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nalin [4]
1 year ago
12

Automobile license plates for a state consist of four letters followed by a dash and two single digits. How many different licen

se plate combinations are possible if exactly one letter is repeated exactly once, but digits cannot be repeated
Mathematics
1 answer:
Sauron [17]1 year ago
4 0

The number of different license plate combinations that are possible if exactly one letter is repeated exactly once, but digits cannot be repeated is 8,424,000.

<h3>What is combination?</h3>

A combination is just a mathematical technique for determining the number of potential arrangements in a set of objects where the order of a selection is irrelevant.

You can choose the components in any order in combinations. Permutations and combinations are often mistaken.

Now according to the question,

Possible letter combinations

Choose any letter and make it a repeat letter = 26 ways

But, there are ⁴C₂ = 6 spots available for the identical letters.

And there are (25)×(24) other methods for selecting the other two letters.

The total amount of "words" equals ⁴C₂ × 26 × 25 × 24 = 93600.

Furthermore, because the numerals cannot be repeated = 10 × 9 = 90

So, the total number of choices = 93600 × 90 = 8,424,000

Therefore, the total combinations in which the letters can be chosen for the license plates is  8,424,000.

To know more about the combination, here

brainly.com/question/11732255

#SPJ4

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A recursive rule for the arithmetic sequence is a1=-3;an=an-1+7
Shkiper50 [21]
The explicit rule for any arithmetic sequence is:

a(n)=a+d(n-1), a=initial term, d=common difference, n=term number

In this case a=-3 and d=7 so:

a(n)=-3+7(n-1)

a(n)=-3+7n-7

a(n)=7n-10
8 0
3 years ago
A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation
Alexxx [7]
Ok

y=-0.04x^2+8.3x+4.3
when the rocket reaches the ground (when height=0, ie when y=0), then the rocket will land, find the x coordinate

set y=0
0=-0.04x^2+8.3x+4.3
use quadratic formula
if you have ax^2+bx+c=0, then
x=\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}
a=-0.04
b=8.3
c=4.3
x=\frac{-8.3+/- \sqrt{8.3^{2}-4(-0.04)(8.3)} }{2(-0.04)}
x=208.017 or -0.516785
xrepresents horizontal distance
you cannot have a negative horizontal distance unless you fired and theh wind blew it backwards
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7 0
3 years ago
8 – 6 ∙ 4 + 10 ÷ 2 =
igor_vitrenko [27]

Answer:

-11

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Write the equation of the line that is perpendicular to the line 3x + y = 7 and passes through the point (6, -1).
ira [324]
Line:
3x+y=7
y=-3x+7

Slope of Perpendicular Line: 1/3x

For the perpendicular line to contain point (6,-1) the y-intercept would be (0,1), thus the equation of the line would be y=1/3x+1

y=1/3x+1

5 0
3 years ago
Which of the following is a like radical to RootIndex 3 StartRoot 6 x squared EndRoot? x (RootIndex 3 StartRoot 6 x EndRoot) 6 (
aliya0001 [1]

Answer:

4 (RootIndex 3 StartRoot 6 x squared EndRoot)  = 4\sqrt[3]{6x^2}

Step-by-step explanation:

  • <em>Added radical forms to the question for better visibility.</em>

Which of the following is a like radical to RootIndex 3 StartRoot 6 x squared EndRoot = \sqrt[3]{6x^2} ?

  1. x (RootIndex 3 StartRoot 6 x EndRoot) =  x\sqrt[3]{6x}
  2. 6 (RootIndex 3 StartRoot x squared EndRoot)  = 6\sqrt[3]{x^2}
  3. 4 (RootIndex 3 StartRoot 6 x squared EndRoot)  = 4\sqrt[3]{6x^2}
  4. x (RootIndex 3 StartRoot 6 EndRoot) = x\sqrt[3]{6}
<h3>Solution</h3>
  • <em>Like radicals are radicals that have the same root number and expression under the root.</em>

1)  x\sqrt[3]{6x} = \sqrt[3]{6x^4}

  • No, incorrect

2) 6\sqrt[3]{x^2} = \sqrt[3]{6^3x}

  • No, incorrect

3) 4\sqrt[3]{6x^2}

  • Yes, correct

4) x\sqrt[3]{6} = \sqrt[3]{6x^3}

  • No, incorrect

Compared with the given radical, we can see from the given choices only 3rd choice is like radical with \sqrt[3]{6x^2}

3 0
3 years ago
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