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3 years ago

5. PA license plates have 3 letters followed by 4 numbers.

Mathematics

1 answer:

posledela3 years ago

6 0

Answer:

A. 175,760,000

B. 156,000,000

Step-by-step explanation:

For part A:

There are 26 letters in the alphabet. Therefore, if there are 3 spots to use 26 letters, that is represented as $26^3$ . As for numbers, there are 10 digits from 0-9. So if there are 4 spots for numbers, the total possible number of sequences is $10^4$ . So you simply multiply $26^3$ and $10^4$ to get 175,760,000 possible combinations.

For part B:

If the same letter can't be repeated, instead of using an exponent, we have to use a factorial, but only for the 3 digits required in the license plate. These are called permutations and can be expressed as $_2_6P_3$ , which is the same as saying 26 x 25 x 24. Since there is no change to number of numbers, that remains the same.

$_2_6P_3 * 10^4 =26*25*24*10^4=156,000,000$

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Answer:

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Step-by-step explanation:

It is given that,

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3 years ago

A museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Let x represent the amount borrowed at 7%, y rep

Ivahew [28]

Answer:

Step-by-step explanation:

Total amount borrowed by the museum is $2000000

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l = PRT/100

Where

I = interest

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R = rate

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For a Pincipal of $x borrowed at a rate of 7% and the time is 1 year,

the simple interest would be expressed as

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I = (x × 8.5 × 1)/100 = 0.085y

For a Principal of $z borrowed at rate of 9.5% and a duration of 1 year,

the simple interest would be expressed as

I = (x × 9.5 × 1)/100 = 0.095z

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169750 = 0.07x + 0.34z + 0.095z

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irina1246 [14]

Answer:

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