There are two cases to consider.
A) The removed square is in an odd-numbered column (and row). In this case, the board is divided by that column and row into parts with an even number of columns, which can always be tiled by dominos, and the column the square is in, which has an even number of remaining squares that can also be tiled by dominos.
B) The removed square is in an even-numbered column (and row). In this case, the top row to the left of that column (including that column) can be tiled by dominos, as can the bottom row to the right of that column (including that column). The remaining untiled sections of the board have even numbers of rows, so can be tiled by dominos.
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Perhaps the shorter answer is that in an odd-sized board, the corner squares are the ones that there is one of in excess. Cutting out one that is of that color leaves an even number of squares, and equal numbers of each color. Such a board seems like it <em>ought</em> to be able to be tiled by dominos, but the above shows there is actually an algorithm for doing so.
Arithmetic sequences have a common difference (addition)
geometric sequences have a common ratio (multiplication)
Answer:
The probability that you would choose lemon-lime and then orange is 3/11 =.273.
Step-by-step explanation:
These are 'dependent events', which mean that your the event is affected by previous events. So, because you have eleven total bottles (five lemon-lime and six orange) and you do not replace the first bottle, that would only leave you with ten bottles remaining. The probability that you will pick the lemon-lime on the first choice is 5/11 because all of the bottles are there. However, your second choice will only include ten total bottles since you already took one. The probability that you would choose orange would be 6/10. When you multiply these two fractions and reduce to simplest form, you get 3/11.
Beach invasions beach invasions
Answer:
Step-by-step explanation:
So we have the inequality:
Definition of Absolute Value:
Note that the sign is flipped in the second case because we multiplied by a negative.
Add 5 to both sides to both equations:
Merge:
And we're done!
