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olga55 [171]
3 years ago
12

Serial numbers for a product are to be made using 2 letters followed by 3 numbers. If the letters are to be taken from the first

6 letters of the alphabet with no repeats and the numbers are taken from the digits 0 through 9 with repeats possible, how many serial numbers can be generated?
Mathematics
1 answer:
Daniel [21]3 years ago
8 0
2 Letters chosen among 6 with no repeat:
a) the first has 6 ways
    the second has 5  ways

Then to choose 2 letters among 6, with no repeat, there are 6x5 = 30 ways

 b) 3 numbers are taken from the digits 0 through 9 with repeats (total = 10)
     the first has 10 ways
     the second has 10  ways
    the third has 10  ways

Then to choose 3 numbers among 10, with repeat, there are 10x10x10= 1000 ways
And the total serial numbers that can be generated is
30 x 1000 = 3000
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Eduardwww [97]
(0.6x^4)(0.2x^6) 
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  =<span><span>0.6<span>x^4</span></span>*<span>0.2<span>x^6</span></span></span></span><span>
  =<span><span><span>0.6*<span>x^4</span></span>*0.2</span>*<span>x^6</span></span></span><span>
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3 years ago
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Put the quadratic into vertex form and state the coordinates of the vertex. y= y= \,\,x^2-6x-3 x 2 −6x−3
enot [183]

Answer:

y = (x - 3)^2 - 12

(3,-12)

Step-by-step explanation:

Given

y = x^2 - 6x - 3

Solving (a): In vertex form

The vertex form of an equation is:

y = a(x - h)^2 + k

To do this, we make use of completing the square method.

We have:

y = x^2 - 6x - 3

------------------------------------------------------------------

Take the coefficient of x (i.e. -6)

Divide by 2; -6/2 = -3

Square it: (-3)^2 = 9

Add and subtract the result to the equation

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y = x^2 - 6x - 3

y = x^2 - 6x + 9 - 9 - 3

y = x^2 - 6x + 9 - 12

Factorize x^2 - 6x + 9

y = x^2 - 3x-3x + 9 - 12

y = x(x - 3)-3(x - 3) - 12

Factor out x - 3

y = (x - 3)(x - 3) - 12

Express as squares

y = (x - 3)^2 - 12

Hence, the vertex form of y = x^2 - 6x - 3 is: y = (x - 3)^2 - 12

Solving (b): State the coordinates of the vertex.

In y = a(x - h)^2 + k; the vertex is: (h,k)

The vertex of y = (x - 3)^2 - 12 will be (3,-12)

3 0
3 years ago
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steposvetlana [31]

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5 0
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aleksandrvk [35]
An <u>example of a problem</u> where I <em>would not</em> group the addends differently is:

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In the <u>second problem</u>, I would regroup like this:
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This is because 2+8=10, which makes the problem "easier" for us to add.  Since we can get a number like this that shortens the process, we can regroup the addends.
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