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2 years ago

Which would most likely be graphed using a continuous graph? Check all that apply. (Medal for correct answer.

Mathematics

1 answer:

zlopas [31]2 years ago

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1. The population of a city is 85,000 and is growing at a rate of 3% each year. Find how many people live in this city after 13

krek1111 [17]

Answer:

85000 x 0.03 = 2550 (per year)

2550 x 13 = 33150

85000 + 33150 = 118150

Step-by-step explanation:

Hope that helped! Have a nice day!

8 0

2 years ago

Let X ~ N(0, 1) and Y = eX. Y is called a log-normal random variable.

Cloud [144]

If $F_Y(y)$ is the cumulative distribution function for $Y$ , then

$F_Y(y)=P(Y\le y)=P(e^X\le y)=P(X\le\ln y)=F_X(\ln y)$

Then the probability density function for $Y$ is $f_Y(y)={F_Y}'(y)$ :

$f_Y(y)=\dfrac{\mathrm d}{\mathrm dy}F_X(\ln y)=\dfrac1yf_X(\ln y)=\begin{cases}\frac1{y\sqrt{2\pi}}e^{-\frac12(\ln y)^2}&\text{for }y>0\\0&\text{otherwise}\end{cases}$

The $n$ th moment of $Y$ is

$E[Y^n]=\displaystyle\int_{-\infty}^\infty y^nf_Y(y)\,\mathrm dy=\frac1{\sqrt{2\pi}}\int_0^\infty y^{n-1}e^{-\frac12(\ln y)^2}\,\mathrm dy$

Let $u=\ln y$ , so that $\mathrm du=\frac{\mathrm dy}y$ and $y^n=e^{nu}$ :

$E[Y^n]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{nu}e^{-\frac12u^2}\,\mathrm du=\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{nu-\frac12u^2}\,\mathrm du$

Complete the square in the exponent:

$nu-\dfrac12u^2=-\dfrac12(u^2-2nu+n^2-n^2)=\dfrac12n^2-\dfrac12(u-n)^2$

$E[Y^n]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{\frac12(n^2-(u-n)^2)}\,\mathrm du=\frac{e^{\frac12n^2}}{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-\frac12(u-n)^2}\,\mathrm du$

But $\frac1{\sqrt{2\pi}}e^{-\frac12(u-n)^2}$ is exactly the PDF of a normal distribution with mean $n$ and variance 1; in other words, the 0th moment of a random variable $U\sim N(n,1)$ :

$E[U^0]=\displaystyle\frac1{\sqrt{2\pi}}\int_{-\infty}^\infty e^{-\frac12(u-n)^2}\,\mathrm du=1$

so we end up with

$E[Y^n]=e^{\frac12n^2}$

3 0

2 years ago

The sum of two numbers is 41 . The smaller number is 11 less than the larger number . What are the numbers ?

AleksAgata [21]

26 and 15 is the answer!

4 0

3 years ago

Marys family had to pay 3$ for the car plus 2$ for each number of people in the car.

Gala2k [10]

Answer:

y=2x+3

Step-by-step explanation:

Y is the total amount that the family pays. 2x represents 2 dollars for every person (so, 2 multiplied by the number of people). Finally, 3 represents the initial amount that they must pay, no matter how many are in the car.

8 0

2 years ago

Read 2 more answers

Select the order in which the flow of current is listed from greatest to least

noname [10]

Answer:Short circuit, closed circuit, open circuit

8 0

3 years ago