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stellarik [79]
3 years ago
13

Let: f(x)=x+1 and g(x)=x^2-2 find: f(x)•g(x)

Mathematics
1 answer:
lesya692 [45]3 years ago
3 0

Answer: x3+x2−2x−2

Step-by-step explanation: Use the given functions to set up and simplify f ( x ) ⋅ ( g ( x ) ) .

Brainliest or a thank you please! have a great day/night

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Does this graph show a function? Explain how you know.
Hatshy [7]

Answer:

A. No, the graph fails the vertical line test

8 0
1 year 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 nth 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
20 oz. of taco meat is $5.36 find the unit price
tensa zangetsu [6.8K]

Answer: $0.268

Step-by-step explanation: 5.36 divided by 20 = 0.268

7 0
2 years ago
Read 2 more answers
The monthly salaries of a sample of 100 employees were rounded to the nearest ten dollars. they ranged from a low of $1,040 to a
never [62]
1720 - 1040 = 680
680/7 = 97.1

I would put them in intervals of 100




6 0
3 years ago
A cable installer charges $40.00 per hour plus a $60.00 service charge. Your father's firm hires him to hook up his company's in
balandron [24]
Set up the equation ... 60 + 40X = total charges... where X is the number of hours (8.5)

60 + 40(8.5) = ?
60 + 340 = ?
400 = total charges
7 0
2 years ago
Read 2 more answers
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