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3 years ago

Convert 15 g to kilograms

Mathematics

1 answer:

Mama L [17]3 years ago

3 0

15 grams is equal to 0.015 kilograms

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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

Please help me ASAP will mark brianlest

Paul [167]

Answer:

idk a or c

Step-by-step explanation:

5 0

3 years ago

The geometric mean of a number and four times the number is 22. What is the number?

Misha Larkins [42]

2 square root x • 4x= 22

2x=22

x=11

Answer is 11

8 0

2 years ago

Find the length of the third side to the nearest tenth.<br> Hurry need help asap!!

gavmur [86]

Answer:

2.8

Step-by-step explanation:

6 0

3 years ago

3x-1upon5 =x-1upon3<br> Solution for this linear equation

BabaBlast [244]

The solution to the linear equation is 2

<h3>How to solve the linear equation?</h3>

The linear equation is given as:

3x - 1 upon 5 = x - 1 upon 3

Rewrite properly as

(3x - 1)/5 = (x - 1)/3

Cross multiply

9x - 3 = 5x- 5

Evaluate the like terms

4x = 8

Divide by 4

x = 2

Hence, the solution to the linear equation is 2

Read more about linear equations at:

brainly.com/question/14323743

#SPJ1

7 0

1 year ago