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2 years ago

Convert the equation `5x+2y=-8`into slope-intercept form.

Mathematics

2 answers:

NemiM [27]2 years ago

5 0

Answer:

y= -2.5x-4

Step-by-step explanation:

we have to isolate our y

subtract 5x from 5x+2y=-8 and move it to the right side

2y= -5x-8

divide everything by 2

y=-2.5x-4

I hope this helped you :)

Mila [183]2 years ago

3 0

Bradley C.
Apr 22, 2018
5
x
−
2
y
=
8
subtract
5
x
from both sides
−
2
y
=
8
−
5
x
y=
8
−
5
x
2
y=
−
5
x
2
−
4
s
l
o
p
e
=
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5
x
2
y-intercept:
(
0
,
−
4
)

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2 years ago

The lifetime X (in hundreds of hours) of a certain type of vacuum tube has a Weibull distribution with parameters α = 2 and β =

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I'm assuming $\alpha$ is the shape parameter and $\beta$ is the scale parameter. Then the PDF is

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a. The expectation is

$E[X]=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\frac29\int_0^\infty x^2e^{-x^2/9}\,\mathrm dx$

To compute this integral, recall the definition of the Gamma function,

$\Gamma(x)=\displaystyle\int_0^\infty t^{x-1}e^{-t}\,\mathrm dt$

For this particular integral, first integrate by parts, taking

$u=x\implies\mathrm du=\mathrm dx$

$\mathrm dv=xe^{-x^2/9}\,\mathrm dx\implies v=-\dfrac92e^{-x^2/9}$

$E[X]=\displaystyle-xe^{-x^2/9}\bigg|_0^\infty+\int_0^\infty e^{-x^2/9}\,\mathrm x$

$E[X]=\displaystyle\int_0^\infty e^{-x^2/9}\,\mathrm dx$

Substitute $x=3y^{1/2}$ , so that $\mathrm dx=\dfrac32y^{-1/2}\,\mathrm dy$ :

$E[X]=\displaystyle\frac32\int_0^\infty y^{-1/2}e^{-y}\,\mathrm dy$

$\boxed{E[X]=\dfrac32\Gamma\left(\dfrac12\right)=\dfrac{3\sqrt\pi}2\approx2.659}$

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$E[X^2]=\displaystyle\int_{-\infty}^\infty x^2f_X(x)\,\mathrm dx=\frac29\int_0^\infty x^3e^{-x^2/9}\,\mathrm dx$

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$u=x^2\implies\mathrm du=2x\,\mathrm dx$

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$E[X^2]=\displaystyle2\int_0^\infty xe^{-x^2/9}\,\mathrm dx$

Substitute $x=3y^{1/2}$ again to get

$E[X^2]=\displaystyle9\int_0^\infty e^{-y}\,\mathrm dy=9$

Then the variance is

$\mathrm{Var}[X]=9-E[X]^2$

$\boxed{\mathrm{Var}[X]=9-\dfrac94\pi\approx1.931}$

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$P(X\le 3)=\displaystyle\int_{-\infty}^3f_X(x)\,\mathrm dx=\frac29\int_0^3xe^{-x^2/9}\,\mathrm dx$

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$\boxed{P(X\le 3)=\dfrac{e-1}e\approx0.632}$

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$P(1\le X\le3)=P(X\le3)-P(X\le1)$

and

$P(X\le1)=\displaystyle\int_{-\infty}^1f_X(x)\,\mathrm dx=\frac29\int_0^1xe^{-x^2/9}\,\mathrm dx=\frac{e^{1/9}-1}{e^{1/9}}$

Then

$\boxed{P(1\le X\le3)=\dfrac{e^{8/9}-1}e\approx0.527}$

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2 years ago

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Answer:

The car must drive at 108 km/h to cover the same journey.

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Distance = Speed * Time

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Speed = $45*\frac{60}{25}$

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2 years ago

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Complete question

Which sequence of a transformation will result in an image that maps onto itself? A) rotate 180 degrees counterclockwise and then reflect across the x axis b) reflect over the y axis and then reflect over the x axis c) rotate 180 degrees counterclockwise and then reflect across the y axis d) reflect over the y axis and then reflect again over the y axis

Step-by-step explanation:

Reflecting a figure across the y axis then repeating the same procedure will take you to the original position. This means mapping the figure onto itself.When coordinates(x,y) are reflected on the y axis the image coordinates are (-x,y) thus repeating this will form the second image coordinates as (x,y).

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Transformation : brainly.com/question/10656536

Keyword : transformation

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2 years ago

Read 2 more answers

a movie ticket used to cost $4.25 back in 1990. inflation exist because products increase in value over time. the inflation rate

Andrews [41]

In the year 1998, movie tickets will be greater than $5.50 as determined by solving the equation y=4.25[(1.035)^x].

What is an equation?

Math can be used to analyze an equation or a set of equations.
An equation is a sentence that maintains the equivalence of two expressions. Most of the time, it is easy to solve the arithmetic equations given in an exact manner.
While perfect solutions can occasionally be found, it is more typical to find approaches that are just as accurate. It speaks to the particular guidelines for quadratic mathematical equations.

A movie ticket cost $4.25 in 1990.

The inflation rate is about 3.5%

Rate increased ,r=100%+3.5%=103.5%=1.035

equation generated is,

y=4.25[(1.035)^x]

Solving the equation for each year, we get the following data:

Tabulating the data

Year cost

1990 4.25

1991 ....

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1998 5.5964~ 5.6

In the year 1998, the will be greater than $5.50.

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4 months ago