Find the difference. use your answer in the simplest terms, using the slash ( / ) as the fraction bar.
1/2 - 1/4

A convergence radius calculator is a tool used in calculus to calculate the radius of convergence for a power series using the ratio test.

To calculate the convergence radius of a power series, one can use a formula known as the "ratio test". The ratio test involves taking the limit of the absolute value of the ratio of successive terms in the series, as n approaches infinity. If this limit exists and is less than 1, then the series converges absolutely. The convergence radius can then be found as the reciprocal of this limit.

For example, given the power series:

∑(n=0 to infinity) [tex](x-2)^n / n^2[/tex]

we can use the ratio test to find the convergence radius as follows:

[tex]|(x-2)^(n+1) / (n+1)^2| / |(x-2)^n / n^2|[/tex]

= [tex]|(x-2) / (n+1)|^2 * (n^2 / (x-2)^2)[/tex]

= [tex](n^2 / (n+1)^2) * (1 / (x-2)^2)[/tex]

= [tex]n^2 / ((n+1)^2 * (x-2)^2)[/tex]

Taking the limit of this expression as n approaches infinity, we get:

[tex]lim(n- > ∞) (n^2 / ((n+1)^2 * (x-2)^2))[/tex]

= [tex]1 / (x-2)^2[/tex]

Since this limit exists and is less than 1 for all x except x=2, the power series converges absolutely for all values of x within a radius of [tex]1/(x-2)^2[/tex] centered at x=2. Therefore, the convergence radius of the power series is 1.

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The math topics covered in the grade 6 math worksheets are algebra,geometry,measurement, number operation.

1. Number sense and operations: This includes understanding numbers, fractions, decimals, and integers, as well as performing operations with them.

2. Algebra: This includes understanding algebraic expressions and equations, and using them to solve problems.

3. Geometry: This includes understanding basic geometric concepts, such as lines, angles, and shapes, and using them to solve problems.

4. Measurement: This includes understanding measurement concepts, such as length, area, and volume, and using them to solve problems.

5. Data analysis and probability: This includes understanding basic concepts of statistics, such as mean, median, and mode, and using them to analyze data and make predictions.

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By using synthetic division, we can find all the roots of the function f(x) = x³ + 3x² - x - 3 and determine that the roots are 1, -1, and -3.

A root of a function is a value for x that makes the function equal to zero.

In this case, we have a function f(x) = x³ + 3x² - x - 3 and we know that f(1) = 0. To find all the roots of this function, we can use the remainder theorem.

The remainder theorem states that if we divide a polynomial by a linear expression (such as x - a), the remainder will be equal to the value of the polynomial at that value of x (a). In other words, if we write f(x) = (x - a)q(x) + r, where r is the remainder, then f(a) = r.

So, if we divide our function f(x) by x - 1, the remainder will be equal to f(1), which we know is zero. Therefore, (x - 1) is a factor of f(x), and the function has a root at x = 1.

Next, we can divide f(x) by (x - 1) to get a quotient, q(x), and a new remainder, r. We can repeat this process, dividing q(x) by another linear expression until we have no more remainders.

The roots of f(x) will be the values of x that we used as factors in each step of the division process.

This process of dividing a polynomial by a linear expression to find its roots is called synthetic division.

Complete Question

If f(1) = 0, what are all the roots of the function f(x) = x³ + 3x² - x - 3. Use the remainder theorem.

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From the given information provided, 20% off 250000 is 50000, and the discounted price is 200000.

The formula for calculating percentage is:

percentage = (part/whole) x 100

Here's an example:

Let's say you got 35 out of 50 questions correct on a test. To calculate the percentage of questions you answered correctly, you would use the formula as follows:

percentage = (35/50) x 100

percentage = 0.7 x 100

percentage = 70%

To calculate 20% off 250000, you can multiply 250000 by 20% (which is 0.20 in decimal form) and then subtract the result from 250000:

250000 - (0.20 x 250000) = 250000 - 50000 = 200000

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Answer:

8.31, 8.3, 8.296, 8.06

Step-by-step explanation:

8.31, 8.296, 8.06, 8.3

The order of decimals from greatest to least is

8.31, 8.3, 8.296, 8.06

Answer:

A. 10

Step-by-step explanation:

2/4 = x/20

1/2 = x/20

2x = 20

x = 10

Answer: 10

Answer:

Step-by-step explanation:

y= -2x + 5

The area of the logo is given as 139 cm

In order to get the area of the shape, i would have to get the area of the triangles first

area of a triangle = 1/2 b * h

base = 9 / 2 = 4.5

h = 6

area = 1/2 * 9 * 6

= 27

Area of 2 triangle = 2 x 27

= 58

The are aof the square = a * a

= 9 * 9

= 81

The total area of the logo is given as 81 + 58

= 139 cm

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If a 2020 study showed that the presence of male pattern baldness and a severe reaction to COVID-19 had a strong association: A. Age is the most likely lurking variable in this scenario.

In this case, the relationship between male pattern baldness and severe COVID-19 reactions may be influenced by age, as older individuals are more likely to experience both male pattern baldness and severe COVID-19 symptoms.

Age could also affect other factors such as overall health and immune system function, which may contribute to the severity of COVID-19 symptoms.

Diet, height, and weight may also be related to overall health and immune system function, but they are less likely to be related specifically to male pattern baldness

Therefore, age is the most likely lurking variable in this scenario.

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The resultant of the given expression (5x-2)(2x+7) is  10x² + 31x - 14

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that contains variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent mathematical relationships and can be used to solve equations and perform calculations.

For example, the expression "3x + 2" is an algebraic expression that contains the variable "x", the numbers "3" and "2", and the mathematical operations of addition and multiplication.

Given expression ,

(5x-2)(2x+7)

= (5x-2)(2x+7) = 5x(2x) + 5x(7) - 2(2x) - 2(7)

= 10x² + 35x - 4x - 14

= 10x² + 31x - 14

Therefore, The resultant of the given expression (5x-2)(2x+7) is  10x² + 31x - 14

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Answer:

y = 6x

Step-by-step explanation:

The line is sloping up at a rate of 6 y units per 1 x unit. So the slope is 6/1 (6x)

To convert 200 micrograms (mcg) to milligrams (mg), we need to use the conversion factor that 1 milligram is equal to 1000 micrograms, 200 micrograms (mcg) is equal to 0.2 milligrams (mg).

When we want to convert a unit of measurement to another unit of measurement, we use conversion factors to make the conversion. In the case of converting micrograms (mcg) to milligrams (mg), we need to know that 1 milligram is equal to 1000 micrograms. This means that to convert any value from micrograms to milligrams, we need to divide by 1000.

To convert 200 micrograms (mcg) to milligrams (mg), we need to use the conversion factor that 1 milligram is equal to 1000 micrograms.

So, to convert 200 mcg to mg, we divide 200 by 1000:

200 mcg ÷ 1000 = 0.2 mg

Therefore, 200 micrograms (mcg) is equal to 0.2 milligrams (mg)

It is important to understand the concept of unit conversions because it is a crucial aspect of many scientific and engineering calculations. Knowing how to convert units of measurement allows us to work with data that is expressed in different units and compare results from different experiments. In addition, being able to convert units is a valuable skill for everyday life, such as when reading nutrition labels or measuring medication dosages.

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The solution is,  total interest will you pay is  $13750.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

given that,

A loan of $25,000 has an annual simple interest rate of 5.5%.

The total cost of the loan is $38,750.

so, total interest will you pay = $(38750 - 25000)

                                                 = $13750

Hence, The solution is,  total interest will you pay is  $13750.

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To find the two largest numbers in an array in Matlab, you can use the sort function and indexing to access the two largest elements.

Here's an example:

array = [3, 8, 2, 10, 5];

sorted_array = sort(array, 'descend');

largest_number = sorted_array(1);

second_largest_number = sorted_array(2);

In this example, we have an array of numbers called array. We use the sort function to sort the array in descending order, which means that the largest numbers will be at the beginning of the array. The resulting sorted array is assigned to a new variable called sorted_array.

We then use indexing to access the first and second elements of the sorted array, which will be the two largest numbers. These numbers are assigned to the variables largest_number and second_largest_number, respectively.

It's important to note that if the array contains duplicate values, this method will return the two largest unique values. If you want to find the two largest values including duplicates, you can use the max function twice with the 'omitnan' parameter to handle any NaN values in the array:

array = [3, 8, 2, 10, 5, 10];

largest_number = max(array, [], 'omitnan');

array_without_largest_number = array(array < largest_number);

second_largest_number = max(array_without_largest_number, [], 'omitnan');

In this example, we first find the largest number in the array using the max function with the 'omitnan' parameter to ignore any NaN values. We then create a new array that excludes the largest number, and use the max function again to find the second largest number in the new array.

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Answer:15

Step-by-step explanation:

The magnitude of given operations of vectors are found.

Quantities with the independent characteristics of magnitude and direction are called vectors.

Given:

u = (-3, 8) and v = (-14, 6)

So, 3u = (-9, 24) and 2v = (-28, 12)

3u - 2v = (-9+28, 24-12)

3u - 2v = (19, 12)

Magnitude of 3u - 2v = √19² + 12²  = √505 units

2u = (-6, 16) and 3v = (-42, 18)

2u - 3v = (36, -2)

Magnitude = √36² + (-2)²  = √1300 units

u = (-3, 8) and 4v = (-56, 24)

u + 4v = (-59, 32)

Magnitude = √(-59)² + 32²  = √4505  units

5u = (-15, 40) and v = (-14, 6)

5u - v = (-1, 34)

Magnitude = √1157  units

7u = (-21, 56) and 2v = (-28, 12)

7u - 2v = (7, 44)

Magnitude = √1985 units.

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The length of the rise x is 25.5

From the question, we have the following parameters that can be used in our computation:

Length = 17

Angle = 27 degrees

The rise, x is then calculated using the following laws of tangent

tan(27) = 13/x

Make x the subject

So, we have the following representation

x = 13/tan(27)

Evaluate the expression

This gives

x = 25.5

Hence, the value of x is 25.5

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Answer:

The graph in the attached figure

we have

----> inequality A

The solution of the inequality A is the shaded area below the dashed line

The slope of the dashed line A is  positive m=2

The y-intercept of the dashed line A is (0,-5)

The x-intercept of the dashed line A is (2.5,0)

----> inequality B

The solution of the inequality B is the shaded area above the dashed line

The slope of the dashed line B is  negative m=-3

The y-intercept of the dashed line B is (0,1)

The x-intercept of the dashed line B is (1/3,0)

The solution of the system of inequalities is the shaded area between the two dashed lines

using a graphing tool

The graph in the attached figure

GIVE ME BRAINLIEST IF IM CORRECT :)

An equation of the line that passes through the points (4, -3) and (8,5) is y + 3 = 2(x - 4).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data points (4, -3), a linear equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-3) = (5 - (-3))/(8 - 4)(x - 4)

y + 3 = 8/4(x - 4)

y + 3 = 2(x - 4)

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Given    To find    Solution:  First, we replace  with  and  with :      Now, we finally replace  with   Therefore, the inverse of  is

Answer:y=(x-2)/4

Step-by-step explanation:

y=4x+2

4x=y-2

x=(y-2)/4

y=(x-2)/4

The inverse of function is  f(x) = (x - 4)³/8 + 3

A function that reverses the results of another function is known as an inverse function. If y = f(x), then x = g(y), then a function g is the opposite of a function f. To put it another way, applying f and then g is equivalent to doing nothing. This can be expressed as g(f(x)) = x in terms of how f and g are made up.

Given g(x) = 2(∛x-3)+4

let g(x) = y

y = 2(∛x-3)+4

change the variables since options are in form of x

x =  2(∛y-3)+4

simplify for y

subtract 4 from both side

x - 4 = 2(∛y-3)+4 - 4

x - 4 = 2(∛y-3)

divide both side by 2

(x - 4)/2 = (2(∛y-3))/2

(x - 4)/2 = (∛y-3)

cube both side

((x - 4)/2)³ = ((∛y-3))³

(x - 4)³/8 = y - 3

(x - 4)³/8 + 3 = y

Hence  the value f(x) =  (x - 4)³/8 + 3 .

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The simplest form of the given ratio 32 min : 36 min is equal to  

option a. 8 : 9.

Ratio  is equal to

32 min : 36 min

Factors of 32 are = 1, 2, 4, 8, 16, 32

Factors of 36 are = 1, 2, 3, 4, 6, 9, 12, 18, 36

Greatest common factor of 32 and 36 is equal to 4

Simplest form of the given ratio is equal to

32 min : 36 min

= ( 8 × 4 ) min : ( 9 × 4 ) min

'4' get cancelled with other we get,

= 8 min : 9 min

Therefore, the simplest form of the given ratio by taking out common factors is equal to option a. 8 : 9 .

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Answer: 35m2

Step-by-step explanation:took the test and i got it right

An isosceles trapezoid with a short base of 3 meters and a height of 5 meters then the area of the trapezoid is 35 m²

What is the area of the trapezoid?

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

We can start by finding the length of the long base. Since the trapezoid is isosceles, we know that the length of the portion of the large base from the left vertex to the perpendicular is equal to the length of the portion from the right vertex to the perpendicular. Let's call the length of the long base "x":

x = 4 + 7 = 11 meters

Now we can use the formula for the area of a trapezoid:

Area = (1/2) * (short base + long base) * height

Substituting the values we have:

Area = (1/2) * (3 + 11) * 5

Area = 7 * 5

Area = 35 m²

Therefore, the area of the trapezoid is 35 m².

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The simplified expression is given as follows:

-27j/10 - 1/8.

The expression for this problem is defined as follows:

-j/5 + 3/4 - (5j/2 + 7/8).

The negative sign means that every term in the parenthesis has the signal exchanged, hence:

-j/5 + 3/4 - 5j/2 - 7/8.

Then the expression is simplified combining the like terms, as follows:

Meaning that the expression is of:

-27j/10 - 1/8.

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The diameter of the Ferris wheel will be the difference between two consecutive maximum height and minimum height of the ferris wheel.

Diameter is the line jwhich passes through the center of a circle and joins two points on the circumference of the circle.

To find the diameter of the Ferris wheel which is a circle, we see that the grpah gives the height of a passenger on the Ferris wheel as a function of the number of complete cycles since the ride started.

Now, the diameter of the Ferris wheel will be the difference between two consecutive maximum height and minimum height of the ferris wheel.

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The correct classification of the terms is:

Expression; 4x+20

Inequality: 4x+20 > 40

Equation: 4x+20 = 40

What is an expression?

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

Here, we have

Given: 4x+20

4x+20>40

4x+20=40

We have to find their correct classification.

We concluded from an expression that

When an expression has the "=", then the expression is an equation.

When an expression has any of the following signs">, <, >=, <= or != ", then the expression is an inequality.

When the expression is neither an equation nor an inequality, then it is just an expression.

Hence, the correct classifications are:

Expression; 4x+20

Inequality: 4x+20 > 40

Equation: 4x+20 = 40

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Answer: Increases by 16 students per year

Step-by-step explanation:

100% = 800

2% = x

So between 100% and 2%, the scale factor would be 50 since 100 / 2 = 50

Then 800 / 50 would be 16

So..

1 Year = 816 students

2 Years = 832 students

3 Years = 848 students

4 Years = 864

And so on..

Answer:

4/12

Step-by-step explanation:

8/12 ÷ 2 = 4/12

Answer: 1/3

Step-by-step explanation:

8/12 divided by 2 is 1/3