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3 years ago

13

You want to buy a new car . The car averages 45 miles per gallon . It has a range of 675 miles on one tank of gas . How many gal

lons of gas will the car holder when the tank is full

1 answer:

11111nata11111 [884]3 years ago

7 0

675 mi / 45 mpg = 15 Gallons

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What is the answer to 7(2x + 9)

Damm [24]

Answer:

14x + 63

Step-by-step explanation:

$7(2x+9)\\\\14x+63\\\\\left \{ {{7*2x=14x} \atop {7*9=63}} \right.$

Hope this helps.

7 0

2 years ago

In Gwinnett, the sales tax is 6%. You buy a watch that costs $45.50. What is the TOTAL cost including tax?

STatiana [176]

Answer:The answer is 48.23

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

55% of what number is 25

Valentin [98]

55% of a number is 25 so divide 25 by .55 then the answer is 45.45

4 0

3 years ago

Read 2 more answers

The odd- and even - number hotel rooms are on different sides of the hall. Room 231 is between witch two rooms

mario62 [17]

The first odd number before 231 which would be on the same side of the hall is 229. The first odd number after would be 233.
On the odd side of the hall, the order would be room 229, room 231, room 233.

8 0

3 years ago