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Kay [80]
2 years ago
12

A state offers specialty license plates that contain 5 numbers followed by 2 letters. License plates are assigned randomly. All

license plates are equally likely. Find the number of possible license plates that can be issued using this system.
Mathematics
1 answer:
FrozenT [24]2 years ago
3 0

The number of possible license plates that can be issued using this system is 67600000.

<h3>What is Combination?</h3>

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.

Here, number plate contains 5 numbers and 2 letters

Total possible number (0-9) = 10

Total possible letters (A-Z) = 26

Possible number plates which contains 5 numbers and 2 letters are

          ¹⁰C₁ X  ¹⁰C₁ X  ¹⁰C₁ X  ¹⁰C₁ X  ¹⁰C₁ X ²⁶C₁ X ²⁶C₁

             10 X 10 X 10 X 10 X 10 X 26 X 26

                 10⁵ X 26²

                   676 X 10⁵

                 67600000

Thus, the number of possible license plates that can be issued using this system is 67600000.

Learn more about Combinations from:

brainly.com/question/19692242

#SPJ1

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y=-2.95836 x +234.56159

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479

\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694

\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897

\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226

\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22

And the slope would be:

m=-\frac{-4152.222}{1403.556}=-2.95836

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222

\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111

And we can find the intercept using this:

b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159

So the line would be given by:

y=-2.95836 x +234.56159

7 0
2 years ago
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