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Over [174]
3 years ago
6

A conjecture and the paragraph proof used to prove the conjecture are shown.

Mathematics
2 answers:
arlik [135]3 years ago
6 0

Answer:

1. DF (option 3)

2. segment addition postulate

3. segment congruence postulate

4. DF (option 5)


Ierofanga [76]3 years ago
6 0

Answer with explanation:

Given: E is the mid point of DF.

Prove: 2 DE=D F

Proof with explanation:

   It is given that \Bar{DE} is mid point of \Bar{DF}.

1.→

 So, \Bar{DE}\cong\Bar{DF}

                       -------------------------By Definition of mid point

2.→ DE=E F----------------Segment Congruence Postulate

3.→DE+E F=D F ----------------Segment Addition Postulate

4.→DE+DE=D F-------------By Substitution

5.→Simplifying gives

  2 DE=D F

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3 years ago
It is known that 10% of the 9-year old children in a town have three siblings. Fifteen 9-year old children are selected at rando
inn [45]

Using the binomial distribution, it is found that there is a 0.0555 = 5.55% probability that more than 3 of these selected children have three siblings.

<h3>What is the binomial distribution formula?</h3>

The formula is:

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

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

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem, for the parameters, we consider that:

  • 10% of the 9-year old children in a town have three siblings, hence p = 0.1.
  • Fifteen 9-year old children are selected at random, hence n = 15.

The probability that more than 3 of these selected children have three siblings is given by:

P(X > 3) = 1 - P(X \leq 3)

In which:

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Then:

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

P(X = 0) = C_{15,0}.(0.1)^{0}.(0.9)^{15} = 0.2059

P(X = 1) = C_{15,1}.(0.1)^{1}.(0.9)^{14} = 0.3432

P(X = 2) = C_{15,2}.(0.1)^{2}.(0.9)^{13} = 0.2669

P(X = 3) = C_{15,3}.(0.1)^{3}.(0.9)^{12} = 0.1285

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.2059 + 0.3432 + 0.2669 + 0.1285 = 0.9445

P(X > 3) = 1 - 0.9445 = 0.0555

0.0555 = 5.55% probability that more than 3 of these selected children have three siblings.

More can be learned about the binomial distribution at brainly.com/question/24863377

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