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mamaluj [8]
3 years ago
5

a product code consists of picking a two-digit number (including 00) and 3 not necessarily distinct letters. How many codes are

possible? how many codes contain at least one 9? What is the probability that a code does not contain the number 9?
Mathematics
1 answer:
Brrunno [24]3 years ago
4 0

Answer:

The codes are:

N,_,_,_

Where each _ represents a possible letter, out of 26.

And N is a number of two digits.

So in total we can think that we have 5 empty slots.

_,_,_,_,_

In the first slot we can put any digit between 0 and 9, so here we have 10 options.

In the second slot we can put any digit between 0 and 9, so here we have 10 options.

In the third slot we can put any letter, so here we have 26 options (and exactly the same for the fourth and fifth slots)

The total number of different combinations is equal to the product of the number of options for each slot.

C = 10*10*26*26*26 = 1,757,600

Now, if we want to have at least one nine, we can fix it in the first slot.

Then we have:

in the first slot we have only one option (the 9)

In the second slot we can put any digit between 0 and 9, so here we have 10 options.

In the third slot we can put any letter, so here we have 26 options (and exactly the same for the fourth and fifth slots)

The number of combinations is:

C = 1*10*26*26*26 = 175,760

But we also should consider the case where we fix the 9 in the second slot, so the actual number of combinations is twice the number above.

C = 2*175,760 = 351,520

The probability that the code does not contain the number 9.

Now in the first slot we have only 9 options, all the whole numbers between 0 and 8.

The same for the second slot, 9 options.

For the third, fourth and fifth slot is the same as before.

The total number of combinations is:

C = 9*9*26*26*26 = 1,423,656

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AURORKA [14]

Answer:

2x+50 and 5x-55 both are congruent or have same measure.

Step-by-step explanation:

Since we want to prove that both lines are parallel, this means no theorems that involve with parallel lines apply here.

First of, we know that AC is a straight line and has a measure as 180° via straight angle.

x+25 and 2x+50 are supplementary which means they both add up to 180°.

Sum of two measures form a straight line which has 180°.

Therefore:-

x+25+2x+50=180

Combine like terms:-

3x+75=180

Subtract 75 both sides:-

3x+75-75=180-75

3x=105

Divide both sides by 3.

x=35°

Thus, x = 35°

Then we substitute x = 35 in every angles/measures.

x+25 = 35°+25° = 60°

2x+50 = 2(35°)+50° = 70°+50° = 120°

5x-55 = 5(35°)-55 = 175°-55° = 120°

Since 2x+50 and 5x-55 have same measure or are congruent, this proves that both lines are parallel.

5 0
2 years ago
Read 2 more answers
(3x – 1) : (x - 2) = x – 2x (x—4)<br> срочно, сор.
RSB [31]

\frac{3x-1}{x-2}=x-2x(x-4)  \frac{3x-1}{x-2}=x-2x^{2} +8x \\\frac{3x-1}{x-2}=-2x^{2} +9x3x-1= (-2x^{2} +9x)(x-2)\\3x-1= -2x^3+4x^{2} +9x^{2} -18x\\3x-1=-2x^3+13x^{2} -18x\\2x^3 -13x^{2} +18x+3x -1=0\\2x^3 -13x^{2}+21x-1=0\\ x =0.05 /or/x=3.7

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2 years ago
Show your work !!!!!!!!!!!!
sdas [7]
-1/2 < -x/3 < -1/4 = -6/12 < -x/12 < -3/12

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7 0
3 years ago
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fomenos
Mmm looks like a test. I don't know if we should be answering this.
3 0
3 years ago
A park has a large circle painted in the middle of the playground area.thecircle is divided into 4 equal sections And each secti
lilavasa [31]

Answer:

The area of each section of the circle is 25\pi\ m^{2}

Step-by-step explanation:

we know that

The area of a circle is equal to

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substitute

A=\pi (10^{2})=100\pi\ m^{2}

To find the area of each section divide the complete area of the circle by 4

so

100\pi\ m^{2}/4=25\pi\ m^{2}

8 0
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