1 1. Determine if the series (-1)*4k converges or diverges. If it converges k=1 5k - 1 approximate the sum S of the series to within 0.01. (5 pts) +1 -(-1)"+1 Determine if the series converges absolutely, converges conditionally, or n=1 vn diverges.

Answers

Answer 1

The given series is (-1)^n * (4n) with n starting from 1. To determine if the series converges or diverges, we can use the Alternating Series Test. For an alternating series, it converges if:
1. The terms are non-increasing: a_n+1 <= a_n for all n.
2. The limit of the terms as n goes to infinity is 0: lim(n→∞) a_n = 0.
The terms a_n = 4n are increasing and not non-increasing, so the series diverges. Thus, we cannot approximate the sum S of the series to within 0.01.
For the second part of the question, we check the absolute convergence by considering the series with absolute values of the terms: Σ(4n) with n starting from 1. This is a divergent arithmetic series, so the original series does not converge absolutely. Since the original series also diverges, we conclude that the series diverges.

The given series is (-1)*4k. To determine if it converges or diverges, we need to check if its terms approach zero as k goes to infinity. Since the absolute value of each term is 4k, which increases without bound as k goes to infinity, the series diverges.

Next, if we assume k=1 5k - 1 and sum the first few terms of the series, we get:

S = (-1)*4(1) + (-1)*4(2) + (-1)*4(3) + (-1)*4(4) + (-1)*4(5) + (-1)*4(6) + ...

S = -4 -8 -12 -16 -20 -24 -...

We can see that the sum of the series is -4 times the sum of the positive integers, which is a well-known formula with the value of -1/12. Therefore, the sum of the given series is 1/3.

Finally, to determine if the series converges absolutely, converges conditionally, or diverges, we need to check if the absolute value of each term of the series converges or diverges. Since the absolute value of each term is 4k, which increases without bound as k goes to infinity, the series diverges. Therefore, the series converges conditionally.

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Related Questions

Read the numbers and decide what the next number should be. 1 1.25 7 7.50 2 2.25 8

Answers

The next number would be 9.50 because it hours 11.25 to 7 than 7.50

Not sure if I'll ask more questions but please do help!

Answers

Answer:

Drag an drop

$ - \frac{3}{8} \: between \: - 1 \: and \: 0 \\ \\ - 2\frac{1}{2} \: between \: \: \: - 2 \: and \: - 3 \\ $

and

$2\frac{1}{2} \: between \: 2 \: and \: 3 \\ \\ \frac{7}{8} \: between \: 0\: and \: 1\\$

What fraction does point A represent

$What fraction does point A represent$

Answers

Answer:

Are there any options? If so then, I say C

Step-by-step explanation:

I really hope this helped! °ω°

which of the numbered stones shown cannot be mapped to another with a rigid motion?

Answers

Answer:

7,8,11,12,13,14

NO websites or fake links, inappropriate comments, wired, or not helping comments our your reported and show me your steps to each problem

Answers

Answer:

1. They can divide it up so each person gets 2.25 of a cookie.

2. $\frac{1}{12}$

3. $\frac{3}{5}$

4. 4.625

5. $\frac{10}{3}$

Step-by-step explanation:

1. They can each have 9 ÷ 4 = 2.25 of a cookie

2. So we have 4 • 3 = 12 pieces. $\frac{1}{12}$

3. They will get to eat $\frac{3}{5}$ of a bag.

4. 74 ÷ 16 = 4.625

5. Will and his 2 friends = 3 people $\frac{10}{3}$

1. each person would get 2 and a half cookies
2. she had 1/12 of the total cake
3. each friend will get 3/5 bag of chips
4. you can fill 4 whole pitchers and 5/8 of another pitcher
5. each person should get 3 whole candy bars and 1/3 of a candy bar

Using the quadratic formula to solve 2x^2 = 4x - 7, what are the values of x?

Answers

Answer:

Is C.

Step-by-step explanation:

Consider,

2x² = 4x - 7

2x² - 4x + 7 = 0

using Quadratic Formula

Therefore, Option C is correct.

Solve for all three unknowns

I was also hoping for a step by step on how to do this, it’s really confusing me and I just can’t get it.

Answers

Answer:

x= 32.3 (3 s.f.)

θ= 21.8° (1 d.p.)

α= 68.2° (1 d.p.)

Step-by-step explanation:

Applying Pythagoras' Theorem,

x²= 12² +30²

x²= 144 +900

x²= 1044

Square root both sides:

$x = \sqrt{1044} $

x= 32.3 (3s.f.)

$\boxed{ \tanθ = \frac{opp}{adj} }$

$ \tanθ = \frac{12}{30} $

$ θ = \tan^{ - 1} ( \frac{12}{30} )$

θ= 21.801° (3 d.p.)

θ= 21.8° (1 d.p.)

$ \tan\alpha = \frac{30}{12} $

$ \alpha = \tan ^{ - 1} ( \frac{30}{12} )$

$ \alpha $= 68.2° (1 d.p.)

Alternatively,

α +θ +90°= 180° (∠ sum of triangle)

α +21.801° +90°= 180°

α +111.801°= 180°

α= 180° -111.801°

α= 68.199°

α= 68.2° (1 d.p.)

I don't understand this can someone help please

Answers

Answer:

The Money Raised changes by adding 5 per every extra Boxes of Chocolates Sold. constant rate is 5

Step-by-step explanation:

What the question asks is to find whether the rate is constant or not. Since the formula y = 5x (y = Money Raised, k = 5, x = Boxes of Chocolates Sold.) works for the entire table, your answer will be this:

The Money Raised changes by adding 5 per every extra Boxes of Chocolates Sold.

Hope this helps! :D

~Kk

(Not sure if correct, if not I apologize)

Answer:

So the rate of change is 5

because

1*5=5

2*5=10

3*5=15

4*5=20

5*5=25

6*5=30

This equation is Exponential

The Boxes of chocholate sold changes by adding ____ per extra Money Raised

(I cant answer the box because there is no way that it can be adding but, if adding the side boxes then yes it is 5)

Sorry I couldnt complete the adding part but I hope this helps

Step-by-step explanation:

a) what additional info is needed to prove the triangles are congruent by ASA postulate, explain.

b) what additional info is needed to prove the triangles are congruent by the HL theorem, explain.

Answers

Answer:

See below

Step-by-step explanation:

A) If $DF\cong GH$, then both triangles will be congruent by the ASA postulate

B) If $DE\cong GI$, in addition to one of the corresponding leg pairs being congruent to each other (so EF+IH or DF+GH), then the triangles will be congruent by the HL theorem

using 2 jugs of size 100 and 98 gallons, can we measure 3 gallons of water? why? can we measure 4 gallons of water?

Answers

No, we cannot measure 3 gallons of water using 2 jugs of size 100 and 98 gallons. But, we can measure 4 gallons of water using these jugs.

Let's call the two jugs A and B, with A being the 100-gallon jug and B being the 98-gallon jug.

To measure 3 gallons of water, we need to have one jug that is smaller than 3 gallons and another jug that is larger than 3 gallons.

However, both of these jugs are larger than 3 gallons.

This means that it is impossible to measure 3 gallons of water using these jugs.

To measure 4 gallons of water, we can follow these steps:

Fill jug A to the top with water.

Pour the water from jug A into jug B until jug B is full.

This will leave 2 gallons of water in jug A.

Pour the water from jug B down the drain, then pour the 2 gallons from jug A into jug B.

Fill jug A to the top with water.

Pour the water from jug A into jug B until jug B is full.

This will leave 96 gallons of water in jug B, with 4 gallons of water in jug A.

Thus, we can measure 4 gallons of water using these jugs.

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the depth of water in tank a in inches is modeled by a differentiable and increasing function h for

Answers

The depth of water in tank A is modeled by a differentiable and increasing function h.

This means that the function h describes how the depth of water changes as time passes.

The fact that it is differentiable means that the function has a well-defined slope at every point, which indicates how quickly the depth is changing. This means that the function is continuous and smooth, with no sharp turns or corners.
Furthermore, the fact that the function is increasing means that the depth is always getting higher over time.

This makes sense since water is constantly being added to the tank.

Hence, the depth of water in tank A is described by a differentiable and increasing function h, which means that the function has a well-defined slope at every point and that the depth is always getting higher over time.

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Question 4 of 32 Jacob is a construction worker who earns a yearly income given by the expression 2000x + 3000, where x is the number of hours he works each week. Carlos works with Jacob and earns a yearly income given by the expression 3800x – 40000. A manager predicts that if Carlos and Jacob each work 35 hours, they will earn the same amount of money.

PART A:The number of hours that makes the equation true is
Options: 24, 27, 29,31,34

PART B:Round your answer to the nearest whole number. The manager's prediction is
Options: equal to, less than, greater than

the actual number of hours that Carlos and Jacob need to work to earn the same amount of money.

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the expression :

Jacob's yearly income :

2000x + 3000 ; x = number of hours worked per week.

Carlos income :

3800x - 40000

Managers prediction = 35

Jacob.: 2000(35) + 3000 = 73000

Carlos : 3800(35) - 40000 = 93000

Carlos will earn more than Jacob given the manager's prediction.

Number of hours required so they can earn the same amount :

2000x + 3000 = 3800x - 40000

3000 + 40000 = 3800x - 2000x

43000 = 1800x

x = 43000/1800

x = 23.88

x = 24 hours

write the equation of the line in slope-intercept form that has a y-intercept that is -5 and a slope of 8

Answers

Answer:

Step-by-step explanation:

y + 5 = 8(x - 0)

y + 5 = 8x - 0

y = 8x - 5

A, B & C form a triangle where
∠
BAC = 90°.
AB = 12.2 mm and CA = 8.3 mm.
Find the length of BC, giving your answer rounded to 1 DP.

Answers

Answer:

$Pythagoras \ theorem,\\BC^2 = AB^2 + AC^2 = 12.2^2 +8.3^2 =217.73\\\\BC =14.8mm$

(b) an experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. mendel claimed that the proportion of peas with yellow pods should be 25%. we want to know if these data are consistent with mendel's hypothesis. which statistical inference procedures should we use?

Answers

As per Mental hypothesis, the statistical inference procedures that we should use Chi-square test for goodness of fit.

Hypothesis

In probability, an idea or explanation that you then test through study and experimentation is known as hypothesis.

Given,

Here we have given that, an experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. Mendel claimed that the proportion of peas with yellow pods should be 25%. we want to know if these data are consistent with Mendel's hypothesis.

And we need to find in which statistical inference procedures should we use.

According to the definition of Chi-square test for goodness of fit, the claim is that the proportion of peas with yellow pods should be 25%. And then here the researcher wants to check that the experimental and observed counts of yellow offspring peas shows significant difference or not.

So, the statistical procedure used to study this case is Chi-square test for goodness of fit . Hence, option (1) is correct.

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2x2x-2x2 what do u get when u add them together and multiply

Answers

Answer:

4x - 4

Step-by-step explanation:

Hehe just my try hope it helps you(　＾∇＾)

2x2x-2x2 what do u get when u add them together and multiply

1. A woodworker wants to cut a board that is 7.5 feet long into 5 equal-length pieces. How long will each of the cut boards show your work?

Answers

Answer:

it would be 1.5

Step-by-step explanation:

all you have to do is divide 7.5÷5= 1.5

hope this helps

It takes Ryan 1 5 of an hour to bike from home to school. His biking speed is 10 mph.

How far apart are his school and his house?

Answers

Answer:

Step-by-step explanation:

1/5*10

a cannery claims that its sardine cans have a net weight of 8 oz. you take a simple random sample of 30 cans and encounter a sample mean of 7.85 oz, with a standard deviation of 0.1 oz. what is the probability of seeing a sample mean of less than or equal to 7.85 oz if the true mean is 8 oz? report your answer with no more than two decimal places if needed.

Answers

With 95% confidence that the true population mean weight of the sardine cans is between 7.813 oz and 7.887 oz.

What is standard deviation?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

here, we have,

In this scenario, we have a cannery that claims their sardine cans have a net weight of 8 oz. We want to test this claim by taking a simple random sample of 30 cans and measuring their weights

From our sample of 30 cans, we calculated a sample mean of 7.85 oz and a standard deviation of 0.1 oz. The sample mean is an estimate of the population mean, and the standard deviation tells us how much the weights in our sample vary from the mean.

To determine the cutoff values for the middle 95% of the mean weights in this distribution based on the sample data, we can use the t-distribution with n-1 degrees of freedom. The degrees of freedom in this case are 29, which is one less than the sample size.

Using a t-distribution table or calculator, we can find the t-value for a 95% confidence level with 29 degrees of freedom, which is approximately 2.045. We can use this t-value to calculate the margin of error for the sample mean as:

margin of error = t-value * (standard deviation / square root of sample size)

= 2.045 * (0.1 / √(30))

= 0.037

The margin of error tells us how much the sample mean is likely to vary from the true population mean. To find the cutoff values for the middle 95% of the mean weights, we add and subtract the margin of error from the sample mean as follows:

lower cutoff value = sample mean - margin of error

= 7.85 - 0.037

= 7.813

upper cutoff value = sample mean + margin of error

= 7.85 + 0.037

= 7.887

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what is the ordered pair solution for y>= 1/3x+4

Answers

Answer:

Step-by-step explanation:

y > (1/3)x + 4 has an infinite number of solutions. Draw a dashed line representing y = (1/3)x + 4 and then pick points at random on either side of this line. For example, pick (1, 6). Substitute 1 for x in y > (1/3)x + 4 and 6 for y. Is the resulting inequality true? Is 6 > (1/3)(1) + 4 true? YES. So we know that (1, 6) is a solution of y > (1/3)x + 4. Because (1, 6) lies ABOVE the line y = (1/3)x + 4, we can conclude that all points abovve this line are solutions.

x² +12x+27 = 0

Find the roots of each equation by factoring

Answers

Answer:

x = -9, -3

Step-by-step explanation:

$ {x }^{2} + 12x + 27 = 0$

$(x + 3)(x + 9) = 0$

x = -3, -9

Answer:

-3 and -9

Step-by-step explanation:

Standard quaratic form: a² + bx + c = 0

x² + 12x + 27 = 0

find 2 numbers that multiply to 27 (the c-value), but add to 12(the b-value);

The numbers will be 9 and 3, since;

9 x 3 = 27

9 + 3 = 12

Now we can put these numbers in the standard factor form: (x + p) (x + q);

(x + 9) (x + 3) = 0

Now we can set each part equal to 0 and solve;

x + 9 = 0 => x = -9

x + 3 = 0 => x = -3

So the roots are;

-3 and -9

Hope this helps!

This scatter plot shows the relationship between the average study time and the quiz grade. The line of
best fit is shown on the graph.
Explain how you got it please
Need help ASAP!

Answers

The line of best fit represents the trend or average relationship between the average study time and quiz grade. It provides an approximation of the expected quiz grade based on the average study time.

To obtain the line of best fit on a scatter plot, you would typically use a method called linear regression. Linear regression aims to find the best-fitting line that minimizes the overall distance between the line and the data points.

Here's a general overview of the steps involved in obtaining the line of best fit:

Plot the scatter plot with average study time on the x-axis and quiz grade on the y-axis.

Visually observe the distribution of the data points. Look for any overall trend or pattern.

Determine the type of relationship between the variables. In this case, we are looking for a linear relationship.

Use a statistical software or calculator that supports linear regression to perform the analysis. This will generate the equation of the line that best fits the data.

The line of best fit is determined by its slope (m) and y-intercept (b), represented by the equation y = mx + b.

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1.Discuss the population scenario of Dhaka City.? (3 point)

2.How do you want to restructure the population of Dhaka City to mitigate the present traffic jam situation?

Answers

The population scenario of Dhaka City is characterized by rapid urbanization, high population density, and significant population growth.

1. The population scenario of Dhaka City is characterized by rapid urbanization, high population density, and significant population growth. These factors have led to numerous challenges, including increased traffic congestion, inadequate infrastructure, and strain on public services. The city's population is growing at a rapid pace, resulting in overcrowding, housing shortages, and environmental concerns.

2. To mitigate the present traffic jam situation in Dhaka City, a restructuring of the population can be pursued through various strategies. One approach is to promote decentralization by developing satellite towns or encouraging businesses and industries to establish themselves in other regions. This would help reduce the concentration of population and economic activities in the city center. Additionally, improving public transportation systems, including expanding the metro rail network, introducing dedicated bus lanes, and enhancing cycling and pedestrian infrastructure, can provide viable alternatives to private vehicles. Encouraging telecommuting and flexible work arrangements can also help reduce the number of daily commuters. Moreover, urban planning should focus on creating mixed-use neighborhoods with residential, commercial, and recreational spaces to minimize the need for long-distance travel.

By implementing these measures, the population of Dhaka City can be restructured in a way that reduces the strain on transportation systems, alleviates traffic congestion, and creates a more sustainable and livable urban environment.

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Last two questions guys plz answer correctly for 1 more brainliest!!!
Thanks!
:D
Just wanna say thanks to everybody to helped me through this math sheet :3

Answers

Answer:

51. 15×2=30

53. 12×6=72

please mark me as brainliast

Answer:

51.)15×2=30

53.)12×6=72

In which scenarios are surveys appropriate? or when is it appropriate to use experiments?

Answers

Answer:

1. Surveys are used to obtain specific information from a group of people. It is administered by politicians, professionals, sociologists, and other groups to obtain data from their subjects of interest.

2. Experiments are used to establish cause-and-effect relationships. Scientists use them for highly-controlled tests to give/withdraw credence to some hypotheses.

Step-by-step explanation:

Surveys, when applied to human subjects, are used to obtain data from a selected sample of subjects. Surveys, which can be applied through mails, telephones, the internet, in-person, and through other means are aimed at getting the opinions, thoughts, and beliefs of the participants. It is administered by politicians, professionals, sociologists, and other groups to obtain data from their subjects of interest. This data can be qualitative or quantitative.

Experiments are administered to provide support or refute a given hypothesis. They establish cause and effect relationships. Scientists use them for highly-controlled tests to give/deny credence to some hypotheses. Positive controls establish the hypothesis as true. They could be conducted in the laboratory, in the field, or through observations.

4(x+7)=38 find the solution

Answers

Answer:

x=5/2

Step-by-step explanation:

Solve

Distribute

Subtract

from both sides of the equation

4x+28=38

4x+28

Simplify

Subtract the numbers

4x=10

Divide both sides of the equation by the same term

4x=10

Simplify

Cancel terms that are in both the numerator and denominator

Divide the numbers

I think sry if wrong

Answer:

x = 2.5

x = 5/2

Step-by-step explanation:

Distribute

4(x+7)=38

4x +28 =38

Subtract 28 from both sides of the equation

4x + 28 = 38

4x+28-28=38 -28

Simplify

4x = 10

Divide both sides of the equation by the same term

4x/4 = 10/4

Simplify

x = 5/2

Decimal form = x = 2.5

[RevyBreeze]

you have 30 students 1/3 of them walk how many students walk to school

Answers

Answer:

Step-by-step explanation:

30/3=10

Answer:

Step-by-step explanation:

30 ÷ 1/3= 10 so therefore 10 students walk to school.

Another one, thanks in advance!

Answers

Marissa's shape is classified as a scalene and obtuse triangle, considering it's concepts presented in this problem.

How to classify the triangle?

The triangle has three sides of unequal length, as the opposite angle measures are different, hence it is classified as an scalene triangle.

(it would be equilateral if all had the same length, and isosceles if two sides have the same length).

The triangle has one angle larger than 90º, hence it is classified as an obtuse triangle.

(acute with no angles of 90º or greater, right with one angle of exactly 90º).

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Twelve months of sales data are provided in the table below
along with the associated seasonal relatives. This product
experiences a seasonal pattern that repeats every year. Create a
linear regressio

Answers

Linear regression is a technique used in statistics and machine learning to understand the relationship between two variables and how one affects the other.

In this case, we are interested in understanding the relationship between sales and seasonality. We can use linear regression to create a model that predicts sales based on seasonality. Here's how we can do it First, let's plot the data to see if there is a relationship between sales and seasonality.

We can see that there is a clear pattern that repeats every year. This indicates that there is a strong relationship between sales and seasonality. We can use the following equation: y = mx + b, where y is the dependent variable (sales), x is the independent variable (seasonality), m is the slope of the line, and b is the intercept of the line.

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look at the following input/output table and mapping. Determine if the relation is a function and why.