A company makes paper labels for paint cans. As shown below, each can is in the shape of a cylinder with a height of 5 in and a diameter of 6in . The paper label is wrapped around the can and covers only the side of the can (not the top or bottom). If the company has a total of 4521.6in^2 of paper available, how many labels can be made? Use 3.14 for n , and do not round your answer.

Answers

Answer 1

48 labels can be made if the company has a total of 4521.6in² of paper available.

We can calculate the number of labels by finding the surface area of the side of the can.

What is the surface area of the side of the can?

The surface area of the side of the can is the circumference of the base times the height:

C = πd

C = 3.14 x 6

C = 18.84 in

Area = C x h

Area = 18.84 x 5

Area = 94.2 in²

Therefore, each label requires 94.2 in² of paper.

To find the number of labels that can be made, we divide the total amount of paper by the amount needed per label:

Number of labels = Total area of paper / Area per label

Number of labels = 4521.6 / 94.2

Number of labels = 48

Therefore, 48 labels can be made using a total of 4521.6in² of paper.

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Related Questions

Cami cut 17 1\2
inches off a rope that was 50 inches long. How is the length of the remaining rope in inches written in decimal form?

Answers

After Cami cut 17¹/₂ inches of a rope that was 50 inches long, the length of the remaining rope in inches, written in decimal form, is 32.5 inches.

How is the remaining length of the rope determined?

To determine the remaining length of the rope, we apply subtraction operation.

However, since the cut rope was expressed in fractions, we can convert it to decimals before the subtraction.

The total length of the rope = 50 inches

The cut portion of the rope = 17¹/₂ inches

The remaining portion = 32¹/₂ inches or 32.5 inches (50 - 17¹/₂)

Thus, the remaining portion of the rope after Cami cut 17¹/₂ inches is 32.5 inches.

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Apply the nearest neighbor algorithm to the graph above starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDA

Answers

Starting at vertex A and using the nearest neighbor algorithm, the path is: A-C-B-D-A, with a total distance of 95. This means visiting vertices in the order A, C, B, D, and back to A, and the total distance traveled is 95 units.

The nearest neighbor algorithm is used to find the shortest path between a set of points. Here are the steps to apply the algorithm in this case

Start at vertex A. Look for the closest neighboring vertex to A. In this case, the closest vertex is B, which is 7 units away from A. Move to vertex B and mark it as visited. Look for the closest neighboring vertex to B that has not been visited. In this case, the closest vertex is C, which is 11 units away from B.

Move to vertex C and mark it as visited. Look for the closest neighboring vertex to C that has not been visited. In this case, the closest vertex is D, which is 18 units away from C. Move to vertex D and mark it as visited.

Look for the closest neighboring vertex to D that has not been visited. In this case, the closest vertex is B, which is 15 units away from D. Move to vertex B and mark it as visited.

Look for the closest neighboring vertex to B that has not been visited. In this case, the closest vertex is E, which is 20 units away from B. Move to vertex E and mark it as visited.

Look for the closest neighboring vertex to E that has not been visited. In this case, the closest vertex is A, which is 24 units away from E. Move to vertex A and mark it as visited. All vertices have been visited, so the algorithm is complete.

The list of vertices visited, starting and ending at A, is A, B, C, D, B, E, A and the distance is 95.

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Find the measure of EB

Answers

The measure of angle subtended by the arc EB is 96 ⁰.

What is the measure of arc angle EB?

The measure of angle subtended by the arc EB is calculated by applying the following formula.

Based on the angle of intersecting chord theorem, the theory states that, the angle formed by the intersection of two chords at the circumference of a circle is equal to half of the difference between the arc angles of the two chords.

We will have the following equation;

m∠ECB = ¹/₂( 7x + 6 - (4x + 16))

25 x 2 = 7x + 6 - 4x - 16

50 = 3x - 10

60 = 3x

x = 60/3

x = 20

The measure of arc angle EB is calculated as follows;

m∠EB = 4x + 16

m∠EB = 4(20) + 16

m∠EB = 96 ⁰

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For the function value f(−9)=6​, write a corresponding ordered pair.

Answers

Answer:

(-9, 6) This ordered pair is used to find the function value f(-9)=6

or the given function​ value, write a corresponding ordered pair.

Step-by-step explanation:

For the given function​ value, write a corresponding ordered pair.

f(-9) = 6

The ordered pair of each function can be written as (x,y).

For any function, for example, g(x)= 10x, the input is x, and the output y is 10x. So ordered pair is (x,10x)

The given function value is: f(-9) = 6

Here input x=-9 and y value is 6

So, he corresponding ordered pair is (-9, 6)

Sketch the graph of the following function. Describe how
the graph can be obtained from the graph of the basic
exponential function ex.
f(x) = 2 (4-ex)
Use the graphing tool to graph the equation.

someone help pls, im not sure what to put in the little box for the vertical shift and vertical shrink

Answers

The vertical shift and vertical shrink of the exponential function are 2 and 1/2 respectively and the graph of the function is attached below

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The vertical shift and vertical shrink of the function f(x) = 1/2(4 - eˣ) are 2 and 1/2

The vertical shift = 2

vertical shrink = 1/2

Kindly find the attached graph below

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combine like terms 6x^2 - 10x + 21x - 35 = 6x^2 + 11x - 35

Answers

Answer:

Step-by-step explanation:

6x² - 10x + 21x - 35 = 6x² + 11x - 35

6x² - 6x² + 11x - 11x - 35 + 35 = 0

0 = 0

The equation is an identity. Its solution set is {all real numbers}.

PLSSS HELP AND PLEASE SHOW WORK ASWELL


Collin has 100 feet of fencing to enclose a pen for his puppy. He is
trying to decide whether to make the pen
circular or square. He plans to use all of the
fencing.

Part A.) If Collin uses all of the fencing, what
would be the area of each pen? Use 3.14
for pie. Round to the nearest hundredth if
necessary.

Part B.) To have the largest possible area for the pen, which pen should Collin build?

Answers

Answer:

A.

circular: ≈ 795.77 square feet

square: 625

Step-by-step explanation:

the circular pen would have a larger area.

Solving for the radius, we have:

r = 100 / (2 × 3.14) = 15.92 feet (rounded to two decimal places)

Therefore, the area of the circular pen would be:

Area = πr^2 = 3.14 × (15.92 ft)^2 ≈ 795.77 square feet

For a square pen with side length s, the perimeter is given by:

4s = 100

s = 25

The area of a square pen with side length s is given by:

A = s^2 = 25^2 = 625

Part A:

Let's first consider the circular pen. The circumference of a circle is given by 2πr, where r is the radius. In this case, we have 100 feet of fencing, so:

2πr = 100

Solving for r, we get:

r = 100/(2π) = 15.92 feet (rounded to two decimal places)

The area of the circular pen is given by πr^2, so:

Area = π(15.92)^2 = 795.77 square feet (rounded to two decimal places)

Now let's consider the square pen. If we use all 100 feet of fencing, then each side of the square will be 25 feet long. Therefore, the area of the square pen is:

Area = 25^2 = 625 square feet

Part B:

To have the largest possible area for the pen, Collin should build the circular pen. We can see from the calculations above that the area of the circular pen is larger than the area of the square pen. This is because a circle has the largest area for a given perimeter, which in this case is 100 feet.

I have no idea how to solve this problem.

Answers

(a) The domain of f of g is {1, 8}.

(b) The range of f of g is {0, 1}.

What is the domain and range of f of g?

The domain of f of g consists of all the inputs in the domain of g that are also in the domain of f.

(a) Domain of f of g:

The inputs in the domain of g that are also in the domain of f are 1, and 8. Therefore, the domain of f of g is {1, 8}.

To find the range of f of g, we need to apply the function composition f(g(x)) to each input in the domain of f of g, and collect all the outputs.

(b) Range of f of g:

The range of f of g consists of all the outputs obtained by applying f(g(x)) to each input in the domain of f of g.

We have:

f(g(1)) = f(8) = 0

f(g(4)) = f(2) = 1

f(g(8)) = f(0) = 1

Therefore, the range of f of g is {0, 1}.

Thus, in set notation, the domain of f of g is {1, 8}, and the range of f of g is {0, 1}.

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A bug crawls 5 1/2 feet in 28.6 seconds. At that pace, how many seconds does it take the bug to crawl one foot?

Answers

Answer:

5.2 seconds

Step-by-step explanation:

To get one foot, we need to divide by 5.5

Set up a proportion:

[tex]\frac{5.5}{5.5}=\frac{28.6}{5.5}[/tex]

Solve:

[tex]1ft.=5.2secs.[/tex]

what are the answers to these questions?

Answers

The height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.

The total surface area of the can is therefore:

A = 2πr² + 2πrh

We know that the volume of the can is 810 cm³, which is given by:

V = πr²h

We can solve this equation for h to get:

h = V/(πr²)

Substituting this expression for height h into the equation for the surface area, we get:

A = 2πr² + 2πr(V/(πr²))

Simplifying, we get:

A = 2πr² + 2V/r

Now we have an equation for the surface area of the can in terms of the radius, r.

To minimize the surface area, we need to take the derivative of this equation with respect to r, set it equal to zero, and solve for r.

dA/dr = 4πr - 2V/r² = 0

Solving for radius r, we get:

[tex]r = (810/\pi)^1^/^3[/tex]

r=∛810/3.14

r=6.35 cm

Now find h:

h = 810/πr²

h=810/3.14×6.35²

h=810/126.6

h=6.39 cm

Hence, the height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.

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Express the following probability as a simplified fraction and as a decimal.
If one person is selected from the population described in the​ table, find the probability that the person is or .

Answers

Note that  the following probability as a simplified fraction and as a decimal is:  0.88617886178 and 109/123

How is this so?

Note that the key phrase here is “given that this person is a man.

This means that all we are interested in is the row labeled Male.

           Married      Never      Div       Widowed    Total

Male    69                  40       11                   3           123    

We are asked to find the probability that the person was either Married or Never. So the fraction you want is (69 + 40) / 123.

⇒ (69 + 40) / 123.

⇒ 109/123

or 0.886179

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Express the following probability as a simplified fraction and a decimal.

if one person is selected from the population described in the table, find the probability that the person has never been married or is married, given that this person is a man.

  Married  Never Married  Divorced   Widowed   Total

Male    69    40     11     3     123

Female  67    33     20     5     125

Total    136    73     31     8     248

Question 1.Express the probability as a simplified fraction

Here are five spinners with orange and white sectors. Each spinner is divided into equal sectors. A a) b) a) For one of the spinners, the probability of spinning orange is Which spinner is this? B A b) For two of the spinners, the probability of spinning orange is more than 40%. Which two spinners are these? ​

Answers

Spinner B is the spinner that has a probability of 1/3 of spinning orange.

How to find the he probability of spinning orange is more than 40%

a) For one of the spinners, the probability of spinning orange is 1/3. To identify which spinner this is, we need to find the spinner that has exactly one orange sector out of three total sectors.

From the given spinners, Spinner B is the only spinner that has one orange sector out of three, so Spinner B is the spinner that has a probability of 1/3 of spinning orange.

b) For two of the spinners, the probability of spinning orange is more than 40%. To find these spinners, we need to look for the spinners that have at least three orange sectors out of a total of eight sectors (since 3/8 is greater than 40%).

From the given spinners, Spinner A and Spinner C both have three orange sectors out of eight total sectors, so they are the two spinners for which the probability of spinning orange is more than 40%.

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What does the circled portion represent in the confidence interval formula?
p±z.
O Sample proportion
O Margin of error
p(1-p)
n
Confidence interval
O Sample Size

Answers

The circled portion in the confidence interval formula p ± z represents the Margin of Error, which plays a crucial role in interpreting the range of plausible values for the population parameter.

In the confidence interval formula p ± z, the circled portion represents the Margin of Error.

The Margin of Error is a critical component of a confidence interval and quantifies the level of uncertainty in the estimate.

It indicates the range within which the true population parameter is likely to fall based on the sample data.

The Margin of Error is calculated by multiplying the critical value (z) by the standard deviation of the sampling distribution.

The critical value is determined based on the desired level of confidence, often denoted as (1 - α), where α is the significance level or the probability of making a Type I error.

The Margin of Error accounts for the variability in the sample and provides a measure of the precision of the estimate.

It reflects the trade-off between the desired level of confidence and the width of the interval.

A larger Margin of Error indicates a wider confidence interval, implying less precision and more uncertainty in the estimate.

Conversely, a smaller Margin of Error leads to a narrower confidence interval, indicating higher precision and greater certainty in the estimate.

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Find m/_U. Write your answer as an integer or as a decimal rounded to the nearest tenth.

Answers

The measure of angle U = 41.83 degree.

In the given right angle triangle

VW = 6

UV = 9

Since sinΘ  = (opposite side)/(hypotenuse)

Therefore,

sin U = VW/UV

        = 6/9

        = 0.667

Take inverse of sin both sides

     ∠U =  arcsin(0.667)

            = 41.83

Hence  ∠U = 41.83 degree

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real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home. To do so, the agent obtained a list of 10 comparable homes just listed for sale that were currently empty. He randomly assigned 5 of the homes to be "staged," meaning filled with nice furniture and decorated. The owners of the 5 homes all agreed to have their homes staged by professional decorators. The other 5 homes remained empty. The hypothesis is that empty homes are not as appealing to buyers as staged homes and, therefore, sell for lower prices than staged homes. The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the 5 staged homes was $175,000 with a standard deviation of 35,000. A dotplot of each sample shows no strong skewness and no outliers.

Answers

Real-estate agent tested the effect of staging on home sale prices. Out of 10 comparable homes, 5 were staged. Staged homes sold for $15k more on average, with no skewness or outliers.

Based on the information given, the real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home.

The hypothesis is that empty homes sell for lower prices than staged homes. The agent randomly assigned 5 empty homes to be staged and obtained a list of 10 comparable homes.

The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the 5 staged homes was $175,000 with a standard deviation of 35,000. There was no strong skewness or outliers in the dot plots of the two samples.

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A card is drawn from a deck of 52 cards. What is the probability that it is a 3 or a spade?

Answers

Answer:

P = 4/13 = 0.308

Step-by-step explanation:

3 cards 3

13 spade cards (includes the card 3 of spades)

[tex]P=(3+13)/52= 16/52 = 4/13=0.308[/tex]

Hope this helps.

On a sample tray, 3 out of 6 cake samples are chocolate.
What is the probability that a randomly selected piece of cake will be chocolate?
Write your answer as a fraction or whole number.

Answers

The probability that a randomly decided piece of cake maybe chocolate is 1/2 or half of or 0.

The proportion of chocolate cakes to all other cakes can be used to calculate the probability that a person will pick a chocolate cake from the pattern tray.

In this case, there are 3 chocolate cakes out of a total of 6 cakes.

So the probability of selecting a chocolate cake is:

3/6 = 1/2 (Dividing the numerator and denominator by their greatest common factor, in this case, 3 will simplify the fraction 3/6.)

Therefore, the probability of selecting a chocolate cake is 1/2 or 0.5 when expressed as a decimal.

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Samantha gets paid $18.50 for each soccer game she referees. If she is a referee for 12 games and spends $59.99 for a new pair of cleats, how much money
does she have?

Answers

Samantha's earnings from refereeing 12 soccer games would be:

$18.50 x 12 = $222

After spending $59.99 on new cleats, Samantha's total earnings become:

$222 - $59.99 = $162.01

Answer:

$162.01

Step-by-step explanation:

amount of money she earns: 12($18.50) = $222

spends $59.99

amount of money after her purchase: $222-$59.99=$162.01

What is 0.08% written as a decimal?

Answers

It is written as 0.0008 because you move the decimal two places to the left

3.4 MIXED FACTORING

1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.

a. x² - 4x-2x+8

Answers

Answer:

  (x -2)(x -4)

Step-by-step explanation:

You want to factor x² - 4x -2x +8.

Factor by grouping

We recognize that the product of the coefficients of the two linear terms is equal to the contant, so this is more easily factored by not combining like terms prior to factoring.

Grouping the terms in pairs, we find we can factor each pair:

  (x² -4x) + (-2x +8)

  = x(x -4) -2(x -4) . . . . . these terms have a common factor of (x -4)

  = (x -2)(x -4) . . . . . . . factored form of the expression

50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answers

Answer: C {m | m  > 2}

Step-by-step explanation:

write the number in exponential form with the base of 2

2^3m-4 > 2^2

compare the exponents = 3m-4 >2

move the constant to the right and then change the sign

3m> 2+4  add

3m>6 divide

m>2


At 10.30 a.m, a van left Town X travelling at an average speed of 64 Km/h.
At 11.15 a.m., a car left Town X, travelling on the same road at an average speed of
80 Km/h.
a) At what time did the car catch up with the van?

b) How far from Town X did each vehicle travel when they passed each other?

Answers

Answer:

  a) 2:15 pm

  b) 240 km

Step-by-step explanation:

You want to know the time and place where a car leaving at 11:15 a.m. at 80 km/h catches up with a van leaving at 10:30 a.m. at 64 km/h.

Head start

The van travels for 11:15 -10:30 = :45, or 3/4 hour, before the car starts. This gives it a distance advantage of (3/4 h)(64 km/h) = 48 km.

Closing speed

The speed at which that distance is reduced is the difference between the car speed and the van speed:

  80 km/h -64 km/h = 16 km/h

Closing time

The time it takes for the head-start distance to be reduced to zero is ...

  time = distance/speed

  time = (48 km)/(16 km/h) = 3 h

a) Meeting time

Three hours after the car leaves, it will catch up with the van. That time is ...   11:15 +3:00 = 14:15 = 2:15 p.m.

b) Meeting distance

In 3 hours, the car travels (3 h)(80 km/h) = 240 km.

Note that the van has been traveling 3 3/4 hours, so will have also traveled (3 3/4 h)(64 km/h) = 240 km. The two vehicles need to be in the same place at the same time if they are to pass each other.

__

Additional comment

The attached graph shows the two vehicles will have traveled 240 km when they mean at 2:15 pm. The horizontal axis is hours after midnight. The vertical axis is kilometers from town X. The relation graphed is distance = speed × time.

PLEASE HELP WITH THE IMAGE!! DUE TOMORROW!!!

Answers

The calculations of the down payments, monthly income or payments are as follows:

Part 1:

Annual income = $226,000

Federal Tax = $62,582

State Tax = $16,385

Local Tax = $5,537

Healthcare = $4,520

Yearly income = $136,976

Monthly income = $11,414.67.

Part 2:

Down payment = $150,000

The amount to borrow (Mortgage loan) = $600,000

Estimated interest = $810,000

Total installment payments = $1,410,000

Monthly payment = $3,916.67.

Part 3:

Down payment = $2,902.50

Mortgage loan = $16,447.50

Estimated interest = $3,700.69

Interest + Mortgage loan = $20,148.19

Monthly payment = $335.80.

How the down payments and monthly payments are determined:

Part 1:

Annual income = $226,000

Federal Tax:

25% of $89,350 = $22,337.50

28% of $97,000 = $27,160.00

33% of $39,650 = $13,084.50

Total federal tax = $62,582

State Tax = 7.25% of $226,000 = $16,385

Local Tax = 2.45% of $226,000 = $5,537

Healthcare = 2% of $226,000 = $4,520

f) Total of Federal, State, Local, and Healthcare = $89,024

Yearly income = $136,976 ($226,000 - $89,024)

Monthly income = $11,414.67 ($136,976 ÷ 12)

Part 2:

a) House price = $750,000

b) Down payment = 20%

= $150,000 ($750,000 x 20%)

c) Mortgage loan = $600,000 ($750,000 - $150,000)

d) Interest rate = 4.5%

Number of mortgage years = 30 years

Mortgage period in months = 360 months (30 x 12)

Estimated interest = $810,000 ($600,000 x 4.5% x 30)

Interest + Mortgage loan = $1,410,000 ($600,000 + $810,000)

Monthly payment = $3,916.67 ($1,410,000 ÷ 360)

Part 3:

Price of car = $19,350

Down payment = 15%

= $2,902.50 ($19,350 x 15%)

Mortgage loan = $16,447.50 ($19,350 - $2,902.50)

Number of years = 5 years

Mortgage period in months = 60 months (5 x 12)

Estimated interest = $3,700.69 ($16,447.50 x 4.5% x 5)

Interest + Mortgage loan = $20,148.19 ($16,447.50 + $3,700.69)

Monthly payment = $335.80 ($20,148.19 ÷ 60)

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uppose that you are told that the Taylor series of f(x)=x3ex2
about x=0
is
x3+x5+x72!+x93!+x114!+⋯.
Find each of the following:
ddx(x3ex2)∣∣∣x=0=


d7dx7(x3ex2)∣∣∣x=

Answers

a. Using Taylor series d(x³eˣ²)/dx about x = 0 is  x⁴.

b. Using Taylor series d⁷(x³eˣ²)/dx⁷ about x = 0 is  x¹⁰.

What is a Taylor series expansion?

A Taylor series is a polynomial expansion of a function about a given point. It is given by f(x - a) = ∑(x - a)ⁿfⁿ(x - a)/n! where

a = point where f(x) is evaluated fⁿ(a) = nth derivative of f(x) about a and n is a positive integer

Given that the Taylor series of the function f(x) = x³eˣ² about x = 0 is

f(x) = x³ + x⁵ + x⁷/2! + x⁹/3! + x¹¹/4!, (1) we proceed to find the given variables

a. To find d( x³eˣ²)/dx about x = 0, the Taylor series expansion about x = 0 is given by

f(x - a) = ∑(x - a)ⁿfⁿ(a)/n!

f(x - 0) = ∑(x - 0)ⁿf(0)/n!

f(x) = ∑xⁿf(0)/n!

f(x) = x⁰f(x)/0! + xf(x)/1! + x²f(x)/2! + x³f(x)/3! + ....

f(x) = f(x) + xf¹(x) + x²f²(x)/2! + x³f³(x)/3! + ....(2)

Since fⁿ(x) is the nth derivative of f(x), and we desire f¹(x) which is the first derivative of f(x). Comparing equations (1) and (2), we have that

x⁵ =  xf¹(x)

f¹(x) =  x⁵/x

= x⁴

So, d( x³eˣ²)/dx about x = 0 is  x⁴.

b. To find d⁷( x³eˣ²)/dx⁷ about x = 0, the Taylor series expansion about x = 0 is given by

f(x - a) = ∑(x - a)ⁿfⁿ(a)/n!

f(x - 0) = ∑(x - 0)ⁿf(0)/n!

f(x) = ∑xⁿf(0)/n!

f(x) = x⁰f(x)/0! + xf(x)/1! + x²f(x)/2! + x³f(x)/3! + ....

Expanding it up to the 8 th term, we have that

f(x) = f(x) + xf¹(x) + x²f²(x)/2! + x³f³(x)/3! + x⁴f⁴(x)/4! + x⁵f⁵(x)/5! + x⁶f⁶(x)/6!  + x⁷f⁷(x)/7!.....(3)

Now expanding equation (1) above to the 8th term by following the pattern, we have that

f(x) =   x³ + x⁵ + x⁷/2! + x⁹/3! + x¹¹/4! + x¹³/5! + x¹⁵/6!  + x¹⁷/7!.....(4)

Since fⁿ(x) is the nth derivative of f(x), and we desire f⁷(x) which is the seventh derivative of f(x). Comparing equations (3) and (4), we have that

x⁷f⁷(x)/7! = x¹⁷/7!  

f⁷(x) =  x¹⁷/x⁷

= x¹⁰

So, d⁷( x³eˣ²)/dx⁷ about x = 0 is  x¹⁰.

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y= +- 3/5 is equivalent to?

Answers

The equivalent value of the expression is y = + 3/5 and y = -3/5

Given data ,

Let the expression be represented as A

Now , the value of A is

y = ±3/5

On simplifying the equation , we get

y = +3/5

And, y = -3/5

Now , the decimal values of y are

y = ±0.6

Hence , the expression is y = ±0.6

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limit x->oo (sqrt(x^2-9x+1)-x)=?

I solved it up until -9x+1/((√x^2-9x+1)+x) but I don't know what to do after this.

Answers

Note that the limit of the expression as x approaches infinity is 1/2.

How did we arrive at this  conclusion ?

start by multiplying both the numerator and denominator by the conjugate  expression

√ (x ² - 9x + 1) + x,

this will eliminates the root in the numerator

lim x->∞ [(√(x ² - 9x + 1) - x)  * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)

Expanding the numerator

lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)

Simplifying further:

lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)

we can see that the 1/x ² term approaches zero, and the expression simplifies to

lim x->∞ [(1 - 0)]  / (√(1 - 0) + 1)

= 1/2

So it is correct to state that the limit of the expression as x approaches infinity is 1/2.

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Write the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) in slope intercept form.

Answers

Answer: y = (9/5)x + 5.

Step-by-step explanation:

The slope of the given line is -5/9. The slope of a line perpendicular to it would be the negative reciprocal of -5/9, which is 9/5. Using the point-slope form of a line, we can write the equation of the line as y - (-4) = (9/5)(x - (-5)). Simplifying this equation gives y + 4 = (9/5)x + 9. Solving for y, we get y = (9/5)x + 5. This is the equation of the line in slope-intercept form.

In summary, the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) is y = (9/5)x + 5.

Andy has $100 in an account. The interest rate is 6% compounded annually.
To the nearest cent, how much will he have in 2 years?

Answers

The amount that will be in Andy's account in 2 years after the addition of interest is $112.36

How to calculate the amount in Andy's account after 2 years ?

Andy has $100 in an account

An interest rate of 6% is compounded annually

The amount that will be present in the account after 2 years can be calculated as follows

= 100(1+ 6/100)²

= 100(1 + 0.06)²

= 100(1.06)²

= 100(1.1236)

= 112.36

Hence the amount that will be present in the account after 2 years with the addition of interest is $112.36

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PLEASE SOMEONE HELP ME DO THIS MATH PROBLEM

i am having a mental breakdown rnn :(.

Answers

Check the picture below.

y + 6 < 10 or 2y - 3> 9

Answers

Answer:

2y - 3> 9 it is not y + 6< 10

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