suppose that the radius of convergence of the power series ∑cn^ x^n is R. what is the radius of convergence of the power series ∑cn x^3n ?

Answer:

Eminem.

Rakim.

Nas.

Andre 3000.

Lauryn Hill.

Ghostface Killah.

Kendrick Lamar.

Lil Wayne

Step-by-step explanation:

Answer:

Logic

Step-by-step explanation:

The length of a vector 'v' in an n-dimensional Euclidean space is calculated as the square root of the dot product of the vector with itself, or ‖v‖ = \(\sqrt{(v.v)}\) = \(\sqrt{(v1^{2}+v2^{2} +.... + vn^{2} )}\).

The length of a vector 'v' in an n-dimensional Euclidean space is denoted as ‖v‖ and can be calculated asthe vector's dot product with itself, square root:

‖v‖ = \(\sqrt{(v.v)}\) = \(\sqrt{(v1^{2}+v2^{2} +.... + vn^{2} )}\)

So, to find the length of the vector 'v', we simply substitute its components in the above equation.

The length of a vector, also known as its magnitude or norm, is a scalar value that represents the magnitude of the vector in a given space. In the context of an n-dimensional Euclidean space, the length of a vector can be calculated as the square root of the dot product of the vector with itself. This calculation is based on the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares formed by the other two sides' lengths.

In mathematical terms, the length of a vector 'v' in an n-dimensional Euclidean space is calculated as follows:

‖v‖ = \(\sqrt{(v.v)}\) = \(\sqrt{(v1^{2}+v2^{2} +.... + vn^{2} )}\)

where 'v' is the vector, and 'v1', 'v2', ..., 'vn' are its components in the n-dimensional space. The dot product of the vector with itself (v · v) is equivalent to the sum of the squares of its components. The square root of this sum is the final length of the vector.

The length of a vector is an important concept in linear algebra and geometry. It is used to measure the distance between two points in a space, to calculate angles between vectors, to normalize vectors, and for various other mathematical and practical applications.

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(a) The number of ways that the event can occur is 6.

(b) Probabilities are :

1) 1/2, 2) 1/6 and 3) 1/3.

(a) Given a bag of different shapes.

Total number of shapes = 6

So, if we select one shape from random,

total number of ways that the event can occur = 6

(b) Number of squares in the bag = 3

Probability of choosing a square = 3/6 = 1/2

Number of circles in the bag = 1

Probability of choosing a circle = 1/6

Number of stars in the bag = 2

Probability of choosing a star = 2/6 = 1/3

Hence the required probabilities are found.

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Answer:

You have to substitute x for 3. Then you mutiply -2 and 3 and get -6 then add 1 and then you will get -5.

Step-by-step explanation:

Hope this helps

If a between-subjects design uses random assignment, the design will be called an independent groups design.

This means that participants are randomly assigned to either the experimental or control group, ensuring that the groups are equivalent at the start of the study. This type of design allows for a comparison of the effects of the independent variable on the dependent variable between the groups. I

t is important to note that an independent groups design is different from a matched groups design, in which participants are paired based on certain characteristics before being assigned to different groups. The use of random assignment in an independent groups design helps to control for extraneous variables and increase the internal validity of the study.

If a between-subjects design uses random assignment, the design will be called a(n) c. independent groups design. This design involves assigning participants to different experimental groups or conditions using random allocation. This ensures that each participant has an equal chance of being assigned to any group, reducing potential confounds and increasing the validity of the results. The independent groups design allows for comparison between the groups and the examination of the effects of the independent variable on the dependent variable.

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Answer:

Hello! answer: angle n is. 51

Step-by-step explanation:

This is a complementary angle meaning it will add up to 90 degrees so...

3 × 8 = 24 24 + 15 = 39

2 × 8 = 16 16 + 35 = 51

39 + 51 = 90 therefore angle n is 51 hope that helps!

Answer:

168.96

Step-by-step explanation:

21.12 x 8 = 168.96

Answer:

$2.26

Step-by-step explanation:

21.12/8

just divide

Answer:

It is x=908.

Might be wrong tho so dont jump me

Answer: 908

Step-by-step explanation:

x/4 = 89 + 138

x/4 = 227

x = 227 x 4

x = 908

Step-by-step explanation:

Calculate the percent value:

0.8 =

0.8 × 100/100 =

(0.8 × 100)/100 =

80/100 =

80%;

The appropriate simulation applet to calculate an approximate p-value is 0.0077.

The strong evidence that a short delay hinders the memorization process is strong data suggests that a brief delay impairs memorization.

Delay or no delay, answer: the number of words remembered

The mean distance between words remembered with and without delay over time is null, or zero.

Alt: The mean distance in words remembered over the long term (with no delay minus with delay) is higher than 0.

Yes, the majority of the lines do skew to the right. The mean for no delay is 10.55 whereas that for with delay is 8.7.

The mean distance in words remembered is 1.85.

1)0.0077 as the p-value

2)Strong data suggests that a brief delay impairs memorization.

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According to cylindrical coordinates, the mass of the solid Q is 69kπ.

The density function for the solid is given by rho (x,y,z) = k(x^2+y^2).

Where the solid Q is defined by the following inequality:

\(Q={(x,y,z):0≤z≤9−x−2y,x^2+y^2≤36}\)

To compute the mass of this solid Q, we first need to calculate the volume of the solid.

The volume V of the solid can be computed using triple integrals in cylindrical coordinates as follows:

\(V = ∫∫∫ρ(r, θ, z) r dz dr dθ\)

where \(ρ(r, θ, z) = k(r^2)\)

The bounds for the triple integral are as follows:

\(r ∈ [0, 6]θ ∈ [0, 2π]z ∈ [0, 9-r cos(θ) - 2r sin(θ)]\)

So, the mass of the solid Q is given by:

\(M = ∫∫∫ρ(r, θ, z) dV= k∫∫∫(r^3) dz dr dθ= k∫0^{2π}∫0^6∫0^{9-r cos(θ) - 2r sin(θ)}(r^3) dz dr dθM= k∫0^{2π}∫0^6 [(r^3)(9-r cos(θ) - 2r sin(θ))] dr dθ= k∫0^{2π} [2(3/4)(46-6r^2 sin(θ) - 3r^2 cos(θ))] dθ= k(69π)\)

Therefore, the mass of the solid Q is 69kπ.

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Answer:

C-All real numbers less than or equal to 40

Step-by-step explanation:

none of the other answers make any sense

Answer:

Step-by-step explanation:

The ant will be on the side of the pentagon that is adjacent to the corner P, when it has covered 5/8th of the total distance around the pentagon.

Solution:

To determine the answer to this question, we will use two formulas.

The first formula is the formula for the interior angles of a regular polygon

The second is the formula for the distance around a regular polygon.

Formula for the interior angles of a regular polygon:

=((n-2) ×180) ÷ n,

where n is the number of sides.

Formula for the distance around a regular polygon:

=ns,

where n is the number of sides and s is the length of each side.

We are given that PQRST is a regular pentagon. Therefore, it has five equal sides.

Let the length of each side be s.

We need to find the total distance around the pentagon, which is given by 5s.

Next, we will use the formula for the interior angles of a regular pentagon.

((n-2) ×180) ÷ n

= ((5-2) × 180) ÷ 5

= 108°.

Each interior angle of a regular pentagon is 108°.

Therefore, the exterior angle of a regular pentagon is 180 - 108 = 72°.

This means that the ant covers 72° each time it crawls around a corner.

5/8th of the total distance around the pentagon is given by:

(5/8) × 5s = (25/8)s.

This means that the ant will have covered :

(72/360) × (25/8)s

= (5/4)s

= 1.25s when it has covered 5/8th of the total distance around the pentagon.

Therefore, the ant will be on the side of the pentagon that is adjacent to the corner P.

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The relation which represents the relationship in the table t = 12h.

What is the equation?

An equation is a mathematical statement that shows the equality between two expressions, typically using variables, constants, and mathematical operators.

# OF HOURS (H)      1     2     3    4     5

TOTAL EARNINGS (T)  12   24    36    48    60

A. h = 12t

B. t = 12h

C. h = c/12

D. c = h/12

To determine the equation that best represents the relationship in the table, we need to look for a pattern or relationship between the hours worked and the total earnings. From the table, we can see that the total earnings increase by $12 for each additional hour worked. This suggests a linear relationship between the hours worked and the total earnings, with a slope (rate of change) of $12 per hour.

The equation that represents this relationship is:

t = 12h

where T is the total earnings and H is the number of hours worked.

Hence, the relation which represents the relationship in the table t = 12h.

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The equation Q = -L³ + 15 represents the production function of Plainfield Electronics, where Q is the quantity of industrial control panels produced and L is the level of labor input.

In this production function, the term -L³ indicates that there is diminishing returns to labor. As the level of labor input increases, the additional output produced decreases at an increasing rate. The term 15 represents the level of output that would be produced with zero labor input, indicating that there is some fixed component of output. To maximize production, the firm would need to determine the optimal level of labor input that maximizes the quantity of industrial control panels produced. This can be done by taking the derivative of the production function with respect to labor (dQ/dL) and setting it equal to zero to find the critical points. dQ/dL = -3L². Setting -3L² = 0, we find that L = 0.

Therefore, the critical point occurs at L = 0, which means that the firm would need to employ no labor to maximize production according to this production function. However, this result seems unlikely and may not be practically feasible. It's important to note that this analysis is based solely on the provided production function equation and assumes that there are no other factors or constraints affecting the production process. In practice, other factors such as capital, technology, and input availability would also play a significant role in determining the optimal level of production.

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The following is the expected value of a number of books a student buys at the next book fair is 2.404 books.

The random variable b's expected value is then calculated as follows:

E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 E(X)  = 2.404 books.

Thus, the expected value of discrete probability distribution is 2.404 books.

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The graph for the question is attached.

The solution to the system of differential equations is x(t) = -\(3e^{(31t)\) and z(t) = -\(3e^{(31t\)).

To solve the given system of differential equations, we'll begin by finding the eigenvalues and eigenvectors of the coefficient matrix.

The coefficient matrix is A = [[-22, 54], [-9, 23]]. To find the eigenvalues λ, we solve the characteristic equation det(A - λI) = 0, where I is the identity matrix.

det(A - λI) = [[-22 - λ, 54], [-9, 23 - λ]]

=> (-22 - λ)(23 - λ) - (54)(-9) = 0

=> λ^2 - λ(23 + 22) + (22)(23) - (54)(-9) = 0

=> λ^2 - 45λ + 162 = 0

Solving this quadratic equation, we find the eigenvalues:

λ = (-(-45) ± √((-45)^2 - 4(1)(162))) / (2(1))

λ = (45 ± √(2025 - 648)) / 2

λ = (45 ± √1377) / 2

The eigenvalues are λ₁ = (45 + √1377) / 2 and λ₂ = (45 - √1377) / 2.

Next, we'll find the corresponding eigenvectors. For each eigenvalue, we solve the equation (A - λI)v = 0, where v is the eigenvector.

For λ₁ = (45 + √1377) / 2:

(A - λ₁I)v₁ = 0

=> [[-22 - (45 + √1377) / 2, 54], [-9, 23 - (45 + √1377) / 2]]v₁ = 0

Solving this system of equations, we find the eigenvector v₁.

Similarly, for λ₂ = (45 - √1377) / 2, we solve (A - λ₂I)v₂ = 0 to find the eigenvector v₂.

The general solution of the system is x(t) = c₁e(λ₁t)v₁ + c₂e(λ₂t)v₂, where c₁ and c₂ are constants.

Using the initial condition x(0) = -3, we can substitute t = 0 into the general solution and solve for the constants c₁ and c₂.

Finally, substituting the values of c₁ and c₂ into the general solution, we obtain the particular solution for x(t).

Since z(t) = x(t), the solution for z(t) is the same as x(t).

Therefore, the solution to the system of differential equations is x(t) = \(-3e^{(31t)\) and z(t) = -\(3e^{(31t)\).

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Inequality (C) -3.2 + 1.5n ≤ 8.6 correctly represents the sentence "the sum of negative 3.2 and 1.5 times a number is a maximum of 8.6."

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

Both mathematical phrases, equations, and inequalities are created by connecting two expressions.

The equal sign (=) indicates that two expressions in an equation are believed to be equivalent.

The symbols >, <, ≤ or ≥ indicate that the two expressions in inequality are not always equal.

So, the sentence we have is:

the sum of negative 3.2 and 1.5 times a number is a maximum of 8.6

Which can be written in inequality as:

-3.2 + 1.5n ≤ 8.6

Therefore, inequality (C) -3.2 + 1.5n ≤ 8.6 correctly represents the sentence "the sum of negative 3.2 and 1.5 times a number is a maximum of 8.6."

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Correct question:
Which inequality represents the sentence?

the sum of negative 3.2 and 1.5 times a number is a maximum of 8.6.

a. -3.2n + 1.5 less-than-or-equal-to 8.6

b. -3.2n -  1.5 greater-than-or-equal-to 8.6

c. -3.2 +  1.5n less-than-or-equal-to 8.6

d. -3.2 -  1.5n less-than-or-equal-to 8.6

To find the slope of the curve \(y=x^2-4x-5\) at the point P(3,-8) using the limit of the secant slopes, we need to calculate the slope between P and nearby point on curve as distance between points approaches zero.

The slope of a curve at a specific point can be approximated by calculating the slope of a secant line that passes through that point and a nearby point on the curve. In this case, we are interested in finding the slope at point P(3,-8). Let's choose another point on the curve, Q, with coordinates (x, y). The slope of the secant line passing through points P and Q is given by (y - (-8))/(x - 3). To find the slope of the curve at point P, we need to calculate the limit of this expression as the point Q approaches P.

To do this, we substitute the equation of the curve, \(y=x^2-4x-5\), into the expression for the slope of the secant line. We have (x^2-4x-5 - (-8))/(x - 3). Simplifying this expression gives \((x^2-4x+3)/(x-3)\). Taking the limit of this expression as x approaches 3, we get \((3^2-4(3)+3)/(3-3)\), which becomes (9-12+3)/0. Since we have a 0 in the denominator, we cannot directly evaluate the limit. However, this form suggests that we have a factor of (x-3) in both the numerator and denominator. Factoring the numerator further gives ((x-3)(x-1))/(x-3). Canceling out the common factor (x-3), we are left with (x-1). Substituting x=3 into this expression gives the slope of the curve at point P as (3-1), which is equal to 2.

Therefore, the slope of the curve \(y=x^2-4x-5\) at point P(3,-8) is 2.

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Answer: A, D, and E

Step-by-step explanation: you can solve them just by adding with no additional steps

The highest/most positive possible 16-bit offset/biased-N representation value can be obtained by assigning the maximum value to each bit in the 16-bit binary pattern.

In a 16-bit representation, each bit can have a value of either 0 or 1. To represent the highest/most positive value, we assign 1 to each bit. Thus, the binary pattern would be: 1111111111111111

In this pattern, all 16 bits are set to 1, indicating the highest possible value in a 16-bit offset/biased-N representation. This binary pattern represents the maximum positive value that can be represented using 16 bits.

It is important to note that this pattern represents the highest value within the constraints of a 16-bit representation. If we were to convert this binary pattern to decimal, it would correspond to the decimal value 65535.

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Answer:

m=9n

Step-by-step explanation:

Linear equation, straight forward m=3n. Highlighted point is n=3 and m=9*3=27

The equation for the total money raised will be m = 9n.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that the drama club sells sweatshirts for $9 dollars each to raise money for their club.

From the table:-

The number of Sweatshirts               Money raised

       1                                                            9

       3                                                          27    

       4                                                           36

The equation will be written as:-

m = 9n

m = 9 x 1 = 9

m = 9 x 3 = 27

m = 9 x 4 = 36

Therefore, the equation for the total money raised will be m = 9n.

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Answer:

x=

Step-by-step explanation:

Answer:

Do you have a picture that goes with the question that you can post?

Step-by-step explanation:

$98 is the final price of the sneaker be after the discount is taken off

percentage, a relative value indicating hundredth parts of any quantity.

Given that in macy's department store, every item has a 30% discount or markdown.

The original price of a pair of Adidas sneakers cost $140

We need to find the final price of the sneaker be after the discount is taken off

Let us find 30% of 140

Convert 30% to decimal value by dividing with 100

30/100×140

0.3×140=42

So 30% of 140 is 42.

After removing discount the amount will be 140-42=98

Hence, $98 is the final price of the sneaker be after the discount is taken off

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The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.