What is the nearest integer: 4.18/0.68

Help me w math, need it ASAP

Alex17521 [72]

Answer:

Step-by-step explanation:

See attached image.

6 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

ASAP ASAP ASAP SHOW WORK TOO !!!!!!!!!!!!!!! thanks soo much

k0ka [10]

A.
(64x² + 96x + 36) / (16x + 12)
= 4(16x² + 24x + 9) / 4(4x + 3)
= 4*(4x + 3)(4x + 3) / 4(4x + 3)
= 4x + 3

b.
1.79 x 10^5 = 1.79 * 100,000 = 179,000

c.
(5.9736 x 10^24) + (4.8685 x 10^24)
= (5.9736 + 4.8685) x 10^24
= 10.8421 x 10^24
= 1.08421 x 10^25

4 0

3 years ago

-(7c-18)-2c>0

e-lub [12.9K]

Solution above is incorrect, simplify as follows:
-(7c-18)-2c > 0

-7c+18-2c > 0
-9c > -18
c < 2

8 0

3 years ago

HELP ME PLEASE WHAT IS THE ANSWER TO THESE QUESTIONS

sergejj [24]

Answer:

question 3.3 Answer: Angle 3

question 3.4 Answer: ABD and DBC are complementary angles

question 3.5 Answer: x is 7 degrees (first answer option)

Step-by-step explanation:

First question:

Recall that suplementary angles are those whose addition gives 180 degrees. Therefore the supplementary angle to angle 8 is angle 3.

Second question:

Recall that complementary angles are those angles which added give 90 degrees. Therefore, the only correct answer for this question is the third one: ABD and DBC are complementary angles.

Third question:

Notice that the two angles added should render 90 degrees, therefore, their expression should as well add to 90 degrees. Such can be written in equation form as:

( 6 x - 20 ) + (4 x + 40 ) = 90

combining like terms and later solving for x we get:

6 x + 4 x - 20 + 40 = 90

10 x + 20 = 90

10 x = 90 - 20

10 x = 70

x = 7

Therefore x is 7 degrees

5 0

3 years ago