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puteri [66]
3 years ago
15

An aquarium has a base in the shape of a trapezoid. The base is 100

Mathematics
1 answer:
Nat2105 [25]3 years ago
4 0

Answer:

Volume = 210L

Step-by-step explanation:

Given

Base:

Front = 100cm

Back = 50cm

Width = 40cm

Height = 70cm

Required

Determine the volume (in litres)

First, we need to calculate the area;

Base on the parameters given, we have:

Area = \frac{1}{2}(Front + Back) * Width

Area = \frac{1}{2}(100cm + 50cm) * 40cm

Area = \frac{1}{2}(150cm) * 40cm

Area = 75cm * 40cm

Area = 3000cm^2

Volume = Area * Height

Volume = 3000cm^2 * 70cm

Volume = 210000cm^3

1cm^3 = 0.001L

So:

Volume = 210000 * 0.001L

Volume = 210L

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Answer:

(-3a -3b -5)

Step-by-step explanation:

So you have to add numbers with same valuables

  1. 8a+(-11a) Answer: -3a
  2. 2b+(-5b) Answer: -3b
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Explain the relationship between multiplying and dividing by 10, 100, and 1000 and moving the decimal point to the right and to
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5 0
3 years ago
The yearly Penn rock-paper-scissors tournament has come down to the final series between Zach and Shaya. They play a best-of-thi
Zepler [3.9K]

Answer:

p=41.79%

Step-by-step explanation:

First let us remember the calculation of a probability:

p=\frac{number of favorable outcomes}{total number of possible outcomes}

In this case let's calculate the number of possibilities of winning the tournament when either one of them, Zach(Z) or Shaya(S), wins the first game (number of favorable outcomes). That is:

Given that Z or S won the first game, the player has another 6 possibilities of winning among 12 remaining games, which is a combination:

number of favorable outcomes = 12C6 = 924

Therefore, the winner of the first game has 924 opportunities of winning 6 other games among 12 games and be the tournament winner.

Now, we must find the number of total possible outcomes, which we may analize as it follows:

Assuming that the first winner Z or S loses the tournament we have several outcomes:

1. After winning the first game, the player doesn't win again, then we have 0 possbilities among 7 other games, this is because the next player would win the tournament winning 7 games in a row. We then have the combination 7C0.

2. The player wins just one more game, but doesn't win again. Now we have 1 possibility among 8 games, given that the other player would win the other 7 games. We then have the combination 8C1.

3. The player wins just two more games, but doesn't win again,  now we have 2 possibilities among 9 games, given that the other player would win the other 7 games. We then have the combination 9C2.

And so on until we reach the outcome where the player wins 5 more games, but doesn't win again,  then we have 5 possibilities among 12 games, given that the other player would win the other 7 games. We then have the combination 12C5.

Now, we must also consider all the outcomes where the first winner wins the tournament, that is the first combination we calculated: 12C6

Therefore we obtain the following:

total number of possible outcomes = 7C0+8C1+9C2+10C3+11C4+12C5+12C6

total number of possible outcomes = 2,211

We have now the elements to calculate the probability:

p=\frac{924}{2,211}=0.4179

Hence, the probability that the winner of the first game wins the tournament is 41.79%

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