how many sixths are there in 5 1/2

If a power series matches a function f(x) exactly everywhere, then the radius of convergence is infinite.

This means that the power series converges for all values of x. In other words, the power series can be used to approximate the function f(x) with arbitrary accuracy for any value of x.

This is a very powerful tool in mathematics and has many practical applications in science, engineering, and other fields.

The proof that a power series with infinite radius of convergence matches a function f(x) exactly everywhere is based on the fact that a power series is a sum of infinitely many terms, each of which is a polynomial in x.

By adding up these polynomials, we can approximate any function f(x) to an arbitrary degree of accuracy. The only limitation is that we need to know the coefficients of the power series,

which can be obtained by differentiating or integrating the function f(x) or by using other mathematical techniques. Once we have the coefficients, we can plug them into the power series formula and get an exact match for the function f(x).

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Answer:

- 4+23e

Step-by-step explanation:

Answer:

x =0    x=2

Step-by-step explanation:

3x^2 -6x = 0

Factor out a 3x

3x(x -2)=0

Using the zero product property

3x = 0  x-2 =0

x =0    x=2

The probability of landing on yellow is less than the probability of landing on blue

Probability is the likelihood of a desired event happening.

Since there are one orange, two purple, two yellow, and three blue and the spinner divided into eight equal colored sections.

Thus, we can write the probabilities as follow:

probability of orange = 1/8

probability of purple = 2/8 = 1/4

probability of yellow = 2/8 = 1/4

probability of blue = 3/8

Therefore, the probability of landing on yellow is less than the probability of landing on blue is the true statement

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I suppose your teacher want you to make a (a-b)^3 formula

Answer:

8 x^3 - 144 x^2 y + 864 x y^2 - 1728 y

Step-by-step explanation:

A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of 5 line pairs per millimeter (B).

A sampling frequency of 10 pixels per millimeter would produce a spatial resolution of B. 5 line pairs per millimeter.
Here's a step-by-step explanation:

1. The sampling frequency is given as 10 pixels per millimeter.
2. According to the Nyquist-Shannon sampling theorem, the maximum spatial frequency (in line pairs per millimeter) that can be accurately represented is half of the sampling frequency.
3. Divide the sampling frequency (10 pixels per millimeter) by 2: 10/2 = 5 line pairs per millimeter.

So, the answer is B. 5 line pairs per millimeter.

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By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.

An even number can be defined as a type of number which is divisible by two (2) without any remainder.

Since this 2-digit numbers are even and its digits are distinct, we can infer and logically deduce the following points:

By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.

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Answer:

-3

Step-by-step explanation:

Based on his weekly salary and commission, we can calculate that Mr. Randall sold goods worth $1,800.

In the formula given, sales is represented as s. To find the total sales, you can solve the equation:

300 + 0.07s = 426

0.07s = 426 - 300

s = 126 / 0.07

= $1,800

In conclusion, Mr. Randall sold $1,800 worth of goods.

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take the natural logarithm of both sides:

Divide both sides by ln(12):

Francis made an error in writing the explicit formula. The correct formula should be an = 4 * (1/4)⁽ⁿ⁻¹⁾, not an = 4 * (1/4)ⁿ⁻¹. The exponent should be (n-1), not just n, to correctly represent the sequence where the second term is 8 and the fourth term is 2.

To determine the error in Francis' formula, we need to apply it to the known terms of the sequence and see if it produces the correct values. For example, for the second term, n = 2, so using Francis' formula:

an = 4 * (1/4)⁽ⁿ⁻¹⁾ = 4 * (1/4)¹ = 4 * 1/4 = 1

But the second term of the sequence is 8, not 1. So the formula is incorrect.

Similarly, for the fourth term, n = 4, so using Francis' formula:

an = 4 * (1/4)⁽ⁿ⁻¹⁾ = 4 * (1/4)³ = 4 * 1/64 = 1/16

But the fourth term of the sequence is 2, not 1/16. So the formula is still incorrect.

Therefore, we can conclude that the formula written by Francis is not correct and needs to be corrected to accurately describe the sequence.

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The value of the f(3) is -8 or f(3)=-8 if the equation of the function f(x) = -8(3)⁰ or f(x) = -8 option (C) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

For the function, f(x) = -8

f(x) = -8

For all values of x:

The above function can be written as follows:

f(x) = -8x⁰

PLug x = 3 in the function:

f(x) = -8(3)⁰

f(x) = -8

Thus, the value of the f(3) is -8 or f(3)=-8 if the equation of the function f(x) = -8(3)⁰ or f(x) = -8 option (C) is correct.

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As there is a common ratio between each term so this is a geometric sequence.

The idea of geometric progression can be used to determine how much money you will have in your account after a particular number of years if you deposit money in a bank that offers a fixed annual rate of interest.

In a geometric progression or series, each term is equal to the one before it times the common factor, which is a fixed non-zero multiplier. The number of terms in a geometric series might be either finite or infinite.

Since in 6 12 and 24 the common ratio r=2. That is if we multiply the previous term by 2 we will get the next term so the given sequence is geometric sequence.

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Answer:

3/4

Step-by-step explanation:

We need two points to find the slope

( 20,20) and (60,50)

m = (y2-y1)/(x2-x1)

   = (50-20)/(60-20)

   = 30/40

   = 3/4

Using it's concept, the probability that a student plays basketball or soccer is given as follows:

B. 7/10.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

P(A or B) is the probability that a student plays basketball or soccer, hence, from the Venn diagram:

Hence the probability P(A or B), that is, the probability that a student plays basketball or soccer, is given as follows:

p = 7/10.

Which means that option B is correct.

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Answer:

0.75 was how much she paid for each postcard.

Step-by-step explanation:

6.04-3.79

=2.25

so take 2.25 divided by 3

= o.75

equations would be 6.04-3.75=b/ 3

Answer:

(b) 3 times the other pls write how u did it pls and thank u​

Step-by-step explanation:

The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

What is the domain and range?

The domain and range are fundamental concepts in mathematics that are used to describe the input and output values of a function or relation.

The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined.

The range of a function refers to the set of all possible output values, or y-values.

To find the domain and range of functions and represent them in different formats.

To find the domain and range of a function:

The domain refers to the set of all possible input values (x-values) for the function.

The range refers to the set of all possible output values (y-values) for the function.

To represent the function as a table, you would list the input-output pairs. For example:

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

To represent the function as a mapping, you would indicate the correspondence between the input and output values.

For example:

-3     ->   -4

-1     ->     2

0     ->     0

-3    ->     5

2     ->     4

To represent the function as a graph, The x-values would be on the horizontal axis, and the y-values would be on the vertical axis.

The points (-3, -4), (-1, 2), (0, 0), (-3, 5), and (2, 4) would be plotted accordingly.

Hence, The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

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Menara JLand project is a 30-storey high rise building located at the Johor Bahru city centre, featuring an ultra-modern facade with a unique combination of geometrically complex glass forms.

The Menara JLand project is an impressive 30-storey high rise building situated in the heart of Johor Bahru. Its standout feature is the ultra-modern facade that incorporates a stunning combination of unique geometrically complex glass forms. This design not only adds visual appeal but also reflects the contemporary and forward-thinking nature of the project.

One distinctive aspect of the building is the inclusion of a seven-storey podium, which enhances accessibility and functionality. The podium is accessible from the ground level, as well as the sixth and seventh floors, providing convenient access points for occupants and visitors. This design consideration ensures that the building caters to the needs of a diverse range of users and maximizes the efficient use of space.

The location of the Menara JLand project in Johor Bahru's city centre adds to its appeal and desirability. Being situated in a prominent area allows for easy access to various amenities and services, such as transportation hubs, restaurants, shopping centers, and other businesses. This central location ensures that the building serves as an ideal corporate office tower, offering a strategic advantage to businesses that choose to operate within it.

In conclusion, the Menara JLand project is an architecturally impressive 30-storey high rise building with a unique and striking ultra-modern facade. Its incorporation of a seven-storey podium and strategic location in Johor Bahru's city centre further enhances its appeal and functionality. This project is set to be a prominent landmark, embodying modern design principles while catering to the needs of businesses and occupants in the area.

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An obtuse triangle and right angle triangle can always be used as counter examples to the given statement.

What is acute angle?

An angle which is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle

What is obtuse angle?

An obtuse angle is a type of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.

What is right angle?

A right angle is an angle of exactly 90 degrees or \pi /2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles..

Hence, an obtuse triangle and right angle triangle can always be used as counterexamples to the given statement " All angles in a triangle are acute".

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The median of a distribution of one random variable, X, is a value of x of X, such that P(X=x) = 1/2. If there exists such a value, x, then it is called the median.

The probability distribution is given by `f(x) = 0.5x`, where `x = 1, 2, 3, .....`We have to find the median of the given distribution.To find the median, we have to find the value of x such that P(X = x) = 0.5.Now, we have to find the value of x such that the probability of X is 0.5.The probability distribution of X is given by f(x) = 0.5x, where x = 1, 2, 3, ....Therefore, we have to find the value of x such thatP(X = x) = 0.5f(x) = 0.5xP(X = x) = f(x)0.5x = 0.5x2 = xThus, the median of the distribution is 2.

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Answer:

15.7

Step-by-step explanation:

5 x 3.14(pi) = 15.7

Answer:

9.3 ft

Step-by-step explanation:

The probability that the mean of a sample of 7777 computers would be less than 82.59 months is 100%, or close to 1.

The probability that the mean of a sample of 7777 computers would be less than 82.5982.59 months, assuming a mean life of 80 months and a variance of 6464, can be calculated using the central limit theorem and the standard normal distribution.

First, we calculate the standard error of the mean using the formula:

standard error of the mean = σ/√n

where σ is the population standard deviation, n is the sample size.

Here, σ² = 6464, so σ = √6464 = 80.3

n = 7777

standard error of the mean = 80.3/√7777 ≈ 0.907

Next, we calculate the z-score using the formula:

z = (\(\bar{x}\) - μ) / (σ/√n)

where \(\bar{x}\) is the sample mean, μ is the population mean, σ is the population standard deviation, n is the sample size.

Here, \(\bar{x}\) = 82.59, μ = 80, σ = 80.3, n = 7777

z = (82.59 - 80) / (80.3/√7777) ≈ 8.6

We find that the probability of z being less than 8.6 is very close to 1, or 100%.

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Answer:

y = (1/3)x + 1

Step-by-step explanation:

A parallel line has the same slope as the reference line.  This means the new equation would have a slope of (1/3).  The y-intercept, -5, needs to be different.  But since the line needs to pass through point (3,2), we need a value of b that will cause that to happen.

We can start with y = (1/3)x + b.  As long as b is not -5, the line will be different and parallel.  To force it through point (3,2), just enter those values and solve for b:

y = (1/3)x + b

2= (1/3)*3 + b

2 = 1 + b

b = 1

The equation becomes y = (1/3)x + 1.

See attached image.

Answer:

11

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

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