An artist has completed 1 4 of a painting in 2 weeks. At what rate is she working? Simplify your answer and write it as a proper fraction, mixed number, or whole number.

There are 1,08,108 different committees that are possible.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by \(^nC_r\).

The general formula for combination is:

\(^nC_r=\frac{n!}{r!(n-r)!}\)  ,where 0 ≤ r ≤ n.

In a committee, we can choose 13 men from 5 men in ¹³C₅ ways. similarly, we can choose 3 women from 9 women in ⁹C₃ ways.

total ways in which we can choose 13 men and 9 women to form a committee= ¹³C₅*⁹C₃

\(\frac{13*12*11*10*9}{5*4*3*2*1} *\frac{9*8*7}{3*2*1}\)

⇒154440/120*504/6

⇒1287*84

⇒108180

Hence, there are 1,08,180 committees are possible.

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\( \frac{1}{a} = \frac{1}{b} + \frac{1}{c} \\ \\ \frac{1}{12} = \frac{1}{b} + \frac{1}{22} \\ \\ \frac{1}{b} = \frac{1}{12} - \frac{1}{22} \\ \\ \frac{1}{b} = \frac{11}{132} - \frac{6}{132} \\ \\ \frac{1}{b} = \frac{11 - 6}{132} \\ \\ \frac{1}{b} = \frac{5}{132} \\ \\ 5b = 132 \\ \\ b = \frac{132}{5} \\ \\ b = 26.4 \\ \\ b = 26\)

I hope I helped you^_^

Answer:

I got about 28.01 ft you might want to round or something

hope this helped

The required stopping distance of the car is 17.24 metes.

A child appears to be running into the street ahead. It takes 2.3 seconds for the driver to react and begin to brake, but this time at a rate of -7.5 m/s2. What is the stopping distance for the car in this situation is to be determined.

Speed is ratio of distance to the time. speed = distance / time.

The intial speed of the driver is 11m/s

Now total stopping distance = thinking distance + break applying distance
                                           =  v*t  + u²/2a
                                           =  11 * 2.3 - 11²/2*7.5
                                           = 17.24 meters,

Thus, the required stopping distance of the car is 17.24 metes.

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Answer:

Step-by-step explanation:

The average age of 18 girls is 12.

Total age of girls:

The average age of 15 boys is 17

Total age of boys:

Total age of children:

Total number of children:

Average age of children:

Answer:

The two hypotenuses.

Step-by-step explanation:

HL or Hypotenuse-Leg Theorem: two right triangles are congruent if and only if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of the other right triangle.

Since we already know the bottom leg of each triangle is congruent, we only need to know the two hypotenuses.

Answer:

AB=ED

Step-by-step explanation:

The roots of the given equation is real and equal.

Given , 5\(x^{2} \\\) - 10x+ k=0

The quadratic equation is b² - 4ac = 0

Here, a= 5, b= -10, c= k

substitute in b² - 4ac = 0

(-10)² - 4 * 5* k =0

100 - 20k =0 , let this be equation (1)

100 = 20k

k = \(\frac{100}{20}\)

k = 5.

now, substitute  k= 5 in equation (1)

100 -20k = 0

100 - 20*5 = 0

100 - 100 = 0

Therefore, the given equation is real and equal .

The correct question is 5x² - 10x + k =0

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If I want to buy 3 packages of 10 cans it will cost me around $1.4 per can.

It is given that the price of a package of 10 cans of soup = $14

and the price of an individual can = $2

Now, if I want to purchase at least 25 individual cans there can be two possible ways to do this:

Therefore, if I decided to buy 3 packages of 10 cans it will cost me $42 and I will pay $1.4 for each can.

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a. The degree of the polynomial is 6.

b. Factoring the equation, we have:

x6 - 49x^4 = x^4(x^2 - 49) = x^4(x - 7)(x + 7)

a.The degree of the polynomial equation x^6 - 49x^4 = 0 is 6. This is determined by the highest exponent of x in the polynomial, which is 6.

b. The two roots of multiplicity 1 can be found by factoring the equation as x^4(x^2 - 49) = 0. Setting each factor equal to zero, we have x^4 = 0 and x^2 - 49 = 0.

From x^4 = 0, we find the root x = 0 with multiplicity 4.

From x^2 - 49 = 0, we get (x - 7)(x + 7) = 0. Therefore, the roots x = 7 and x = -7 each have multiplicity 1.

In summary, the equation x^6 - 49x^4 = 0 has a degree of 6, and the roots with multiplicity 1 are x = 0, x = 7, and x = -7.

So the roots of the equation are:

x = 0 (multiplicity 4)

x = 7 (multiplicity 1)

x = -7 (multiplicity 1)

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Based on the histogram, it seems that the percentage of men with cholesterol levels above 220 is around 15%. To calculate this, we can look at the total area of the bars to the right of 220 and divide it by the total area of the entire histogram.

To be more specific, we can count the number of bars to the right of 220, which is 3. Each of these bars has a width of 5 and a height (frequency) of 4, 6, and 2 respectively. So the total area of these bars is 5 x (4 + 6 + 2) = 60.

The total area of the entire histogram is 5 x 20 = 100. Therefore, the percentage of men with cholesterol levels above 220 is (60/100) x 100 = 60%.

So the answer is not provided in the answer choices, but it would be closest to 60% based on the given histogram.
The histogram displays the distribution of serum cholesterol levels in milligrams per deciliter (mg/dL) for a sample of men. To determine the percentage of men with cholesterol levels above 220 mg/dL, you should examine the histogram and identify the relevant bars that represent cholesterol levels above 220 mg/dL. Then, calculate the number of men in these bars and divide it by the total number of men in the sample, and finally multiply the result by 100 to obtain the percentage.

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The asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\) is f(n) ∈ Θ(g(n)). Therefore, the growth rates of f(n) and g(n) are primarily determined by the cubic terms, and they grow at the same rate within a constant factor.

To determine the asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\), we need to compare their growth rates as n approaches infinity.

Θ (Theta) Notation: f(n) ∈ Θ(g(n)) means that f(n) grows at the same rate as g(n) within a constant factor. In other words, there exists positive constants c1 and c2 such that c1 * g(n) ≤ f(n) ≤ c2 * g(n) for sufficiently large n.

o (Little-o) Notation: f(n) ∈ o(g(n)) means that f(n) grows strictly slower than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) < c * g(n) for all n > n0.

ω (Omega) Notation: f(n) ∈ ω(g(n)) means that f(n) grows strictly faster than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) > c * g(n) for all n > n0.

Now let's analyze the given functions:

\(f(n) = n^3 (8 + 2 cos 2n)\\g(n) = n^2 + 2n^3 + 3n\)

Since both functions have the same dominant term, we can say that f(n) ∈ Θ(g(n)) because they grow at the same rate within a constant factor. The other notations, o and ω, are not applicable here because neither function grows strictly faster nor slower than the other.

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Answer:

1 can of green beans at Village Market is $0.74.  At Sam's Club, one can of green beans is $0.69. Therefore, Sam's Club is the better buy, by being cheaper than Village Market's by $0.05.

Step-by-step explanation:

Answer: 5.1 = 20.4 and = 30.6

Step-by-step explanation: Add a fraction to 5.1 + 5.1 if you keep adding by 5.1 gets an answer

B & C

A= 3.6:1

B= 5:1

C= 5.1

Cot A=1/tan A=12/5

cos A= 12/13

sin A=5/13

Draw a right angled triangle

the hypotenuse is the longest side which is 13 using Pythagoras theorem

the side opposite the angle A is 5

the side closest to the angle A which is called the adjacent is 12

sinA =opp/hyp

cos A= adj/hyp

cotA =1/tanA=cos A/sinA

Note: Pythagoras theorem is

hyp²=opp²+adj²

Answer:

Step-by-step explanation:

\(tan \ A = \frac{5}{12}=\frac{opposite \ site}{adjacent \ side}\)

hypotenuse² = (opposite side)² + (adjacent side)²

                      =  5² + 12²

                      = 25 + 144

                      = 169

hypotenuse = √169 = √13*13 = 13

\(Cot \ A = \frac{adjacent \ side}{opposite \ side}=\frac{12}{5}\\\\Cos \ A = \frac{adjacent \ side}{hypotenuse}=\frac{12}{13}\\\\Sin \ A = \frac{opposite \ side}{hypotenuse}=\frac{5}{13}\)

Answer:

Step-by-step explanation: i think it is a 1.50

There is no solution to the problem. We cannot determine how much each of them has.

Let's solve this problem using algebraic equations. Let x represent the amount Yi Hao has and y represent the amount Vani has. From the first statement, we can set up the equation y + 3 = 2(x - 3), because if Vani receives $3, she will have twice as much as Yi Hao. Simplifying this equation, we get y + 3 = 2x - 6.

From the second statement, we can set up the equation x + 5 = 2(y - 5), because if Yi Hao receives $5, he will have twice as much as Vani. Simplifying this equation, we get x + 5 = 2y - 10.

Now, we can solve these two equations simultaneously. By substituting the value of x from the first equation into the second equation, we get (2x - 9) + 5 = 2x - 10. Simplifying this equation, we get 2x - 4 = 2x - 10. This equation is not possible to solve because the equation simplifies to -4 = -10, which is not true. Therefore, there is no solution to this problem. We cannot determine how much each of them has.

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During the Urbana student Missionary conventions, commitment to missions reportedly jumped from 7% in 1970 to a higher percentage in 1976, and it has remained above this level ever since.

The Urbana student Missionary conventions, organized by InterVarsity Christian Fellowship, have been influential in mobilizing students for mission work. In 1970, the reported commitment to missions among attendees was 7%. However, by 1976, this percentage had significantly increased, although the exact figure is not provided in the question.

The conventions served as a catalyst for inspiring and equipping young Christians to actively engage in missionary work around the world. The conventions provided a platform for speakers, workshops, and networking opportunities that encouraged attendees to consider missions as a vital aspect of their faith. This emphasis on missions, combined with the passionate and energetic atmosphere of the conventions, likely contributed to the substantial increase in commitment observed during this period.

Since the surge in commitment in 1976, the percentage of attendees committed to missions has remained above the reported figure. The Urbana student Missionary conventions continue to draw thousands of students from various Christian denominations, providing them with opportunities to explore missions, engage in cross-cultural experiences, and receive training and guidance for effective mission work.

The conventions' impact on commitment to missions can be attributed to the powerful messages delivered by renowned speakers, the testimonies of missionaries sharing their experiences, and the networking and mentorship opportunities available to attendees. The sustained high level of commitment indicates the enduring influence of the conventions in mobilizing young Christians for global mission work and underscores the lasting impact of the Urbana movement.

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The mistake that the researcher made is that; neither critical nor obtained Chi squares can have negative values

A chi-square statistic is one way to show a relationship between two categorical variables. In statistics, there are two types of variables: numerical (countable) variables and non-numerical (categorical) variables.

The chi-squared statistic is a single number that tells you how much difference exists between your observed counts and the counts you would expect if there were no relationship at all in the population.

Now, Chi square (χ²) is the sum of a set of squared values, and as such it can never be negative. The minimum chi - squared value would be obtained if each Z = 0 so that χ² would also be 0. There is no upper limit to the χ² value. Similarly, the critical chi square cannot also be negative.

Thus, we can conclude that the mistake that the researcher made is that neither critical nor obtained Chi squares can have negative values

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a. The replacement free cash flows is $255,000

b.  The Payback Period time required to recover the initial investment is 2.7778 years.

d. By calculating the NPV at various discount rates, we can determine the rate at which NPV is closest to zero.

a. To calculate the replacement free cash flows, we need to consider the cash flows associated with the new fleet of trucks. Here's the calculation:

Initial cash outflow: Purchase cost of new trucks + Shipping cost

= $350,000 + $50,000

= $400,000

Annual cash flows:

Operating cost savings:

Diesel fuel savings: $250,000 - $150,000 = $100,000

Maintenance cost savings: $35,000 - $10,000 = $25,000

Net operating working capital reduction: $20,000

Total operating cost savings per year: $100,000 + $25,000 + $20,000 = $145,000

Revenue increase:

Revenue growth rate: 10%

Year 1 revenue increase: $800,000 * 10% = $80,000

Year 2 revenue increase: $800,000 * 10% = $80,000

Year 3 revenue increase: $800,000 * 10% = $80,000

Year 4 revenue increase: $800,000 * 10% = $80,000

Year 5 revenue increase: $800,000 * 10% = $80,000

Salvage value: Market value of the new trucks at the end of 5 years = $30,000

Free cash flows:

Year 0: Initial cash outflow = -$400,000

Year 1: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 2: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 3: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 4: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 5: Cash flow = Operating cost savings + Revenue increase + Salvage value = $145,000 + $80,000 + $30,000 = $255,000

b. The Payback Period is the time required to recover the initial investment. To calculate it, we sum the cash flows until they equal or exceed the initial investment. Here's the calculation:

Payback Period = Number of years to recover initial investment

= 2 years (Year 1 cash flow + Year 2 cash flow)

+ (Remaining investment / Year 3 cash flow)

= 2 years + ($400,000 - $225,000) / $225,000

= 2 years + 0.7778 years

= 2.7778 years

c. To calculate the Net Present Value (NPV) and Profitability Index (PI), we need to discount the cash flows using the given discount rate of 15%. Here's the calculation:

Discount rate: 15%

Present value factor for each year:

Year 0: 1 / (1 + Discount rate)^0 = 1

Year 1: 1 / (1 + Discount rate)^1 = 0.8696

Year 2: 1 / (1 + Discount rate)^2 = 0.7561

Year 3: 1 / (1 + Discount rate)^3 = 0.6575

Year 4: 1 / (1 + Discount rate)^4 = 0.5718

Year 5: 1 / (1 + Discount rate)^5 = 0.4972

NPV calculation:

NPV = (Year 0 cash flow) + (Year 1 cash flow * Present value factor) + (Year 2 cash flow * Present value factor) + ...

= -$400,000 + ($225,000 * 0.8696) + ($225,000 * 0.7561) + ($225,000 * 0.6575) + ($225,000 * 0.5718) + ($255,000 * 0.4972)

Profitability Index calculation:

PI = NPV / Initial investment

= NPV / $400,000

d. To calculate the Internal Rate of Return (IRR), we find the discount rate that makes the NPV equal to zero. Here's the calculation:

IRR = Discount rate that makes NPV equal to zero

By calculating the NPV at various discount rates, we can determine the rate at which NPV is closest to zero.

e. Based on the information provided, we can determine if the fleet should be replaced by considering the Payback Period, NPV, Profitability Index, and IRR.

If the Payback Period is within the company's acceptable timeframe and the NPV is positive, or the Profitability Index is greater than 1, and the IRR exceeds the company's required rate of return, then replacing the fleet would be financially favorable. If any of these criteria are not met, it would indicate that the replacement may not be the best option.

Please note that the calculation of IRR requires further information, and the final decision should consider additional factors such as qualitative aspects, operational requirements, and strategic considerations.

Without the specific values for cash flows in each year, it is not possible to provide a definitive answer to whether the fleet should be replaced based on the given information.

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The projection matrix P describes the projection of R4 onto V = span{| 1 1 0 -2 | , | 1 5 1 1 |}.

To get the projection matrix P describing the projection of R4 onto V = span{| 1 1 0 -2 | , | 1 5 1 1 |}, follow these steps:
First, create a matrix A using the given spanning vectors as columns: A = [| 1 1 0 -2 | , | 1 5 1 1 |]
Compute the matrix product A * A^T: A * A^T = [| 1 1 0 -2 | , | 1 5 1 1 |] * [| 1  1 | , | 1  5 | , | 0  1 | , |-2  1 |]
Calculate the inverse of the resulting matrix (A * A^T)^(-1): (A * A^T)^(-1) = Inverse of the matrix obtained in step 2
Compute the matrix product A^T * (A * A^T)^(-1):
A^T * (A * A^T)^(-1) = [| 1  1 | , | 1  5 | , | 0  1 | , |-2  1 |] * Inverse of the matrix from step 3
Finally, calculate the projection matrix P: P = A * A^T * (A * A^T)^(-1) * A^T
The projection matrix P describes the projection of R4 onto V = span{| 1 1 0 -2 | , | 1 5 1 1 |}.

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Answer:

4

Step-by-step explanation:

2-1=1

?-2=2

7-?=3

11-7=4

16-11=5

22-16=6

? must be 2+2= 4 since its true in both cases

hope this helped!

Check the picture below.

\(\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x\)

Answer:

Pretty sure its coefficient

Step-by-step explanation:

Answer:

The answer is graph D since y int = 3(1)+4 which is 7, that graph crosses y at 7

Answer:

167°

Step-by-step explanation:

The supplement of an angle will always be the measure of an angle, when added to the original, will equal 180°.

If we know the measure of 1 of these angles, we can easily find the measure of the other, assuming x is the missing angle measure.

\(13+x=180\)

We can subtract 13 from both sides to get the value of x.

\(13+x-13=180-13\\\\x=167\)

Hope this helped!

Answer:

167

Step-by-step explanation:

Supplementary angles add to 180

x+13 = 180

Subtract 13 from each side

x = 180-13

x =167

The supplement to 13 is 167

First step is to write the equation in slope-intercept form

\(x - 5y = 5\\-5y = -x+5\)      To make simplification easier, multiply negative to both sides

\(5y = x-5\\\)  Now, you must divide 5 to both sides to isolate the variable

\(y = \frac{x}{5} - 1\) To tell the slope more easily, turn \(\frac{x}{5}\) into \(\frac{1}{5} x\)

To rewrite the equation: \(y = \frac{1}{5} x - 1\)

Now, you are able to see the slope(m) being \(\frac{1}{5}\)

Next, you use the formula y=mx+b to solve for b (replace your newly found slope and points "x" and "y"

\(20 = (\frac{1}{5} *-15) + b\\20 = -3 + b\\b -3 = 20\\b = 23\)

Final Answer:   \(y = \frac{1}{5} + 23\)

Hope this helps :)

The volume of the cylinder is  1696.5652 cubic inches.

To calculate the volume of a cylinder, use the formula:

Volume = π × r² × h

where π is approximately 3.14159, r is the radius of the base, and h is the height of the cylinder.

Given that the diameter of the cylinder's base is 12 inches, the radius  calculated as half of the diameter:

Radius = 12 inches / 2 = 6 inches

The height of the cylinder is given as 1.25 feet, but we need to convert it to inches to match the units of the radius:

Height = 1.25 feet × 12 inches/foot = 15 inches

All the values needed to calculate the volume:

Volume = 3.14159 × 6² × 15

Simplifying the expression:

Volume = 3.14159 × 36 × 15

= 1696.5652 cubic inches

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a) Demand function: Qd = 30,000 - 100P, Supply function: Qs = -P b) Equilibrium price: $303.03, Equilibrium quantity: 27,697 vehicles. c) New equilibrium price: $333.33, New equilibrium quantity: 24,000 vehicles. d) Excess demand of 417 vehicles. e) New equilibrium price: $250, New equilibrium quantity: 24,750 vehicles.

a) The demand function for the bridge usage can be written as:

Qd = 30,000 - 100P

Where Qd represents the quantity demanded (number of vehicles crossing the bridge) and P represents the toll price.

The supply function for the bridge usage can be written as:

Qs = -P

Where Qs represents the quantity supplied (number of vehicles allowed to use the bridge by the city) and P represents the toll price.

b) To find the equilibrium price and quantity, we set the quantity demanded equal to the quantity supplied:

30,000 - 100P = -P

Simplifying the equation, we get:

30,000 = 99P

P = 303.03

Substituting the value of P back into either the demand or supply function, we find:

Qd = 30,000 - 100(303.03)

Qd = 27,697

Therefore, the equilibrium price is $303.03 and the equilibrium quantity is 27,697 vehicles.

c) If the demand for the bridge usage decreases by 10%, the new demand function becomes:

Qd = 0.9(30,000 - 100P)

Setting the new demand equal to the supply function:

0.9(30,000 - 100P) = -P

Solving the equation, we find:

P = 333.33

Substituting the value of P back into the demand or supply function, we get:

Qd = 0.9(30,000 - 100(333.33))

Qd = 24,000

Therefore, the new equilibrium price is $333.33 and the new equilibrium quantity is 24,000 vehicles.

d) With a toll charge of $100, we use the demand function from part c) and the original supply function:

0.9(30,000 - 100P) = -100

Solving the equation, we find:

P = 305.56

Substituting the value of P back into the demand or supply function, we get:

Qd = 0.9(30,000 - 100(305.56))

Qd = 24,417

Since the quantity demanded is greater than the quantity supplied, there is an excess demand of 24,417 - 24,000 = 417 vehicles.

e) If the supply of the bridge usage decreases by half, the new supply function becomes:

Qs = -0.5P

Setting the new supply equal to the demand function from part c):

0.9(30,000 - 100P) = -0.5P

Solving the equation, we find:

P = 250

Substituting the value of P back into the demand or supply function, we get:

Qd = 0.9(30,000 - 100(250))

Qd = 24,750

Therefore, the new equilibrium price is $250 and the new equilibrium quantity is 24,750 vehicles.

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Answer:

Step-by-step explanation:

2x + 6 = 6 + 2x

4 + 6 = 6 + 4

10 = 10

R = 1/3.

a. R = Does not converge
b. R = Cannot be determined without knowing the value of sum.gif
c. R = 1
d. R = 1
e. R = 1/3

To find the radius of convergence, R, of the series, we need to use the ratio test. The series is given by:

sum(n=1 to infinity) of a_n

where a_n is given by:

a_n = x^n * n^43^n

Applying the ratio test, we get:

lim (n → ∞) |a_n+1 / a_n| = lim (n → ∞) |x^(n+1) * (n+1)^43 * 3^(n+1) / (x^n * n^43 * 3^n)|

= lim (n → ∞) |x * (n+1)^43 * 3 / n^43|

= |x| * lim (n → ∞) ((n+1)/n)^43

= |x|

The series converges if the limit is less than 1 and diverges if the limit is greater than 1. Therefore, we need to solve the inequality |x| < 1 to find the radius of convergence, R.

a. If x = infinity, then the series diverges.

b. If x = sum.gif, then the series converges if |sum.gif| < 1. We cannot simplify this expression further without knowing the value of sum.gif.

c. If x = 1, then the series becomes:

sum(n=1 to infinity) of n^43

This is a p-series with p = 43 > 1, which converges. Therefore, R = 1.

d. If x = -1, then the series becomes:

sum(n=1 to infinity) of (-1)^n * n^43

This is an alternating series with decreasing terms. We can apply the alternating series test to show that it converges. Therefore, R = 1.

e. If x = 3, then the series becomes:

sum(n=1 to infinity) of n^43 * 3^n

This is a geometric series with a common ratio r = 3 > 1. Therefore, the series diverges.

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