:
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Step-by-step explanation:
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If there are n people, each person could shake hands with 0 people, 1 person, 2 people,... on up to shaking hands with n − 1
people. Count how many different answers there are to asking the person the question "How many hands did you shake?" How many people are there? If the people are the pigeons, and the possible answers to the question "how many hands did you shake" are the holes, can we conclude anything yet? No? How about now noticing that at least one of the holes "I shook hands with noone" or "I shook hands with everyone" has to be empty... now what?
"Since there are more pigeons than holes there must be a hole with at least two pigeons in the same hole" Now, replace the word "pigeons" and "holes" with the appropriate terms for the context of your specific question, remember we are talking about people and number of handshakes they participated in.
Your intention with the wording "consecutive integers of 12 feet" is not clear. Shown are triangles with sides 12 and 13 (a nice Pythagorean triple) as well as 11 and 12.
Answer: the first option is the correct answer.
Step-by-step explanation:
Let x represent the number of necklaces that he makes in a year.
Profit = Revenue - cost
The cost of making each necklace is $5. In making necklaces in a year, the fixed cost is $5000. This means that the total cost of making x necklaces in a year is
5x + 5000
Sam sells each necklace for $10 each. This means that the total amount made from selling x necklaces is $10x.
For Sam to make profit of $1000 in a year, the number of necklaces that she must sell would be
1000 = 10x - (5x + 5000)
1000 = 10x - 5x - 5000
10x - 5x = 1000 + 5000
5x = 6000
x = 6000/5
x = 1200