Let’s suppose that Georgia wants to adopt a new license plate numbering system. The new license plates will be of the form X--XX where N’s are numbers and X’s are letters. However, license plate numbers can’t begin or end with O and the 2nd # can’t be a 0.
How many different license plates are there under this system?

Explanation:

For the first and last X, there are 25 choices. This is because there are 26 letters, but we can't use the letter O. The second to last X has 26 choices.

So far we have 25*26*25 = 16250 different permutations for the letter portion of the license plate.

Now onto the number portion. The first N can't be zero, but it can be any other positive single digit number. We have 9 choices for this slot. The other N's can be zero or any other positive single digit number. We have 10 choices for each of these slots.

So we have 9*10*10*10 = 9000 different permutations for the number portion of the license plate.

Overall, there are 16250*9000 = 146,250,000 different license plates that can be formed. This is a little bit over 146 million.

If you want to do the all of the multiplication as one single step, then it might look like this:

25*9*10*10*10*26*25 = 146,250,000

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

read more on -

it has the same slope and a different y-intercept

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