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kirill115 [55]
3 years ago
13

Use the Euclidean Algorithm to find the greatest common divisor of the polynomials f(x) = x^3 + 3x^2 + 6x + 1 and g(x) = 5x^4 +

2x^2 +x + 1 in Z7[x] .

Mathematics
1 answer:
fomenos3 years ago
5 0

Answer:

3x+1.

Step-by-step explanation:

First we divide g(x)/f(x) (the process is in the first image):

5x-15 in Z7[x] is 5x-1 and 17x^2+86x+16 is r(x)= 3x^2+2x+2 in Z7[x]. So

g(x)/f(x) = (5x-1)(x^3+3x^2+6x+1)+3x^2+2x+2

Now gcd(g,f) = gcm(f,r).

f(x)/r(x) = 5x(3x^2+2x+2) + 3x+1

Then, gcd(f,r) = gcd(r,3x+1).

r/(3x+1) = (x+5)(3x+1) +4

Then, gcd(r, 3x+1) = gcd(3x+1,4) = 3x+1.

So, gcd(f,g) = 3x+1.

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A random variable x follows a normal distribution with mean d and standard deviation o=2. It is known that x is less than 5 abou
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Answer:

The mean of this distribution is approximately 3.96.

Step-by-step explanation:

Here's how to solve this problem using a normal distribution table.

Let z be the

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To solve for \mu, the mean of this distribution, the only thing that needs to be found is the value of z. Since

The problem stated that P(X \le 5) = 69.85\% = 0.6985. Hence, P(Z \le z) = 0.6985.

The problem is that the normal distribution tables list only the value of P(0 \le Z \le z) for z \ge 0. To estimate  z from P(Z \le z) = 0.6985, it would be necessary to find the appropriate

Since P(Z \le z) = 0.6985 and is greater than P(Z \le 0) = 0.50, z > 0. As a result, P(Z \le z) can be written as the sum of P(Z < 0) and P(0 \le Z \le z). Besides, P(Z < 0) = P(Z \le 0) = 0.50. As a result:

\begin{aligned}&P(Z \le z)\\ &= P(Z < 0) + P(0 \le Z \le z) \\ &= 0.50 + P(0 \le Z \le z)\end{aligned}.

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\begin{aligned}&P(0 \le Z \le z) \\ &= P(Z \le z) - 0.50 \\&= 0.6985 - 0.50 \\&=0.1985 \end{aligned}.

Lookup 0.1985 on a normal distribution table. The corresponding z-score is 0.52. (In other words, P(0 \le Z \le 0.52) = 0.1985.)

Given that

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Solve the equation \displaystyle z = \frac{x - \mu}{\sigma} for the mean, \mu:

\displaystyle 0.52 = \frac{5 - \mu}{2}.

\mu = 5 - 2 \times 0.52 = 3.96.

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