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2 years ago

Find the missing side or angle. Round to the nearest tenth.

Mathematics

1 answer:

LenaWriter [7]2 years ago

8 0

Answer:

6√6 or 14.7

Step-by-step explanation:

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No links! & help me please

melamori03 [73]

Answer:

150.72 units³

Step-by-step explanation:

The formula for solving the volume of a cylinder is:

V = pi (3.14) r² h

V = (3.14) (4) (3)

V = 150.72 units³

6 0

3 years ago

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

Given that a = 10,

tankabanditka [31]

Since $a = 10$ and $b = 2x + 5$ , we have

$ab=10(2x+5)=20x+50$

So, the equation becomes

$ab = 6x^2 +11x-10 \iff 20x+50= 6x^2 +11x-10 \iff 6x^2-9x-60=0$

The solutions to this equation are 4 and -5/2, so I'm afraid there's a typo in your question.

3 0

2 years ago

A street sign is 82 inches tall. How tall is it in feet and inches?

Neko [114]

It is 6 feet and 10 inches .

7 0

3 years ago

Given WRST is a parallelogram and

daser333 [38]

It would be a parallelogram

3 0

3 years ago