Use the Integral Test to determine whether the series is convergent or divergent. 9 n= 1 Evaluate the following integral. oo 9 dx 5 х 0 X finite, the series is divergent Since the integral is not Need Help? Talk to a Tutor Read It Watch It Master It
Expert Answer

Answer:

A

Step-by-step explanation:

To find the perpendicular line you need to find the negative reciprocal of 4/7x which is -7/4x, so A is the correct answer

I hope this helps!!

Answer: x = 3/4

Step-by-step explanation:

1/3x + 3 = 4 - x

Subtract 3 from both sides

1/3x = 1 - x

Then times 3 from both sides

x = 3 - 3x

Add 3x on both sides

4x = 3

Divided by 4, both side

x = 3/4

Answer:

do you mean this 2/x=16

or this 2^x=16

The smallest sample in the following list that meets the requirements for using a normal model to depict the sampling distribution is 0.0349.

A standard deviation (or) is a measure of how widely distributed the data is in reference to the mean. A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out. Statisticians have concluded that numbers with a margin of error of no more than 2 SD reflect measures that are closer to the real value than those with a margin of error more than 2SD. As a result, most QC procedures mandate that remedial action be taken for data points that consistently fall outside of the 2SD range.

Here,

Probability that students surveyed rarely or never use academic advising services = 32% = 0.32

In reality, students rarely or never use academic advising services at their college = 42% = 0.42

Sample size, n = 200

The sampling distribution of sample proportion will be approximately normal with mean.

therefore,

Mean, = p

= 0.42

now, the standard deviation is given using the formula

on substituting the respective values, we get

= √0.001218

= 0.0349

The smallest sample in the list below that will satisfy the conditions for the use of a normal model to represent the sampling distribution is 0.0349.

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The equation representing the area of the burn, `a`, after `t` weeks is \(`a = a_0 e^{-kt}`\), where `a_0` is the initial area and `k` is the rate of decay. After 7 weeks, the area of the burn is\(`a_0 e^{-7k}`\).

To calculate the fraction of the burn area remaining each week, we must first write an equation representing the area of the burn, `a`, after `t` weeks. This equation is given by \(`a = a_0 e^{-kt}`\), where `a_0` is the initial area and `k` is the rate of decay.

To calculate the area of the burn after 7 weeks, we plug `t = 7` into the equation, giving us \(`a = a_0 e^{-7k}`\). To calculate `k`, we can use the initial area and the area after 1 week. We plug these values into the equation, giving us \(`a_0 = a_1 e^{-k}`\). We then solve for `k`, giving us `k = ln(a_1/a_0)`.

Finally, we plug `k` and `t = 7` into the equation, giving us `\(a = a_0 e^{-7ln(a_1/a_0)}`.\) This is the area of the burn after 7 weeks.

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\(4x^2 - 38x + 34 = 0\) ; This is a quadratic equation that can be solved using the quadratic formula. Once we solve for x, we can find the width of the border.

Let's assume that the width of the border around the text is x inches. Then the dimensions of the rectangle including the border will be:

Length = 11 inches

Width = 8 inches

The dimensions of the rectangle containing only the text will be:

Length = 11 - 2x inches (because there are two borders, one on each side)

Width = 8 - 2x inches (because there are two borders, one at the top and one at the bottom)

The area of the rectangle containing only the text will be:

Area = (11 - 2x) × (8 - 2x)

We know that the area of the rectangle containing only the text is 54 square inches. So we can set up the equation:

(11 - 2x) × (8 - 2x) = 54

Expanding the left-hand side of the equation, we get:

\(88 - 38x + 4x^2 = 54\)

Rearranging and simplifying, we get:

\(4x^2 - 38x + 34 = 0\)

This is a quadratic equation that can be solved using the quadratic formula. Once we solve for x, we can find the width of the border.

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Answer:

I think the answer is 94 1/2

Andrea has 28 stuffed animals, while Tyronne has 14 stuffed animals.

Let's represent the number of stuffed animals in Tyronne's collection as "x." According to the given information, Andrea has 2 times as many stuffed animals as Tyronne, so the number of stuffed animals in Andrea's collection can be represented as "2x."

The total number of stuffed animals in their collections is 42, so we can write the equation:

x + 2x = 42

3x = 42

Dividing both sides by 3, we find:

x = 14

Therefore, Tyronne has 14 stuffed animals.

Andrea's collection has 2 times as many stuffed animals, so we can calculate Andrea's collection:

2x = 2 * 14 = 28

Therefore, Andrea has 28 stuffed animals.

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Solution

For this case we can do the following:

Answer:

x = -100

Step-by-step explanation:

They cancel each other out

Answer:

-100

Step-by-step explanation:

-100 +100=0

They cancel each other out.

Answer:

8 feet

Step-by-step explanation:

w = width

2s = length

Find 'w' by multiplying the new dimensions:

(w+5)(2w+3) = 2w² + 3w + 10w + 15 = 99

simplify:

2w² + 13w - 84 = 0

Factor:

(2w + 21)(w - 4) = 0

w = -21/2   ** disregard because a measurement cannot be negative **

w = 4

original width was 4

orginal length was twice 4 or 8 feet

Answer:

gradient = \(\frac{1}{2}\) , y- intercept = - \(\frac{3}{2}\)

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope ( gradient) and c the y- intercept )

given

x - 2y = 3 ( subtract x from both sides )

- 2y = - x + 3 ( divide through by - 2 )

y = \(\frac{-1}{-2}\) x + \(\frac{3}{-2}\) = \(\frac{1}{2}\) x - \(\frac{3}{2}\) ← in slope- intercept form

with gradient m = \(\frac{1}{2}\) and y- intercept c = - \(\frac{3}{2}\)

Answer:

Step-by-step explanation:

Answer:

isabel saves the most of their salary each month

Step-by-step explanation:

Let us assume the Salary of Gavin, Harry & Isabel be $100

Since

Gavin saves 28%

So his saving amount is Gavin

= 28% of $100

= $28

As harry spends 3 ÷ 4 of his salary

So Harry Spenings is

= (3  ÷ 4) of $100

= $75

Now

Harry Saving is

= $100 - $75  

= $25

Also the ratio between isabel saves, and spend is 3:7

3k + 7k = 10k = 100S

 k = $10

Now

the amount of salary isabel saves

= 3k

= 3 × $10

= $30

Now

$30 > $28 > $25

i.e.

isabel Saving >  Gavin Savings > Harry Savings

Hence, isabel saves the most of their salary each month

Here is the set up:

A = area of rectangular garden = 6/7.

Let l = length = 3/5.

Let w = width

A = lw

6/7 = (3/5)w

Solve for w.

Answer:

Please read the assumptions that lead to the proposed answer of options a, b, and e being correct.  Options c and d are easily rejected.  The question is ambiguous about the locations of the angles.

Step-by-step explanation:

Parallel lines have slopes that are identical.  Lines p and q have the same slopes.

It is difficult imagining what angles are represented by x, y, and z.  There are only 2 lines, and they do not intersect.  The locations of the angles are not identified.  The lack of an intersecting point means it is free range as to where we assign the angles.

The attached graph illustrates some possibilities for x, y, and z.  It uses two simple equations as examples, with the same slope to make them parallel.  Assinment of any angles requires the use of an imaginary line that intersects the two parallel lines.  Even then, there aren't many unique locations for the angles.  To illustrate the analysis, lets assign the angles x, y, and z to thelocations shown on the graph.  

Even with this huge step, there is limited information to be able to identify which of the answer options is correct.  We can say that:

x = z

x+y=180

y+z=180

The answer options (below) appear to have similar relationships, so let's agree that the use of the imaginary line, plus the locations of x, y, and z are valid.  Looking at the answer options, we can match choices a, b, and e to the conclusions above.  d makes no sense because it is not an equation.  c says that both lines must be perpendicular to the x axis, a limitation that is relatively immaterial to whether they are parallel.  The condition of being parallel depends on those two angles being the same (e.g., 45 and 45, 22 and 22, etc.) and not require that they both be 90.

Answer Options               Guarantee Parallel?

a. x = z                                     Yes

b. x + y = 180 degree              Yes

c. x + z = 180 degree              No

d. x + y                                     No

e. y + z = 180                           Yes

(i) The exact values of a,b and the function f(r) are a=b=4, f(r)=1-r2

(ii) The triple integral V in cylindrical coordinates form is 8π/5, in terms of π

The triple integral in cartesian coordinates is given by V=∫ 0 1​ ∫ 0 1−y2​ ​ ∫ 0 4−x2−y2​ ​ zdzdxdy.

(i) The given triple integral is V=∫ 0 1​ ∫ 0 1−y2​ ​ ∫ 0 4−x2−y2​ ​ zdzdxdy

Convert it into cylindrical coordinates .The volume element is

dV=r dz dr dθ

Given that V=∫ 0 1​ ∫ 0 1−y2​ ​ ∫ 0 4−x2−y2​ ​ zdzdxdy

The bounds of the triple integral in cylindrical coordinates are as follows: Volume of a cylinder of radius r and height h is given by

V=πr2h

=πa2b

=∫ 0a​ ∫ 0b​ ∫

0f(r)​ rzdzdrdθ.

On comparing the above expressions with the volume element in cylindrical coordinates,

a=b=4, f(r)=1-r2

(ii) Now, the triple integral in cylindrical coordinates is

∫ 0 4​ ∫ 0 4​ ∫ 0 1-r2​ rzdzdrdθ

=π∫ 0 4​ ∫ 0 1-r2​ r2zdzdr

=π∫ 0 4​ [r2z/2]01-r2​ dr

=π∫ 0 4​ [r2(1-r2/2)] dr

=π(2/15)×(43)=8π/5

Thus, the triple integral V in cylindrical coordinates form is 8π/5, in terms of π.

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The rectangular coordinates (in simplest radical form) are (2, -2√3).

To convert polar coordinates (r, θ) into rectangular or Cartesian form (x, y), we can use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

In this case, the polar coordinates are (4, 5π/3). Therefore, we have:

r = 4

θ = 5π/3

Using the formulas, we can calculate the rectangular coordinates as follows:

x = 4 * cos(5π/3)

y = 4 * sin(5π/3)

To evaluate cos(5π/3) and sin(5π/3), we can use the unit circle or trigonometric identities.

In the unit circle, we know that cos(5π/3) = cos(π/3) = 1/2, and sin(5π/3) = -sin(π/3) = -√3/2.

Substituting these values into the formulas:

x = 4 * (1/2) = 2

y = 4 * (-√3/2) = -2√3

Therefore, the rectangular coordinates (in simplest radical form) are (2, -2√3).

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Given question is incomplete, the complete question is below:

Convert the polar coordinates (4, 5π/3) into rectangular form. Express your answer in simplest radical form.

A direct, consistent relationship between the independent variable and the dependent variable is called "dose-response relationship."

The effect on an organism and, more specifically, the risk of a defined outcome caused by a set quantity of an agent or level of exposure.

Some key features regarding the dose-response relationship are-

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The reliability function is a useful tool for modeling the probability of failure of a system over time. And the probability of failure within 400 hours is approximately 14%.

The reliability function is a common tool used to model the probability of failure of a system over time. In this case, we will use an exponential distribution to model the failure rate of a light bulb.

Assuming an exponential distribution, a particular light bulb has a failure rate of 0.002. The failure rate is the average number of failures per unit of time. The exponential distribution has the property that the probability of failure is proportional to the length of time the system has been in operation.

The reliability function for an exponential distribution is given by R(t) = e^(-λt), where λ is the failure rate. The reliability function gives the probability that the system will still be functioning after t units of time.

So, the probability of failure within 400 hours is given by 1 - R(400), where R(400) is the reliability function evaluated at 400 hours.

1 - R(400) = 1 - e^(-0.002 * 400) = approximately 0.14

So, the probability of failure within 400 hours is approximately 14%.

By assuming an exponential distribution, the reliability function is given by R(t) = e^(-λt), where λ is the failure rate. In this case, the reliability function can be used to calculate the probability of failure within a given time period, such as 400 hours for the light bulb.

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Based on the advertiser's decision to reject the null hypothesis, the conclusion is that there is evidence to suggest that more than 61% of the newsletter publisher's readers own a Rolls Royce.

Based on the given information, the newsletter publisher believes that over 61% of their readers own a Rolls Royce.

The potential advertiser conducted a test at the 0.02 level of significance to verify this claim and decided to reject the null hypothesis.

In hypothesis testing, the null hypothesis (H0) typically represents the claim or assumption being tested, while the alternative hypothesis (Ha) represents the claim that opposes the null hypothesis.

The null hypothesis would be that 61% or fewer readers own a Rolls Royce, while the alternative hypothesis would be that more than 61% of the readers own a Rolls Royce.

Since the advertiser rejected the null hypothesis at the 0.02 level of significance, it means that the observed data provided strong evidence against the claim that 61% or fewer readers own a Rolls Royce.

The decision to reject the null hypothesis suggests that there is sufficient evidence to support the alternative hypothesis, which states that more than 61% of the readers own a Rolls Royce.

It's important to note that the conclusion does not provide an exact percentage or statistical evidence supporting the alternative hypothesis. It only indicates that the observed data was significant enough to reject the claim of 61% or fewer Rolls Royce owners among the readers.

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The true statement is that the radius is 10

From the question, we have the following parameters that can be used in our computation:

A circle has a diameter of 20

This means that

Diameter = 20

Divide both sides by 2 to determine the radius

So, we have

Radius = 10

This means that the true statement is that the radius is 10

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Step-by-step explanation:

(0,5) and (-2,-3)

y=mx+b

find m

\( \frac{y1 - y2}{x1 - x2} \\ = \frac{5 - ( - 3)}{0 - ( - 2)} \\ = \frac{8}{2} \\ = 4 \\ \)

m=4

Substitute (0,5) or (-2,-3)

For easy processing substitute : (0,5)

y=4x+b

5=b

y=4x+5 is the answer

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Answer:

c

Step-by-step explanation:

because you can simplify 4/6 by 2.

2 goes into 4 twice and then 2 goes into 6 3 times

2/3

Answer:

2. y - (-5) = -3 (x - 5)

3. y = -5/2

Step-by-step explanation:

Point intercept form: y - y₁ = m (x - x₁)

Where y and x are just kept as y and x, y₁ and x₁ are the parts of a coordinate, and m = slope.

2. The points are (5, -5) and the slope is -3. Plug this into y - y₁ = m (x - x₁) to get

y - (-5) = -3 (x - 5)

3. As stated, parallel lines have the same slope, so the slope of the line would be -5/2. The origin is (0, 0), so plug these two numbers in.

y - y₁ = m (x - x₁)

y - 0 = -5/2 (x - 0)

y = -5/2

In statistics, a hypothesis is an assumption about a population parameter. A research question is a question that a research study intends to answer. In research studies, hypotheses and research questions are used to guide the research process and help researchers to focus their attention on specific topics.

The following are examples of potential hypotheses or research questions to relate variables in each of the following examples.
Example 1:
Variables: Gender and job satisfaction
Research Question: Does gender have an impact on job satisfaction?
Hypothesis: Job satisfaction is not dependent on gender.

Example 2:
Variables: Education and income
Research Question: Is there a relationship between education and income?
Hypothesis: There is a positive relationship between education and income.

Example 3:
Variables: Exercise and mental health
Research Question: Does exercise have a positive effect on mental health?
Hypothesis: Exercise is associated with improved mental health.

Example 4:
Variables: Age and technology use
Research Question: Is there a relationship between age and technology use?
Hypothesis: Younger people use technology more than older people.

Example 5:
Variables: Stress and sleep
Research Question: Does stress affect sleep quality?
Hypothesis: Higher levels of stress lead to poorer sleep quality.
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Using trigonometric ratio and the angle of elevation given, the height of the antenna is 4.5m

Using trigonometric ratio;

tan(41°) = height of building / 16 meters

height of building = 16 meters * tan(41°)

height of building =13.91 m

We also know that the angle of elevation from Kayden's eyes to the top of the antenna is 49°. This means that the tangent of 49° is equal to the height of the antenna plus the height of the building divided by 16 meters. We can use this to find the height of the antenna:

tan(49°) = (height of antenna + height of building) / 16 meters

height of antenna + height of building = 16 meters * tan(49°)

`

height of antenna + 13.91 meters = 16 meters * tan(49°)

height of antenna = 16 meters * tan(49°) - 13.91 meters

height of antenna = 4.5 meters

The height of the antenna = 5m

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Answer:

The solutions to x^2-2x-1=0 are the same as the solutions to x^2-2=2x-1

Step-by-step explanation:

hope this helps

Answer:

The volume is multiplied by 8.

Step by step explanation:

Let the length equal l, the width equal w, and the height equal h for the original rectangular prism.

The volume of a right rectangular prism with length l, width w, and height h is V=lwh.

Therefore, the volume of the original prism is lwh.

The new rectangular prism has dimensions that are twice those of the original rectangular prism: the length equals 2l, the width equals 2w, and the height equals 2h.

To calculate the volume of the rectangular prism, substitute the doubled values into the formula for the volume of a rectangular prism.

V=2l·2w·2h

Simplify.

V=8lwh

The new volume is 8lwh.

If the length, width, and height of a right rectangular prism are doubled, the volume is multiplied by 8.

Therefore, the new volume is the original volume multiplied by 8.