Determine whether the following series converges or diverges. In the case of convergence, state whether the convergence is conditional or absolute. sigma^infinity_k = 0 9(-1)^k/k^4 + 2 Which test should be used to test whether the given series converges? The Test with a_k = Find lim_k rightarrow infinity a_k. lim_k rightarrow infinity a_k = Are the terms of the series nonincreasing in magnitude for k greater than some index N? A. Yes. because there is an exponent in the denominator and whenever there is an exponent in the denominator, the terms of a series are nonincreasing in magnitude. B. No. only the first two terms of the series are nonincreasing in magnitude, and the rest of the terms increase. C. No. only the first five terms of the series are nonincreasing in magnitude, and the rest of the terms increase. D. Yes. all the terms of the series are nonincreasing in magnitude. Does the series converge or diverge? A. The series diverges. B. The series converges. In the case of convergence, state whether the convergence is conditional or absolute. Choose the correct answer below. A. From the Limit Comparison Test, the series converges conditionally. B. From the Integral Test, the series converges absolutely. C. From the Limit Comparison Test, the series converges absolutely. D. From the Integral Test, the series converges conditionally. E. The series diverges.

Over the line y = x, a function and its inverse are reflected. It only takes one step to graph a function and its inverse: first, graph the function, then, to graph the inverse, switch all x and y values at each point.

Given,

Inverse function;

A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "f-1" or "F-1."

Here,

To graph the inverse, you only need to alter the x and y values in each point on the function graph. Just take a look at all the numbers that are being reflected along the line y = x as they move from the f(x) function to its inverse g(x) and back again.

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The probability that Hamid guesses both answers correctly is 10%.

Probability means that it is possible. It is a branch of statistics that deals with the occurrence of a random event. The number is expressed from 0 to 1 where 0 represents an impossible event and 1 represents a sure event.

Probability Formula

The probability formula is defined as the ratio of favorable outcomes to the ratio of total outcomes. For any event (E), this can be shown as

P(E)=Number of favorable outcomes /Number of total outcomes

Since Hamid is playing a trivia game with multiple choice questions, and each question has 2 correct answers among 5 answer choices, and Hamid has no idea what the answers to a certain question are, so he needs to choose two different answers at random, to determine what is the probability that Hamid guesses both answers correctly the following calculation must be performed:

2/5 x 1/4 = X

0.4 x 0.25 = X

0.1 = X

0.1 x 100 = 10

Therefore, the probability that Hamid guesses both answers correctly is 10%.

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Probability denotes possibility. The occurrence of a random event is the subject of this area of statistics. The number is expressed as a number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event.

Statistical Formula

The ratio of favorable outcomes to the ratio of all outcomes is the definition of the probability formula. This can be shown as for any event (E) as

P(E) = Number of positive results / Number of total results

Given that each question in a multiple-choice trivia game has two correct answers out of a possible five, and that Hamid must choose two answers at random because he doesn't know what the answers are, the following calculation must be done to ascertain the likelihood that Hamid will correctly guess both answers:

2/5 x 1/4 = X

0.4 x 0.25 = X

0.1 = X

0.1 x 100 = 10

The nature of the roots of the equation 5x² + 3x + 2 = 0 are x = -7.123 and x = 0.878.

The equation 5x² + 3x + 2 = 0 has two solutions, or roots, which can be found using the quadratic formula:

x = [-b ± √(b² - 4ac)] / 2a

Where a = 5, b = 3 and c = 2,

x = [-3 ± √(3² - 4(5)(2))] / 2(5)

x = [-3 ± √17] / 10

x = (-3 ± 4.123) / 10

x = (-7.123) / 10,  0.878

The roots of the equation 5x² + 3x + 2 = 0 are x = -7.123 and x = 0.878.

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I don't see the picture. Can you send it in the message.

Answer:

x     0    2    4    6

y     3    4    5    6

Step-by-step explanation:

y = x/2 + 3

x = 0

y = 0/2 + 3 = 0 + 3 = 3

x = 2

y = 2/2 + 3 = 1 + 3 = 4

x = 4

y = 4/2 + 3 = 2 + 3 = 5

x = 6

y = 6/2 + 3 = 3 + 3 = 6

Examples of perpendicular slope are the sides of a fixed square, a window, and the Red Cross emblem.

Lines that are vertical and horizontal are perpendicular to one another. In this instance, the perpendicular line's slope would be equal to a horizontal line's slope, which would be 0. The slope of the perpendicular line is zero, but the slope of the parallel line is unknown. By taking the negative reciprocal of the slope of the provided line, one can determine the slope of a perpendicular line from that line. We obtain m2 = -1/m1 if the slope of the provided line is m1 and the slope of a perpendicular line is m2.

Given

There are a lot of perpendicular lines that we may see in reality. The corners of the chalkboard, the arms of a clock at specific times of the day, the sides of a fixed square, a window, and the Red Cross emblem are a few examples.

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Answer:

Step-by-step explanation:

Let X be the original number.

The problem can be written as the following equation:

(X + 110) / 3 = 4X

Multiplying both sides by 3 gives:

X + 110 = 12X

Subtracting X from both sides gives:

110 = 11X

Dividing both sides by 11 gives:

X = 10

Therefore, the original number is X = 10.

Answer:

(x + 110)/3 = 4x      (multiple both side by 3)

x + 110 = 12x

110 = 11x

x = 10

(x + 110)/3 = 4x  

(10 + 110)/3 = 4(10)

120/3 = 40

40/40

Step-by-step explanation:

The four basic graphs used in statistics include bar, line, histogram and pie charts.

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The inequality could be represented by 59 + 30r ≤ 125

According to the given information

Money charged for first room = $59

Money charged for per additional room = $30

The money that the customer could pay = $125

So

We need to write the inequality to determine the situation

Let the number of carpets be r

Firstly , determining an expression for the cleaner charges

59 + 30*r

Since

The customer cannot pay more than $125  

Hence

According to the given situation

59 + 30r ≤ 125

30r ≤ 66

r ≤ 2.2

The inequality could be represented by 59 + 30r ≤ 125

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Answer: 6 square root 23

Step-by-step explanation:

10^3 + 8^2

A line, line segment, or ray that divides an angle into two congruent angles is called an angle bisector.

What are supplementary angles example?

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly, complementary angles add up to 90 degrees.

What do you mean by angle bisector?

If the angle is divided by the line and the angle is divided such that the angles are equal to each other then the line is called the angle bisector.

The word congruent means equal of the things. In this, the angles are congruent to each other which means the angles are equal to each other.

Thus, the black space is to be filled by the angle bisector.

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In the equation y = mx + b, m is the slope of the line and b is the intercept.

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The ratio of trees to flowering plants in Marsha’s backyard is shown on the ratio table.

30 numbers complete the ratio table to make an equivalent ratio.

When we compare two ratios, they are said to be equivalent. To determine if two or more ratios are comparable, they can be compared to one another.

Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you may get the corresponding ratio. Finding comparable fractions follows the same procedure.

Here in this case,

for trees: 2: 12    [ 2 to 12, 6 times more ]

for plants: 5: 30  [ 5 to 30, it is also 6 times more]

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The below would be most important Algebra 1 Formulas for CST.

Linear Equation:

[tex]Ax + By + C = 0[/tex]

Equation of Straight Line or Slope:

[tex]y = mx+b[/tex]

Point-slope form:

[tex]y-y_{1} = m(x-x_1)[/tex]

Slope when 2 points are given:

[tex]m = \frac{(y_2 - y_1)}{(x_2-x_1)}[/tex]

Quadratic Equation:

[tex]Ax^2 + Bx +C = 0[/tex]

When lines are parallel:

Slope of both lines are equal. [tex]m_1 = m_2[/tex]

When lines are perpendicular:

Slope of perpendicular lines are opposite reciprocals, meaning if the slope of a line [tex]l_1[/tex] is [tex]\frac{1}{2}[/tex]. The line [tex]l_2[/tex] perpendicular to [tex]l_1[/tex] is [tex]-\frac{2}{1}[/tex].

Work Formula:

Total Work Done = Number of Days [tex]\times[/tex] Efficiency

where Efficiency is inversely proportional to Time Taken.

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Applying the derivative to the provided line with respect to "x," using the equation of the given line, The response is 3.

In mathematics, the derivative of a function of a real variable measures the sensitivity of the function's value to changes in its argument. The derivative is the fundamental tool in calculus. a function's rate of evolution in respect to a variable Problems involving calculus and differential equations need the use of derivatives.

The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line. Calculate the percentage by dividing the elevation difference between two places by their separation. slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

y(x) = 3x +1

derivate y(x) with respect to x. we get,

= 3

slope =3

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Answer:

x=4.04 y=7.66

Step-by-step explanation:

the exponential function is n(t) =n° (1+r)∧t, where t is the power refers the time in months after opening and n denotes average customer.

when the rate of increases is occurred very rapidly. In this question, the trendy restaurant has earned reputation.

Given, average number of customers after 11 months of opening = n(11) =310

average number of customers after 15 months of opening= n(15) =456

during this 4 month increases of customer =456 -310 =146

increasing rate of customer per month = 146/4 = 36.5

now increasing rate in percentages = 36.5 %

exponential growth rate, r= 0.365

let, n° is the initial number of customer while opening at t=0 month

now, the exponential function n(t) that model's average number of customers, n after t months of being open will be

  n(t) = n° ( 1+r)∧t

we are given that after 11 months of opening average customer n(11) = 310

now, 310 = n° (1+ 0.365)∧11

n°  = 10

hence, the exponential function = n(t) = 10(1+r)∧t

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Thermal energy that comes from the movement of particles.

The energy present in a system that determines its temperature is referred to as thermal energy. Thermal energy flows as heat. Thermodynamics is a whole field of physics that studies how heat is transmitted between various systems and how the procedure is carried out (see the first law of thermodynamics).

The energy that results from a substance's temperature is known as thermal energy. The amount of molecular vibration increases with temperature, increasing thermal energy.

Heat energy is another name for thermal energy. A moving object's kinetic energy is its energy. Thermal energy is a type of kinetic energy because it is produced by moving particles.

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Answer:

Therefore, the measure of angle ABC is 55 cm².

Step-by-step explanation:

In order to solve this problem, we need to use the property of angles in a linear pair, which states that the measures of the two angles in a linear pair add up to 180 degrees.

If angle ABC and angle PQR form a linear pair, then the measure of angle ABC is 180 degrees minus the measure of angle PQR.

Since the measure of angle PQR is 125 cm² and the measure of angle ABC is 180 degrees minus the measure of angle PQR, the measure of angle ABC is:

180 degrees - 125 cm² = 55 cm²

The solution is Option C.

The equation f'( 2 ) ≤ 0 is true

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

[tex]f ( x ) = \lim_{n \to \infty} [ \frac{( n^{n} ( x + n ) ( x + \frac{n}{2} ) ....( x + \frac{n}{n} )}{n! (x^{2}+n^{2}) ( x^{2} + \frac{n^{2}}{4} ) ....( x^{2} +\frac{n^{2}}{n^{2} } ) } ]^{\frac{x}{n} }[/tex]

Taking logarithm on both sides of the equation , we get

[tex]ln f ( x ) = \lim_{n \to \infty} \frac{x}{n} [\sum _{r=1}^nln\frac{1}{r/n} + \sum _{r=1}^nln\frac{(x + \frac{1}{r/n} )}{(x^{2} + (\frac{1}{r/n})^{2} ) }[/tex]

On simplifying the derivatives of the equation , we get

[tex]ln f ( x ) = x [\int\limits^1_0 {ln ( 1/t )} \, dt + \int\limits^1_0 {ln \frac{( x+1/t )}{(x^{2} + 1/t^{2} ) } } \, dt][/tex]

Now , substituting the limits in the equation , we get

[tex]ln f ( x ) = x [ \int\limits^1_0 {( - ln t+ ln (tx+1)-lnt-ln(t^{2} x^{2}+1)+lnt^{2}] } \, dt[/tex]

Substitute the value of tx = z in the equation , we get

[tex]ln f ( x ) = \int\limits^1_0 {ln\frac{(1+z)}{1+z^{2} } } \, dz[/tex]

Taking exponential on both sides of the equation , we get

[tex]f ( x ) = e^{\int\limits^x_0 {{ln\frac{(1+z)}{1+z^{2} } } \, dz} \, }[/tex]

Differentiating with respect to x , we get

[tex]\frac{f' (x ) }{f ( x ) } = ln\frac{1+x}{1+x^{2} }[/tex]

Now , on further simplification of the equation , we get

f ( x ) > 0 for x > 0

And , f' ( x ) > 0

[tex]ln\frac{1+x}{1+x^{2} } > 0[/tex]

And ,

x > x²

0 < x < 1

Therefore , f ( x ) is increasing ∀ x ∈ ( 0 , 1 )

Hence , the equation f' ( 2 ) ≤ 0 is true

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Explanation:

[tex] \rm f(x) = \lim \limits_{n \to \infty } \left( \dfrac{ \displaystyle \rm \prod \limits_{r = 1}^n \left(1 + \dfrac{rx}n \right ) }{\displaystyle \rm\prod \limits_{r = 1}^n \left(1 + \bigg(\dfrac{rx}n \bigg)^{2}\right )} \right)^{ \dfrac{x}{n} }[/tex]

[tex] \large \rm = {e}^{ x \int \limits_{0}^{1} ln(1 + xy)dy - ln(1 + (xy {)}^{2} ) dy }[/tex]

[tex]\rm f'(x)=f(x) \ln \bigg( \dfrac{1 + x}{1 + {x}^{2} } \bigg)[/tex]

[tex]\rm For \: x \in(0,1) \: it \: i s \: increasing \: function[/tex]

[tex]\rm f'(2) = f(2) \ln( \frac{3}{5} ) < 0[/tex]

[tex]\rm \dfrac{f'(3)}{f(3)} =ln \bigg( \dfrac{2}{5} \bigg), \dfrac{f'(2)}{f(2)} = ln \bigg( \dfrac{3}5 \bigg) [/tex]

Answer:

81 degrees

Step-by-step explanation:

Because of exterior angles u=u-41+u-40

Solve:

u=2u-81

0=u-81

u=81

The end behavior of a graph can be determined by looking at the leading term in the equation. If the leading term is a positive or negative power of x, then the end behavior of the graph will be either a horizontal asymptoteor an oblique asymptote. If the leading term is a constant, then the end behavior of the graph will be a horizontal line at that constant value.

To determine the end behavior of a graph from an equation, we first look at the leading term in the equation. If the leading term is a positive or negative power of x, then the end behavior of the graph will be either a horizontal asymptote (positive or negative infinity) or an oblique asymptote (slanted line). If the leading term is a constant, then the end behavior of the graph will be a horizontal line at that constant value. For example, if the leading term of an equation is 3x2, then the end behavior of the graph will be a horizontal asymptote at positive infinity. If the leading term of the equation is 4, then the end behavior of the graph will be a horizontal line at y=4. To determine the exact shape of the asymptote, we must look at the coefficient of the leading term. A positive coefficient will create a positive asymptote (sloping up), while a negative coefficient will create a negative asymptote (sloping down). Additionally, if the graph oscillates around a single point, then the end behavior of the graph is a limit cycle.

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The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is  52!/(47! * 5!).

The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is 52 choose 5, which is equal to 52!/(47! * 5!), where the exclamation point indicates the factorial function. This is known as the binomial coefficient, and it represents the number of ways to choose a certain number of items from a larger set. In this case, the binomial coefficient is used to find the number of ways to choose 5 cards from a deck of 52 cards.

The order of the cards is irrelevant in card games like poker. A five-card draw of 1,2,7,9, K is equivalent to a draw of K,7,9,1,2. What counts is the fundamental overall group.

Order is irrelevant, therefore we utilize a combination (instead of a permutation)

We will substitute n = 52 and r = 5 into the nCr combination formula, which is n C r = (n!)/(r!*(n-r)!)

so we obtain:

n C r = r!*(n-r)!/(n!)

52 C 5 = (52!)/(5!*(52-5)!)

52 C 5 = (52!)/((52-5)!*5!)

The complete question is:-

Which expression can you use to find the number of ways to choose 5 cards from a 52-card deck?

a) (52-5)! / 52!5!

b) 52! / (52-5)!

c) 52! / (52-5)!5!

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By using fraction, it can be calculated that 416 people choose neither blue nor red as their favorite color.

What is fraction?

Suppose there is a collection and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.

The upper part of the fraction is the numerator and the lower part of the fraction is called denominator.

This is a word problem on fraction.

Fraction of people choose blue as their favorite color = [tex]\frac{1}{3}[/tex]

Fraction of people choose red as their favorite color = [tex]\frac{2}{7}[/tex]

Fraction of people choose neither red nor blue as their favorite color =

                                                                               [tex]1- (\frac{1}{3}+\frac{2}{7})\\\\1 - (\frac{7 + 6}{21})\\\\1-\frac{13}{21}\\\\\frac{21-13}{21}\\\\\frac{8}{21}[/tex]

Total number of people surveyed = 1092

Number of people choose neither red nor blue as their favorite color =

                                                                                           [tex]\frac{8}{21}\times 1092[/tex]

                                                                                          = 416          

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Answer:[tex]-3r+7[/tex]

Step-by-step explanation:

given the equation

[tex](-8r-2)-(-5r-9)[/tex]

Distribute the negative

[tex]-8r-2+5r+9[/tex]

Combine like terms

[tex](-8r+5r)+(-2+9)[/tex]

[tex](-3r)+(7)=[/tex]

[tex]-3r+7[/tex]

Hope this helps!

The three statistical measures of central tendency are mean, median, and mode. While describing a set of data, we point out its primary location. This is referred to as the central tendency measure.

The arithmetic mean of a given data is the sum of all observations divided by the number of observations.

The data set's median is the value in the center. Put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them together, and divide by two. Your median will be that value.

A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.

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Answer:

A

Step-by-step explanation:

To compare the initial out-of-pocket cost for the lease and loan options, we need to calculate the total cost for each option.

For the loan option, we can calculate the total cost as follows:

Total cost = MSRP + down payment + interest

= $15,000 + $1,500 + $1,050 (7% of MSRP)

= $17,550

For the lease option, we can calculate the total cost as follows:

Total cost = (MSRP x money factor x 36) + acquisition and documentation fees + security deposit

= ($15,000 x 0.00271 x 36) + $1,250

= $5,925 + $1,250

= $7,175

Since the total cost for the lease option is less than the total cost for the loan option, the initial out-of-pocket cost is less for the lease. Therefore, the correct statement is:

a. The initial out-of-pocket cost is less for the lease.

Answer:

C. [tex]3[/tex]

Step-by-step explanation:

[tex]y=-2x^2 + 8x-5 \\ \\ =-2(x^2 -4x)-5 \\ \\ =-2(x^2-4x+4-4)-5 \\ \\ =-2((x-2)^2 -4)-5 \\ \\ =-2(x-2)^2 +8-5 \\ \\ =-2(x-2)^2 + 3[/tex]

For a 60% confidence interval, the number of cis that we expect to contain the true mean is of 60% of the total amount.

The interpretation of a x% confidence interval it is x% likely that the population parameter(mean/proportion/standard deviation) is between a and b, which are the bounds of the confidence interval.

The bounds a and b of the confidence interval are given by the estimate plus/minus the margin of error.

The interpretation also means that out of n samples, the percentage which are expected to contain the true mean is of x, hence the percentage for this problem is of 60%, as it is the confidence level.

The problem is incomplete, hence only the first part could be answered.

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Answer:

GT: 10

TA: 6

Step-by-step explanation:

use the ratio of GR:RE to find GT:TA

since the ratio of GR:RE is 5:3, the ratio of GT:TA=5:3. The total length of GT+TA=16.

5x+3x=16, 8x=16, x=2.

By plugging in the x value, it is shown that GT=10 and that TA=6

Answer:

Step-by-step explanation:

x= -3  

y= 3