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alisha [4.7K]
2 years ago
11

A certain stock exchange designates each stock with a one-, two-, or three-letter code, where each letter is selected from the 2

6 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?
Mathematics
1 answer:
mariarad [96]2 years ago
6 0

Answer:

There are 16276 different stocks which are possible to uniquely designate with these codes

Step-by-step explanation:

The information we have is that

1. There are 26 different letters.

2. The stock can be designated with a one, two or three letter code and the letters may be repeated (We always have 26 options for the first, second and third letter)

3. Order matters (different order constitute a different code), which means we're talking about permutations.

The total codes we can make would be:

P_{26|1} + P_{26|2}+ P_{26|3}   \\26+650+15600= 16276

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To get the most accurate answer possible, we're going to have to go into some unsightly calculation, but bear with me here:

Assessing the situation:

Let's get a feel for the shape of the problem here: what step should we be aiming to get to by the end? We want to find out how long it will take, in minutes, for the tank to drain completely, given a drainage rate of 400 L/s. Let's name a few key variables we'll need to keep track of here:

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We're about ready to set up an expression using those variables, but first, we should address a subtlety: the question provides us with the drainage rate in liters per second. We want the answer expressed in liters per minute, so we'll have to make that conversion beforehand. Since one second is 1/60 of a minute, a drainage rate of 400 L/s becomes 400 · 60 = 24,000 L/min.

From here, we can set up our expression. We want to find out when the tank is completely drained - when the water volume is equal to 0. If we assume that it starts full with a water volume of V L, and we know that 24,000 L is drained - or subtracted - from that volume every minute, we can model our problem with the equation

V-24000t=0

To isolate t, we can take the following steps:

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So, all we need to do now to find t is find V. As it turns out, this is a pretty tall order. Let's begin:

Solving for V:

About units: all of our measurements for the cone-shaped tank have been provided for us in meters, which means that our calculations will produce a value for the volume in cubic meters. This is a problem, since our drainage rate is given to us in liters per second. To account for this, we should find the conversion rate between cubic meters and liters so we can use it to convert at the end.

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Bringing it home:

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\bf ~~~~~~~~~~~~\textit{function transformations}
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% templates
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f(x)=  A\sqrt{  Bx+  C}+  D
\\\\
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f(x)=  A sin\left( B x+  C  \right)+  D
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\bf \bullet \textit{ stretches or shrinks horizontally by  }   A\cdot   B\\\\
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\bf ~~~~~~if\ \frac{  C}{  B}\textit{ is positive, to the left}\\\\
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notice, in g(x)

B = 1, no change from parent

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