2/3 x -9/8 x -4/5 x -1

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive an

GaryK [48]

Answer:

The series representation is $\sum_{n=0}^{\infty}(-1)^n\frac{x^n}{6^{n+1}}$ and the interval of convergence is (-6,6)

Step-by-step explanation:

We want to find a series, such that f(x) = \sum_{n=0}{\infty}a_n(x-a)^{n}[/tex], were a is the value that we are using to center the series expansion. In our case, a=0.

We will use the geometric series formula as follows. For |r|<1 then

$\frac{1}{1-r}=\sum_{n=0}^{\infty} r^n$

In our case, with some algebreaic manipulation we have that

$f(x) = \frac{1}{6+x} = \frac{1}{6}\frac{1}{1-(\frac{-x}{6})}$

Taking $r = \frac{-x}{6}$ we get that

$f(x) = \frac{1}{6}\sum_{n=0}^{\infty} (\frac{-x}{6})^n = \sum_{n=0}^{\infty}(-1)^n\frac{x^n}{6^{n+1}}$

This representation is valid (that means that the series converges to the value of f(x)) only for |r|<1. That is

$\left|\frac{-x}{6}\right|= \left|\frac{x}{6}\right|$

which implies that |x|<6. So the interval of convergence is (-6,6).

4 0

4 years ago

The graph shows the probability distribution of a random variable.

Natasha2012 [34]

The answer is 0.50.

P(4<=X<=8)=P(x=4)+ P(x=5)+ P(x=6)+ P(x=7)+ P(x=8)= 0.05+ 0.15+0.15+0.15 +0 = 0.50

Notice that in 8 the line touches the x axis so it’s corresponding probability is 0.

5 0

2 years ago

Writing an Equation in Vertex Form

pickupchik [31]

We get the value of h and k as 9 and -8

The quadratic function g(x) = a(x - h)^2 + k, if a is not equal to 0,which means that equation has a quadratic value then it is said to be in standard quadratic form.

If a is positive, then the graph opens upwards,

If a is negative, then it opens downwards.

The line of symmetry of the quadratic equation is the vertical line x = h, and the co-ordinate of the point of vertex is (h,k).

We are given the co-ordinate of the vertex point in the question and hence all that is required is to equate it.

Therefore, the values of h and k are 9 and -8 in the given equation in vertex form

You can learn more about quadratic equation in standard form here:

brainly.com/question/25025116?referrer=searchResults

Disclaimer: the question may be incomplete and hence has been answered accordingly

#SPJ9

7 0

2 years ago

PLEASE HELP ME WITH QUESTIONS 1 AND 2! NO LINKS OR SPAMS!!! THANKS!!!!!!!!!

Neko [114]

Confused lol... can u give me more information

8 0

3 years ago

In a statewide lottery, one can buy a ticket for $1. With probability .0000001, one wins a million dollars ($1,000,000), and wit

Dahasolnce [82]

Using the expected value, it is found that the mean of the distribution equals $0.1.

The expected value, which is the mean of the distribution, is given by <u>each outcome multiplied by it's probability</u>.

The probabilities of <u>each outcome</u> are:

.0000001 probability of earning $1,000,000.
.9999999 probability of earning $0.

Thus, the mean is given by:

$E(Y) = 0.0000001(1000000) + 0.9999999(0) = 0.1$

Thus showing that the expected value is $0.1.

A similar problem is given at brainly.com/question/24855677

6 0

3 years ago