If f(x)=ex and the 4th degree Taylor polynomial of f(x) centered at 2, what is T4(2.4)?


Round your answer to four decimals.

The given system of equations has a solution (16/11, 24/11), so they are consistent and independent.

The given system of equations are 4x+y=8 and x+3y=8.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Here, 4x+y=8 ----------(I) and x+3y=8 ----------(II)

Multiply equation (I) by 3, we get

12x+3y=24 ----------(III)

Now, subtract equation (II) from (III), we get

12x+3y-(x+3y)=24-8

11x=16

⇒ x=16/11

Substitute x=16/11 in equation (II), we get

16/11 +3y=8

⇒ 3y=8- 16/11

⇒ 3y=72/11

⇒ y=24/11

If equation as one solution, then they are consistent and independent.

Therefore, the given system of equations has a solution (16/11, 24/11), so they are consistent and independent.

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The answer that correctly fills the missing portions is option A.

The full sentence is: When the Bureau of Labor Statistics (BLS) calculates an increasing Consumer Price Index (CPI); the Federal Reserve (FED) may choose to Quantitative Easing.

Quantitative easing is a monetary policy operation in which a central bank buys government bonds or other financial assets to infuse monetary reserves into the economy in order to encourage economic activity.

The goal of QE is to level the playing field in order to make spending and investing money more enticing and accessible to people. Lower interest rates may improve the possibility that company and civilian borrowers will borrow to make purchases, promoting economic activity.

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Full Question:

When the ___ calculates an increasing ___ ; the ___ may choose to decrease______.

A) BLS, CPI. FED, QE

B) OECD, QE, BLS, CPI

C) BEA, GDP, BLS, CPI

D) BEA, CPI, OECD, GDP

The equation which has an axis of symmetry with the equation x = 3 as required in the task content is; y = x² - 6x +3.

It follows from the task content that the equation which has an axis of symmetry; x = 3 be determined among the answer choices.

By expressing the equation; y = x² - 6x +3 in vertex form; y = ( x - h )² + k; where the axis of symmetry is given by; x = h; we have that;

y = ( x - 3 )² - 6

On this note, it can be concluded that the axis of symmetry of the considered equation; y = x² - 6x +3 is; x = 3.

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The area of the board is 5/12 yard², then the length of the board will be equal to 5/8 yard.

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Area of board = 5/12 yard²

Width, W = 2/3 yard

Use the equation of area,

A = LW

5/12 = L(2/3)

L = (5/12)×(3/2)

L = 5/8 yard.

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For the given matrix the additive inverse property is shown.

What is additive inverse of matrix?

The matrix that is created by changing the sign of each matrix element is known as the additive inverse. -(-A)=A is the notation for the additive inverse of the matrix A.

Rows and columns serve as a measure of a matrix's dimensions. Given that it has three rows and three columns, for instance, the matrix below has a dimension of 3 x 3. Three by three can be read off as the matrix's dimension. We consequently obtain the additive inverse of the matrix

M = - M.

Consider the given matrix,

[tex]\left[\begin{array}{ccc}-6&15&-2\\9&0&-3\end{array}\right] + \left[\begin{array}{ccc}6&-15&2\\-9&0&3\end{array}\right] = \left[\begin{array}{ccc}0&0&0\\0&0&0\end{array}\right][/tex]

Here each element in first matrix is negative of the element of second matrix.

That is each element is inverse of the element in second matrix.

And the addition of elements is 0.

Hence, for the given matrix the additive inverse property is shown.

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The correct statements regarding the functions are given as follows:

a)

b)

For item a, the functions are given as follows:

The multiplication by -1/3 means that the vertically compressed by a factor of 3 and reflected over the x-axis, due to the multiplication by the negative number.

For item b, the functions are given as follows:

The transformation is:

x -> x - 2, meaning that the function was shifted right two units.

The intersection with the y-axis is at the value of y when x = 0.

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1. Average rate of change of function over the interval is d. -3/2

2. Average rate of change of function over the interval is 2. 12

3. Average rate of change of function over the interval is 1. -1

4. h(12) has the value of 61

What is the average rate of change of function?

The average rate of change function is defined as the average rate at which one quantity is changing with respect to something else changing.

Formula ----- A(x) = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

Solution:

1.Given a = 2, b = 10

A(x) = [tex]\frac{f(10)-f(2)}{10-2}[/tex]

A(x) = [tex]\frac{-3-9}{8}[/tex]

∴A(x) = -[tex]\frac{3}{2}[/tex]

2. Given a= 3, b = 9

f(x) = x²

A(x) = [tex]\frac{9^{2}-3^{2} }{9-3}[/tex]

A(x) = [tex]\frac{72}{6}[/tex]

∴ A(x) = 12

3. Given a = 1, b = 7

f(x) = Given graph

f(7) = 0, f(1) = 6

A(x) = [tex]\frac{0-6}{7-1}[/tex]

A(x) = -1

4. Given h(5)= 12, a=5, b=9, A(x) = 7

To find: h(12)=?

A(x) = [tex]\frac{h(12)-h(5)}{12-5}[/tex]

7 = [tex]\frac{h(12)-12}{12-5}[/tex]

h(12) = 7×7 + 12

∴ h(12) = 61

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1. Average rate of change of function over the interval is d. -3/2

2. Average rate of change of function over the interval is 2. 12

3. Average rate of change of function over the interval is 1. -1

4. h(12) has the value of 61

What is the average rate of change of function?

The average rate of change function is defined as the average rate at which one quantity is changing with respect to something else changing.

Formula ----- A(x) = (f(b)-f(a))/b-a

Solution:

1.Given a = 2, b = 10

A(x) = -3-9/10-2

∴A(x) = -3/2

2. Given a= 3, b = 9

f(x) = x²

A(x) = 81-9/9-6

∴ A(x) = 12

3. Given a = 1, b = 7

f(x) = Given graph

f(7) = 0, f(1) = 6

A(x) = 0-6/7-1

A(x) = -1

4. Given h(5)= 12, a=5, b=9, A(x) = 7

To find: h(12)=?

A(x) = (f(b)-f(a))/b-a

7 = h(12) = 7×7 + 12

∴ h(12) = 61

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The equation is 2x+3=9, x is the unknown number. After solving the equation, we get x=3.

A mathematical expression shows the equality between two terms.

In mathematics variables are used to denote any unknown number and equations are developed based on an expression. Finally, equations are solved, and unknown values are determined.

let, x is the unknown number. As per question the equation will be 2x+3=9

the equation is solved, and x is determined

2x=9-3

x=6/2

x=3

hence, x=3, 3 is the number.

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Answer:

[tex] \sf \: 2x + 3 = 9, \: x = 3[/tex]

Step-by-step explanation:

Given statement,

→ Sum of 2 times a number & 3 is 9.

Let the unknown number be,

→ [tex] \sf \pink{x}[/tex]

Forming the equation,

→ (2 × x) + 3 = 9

→ 2x + 3 = 9

Now the value of x will be,

→ 2x + 3 = 9

→ 2x = 9 - 3

→ 2x = 6

→ x = 6/2

→ [ x = 3 ]

Hence, the value of x is 3.

6x − y < −3 , inequality matches the graph.

Step 1:

Find the equation of the line

we have A(0,3) , B(1,9)

The formula to calculate the slope between two points is equal to

m = (y₂-y₁) / (x₂-x₁)

Substitute the values:

m = (9-3) / (1-0)

m = 6/1

m = 6

The equation of the line into slope intercept form is equal to

y = mx + c

where

m is the slope

b is the y-intercept

In this problem we have

m = 6

b = 3 ---->  the y-intercept is the point B

Substitute the values:

y = 6x + 3

Step -2

Find the equation of the inequality

we know that:

The solution is the shaded area above the dashed line

so, the inequality is equal to

y > 6x + 3

rewrite

-6x + y > 3

6x - y < -3

Step 3

Using a graphing tool

The x-intercept is the point

The y-intercept is the point

The slope of the dashed line is positive, the graph in the attached figure.

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Answer:

8

Step-by-step explanation:

The mean of numbers is the sum of the numbers divided by the number of numbers. By this definition, we first have to add up all of these numbers. If we do, we get 48. Now, we figure out the number of numbers, which is 6. Finally, we divide 48 by 6 to get 8.

The area represents the aim tariff revenue the United States government collects is D. f

Tariffs are taxes levied by the government of a country or a supranational union on goods imported or exported. Import duties, in addition to being a source of revenue for the government, can also be a form of foreign trade regulation and policy that taxes foreign products in order to encourage or safeguard domestic industry.

Tariffs serve three primary functions: they generate revenue, they protect domestic industries, and they correct trade distortions (punitive function). The revenue function stems from the fact that tariff revenue provides governments with a source of funding. This was illustrated as f in the diagram.

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Answer: m = 22

Step-by-step explanation:

First, you subtract $2.50 from the total of $79.50 (because that is the static fee) to get $77.00. Now, because every mile is $3.50 and we want to find the number of miles, we divide $77 by $3.50 to get 22. (An easy way to do this mentally is to divide 77 by 7 and multiply by 2.) Therefore, m = 22.

(a) The Explicit Rule for f(n) is 0.1 × 3n The Recursive Rule for f(n) is f(n-1) × 3.  (b) The Explicit Rule for f(n) is 100 × 0.1ⁿ The Recursive Rule for f(n) is f(n-1) × 0.1

The explicit rule states that the value of the sequence at each term is 0.1 multiplied by 3 raised to the power of n. The recursive rule states that the value of the sequence at each term is equal to the value of the preceding term multiplied by 3. This can be seen in the table of values where each value is 3 times the preceding value.

Given,        

n = 0,1,2,3,4…        

f(n) = 0.1,0.3, 0.9, 2.7, 8.1

(b) The Explicit Rule for f(n) is 100 × 0.1ⁿ, The Recursive Rule for f(n) is f(n-1) x 0.1

Given,      

n= 0,1,2,3,4..      

f(n) = 100, 10, 1,0.1, 0.01

The explicit formula is the formula to calculate the value of the sequence directly without using any previous terms. The recursive formula uses the previous term to calculate the value of the current term.

In this example, the explicit formula is 100 × 0.1ⁿ and the recursive formula is f(n) = f(n-1) × 0.1. This means that each term in the sequence is equal to the previous term multiplied by 0.1.

For example, the third term in the sequence is 1, so the fourth term is 1 × 0.1 = 0.1.

(c) The Explicit rule for f(n) is 1000 × 0.1⁽ⁿ ⁻ ¹⁾, The Recursive rule for f(n) is f(n-1) x 0.1    

To solve,

f(5) = 1000 × 0.1⁽⁵ ⁻ ¹⁾(5-1)

     = 1000 × 0.1⁴

     = 1000 × 0.0001

     = 0.1

Given,        

n= 1,2,3,4,5…        

f(n) = 1000, 100, 10, 1, 0.1

The explicit and recursive rules for this geometric sequence are both written as f(n) = 1000 × 0.1⁽ⁿ ⁻ ¹⁾.  This means that the value of the sequence at any given point n will be equal to 1000 multiplied by 0.1 raised to the power of n-1. This means that the value of the sequence decreases by a factor of 0.1 for every increase in n.

In this case,

f(5) = 1000 x [tex]0.1^4[/tex]

     = 0.1.

(d) The Explicit Rule for this geometric sequence is f(n) = 10⁽⁵⁰ ⁻ ³ⁿ⁾, where n is the term number of the sequence.

The Recursive Rule for this geometric sequence is f(n) = f(n-1) ÷ 10³, where f(n) is the value for the nth term of the sequence and f(n-1) is the value for the (n-1)th term of the sequence.

Given,    

n= 1,2,3,4,5..    

f(n) = 10⁵⁰,10⁴⁷, 10⁴⁴, 10⁴¹, 10³⁸….

The value for the 5th term of the sequence is f(5) = 10⁽⁵⁰ ⁻ ³⁽⁵⁾⁾ = 10³⁸. The explicit rule for this geometric sequence is f(n) = 10⁽⁵⁰ ⁻ ³ⁿ⁾, where n is the term number of the sequence. This means that the value of each term is determined by taking 10 to the power of 50 minus 3 multiplied by the term number.

The recursive rule for this geometric sequence is [tex]\frac{f(n-1)}{10^3}[/tex] which means that the value of each term can be calculated by dividing the previous term by 10 cubes. We can use

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452 ÷ 21 is equal to [tex]$21 \frac{11}{21}$[/tex].

What is  Quotient?

When we divide a number, the result we ultimately obtain is the quotient. Division is a mathematical operation that involves dividing items into equal groups. It is represented by the symbol (÷). For instance, three groups of 15 balls each need to be equally split. Therefore, the division formula is 15 3 = 5 when we divide the balls into three equal groups. Here, the quotient is 5, so. This implies that there will be 5 balls in each group.

[tex]$\frac{452}{21}=21$[/tex] Remainder 11

Convert to mixed number: Quotient= [tex]$\frac{\text { Remainder }}{\text { Divisor }}$[/tex]

[tex]$\frac{452}{21}=21 \frac{11}{21}$[/tex]

[tex]$=21 \frac{11}{21}$[/tex]

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At year-end, Factory Overhead is debit of $34000.

What is profit and loss?

A profit and loss (P&L) statement could be a monetary report that has a outline of a company’s revenue, expenses and profit. It provides investors and alternative interested parties an insight into however an organization is working and whether or not it's the flexibility to get a profit.

Main Body:

Estimated total overhead costs = $456,000

Estimated direct labor costs = $2,280,000

Actual overhead costs= $422,000

Actual direct labor costs= $1,940,000

To calculate the factory overhead, we need to first calculate Estimated overhead rate.

Estimated overhead rate = Estimated total overhead costs / Estimated direct labor costs

= $456,000 / $2,280,000

= 0.2

= 20%

Therefore;

Actual Factory overhead = Actual direct labor cost × application rate

= $1,940,000 × 20%

= $388,000

We can get the balance in the overhead account as shown below;

Balance = Actual overhead cost - Actual cost that should be applied

= $422,000 - $388,000

= $34,000 (Debit).

Hence there is debit of $34000.

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Step-by-step explanation:

Hello. Can you repost the question and just for clarification is this Taylor, Maclaurin Series?

Answer: C

Step-by-step explanation:

30 x 1.029

30.87

The x-intercept of the given line having equation 2x–4y= -12 is -6

How to find x-intercept of a line?

An x-intercept is a point where the graph of a function or relation intersects with the x-axis of the coordinate system.

To find x-intercept of a line, put y = 0 in the given equation of line

According to the given question:

The equation of line is 2x - 4y = -12

Putting y = 0 in the above equation we get

2x - 4(0) = -12

        2x = -12

          x = -6

Therefore, x-intercept of the line 2x–4y= -12 is -6

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The number of prizes that Chris won out of 60 will be 13.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

At the Mayfair Stella, Mary, Cris, and Elli won 60 awards altogether. Mary won 1/3 of them, Stella won 1/5 of them, and Elli got 1/4 of the aggregate.

Then the number of prizes that Chris won is given as,

⇒ 60 - 60 / 3 - 60 / 5 - 60 / 4

⇒ 60 - 20 - 12 - 15

⇒ 60 - 47

⇒ 13

The number of prizes that Chris won out of 60 will be 13.

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Answer: $180

Step-by-step explanation: To calculate the total tip, you would add 10% to the bill,

Total bill = $159.67 x 1.10+ 175.637 or $175.64

$175.64 rounded to the nearest $10 dollars is $180 as the number in the 1s column is greater than 5.  Because of this, you round up to get the nearest $10.  

Total bill equals $180

Answer:3.9

Step-by-step explanation:

Divide -19.50 by 5

=3.9

Answer:

$23.02

Step-by-step explanation:

You add what she earned to what she had before

$14.27 + $8.75 = $23.02

The number of banquets that can be formed is 6 and total number of flowers are 2+3=5.

What is the greatest common divisor?

the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, and y.

We have given,

Petal and Leaf florists currently have 30 roses, 36 carnations, and 54 tulips

Since it is given that there are 75 rose and 45 lily flowers. Therefore,

Factorise 30 as follows:

30 = 2 × 3 × 5

Factorise 36 as follows:

36 = 2 × 2 × 3 × 3

Factorise 54 as follows:

54 = 2 × 3 × 3 × 3

We know that HCF is the highest common factor.

Since the common factor between the numbers 30, 36, and 54 is 2×3=6.

Hence, the number of banquets that can be formed is 6 and total number of flowers are 2+3=5.

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A pivot in every row means that the linear system A x=b has at least one solution, for every b.

If every column has a pivot, then the linear system A x=b has at most one solution.

If both hold (which can happen only if A is a square matrix), we get that the system A x=b has unique solution for every b.

A pivot in every row is equivalent to A having a right inverse, and equivalent to the columns of A spanning

[tex]$\mathbb{R}^m$ ( $m$[/tex] is the number of rows).

A pivot in every column is equivalent to A having a left inverse, and equivalent to the columns of A being linearly independent

A pivot means fundamentally changing the direction of a business when you realize the current products or services aren't meeting the needs of the market. The main goal of a pivot is to help a company improve revenue or survive in the market, but the way you pivot your business can make all the difference.

The first nonzero item of each row in a matrix in row-echelon form is known as a pivot, and the columns in which pivots appear are known as pivot columns.

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Answer:

2x + y - 12 = 0

Step-by-step explanation:

The Tangent line will Always be perpendicular to the radius of a circle.

1. Find the slope of the radius that goes from the Center to the given point:

  [tex]m=\frac{-2--5}{7-1}=\frac{3}{6}=\frac{1}{2}[/tex]

2. The slope of the Tangent at (7,-2) is the Negative (opposite) Reciprocal of the slope of the radius:  [tex]\frac{1}{2}= > -2[/tex]

3. Write the equation of the Tangent in Point Slope Form:

   [tex]y+2=-2(x-7)[/tex]

4. Distribute and rewrite in the form ax + by + c = 0

   [tex]y+2=-2(x-7)\\y+2=-2x+14\\2x+y-12=0[/tex]

Option A , if located in a method in the same class, will initialize the variable x to 11 i.e,  int x = function2(4, 5) + function1(1, 3).

function2(4, 5)  = 5-4 = 1

function1(1, 3) = 3+1 = 4

function2(4, 5) + function1(1, 3) = 5

On initializing the function with 11 ,

the output will be 5

A function is a set of statements that take inputs, do some specific computation, and produce output. The idea is to put some commonly or repeatedly done tasks together and make a function so that instead of writing the same code again and again for different inputs, we can call the function.

In simple terms, a function is a block of code that only runs when it is called.

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Answer: exact form is 24/5, decimal form is 4.8 and mixed number form is 4 4/5

Step-by-step explanation:

Answer:

4 4/5 (simplified)

Step-by-step explanation:

Using reciprocals:

4 divided by 5/6 = 4 x 6/5

= 24/5 = 4 4/5

To check: 4 4/5 x 5/6 = 4

You can use the same method for similar problems

Answer:

Step-by-step explanation:

You want the (a) post-order, and (b) pre-order list of visited vertices in a traversal of the tree described by {root, left, center, right}: {d, f, {b, i, h, e}, {a, {c, g}}}.

A tree is traversed in post-order by visiting the left branch, center branch, and right branch before the root. This is accomplished recursively.

For the given tree, the root 'd' has left branch 'f' which has no branches. That means node 'f' is reported first.

The middle branch goes to 'b' which has three branches. Those are reported before their root 'b'.

The right branch from root 'd' goes to 'a', which has branch 'c' going to 'g'. So, 'g' is reported, then 'c', then 'a'.

Finally, 'd' is reported.

Hence, the post-order traversal is f, i, h, e, b, g, c, a, d.

The pre-order traversal reports the root node, then the left, center, and right nodes, recursively. The vertices are effectively visited in the order in which we have defined the tree above: d, f, b, i, h, e, a, c, g.

The two errors that Sterling made in the proof include:

In this case, it should be noted that the step 6. statement must be that LEO is equal to NEO. This is due to the substitution property of equality.

The substitution property of equality states that one value can be substituted for another in an expression or equation and the result will be the same. If the values of x and y are equal, then x and y can be substituted for one another.

Also, the step 7 should be that OLE is identical to ONE. The reason is due to the angle-side-angle postulate. According to the AAS Postulate, if two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another, the triangles are congruent.

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The number of cups of hot chocolate drink Nathan made is 12 cups.

Convert pint to cup:

1 pi-nt = 2 cups

Total cups of hot chocolate Nathan made = Number of cups of milk Nathan heated + Number of cups of melted chocolate + Number of cream

= 6 + 4 + 2

= 12 cups

Therefore, Nathan made 12 cups of hot chocolate drink.

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