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Alchen [17]
3 years ago
8

For a carnival game, containers are arranged in a triangular display. The top row has 1 container. The second row has 2 containe

r. the third row has 3 containers. The pattern continues until the bottom row, which has 10 containers. A contestant knocks down 29 containers on the first throw. How many containers remain?
Mathematics
2 answers:
Ede4ka [16]3 years ago
5 0
For this, you will need to know the triangle numbers. To know how many are on row ten, find the cumulative frequency (running total) of every number up to ten

1 = 1
2 = 3
3 = 6
4 = 10
5 = 15
6 = 21
7 = 28
8 = 36
9 = 45
10 = 55

If there are 55 containers and 29 are knocked down, we do
55 - 29 = 26
26 containers remain
docker41 [41]3 years ago
4 0
26 are left. Its just addition then subtraction.
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Answer:

<h3>x = 22/7</h3>

Step-by-step explanation:

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Send 1 to the right side of the equation

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Divide both sides by 22

x = 7/22

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3 years ago
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DISCLAIMER: Please let me rename b and w the number of black and white balls, for the sake of readability. You can switch the variable names at any time and the ideas won't change a bit!

<h2>(a)</h2>

Case 1: both balls are white.

At the beginning we have b+w balls. We want to pick a white one, so we have a probability of \frac{w}{b+w} of picking a white one.

If this happens, we're left with w-1 white balls and still b black balls, for a total of b+w-1 balls. So, now, the probability of picking a white ball is

\dfrac{w-1}{b+w-1}

The probability of the two events happening one after the other is the product of the probabilities, so you pick two whites with probability

\dfrac{w}{b+w}\cdot \dfrac{w-1}{b+w-1}=\dfrac{w(w-1)}{(b+w)(b+w-1)}

Case 2: both balls are black

The exact same logic leads to a probability of

\dfrac{b}{b+w}\cdot \dfrac{b-1}{b+w-1}=\dfrac{b(b-1)}{(b+w)(b+w-1)}

These two events are mutually exclusive (we either pick two whites or two blacks!), so the total probability of picking two balls of the same colour is

\dfrac{w(w-1)}{(b+w)(b+w-1)}+\dfrac{b(b-1)}{(b+w)(b+w-1)}=\dfrac{w(w-1)+b(b-1)}{(b+w)(b+w-1)}

<h2>(b)</h2>

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This leads to an overall probability of

\left(\dfrac{w}{b+w}\right)^2+\left(\dfrac{b}{b+w}\right)^2 = \dfrac{w^2+b^2}{(b+w)^2}

Of picking two balls of the same colour.

<h2>(c)</h2>

We want to prove that

\dfrac{w^2+b^2}{(b+w)^2}\geq \dfrac{w(w-1)+b(b-1)}{(b+w)(b+w-1)}

Expading all squares and products, this translates to

\dfrac{w^2+b^2}{b^2+2bw+w^2}\geq \dfrac{w^2+b^2-b-w}{b^2+2bw+w^2-b-w}

As you can see, this inequality comes in the form

\dfrac{x}{y}\geq \dfrac{x-k}{y-k}

With x and y greater than k. This inequality is true whenever the numerator is smaller than the denominator:

\dfrac{x}{y}\geq \dfrac{x-k}{y-k} \iff xy-kx \geq xy-ky \iff -kx\geq -ky \iff x\leq y

And this is our case, because in our case we have

  1. x=b^2+w^2
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Answer:

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Assuming that b>0 and c>0:

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Hence a=b³/c²

7 0
3 years ago
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