9. (10%) Consider a linear block code whose generator matrix G is. 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 (a) (2%) Find the parity check matrix H. (b) (3%) What is the minimum distance of the code?

Answers

Answer 1

(a) The parity check matrix H is:

1 1 1 0 1

0 1 0 1 1

0 1 1 0 0

To find the parity check matrix H, we can use the fact that H is the transpose of the generator matrix G with an identity matrix on the right side.

Given the generator matrix G:

1 0 0 1

1 1 1 0

1 0 1 1

0 1 0 0

1 1 0 1

We can rewrite G as:

1 0 0 1 1 1 0 0

1 1 1 0 0 1 1 0

1 0 1 1 1 0 1 1

0 1 0 0 1 1 0 0

1 1 0 1 0 1 1 1

Now, we can obtain the parity check matrix H by taking the transpose of G and removing the rightmost identity matrix:

H = Transpose(G without the rightmost identity matrix)

H =

1 1 1 0 1

0 1 0 1 1

0 1 1 0 0

Therefore, the matrix H is:

1 1 1 0 1

0 1 0 1 1

0 1 1 0 0

(b) The minimum distance of a linear block code is the smallest number of bit positions in which any two codewords differ. It determines the error detection and correction capability of the code.

To find the minimum distance of the code, we can examine the columns of the parity check matrix H. The number of non-zero entries in the smallest column gives us the minimum distance.

Looking at the parity check matrix H, we see that the smallest column has two non-zero entries in positions 1 and 2. Therefore, the minimum distance of the code is 2.

In conclusion, the minimum distance of the code is 2.

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Related Questions

math is hard help plsp0​

math is hard help plsp0

Answers

Answer:
38.5

Explanation:
55 x .70 = 38.5
Or 55 x .30 =16.5
55-16.5=38.5

Answer:

hgj

Step-by-step explanation:

Newer models of community organizing and community building have fluidity between collaboration and advocacy, and look at community strengths. Group of answer choices True False

Answers

True. Newer models of community organizing and community building emphasize a fluid approach that combines collaboration and advocacy while focusing on community strengths.

In recent years, community organizing and community building have evolved to embrace more dynamic and inclusive approaches. These newer models recognize the importance of collaboration and advocacy as complementary strategies for effecting positive change within communities. Rather than viewing collaboration and advocacy as mutually exclusive, they emphasize the need to strike a balance between the two.

This fluidity allows community organizers and builders to engage in collaborative efforts that bring together diverse stakeholders, including community members, organizations, and institutions. By working together, these stakeholders can pool their resources, expertise, and perspectives to address shared challenges and work towards common goals. Collaboration fosters cooperation, relationship-building, and collective decision-making, enabling the community to tap into its inherent strengths and assets.

Advocacy involves speaking up for community needs, raising awareness about systemic issues, and promoting policy changes that can improve the overall well-being of the community. By combining collaboration and advocacy, community organizers and builders can create a more holistic and comprehensive approach that leverages community strengths, engages a broader range of stakeholders, and promotes sustainable change.

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a manufacture produces wood tables on an assembly line, currently producing 1600 tables per shift. If the production is increased to 2000 tables per shift, labor productivity will increase by?

A) 10%
B) 20%
C) 25%
D) 40%

Answers

If the production of wood tables on an assembly line increases from 1600 tables per shift to 2000 tables per shift, the labor productivity will increase by 25%.We need to determine the percentage change.

To calculate the increase in labor productivity, we need to compare the difference in production levels and determine the percentage change.The initial production level is 1600 tables per shift, and the increased production level is 2000 tables per shift. The difference in production is 2000 - 1600 = 400 tables.

To calculate the percentage change, we divide the difference by the initial production and multiply by 100:

Percentage Change = (Difference / Initial Production) * 100 = (400 / 1600) * 100 = 25%.

Therefore, the correct answer is option C) 25%, indicating that labor productivity will increase by 25% when the production is increased to 2000 tables per shift.

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Graph f(x)=-1/2x-5
will do a brainly

Answers

slope = -1/2
y intercept = (0,-5)

What are the x coordinate and the y coordinate of the center of mass for the uniform plate shown in Figure below if L=5.0 cm?

Answers

From the  X coordinate is -0.45 centimeter and Y coordinate is -2.0 cm of the center of mass for the uniform plate.

According to the Question:

Since the plate is uniform, we can divide it into three rectangles, each with a mass proportional to its area and with its barycenter at its geometric center. We will refer to the large piece of 35cm x 10cm; it occupies 63.6% of the total surface and its barycenter is at

(x₁, y₁) = (−5.0cm,−2.5cm).

Now,

The top 20cm× 5cm piece has 18.2 % of the total area; its center of mass is at (x₂, y₂) = (10cm,12.5cm).  

Now,

The bottom 10cm× 10cm piece (section 3) also has 18.2 % of the total area; its center of mass is at (x₃, y₃)​ = (5cm,−15cm).

(a) The x coordinate of the center of mass for the plate is

   \(X_{com} = (0.636)X_1 + (0.182)X_2 + (0.182)X_3\)

            = -0.45 cm

(b) The y coordinate of the center of mass for the plate is

    \(Y_{com} = (0.636)Y_1 + (0.182)Y_2 + (0.182)Y_3\)

             = -2.0 cm.

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What are the x coordinate and the y coordinate of the center of mass for the uniform plate shown in Figure

Marie bought One-half gallon of milk, which she finished after 6 days. If she drank the same amount of milk each day, how many gallons a day did she drink?

Answers

Answer:

\(\dfrac{1}{12}$ gallons\)

Step-by-step explanation:

\(M$arie bought $ \dfrac{1}{2}$ gallon of milk\)

She exhausted the half gallon in 6 days.

Since she takes equal amount of milk per day

Her Unit Rate of Milk Consumption

\(=\dfrac{1}{2}\div 6\\ =\dfrac{1}{12}$ gallons per day\)

Marie drinks \(\dfrac{1}{12}\) gallons of milk per day.

Answer: 1/12

Step-by-step explanation:

help me with this guys

help me with this guys

Answers

Answer:

no. 1 a=37,no.2 b=12 thanks for your question which help to improve my knowledge

About 20% of software engineers in Silicon Valley earn approximately $50,000 per year.
In a random sample of 80 software engineers, let X represent the number of engineers that earn approximately $50,000 per year.
a. Find the probability that at most 20 earn approximately $50,000 per year.

Answers

173 because I guess the answer

What is the first step when examining a data set? *
Calculate the mean
Calculate the median
Put the data in order from least to greatest.

Answers

put the data in order

What is the sum of the geometric sequence 1, 3, 9, ... if there are 14 terms? (5 points)

Answers

Answer:

287

Step-by-step explanation:

the formulae is Sn=n\2(2a+(n-1)d) where n=14, d=3and a=1therefore,Sn=14\2(2*1+(14-1)3)Sn=7(2+(13)3)Sn=7(2+39)Sn=7(41)Sn=287

how many solutions does 6 -3x = 12 - 6x have?
A. two solutions.
B. no solutions.
C. one solution.
D. infinitely many solutions.

Answers

Answer:

Step-by-step explanation:

6-3x=12-6x

Only one solution of  x=2

What is the least common denominator for 1/6 and 3/8​

Answers

Answer:

24

Step-by-step explanation:

bc if you were to find what the fractions were before they were simplified, it would be 4/24 (for 1/6) and 9/24 (for 3/8)

The least common denominator for  1/6 and 3/8​ is 24.

What is the least common denominator?

When two or more fractions are supplied, the least common denominator is the smallest number among all the common multiples of the denominators.

Given, two fraction numbers 1/6 and 3/8​

We need to find the least common denominator of them. for that,

We will take the LCM of the denominator of both factors.

LCM of 6 and 8 = 24

Therefore, for fractions 1/6 and 3/8​, 24 is the least common denominator.

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Which equation is the inverse of y = 16+ 1?

Choices

Which equation is the inverse of y = 16+ 1?Choices

Answers

Answer:

d

Step-by-step explanation:

you could see it is x-1 and the the square root of 16 is 4.

Answer:

Answer is the very bottom one

Step-by-step explanation:

hope this helped ^^

Consider a 12-sided (dodecahedral) unfair die. In rolling this die, the even numbered sides are twice as likely as the odd numbered sides. Define the events: A = {odd numbered side} and B = {4, 5, 6, 7, 8}.
(a)Find the probability Pr[A].
(b)Find the probability Pr[B].
(c)Find the probability Pr[AB].

Answers

The probability of event A occurring is 1/3, the probability of event B occurring is 5/18, and the probability of event AB occurring is 1/9.

The probability of an event occurring is the number of favorable outcomes divided by the total number of possible outcomes. In this case, we have an unfair die where the even numbered sides are twice as likely as the odd numbered sides. We can use this information to find the probabilities of events A and B.

Event A = {odd numbered side} = {1, 3, 5, 7, 9, 11}

Event B = {4, 5, 6, 7, 8}

(a) To find the probability of event A occurring, we need to find the number of favorable outcomes and the total number of possible outcomes. There are 6 odd numbered sides on the die, so the number of favorable outcomes is 6. However, since the even numbered sides are twice as likely as the odd numbered sides, we need to account for this in the total number of possible outcomes. The total number of possible outcomes is 12 + 6 = 18. Therefore, the probability of event A occurring is 6/18 = 1/3.

(b) To find the probability of event B occurring, we need to find the number of favorable outcomes and the total number of possible outcomes. There are 5 sides in event B, so the number of favorable outcomes is 5. The total number of possible outcomes is the same as in part (a), which is 18. Therefore, the probability of event B occurring is 5/18.

(c) To find the probability of event AB occurring, we need to find the intersection of events A and B. The intersection of events A and B is {5, 7}, so the number of favorable outcomes is 2. The total number of possible outcomes is the same as in parts (a) and (b), which is 18. Therefore, the probability of event AB occurring is 2/18 = 1/9.

So, the probability of event A occurring is 1/3, the probability of event B occurring is 5/18, and the probability of event AB occurring is 1/9.

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An urn holds 9 identical balls except that 1 is white, 3 are black, and 5 are red. An exp How many outcomes are in the sample space for this experiment? How many outcomes are in the event "no ball is

Answers

Answer c

Step-by-step explanation:

Alicia has a collision deductible of $500 and a bodily injury liability coverage limit of $50,000. She hits another driver and injures them severely. The case goes to trial and there is a verdict to compensate the injured person for $40,000. How much does alicia have to pay? how much does her insurance pay?.

Answers

Alicia have to pay $10,000 and her insurance will pay $10,500.

What is limit of coverage in insurance?

This limit is the most the insurer will pay for sums as damages because of bodily injury or property damage included within the products-completes operations hazard during the policy period.

Given that Alicia has a collision deduction of $500 and a bodily injury coverage limit of $50,000.

And there is a verdict to compensate the injured person for $40,000

Therefore Alicia have to pay

$50,000-$40,000 = $10,000

And her insurance will pay

$10,000 + $500 = $10,500

Hence Alicia have to pay $10,000 and her insurance will pay $10,500.

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Can someone please help me with my homework !

Can someone please help me with my homework !

Answers

Answer:

Nah ;)

Step-by-step explanation:

If you were constructing a 99% confidence interval of the population mean based on a sample of n=30 where the standard deviation of the sample S=0.05, the critical value of t will be 2.7564 2.4922 2.7969

Answers

The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.

A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.

The formula for calculating the confidence interval for the population mean is:

Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)

Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.

Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.

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Starting with the number 10, build a sequence of 5 numbers.

Answers

Answer:

Step-by-step explanation:

To build a sequence, you have to create a rule. For example, if the rule is +2, then you add 2 to 10 to get 12, and then you add 2 to 12 to get 14, and so on. Your sequence would then be 10, 12, 14, 16, 18.

(-11 × 4) + (+15 ÷ -3)

Answers

Answer:

-49

Step-by-step explanation:

Let o(x) = x²+1. Calculate each average rate of change below. Then use the graph provided to illustrate what each calculation represents graphi- cally.
(a) AROC[0,3]
(b) AROC-2,2]
(c) AROC-3,1]

Answers

The AROC [-3, 1] of -2 means that the slope of the secant line joining the points (-3, 10) and (1, 2) is negative and steeper than the function's average slope in the interval [-∞, +∞].

a) Average rate of change from 0 to 3 is the change in the function value divided by the change in the variable. The formula for AROC of the function f(x) from x=a to x=b is: (f(b) - f(a)) / (b - a).Using this formula, we can find the AROC [0, 3] for the function o(x) = x² + 1:Substituting the values, we get: (o(3) - o(0)) / (3 - 0) = (10 - 1) / 3 = 3Therefore, the average rate of change of o(x) from 0 to 3 is 3.

b) Average rate of change from -2 to 2 is the change in the function value divided by the change in the variable. The formula for AROC of the function f(x) from x=a to x=b is: (f(b) - f(a)) / (b - a).Using this formula, we can find the AROC [-2, 2] for the function o(x) = x² + 1:Substituting the values, we get: (o(2) - o(-2)) / (2 - (-2)) = (5 - 5) / 4 = 0Therefore, the average rate of change of o(x) from -2 to 2 is 0.

c) Average rate of change from -3 to 1 is the change in the function value divided by the change in the variable. The formula for AROC of the function f(x) from x=a to x=b is: (f(b) - f(a)) / (b - a).Using this formula, we can find the AROC [-3, 1] for the function o(x) = x² + 1:Substituting the values, we get: (o(1) - o(-3)) / (1 - (-3)) = (2 - 10) / 4 = -2Therefore, the average rate of change of o(x) from -3 to 1 is -2.Graphical illustration of the calculations:
In the above graph, the blue line represents the function o(x) = x² + 1. The AROC [0, 3] of 3 means that the slope of the secant line joining the points (0, 1) and (3, 10) is positive and steeper than the function's average slope in the interval [-∞, +∞]. The AROC [-2, 2] of 0 means that the slope of the secant line joining the points (-2, 5) and (2, 5) is zero and is parallel to the x-axis.  

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Bradbury scar caught 35 fish with his net 20 percent of the fish had to be thrown back into the sea because they were too small how many fish did Bradbury throw back to sea

Answers

7 fish were thrown back

In the diagram, the measures of 22, 23 and 26 are 40°. The measure of 21
is 140°. Are lines cand d parallel?

In the diagram, the measures of 22, 23 and 26 are 40. The measure of 21is 140. Are lines cand d parallel?

Answers

Answer:

c. Yes because ∠2 and ∠6 are congruent.

Step-by-step explanation:

From the picture attached,

m(∠2) = m(∠3) = m(∠6) = 40°

m(∠1) = 140°

Since (∠2 ≅ ∠6) (corresponding angles)

Therefore, by the converse theorem of corresponding angles lines c and d are parallel.

Option c is the answer.

Jonathan’s math test scores were 87, 93, 85, 62, and 95. What was his mean score?

Answers

Answer:

Jonathan's mean score is:

(87+93+85+62+95)/5

=422/5

=84.4

What property is 7 + (5 + 8)

Answers

Answer: 20

Step-by-step explanation:

7 + the sum of 5 + 8 = 20

Determine the mean and standard deviation of the variable X in each of the following binomial distributions. a. n=5 and π=0.10 b. n=3 and π=0.40 c. n=5 and r=0.50 d. n=3 and π=0.80 a. When n=5 and π=0.10, determine the mean. μ= (Type an integer or a decimal. Do not round.)

Answers

The mean (μ) for the given binomial distribution is 0.50.

To calculate the mean (μ) of a binomial distribution, we multiply the number of trials (n) by the probability of success in a single trial (π). Let's examine each scenario in detail:

a. When n = 5 and π = 0.10:

μ = 5 * 0.10

  = 0.50

For this binomial distribution, with 5 trials and a success probability of 0.10, the mean (μ) is 0.50. This means that, on average, we would expect to have 0.50 successes per trial.

b. When n = 3 and π = 0.40:

μ = 3 * 0.40

  = 1.20

In this case, the mean (μ) of the binomial distribution is 1.20. It indicates that, on average, there would be 1.20 successes per trial when there are 3 trials and a success probability of 0.40.

c. When n = 5 and π = 0.50:

μ = 5 * 0.50

  = 2.50

For a binomial distribution with 5 trials and a success probability of 0.50, the mean (μ) is 2.50. This means that, on average, we would expect to have 2.50 successes per trial.

d. When n = 3 and π = 0.80:

μ = 3 * 0.80

  = 2.40

In this scenario, the mean (μ) of the binomial distribution is 2.40. It suggests that, on average, we would expect to have 2.40 successes per trial when there are 3 trials and a success probability of 0.80.

The mean (μ) provides a measure of the central tendency or the average number of successes in a binomial distribution based on the given parameters.

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which of the following quantities are discrete 1. the number of students who passed the english test 2. the speed of a car 3. the temperature throughout the day 4. the number of pages in a book

A. only 4
B. 2 and 3
C. 1, 2, and 3
D. 1 and 5​

Answers

Answer:

A. only 4

Step-by-step explanation:

13.10 − Let Mn​ be the maximum of n independent U(0,1) random variables. a. Derive the exact expression for P(∣Mn​−1∣>ε). Hint: see Section 8.4. b. Show that limn→[infinity]​P(∣Mn​−1∣>ε)=0. Can this be derived from Chebyshev's inequality or the law of large numbers?

Answers

This can be derived using Chebyshev's inequality, as Chebyshev's inequality and the law of large numbers are different in nature.

Let M_n be the maximum of n independent U(0, 1) random variables.

To derive the exact expression for P(|M_n − 1| > ε), we need to follow the below steps:

First, we determine P(M_n ≤ 1-ε). The probability that all of the n variables are less than 1-ε is (1-ε)^n

So, P(M_n ≤ 1-ε) = (1-ε)^n

Similarly, we determine P(M_n ≥ 1+ε), which is equal to the probability that all the n variables are greater than 1+\epsilon

Hence, P(M_n ≥ 1+ε) = (1-ε)^n

Now we can write P(|M_n-1|>ε)=1-P(M_n≤1-ε)-P(M_n≥1+ε)

P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n.

Thus we have derived the exact expression for P(|M_n − 1| > ε) as P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n

Now, to show that $lim_{n\to\∞}$ P(|M_n - 1| > ε) = 0 , we can use Chebyshev's inequality which states that P(|X-\mu|>ε)≤{Var(X)/ε^2}

Chebyshev's inequality and the law of large numbers are different in nature as Chebyshev's inequality gives the upper bound for the probability of deviation of a random variable from its expected value. On the other hand, the law of large numbers provides information about how the sample mean approaches the population mean as the sample size increases.

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Creed wanted to know if there was a correlation between number of years of education and income. He collected data and created the scatterplot shown: scatter plot with points loosely scattered going up to the right Determine the closest correlation coefficient (r value) for this data. 0 0. 8 1 −1.

Answers

The closest correlation coefficient of the scatter plot with points loosely scattered going up to the right would be: 0.8.

Correlation CoefficientCorrelation coefficient is a measure of the mutual relationship between two variables.Correlation coefficient, r, ranges from 1 to -1.On a scatter plot, if the data points are clustered along the line of best-fit, the correlation coefficient is strong and away from 0, and vice versa, also it is positive if the line of best-fit or trend slopes upwards from left to right, and vice versa.

Therefore, the closest correlation coefficient of the scatter plot with points loosely scattered going up to the right would be: 0.8.

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Answer:

0.8

Step-by-step explanation:

LIVE
Carlos is saving money to buy a set of golf clubs that cost $530. He already has $80.00 saved and can earn the rest of the money by mowing 15
lawns. If m represents how much he earns for mowing each lawn, which of the following equations can be solved to find how much Carlos is paid for
mowing each lawn?

Answers

Answer:

15m+80 would be the correct equation

Answer:

15*m=(530-80)

Step-by-step explanation:

30$ per lawn. 530-80=450. This gives us how much money he still needs to buy his gulf clubs. But, the question says that Carlos can earn the rest of the money ($450) by mowing 15 lawns.

Here's how we model that as an expression:

15m=(530-80)

15 lawns for m dollars would get him 530-80 (450) or the remaining amount.

Hope this helps!

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