Cell phone Plan A costs $70 per month and comes with a free $500 phone. Cell phone Plan B costs $50 per month but does not come with a phone. If you buy the $500 phone and choose Plan B, how many months is it until your cost is the same as Plan A's? Let m represent the monthly cost.

Answer:

  13/32

Step-by-step explanation:

You want the area of the shaded portion of the unit square shown.

Points B, C, E are shown as equidistant from point F, so will lie on a circle centered at F. The center of that circle is at the point of coincidence of the perpendicular bisectors of BE, BC, and CE.

Without loss of generality, we can let line EF lie on the x-axis such that E is at the origin. Chord EB of the circle has a rise of 1/2 for a run of 1, so a slope of 1/2. Its midpoint is (1, 1/2)/2 = (1/2, 1/4). The perpendicular line through this point will have slope -2, so its equation can be written ...

  y -1/4 = -2(x -1/2)

  y = -2x +5/4

Then the x-intercept (point F) will have coordinates (0, 5/8):

  0 = -2x +5/4 . . . . . y=0 on the x-axis

  2x = 5/4

  x = 5/8

Trapezoid EFCD will have upper base 5/8, lower base 1, and height 1/2. Its area is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(5/8 +1)(1/2) = (1/4)(13/8) = 13/32

The shaded area is 13/32.

__

Additional comment

The point-slope equation of a line through (h, k) with slope m is ...

  y -k = m(x -h)

The area of the pie is approximately 113.0 square inches.

The ratio of a circle's circumference to its diameter is denoted by the mathematical constant pi . It is roughly equivalent to 3.14159 and is not repetitive or terminal. As pi is an irrational number, it cannot be written as an exact fraction of two integers and its decimal representation never ends. Pi is used to compute the characteristics of circles, spheres, cylinders, and other curved objects in many branches of mathematics and science, including geometry, trigonometry, calculus, physics, and engineering.

The area of the circle is given as:

A = πr²

Here, diameter = 12, thus radius is 6 inches.

Substituting the values:

area = 3.14 x (6)²

area = 113.04 square inches

Hence, the area of the pie is approximately 113.0 square inches.

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Area of the solid composite shape with triangle and rectangle is =832cm².

The area of a composite shape can be determined by adding or subtracting its component pieces.

Hence, we can use two formulas:

Area of Composite Shape + Area of Composite Shape + Area of Basic Shape A (additive)

Basic Shape Area A, Basic Shape Area B, and Composite Shape Area (subtractive)

In the figure,

Dimensions of the triangle are height, h = 16cm and base, b = 12cm.

Area = 1/2 ×b ×h

= 1/2 × 16× 12

=96cm²

There are two triangles, so the total area = 96+ 96 = 192cm².

Now area of the rectangle = length × width

= 20 × 32

= 640cm².

Total area of the solid= 192 + 640 = 832cm².

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If a water bottle contains 375 ml, So the volume in quarts is 0.396 qt.

       The volume of a water bottle containing 375 ml can be converted into a quart using the conversion formula.

          One can use the following conversion formula to convert a given volume in ml to quarts.

          The conversion formula for ml to quarts is given as;

                      1 ml = 0.00105669 quarts

Volume in quarts = Volume in ml × 0.00105669

     Now, to calculate the volume of 375 ml of the water bottle in quarts,

     We will substitute the given volume in the above conversion formula as follows,

      Volume in quarts = 375 ml × 0.00105669

                                    = 0.396 qt

       Hence, the volume of the water bottle containing 375 ml is 0.396 qt.

      Therefore, the correct option is C. 0.396 qt.

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Answer:

1+2=90° .so complementary angle

1.  Exponential decay 2. Josh's function represents the situation correctly 3. V(x) = 1275(0.835)ˣ,  V(x) = 1275(1-0.165)ˣ

An exponential decay function is a mathematical function that describes the decrease in value of a quantity over time or through a series of events. It is often used to model natural phenomena such as radioactive decay or the spread of diseases.

In an exponential decay function, the value of the quantity decreases exponentially over time. This means that the rate of decrease is proportional to the value of the quantity at any given time.

The exponential decay function is characterized by a decreasing graph that approaches zero but never touches the x-axis. The rate of decay slows down over time, but the quantity never completely disappears. The function is used in various fields such as physics, chemistry, biology, finance, and economics, to name a few.

1. This situation represents exponential decay because the value of the computer decreases by 16.5% each year.

2. Josh's function represents the situation correctly because it involves the decay factor (0.835) which is less than 1, reflecting the decrease in value each year. Eve's function represents exponential growth which is not consistent with the situation where the value of the computer decreases each year.

3. V(x) = 1275(0.835)ˣ represents the function using the form V(x) = a(b)ˣ where a = 1275 and b = 0.835.

Alternatively, V(x) = 1275(1-0.165)ˣ represents the function using the form V(x) = a(1-r)ˣ where a = 1275 and r = 0.165.

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Therefore, approximately 68.26% of people are expected to score higher than 2.5 but lower than 3.5.

Based on the information provided, the mean (X) is 3.00 and the standard deviation (SD) is 0.50. To find the percentage of people expected to score higher than 2.5 but lower than 3.5, we will use the standard normal distribution (z-score) table.

First, we need to calculate the z-scores for both 2.5 and 3.5:
z1 =[tex] (2.5 - 3.00) / 0.50 = -1.0[/tex]
z2 = [tex](3.5 - 3.00) / 0.50 = 1.0[/tex]

Now, we can use the standard normal distribution table to find the probability of the z-scores. For z1 = -1.0, the probability is 0.1587 (15.87%). For z2 = 1.0, the probability is 0.8413 (84.13%).

To find the percentage of people expected to score between 2.5 and 3.5, subtract the probability of z1 from the probability of z2:

Percentage = [tex](0.8413 - 0.1587) x 100 = 68.26%[/tex]

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The probability of randomly chosen, a 50-year-old or older voter from the winning party is 45.84%

Given the table of values

From the table of values, we have the winning party to be

New Democratic

From the column of New Democratic, we have

Total = 9422

50-year-old or older voter = 4319

So, the required probability is

Probbaility = 4319/9422

Evaluate

Probbaility = 0.45839524517

This gives

Probbaility = 45.839524517%

Approximate

Probbaility = 45.84%

Hence, the probability is 45.84%

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The closest option is (A) (3,3), which is the correct solution to the system of equations.

To find the solution to the system of equations, we need to substitute the value of y in the first equation with the value given in the second equation:

-6x + y = -21 ...(1)

2x - 1/3 y = 7 ...(2)

Substituting y=7 in the first equation, we get:

-6x + 7 = -21

Simplifying the above equation:

-6x = -28

Dividing both sides by -6, we get:

x = 28/6 = 14/3

Substituting x=14/3 and y=7 in the second equation, we get:

2(14/3) - 1/3(7) = 7

Simplifying the above equation, we get:

28/3 - 7/3 = 7

21/3 = 7

Therefore, the solution to the system of equations is (14/3, 7).

Hence, the answer is not in the given options, but the closest option is (A) (3,3), which is not the correct solution to the system of equations.

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Around 0.13% or 0.0013 of children find relief for less than four hours.

The percentage of children who experience relief for less than four hours if the relief time follows a lognormal distribution is determined as follows:

Step 1: Define the parameters of the problem. Assume that relief times are normally distributed with a mean of μ = 5.5 hours and a standard deviation of σ = 0.5 hours. We want to find the percentage of children who experience relief for less than four hours.

Step 2: Convert the normal distribution to the standard normal distribution using the formula: z = (x - μ) / σwhere x is the relief time in hours.

Step 3: Find the z-score corresponding to the value of x = 4:z = (4 - 5.5) / 0.5 = -3

Step 4: Use a standard normal distribution table to find the percentage of the area under the curve to the left of z = -3. This is equivalent to the percentage of children who experience relief for less than four hours.

Using the standard normal distribution table or calculator, we get that the percentage of children who experience relief for less than four hours is approximately 0.13% or 0.0013.


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A) 35. 8 million; thirty-five million eight hundred thousand, or thirty-five million eight hundred thousand dollars ,(b)115. 2 thousand; one hundred and fifteen thousand two hundred.(c) 97.8 million eight hundred thousand; 97.8 million eight hundred thousand. or 978 million.

What significance do numbers have?

We need good numeracy skills as parents to assist our children to develop, as patients to grasp healthcare information, and so as politicians to make sense of numbers and economic news. Selections in life were frequently based upon numerical data; in order to arrive at optimal decisions, we must be good at maths.

How are numbers used in everyday life?

Numbers are utilized in a variety of mathematical operations such as summation, subtraction, multiplication, division, percentage, and so on, that we employ in the everyday companies and exchanges. Quantities are numerical symbols representing integers that may be used for numbering, estimating, and doing other arithmetic operations.

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The correct answer to the question, "Which of the following is equivalent to the probability of getting less than 50% democrats in a random sample of size 100?" is: B. P( z < 50 — 55/ √55(45)/100).

To find the probability, we first calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value (50%), μ is the mean (55%), and σ is the standard deviation.

The standard deviation can be calculated as:

σ = √(np(1-p))

where n is the sample size (100) and p is the proportion of democrats (0.55).

Now, plug in the values into the z-score formula:

z = (50 - 55) / √(100 * 0.55 * 0.45)

The probability is then found as P(z < z-score), which is represented by the option B.

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The value of x using similar triangles theorem is = 13/3.

Triangles that resemble one another but may not be exactly the same size are said to be comparable triangles.

When two objects have the same shape but different sizes, they can be said to be comparable.

This indicates that comparable shapes superimpose one another when amplified or de-magnified.

The term "Similarity" refers to this characteristic of like shapes.

Now in the given figure,

the proportion of the triangles' side is same.

So, 12/4 = 13/x

x = 13/3

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Answer:c

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Answer:

≈283,39 mm^2

Step-by-step explanation:

The diameter is 19 mm, so the radius is half diameter (9,5 mm)

[tex]a = \pi \times {r}^{2} = 3.14 \times {9.5}^{2} = 3.14 \times 90.25 ≈ 283.39[/tex]

The point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.

Let P = (x, y) be the point that partitions segment AB in a 1:4 ratio, where AP:PB = 1:4. Then, we have:

[tex]$\frac{AP}{AB} = \frac{1}{1+4} = \frac{1}{5}$$[/tex]

and

[tex]$\frac{PB}{AB} = \frac{4}{1+4} = \frac{4}{5}$$[/tex]

Using the distance formula, we can find the lengths of AP, PB, and AB:

[tex]AP &= \sqrt{(x+3)^2 + (y-2)^2} \\PB &= \sqrt{(x-7)^2 + (y+10)^2} \\\ AB &= \sqrt{(7+3)^2 + (-10-2)^2} = \sqrt{244}[/tex]

Substituting these into the section formula, we have:

[tex]$\begin{aligned}x &= \frac{4\cdot(-3) + 1\cdot(7)}{1+4} = -1 \ y &= \frac{4\cdot2 + 1\cdot(-10)}{1+4} = -\frac{2}{5}\end{aligned}$$[/tex]

Therefore, the point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

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The arithmetic mean return is 3.6%, and the standard deviation is 2.14%.

To find the arithmetic mean, we add up the five returns and divide by the number of returns (in this case, 5):

(3% + 6% + 0% + 6% + 3%) / 5 = 3.6%

To find the standard deviation, we first need to find the variance. We can do this by taking each return, subtracting the mean return (3.6%), squaring the result, summing these values, and dividing by the number of returns minus 1 (4 in this case):

((3% - 3.6%)^2 + (6% - 3.6%)^2 + (0% - 3.6%)^2 + (6% - 3.6%)^2 + (3% - 3.6%)^2) / 4 = 0.046

The standard deviation is the square root of the variance:

√0.046 = 0.214 or 2.14%

Therefore, the arithmetic mean return for security y is 3.6%, and the standard deviation (sample) is 2.14%.


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Mr. Kha Lipat should invest $5,000 today in order to receive $400.00 in interest one year from now at an 8% interest rate.

To calculate how much money Mr. Kha Lipat should invest today to receive $400.00 one year from now at an 8% interest rate, we can use the formula for calculating simple interest though compound intrest:

I = P * r * t

where I is the interest earned, P is the principal (the initial amount invested), r is the interest rate (as a decimal), and t is the time period (in years).

We know that Mr. Kha Lipat wants to earn $400.00 in interest, the interest rate is 8% or 0.08 (as a decimal), and the time period is 1 year. We can plug these values into the formula and solve for P:

I = P * r * t

400 = P * 0.08 * 1

400 = 0.08P

P = 400 / 0.08

P = 5000

Therefore, Mr. Kha Lipat should invest $5,000 today in order to receive $400.00 in interest one year from now at an 8% interest rate.

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Proportionately, the cost of the board game without the sales tax is $28.00.

The sales tax is the levy imposed by the government on the consumption and production of certain goods and services.

The purposes of imposing sales taxes are to discourage consumption and to increase governmental revenue.

Proportion refers to the equation of two ratios.

In this situation, we can equate the value of the sales tax with its percentage to determine the cost of the board game.

The sales tax in dollars = $1.54

The sales tax rate = 5.5%

Proportionately, the value of the board game without the sales tax = $28.00 ($1.54/5.5%).

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How how is the cost?

Hence, the answer is (4, 3, 1).In conclusion The answer provided above is concise and ng factually correct, and it addresses the question directly.

In order to determine the number of total electron groups, bondiroups, and lone pairs for geometry (a), we need to use the VSEPR theory. According to this theory, the electron groups around a central atom in a molecule will arrange themselves in a way that minimizes their repulsion. The total number of electron groups includes both the bonding and lone pairs of electrons.To determine the number of electron groups for geometry (a), we first need to determine the molecular geometry of the molecule.

From the given name, we can assume that geometry (a) is tetrahedral. In a tetrahedral molecule, there are four electron groups: three bonding groups and one lone pair. Therefore, the number of total electron groups for geometry (a) is four, the number of bonding groups is three, and the number of lone pairs is one.

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The GCF (Greatest Common Factor) of the variables of a polynomial has the least exponent of any variable term in the polynomial because it represents the largest factor that is common to all the terms in the polynomial.

To understand this better, consider a polynomial like 6x²y³ + 9x³y². The GCF of this polynomial would be 3x²y², which is the largest factor that can divide both terms evenly.

Notice that the exponent of each variable in the GCF is the smallest exponent among the corresponding variable terms in the polynomial.

This is because any factor that is common to all terms in the polynomial must be able to divide each term without leaving a remainder. Therefore, the exponent of each variable in the GCF must be less than or equal to the exponent of that variable in every term of the polynomial.

In summary, the GCF of the variables of a polynomial has the least exponent of any variable term in the polynomial because it represents the largest factor that can divide all terms in the polynomial evenly, and therefore, it must have the smallest exponent of each variable among all terms in the polynomial.

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Answer:Hence, Nathan rode 2 miles

Step-by-step explanation:ask if you need any questions

Answer:  ^4√11^5 = 11^(5/4)

Step-by-step explanation: When we apply a radical, we are asking what number, when raised to a certain power, gives us the number under the radical. For example, ^4√16 is asking what number, when raised to the fourth power, gives us 16. The answer is 2, since 2^4 = 16.

So, ^4√11^5 is asking what number, when raised to the fourth power, gives us 11^5. We can simplify this expression using the exponent laws:

^4√11^5 = (11^5)^(1/4) = 11^(5/4)

Therefore, the simplified expression for ^4√11^5 is 11^(5/4). This expression does not have any radicals, making it easier to work with and manipulate.

Hope this helps, and have a great day!

After answering the prοvided questiοn, we can cοnclude that As a result, expressiοn the pizza place is abοut a mile away frοm the schοοl.

In mathematics, an expressiοn is a grοup οf representatiοns, digits, and cοnglοmerates that resemble a statistical cοrrelatiοn οr regimen. An expressiοn can be a real number, a mutable, οr a cοmbinatiοn οf the twο. Additiοn, subtractiοn, rapid spread, divisiοn, and expοnentiatiοn are examples οf mathematical οperatοrs.

Arithmetic, mathematics, and shape all make extensive use οf expressiοns. They are used in mathematical fοrmula representatiοn, equatiοn sοlutiοn, and mathematical relatiοnship simplificatiοn.  

If the pizza place is 7 miles frοm yοur friend's hοuse and her hοuse is 8 miles frοm schοοl, the distance between the twο can be calculated as fοllοws:

distance frοm pizza shοp tο schοοl = distance frοm friend's hοuse tο schοοl - distance frοm friend's hοuse tο pizza shοp

8 miles minus 7 miles = distance frοm pizza place tο schοοl

1 mile frοm the pizza place tο the schοοl

As a result, the pizza place is abοut a mile away frοm the schοοl.

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A horizontal curve is to be designed with a 2000 feet radius. The curve has a tangent length of 400 feet and its pi is located at station 103+00. Determine the stationing of the PT.

A horizontal curve is a curve that is used to provide a transition between two tangent sections of a roadway. To connect two tangent road sections, horizontal curves are used. Horizontal curves are defined by a radius and a degree of curvature. The curve's radius is given as 2000 feet. The tangent length is 400 feet.

The pi is located at station 103+00.

To determine the stationing of the PT, we must first understand what the "pi" means. PC or point of curvature, PT or point of tangency, and PI or point of intersection are the three primary geometric features of a horizontal curve. The point of intersection (PI) is the point at which the back tangent and forward tangent of the curve meet. It is an important point since it signifies the location of the true beginning and end of the curve. To calculate the PT station, we must first determine the length of the curve's arc. The formula for determining the length of the arc is as follows:

L = 2πR (D/360)Where:

L = length of the arc in feet.

R = the radius of the curve in feet.

D = the degree of curvature in degrees.

PI (103+00) indicates that the beginning of the curve is located 103 chains (a chain is equal to 100 feet) away from the road's reference point. This indicates that the beginning of the curve is located 10300 feet from the road's reference point. Now we need to calculate the degree of curvature

:Degree of curvature = 5729.58 / R= 5729.58 / 2000= 2.8648 degrees. Therefore, the arc length is:

L = 2πR (D/360)= 2π2000 (2.8648/360)= 301.6 feet.

The length of the curve's chord is equal to the length of the tangent, which is 400 feet. As a result, the length of the curve's long chord is: Long chord length = 2R sin (D/2)= 2 * 2000 * sin(2.8648/2)= 152.2 feet To determine the stationing of the PT, we can use the following formula: PT stationing = PI stationing + Length of curve's long chord= 10300 + 152.2= 10452.2Therefore, the stationing of the PT is 10452+2.

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Answer: multiplied by 5 or squared

Step-by-step explanation:

If the number 5 goes in and 25 is the result, the rule could be multiplying by 5 or squaring the number that goes in (input).

5 x 5 = 25

5^2 = 25.

We can claim that after answering the above question, the Therefore, the solution to the original equation is: [tex]q = 9^x\\[/tex]

In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" states that the sentence "2x Plus 3" equals the value "9". The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

given equation:

[tex]1/4xln(16q^8) - ln3 = ln24\\1/4xln(16q^8) = ln(24 * 3)\\1/4xln(16q^8) = ln72\\ln(16q^8)^(1/4x) = ln72\\16q^8^(1/4x) = 72\\16q^8 = 72^(4x)\\ln(16q^8) = ln(72^(4x))\\[/tex]

[tex]ln(16) + ln(q^8) = 4x ln(72)\\ln(q^8) = 4x ln(72) - ln(16)\\ln(q^8) = ln(72^(4x)) - ln(16^1)\\ln(q^8) = ln((72^(4x))/16)\\q^8 = e^(ln((72^(4x))/16))\\q^8 = (72^(4x))/16\\q^8 = 9^(8x)\\q = 9^x\\[/tex]

Therefore, the solution to the original equation is:

[tex]q = 9^x\\[/tex]

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Certainly, there is a significant difference in the mean amount of e.coli bacteria detected by the two methods for this type of beef. This can be supported statistically by conducting a hypothesis test.

           The null hypothesis ([tex]H_0[/tex]) is that there is no significant difference in the mean amount of E. coli bacteria detected by the two methods. The alternative hypothesis ([tex]H_a[/tex]) is that there is a significant difference in the mean amount of e.coli bacteria detected by the two methods.

          The two-sample t-test can be used to test the hypothesis. The t-test compares the means of two independent groups and determines whether they are significantly different. The t-test assumes that the two samples are normally distributed and have equal variances.

          If the sample sizes are large, then the t-test can still be used even if the samples are not normally distributed.

          The formula for the t-test is:

                   [tex]t = (x_1 - x_2) / [s^2(1/n_1 + 1/n_2)][/tex]

       Where:

                     [tex]x_1[/tex] = the sample mean for method 1

                     [tex]x_2[/tex] = the sample mean for method 2

                     [tex]s^2[/tex] = the pooled variance of the two samples

                     [tex]n_1[/tex] = the sample size for method 1

                     [tex]n_2[/tex] = the sample size for method 2

        The t-value can then be compared to the critical value of  [tex]t[/tex] for the desired level of significance (usually 0.05).

         If the t-value is greater than the critical value of [tex]t[/tex], then the null hypothesis can be rejected and it can be concluded that there is a significant difference in the mean amount of E. coli bacteria detected by the two methods.

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The given series diverges to negative infinity as the terms cancel out, leaving only two terms at the beginning and end of the series.

To determine the convergence of the given series, we can use the telescoping series method.

Let's write out a few terms of the series to see if we can spot a pattern:

n=1: 1/2 - 3/4 = -1/4

n=2: 2/3 - 4/5 = -2/15

n=3: 3/4 - 5/6 = -1/8

n=4: 4/5 - 6/7 = -2/35

...

We can see that the terms of the series cancel out, leaving only two terms at the beginning and end of the series. Therefore, we can write the series as:

∑ (n/n+1 - n+2/n+3) = 1/2 - (n+2)/(n+3)

As n approaches infinity, the second term approaches 1, so the series diverges to negative infinity.

Therefore, the given series diverges.

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_____The given question is incomplete, the complete question is given below:

Which of the series in exercises 17–56 converge, and which diverge? use any method, and give reasons for your answers

(∑ ∞ to n = 1) = (n/n+1 - n+2/n+3)