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sladkih [1.3K]
3 years ago
8

Bennett has been practicing the cello for an hour each day. 3/4of the hour, he spends practicing musical pieces in preparation f

or his upcoming orchestra concert. He spends the other 1/4of the hour practicing scales. If he spends 2/5of his practice time on musical pieces playing one of the orchestra pieces, Excerpts from Pirates of the Caribbean, how much of the hour does he spend playing that music?
Mathematics
1 answer:
mina [271]3 years ago
7 0

Answer:

Orchestral\ Time = \frac{3}{10}\ hour

Step-by-step explanation:

Given

Time = 1\ hour

Musical\ Pieces = \frac{3}{4}\ hour

Practicing\ Sales = \frac{1}{4}\ hour

Orchestral = \frac{2}{5} of music practice time

Required

Determine time spent on orchestral pieces

From the given parameters, we have:

Orchestral = \frac{2}{5} of music practice time

Substitute \frac{3}{4}\ hour for music practice time.

So, we have:

Orchestral\ Time = \frac{2}{5} * \frac{3}{4}\ hour

Orchestral\ Time = \frac{1}{5} * \frac{3}{2}\ hour

Orchestral\ Time = \frac{3}{10}\ hour

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Answer:

The fifth term is -1/4.

Step-by-step explanation:

We know that the first three terms of the geometric sequence is <em>x, x</em> + 2, and <em>x </em>+ 3.

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Square:

\displaystyle x+3 = x\Big( \frac{(x+2)^2}{x^2} \Big)

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\displaystyle x+3=\frac{(x+2)^2}{x}

We can multiply both sides by <em>x: </em>

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Isolate the <em>x: </em>

-x=4

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3 years ago
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Step-by-step explanation:

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Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered
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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?

$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 24$

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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.

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