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3 years ago

Which statements are true about the polynomial function?

Mathematics

1 answer:

mixas84 [53]3 years ago

3 0

Answers:

First statements: True

$(-5)^4+5(-5)^3+(-5)^2-5(-5)=0$

Second statement: False

$\frac{x^4+5x^3+-x^2-5x}{x+5} = x (x - 1) (x + 1)$

Third statement: False

5 is not a root of this polynomial, therefore (x-5) is not one of its factors/

Fourth statement: False

5 is not a root of this polynomial, therefore f(5) does not equal 0.

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The sum of 2 numbers is 20 and their difference is 6. What are the two numbers

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Answer:

12 and 8

Step-by-step explanation:

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3 years ago

Read 2 more answers

It is estimated that 75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell

Mademuasel [1]

Answer:

a) 75

b) 4.33

c) 0.75

d) $3.2 \times 10^{-13}$ probability that no one in a simple random sample of 100 young adults owns a landline

e) $6.2 \times 10^{-61}$ probability that everyone in a simple random sample of 100 young adults owns a landline.

f) Binomial, with $n = 100, p = 0.75$

g) $4.5 \times 10^{-8}$ probability that exactly half the young adults in a simple random sample of 100 do not own a landline.

Step-by-step explanation:

For each young adult, there are only two possible outcomes. Either they do not own a landline, or they do. The probability of an young adult not having a landline is independent of any other adult, 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.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.

This means that $p = 0.75$

(a) On average, how many young adults do not own a landline in a random sample of 100?

Sample of 100, so $n = 100$

$E(X) = np = 100(0.75) = 75$

(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100(0.75)(0.25)} = 4.33$

(c) What is the proportion of young adults who do not own a landline?

The estimation, of 75% = 0.75.

(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?

This is P(X = 100), that is, all do not own. So

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

$P(X = 100) = C_{100,100}.(0.75)^{100}.(0.25)^{0} = 3.2 \times 10^{-13}$

$3.2 \times 10^{-13}$ probability that no one in a simple random sample of 100 young adults owns a landline.

(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?

This is P(X = 0), that is, all own. So

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

$P(X = 0) = C_{100,0}.(0.75)^{0}.(0.25)^{100} = 6.2 \times 10^{-61}$

$6.2 \times 10^{-61}$ probability that everyone in a simple random sample of 100 young adults owns a landline.

(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?

Binomial, with $n = 100, p = 0.75$

(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?

This is P(X = 50). So

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

$P(X = 50) = C_{100,50}.(0.75)^{50}.(0.25)^{50} = 4.5 \times 10^{-8}$

$4.5 \times 10^{-8}$ probability that exactly half the young adults in a simple random sample of 100 do not own a landline.

8 0

2 years ago

Describe the difference between a probability derived from the analytic view (logical analysis), the Relative Frequency view (sa

oee [108]

Answer:

See the explanation

Step-by-step explanation:

<h2>Analytic View:</h2>

If and event can occur in A number of way and fail in B number of ways, then probability of its occurrence is:

$P(A)= \frac{A}{A+B}$

or probability of its failing is:

$P(B)=\frac{B}{A+B}$

<h3>Example:</h3>

Rolling a number smaller than 3 in a dice.

A= 2 (1,2)

B = 4 (3,4,5,6)

$P(A)= \frac{2}{2+4}=\frac{1}{3}$

<h2>Relative Frequency View:</h2>

Definition of Probability in terms of past performances (data). It can be taken as how often things happens divided by all outcomes.

<h3>Example:</h3>

A batter has 50 safe hits at 200 bats, which makes his batting average $\frac{50}{200}= 0.25$ which is the probability.

<h2>Subjective View:</h2>

When you define a probability due to personel beleif in the likelihood of an outcome. It involve no formal calculations and varies from person to person, depending on their past experience.

<h3>Example:</h3>

A person beleives that probability that the batter will hit safely in the next bat is 0.75

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3 years ago

suppose a population consists of 5000 being surveyed could result in sample statistic but not parameter

Talja [164]

Huh? What is the question here???

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2 years ago

Santos walks 2 kilometers south and then a certain number of kilometers east. He ends 5 kilometers away from his starting positi

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