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2 years ago

Find the exact volume of the cylinder.

Mathematics

1 answer:

Taya2010 [7]2 years ago

5 0

Answer:

1608.5mm²

Step-by-step explanation:

the formula to it is π r²h so 8 times itself or the radius and times it with pi so it equals to 201.0619298297. then you times it with 8 aka the height and you get 1,608.4954386376. then you round it and you get 1608.5.

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f one pump can inflate an air mattress in 21 minutes and a second pump can inflate the same mattress in 42 minutes, find the am

Schach [20]

Answer:

14 minutes

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

Well, what I do for these problems is do 1/x with x being the amount of time given.

1/21+1/42=3/42

3/42=1/14

Together, they would take 14 minutes!

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

3 0

3 years ago

What is the equation of the line that is parallel to the given

slamgirl [31]

Answer:

$y=\frac{1}{5}x+\frac{12}{5}$

Step-by-step explanation:

<u><em>Complete Question:</em></u> What is the equation of line that is parallel to the line $y=\frac{1}{5}+4$ and passes through $(-2,2).$

$Let\ the\ equation\ of\ line\ is\ y=mx+c\\\\Since\ it\ is\ parallel\ to\ the\ line\ y=\frac{1}{5}x+4,\ the\ slope\ of\ both\ the\ lines\ will\ be\ same.\\\\Slope\ of\ y=\frac{1}{5}x+4\ is=\frac{1}{5}\\\\m=\frac{1}{5}\\\\Equation: y=\frac{1}{5}x+c\\\\It\ passes\ through\ (-2,2),\ This\ point\ will\ satisfy\ the\ equation.\\\\2=\frac{1}{5}\times (-2)+c\\\\c=2+\frac{2}{5}\\\\c=\frac{12}{5}\\\\The\ Equation\ is: y=\frac{1}{5}x+\frac{12}{5}$

7 0

2 years ago

Sophie Ruth is eating a 5 0 50-gram chocolate bar which contains 3 0 % 30% cocoa. How many grams of cocoa are in the chocolate b

tatiyna

Answer:

15 grams.

Step-by-step explanation:

That would be 30% of 50 g.

= 0.30 * 50 = 15 g (answer).

3 0

3 years ago

If X is a r.v. such that E(X^n)=n! Find the m.g.f. of X,Mx(t). Also find the ch.f. of X,and from this deduce the distribution of

astraxan [27]

$M_X(t)=\mathbb E(e^{Xt})$
$M_X(t)=\mathbb E\left(1+Xt+\dfrac{t^2}{2!}X^2+\dfrac{t^3}{3!}X^3+\cdots\right)$
$M_X(t)=\mathbb E(1)+t\mathbb E(X)+\dfrac{t^2}{2!}\mathbb E(X^2)+\dfrac{t^3}{3!}\mathbb E(X^3)+\cdots$
$M_X(t)=1+t+t^2+t^3+\cdots$
$M_X(t)=\displaystyle\sum_{k\ge0}t^k=\frac1{1-t}$

provided that $|t|$ .

Similarly,

$\varphi_X(t)=\mathbb E(e^{iXt})$
$\varphi_X(t)=1+it+(it)^2+(it)^3+\cdots$
$\varphi_X(t)=(1-t^2+t^4-t^6+\cdots)+it(1-t^2+t^4-t^6+\cdots)$
$\varphi_X(t)=(1+it)(1-t^2+t^4-t^6+\cdots)$
$\varphi_X(t)=\dfrac{1+it}{1+t^2}=\dfrac1{1-it}$

You can find the CDF/PDF using any of the various inversion formulas. One way would be to compute

$F_X(x)=\displaystyle\frac12+\frac1{2\pi}\int_0^\infty\frac{e^{itx}\varphi_X(-t)-e^{-itx}\varphi_X(t)}{it}\,\mathrm dt$

The integral can be rewritten as

$\displaystyle\int_0^\infty\frac{2i\sin(tx)-2it\cos(tx)}{it(1+t^2)}\,\mathrm dt$

so that

$F_X(x)=\displaystyle\frac12+\frac1{2\pi}\int_0^\infty\frac{\sin(tx)-t\cos(tx)}{t(1+t^2)}\,\mathrm dt$

There are lots of ways to compute this integral. For instance, you can take the Laplace transform with respect to $x$ , which gives

$\displaystyle\mathcal L_s\left\{\int_0^\infty\frac{\sin(tx)-t\cos(tx)}{t(1+t^2)}\,\mathrm dt\right\}=\int_0^\infty\frac{1-s}{(1+t^2)(s^2+t^2)}\,\mathrm dt$
$=\displaystyle\frac{\pi(1-s)}{2s(1+s)}$

and taking the inverse transform returns

$F_X(x)=\dfrac12+\dfrac1\pi\left(\dfrac\pi2-\pi e^{-x}\right)=1-e^{-x}$

which describes an exponential distribution with parameter $\lambda=1$ .

6 0

3 years ago

In the diagram below what is the relationship between the number of rectangles in the perimeter of the figure they form?

Wewaii [24]

Answer:

the correct answer is the third one. (1, 16), (2, 20), (3, 24)

Step-by-step explanation:

A perimeter is a path that surrounds a two-dimensional shape.

In the first case, 1 rectangle, the perimeter is the sum of all the sides:

Perimeter = 6 + 2 + 6 + 2 = 16

In the second case, 2 rectangles, the perimeter is the sum of all external sides:

Perimeter = 6 + 2 + 2 + 6 + 2 + 2 = 20

In the third case, three rectangles, the perimeter is the sum of all external sides:

Perimeter = 6 + 2 + 2 + 2 + 6 + 2 + 2 + 2 = 24

In none of the cases, you take into consideration the interal sides. Just the external sides, so the correct answer is the third one.

8 0

3 years ago