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2 years ago

What is the remainder obtained by dividing x7 x5 1 by the generator polynomial x3 1?

Mathematics

2 answers:

posledela2 years ago

4 0

The remainder obtained by dividing on ${x^7} + {x^5} + 1$ the generator polynomial ${x^3} + 1$ is $\boxed{{-x^2} + {x} +1}$

Given:

The generator polynomial is ${x^3} + 1.$

The polynomial is ${x^7} + {x^5} + 1$

Explanation:

There are two methods of dividing the two polynomials.

(1). Synthetic division

(2). Long division method

The fraction can be expressed as,

${\text{Fraction}}= \dfrac{{{x^7} + {x^5} + 1}}{{{x^3} + 1}}$

The denominator of the fraction is ${x^3} + 1$ and the numerator of the fraction is ${x^7} + {x^5} + 1.$

Divide ${x^7} + {x^5} + 1$ by ${x^3} + 1$ to obtain the remainder and the quotient of the polynomial.

The remainder obtained by dividing on ${x^7} + {x^5} + 1$ the generator polynomial ${x^3} + 1$ is $\boxed{{-x^2} + {x} +1}$

Kindly refer the image attached below.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Long division method

Keywords: division, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree, cubic polynomial, quadratic equation.

vivado [14]2 years ago

3 0

Please, use " ^ " to indicate exponention. x7 and x3 are meaningless.

I must assume you mean x^7 + 0 x^6 + 0x^5 + 0x^4 + 0x^3 + 0x^2 + 0x + 1
and that your "generator polynomial" is x^3 + 0x^2 + 0x + 1. If this is not the case, then you really need to work on your presentation of polynomials.

Divide (x^3 + 0x^2 + 0x + 1 into
x^7 + 0 x^6 + 0x^5 + 0x^4 + 0x^3 + 0x^2 + 0x + 1

Dividing x^3 into x^7 leaves a partial quotient of x^4. Multiply (x^3 + 1) by this x^4 and write your result under x^7 + 0x^6 + 0x^5 ... + 1
Subtract.

Can you now finish this problem? If not, what do you need to know so that you can finish it?

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Suppose that 4% of the 2 million high school students who take the SAT each year receive special accommodations because of docum

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Answer:

a. 0.0122

b. 0.294

c. 0.2818

d. 30.671%

e. 2.01 hours

Step-by-step explanation:

Given

Let X represents the number of students that receive special accommodation

P(X) = 4%

P(X) = 0.04

Let S = Sample Size = 30

Let Y be a selected numbers of Sample Size

Y ≈ Bin (30,0.04)

a. The probability that 1 candidate received special accommodation

P(Y = 1) = (30,1)

= (0.04)¹ * (1 - 0.04)^(30 - 1)

= 0.04 * 0.96^29

= 0.012244068467946074580191760542164986632531806368667873050624

P(Y=1) = 0.0122 --- Approximated

b. The probability that at least 1 received a special accommodation is given by:

This means P(Y≥1)

But P(Y=0) + P(Y≥1) = 1

P(Y≥1) = 1 - P(Y=0)

Calculating P(Y=0)

P(Y=0) = (0.04)° * (1 - 0.04)^(30 - 0)

= 1 * 0.96^36

= 0.293857643230705789924602253011959679180763352848028953214976

= 0.294 --- Approximated

The probability that at least 2 received a special accommodation is given by:

P (Y≥2) = 1 -P(Y=0) - P(Y=1)

= 0.294 - 0.0122

= 0.2818

d. The probability that the number among the 15 who received a special accommodation is within 2 standard deviations of the number you would expect to be accommodated?

First, we calculate the standard deviation

SD = √npq

n = 15

p = 0.04

q = 1 - 0.04 = 0.96

SD = √(15 * 0.04 * 0.96)

SD = 0.758946638440411

SD = 0.759

Mean =np = 15 * 0.04 = 0.6

The interval that is two standard deviations away from .6 is [0, 2.55] which means that we want the probability that either 0, 1 , or 2 students among the 20 students received a special accommodation.

P(Y≤2)

P(0) + P(1) + P(2)

P(0) + P(1) = 0.0122 + 0.294

Calculating P(2)

P(2) = (0.04)² * (1 - 0.04)^(30 - 2(

P(2) = 0.00051

So,

P(0) +P(1) + P(2). = 0.0122 + 0.294 + 0.00051

= 0.30671

Thus it 30.671% probable that 0, 1, or 2 students received accommodation.

The expected value from d) is .6

The average time is [.6(4.5) + 19.2(3)]/30 = 2.01 hours

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As an example, 15,000 Men 18-34 watched program X at 7-8 pm on Monday night. 32,000 Men 18-34 had their TV on during the same ti

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Answer:

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The computation of the rating for Men 18-34 for program X is shown below:

Given that

Number of men 18 -34 watched a program X = 15,000 = X

Number of men 18 - 34 watched in a same time = 32,000

And, the total households in the market = 200,000 = Y

So, the rating for men 18-34 for program x is

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Answer:

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The probability of obtaining any of these numbers is:

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