Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. ln(6)/6 + ln(7)/7 + ln(8)/8 + ln(9)/9 + ln(10)/10 + ... integral_1^infinity ln(x + 5)/x + 5 dx = O converges O diverges

Answer:

Tthe length of the A4 sheet of paper is √(1/6m² * √2) and the breadth is √(1/6m² * √2) / √2

Step-by-step explanation:

To calculate the length and breadth of an A4 sheet of paper, we can use the information provided in the problem.

First, we know that the ratio of the length to the breadth is √2:1. This means that for every √2 units of length, there is 1 unit of breadth.

Next, we know that the area of the sheet is 1/6m². To find the length and breadth, we can use the formula for the area of a rectangle, which is length x breadth.

So, we can set up the equation:

(length) x (breadth) = 1/6m²

We can then use the information about the ratio of length to breadth to set up a proportion:

length/breadth = √2/1

Now we can cross-multiply and substitute this proportion into our area equation:

length x breadth = 1/6m²

length x (length/√2) = 1/6m²

length^2 = 1/6m² * √2

length = √(1/6m² * √2)

To find the breadth we can use proportionality again

breadth = length/√2

So, the length of the A4 sheet of paper is √(1/6m² * √2) and the breadth is √(1/6m² * √2) / √2

The number of sausage rolls is 8 and the chicken pie is 12.

How many of each item did she buy?

The first step is to form a system of equations using the information in the question:

c + s= 20 equation 1

2.50c - 1.50s = 18 equation 2

Where:

c = number of chicken pies bought

s = number of sausage rolls bought

The elimination method would be used to determine the required values.

Multiply equation 1 by 2.50

2.5c + 2.5s = 50 equation 3

Subtract equation 2 from equation 3:

4s = 32

Divide both sides of the equation by 4

s = 32 / 4

s = 8

Substitute for s in equation 1:

c + 8= 20

c = 20 - 8

c = 12

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The answer to the query is that $14.28 is left on your credit throughout 44 minutes of calls.

When any term's greatest degree is two or higher, an equation is said to be nonlinear. This is a sample of a numerical solution since formula has the highest degree of 2, whereas equation 2 includes the variables x and y. 3x + 4y = 5, etc., where + 2x + 1 = 0.

Let y be the remaining credit (in dollars) and x be the calling time (in minutes). Based on the information given, we have two points on the line: (24, 16.88) and (38, 15.06).

Using these two points, we can find the equation of the line using the point-slope form:

y - 16.88 = m(x - 24)

where m is the slope of the line. Substitute one of the points to find m:

15.06 - 16.88 = m(38 - 24)

-1.82 = m(14)

m = -1.82/14 = -0.13

Now we have the slope of the line, we can write the equation of the line using the point-slope form:

y - 16.88 = -0.13(x - 24)

To find the remaining credit after 44 minutes, substitute x = 44 into the equation:

y = -0.13(44 - 24) + 16.88

y = -0.13(20) + 16.88

y = 16.88 - 2.6

y = 14.28

So the remaining credit after 44 minutes of calls is $14.28.

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Answer:

the answer is diet coke divided by the square root times the 10/4

Step-by-step explanation:

The manager is mistaken in believing that the set of integers is the best domain for this model. The domain in this case represents the times of day when shoes were sold.

Hours are continuous values that can be any real number between 0 and 24. As a result, a set of real numbers such as 0 = t = 14, where t represents the hour of the day, would be a better domain for this model.

The manager wants to achieve by analyzing the data. This could be to gain insights into customer behavior, identify areas for improvement, measure the success of marketing efforts, etc.

The domain of integers would be appropriate only if the number of pairs of shoes sold could only be an integer value, which is not the case for online shoe sales.

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$2360 was invested at 7% and $1910 was invested at 8% to get a total interest of $318

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of money invested at 7% and y represent the amount of money invested at 8%.

The total interest is $318, hence:

0.07x + 0.08y = 318   (1)

she has $450 more in the 8% account, hence:

y = x + 450    (2)

Solving both equations simultaneously:

x = 2360, y = 1910

$2360 was invested at 7% and $1910 was invested at 8%.

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Answer:

To solve for x, you can use the equation 6x = 5. This gives x = 5/6.

In a case whereby formula for the area of a triangle is A=1/2bh. Kevins answer for the area of this triangle is 40 inches2, then Kevins solution is not correct because the correct solution is 20inches.

The concep[t that will be used is the area of triangle, The area of the triangle can be calculated using

A=1/2bh

where  A = area

b = base=5

h= height =8

then A=1/2*8*5= 20 inches

Therefore, the correct area of triangle from the fiqure is 20 inches

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Answer: The area of the rectangular region is 27 m².

Step by step explanation:

Data :

We calculate the area taking into account the formula that I will give you:

[tex] \bold{A = b * h }[/tex]

We simplify according to the given formula:

[tex]\bf A = 9(3)[/tex]

[tex]\boxed{ \bf A = 27 \: {m}^{2} }[/tex]

Rpt: The area of the rectangular region is 27 m².

Answer:

Below

Step-by-step explanation:

A.) Finding velocity from position requires deriving it

s' = v(t) = 21t^2 + 5

B.) Now it's plug and play

v(3) = 21(3)^2 + 5

= 21(9)+5

=194m/s

C.) Same thing, well derive the v(t)

v' = 42t

D.) One more plug and play

a = 42(3)

= 126m/s^2

The required cost of the computer after 3 years is given as $548.43.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Here,
A laptop computers purchase for $1300 after each year the resale value decreases by 25%.
Price of the laptop after x years,

y = 1300[1 - 0.25]ˣ

Put x = 3
y = 1300[0.75]³

y =  $548.43

Thus, the required cost of the computer after 3 years is given as $548.43.

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Answer: I'm sorry, but I'm unable to answer your question as you haven't provided any information about the minimum payment that he must make to CreditFirst and Sun Money. Please provide more details and I'll do my best to help you.

Step-by-step explanation:

Answer:

No.C 5 is the correct answer

Answer:

c is the correct answer..

Answer:

Step-by-step explanation:

Labor rate: $60/hr

Labor time: 0.3hr

Labor cost= 60*0.3=$18

Battery cost= $69.95

Tax=5%

Total battery cost is 69.95*1.05= 73.4475≈$73.45

Total cost= $73.45+$18= $91.45

The total bill with 6 percent of tax is $36.87, for which the server must be paid one $20 bill, one $10 bill, one $5 bill, one $1 bill and 0.87 pennies.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

The amount for total bill is $34.78.

The sales tax percentage added is 6%.

The total bill including tax will be -

Final Bill = Total Bill + (Total Bill × tax)

Substitute the values into the equation -

Final Bill = 34.78 + (34.78 × 6%)

Final Bill = 34.78 + (34.78 × 0.06)

Final Bill = 34.78 + 2.0868

Final Bill = 36.8668 ≈ 36.87

Therefore, the final bill is $36.87.

The amount of $20 bill = 1

The amount of $10 bills = 2

The amount of $5 bills = 1

The amount of $1 bills = 5

The amount of pennies = x

So, the amount of bill given to server to make a total of $36.87 is -

1 × ($20) + 1 × ($10) + 1 × ($5) + 1 × ($1) + x = $36.87

20 + 10 + 5 + 1 + x = 36.87

36 + x = 36.87

x = 36.87 - 36

x = 0.87

Therefore, along with 1 bill each 0.87 pennies should be given to the server.

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The correct answer is option B.

The entire length of hose

Since the early 17th century, primrose and cowslip have been cultivated as Hose in Hose mutants, which exhibit strong homeotic sepal to petal conversion. The S locus, which regulates floral heteromorphy in Primula species, is linked to the phenotypic, which exhibits varying penetrance and expressivity. Here, we show that the primrose B-function MADS box genes PvDef and PvGlo are upregulated in the first floral whorl in association with the homeotic conversion of sepals to petals in Hose in Hose. We have found and characterized a retrotransposon insertion in the PvGlo promoter that is connected to the up-regulated expression of PvGlo, as well as a restriction fragment length polymorphism linked with PvGlo that cosegregates with the Hose in Hose phenotype.

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Answer:

The patient's blood sugar levels should stay within the range of 73 to 93 milligrams per deciliter in order to be considered within the normal range. Any blood sugar level below 73 milligrams per deciliter or above 93 milligrams per deciliter should be monitored closely and adjustments may need to be made to their diet or medications.

Based on the information in the graph, we can infer that the correct answer is A. None of the above, since none of the options represents the intersection of the set A and B.

The symbol ∩ is used in set theory to refer to the set that contains all those elements that A and B have in common.

Based on the above, we can infer that this refers to the central set in which the number 1 is found. However, none of the options have this value, so the correct answer would be A. none of the above.

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The measure of angle AOB is 180°.

Since COE and BOD are right angles, the measure of both angles is 90°.

The measure of COD is 1/4th of the measure of BOC, which is 90°. Therefore, the measure of COD is 90/4 = 22.5°.

Adding the measures of all three angles gives us 180°.

Therefore, the measure of AOB = 180 - (90 + 22.5) = 67.5°

Step-by-step explanation:

The equation of the function is y = 1/2x.

Random sampling is a method of selecting a sample of items from a population in which the probabilities of selecting each item are the same.

Random sampling is used to ensure that each item in the population has an equal opportunity to be selected in the sample.

In this scenario, a random sample of size 40 is needed from a population of 200 items. The random start of 4 will be used to begin the sample selection process.

To begin, a list of all the items in the population should be created. Then, a random number generator can be used to select the first item in the sample, based on the random start of 4.

The next item in the sample should be selected at random from the remaining items in the population, and so on until the desired sample of 40 items is obtained.

Random sampling is an important method for ensuring that a sample is representative of the population it is drawn from.

This method helps to eliminate bias from the sample selection process and ensures that the sample accurately reflects the characteristics of the population.

Random sampling is used in many areas of research, including surveys, data collection, and experiments.

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The complete question is: Given a population of 200 items, select A sample of size 40 using a random number 4.

The value of C is 1/3 for the probability density function f(x)=cx , 0<x<2.

The probability density function is a function of a continuous random variable, whose integral across an interval gives the probability that the value of the variable lies within the same interval.

Given that the function as;

f(x)={cx} ,at 0,

0≤x≤2

Here, we can see that the value of x is varies as 0,1,2

So, at 0,1,2 the value of the function is

f(1) = c

f(2) = 2c

Thus, the probability density function is given as:

f(x) = f(1) + f(2)

f(x) =c + 2c = 1

3c = 1

c = 1/3

Therefore, the value of C=1/3

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This fraction can be simplified to its lowest terms, which is 8/15.

In mathematics, a fraction is in its lowest terms when its numerator and denominator cannot be divided by any other number than one. This means that the numerator and denominator of the fraction do not share any common factors, except one. To convert a fraction to its lowest terms, divide the numerator and denominator by any common factors they may have.

To solve this problem, we need to first convert both fractions to have the same denominator. To do this,

we can multiply the denominator of 4/9 by 5/5,

which is equal to 20/45.

Then, we can multiply the denominator of 6/15 by 3/3,

which is equal to 18/45.

Now that both denominators are the same,

we can add the numerators together to get a sum of 8/15.

This fraction can be simplified to its lowest terms,

which is 8/15.

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Answer: The equation -0.67x + 0.47x = 6.4 is equivalent to -0.2x = 6.4

Step-by-step explanation: To solve this equation for x, we can divide both sides of the equation by -0.2

x = 6.4 / -0.2

x = -32

Therefore, x = -32 is the solution to the equation -0.67x + 0.47x = 6.4

This solution represents the value of x that makes the equation true.

Answer:

approximately 87,178,291,200

Step-by-step explanation:

The number of ways to arrange the letters of the word 'jvuyojzrxccome' is 14! (14 factorial), since there are 14 distinct letters in the word. This is a very large number, approximately 87,178,291,200.

To fit the mascot's digital image on the school's Web page, it needs to be resized. To determine the largest image that will fit, we need to find the aspect ratio of the Web page and the aspect ratio of the digital image and keep the aspect ratio the same after resizing.

How is the ratio defined?

A ratio depicts the quantity of one object in relation to another. Ordinarily, ratios are expressed in the format a:b. If you're preparing orange squash, the ratio of orange to water will be one part orange to four parts water (1 to 4).

The aspect ratio of the Web page is 176 pixels wide / 110 pixels high = 1.6.

The aspect ratio of the digital image is 600 pixels wide / 375 pixels high = 1.6.

Since both aspect ratios are the same, we can simply choose the smaller dimension from the Web page (110 pixels) to determine the size of the resized image.

So, the resized image will be 110 pixels high and the width will be 110 pixels * 1.6 aspect ratio = 176 pixels.

Therefore, the largest image of the mascot that will fit on the Web page is 176 pixels wide by 110 pixels high.

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The line with slope -2 through the point (-13, 21) is y = -2x + b where b= y intercept, found by plugging in the values x=-13 and y=21.

21 =-2(-13) + b

b = 21 -26 = -5

y =-2x -5 is the equation in slope intercept form

or

2x +y =-5 in standard form the graph is a downward sloping straight line

y intercept is (0,-5), x intercept is (-5/2, 0) = (-2 1/2, 0)

plot those two points,  connect them with a straight line

add arrows on both ends of the line to indicate the line goes forever in both directions

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The best course grade your friend can earn is 92%.

To earn a 75% for the course, your friend would need to score a minimum of 18.75% on the final exam.

This is calculated by:

(0.75 - 0.82) / 0.25

= (0.18) / 0.25

= 0.1875 or 18.75%.

As a result, the best course grade your friend can earn is 92% and the your friend would need to score a minimum of 18.75% on the final exam.

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The limit of the function [tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] is 12 and from the graph, we can say that for x = 2, g (x) is continuous while f (x) is not.

The function is [tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex].

We firstly simplify the expression.

We can write the function as:

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] = [tex]\lim_{x\rightarrow 2}\frac{(x)^3-(2)^3}{x-2}[/tex]

Using the formula, [tex](a)^3-(b)^3 = (a-b)(a^2+ab+b^2)[/tex]

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] = [tex]\lim_{x\rightarrow 2}\frac{(x-2)(x^2+2x+4)}{x-2}[/tex]

Simplify

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] = [tex]\lim_{x\rightarrow 2}[/tex](x^2 + 2x + 4)

Using, [tex]\lim_{x\rightarrow c}[/tex] f(x) = f(c)

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] = [(2)^2 + 2×2 + 4]

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] = (4 + 4 + 4)

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex] = 12

We have [tex]\frac{x^3-8}{x-2}[/tex] = (x^2 + 2x + 4)

So the simpler function is

g(x) = (x^2 + 2x + 4)

that agrees with the function f(x) = [tex]\frac{x^3-8}{x-2}[/tex] except x = 2.

Now we graph the function f(x) and g(x).

We can see that for x = 2, g (x) is continuous while f (x) is not.

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The complete question is:

Write a simpler function that agrees with the given function at all but one point. Then find the limit of the function. Use a graphing utility to confirm your result.

[tex]\lim_{x\rightarrow 2}\frac{x^3-8}{x-2}[/tex]

Answer:

(1,-9) or d(0,9) ahahahshaiaiahsiaoajaj

Answer:

(1,-9), (-1,-9)

Step-by-step explanation:

Given:  y+9=0

Therefore: y=-9