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The greatest number of pieces will be 12 where each piece will have a different length and the length of each piece is a whole number, in inches and the remaining piece length will be 12 in(90 - 78).
<h3>What is a sequence?</h3>It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
The total length of the wood = 90 in
We have to cut it into the greatest number of pieces, where each piece will have a different length and the length of each piece is a whole number, in inches.
We can cut it like:
1 in, 2 in, 3 in, 4 in, and so on
The above shows the arithmetic sequence,
The sum of the n natural number is given by:
After solving, we will get a quadratic equation:
n² + n -180 = 0
After solving, we will get:
n = 12.92 and n = -13.92(term can not be negative)
n = 12 (taking whole number)
Thus, the greatest number of pieces will be 12 where each piece will have a different length and the length of each piece is a whole number, in inches and the remaining piece length will be 12 in(90 - 78).
Learn more about the sequence here:
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1. Consider the tree diagram in the picture attached.
2 Each of the games picked can be a W (win) or a L (lose), the chances are equal
3. All that could happen in 4 picked games is shown in the picture:
2 w 2 l can happen in the following 6 ways: {(W,W,L,L)(W,L,W,L)(W,L,L,W)(L,W,W,L)(L,W,L,W)(L,L,W,W)}
4. P(2W,2L)=6/16=3/8
2 Each of the games picked can be a W (win) or a L (lose), the chances are equal
3. All that could happen in 4 picked games is shown in the picture:
2 w 2 l can happen in the following 6 ways: {(W,W,L,L)(W,L,W,L)(W,L,L,W)(L,W,W,L)(L,W,L,W)(L,L,W,W)}
4. P(2W,2L)=6/16=3/8