Question

please help: New York states license plates contain 3 letters followed by 4 digits. The letters O and I are not allowed to be used on license plate. A) If letters and numbers are allowed to be replaced, how many different plates can be made?

Answer 1

b) if the first letter has to be a vowel , how many less plates can be made?
c: if the first place can be either a number or a letter, how many more license plates can be made than part a?

Answer 2

a) The number of different permutations of n different things taken k at a time with repetitions is\[n ^{k}\]
The number of permutations of the 24 allowable letters is
\[24^{3}\]
The number of permutations of the 10 digits 0 ~ 9 is
\[10^{4}\]
Each permutation of the letters can be taken with each of the possible permutations of digits. So the number of different plates that can be made is
\[24^{3}\times 10^{4}=you\ can\ calculate\]

Answer 3

so thats part a right?

Answer 4

Okay i need help with part b and c?

Answer 5

@kropot72 thanks for your help

Answer 6

b) The vowels O and I are not allowed.
If the letters start with the vowel A the number of permutations with the remaining 23 letters is 23^2. Similarly with the letters starting with the vowels E and U there are 23^2 permutations.
So the total number of permutations of letters becomes
\[3\times 23^{2}\]
Each of these permutations of letters can be taken with each of the possible permutations of digits. So the total number of licence plates is
\[3\times 23^{2}\times 10^{4}\]
The reduction in the number of plates that can be made is
\[(24^{3}\times 10^{4})-(3\times 23^{2}\times 10^{4})=you\ can\ calculate\]

Answer 7

okay part c?

Answer 8

c) Sorry, I can't understand this part of the question. Have you posted it exactly as the original? If not please post part c) again.

Answer 9

Does part c) mean that the number plate would have an increase in the number of characters from 7 up to 8, with the first character being either a letter or a digit?

Answer 10

if the first place can be either a number or a letter, how many more license plates can be made than in part a?

Answer 11

hmmm... You want help on this last one?^^ Because it looks like your other questions got answered.

Answer 12

yeah I got the others

Answer 13

need help with the last ine!

Answer 14

Okay! Just a second. :) Unless kropot here has it...

Answer 15

@tafkas can u help me with another problem:)
http://ms210q.schoolwires.net/cms/lib2/NY01001558/Centricity/Domain/150/HW%2098.pdf

Answer 16

If there is an eighth character in the first position there are 10 digits that can be used and 24 allowable letters. In that case 10 + 24 = 34 times as many number plates can be made.

Answer 17

34 times as many number plates can be made. thats the answer right?

Answer 18

You need all three of these?

Answer 19

yeah

Answer 20

Okay, give me just a moment to be sure that *I* know how to do these, hee hee. :)

Answer 21

okay! thanks!

Answer 22

I confirm the answer to c) is 34 times as many number plates as in a).

Answer 23

okay only #B okay thanks

Answer 24

for the first one, you can pick any two ordered pairs and find the slope from there. Do you know the slope formula?

Answer 25

yeah i didit that already and got slope is 2

Answer 26

@kropot72 thanks!

Answer 27

Now I need B please?

Answer 28

hello?

Answer 29

Great!

When they say, graph the data, they mean plot the points. They gave you points in part "A". Just plot them, and then you will see that the slope can be calculated visually, like so:

Answer 30

hey! where'd my drawing go? >(

Answer 31

so can I write on the grpah rise 4 run 2 thats how you can get slope

Answer 32

do I need arrows?

Answer 33

Great! Well, in theory, yes, because the arrows show that your line goes in opposite directions indefinitely (for infinity). The arrows wouldn't be there if you had a specific starting point, but you don't in this question.

Answer 34

thanks!

Answer 35

You're welcome! :D

Answer 36

Show how to write an equation for the table and graph. Verify that the equation
works with the table and the graph.
is y=2x right?

Answer 37

yeah

Answer 38

Well, yes! :D

Answer 39

Great work! ;)