1) Two triangles are similar if they have congruent angles and proportional sides (for each corresponding leg).
2) So let's check whether there are similar triangles by setting a proportion:

3) So yes they are similar, i.e. ΔCAB ~ΔHGJ
Answer:
8.9 feet to the nearest tenth.
Step-by-step explanation:
The volume of a cone is 1/3 π r^2 h where r = the radius of the base and h = the height.
So we have the equation:
208 = 1/3 π r^2 10
r^2 = 208 / (1/3 * π * 10)
r^2 = 19.85 sq feet
so r = √19.86
= 4.457 feet.
So the diameter = 2 * 4.457 = 8.914 feet.
Complete Question
1. (12 points) The tennis team at Taft High School has 8 players, and the tennis team at McKinley High School has 7 players. Rebecca is on the team at Taft, and her sister Leah is on the team at McKinley. The two teams are going to play a tournament with 4 rounds. In each round, one player from Taft will play a match against one player from McKinley. Each player can play in at most one match. A schedule for the tournament consists of an ordered list of the names of the players from each school who will play in each of the four rounds. The schedule does not include the results of each match.
(a) How many schedules are there?
(b) How many schedules include neither sister?
Answer:
a

b
Step-by-step explanation:
From the question we are told that
The number of players in Taft High School is t = 8
The number of players in McKinley High School is k = 7
The number of rounds is n = 4
The highest number of match each player can play is w = 1
Generally the total number of schedules is


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Generally the number of schedules that include neither of the sisters is mathematically represented as


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Answer:
15
Step-by-step explanation:
Let n, d, q represent the numbers of nickels, dimes, and quarters. The problem statement tells us ...
n +d +q = 37
n = d +4
q = n +2
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Rearranging the second equation gives ...
d = n -4
Substituting that into the first, we get ...
n + (n -4) +q = 37
2n +q = 41 . . . . . . . add 4 and simplify
Rearranging the third original equation gives ...
n = q -2
Substituting into the equation we just made, we get ...
2(q -2) +q = 41
3q = 45 . . . . . . . . add 4 and simplify
q = 15 . . . . . . . . . divide by 3
Joe has 15 quarters.
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<em>Check</em>
The number of nickels is 2 fewer, so is 13. The number of dimes is 4 fewer than that, so is 9. The total number of coins is 15 + 13 + 9 = 37, as required.
Cherry sales as a % of total sales = (0.5 x 1.2)/(0.5 x 1.2 + 0.2 x 1.4 + 0.3 x 1.6) = 0.6 / (0.6 + 0.28 + 0.48) = 0.6 / 1.36 = 0.4412 = 44.12%
Therefore, 44.12% of the total sales will be cherry.