Jamie took 20 pieces of same-sized colored paper and put them in a hat. Four pieces were red, three pieces were blue, and the re
1 answer:
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Answer: 999 games
Step-by-step explanation:
There are many ways to illustrate the rooted tree model to calculate the number of games that must be played until only one player is left who has not lost.
We could go about this manually. Though this would be somewhat tedious, I have done it and attached it to this answer. Note that when the number of players is odd, an extra game has to be played to ensure that all entrants at that round of the tournament have played at least one game at that round. Note that there is no limit on the number of games a player can play; the only condition is that a player is eliminated once the player loses.
The sum of the figures in the third column is 999.
We could also use the formula for rooted trees to calculate the number of games that would be played.
where i is the number of "internal nodes," which represents the number of games played for an "<em>m</em>-ary" tree, which is the number of players involved in each game and l is known as "the number of leaves," in this case, the number of players.
The number of players is 1000 and each game involves 2 players. Therefore, the number of games played, i, is given by
Answer:
C. A horizontal stretch to produce a period of and a vertical compression.
Step-by-step explanation:
We are given the parent function as
It is given that, transformations are applied to the parent function in order to obtain the function i.e.
That is, we see that,
The parent function is stretched horizontally by the factor of
which gives the function
.
Further, the function is compressed vertically by the factor of which gives the function
.
Now, we know,
If a function f(x) has period P, then the function cf(bx) will have period .
Since, the period of is
, so the period of
is
=
Hence, we get option C is correct.