Help due tonight!!!!

The series converges absolutely since there exist a p-series with p=6, and since p>1, therefore series converges absolutely.

To determine whether the series ∑(n=1 to infinity) (−1)^n(1 + 1/n^6) converges absolutely, conditionally, or not at all, we need to analyze the terms of the series.

First, let's check for absolute convergence. To do this, we take the absolute value of the terms in the series:
| (−1)^n(1 + 1/n^6) | = | (−1)^n | * | 1 + 1/n^6 |

Since | (−1)^n | = 1, this simplifies to:
| 1 + 1/n^6 |

Now, we need to test this new series for convergence. We can use the comparison test, by comparing it to the series ∑(n=1 to infinity) (1/n^6), which is a p-series with p = 6.

Since 6 > 1, the p-series converges, and because 1 + 1/n^6 > 1/n^6 for all n, the original series also converges absolutely.

Therefore, the series ∑(n=1 to infinity) (−1)^n(1 + 1/n^6) converges absolutely.

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Answer:

64

Step-by-step explanation:

x+y = 7

xy = 10

2x+2y+5xy = 2(x+y)+5(xy) = 2*7+5*10 = 14 + 50 = 64

Answer:

The answer is G = -5

Step-by-step explanation:

your welcome :)

A sample size of approximately 1244 would provide a margin of error of 2 at a 95% confidence level.

a. The planning value for the population standard deviation can be estimated as half of the estimated range. Since the estimated range is 36, the planning value for the population standard deviation would be 36/2 = 18.

b. To determine the sample size required to achieve a margin of error of 3 at a 95% confidence level, we can use the formula:

n = (Z * σ / E)^2

Where:

n = sample size

Z = Z-score corresponding to the desired confidence level (95% confidence corresponds to a Z-score of approximately 1.96)

σ = population standard deviation (estimated as 18 in this case)

E = margin of error (3 in this case)

Plugging in the values:

n = (1.96 * 18 / 3)^2

n ≈ (35.28)^2

n ≈ 1243.58

Therefore, a sample size of approximately 1244 would provide a margin of error of 3 at a 95% confidence level.

c. Similarly, to achieve a margin of error of 2 at a 95% confidence level, we can use the same formula:

n = (Z * σ / E)^2

Plugging in the values:

n = (1.96 * 18 / 2)^2

n ≈ (35.28)^2

n ≈ 1243.58

Therefore, a sample size of approximately 1244 would provide a margin of error of 2 at a 95% confidence level.

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The numerical form of the statement is 4n + 7 = 2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A statement the sum of 4 times a number and 7 is equal to 2.

Let, The number be 'n'.

The numerical form of the statement will be,

4n + 7 = 2.

4n = 2 - 7.

4n = - 5.

n = - 5/4.

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Answer: \(= (\frac{5\sqrt{3} }{3x })\)      

Step-by-step explanation:

I can't see B but I will do C

C)

\(\frac{\sqrt{5} }{\sqrt{3x^{2} } }\)                            >the x² can come out because √x² = x

\(=\frac{5}{x\sqrt{3} }\)                         >You cant have a root on bottom so multiply by \(\frac{\sqrt{3} }{\sqrt{3} }\)

\(=\frac{5}{x\sqrt{3} } (\frac{\sqrt{3} }{\sqrt{3} })\)

\(= (\frac{5\sqrt{3} }{3x })\)      >This is your simplified answer

The number of players on a basketball team is a discrete random variable.

Explanation:

A discrete random variable is a variable that can only take on a countable number of distinct values.

In this case, the number of players on a basketball team can only be a whole number, such as 5, 10, or 12. It cannot take on fractional values or values in between whole numbers. Therefore, it is a discrete random variable.

On the other hand, the length of people's hair, the height of students in a class, and the weight of newborn babies are continuous random variables. These variables can take on any value within a certain range and are not restricted to only whole numbers.

For example, hair length can vary from very short to very long, height can range from very short to very tall, and weight can vary from very light to very heavy. These variables are not countable in the same way as the number of players on a basketball team, and therefore, they are considered continuous random variables.

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Answer:

Step-by-step explanation:

(1) 6x-2y=156

2×(2) ; 2(x-y=18)

;2x-2y=36

from (1)-2×(2)

is 6x-2y=156 -

2x-2y=36

4x=120

x=30

from (2)

x-y=18

x-18=y

y=30-18

y=12

Answer:

Samuel : x

wife : y

sum of their age : 2+ x : 10

Answer:

Graph A

Step-by-step explanation:

The electron domain charge cloud geometry of \(BrF_5\) is trigonal bipyramidal.

To determine the electron domain charge cloud geometry of \(BrF_5\), we need to examine the number of electron domains around the central atom (Br).

\(BrF_5\) consists of one central bromine atom (Br) surrounded by five fluorine atoms (F). Each bond and lone pair of electrons represents an electron domain.

In \(BrF_5\), there are five bonding pairs (Br-F) and no lone pairs around the central bromine atom. Therefore, the total number of electron domains is five.

Based on this information, the electron domain charge cloud geometry of \(BrF_5\) is trigonal bipyramidal.

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Answer:

sum

Step-by-step explanation:

The sum of c and d is c+d.

Answer:

1)probability of choosing a yellow marble is 6/14 or 3/7(in lowest terms)

2)probability of showing its heads is 1/2

The domain of a function represents all the possible input values, or values of x, for which the function is defined. In the case of the function f(x) = ln(10-x), we need to consider the restrictions on the natural logarithm function.

The natural logarithm function ln(x) is defined only for positive real numbers. Specifically, ln(x) is defined for x > 0. Therefore, in order for f(x) = ln(10-x) to be defined, we must have 10-x > 0.

To find the domain, we solve the inequality 10-x > 0 for x:

10-x > 0

-x > -10

x < 10

So, the domain of f(x) is all real numbers less than 10. In interval notation, we can express the domain as (-∞, 10).

However, we also need to consider any potential restrictions on the function due to other mathematical operations or expressions within f(x). In this case, since we have a logarithmic function as the main expression, the only restriction is that the argument of the logarithm, 10-x, must be positive. Therefore, we need to exclude any values of x that would make 10-x ≤ 0.

From our earlier inequality, x < 10. So, to ensure that 10-x is positive, we need to exclude x values that are greater than or equal to 10. Therefore, the final domain of f(x) is (-∞, 10).

In summary, the domain of the function f(x) = ln(10-x) is (-∞, 10), meaning that any real number less than 10 can be input into the function.

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Answer:

x=1/3

hope this helps!!! :)

Answer:

70°

Step-by-step explanation:

All triangles' angles are added up to 180°

30 + 80 + x = 180

110 + x = 180

x = 180 - 110

x = 70

Answer:

\(x = 70\)

Step-by-step explanation:

\(x = 180 - (30 + 80)\)

\(x = 180 - 110\)

\(x = 70\)

to be sure

\(70 + 80 + 30 { = }^{?} 180\)

\(100 + 80 { = }^{?} 180\)

\(180 = 180\)

Answer: 12x

Step-by-step explanation:

12 times x = 12x

Hope it helped u,

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Tony must give 3 pencils to Peter,

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Let Peter has x pencils and Tony has y pencils.

Then, we have equation x=3y (Peters pencils are 3 times as Tony).

Total pencils =  30+14

                     = 44 pencils.

So, x + y=44

Put x= 3y we get

3y+ y= 44

4y= 44

y= 11

Thus, Tony must give 3 pencils to Peter,

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The probability that a student's score is less than 81 points on the reading ability test is 0.9772. We would expect approximately 489 students to earn a score less than 81 points if 500 students took the reading ability test. The probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

To find the probability that a student's score is less than 81 points, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the student's score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get:

z = (81 - 65) / 8 = 2.00

Using a standard normal distribution table or calculator, we can find the probability of a z-score less than 2.00 to be approximately 0.9772. Therefore, the probability that a student's score is less than 81 points is 0.9772.

Since the distribution is normal, we can use the normal distribution to estimate the number of students who would earn a score less than 81. We can standardize the score of 81 using the z-score formula as above and use the standardized score to find the area under the normal distribution curve. Specifically, the area under the curve to the left of the standardized score represents the proportion of students who scored less than 81. We can then multiply this proportion by the total number of students (500) to estimate the number of students who would score less than 81.

z = (81 - 65) / 8 = 2.00

P(z < 2.00) = 0.9772

Number of students with score < 81 = 0.9772 x 500 = 489

Therefore, we would expect approximately 489 students to earn a score less than 81 points.

The distribution of the sample mean reading ability test scores is also normal with mean μ = 65 and standard deviation σ / sqrt(n) = 8 / sqrt(35) ≈ 1.35, where n is the sample size (number of students in the sample). To find the probability that the sample mean score is between 66 and 68, we can standardize using the z-score formula:

z1 = (66 - 65) / (8 / sqrt(35)) ≈ 0.70

z2 = (68 - 65) / (8 / sqrt(35)) ≈ 2.08

Using a standard normal distribution table or calculator, we can find the probability that a z-score is between 0.70 and 2.08 to be approximately 0.2190. Therefore, the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

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Step-by-step explanation:

I think...

18×9=9×18

hope it helps

Answer:

Let the width be x feet. As length is 3 feet longer, it is x+3 feet. As perimeter is twice of te sum of length and width, it is 2×(x+3+x)=2×(2x+3)=4x+6 feet.

Step-by-step explanation:

Answer:

240gb

Step-by-step explanation:

Answer:

SAS ( Side, Angle, Side)

Step-by-step explanation:

Both triangles - shown by the arcs labelled on them - have two known congruent sides, and an angle which they are both equal to.

(No units are needed as this shows already that both triangles are congruent to each other)

Hope this helps

The differential equation to be solved is Nxy - 0.5ye-0.1x for osx54 with y(0) = 6.5 dx. This can be solved using Euler's method in MATLAB.

Follow the steps below.

Step 1: Create a function file - The differential equation needs to be defined in a function file first. Let's create a function file named "odefun.m".function dydx = odefun(x,y)

dydx = N*x*y - 0.5*y*exp(-0.1*x);

where N is a constant value that needs to be defined.

Step 2: Define the given values - Define the given values such as N, initial value y(0), and step size dx.

N = ...; %

Define N herey 0 = 6.5; %

Define initial value of y here. dx = ...; %

Define step size here

Step 3: Use Euler's method to solve the differential equation - Now, use Euler's method to solve the differential equation using a for loop. The MATLAB code is as follows: x = 0:dx:54; %

Define range of x values here y = zeros(size(x)); %

Initialize y as a vector of zeros y(1) = y0; %

Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end

Step 4: Plot the solution - Finally, plot the solution using the MATLAB command plot(x,y).

The complete MATLAB code is given below:

N = ...; %

Define N here y0 = 6.5; %

Define initial value of y here dx = ...; %

Define step size here x = 0:dx:54; %

Define range of x values here y = zeros(size(x)); % Initialize y as a vector of zeros y(1) = y0; %

Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end plot(x,y)

The plot of the solution will be displayed.

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Answer:

decay factor is 0.43

Step-by-step explanation:

1-0.57=0.43

Answer: 5

5/8/1/8, you can do 5x8 and also do 8x1 because you can not divide fractions after that you get 40/8 then you divide 40/8 is 5 so the answer is 5