Ask question

Ask question

All categories

3 years ago

7

The coordinates of a point on a coordinate grid are (−3, 7). The point is reflected across the x-axis to obtain a new point. The

coordinates of the reflected point are

1 answer:

Katena32 [7]3 years ago

5 0

The y-value changes sign when a point is reflected across the x-axis. The reflected point is (-3, -7).

You might be interested in

Please help convert .. 1 yard of sand weights 1.13 tons , I paid $45.79 per ton what do I charge for a yard ?

saw5 [17]

The definite answer is 51.7427

5 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

I am greater than 30 and less than 40. The sum of my digits is less than 5

Zielflug [23.3K]

The answer will be 31.

5 0

3 years ago

Read 2 more answers

Claire's bedroom measures 16 feet by 18 feet if the purple carpet that she wants to buy costs $3.59 per square foot what will it

katovenus [111]

Answer:

Cost of purple carpet for Claire's bedroom is $1033.92.

Step-by-step explanation:

Given:

The dimension of bedroom are given as 16 feet and 18 feet.

Hence we can say that;

Length = 18 feet

width = 16 feet

Cost of carpet per square feet = $3.59

We will first find the area of the bedroom.

Area of bedroom can be calculated by multiplying length with width.

Area of bedroom = $16 \times 18 = 288 ft^2$

Hence Area of bedroom is 288 square feet.

Now we know that;

Cost of carpet per square feet = $3.59

Hence Cost of carpet for 288 square feet is ;

we will unitary method to find the same;

Cost of carpet for bedroom = $\$3.59 \times 288 = \$1033.92$

Hence Cost of carpet for Claire's bedroom is $1033.92.

Step-by-step explanation:

6 0

3 years ago

hi!! <3 i attached a picture of a easy trigonometry question can you please help if you don’t mind <33

Inessa05 [86]

Answer:

Side AB has a length of 4, and side BC has a length of 11.7

7 0

3 years ago