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3 years ago

What is the volume of a sphere that has a 12m diameter?

1 answer:

5 0

Volume of Sphere = (4/3)*(pi)*(r^3)

r = (D/2) = 6 m

 =(4/3)*(pi)*((6^3)

 = 904.7786.. m^3
I hope this helps.

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Use the Law of Cosines to find the values of x and y. (PLEASE HELPPP!!!!)

vredina [299]

Answer:

$x = 49.8^\circ\\y = 54.6^\circ$

Step-by-step explanation:

Kindly refer to the image attached in the answer region for labeling of triangle.

AB = 16

BC = 19

AC = 15

$\angle ABC = x^\circ\\\angle ACB = y^\circ$

We have to find the angles x and y i.e. $\angle B \text{ and }\angle C$ .

Formula for cosine rule:

$cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}$

Where

a is the side opposite to $\angle A$ ,

b is the side opposite to $\angle B$ and

c is the side opposite to $\angle C$ .

$\Rightarrow cos x = \dfrac{19^{2}+16^{2}-15^{2}}{2 \times 19 \times 16}\\\Rightarrow cos x = \dfrac{392}{608} \\\Rightarrow x = 49.8^\circ$

Similarly, for finding the value of y:

$cos C = \dfrac{a^{2}+b^{2}-c^{2}}{2ab}\\\Rightarrow cos y = \dfrac{19^{2}+15^{2}-16^{2}}{2 \times 19 \times 15}\\\Rightarrow cos y = \dfrac{330}{570}\\\Rightarrow y = 54.6^\circ$

Hence, the values are:

$x = 49.8^\circ\\y = 54.6^\circ$

7 0

3 years ago

A class of 10 students hang up their coats when they arrive at school. Just before recess, the teacher hands one coat selected a

Fittoniya [83]

Answer:

0.1274

Step-by-step explanation:

Let X be the random variable that measures the number of children who get their own coat.

Then, the expected value of X is

E[X] = 1P(X=1) + 2P(X=2)+3P(X=3)+...+10P(X=10)

The probability that a child gets her or his coat is

P(X=1) = 1/10

To compute the probability that 2 children get their own coat, we notice that there are 10! possible permutations of coats. The two children can get their coat in only one way, the other 8 coats can be arranged in 8! different positions, so the probability that 2 children get their own coat is

P(X=2) = 8!/10! = 1/(10*9) and

2P(X=2) = 2/(10*9)

Similarly, we can see that the probability that 3 children get their own coat is

P(X=3) = 7!/10! = 1/(10*9*8) and

3P(X=3) = 3/(10*9*8*7)

and the expected value of X would be

E[X] = 1/10 + 2/(10*9) + 3/(10*9*8)+...+10/10! = 0.1274

6 0

3 years ago

Rationalize the denominator of the fraction and enter the new denominator below. 8/2-√12

Studentka2010 [4]

$\frac{8}{2-\sqrt{12}}=\frac{8}{2-\sqrt{4\cdot3}}=\frac{8}{2-2\sqrt3}=\frac{8}{2(1-\sqrt3)}=\frac{4}{1-\sqrt3}\\\\\frac{4}{1-\sqrt3}\cdot\frac{1+\sqrt3}{1+\sqrt3}=\frac{4(1+\sqrt3)}{1^2-(\sqrt3)^2}=\frac{4(1+\sqrt3)}{1-3}=\frac{4(1+\sqrt3)}{-2}=-2(1+\sqrt3)}\\\\=-2-2\sqrt3$

$if\ \frac{8}{2}-\sqrt{12}=4-\sqrt{4\cdot3}=4-2\sqrt3$

8 0

3 years ago

Read 2 more answers

I need help tell me what the voulume is

Vladimir [108]

Answer:

8 3/4 cubic or 8.75

Step-by-step explanation:

To find volume it’s

Length * width * height

4 0

3 years ago

A random variableX= {0, 1, 2, 3, ...} has cumulative distribution function.a) Calculate the probability that 3 ≤X≤ 5.b) Find the

olchik [2.2K]

Answer:

a) P ( 3 ≤X≤ 5 ) = 0.02619

b) E(X) = 1

Step-by-step explanation:

Given:

- The CDF of a random variable X = { 0 , 1 , 2 , 3 , .... } is given as:

$F(X) = P ( X =< x) = 1 - \frac{1}{(x+1)*(x+2)}$

Find:

a.Calculate the probability that 3 ≤X≤ 5

b) Find the expected value of X, E(X), using the fact that. (Hint: You will have to evaluate an infinite sum, but that will be easy to do if you notice that

Solution:

- The CDF gives the probability of (X < x) for any value of x. So to compute the P ( 3 ≤X≤ 5 ) we will set the limits.

$F(X) = P ( 3=$

- The Expected Value can be determined by sum to infinity of CDF:

E(X) = Σ ( 1 - F(X) )

$E(X) = \frac{1}{(x+1)*(x+2)} = \frac{1}{(x+1)} - \frac{1}{(x+2)} \\\\= \frac{1}{(1)} - \frac{1}{(2)}\\\\= \frac{1}{(2)} - \frac{1}{(3)} \\\\= \frac{1}{(3)} - \frac{1}{(4)}\\\\= ............................................\\\\= \frac{1}{(n)} - \frac{1}{(n+1)}\\\\= \frac{1}{(n+1)} - \frac{1}{(n+ 2)}$

E(X) = Limit n->∞ [1 - 1 / ( n + 2 ) ]

E(X) = 1

8 0

3 years ago