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3 years ago

What are some ways to decribe the relationships between sets of numbers

Mathematics

1 answer:

lina2011 [118]3 years ago

4 0

By their increase or decrease

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Suppose that the length of a side of a cube X is uniformly distributed in the interval 9

Nastasia [14]

Answer:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

Step-by-step explanation:

Given

$9 < x < 10$ --- interval

Required

The probability density of the volume of the cube

The volume of a cube is:

$v = x^3$

For a uniform distribution, we have:

$x \to U(a,b)$

and

$f(x) = \left \{ {{\frac{1}{b-a}\ a \le x \le b} \atop {0\ elsewhere}} \right.$

$9 < x < 10$ implies that:

$(a,b) = (9,10)$

So, we have:

$f(x) = \left \{ {{\frac{1}{10-9}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Solve

$f(x) = \left \{ {{\frac{1}{1}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$

Recall that:

$v = x^3$

Make x the subject

$x = v^\frac{1}{3}$

So, the cumulative density is:

$F(x) = P(x < v^\frac{1}{3})$

$f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.$ becomes

$f(x) = \left \{ {{1\ 9 \le x \le v^\frac{1}{3} - 9} \atop {0\ elsewhere}} \right.$

The CDF is:

$F(x) = \int\limits^{v^\frac{1}{3}}_9 1\ dx$

Integrate

$F(x) = [v]\limits^{v^\frac{1}{3}}_9$

Expand

$F(x) = v^\frac{1}{3} - 9$

The density function of the volume F(v) is:

$F(v) = F'(x)$

Differentiate F(x) to give:

$F(x) = v^\frac{1}{3} - 9$

$F'(x) = \frac{1}{3}v^{\frac{1}{3}-1}$

$F'(x) = \frac{1}{3}v^{-\frac{2}{3}}$

$F(v) = \frac{1}{3}v^{-\frac{2}{3}}$

So:

$f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.$

8 0

2 years ago

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?

DedPeter [7]

Answer:

obtuse because 62 + 102 < 122

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1 year ago

Read 2 more answers

If the circumference of a circle measures 8 pi cm, what is the area of the circle in terms of pi?

Effectus [21]

Answer:

803.84

Step-by-step explanation:

the formula for the area of a circle is A = π r2 which is pi times the radius squared.n in this case if the circumference is 8 cm then the radius would be half of the circumference which is 4. then you square 4 which is equal to 256. Then take 256 and multiply it by pi. 256 × 3.14 = 803.84. i hope this helped you.

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2 years ago

John paid $100 for renting a canoe for 5 hours. Which graph shows the relationship between the cost of renting a canoe for diffe

Anarel [89]

Answer:

The answer is B.

Step-by-step explanation:

You would pay about $20 each hour

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3 years ago

Which conversion requires division?

chubhunter [2.5K]

Are there any answer choices?

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3 years ago