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B(n)=2^n A binary code word of length n is a string of 0's and 1's with n digits. For example, 1001 is a binary code word of length 4. The number of binary code words, B(n), of length n, is shown above. If the length is increased from n to n+1, how many more binary code words will there be? The answer is 2^n, but I don't get how they got that answer. I would think 2^n+1 minus 2^n would be 2. Please help me! Thank you!

Answers

Answer 1

Answer:

Answer:

More number of words that can be made: $\bold{2^n}$

Please refer to below proof.

Step-by-step explanation:

Given that:

The number of binary code words that can be made:

$B(n) =2^n$

where n is the length of binary numbers.

Binary numbers means 2 possibilities either 0 or 1.

Here, suppose if we have 5 as the length of binary number.

And there are 2 possibilities for each digit.

So, total number of possibilities will be $2* 2* 2* 2* 2 = 2^5$

If the length of binary number is 2.

The total words possible are $2^2$ .

These numbers are:

{00, 01, 10, 11}

If the length of binary number is 3. (increasing the 'n' by 1)

The total words possible are $2^3$ .

These words are:

{000, 001, 010, 100, 011, 101, 110, 111}

So, number of More binary words = 8 - 4 = 4 or $2^2$ or $2^n$ .

So, the answer is $2^n$ .

Let us try to prove in generic terms:

$B(n) = 2^n$

Increasing the n by 1:

$B(n+1) = 2^(n+1)$

Number of more words made by increasing n by 1:

$B(n+1) -B(n)= 2^(n+1) -2^n\n\Rightarrow 2* 2^(n) -2^n\n\Rightarrow 2^n(2-1)\n\Rightarrow \bold{2^n}$

Hence, proved that:

More number of words that can be made: $\bold{2^n}$

Answer 2

Answer:

Final answer:

When the length of a binary code word increases from n to n+1, the number of additional binary code words is equal to the number of binary code words of length n, which is $2^n$ .

Explanation:

When the length is increased from n to n+1, the number of binary code words of length n+1 is equal to the number of binary code words of length n multiplied by 2. This is because for each binary code word of length n, we can append a 0 or a 1 to create two new binary code words of length n+1. Therefore, the number of additional binary code words is equal to the number of binary code words of length n, which is $2^n$ .

Learn more about Binary code words here:

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$641.29 is what percent of $986,60?

I need this ASAP

Answers

Answer:

65%

Step-by-step explanation:

You start by dividing 641.29 by 986.60 (641.29/986.60). This gets you .65, which as a percentage is 65%

65% use a website for calculating percentages

Suppose an interval estimate for the population mean was 62.84 to 69.46. The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. The mean of the sample was: A. 56.34 B. 62.96 C. 6.62 D. 66.15

Answers

Answer: Option D.

Step-by-step explanation:

The given interval for population mean was 62.84 to 69.46.

The sample mean will be at the midpoint of the interval.

That is: $(\left(62.84+69.46\right))/(2)=66.15$ .

Learn more: brainly.com/question/12049968

Answer:

$\bar X = 69.46-3.31= 66.15$

$\bar X = 62.84+3.31= 66.15$

Because the confidence interval is defined as $(\bar X -ME, \bar X + ME)$

The best option is : D. 66.15

Step-by-step explanation:

Previous concepts

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

$\bar X$ represent the sample mean (variable of interest)

$\mu$ population mean

$\sigma=6.50$ represent the population standard deviation

n=100 represent the sample size

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma=6.5)$

The sample mean $\bar X$ is distributed on this way:

$\bar X \sim N(\mu, (\sigma)/(√(n)))$

The confidence interval on this case is given by:

$\bar X \pm z_(\alpha/2)(\sigma)/(√(n))$ (1)

We have a confidence interval given (62.84, 69.46). W ecan find the margin of error for this interval with this:

$ME= (69.46-62.84)/(2)=3.31$

With the margin of error we can find the sample mean with this:

$\bar X = 69.46-3.31= 66.15$

$\bar X = 62.84+3.31= 66.15$

Because the confidence interval is defined as $(\bar X -ME, \bar X + ME)$

The best option is : D. 66.15

Y-3=2(x+1) please please help

Answers

Answer:

y=2x+5

Step-by-step explanation:

distribute 2 to x and 1, do this by multiplying each.

you should get y-3=2x+2.

then you have to move the -3 from the left to the right. but when you do this you have to change the -3 to a positive 3. then combine 3 and 2.

you then get the answer, y=2x+5.

11 ounces to 5 ounces

Answers

Answer: what is the question to this?

Step-by-step explanation: thanks let me know okay

Answer:

(11/5) (a ratio)

Step-by-step explanation:

11 ounces to 5 ounces could be rewritten as

11 oz.

---------- = (11/5) (a ratio)

5 oz

Write in standard form 80010000

Answers

Answer:

8.001 × 10^7

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 1010. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:8.001 x 10^7

Step-by-step explanation:

80010000=8.001 x 10^7

Two parallel lines are crossed by a transversal.What is the value of x?

Could someone tell me how to solve this?

Answers

because both lines are parallel, if you add the 5x+5 to the 115 those would equal 180 degrees

so you have 5x+5 + 115 = 180

combine like terms:

5x + 120 = 180

subtract 120 from both sides

5x = 60

x = 60/5
x = 12

Okay so (5x+5)+115 is going to equal 180.

1.) (5x+5)+115=180

The next steps is to isolate the x.

2.) 5x+120=180
3.) -120=-120
4.) 5x=60
5.) /5=/5
6.) x=12 degrees

Then, you check your work by plugging in the numbers.
7.) 5(12)+5+115=180
8.) 60+5+115=180
9.)180=180

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