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Illinois license plates used to consist of either three letters followed by three digits or two letters followed by four digits.

DENIUS [597]

Answer:

The probability that a randomly chosen plate contains the number 2222 is 0.000028 approximately.

The probability that a randomly chosen plate contains the sub-string HI is 0.002548 approximately.

Step-by-step explanation:

Consider the provided information.

Illinois license plates used to consist of either three letters followed by three digits or two letters followed by four digits.

Part (A)

Let A is the ways in which plates consist of three letters followed by three digits and B is the ways in which two letters followed by four digits.

Here repetition is allow. The number of alphabets are 26 and the number of distinct digits are 10.

The numbers of ways in which three letters followed by three digits can be chosen is: $26\times 26\times 26 \times 10 \times 10 \times10$

$26^3\times 10^3=17576000$

The numbers of ways in which two letters followed by four digits can be chosen is: $26\times 26\times 10 \times 10 \times 10 \times10$

$26^2\times 10^4=6760000$

Hence, the total number of ways are 17576000 + 6760000 = 24336000

Randomly chosen plate contains the number 2222 that means the first two letter can be any alphabets but the rest of the digit should be 2222.

Thus, the total number of ways that a randomly chosen plate contains the number 2222 number are: $26^2=676$

The probability that a randomly chosen plate contains the number 2222 is:

$\frac{676}{24336000} \approx 0.000028$

Part (B)

The number of ways in which chosen plate contains the sub-string HI:

If three letters followed by three digits plate contains the sub-string HI, then the number of possible ways are:

$26\times 1\times10^3+1\times 26\times10^3$

If two letters followed by four digits plate contains the sub-string HI, then the number of possible ways are:

$1\times 10^4$

Thus, the total number of ways that a randomly chosen plate contains the sub-string HI are:

$1\times 10^4+26\times 1\times10^3+1\times 26\times10^3$

$62000$

From part (A) we know that the total number of ways to chose a number plate is 24336000.

The probability that a randomly chosen plate contains the sub-string HI is:

$\frac{62000}{24336000} \approx 0.002548$

7 0

3 years ago

Reduce 18/45 to the simplest form.

horrorfan [7]

The simplest form of 18/45 is 2/5

4 0

2 years ago

Read 2 more answers

During a school visiting day,a mother visited her daughter.She carried a bag containing 12 oranges,16 apples, and 8 mangoes,all

kondaur [170]

3 oranges because the mother wouldn’t draw mangoes- because it would be too hard. And she wouldn’t get an apple

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3 years ago

Find, explain, and correct the error in the student work below.

Artemon [7]

The correct answer is 0

6 0

2 years ago

Use the formula for compound interest, a P 1 i n = ^ h + , to determine how many years it will take for an investment of W10 000

Sergeu [11.5K]

The money will be triple after 15 years and 303 days.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

Given:

Principle (P) = $10,000

The amount will be triple.

So, Amount (A) = $30,000

Rate (r) = 7% = 0.07

The interest is compounded quarterly.

n = 4

We have to find the value of t.

Let,

$A = P(1+\frac{r}{n})^n^t\\ 30000 = 10000(1+\frac{0.07}{4})^4^t\\\frac{30000}{10000} = (1 + 0.0175)^4^t\\ 3 = (1.0175)^4^t$

Apply logarithm on both sides,

$log(3) = log(1.0175)^4^t\\log(3) = 4t log(1.0175)\\t = \frac{log(3)}{4(log(1.0175))} \\t = \frac{0.4771212547}{4(0.0075344179)} \\t = \frac{0.4771212547}{0.0301376716} \\t = 15.83139$

Hence, the money will be triple after 15 years and 303 days.

To know more about compound interest, click on the link

brainly.com/question/24274034

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6 0

11 months ago