4. Write an expression that shows three-fourths of v subtracted from 6 times two-ninths y

Show that [infinity] 0 e−x9 is convergent. SOLUTION We can't evaluate the integral directly because the antiderivative of e−x9 i

strojnjashka [21]

Step-by-step explanation:

Just remember that

$e^{-x^9} < e^{-x}$

That is the most important part, therefore,

$\int\limits_{0}^{\infty}{e^{-x^9}} \, dx < \int\limits_{0}^{\infty}{e^{-x}} \, dx\\$

Since

$\int\limits_{0}^{\infty}{e^{-x}} \, dx = \lim\limits_{n \to \infty} -e^{-x} + e^{-1} = e^{-1}$

and the integral

$\int\limits_{0}^{1} e^{-x^9} \, dx$

is an integral over a bounded interval and

$\int\limits_{0}^{\infty} {e^{-x^9}} \, dx = \int\limits_{0}^{1} {e^{-x^9}} \, dx + \int\limits_{1}^{\infty} {e^{-x^9}} \, dx$

The integral

$\int\limits_{0}^{\infty} {e^{-x^9}} \, dx$

converges.

5 0

4 years ago

Mind lending a hand?

ivann1987 [24]

Answer:

The second one

Step-by-step explanation:

Note that he can spend a MAXIMUM of $40 meaning that he can either spend less than or exactly 40 dollars. So if we are creating an inequality the inequality sign must face $40 and it can be equal to 40 therefore we know the inequality must start off with 40≥ or end with ≤40

The movie ticket cost 10$

The amount of money that can be spent on food can be represented by d

the amount of money that can be spent on food plus the cost of the ticket (10) must be equal to or less that 40

Therefore 10 + d ≤ 40

The answer is the second one

5 0

2 years ago

Read 2 more answers

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with a

Naya [18.7K]

Answer:

P(X<240)=0.0521

P(240<X<270)=0.5466

280 days

Step-by-step explanation:

we are given the following information

mean=μ=266 days

standard deviation=σ=16 days

P(X<240)=P(X-μ/σ<240-266/16)=P(z<-1.625)

This probability can either be determined by utilizing normal distribution table or using Excel.

Using Excel function NORM.S.DIST(-1.625,TRUE) we get

P(X<240)=0.0521

P(240<X<270)=P((240-266)/16<X-μ/σ<(270-266)/16)=P(-1.625<z<0.25)

P(-1.625<z<0.25)=P(z<0.25)-P(z<-1625)

Using Excel function

NORM.DIST(270,266,16,TRUE)-NORM.DIST(240,266,16,TRUE) we get

P(240<X<270)=0.5466

P(X>x)=0.20

P(z>(x-266)/16)=0.20

Using Excel function NORM.INV(0.8,266,16) we get

x=280

OR

P(X>x)=0.2

The area to the right of x is 0.2 and the area between mean and x is

0.5-0.2=0.3

Looking for 0.3 in the normal distribution table we don't find 0.3 but the closest value is .3023 and it corresponds to z-value 0.85.

z=0.85

z=x-μ/σ

σ*z+μ=x

x=16*0.85+266

x=279.6≅280

The longest 20% of pregnancies lasts 280 days

4 0

4 years ago

Can anyone help with this probelm???

patriot [66]

We need to look at 2 similar triangles

1) big one: legs - a,b, and hypotenuse - c

2)small one: legs - h,s, and hypotenuse - b.

Corresponding sides:

hypotenuse - c and hypotenuse - b,

big leg - b and big leg - s,

small leg - a, and small leg h.

?(/b(big leg, big triangle)= b(hypotenuse, small triangle )/s (big leg, small triangle)

? should be hypotenuse of the big triangle, c.

Answer is second one c.

8 0

3 years ago

Which of the following is a correct solution to the inequality 3x - 12 > 15?

pishuonlain [190]

Solve the inequality just like you would solve an equation
3x - 12 > 15
add 12 to both sides
3x > 27
divide both sides by 3
x > 9
Or read as "the solution to 3x - 12 > 15 is x is greater than 9"

Hope this helps :)

4 0

3 years ago