A formal power series over R is a formal infinite sum f = X[infinity] n=0 anxn, where the coefficients an ∈ R. We add power series term-by-term, and two power series are the same if all their coefficients are the same. (We don’t plug numbers in for x, because we don’t want to worry about issues with convergence of the sum.) There is a vector space V whose elements are the formal power series over R. There is a derivative operator D ∈ L(V ) defined by taking the derivative term-by-term: D X[infinity] n=0 anxn ! = X[infinity] n=0 (n + 1)an+1xn What are the eigenvalues of D? For each eigenvalue λ, give a basis of the eigenspace E(D, λ). (Hint: construct eigenvectors by solving the equation Df = λf term-by-term.)

Answers

Answer 1

Answer:

Answer:

Check the explanation

Step-by-step explanation:

where the letter D is the diagonal matrix with diagonal entries λ1,…,λn. Now let's assume V is invertible, that is, this particular given eigenvectors are linearly independent, you get M=VDV−1.

Kindly check the attached image below to see the step by step explanation to the question above.

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Find the missing values on the diagram below. Assume that each line is evenly divided

A shipment of beach balls with a mean diameter of 28 cm and a standard deviation of 1.3 cm is normally distributed. By how many standard deviations does a beach ball with a diameter of 26.7 cm differ from the mean?a. 1

b. 1.3

c. 2

d. 3

Answers

Answer: a. 1

Step-by-step explanation:

Given : Population mean : $\mu=28\ cm$

Standard deviation : $\sigma=1.3\ cm$

Let n be the number of times a beach ball with a diameter of 26.7 cm differ from the mean.

Then, we have

$28-n(1.3)=26.7\n\n\Rightarrow\ 1.3n=28-26.7\n\n\Rightarrow\ 1.3 n=1.3\n\n\Rightarrow\ n=1$

Hence, a beach ball with a diameter of 26.7 cm is 1 standard deviation differ from the mean.

Express the number as a ratio of integers. 3.469 = 3.469469469

Answers

If you're looking for a fractional representation of the non-terminating decimal,
3.469469469....
then:

Let x=3.469469469.....
then
1000x-x=(3469.469469469...) - (3.469469469....)
999x = 3466
x=3466 / 999
= 3+469/999
$=3(469)/(999)$

sarah can complete a project in 90 minutes and her sister betty can complete it in 120 minutes if they both work on the project at the same time how long will it take them to complete the project

Answers

Answer:

It will take them approximately 51.43 minutes to complete the project together

Step-by-step explanation:

This is what is called a "shared job" problem.

The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.

So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project

Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.

We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).

Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.

In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:

$(1)/(x) =(1)/(90) +(1)/(120)\n(1)/(x) =(4)/(360) +(3)/(360)\n(1)/(x) =(7)/(360) \nx=(360)/(7) \nx=51.43\,\,min$

So it will take them approximately 51.43 minutes to complete the project together.

A publisher reports that 42%42% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 250250 found that 35%35% of the readers owned a particular make of car. Find the value of the test statistic. Round your answer to two decimal places.

Answers

Answer:

$z=\frac{0.35 -0.42}{\sqrt{(0.42(1-0.42))/(250)}}=-2.24$

Step-by-step explanation:

Data given and notation

n=250 represent the random sample taken

$\hat p=0.35$ estimated proportion of readers owned a particular make of car

$p_o=0.42$ is the value that we want to test

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that that the percentage is actually different from the reported percentage.:

Null hypothesis: $p=0.42$

Alternative hypothesis: $p \neq 0.42$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.35 -0.42}{\sqrt{(0.42(1-0.42))/(250)}}=-2.24$

Please help me 80% of what number is 16 What is the part?
What is the total?
What is the percent?
What is the answer?

Answers

Answer:

80 percent of 16 is 12.8 I'm sorry but that's all I know

Given point A(−2, 6) and point B(3, 4), find the coordinates of point C that divide AB so that the ratio AC:CB is 2:3.The coordinates of point C are

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