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3 years ago

Owen earns $27,980 per year in take-home pay. What is the most money a

Mathematics

1 answer:

Mila [183]3 years ago

7 0

B. $582.92 I’m not sure I just picked sorry

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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

Help please help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

horsena [70]

Answer:

x=2/5

Step-by-step explanation:

4 0

2 years ago

Solve this equation for x 0.95 = log x

Lelechka [254]

Answer:

8.91

Step-by-step explanation:

Given: 0.95 = log x,

we can conclude that:

0.95 log x

10 = 10

0.95

which in turn is equivalent to x = 10 whose value is 8.91

5 0

3 years ago

Tell me a joke, who ever's joke I like better will get a Brainlist

FromTheMoon [43]

I wanted to be king because I saw dream of king

one day when I visit to dentist

Dentist: "You need a crown." -

Patient: "Finally someone who understands me"

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2 years ago

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A sledgehammer weighs 18 pounds on Earth and 4 pounds on the planet Namar.

Advocard [28]

It would weight 18lbs i believe

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3 years ago

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