Pls help me on this ​

The function g(x) = 2/(x^2 - 1) can be represented as a power series by finding its Taylor series expansion about the point x = 1.

We know that the power series representation of the function 1/(1-x) is given by the summation from n=0 to infinity of x^n.

So we can write:

g(x) = 2/(x^2 - 1) = 2*(1/(1-x))(1/(1+x)) = 2(1/(1-x^2))

We can use the formula for the Taylor series of a function:

f(x) = SUM(n=0 to infinity) (f^n(a)/n!) * (x-a)^n

where f(x) is the function, a is the point about which we are expanding, and n! is the factorial of n.

So we have:

g(x) = 2* SUM(n=0 to infinity) ( (1/(1-x^2))^n * (x-1)^n )

g(x) = 2* SUM(n=0 to infinity) ( (1/(1-x^2))^n * SUM(k=0 to n) (nCk * x^k * (-1)^(n-k) ) )

g(x) = 2* SUM(n=0 to infinity) ( SUM(k=0 to n) ( (1/(1-x^2))^n * (nCk) * x^k * (-1)^(n-k) ) )

where nCk is the binomial coefficient which is equal to n!/(k!(n-k)!).

So we have the power series representation of the function g(x) = 2/(x^2 - 1) as:

g(x) = 2 * SUM(n=0 to infinity) SUM(k=0 to n) ( (nCk) * ((-1)^(n-k) * (1/(1-x^2))^n) * x^k )

It's important to note that this power series is only valid for |x| < 1.

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The answer is 13. The Pythagorean theorem can be used to determine the hypotenuse.

A triangle's third side must always be between (but not exactly equal to) the other two sides' total and difference in length. The answer is 13. The Pythagorean theorem can be used to determine the hypotenuse.The theorem informs us that if we designate that side as side "c"

c² = 5² + 12²\s c² = 25 +144 = 169\s c = √169 = 13

The third side measures 13 units in length.

Further commentary

The three digits (5, 12, and 13) form a "Pythagorean triple."

They can be utilized to create a right triangle because they are integers.

The triples (3, 4, 5), (7, 24, 25), and (8, 15, 17) are other triples that are frequently encountered in algebraic problems.

It might be worthwhile for you to keep these in mind.

The third side is 13 when you observe side lengths of 5 and 12, therefore you don't need to do any math to determine this.

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The polynomial:

5x²*y²*z + 10*x²*y²*z

Is a monomial (it can be rewritten as 15*x²*y²*z)

And the degree is 5.

Remember that the degree of a polynomial is equal to the maximum sum of exponents that we have on a single term.

The given polynomial here is:

5x²*y²*z + 10*x²*y²*z

First, notice that we can take "x²*y²*z" as a common factor, then we can rewrite:

5x²*y²*z + 10*x²*y²*z = 15*x²*y²*z

So we have only a term, thus, this is a monomial.

And the degree is the sum of the exponents, we will get:

2 + 2 + 1= 5

So the degree is 5.

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In the year 2046 the price of the stamp will reach 75 cents. The solution has been obtained using linear function.

What is a linear function?

A linear function is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear function with exponents greater than 1. Such a function on the graph, forms a straight line.

We are given y= -0.71 + 0.86x, where y represents the predicted price , in cents of a stamp and x represents the number of years since 1958

We need to find the year in which the price of the stamp will reach 75 cents. This means that

y = 75

Putting this in the equation, we get

⇒75= -0.71 + 0.86x

⇒x= 75.71/0.86

⇒x= 88.03

This means that after around 88 years from 1958 i.e. in 2046 the price of the stamp will reach 75 cents.

Hence, in the year 2046 the price of the stamp will reach 75 cents.

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Since, the question is incomplete, the complete question is attached below

Finn has 3 hamsters and 8 fish at home, the ratio of fish to total number of pets is -  8 : 11

The ratio refers to the number that may be used to represent one quantity as a percentage of another, to put it simply. Only when the ratio's two numbers use the same unit can they be compared. To compare two objects, we utilize ratios. When the second integer in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. A percentage seems to be an equation in which two proportions are made equal to one another. Ratio, which is comfortably pronounced as the ratio, was directly derived from the Latin term. Everything from "reason," "calculation," and "proportion" were all included in the Latin word ratio.

Given that,

Hamsters: 3

Fish: 8

Thus, total = 3 + 8 = 11

Now, ratio of fish total number of pets:

= 8 : 11

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The number of people in attendance who would prefer chili on a hotdog is 3,380.

Option B is the correct answer.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of attendance = 8450

Number of people who prefer chili on a hotdog out of 150.

= 60

The percentage of people who prefer chili on a hotdog out of 150.

= 60/150 x 100

= 40%

Now,

The number of people who prefer chili on a hotdog from 8450 attendance.

= 40% of 8450

= 40/100 x 8450

= 3380

Thus,

3,380 in attendance would prefer chili on a hotdog.

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Answer Y=-X+9

Step-by-step explanation:

Desmos Calculator.

Here, both equations are graphed and the answer is shown going through the required coordinate.

The interest after three years is $117.711 and new balance after three years is $1347.711

Simple interest is a type of interest calculated on the initial principal or starting amount of a loan or investment.

The formula for simple interest is:

I = PRT/100

Where:

I = Interest

P = Principal or starting amount

R = Interest rate

T = Time

a. Interest after three years:

I = PRT/100

P = $1,230, R = 3.19% and T = 3 years

I = (1,230 ×3.19 × 3)/100

I =  $117.711

b.  New balance after three years:

New balance = P + I

New balance =  $1,230 + $117.711 = $1347.711

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The number of cubes that can be filled in the rectangular prism is 720.

Volume of a three dimensional shape is the space occupied by the shape.

Volume of a rectangular prism = Length × Width × Height

Given a rectangular prism with side lengths 3inches by 7.5 inches and 4 inches.

Volume of rectangular prism  = 3 × 7.5 × 4 = 90 inches³

Volume of a cube = (side length)³

Given cube has side length 0.5 inch.

Volume of cube = (0.5)³ = 0.125 inches³

Number of cubes that can be filled in the rectangular box = 90 / 0.125

                                                                                                 = 720

Hence 720 cubes can be filled in the rectangular prism.

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ASA: ∆ABC and ∆DEF are congruent if angle B is congruent to angle E. SAS: ∆ABC and ∆DEF are congruent if angle A is congruent to angle D and AB=DE.

What is congruent ?

In geometry, congruent refers to the condition where two or more figures have the same size and shape. Congruent figures have the same dimensions, angles, and proportions. Two figures are congruent if they can be superimposed exactly on each.

1) If, C.) Angle B is congruent to angle E then ∆ABC and ∆DEF are congruent by the ASA criterion.

2) If, D.) Angle A is congruent to angle D then ∆ABC and ∆DEF are congruent by the SAS criterion.

3) ∆ABC and ∆DEF are congruent if B.) AB=DE

ASA criterion: If in two triangles, two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.

ASA: ∆ABC and ∆DEF are congruent if angle B is congruent to angle E. SAS: ∆ABC and ∆DEF are congruent if angle A is congruent to angle D and AB=DE.

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Answer:

infintely many

Step-by-step explanation:

B, C, and D are all questions that should be expected to be answered with variable data

Variable data refers to information that can change or vary, as opposed to fixed or constant data. In the context of statistics and data analysis, variable data refers to data that can take on different values for different individuals or observations.

B, C, and D are all questions that should be expected to be answered with variable data because the answer to each of these questions can change depending on the specific context or situation.

For example, the number of phone calls one makes on a given day can vary, the highest grade on a test can change from test to test, and the number of people who attend a volleyball game can also change.

A. How tall are the students in my class? is a question that should be expected to be answered with fixed data as the height of the students in the class will stay the same unless there is a significant change in their height.

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To maximize the profit only 52 Tables must be manufactured daily and to minimize the profit only 173 chairs must be manufactured working with the efficiency given.

What is efficiency?

The ratio of work accomplished by a machine or process to total energy expended or heat consumed is known as efficiency.

Efficiency refers to how close we can get to a specific outcome from a given input with the least amount of waste. Efficiency is the capacity to waste as little material, work, energy, and time as possible when executing a task or generating a desired outcome.

The ratio of usable output to total input can be used to calculate efficiency. The efficiency of a device is defined as the ratio of energy transferred to a usable form to the total energy provided originally.

Now

For table,

assembly hours=8

finishing hours = 2

profit/table=$90

For Chairs

assembly hours=2

finishing hours = 1

profit/chair=$25

Total assembly hours in a day=400

Total finishing hours in a day=120

As profit for table is more than profit for chair. Therefore, for maximum profit only Tables will be manufactured and will be

=total hours available/Time taken for one chair

=520/10

Tables manufactured=52

and for minimum profit only chairs will be manufactured

=520/3

chairs manufactured=173

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The requried factor pair of the sum of the horses and cows is given as 2 × 2 × 2 × 5.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

here,
Some of the cows and horses = 18 + 22 = 40
The required factor pair of the sum can be formed as,
= 2 × 2 × 2 × 5

Thus, the requried factor pair of the sum of the horses and cows is given as 2 × 2 × 2 × 5.

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Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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Answer:

C. Five hundredths is larger than four hundredths.Five hundredths is larger than four hundredths.

Answer:

C

Step-by-step explanation:

A

[tex] \frac{3}{100} < \frac{4}{10} \times \frac{10}{10} = \frac{40}{100} [/tex]

B

[tex] \frac{3}{100} < \frac{3}{10} \times \frac{10}{10} = \frac{30}{100} [/tex]

C

[tex] \frac{5}{100} > \frac{4}{100} [/tex]

D

[tex] \frac{5}{100} < \frac{4}{10} \times \frac{10}{10} = \frac{40}{100} [/tex]

Answer:

The required number maximum number of copies can be afforded x < 24.28.

Given that,

We have $8.50 and you need to make copies of a flyer at a store that charges $0.35 per copy.

What is inequality?

Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,

Let the number of copies be x,

According to the question,

0.35x < 8.50

x < 8.50 / 0.35

x < 24.28

Thus, the required number maximum number of copies can be afforded x < 24.28.

Step-by-step explanation:

Answer:

i want points

Step-by-step explanation:

get scamed

Answer:

Step-by-step explanation:

No, it is not possible to form a right triangle with the sides as 15 cm, 8 cm, and 17 cm .

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) must equal the square of the longest side (the hypotenuse). In this case, 15^2 + 8^2 = 289 + 64 = 353, which is not equal to 17^2 = 289.

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The equation n = t * 1.029 represents the cost of new cars and trucks next year.

What is the percent increase?

The percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. Mathematically, the formula is expressed as Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100.

The 2.9% increase in cost is represented by the factor of 1.029 (1 + 0.029). To calculate the cost of a car next year, we multiply this year's cost (t) by 1.029.

n = t * 1.029

Where n represents next year's cost and t represents this year's cost.

This equation can also be written as n = t(1 + 0.029) or n = t + 0.029t which shows the relationship between this year's cost and next year's cost.

Hence, The equation n = t * 1.029 represents the cost of new cars and trucks next year.

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Answer:

1400 square feet

Step-by-step explanation:

The area of a rectangle is found by multiplying its length by its width. So the area of Jenny's garden, which is 28 feet by 50 feet, is:

28 x 50 = 1400 square feet

To use mental math, Jenny could use the distributive property of multiplication.

First, she could break down the 28 into 20 and 8, and 50 into 40 and 10.

Then, she could think 20 x 50 = 1000 and 8 x 10 = 80

Finally, she could add 1000 + 80 = 1080.

So, the area of the garden can also be found by breaking down one of the dimensions into smaller parts, multiply them and add the results.

Another way to use mental math is to think of it as a square with side length of 50 ft, and then think of it as 28 rectangles of 1 ft by 50 ft. The area is then 50 x 28 = 1400 sq ft.

The graph represented is a single line  and the solution is

The solution of a sets of linear equations is determined as follows

Since the coordinates are for a line hence it represents lines on the same line and this results to infinitely many solution

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Answer:

Infinite solutions

Step-by-step explanation:

Got it right on the test

Answer:

12

Step-by-step explanation:

The average participation score after dropping the lowest 4 participation scores is = 83.33%

In order to calculate the average participation score after dropping the lowest 4 participation scores, we need to first calculate the participation score for each class.

For the first class, the student answered 2 out of 3 quizzes correctly, so the participation score is (2/3) x 100 = 66.67%.

For the second class, the student answered 1 quiz correctly, so the participation score is 100%.

Now we need to find the average participation score after dropping the lowest 4 scores. Since the student only participated in 2 classes, we don't need to drop any scores, the average participation score is (66.67 + 100)/2 = 83.33%

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Answer:(0,-5)

Step-by-step explanation: to start you add both x’s together then divide by two so you get 0 then you add both of the y’s together divide by 2 and you get -5 the answer you got from the x’s goes first then the answer from the y’s hence (0,-5)

The amount of water drank in 12 hours will be 180 ounces.

The mathematical expression combines 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 denote the logical syntax's operation order and other properties.

Given that Jim drinks 15 ounces of water each hour. The amount of water drank by Jim in 12 hours will be,

Amount of water = 15 x 12

Amount of water = 180 ounces

Hence, the amount of water drank in 12 hours will be 180 ounces.

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The pair of angles ∠4 and ∠7 are alternate interior angles.

In Mathematics, parallel lines can be defined as two (2) lines that are always the same distance apart and they never meet.

In Geometry, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent. Additionally, these angles are generally referred to as alternate interior angles in Mathematics, .

In this scenario, we can logically conclude that angle 4 (m∠4) and angle 7 (m∠4) forms a pair of alternate interior angles because line l is parallel to line m.

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