for what values of x does the series ∑n=0[infinity](2x−3)nn! converge?

Answers

Answer 1

We can use the ratio test to determine the values of x for which the series converges.

The ratio test states that if

lim[n→∞] |an+1/an| = L

then the series converges if L < 1, diverges if L > 1, and the test is inconclusive if L = 1.

In this case, the general term of the series is

an = (2x - 3)^n / n!

So, applying the ratio test, we have

|an+1/an| = |(2x - 3)^(n+1) / (n+1)!| / |(2x - 3)^n / n!|

= |2x - 3| / (n+1)

Taking the limit as n approaches infinity, we get

lim[n→∞] |an+1/an| = lim[n→∞] |2x - 3| / (n+1) = 0

Since the limit is less than 1 for all values of x, the series converges for all values of x.

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Related Questions

4) Manuel buys a ski jacket for $180. The sales tax is 8.5%. What is the total cost
of the jacket?

Answers

$195.30

180x 1.085 = 195.3

Or

180 + (180x8.5/100)=180+15.3=195.3

Answer:

Step-by-step explanation:

$195.30

180x 1.085 = 195.3

there another chose

180 + (180x8.5/100)=180+15.3=195.3

A rectangle has a length of 3x + 9 and a width of 5x - 4.
The perimeter of the rectangle is 106 units. Find the
width of the rectangle.

Answers

Answer:

I hope it helped u.

Step-by-step explanation:

A rectangle has a length of 3x + 9 and a width of 5x - 4.The perimeter of the rectangle is 106 units.

The required width of the rectangle is given as 26 units.

As mentioned in the question, A rectangle has a length of 3x + 9 and a width of 5x - 4. The perimeter of the rectangle is 106 units. The width of the rectangle.

What is the perimeter?

Perimeter is the measure of the figure on its circumference.

Here,
Perimeter of the rectangle  = 2 [ length + width]
Perimeter of the rectangle = 2 [3x + 9 + 5x - 4]
Perimeter of the rectangle = 2 [8x - 5]
106 = 16x - 10
96 = 16x
x = 6
Now,
Width = 5x - 4
Width = 5 [6] - 4
Width = 30 - 4
Width = 26 units,

Thus, the required width of the rectangle is given as 26 units.

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The diameter of ball bearing are ditributed normally. The mean diameter i 81 millimeter and the variance i 16. Find the probability that the diameter of a elected bearing i greater than 85 millimeter. Round your anwer to four decimal place

Answers

the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587

The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.

To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.

We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.

We the look up the probability for a value of 1 in the z-table, which is 0.1587.

This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.

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Apply the distributive property using the greatest common factor to write an equivalent expression.
Enter your answers in the boxes.
0.3x – 2.7 =T0-0)

Apply the distributive property using the greatest common factor to write an equivalent expression.Enter

Answers

Step-by-step explanation:

0.3x = (0.3)(x).

2.7 = (0.3)(9).

Between the 2 terms, the GCF is 0.3.

Hence,

0.3x - 2.7

= (0.3)(x) - (0.3)(9)

= 0.3(x - 9).

the third-degree taylor polynomial for a function f about x=4 is (x−4)3512−(x−4)264 (x−4)4 2. what is the value of f′′′(4)?

Answers

Answer:  the value of f′′′(4) is 3/256.

Step-by-step explanation:

Given the third-degree Taylor polynomial:

f(x) = (x−4)³/512 − (x−4)²/64 + (x−4)⁴/2

To find the value of f′′′(4), we need to differentiate the polynomial three times and evaluate it at x = 4.

First derivative:

f'(x) = 3(x−4)²/512 − 2(x−4)/64 + 4(x−4)³/2

Second derivative:

f''(x) = 6(x−4)/512 − 2/64 + 12(x−4)²/2

Third derivative:

f'''(x) = 6/512 + 24(x−4)/2

Now, substitute x = 4 into f'''(x):

f'''(4) = 6/512 + 24(4−4)/2

= 6/512 + 0

= 6/512

= 3/256

Therefore, the value of f′′′(4) is 3/256.

What is the formula for calculating angle?

Answers

Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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I just need like a step by step I haven't understood what my teacher has taught me here ​

I just need like a step by step I haven't understood what my teacher has taught me here

Answers

You are trying to find the side between the right angle and the degree (This is known as the adjacent)
You are given degree 42
You also given the longest side of 19 (This is known as the hypothenuse)
Cosine: adjacent/hypothenuse
Cos42 = x/19
0.7431448255 = x/19
x = 19 * 0.7431448255
x = 14.11975168, round to tenth

Solution: x = 14.1

Write the equation that models the conditions. Then solve the equation and answer the question. 525 is 75% of what number? The percent equation is Solve the equation, X=

Answers

We will solve as follows:

*525 is the 75% of:

\(x=\frac{525\cdot100}{75}\Rightarrow x=700\)

So, 525 is 75% of 700.

*The percent equation is:

\(525=x(700)\)

*The value of x is:

\(x=0.75\)

Determine what type of sequence this info would make, Identify the Common difference or common ratio and graph it as it expands: many shirts will be printed at a cost of $35 to set up the logo and $18 per shirt.

Answers

Based on the given information, the sequence describes the total cost of printing shirts, which includes a fixed cost of $35 to set up the logo and an additional cost of $18 per shirt. This forms an arithmetic sequence, where the common difference is $18. In an arithmetic sequence, each term is obtained by adding the common difference to the previous term.

The common difference in this case represents the constant amount added to the total cost each time a new shirt is printed. In other words, for each additional shirt, the cost increases by $18. The sequence grows linearly as the number of shirts increases, with the cost increasing steadily at a constant rate.

To graph this sequence as it expands, you can plot the number of shirts on the x-axis and the total cost on the y-axis. Each point on the graph represents a pair (number of shirts, total cost), with the total cost calculated using the formula: Cost(n) = 35 + 18n, where 'n' represents the number of shirts. The resulting graph will be a line with a positive slope, indicating the linear relationship between the number of shirts and the total cost.

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50 squared is rational

True
False

Answers

Answer:

false

Step-by-step explanation:

Answer:

A rational number can be written as a fraction. Try finding the square root of 50 and see if you can rewrite it in fraction form.

Step-by-step explanation:

The quadratic equation is given by: ax 2 +bx+c=0 To find the maximum root of the quadratic equation: - Write a user defined function (with the parameters a,b, and c) that finds the roots of the equation and returns the maximum root. - Use this function in main() function to get a,b, and c parameters from the user and display the maximum root.

Answers

In the main() function, we prompt the user to enter the values of , , and . Then, we call the user-defined function to calculate and display the maximum root.

The quadratic equation is given by: a² + b + c = 0. To find the maximum root of the quadratic equation, a user-defined function is required. The function takes parameters , , and and returns the maximum root. This function can be used in the main() function to obtain the values of , , and from the user and display the maximum root.

To find the maximum root of a quadratic equation, we need to determine the vertex of the parabola represented by the equation. The x-coordinate of the vertex is given by = -/2. By substituting this value into the quadratic equation, we can calculate the maximum root.

The user-defined function will compute the maximum root as follows: Calculate the discriminant, Δ = ² - 4. If Δ < 0, the equation has no real roots, so return an appropriate error message. Calculate the x-coordinate of the vertex, = -/2.

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24+6x=10x

PLS help ASAP!!!

Answers

Answer:

6?

Step-by-step explanation:

24=10x-6x

24=4x

6=x

Choosing a career means you also need to think about your ________ ________ .

Answers

Answer:

Life Path

Step-by-step explanation:

It's two words, and they are both of equal length. I hope that helps.

Of the approximately 41.3 million of the foreign-born population currently living in the United States, how many are considered unauthorized immigrants

Answers

According to data from the Pew Research Center, there were approximately 10.5 million unauthorized immigrants living in the United States in 2017. This number represents around 25% of the total foreign-born population in the country. In conclusion, out of the 41.3 million foreign-born individuals in the U.S., about 10.5 million are considered unauthorized immigrants.

Unauthorized immigrants, also known as undocumented immigrants, are individuals who enter the United States without legal permission or overstay their visas. They are not eligible for most government benefits and are often subject to deportation if caught.

The Pew Research Center estimates that there were 41.3 million foreign-born individuals living in the United States in 2017, which includes both authorized and unauthorized immigrants. Of this population, around 10.5 million were unauthorized immigrants.

Unauthorized immigration is a complex and contentious issue in the United States, with many different opinions on how to address it. Understanding the size and characteristics of this population is an important part of any discussion or policy debate.

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simplify
(8p^6)^1/3
simplifyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

Answers

Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).

the sum of three consecutive integers is three times the second integer. show that this is true for the three consecutive integers 7,8 and 9

Answers

Step-by-step explanation:

7+8+9=24

second integer is 8 so 8*3=24

Help...no links please..

Help...no links please..

Answers

Answer:

c. 12/5

Step-by-step explanation:

tan of triangle= opposite/adjacent

so 12/5 which is 2.4

correct me if im wrong

$10. Find the value of x in the figure.

$10. Find the value of x in the figure.

Answers

Answer:

50+75+ x + 60= 180 (angle sum property)

185+ x =180

x= 180-185

x= -5

What is the area of the parallelogram?

What is the area of the parallelogram?

Answers

The area of the parallelogram is 88 sq. units.

Given is a parallelogram with base 11 units and height 8 units.

We need to find the area of the parallelogram,

The area of the parallelogram = base x height

= 8 x 11

= 88

Hence the area of the parallelogram is 88 sq. units.

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a large container holds 5 gallons of water it begins to leak at a constant rate after 10 minutes the container has 3 gallons of water left at what rate was the water leaking?

Answers

Answer:

The container will take 25 minutes to go from full to empty.

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Aaron travels 125 miles in 2.5 hours. At this rate, how far will he be able to travel in 6 hours?

Answers

Answer:

I believe it is 687.5 miles

Step-by-step explanation:

Answer:

750

Step-by-step explanation:

The cost of a ticket t will be no more than $26.?

Answers

I need more information

Answer:

t≤26

Step-by-step explanation:

Ryan is installing new flooring in house. Ryan can install 196 square feet of flooring in 2 hours How much new flooring can Ryan install in 16 hours? Please let me know !

Answers

Answer:

1568

Step-by-step explanation:

196/2=98

98*16=1586

Ryan can install 1568 square feet of flooring in 16 hours

Hope this helps!

=
If f(x) = 3x – 2 and g(x) = x+2,
find f(g(x)).
3
f(g(x)) = [?]
Simplify your answer as much as possible.

Answers

Answer:

3x+4

Step-by-step explanation:

f(g(x))=3(x+2)-2

=3x+6-2

=3x+4

Answer:

Step-by-step explanation:

f(x) = 3x - 2   When you see something like f(g(x)) it means that wherever you see an x on the right, you put g(x).

f(g(x)) = 3(g(x)) - 2               Now wherever you see g(x) on the right, you put in x + 2

f(g(x)) = 3(x + 2) - 2            Now remove the brackets

f(g(x)) = 3x + 6 - 2

f(g(x)) = 3x + 4

I'm not sure what the 3 in line 4 means. 3x + 4 seems to be the answer you want however.

For each number determine if it can be written as a fraction then state the reason

Answers

Each of the numbers can and cannot be written as a fraction based on the reason shown in the image below.

What is a fraction?

In Mathematics and Geometry, a fraction refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics and Geometry, a rational number is a type of number which comprises fractions, integers, terminating or repeating decimals such as the 22/7, -3/7, etc.

In conclusion, a number can be written as a fraction provided that it is a rational number.

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For each number determine if it can be written as a fraction then state the reason

What is the interest on $600 when it is placed for four years in a bank account that gives 2% simple interest



Answers

Answer:

12, or if its yearly, 48.

Why are security deposits popular for landlords to make tenants pay upfront?

Answers

Landlords might employ security deposits as a financial safety net to cover any damages that a tenant might cause throughout the period of the lease. The landlord can fully refund the security deposit if the renter vacates the property in good condition.

is it possible for two quantities to (a) have the same units but different dimensions or (b) have the same dimensions but different units? explain.

Answers

If two quantities have same units, they will be comprised of the same basic physical quantities and hence their dimensions will be same. Same dimensions do not represent the same physical quantity. For example, The kinetic energy and the potential energy are measured in the same units but they possess different physical quantities.

What is dimensions?

The minimal set of coordinates required to specify any point within a mathematical space is known as the dimension of the space in physics and mathematics. As a result, a line has a dimension of one because a point on it can be specified by a single coordinate, such as the point at 5 on a number line.

Two quantities with the same units will be made up of the same fundamental physical quantities, resulting in identical dimensions. The same physical quantity does not have the same dimensions. For instance, although having different physical properties, kinetic energy and potential energy are measured in the same units.

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Jack, Keith, and Betty draw tiles marked X, Y, and Z from a bag, replacing each tile before the next draw. They repeat this process and record their results in this table.

Letter Times Picked
X 30
Y 36
Z 24

Jack predicts that when he draws a tile without looking, he will draw a tile with the letter X one-third of the time.

Which activity would best allow Jack to test his prediction?
A.
Randomly select a tile and observe if it is the letter X.
B.
Randomly select 60 tiles without replacement. Then, observe how many tiles with the letter X are drawn.
C.
Randomly select and replace a tile 60 times. Then, observe how close to 20 times the letter X is drawn.
D.
Randomly select and replace a tile 60 times. Then, observe how close to 24 times the letter X is drawn.

Answers

The ideal option is B since it involves drawing samples from a large number of tiles (60), which will help to lessen the impact of random variation .

what is probability ?

The likelihood of an event happening is gauged by probability. A number between 0 and 1, where 0 denotes the event's impossibility and 1 denotes its certainty of happening, is used to express it. By dividing the number of likely outcomes by the total number of outcomes in a circumstance, probability is obtained. The likelihood of the event occurring is the value that results. For instance, there are only two outcomes that can occur when we flip a fair coin: heads or tails. As just one of the two possible outcomes (getting heads) is good, the probability of obtaining heads is equal to half (getting heads or tails).

given

We must contrast Jack's prediction with the experiment's actual findings in order to test his claim that he will draw a tile with the letter X one-third of the time. Option B, which involves choosing 60 random tiles without replacement and counting how many of them include the letter X, is the best exercise to do.

We would only receive one data point in option A, which is insufficient to assess the precision of Jack's prediction.

According to Jack's forecast, the value in option C—which attempts to measure how close to 20 times the letter X is drawn—is incorrect.

The ideal option is B since it involves drawing samples from a large number of tiles (60), which will help to lessen the impact of random variation .

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Let C represent the number of hours when the sky is cloudy and L represent the number of hours when the sky
is clear during which the solar panel can generate power without exceeding its capacity.
5C + 32 L < 400
According to the inequality, at what rate does the solar panel generate power when the sky is cloudy, and at
what rate does it generate power when the sky is clear?
The solar panel generates power at the rate of
kilowatts per hour when the sky is clear.
kilowatts per hour when the sky is cloudy, and
Does the solar panel exceed its maximum capacity when the sky is cloudy for 3 hours and clear for 6 hours?

Answers

Answer:

Step-by-step explanation:A large solar panel can generate power at a maximum rate of 400400400 kilowatts per day. It generates power at a constant rate when the sky is cloudy, and it generates power at a constant rate when the sky is clear. Let CCC represent the number of hours when the sky is cloudy and LLL represent the number of hours when the sky is clear during which the solar panel can generate power without exceeding its capacity. 5C+32L \leq 4005C+32L≤4005, C, plus, 32, L, is less than or equal to, 400 According to the inequality, at what rate does the solar panel generate power when the sky is cloudy, and at what rate does it generate power when the sky is clear?

2

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