QUESTION 6
A(7,3) cyclic code, the g(x) =x4 +x3 +x2 +1.
1. Is the given matrix systematic form of generator matrix?
O True
O False
|1001110|
|0100111|
|0011101|
Answers
The answer is False, the given matrix is not the systematic form of the generator matrix for the (7,3) cyclic code with generator polynomial g(x) = x^4 + x^3 + x^2 + 1.
To determine whether the given matrix is the systematic form of a generator matrix for an (7,3) cyclic code with generator polynomial g(x) = x^4 + x^3 + x^2 + 1, we need to check if it satisfies the necessary conditions for a generator matrix.
A generator matrix for an (n,k) cyclic code with generator polynomial g(x) is a k x n matrix G whose rows are linearly independent and whose entries correspond to the coefficients of the polynomials in the code. Additionally, the last n-k columns of G should be the cyclic shifts of the first k columns of G.
The systematic form of a generator matrix is obtained by applying elementary row operations to a non-systematic generator matrix to transform it into a form where the first k columns of the matrix are the identity matrix and the last n-k columns are the parity-check matrix H.
Let's examine the given matrix:
|1 0 0 1 1 1 0|
|0 1 0 0 1 1 1|
|0 0 1 1 1 0 1|
We notice that this matrix satisfies the necessary conditions for a generator matrix: it is a 3 x 7 matrix whose rows are linearly independent, and the last 4 columns are the cyclic shifts of the first 3 columns.
However, the given matrix is not in the systematic form of a generator matrix. To obtain the systematic form of a generator matrix, we need to perform elementary row operations on this matrix to transform it into a form where the first three columns of the matrix are the identity matrix and the last four columns are the parity-check matrix H.
Therefore, the answer is False, the given matrix is not the systematic form of the generator matrix for the (7,3) cyclic code with generator polynomial g(x) = x^4 + x^3 + x^2 + 1.
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Related Questions
36, 27,
81
4
Find the 10th term.
Answers
a_{10} = \frac{177147}{65536} is solution of arithmetic progression (AP).
What is arithmetic progression (AP) in math?
The difference between any two consecutive numbers in an arithmetic progression (AP) is always a fixed amount.The AP cost per invoice is calculated by dividing the total number of invoices paid over a certain time period by all the expenditures incurred to pay those invoices over that same time period. An accurate assessment of a company's AP efficiency can be made using this metric in conjunction with other accounts payable measures.Write the general term through the pattern \(a_{n} = 36( \frac{3}{4} )^{n-1}\)
Substitute and calculate \(a_{10} = \frac{177147}{65536}\)
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Determine the production capacity achieved by an operator with a performance rating leveling factor of 90%, who worked 6.95 hours in an 8- hour shift, for time lost at 15% compensation. The standardized time of operation is 18 seconds per unit.
Answers
Time lost due to compensation = 15% of the total time available in a shift
= 0.15 x 8 hours = 1.2
hours Substituting the given values, we get:Production capacity
= 626 / (6.8 hours) = 92.0588 ]
pieces/hourThe production capacity achieved by an operator with a performance rating leveling factor of 90%, who worked 6.95 hours in an 8-hour shift, for time lost at 15% compensation is approximately 92 pieces/hour.To find out the production capacity achieved by the operator, the time lost due to compensation must be taken into account.
An operator with a performance rating leveling factor of 90%, who worked 6.95 hours in an 8-hour shift, for time lost at 15% compensation can produce 320 pieces. The standardized time of operation is 18 seconds per unit.According to the information given,Total hours worked by an operator
= 6.95 hours (for time lost at 15%compensation)Total time available in an 8-hour shift
= 8 hours Standardized time for the operation
= 18 seconds per unit Performance rating leveling factor of an operator
= 90%Productivity can be determined by using the following formula:Productivity
= Total hours worked x Performance rating leveling factor / Total time available in a shift We have:Productivity
= 6.95 × 90 / 8 = 77.175%
We also have,Total pieces produced
= (Production rate × Operating time × Performance rating leveling factor) / Standardized time of operation Operating time of the operator
= Total hours worked x Performance rating leveling factor
= 6.95 x 0.9 = 6.255 hours
We have been given, Standardized time of operation is 18 seconds per unit Substituting the given values, we get:Total pieces produced
= (3600 / 18) x 6.255
= 800 x 0.78375
= 626.25
Total pieces produced with a round off to the nearest whole number
= 626
Now, we can get the production capacity achieved by an operator using the following formula:Production capacity
= Total pieces produced / Time lost due to compensation We have been given, Time lost due to compensation
= 15% of the total time available in a shift
= 0.15 x 8 hours = 1.2
hours Substituting the given values, we get:Production capacity
= 626 / (6.8 hours)
= 92.0588
pieces/hourThe production capacity achieved by an operator with a performance rating leveling factor of
90%,
who worked
6.95 hours in an 8-hour shift,
for time lost at 15% compensation is approximately
92 pieces/hour.
To find out the production capacity achieved by the operator, the time lost due to compensation must be taken into account.
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how to find principal without interest
Answers
Answer:
Step-by-step explanation:
What Is a Principal Amount?
Principal amount on a loan is the amount borrowed. To better understand, let's look at the story of John. When John bought his first car he didn't have enough money to pay for it in cash, so he had to take out a loan. He borrowed $7,500. According to the terms of the loan, John had to pay it off in five years with an interest rate of 10%. The initial amount that he borrowed, or the $7,500, is called the principal amount of the loan. Keep in mind that the principal amount applies to more than just loans. It can also apply to money that is invested or deposited into an account. For example, if you open a savings account with a $700 deposit, the principal amount is $700.
What About Interest?
Principal amount does not include interest, or a rate paid as a fee for borrowing money. To figure out the amount of interest John paid during the five years, you can use the simple interest formula, which is a formula to calculate interest paid only on the principal amount. This formula is:
or interest equals principal amount times interest rate times amount of time. Using this formula, you will find that the amount of interest on John's $7,500 loan was $3,750. So, at the end of five years, he would end up paying a total of $11,250. This does not include any additional fees that may apply.
Principal Amount Formulas
For John's loan, we were given the principal amount and used it to find the amount of interest. What if we already know the interest rate, amount of interest, and amount of time, but we need to find out the principal amount? We can rearrange the interest formula, I = PRT to calculate the principal amount. The new, rearranged formula would be P = I / (RT), which is principal amount equals interest divided by interest rate times the amount of time.
Let's try this out by finding the principal amount of a loan that has a total interest amount of $18,500 and an annual interest rate of 6.5% over 12 years.
To solve, we input the values into the equation, P = I / (RT). This gives us:
P = $18,500 / (0.065 * 12) = $23,718
The principal amount of the loan is $23,718.
(hope this helps can i plz have brainlist :D hehe)
mr. Smith started 8 yards away from the motion detector, and two seconds later, he was 4 yards away from the detector. The graph below shows Mr. Smith’s motion. What is the difference between the rate of change of the intervals: 1,2 and 2,4?
Answers
The difference between the rate of change of the intervals: 1,2 and 2,4 is; 2
How to find the rate of change over an interval?The average rate of change over the intervals (x₁, y₁) and (x₂, y₂) is given by the formula;
Average rate of change = (y₂ - y₁)/(x₂ - x₁)
Thus, the average rate of change between the intervals (1, 2) and (2, 4) is;
Average rate of change = (4 - 2)/(2 - 1)
Average rate of change = 2/1
Average rate of change = 2
That is the difference between the rate of change over the two given intervals.
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i need help with this ASAP
Answers
Helpppppppppppppppppppppppppppp
Answers
Answer:
x = 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityStep-by-step explanation:
Step 1: Define
10.5x - 1.9 = 19.1
Step 2: Solve for x
Add 1.9 to both sides: 10.5x = 21Divide 10.5 on both sides: x = 2Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 10.5(2) - 1.9 = 19.1Multiply: 21 - 1.9 = 19.1Subtract: 19.1 = 19.1Here we see that 19.1 does indeed equal 19.1.
∴ x = 2 is a solution to the equation.
you wish to survey people who have brought in their cars for service during the past month. you decide to choose a random sample of gas stations in the city and then survey all customers from those stations who had work done during the past month. this procedure is an example of which type of sampling?
Answers
An illustration of "Cluster sampling" is the practice of selecting a random sample of the city's gas stations, and then surveying every station's patrons.
Define the term Cluster sampling?In cluster sampling, a population is divided into clusters, which have been smaller groups. They but choose a sample at random from these clustersOften employed to investigate huge populations, typically those that are substantially geographically distributed, cluster sampling is a probability sampling technique. Often, clusters used by researchers have been groups like cities or schools.As per the given question.
People who brought their autos in for service over the past month should be surveyed. You make the decision to selecting a haphazard sample of the city's petrol stations, after which you interview all of their patrons whom have work done on their vehicles well within previous month.Thus, an implementation of "Cluster sampling" is the practice of randomizing sample of the city's gas stations, and thereafter surveying every station's patrons.
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A machine consists of two components, whose lifetimes have the joint density function f(x, y) = {1/162 x > 0, y > 0, x + y < 18; 0 otherwise The machine operates until both components fail. Calculate the expected operational time of the machine.
Answers
The expected operational time of the machine is 6.75
For given x , y > 0 , the lifetime of the machine is max{x , y} because it stops when the two component will fail.
The life expectancy if therefore the expectancy of max{x, y}
t = E [ max{x,y} ]
So, the max{x , y} can be x or y
We have three integral
I₁ = \(\frac{1}{162}\int\limits^9_0 \, dx \int\limits^{18-x}_{x} y \. dy\)
Solving the integration
=> I₁ = 729 / 162
=> 4.5
I₂ = \(\frac{1}{162}\int\limits^9_0 \, dx \int\limits^{x}_{0} y \. dy\)
=> I₂ = 121.5/162
=> 0.75
=> I₃ = \(\frac{1}{162}\int\limits^9_0 \, dx \int\limits^{18-x}_{x} x \. dy\)
=> I₃ = 243 / 162
=> 1.5
So . the total is 4.5 + 0.75 + 1.5
=> 6.75 is expected operational time
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two car rental companies charge a one-time fee and a millage rate for renting a car the graph below compares the cost for renting cars from the two companies based on the graph which of the following statements appears to be true about the costs of renting cars from the two companies
Answers
From the graph we notice that the lines are parallel. This means that the slopes of the lines representing the cost are the same. Since the slope represents the price per mile travel we conclude that:
The mileage at both companies is the same.
Therefore the answer is B
The solution to the system is (6,2). Select all the equations that could be the other
equation in the
system.
a.y = -3x
C. y=x+6
b.y=-*-* +3
d. y = {x-1
e. y=1&x-1
f.y = 4x - 2
Answers
Answer:
Step-by-step explanation: 645
Answer: C and E
Step-by-step explanation:
i took this on my quiz and got it right :)
Timber Inc. invested profits of $150,000.00 in a GIC at 4.90% compounded quarterly. How long will it take for the investment to grow to a value of at least $223,000.00?____years ____monthsExpress the answer in years and months, rounded to the next month
Answers
Given:
Present value = 150,000
Future value=223000
rate = 4.90% compunded quarterly.
To find the number of periods,
\(\begin{gathered} FV=PV(1+r)^n \\ 223000=150000(1+\frac{0.049}{4})^n \\ 223000=150000(1.01225)^n \\ (1.01225)^n=\frac{223}{150} \\ n=\frac{\ln (\frac{223}{150})}{\ln (1.01225)} \\ n=32.6 \end{gathered}\)Answer: 32.6 years that means 32 years and 6 months.
a printed circuit board has seven different locations in which a component can be placed. if four different components are to be placed on the board, how many possible designs are possible?
Answers
There are 35 possible designs for the printed circuit board with four different components placed on it, assuming each of the seven locations can hold only one component.
To calculate the number of possible designs for the printed circuit board with seven locations for component placement, we can use the combination formula.
The number of combinations of r items from a set of n items is given by the formula:
nCr = n!/r!(n-r)!
In this case, we want to find the number of combinations of four components from seven locations. Thus, we can calculate it as follows:
7C4 = 7!/4!(7-4)! = (7x6x5)/(3x2x1) = 35
Therefore, there are 35 possible designs for the printed circuit board with four different components placed on it, assuming each of the seven locations can hold only one component.
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Vrite your definition of square numbers. Square numbers:
Answers
Answer:
Square numbers are numbers that have been multiplied by themselves.
a grocery store recently sold 12 cans of soup, 6 of which were tomato soup. based on experimental probability, how many of the next 20 cans sold should you expect to be tomato soup?
Answers
We can calculate the experimental probability of selling a can of tomato soup, and then use that probability to predict the number of tomato soup cans sold in the next 20 cans.
Step 1: Calculate the experimental probability of selling a can of tomato soup.
Probability = (Number of tomato soup cans sold) / (Total number of cans sold)
Probability = 6 / 12 = 0.5
Step 2: Use the probability to predict the number of tomato soup cans sold in the next 20 cans.
Expected number of tomato soup cans = Probability × Total number of cans
Expected number of tomato soup cans = 0.5 × 20 = 10
Based on the experimental probability, you should expect 10 of the next 20 cans sold to be tomato soup.
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Suppose that tan 0=-5/12 and 90° <0<180°.
Find the exact values of sin
0/2 and
tan
O/2
Answers
The exact values of sin θ/2 and tan θ/2 given below as:
sin θ/2 = 0.9806tan θ/2 = 4.99What is the exact values of sin θ/2 and tan θ/2 given that tan θ = -5/12?Given that tan θ = -5/12 and θ lies between 90° and 180°, the values of sin θ/2 and tan θ/2 can be found as follows:
tan θ = -5/12
θ = 180 -tan⁻¹-(5/12)
θ = 157.38
sin θ/2 = sin 157.38/2
sin θ/2 = 0.9806
tan θ/2 = tan 157.38/2
tan θ/2 = 4.99
In conclusion, the values of the sine and tangent are found from the given values.
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Can someone help me with this question.
Answers
if you put 25ml of concentrate in a glass how much water should be added
Answers
Answer:
50 ml of water should be added in the glass.
Step-by-step explanation:
An isometric transformation is one in which preserves the shape and size of the pre-image. Which of the following transformations will not prove to be isometric?translationtessellationrotationdilation
Answers
The following transformation that will not prove to be isometric is the dilation. This is the one that will not prove isometric.
Dilation is not isometric because it will enlarge the graph, thus changes the image size.
Rotation, translation, and tesselation won't change the shape and size
what is the slope of a line that passes through the points (-9,-2) and (-9,-6)? write the answer in simplest form.
Answers
\(m = \frac{y2 - y1}{x2 - x1 } \\m = \frac{ - 6 - ( - 2)}{ - 9 - ( - 9)} \\ m = \frac{ - 6 + 2}{ - 9 + 9} \\ m = \frac{ - 4}{0} \)
Slope is undefined since there can't be zero in numerator
Please give brainliest
Answer:
It be undefined
Step-by-step explanation:
Since -9,-2) and (-9,-6) dose not = a number and dose not = 0 it be undefined
If m∠B = 62°, a = 11, and c = 19, what are the measures of the remaining side and angles?
Answers
The remaining side is 16.9 and remaining angles are 83.1 and 34.9.
What is Cosine Formula?The cosine formula to find the side of the triangle is given by:
c = √[a² + b² – 2ab cos C] Where a,b and c are the sides of the triangle.
Given:
m∠B = 62°, a = 11, and c = 19
Now, b² = a² + c² - 2ac cos B.
b = √ a² + c² - 2ac cos B
b = √ 11² + 19² - 2x 11 x 19 cos 62
b= 16.9
Now. a/ sin A = b/ sin B= c/ sin C
So, <C = arc sin ( c sin B /b)
<C = arc sin ( 19 sin 62 /16.9)
<C = 83.1
and, <A = arc sin ( a sin B /b)
<A = arc sin ( 11 sin 62 /16.9)
<A = 34.9
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express the terms of the following geometric sequence recursively 3,6,12,24,4&
Answers
Answer:
aₙ = 2aₙ₋₁ for n ≥ 2
a₁ = 3
Step-by-step explanation:
A geometric sequence can be expressed recursively using the following general equation
aₙ = r . (aₙ₋₁), n ≥ 2
where
aₙ is the nth term
a₁ is the first term of the geometric sequence
r is the common ratio = aₙ/aₙ₋₁
Here we have the terms 3, 6, 12, 24, 48
The common ratio r = 6/3 = 12/6 = ....... = 48/24 = 2
The first term a₁ = 3
So the recursive relation is
aₙ = 2aₙ₋₁ for n ≥ 2
a₁ = 3
the heights of the peach trees in an orchard are normally distributed with a mean of 12.5 feet and a standard deviation of 1.8 feet.
what is the height of a peach tree with a z-score of -0.5?
Enter your answer rounded to the nearest tenth, in the box.
Answers
Answer:
i think 1.8 not sure tho
Answer:
Z-score Formula: z = (x - μ)/σ
Plug in: -0.5 = (x - 12.5)/1.8
Solve: -0.5 * 1.8 = x - 12.5
-0.9 = x - 12.5
-0.9 + 12.5
x = 11.6
Therefore, the height of a peach tree with a z-score of -0.5 is 11.6 feet.
Jayden said the answer is (5x + 2)(x-6). Chelsea said the answer is (5x - 2)(x + 6). Who is correct? Explain your reasoning. ( points)
Answers
Answer:
what is the question?
Answer to what?
a logarithm is defined as the power to which a base must be raised in order to equal a given number, why can't we have negative bases
Answers
Negative bases are not often used in logarithms because they produce complex results. For example, if the base is negative and the exponent is positive, the result will be a complex number.
Logarithms are generally used to solve equations or simplify complex problems. Having a negative base would complicate this process, as it would introduce complex numbers or even imaginary numbers into the equation. Consequently, it is not feasible to use negative bases with logarithms. Furthermore, if both the base and the exponent are negative, the result is undefined. This means that it is not possible to evaluate the expression. Therefore, for these reasons, it is usually not practical to use negative bases when working with logarithms.
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A car travels 174 miles in 3 hours. At this rate, how many miles will the car travel in 12 hour?
A. 348 miles
B. 87 miles
C. 58 miles
D. 29 miles
Answers
Answer: C. 58 miles
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
I know I'm smart
sike I'm autistic
Is x = 6 a solution to the equation 3x + 5 = 17?
Answers
Answer:
FalseStep-by-step explanation:
To check, let's substitute the value of x into the equation.
=> 3x + 5 = 17Substituting value of x.
=> 3(6) + 5 = 17Solving.
=> 18 + 5 = 17=> 23 ≠ 17Since 23 does not equal 17, the statement is false.
Answer:
No
Step-by-step explanation:
No, Because if you plug in 6 into the equation you'd get 23.
To solve this equation you must...
First, subtract 5 from both sides to get 3x=12
Then, divide 12 by 3 to get your answer x=4
You can check this by plugging this into the equation.
3*4=12+5= 17
So, the correct answer to this question would be X=4
Hope this helps!!
Sam takes a taxi in Chicago. The taxi charges $0.75 per mile and a flat fee of $1.60. If he has at most 10 dollars
to spend, how many miles can he travel in the taxi?
Answers
8.40/0.75=11.2 miles
18x + 30 = ???????????
Answers
Answer:
18x+30=12x-6
Step-by-step explanation:
all you do is distribute
Answer:
The first blank you would need to put "12", for the second one put a minus (-) sign, and for the third box put a "6".
Mrs. King needs to rent tables for the 327
guests who will attend her daughter's
wedding reception.
If Mrs. King seats 9 guests at each table,
how many tables should she rent to seat
all the guests?
Answers
Answer:36.33333333 but rounded it is basically 36
Step-by-step explanation:
what you have to do is 327 divided by 9 then you get your answer then round
Select the correct answer. What is the value of the limit lim x 2 (x^2+3x+1/x^3+x+1) ? A. B. 1 C. D.
Answers
So by direct evaluation we can see that the limit when x tends to 2 is equal to 1.
How to get the value of the limit?
Here we want to get the limit:
\(\lim_{x \to \ 2} \frac{x^2 + 3x + 1}{x^3 + x + 1}\)
First, we can try to evaluate directly in x = 2 and see if it does not generate any problem, we will get:
\(\lim_{x \to \ 2} \frac{x^2 + 3x + 1}{x^3 + x + 1} = \frac{2^2 + 3*2 + 1}{2^3 + 2 + 1} = 1\)
So by direct evaluation we can see that the limit when x tends to 2 is equal to 1.
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