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Ksju [112]
3 years ago
10

Suppose that a, b \in \mathbb{Z}a,b∈Z, not both 00, and let d=\gcd(a, b)d=gcd(a,b). Bezout's theorem states that dd can be writt

en as a linear combination of aa and bb, that is, there exist integers m, n \in \mathbb{Z}m,n∈Z such that d = am + bnd=am+bn. Prove that, on the other hand, any linear combination of aa and bb is divisible by dd. That is, suppose that t = ax + byt=ax+by for some integers x, y \in \mathbb{Z}x,y∈Z. Prove that d \, | \, td∣t.
Mathematics
1 answer:
lara [203]3 years ago
3 0

Answer:

Step-by-step explanation:

Recall that we say that d | a if there exists an integer k for which a = dk. So, let d = gcd(a,b) and let x, y be integers. Let t = ax+by.

We know that d | a, d | b so there exists integers k,m such that a = kd and b = md. Then,

t = ax+by = (kd)x+(md)y = d(kx+my). Recall that since k,  x, m, y are integers, then (kx+my) is also an integer. This proves that d | t.

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Answer:

I think the tall of the tree is eight meters

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10 normal six sided dice are thrown.Find the probability of obtaining at least 8 failuresif a success is 5 or 6.
erastova [34]

Answer:

0.2992 = 29.92% probability of obtaining at least 8 failures.

Step-by-step explanation:

For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

A success is 5 or 6.

A dice has 6 sides, numbered 1 to 6. Since a success is 5 or 6, the other 4 numbers are failures, and the probability of failure is:

p = \frac{4}{6} = 0.6667

10 normal six sided dice are thrown.

This means that n = 10

Find the probability of obtaining at least 8 failures.

This is:

P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)

So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 8) = C_{10,8}.(0.6667)^{8}.(0.3333)^{2} = 0.1951

P(X = 9) = C_{10,9}.(0.6667)^{9}.(0.3333)^{1} = 0.0867

P(X = 10) = C_{10,10}.(0.6667)^{10}.(0.3333)^{0} = 0.0174

Then

P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1951 + 0.0867 + 0.0174 = 0.2992

0.2992 = 29.92% probability of obtaining at least 8 failures.

8 0
3 years ago
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Answer:

50 percent

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100 percent divided by 6 (the amount of data) is 16 2/3.

Each number represents 16 2/3 percent.

3 of the numbers are either 2 or 9.

16 2/3x3=50.001

The final answer is a 50% probability.

<u>I think</u>

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The negative solution is -1.

7 0
3 years ago
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