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3 years ago

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The movie club is having a new member sale, so Mindy signs up. The equation -0.4x + 0.05y - 1.25 = 0 relates y, the total cost,

and x, the number of months. What is the y-intercept of the line represented by the equation?

2 answers:

Wewaii [24]3 years ago

6 0

Answer:

Y intercept : ( 0 , 25 )

Step-by-step explanation:

Gekata [30.6K]3 years ago

6 0

Answer:

<h2> (0, 25)</h2>

Step-by-step explanation:

We need to convert function to slope-intrcept form y=mx+b, where:

-0.4x + 0.05y - 1.25 = 0 {multiply both sides by 20}

-8x + y - 25 = 0 {add (8x+25) to both sides}

y = 8x + 25 ⇒ b = 25

Therefore y-intercept of the line is (0, 25)

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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

A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the

Murljashka [212]

Answer:

Step-by-step explanation: The volume of the grain silo can be found by adding the volumes of all the solids of which it is composed (a cylinder and two cones). The silo is made up of a cylinder (with height 10 feet and base radius 5 feet) and two cones (each with height 5 ft and base radius 5 ft). The formulas given at the beginning of the SAT Math section:

Volume of a Cone:

$V=\frac{1}{3} \pi r^2h$

Volume of a Cylinder:

$V=\pi r^2h$

can be used to determine the total volume of the silo. Since the two cones have identical dimensions, the total volume, in cubic feet, of the silo is given by

$V_{silo} =\pi (5^2)(10)+(2)(\frac{1}{3})\pi (5^2)(5)=(\frac{4}{3})(250)\pi$

which is approximately equal to 1,047.2 cubic feet.

<u>The final answer is D.</u>

6 0

3 years ago

Below are two parallel lines intersecting them

slavikrds [6]

Answer:

56

Step-by-step explanation:

corresponding angle to 56 is also opposite to x which means it is also 56

3 0

3 years ago

Find the distance between two points. (1,3)(-2,8)

Natasha2012 [34]

Answer:

4,10

Step-by-step explanation:

add the numbers together

6 0

4 years ago

Read 2 more answers

The corner section of a football stadium has 6 seats on the first row. Each row after that has an additional 3 seats. How many s

julia-pushkina [17]

9514 1404 393

Answer:

63

Step-by-step explanation:

The number of seats in a row will give an arithmetic sequence:

6, 9, 12, 15, ...

The first term is 6; the common difference is 3. The general term is ...

an = a1 +d(n -1) . . . . . . n-th term of sequence with first term a1, difference d

The 20th term of the sequence is ...

a20 = 6 +3(20 -1) = 6 +57 = 63

There would be 63 seats on the 20th row.

7 0

3 years ago