Question

Determine whether the improper integral from 5 to infinity 3/square root x dx converges or diverges, and find the value if it converges.

Select the correct choice below and fill in any answer boxes within your choice.

A. The value of the integral

B.The integral diverges.

Answer #1

Prove that the integral from 0 to Infinity (sin^2(x)e^-x)dx
converges using the comparison test.

Explain whether the following integrals converge or not. If the
integral converges, find the value. If the integral does not
converge, describe why (does it go to +infinity, -infinity,
oscillate, ?)
i) Integral from x=1 to x=infinity of x^-1.4 dx
ii) Integral from x=1 to x=infinity of 1/x^2 * (sin x)^2 dx
iii) Integral from x=0 to x=1 of 1/(1-x) dx

Determine the convergence or divergence if each integral by
using a comparison function. Show work using the steps below:
A. Indicate the comparison function you are using.
B. Indicate if your comparison function is larger or smaller
than the original function.
C. Indicate if your comparison integral converges or diverges.
Explain why.
D. State if the original integral converges or diverges. If it
converges, you don’t need to give the value it converges to.
11. integral from 1 to infinity...

Find the square root that is a real number.
negative StartRoot negative 4
EndRoot
Select the correct choice below and, if necessary, fill in the
answer box within your choice.
A.
The real number square root is
nothing
.
(Simplify your answer. Type an integer or a fraction.)
B.
The square root is not a real number.

Use the ratio test to determine whether∑n=12∞n2+55n
converges or diverges.
(a) Find the ratio of successive terms. Write your
answer as a fully simplified fraction. For n≥12,
limn→∞∣∣∣an+1an∣∣∣=limn→∞
(b) Evaluate the limit in the previous part. Enter ∞
as infinity and −∞ as -infinity. If the limit does
not exist, enter DNE.
limn→∞∣∣∣an+1an∣∣∣ =
(c) By the ratio test, does the series converge,
diverge, or is the test inconclusive?

In the accompanying table, the random variable x represents the
number of televisions in a household in a certain country.
Determine whether or not the table is a probability distribution.
If it is a probability distribution, find its mean and standard
deviation.
x
P(x)
0
0.02
1
0.12
2
0.34
3
0.28
4
0.14
5
0.10
If the table is a probability distribution, what is its mean?
Select the correct choice below and fill in any answer boxes within
your...

A survey asks
15001500
workers, "Has the economy forced you to reduce the amount of
vacation you plan to take this year?"
ThirtyThirty-twotwo
percent of those surveyed say they are reducing the amount of
vacation.
TenTen
workers participating in the survey are randomly selected. The
random variable represents the number of workers who are reducing
the amount of vacation. Decide whether the experiment is a binomial
experiment. If it is, identify a success, specify the values of
n, p, and...

Groups of adults are randomly selected and arranged in groups of
three. The random variable x is the number in the group who say
that they would feel comfortable in a self-driving vehicle.
Determine whether a probability distribution is given. If a
probability distribution is given, find its mean and standard
deviation. If a probability distribution is not given, identify
the requirements that are not satisfied
x
P(x)
0
0.351
1
0.427
2
0.200
3
0.022
Does the table...

Five males with a particular genetic disorder have one child
each. The random variable x is the number of children among the
five who inherit the genetic disorder. Determine whether the table
describes a probability distribution. If it does, find the mean
and standard deviation.
x
0
1
2
3
4
5
P(x)
0.01160.0116
0.08340.0834
0.23990.2399
0.34520.3452
0.24840.2484
0.07150.0715
Find the mean of the random variable x. Select the correct
choice below and, if necessary, fill in the answer box...

A standardized exam's scores are normally distributed. In a
recent year, the mean test score was 1461 and the standard
deviation was 318. The test scores of four students selected at
random are 1900, 1180, 2160, and 1360
Find the z-scores that correspond to each value and determine
whether any of the values are unusual.
Which values, if any, are unusual? Select the correct choice
below and, if necessary, fill in the answer box within your
choice.

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