In the Village League, the team to win two of three softball games becomes the champion. If the probability of Team Alpha beating Team Beta is 60% for every game, what is the probability that Beta wins the championship? Express your answer as a common fr

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MATHCOUNTS
2000 National Competition Countdown Round
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(No Transcript)
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In the Village League, the team to win two of
three softball games becomes the champion. If the
probability of Team Alpha beating Team Beta is
60 for every game, what is the probability that
Beta wins the championship? Express your answer
as a common fraction.
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Answer
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Circles A and B are congruent. Circle A is
rolled around circle B, remaining tangent at all
times. Circle A rolls around circle B exactly
once. How many times will circle A revolve
around its own center before the radii are
lined up again as shown?
A
B
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Answer 2 (times)
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A line that passes through (-5,-8) and (-3,-4)
will cross the y-axis at what y-coordinate?
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Answer 2
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What is the number of inches in the radius of a
circle whose area is one-half the area of a
circle with radius 4 inches? Express your answer
in simplest radical form.
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Answer (inches)
2
2
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A unicycle has a wheel with a radius of 1 foot.
How many complete revolutions will the wheel make
when the unicycle rolls 100 feet? Express your
answer to the nearest whole number.
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Answer 16 (revolutions)
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What is the value of
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-

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1
2
3
4
5
6
.
.
.
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98
99
100
?
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Answer 50
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A 3-foot high tree was planted and grows by an
equal number of feet each year. At the end of the
seventh year, it is 1/9 taller than at the end of
the sixth year. How many feet tall will it be at
the end of the 13th year?
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Answer 16 (feet)
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x, y and z are positive odd integers. What is the
remainder when is divided
by 4?
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Answer 3
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In how many consecutive zeroes does the product
end?
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Answer 23 (zeroes)
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What is the total number of different committees
that can be formed by selecting one or more
persons from a group of six people?
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Answer 63 (committees)
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In ABC, AB 5 cm, BC 10 cm, and the
altitude drawn to AB is 8 cm. What is the number
of centimeters in the length of the altitude to
BC?
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Answer 4 (centimeters)
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When four numbers are added three at a time, the
four sums are 42, 43, 47 and 48. What is the sum
of the four numbers?
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Answer 60
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The average of 11 consecutive even integers is
24. What is the greatest of these integers?
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Answer 34
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What is the fewest possible number of units in
the perimeter of a triangle with side lengths
that are relatively prime integers?
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Answer 12 (units)
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Four distinct digits are used to make 2 two-digit
numbers. What is the greatest possible product of
the two numbers formed?
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Answer 8352
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How many whole numbers from 10 to 99 have a
units digit greater than the tens digit?
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Answer 36 (numbers)
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A 200 increase is the same as a 50 increase
followed by what other percent increase?
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Answer 100 (percent)
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What percent of the first 200 prime numbers have
reciprocals less than 0.05?
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Answer 96 (percent)
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What is the probability that the product of two
numbers chosen randomly from the set of all
positive integers is divisible by 2? Express
your answer as a common fraction.
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Answer
4
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A circle has a radius of 10 centimeters and a
chord of the circle is 16 centimeters long. How
many centimeters is the midpoint of the chord
from the center of the circle?
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Answer 6 (centimeters)
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How many miles per hour is 1298 feet per second?
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Answer 885 (mph)
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The ratio of length to width to height of a
rectangular prism is 321. If the surface area
of the prism is 198 m2, how many cubic meters
are in its volume?
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Answer 162 (cubic meters)
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In 1984, July 4 fell on a Wednesday. On what day
of the week did July 4, 1990, fall?
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Answer Wednesday
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The measures of the angles of a triangle are in
the ratio of . What is the number of
degrees in the measure of the largest angle?
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Answer 80 (degrees)
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How many integers 19 are divisors of the
five-digit number 24,516?
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Answer 6 (integers)