Answer:
2/3
Step-by-step explanation:
Simplifying the Complex Fraction
Convert Mixed Numbers to Fractions
56114=5654
Method 1 : LCD Multiplication
The LCD for 6 and 4 is 12
Multiply top and bottom by the LCD
12×5612×54=1015
convert to mixed numbers and
reduce fractions where possible
=1015=23
Method 2 : Fraction Division
Divide the top fraction by the bottom
(multiply top by reciprocal of bottom)
56÷54
=56×45
=2030
convert to mixed numbers and
reduce fractions where possible
=2030=23
Answer:
Step-by-step explanation:
2005 AMC 8 Problems/Problem 20
Problem
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?
$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 24$
Solution
Alice moves $5k$ steps and Bob moves $9k$ steps, where $k$ is the turn they are on. Alice and Bob coincide when the number of steps they move collectively, $14k$, is a multiple of $12$. Since this number must be a multiple of $12$, as stated in the previous sentence, $14$ has a factor $2$, $k$ must have a factor of $6$. The smallest number of turns that is a multiple of $6$ is $\boxed{\textbf{(A)}\ 6}$.
See Also
2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 19 Followed by
Problem 21
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
Answer:
Step-by-step explanation:
We can use some logarithmic rules to solve this easily.
<em>Note: Ln means 
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Now, lets start with the equation:
Writing left side with logarithmic base e, we have:
We can now use the property shown below to make this into exponential form:
So, we write:
We recognize another property of exponentials:
So, we write:
Also, another property of natural logarithms is:
Now, we simplify:
This is the answer.
You are looking for the perimeter, so you need to add 11+11+7+7. That equals 36.
