Answer: 20
Step-by-step explanation:
Given : Claire bought 180 candies and 140 pens for goody bags for her birthday.
To find : The largest number of goody bags that Claire can make so that each goody bag has the same number of candies and the same number of pens ( such that no pens or candies left).
So we find the GCF ( Greatest common factor ) or Number of candies and Number of pens.
i.e. we need to find GCF of 180 and 140 .
Prime factorization of 180 =
Prime factorization of 140 =
The greatest common factor of 180 & 140 =
∴ Claire can make 20 goody bags so that each goody bag has the same number of candies and the same number of pens.
Answer:
The equations are:
and
Step-by-step explanation:
Given
Represent bones eaten Today with T and yesterday with Y
Required
Write the equation
In the first statement, we have that:
Reading further; In the second statement
Hence, the equations are:
and
Solving further:
Substitute 2Y for T in the second equation
Divide both sides by 4
Recall that
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
