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Nataly [62]
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
Mathematics
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).

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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
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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
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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:

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Answer:

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

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