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3 years ago

Where would you place root 8 on the Venn diagram? A) integers B) natural numbers C) rational numbers D) irrational numbers

Mathematics

1 answer:

tangare [24]3 years ago

7 0

Answer:

Option (D)

Step-by-step explanation:

All rational and irrational numbers are real numbers.

{-2, -1, -1.8, 0, 1, 2.......}

Numbers written in the form of $\frac{p}{q}$ are rational numbers. They are the part of irrational numbers.

{-2.5, -2, -1, 0, 1, 2.....}

Whole numbers with negative or positive notation are integers.

{-3, -2, -1, 0, 1, 2, 3, 4......}

Positive integers are the whole numbers (including zero).

{0, 1, 2, 3, 4, .......}

All whole numbers excluding zero are the natural numbers.

{1, 2, 3, 4,........}

Irrational numbers are the part of real numbers written in the form of $\frac{p}{q}$ .

{ $\sqrt{2},\sqrt{5},\pi, \sqrt{10}$ }

Therefore, $\sqrt{8}$ comes under Irrational numbers.

Option (D) is the answer.

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The port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge, is the largest

Ksenya-84 [330]

Answer:

a) 0.7287

b) 0.9663

c) 0.237

d) 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4.5 million tons of cargo per week

Standard Deviation, σ = 0 .82 million tons

We are given that the distribution of number of tons of cargo handled per week is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P( port handles less than 5 million tons of cargo per week)

P(x < 5)

$P( x < 5) = P( z < \displaystyle\frac{5 - 4.5}{0.82}) = P(z < 0.609)$

Calculation the value from standard normal z table, we have,

$P(x < 5) =0.7287= 72.87\%$

b) P( port handles 3 or more million tons of cargo per week)

$P(x \geq 3) = P(z \geq \displaystyle\frac{3-4.5}{0.82}) = P(z \geq −1.82926)\\\\P( z \geq −1.82926) = 1 - P(z < -1.829)$

Calculating the value from the standard normal table we have,

$1 - 0.0337 = 0.9663 = 96.63\%\\P( x \geq 3) = 96.63\%$

c)P( port handles between 3 million and 4 million tons of cargo per week)

$P(3 \leq x \leq 4) = P(\displaystyle\frac{3 - 4.5}{0.82} \leq z \leq \displaystyle\frac{4-4.5}{0.82}) = P(-1.829 \leq z \leq -0.609)\\\\= P(z \leq -0.609) - P(z < -1.829)\\= 0.271-0.034 = 0.237= 23.7\%$

$P(3 \leq x \leq 4) = 23.7\%$

d) P(X=x) = 0.85

We have to find the value of x such that the probability is 0.85.

P(X > x)

$P( X > x) = P( z > \displaystyle\frac{x - 4.5}{0.82})=0.85$

$= 1 -P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.85$

$=P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.15$

Calculation the value from standard normal z table, we have,

$P( z \leq -1.036) = 0.15$

$\displaystyle\frac{x - 4.5}{0.82} = -1.036\\x = 3.65$

Thus, 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

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2 years ago

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Answer:

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Step-by-step explanation:

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sasho [114]

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UkoKoshka [18]

Answer:

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Step-by-step explanation:

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