A 7 in. medium-angle grinder is on sale for $117.60 and is marked as being 20% off. What was the original list price?

(Type a whole number or an exact decimal. If the decimal does not terminate round two decimal places)

Answer:

8(-2)^3= -64

8(-1)^3= -8

8(0)^3= 0

8(3)^3= 216

Hope this helps! Remember PEMDAS (Please forgive My Dear Aunt Sally)

Answer:

[tex]4\sqrt2[/tex]

Step-by-step explanation:

1) a=4 and b=8

2) Let geometric mean is g. [tex]g=\sqrt ab[/tex] or you can do [tex]g=\sqrt 4 times8[/tex]

3) g=[tex]4\sqrt2[/tex]

so the whole rectangle has an area of 22x18, now there's a tiny triangle on the corner, that we can say it has a base of 22 - 19 = 3, and a height of 18 - 14 = 4, so let's get both areas and subtract that of the triangle's from the rectangle's.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ rectangle }{(22)(18)}~~ - ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{3})(\underset{h}{4})}}\implies 396-6\implies \text{\LARGE 390}~m^2[/tex]

Answers:

=============================================

Explanation:

An exponential function has the template

y = a*b^x

where,

We have b = 1/4 = 0.25 as the base of the exponent.

Since 0 < b < 1 is the case, we have exponential decay

-------------

We can also have this template

y = a*(1+r)^x

I replaced b with 1+r

If we set this equal to 0.25 and solve for r, we get:

1+r = 0.25

r = 0.25-1

r = -0.75

The negative r value is another way to see how we have exponential decay

So we go from 1+r to 1+(-0.75) aka 1-0.75 as the base of the exponential.

In other words, 11600(0.25)^x is the same as 11600(1-0.75)^x

In the second format, it's much easier to see what the r value is.

--------------

The r value r = -0.75 converts to the percentage 75%

It means y decreases by 75% each time x goes up by 1.

Answer:

It depends. Depends on what? Depends on the type of triangle that this shelf forms. If Sandra wants the shelf to fit perfectly, she needs a shelf with the shape of a right triangle, the only type of triangles that have a 90° angle in one of their corners. Any other type of triangle will fit in some ways, but they won't fot perfectly.

Check the attached images to better understand this explanation.

As you can see on the images, the only type of shelf that fits the room's corner perfectly is a right triangle shaped shelf. Any other triangular shelf will fit in a specific orientation, but it won't fit perfectly.

After 2.5 years the price of land and the price of house will be equal.

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

A person purchases a piece of land in Rs.80, 00,000 in 2075 B.S.

And, At the same time of 2075 B.S. a house is constructed on a piece of land in Rs. 2,70,00,000.

Since, The price of land increases at the rate of 20% per annum.

Hence, We get;

A = 80,00,000 (1 + 20/100)ⁿ

And, The price of house depreciates at the rate 20% per annum.

Hence, We get;

A = 2,70,00,000 (1 - 20/100)ⁿ

Let after n years the price of land and the price of house will be equal.

Thus, We get;

80,00,000 (1 + 20/100)ⁿ =  2,70,00,000 (1 - 20/100)ⁿ

8 (120/100)ⁿ = 27 (80/100)ⁿ

8 (6/5)ⁿ = 27 (4/5)ⁿ

Take log both side,

log 8 + n (log 6 - log 5) = log 27 + n (log 4 - log 5)

0.9 + n × 0.8 = 1.4 + n × 0.6

0.9 + 0.8n = 1.4 + 0.6n

0.2n = 0.5

n = 2.5 years

Therefore, After 2.5 years the price of land and the price of house will be equal.

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1. After 13 years of investing $9,500 per period at 10% interest, the investment would be worth approximately $281,461.22.

2. After 50 years of investing $9,500 per period at 9% interest, the investment would be worth approximately $5,967,875.20.

To calculate the future value of an investment, we can use the formula for compound interest:

FV = PV x (1 + r)^n

where FV is the future value of the investment, PV is the present value or initial investment, r is the annual interest rate, and n is the number of compounding periods.

For the first investment:

PV = $9,500 per period

r = 10% per year

n = 13 years

Since we're making regular periodic investments, we can use the formula for the future value of an annuity:

FV = PMT x [(1 + r)^n - 1] / r

where PMT is the regular payment or investment per period. Plugging in the numbers, we get:

FV = $9,500 x [(1 + 0.1)^13 - 1] / 0.1 = $281,461.22

So after 13 years of investing $9,500 per period at 10% interest, the investment would be worth approximately $281,461.22.

For the second investment:

PV = $9,500 per period

r = 9% per year

n = 50 years

Using the same formula for the future value of an annuity, we get:

FV = $9,500 x [(1 + 0.09)^50 - 1] / 0.09 = $5,967,875.20

So after 50 years of investing $9,500 per period at 9% interest, the investment would be worth approximately $5,967,875.20.

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Therefore , the solution of the given problem of expression comes out to be Sunny earned $12x - 15 this week.

Mathematical operations like addition, multiply, and division are necessary. They result in the following when combined: An equation, some information, and a mathematical operator Values, parameters, and arithmetic calculations like additions, subtractions, multiplication and division, and divisions are all found in a statement of fact. Different sentences and words can be contrasted and compared.

Here,

If Sunny worked for x hours and earns $12 per hour, her earnings before the late delivery charge would be:

$12x$

However, since she was charged $15 for the late delivery on Tuesday, her earnings for the week would be:

$12x - 15$

Therefore, Sunny earned $12x - 15 this week.

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The complete question is "Sunny earns $12 per hour delivering cakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late delivery on Tuesday. How much money did Sunny earn this week?"

The equation and solution to find the length of mis teak wood piece is x/3=8 and 24;

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;

We are given:

The length of oak wood is 8inches

Teak wood/3= oak wood

So,

Let the length of teak wood be x;

Now,

x/3=8

x=3x8

x=24

Therefore, by algebra the length of teak wood will be 24;

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The solutions of the given system of linear inequalities are (0, 3) and (6, 2)

A system of inequalities is a set of two or more inequalities in one or more variables. Systems of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions.

Given is a graph of a system of linear inequalities, we need to select the solutions of the following,

The solution of the system of linear inequalities, are given by the combined shaded reason of the graph,

Here, only points (0, 3) and (6, 2) are lies in the common combined part of the graph,

Hence, the solutions of the given system of linear inequalities are (0, 3) and (6, 2)

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Answer:

angle a: 70°

angle d: 70°

angle dce: 35°

x: 15m

y: 14m

Step-by-step explanation:

all triangles add to 180° so 35 + 75 = 110 and 180-110 = 70

where the two triangles connect and cross, the angles will be the same so it will have the same angle measures as the first triangle which makes the triangles similar

knowing that they are similar triangles will help with figuring out the lengths of the sides.

since they are similar, their sides will be proportional, we just need to figure out the ratio

if we lay the triangles on top of each other, the two 75° angles match up and therefore the sides do too so we can make a fraction 12/18 = 10/x

now we can solve for x

multiply both sides by x

12x/18 = 10

now multiply both sides by 18

12x = 180

divide both sides by 12

x = 15

now we do the same for y

12/18 = y/21

12*21/18 = y

y = 14

hope this helps!

The completed blanks in Nyala's solution that is used to prove that the measure of angle x is 40° is as follows;

If we perform a 180° rotation about the point O the following happens

Ray [tex]\overleftrightarrow{EF}[/tex] maps unto ray [tex]\overleftrightarrow{GH}[/tex]

Ray [tex]\overleftrightarrow{GH}[/tex] maps unto ray [tex]\overleftrightarrow{FE}[/tex]x

[tex]\overleftrightarrow{FG}[/tex] maps unto itself

Therefore, the image of angle x will be exactly where the pre-image of 40° was. Since rotation preserve angle measure, the measure of angle x must be 40°.

The measure of an angle is the degree of rotation between the initial side and the terminal side of the angle.

The details of the method Nyala used to prove that the measure of the angle x is 40° can be found as follows;

The rotation of a line 180° about the center of the line maps onto itself, and the rotation of a line about a non colinear point, is parallel to the original line.

Whereby the center of rotation of the line [tex]\overleftrightarrow{EF}[/tex] is equidistant from both the line [tex]\overleftrightarrow{GH}[/tex] which is parallel to the line [tex]\overleftrightarrow{EF}[/tex], the image of the line [tex]\overleftrightarrow{EF}[/tex] maps to the line [tex]\overleftrightarrow{GH}[/tex] following a 180° rotation about the point O, and the rotation of the line [tex]\overleftrightarrow{FG}[/tex] about the point O maps unto itself, such that the angle x maps to the angle 40°, therefore;

∠x ≅ 40° (A rotation transformation is a rigid transformation)

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Answer:

No

Step-by-step explanation:

The y intercept is 7. For it to be proportional it has to go through (0,0).

Answer:

Yes

Step-by-step explanation:

Answer:

A. there is nothing wrong with either division problem

Step-by-step explanation:

The congruent angles in the similar figures are as follows:

∠M ≅ ∠R

∠N ≅ ∠S

∠P ≅ ∠T

∠Q ≅ ∠U

Two figures are said to be similar if they are the same shape.  Similar figures have the corresponding sides in proportion to each other.

Similar figures also have the corresponding angles equal to each other.

Therefore, the figures are similar by MNPQ ~ RSTU

Hence,

∠M ≅ ∠R

∠N ≅ ∠S

∠P ≅ ∠T

∠Q ≅ ∠U

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All frumpable numbers are odd Suppose n is an even integer so n^2 + 2n = (2k)^2 + 2(2k) = 4k^2 + 4k = 4k(k+1)

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Rational numbers are numbers which can be written in the form of \dfrac{a}{b} where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.

Irrational numbers are those real numbers which are not rational numbers.

Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

We are given that;

A integer n is frupable if n2 2n is odd

Now,

Suppose n is an even integer, so n = 2k for some integer k. Then:

n^2 + 2n = (2k)^2 + 2(2k) = 4k^2 + 4k = 4k(k+1)

Since k and k+1 are consecutive integers, one of them is even and the other is odd. Therefore, their product is even. This means that 4k(k+1) is even, and therefore, n^2 + 2n is even.

Since n^2 + 2n is even, it cannot be frumpable by definition. Therefore, if n is frumpable, n must be odd.

We have shown that if n is even, then n^2 + 2n is even and therefore, n cannot be frumpable.

Therefore, by the given numbers all frumpable numbers will be odd and n^2 + 2n = (2k)^2 + 2(2k) = 4k^2 + 4k = 4k(k+1)

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Answer:

6 half-liter

Step-by-step explanation:

To get 3 liters of milk, Toby has two options:

Option 1: Buy 6 half-liter containers

The cost of one half-liter container is $2.43, so the cost of six such containers is 6 x $2.43 = $14.58.

Option 2: Buy 12 250-milliliter containers

The cost of one 250-milliliter container is $1.42, which is equivalent to $5.68 per liter (since 1 liter is equal to 4 250-milliliter containers). Therefore, the cost of 3 liters (which is equivalent to 12 250-milliliter containers) is 12 x $1.42 = $17.04.

Therefore, Toby should buy 6 half-liter containers as it is the cheaper option.

Answer:

Below

Step-by-step explanation:

The dose can be .05 gm  ± .002 gm  =  .048 - .052 gm

The values of the coordinates x and y is P ( 6 , 3 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( x , y )

Let the second point be Q ( 0 , 0 )

Now , the slope of the line is m₁ = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = y / x

m₁ = 1/2

So , y/x = 1/2

And , x = 2y

Now , the third point is R ( 7 , 5 )

m₂ = ( 5 - y ) / ( 7 - x )

m₂ = 2

On simplifying , we get

( 5 - y ) / ( 7 - x ) = 2

Multiply by ( 7 - x ) , we get

5 - y = 14 - 2x

Adding 2x and subtracting 5 on both sides , we get

2x - y = 9

Substitute the value of x from m₁ , we get

2 ( 2y ) - y = 0

3y = 9

Divide by 3 on both sides , we get

y = 3

And , the value of x = 6

Hence , the coordinate of the point P is P ( 6 , 3 )

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Answer50.5

ffffffffffffffff

Answer:

12x^2.

Step-by-step explanation:

let y = 4x^3

If y is increased by a small amount Δy then x is increased by a small amount Δx, so we write:

y + Δy = 4(x + Δx)^3

y + Δy = 4(x^3 + 3x^2 Δx + 3x(Δx)^2 + (Δx)^3)

y + Δy = 4x^3 + 12x^2 Δx + 12x(Δx)^2 + 4(Δx)^3

Δy = 4x^3 + 12x^2 Δx + 12x(Δx)^2 + 4(Δx)^3 - y

    = 4x^3 + 12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2 - 4x^3

Δy/Δx = (4x^3 + 12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2- 4x^3 ) / Δx  

          = (12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2) / Δx

          = 12x^2 + 12x(Δx)^2 + 4Δx

Now as Δx approaches zero, the limit  ( that is the derivative) of f(x)

= 12x^2

- as we can neglect the last 2 terms.

The second part can be solved by the same process.

To construct a 2x2 matrix B such that AB is the zero matrix, we need to find two different nonzero columns for B that will result in the product of AB being the zero matrix. One way to do this is to choose the columns of B such that they are the negatives of the rows of A. This will result in the product of AB being the zero matrix.

Let A = [[a,b],[c,d]]

We can choose the columns of B to be [[-a,-c],[-b,-d]]. This will result in the product of AB being the zero matrix.

So, B = [[-a,-b],[-c,-d]]

AB = [[a,b],[c,d]] * [[-a,-b],[-c,-d]] = [[0,0],[0,0]]

Therefore, the 2x2 matrix B that will result in the product of AB being the zero matrix is B = [[-a,-b],[-c,-d]].

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The annual yield of the bond is 3.50%.

To calculate Mike's profit, we first need to determine the total cost of his investment, including the back-end load. The back-end load is calculated by multiplying the initial investment by the loading rate:

Back-end load = $14,000 * 5.5% = $770

So the total cost of Mike's investment is:

Total cost = $14,000 + $770 = $14,770

To determine the profit, we need to subtract the total cost from the total amount Mike received when he sold his shares:

Profit = ($21.85 - $20.00) * 14,000 - $770 = $2,730

Therefore, Mike made a profit of $2,730.

Note that the problem statement is exactly the same as the previous question. The answer is $2,730.

The annual rental income that Clara Teague needs to receive to achieve an annual yield of 8% can be calculated as follows:

Annual rental income = Total investment * Yield

where Total investment = $115,800 - $25,000 = $90,800

So the annual rental income that Clara Teague needs to receive is:

Annual rental income = $90,800 * 8% = $7,264

To determine the monthly rent, we divide the annual rental income by 12:

Monthly rent = $7,264 / 12 = $605.33

Therefore, Clara should charge a monthly rent of $605.33 to achieve an annual yield of 8%.

The annual yield of the bond can be calculated as follows:

Annual yield = (Annual interest payment / Bond price) * 100%

The annual interest payment is:

Annual interest payment = Bond face value * Annual interest rate = $25,000 * 3.7% = $925

The bond price is quoted at 105.7% of its face value, so the bond price is:

Bond price = Bond face value * 105.7% = $25,000 * 1.057 = $26,425

So the annual yield is:

Annual yield = ($925 / $26,425) * 100% = 3.50%

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The total temperature change over the 5 day period is - 16°F

Temperature is a measure of how hot or cold and object or environment is. It is measured in degree on the calcium where you need or kelvin scale different objects and environment have different temperature.

The total change in temperature over the 5 day period is the products of to the mean temperatures and the numbers of days which gives a value of - 16°F

Mean temperature = - 3.2°F

Number of days = 5

Total change = mean temperature × Number of days

The total temperatures change can be calculated thus :

(-3.2) × 5 = - 16°F

Therefore, the total temperature changes over the 5 day period is - 16°F

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This set {σ ∈ S4 : σ(1) = 3} contains the following elements of S4: (13), (23), (34), (24), (14), (12)(34), (13)(24), (14)(23) and  {σ ∈ S4 : σ(2) = 2} this set contains the following elements of S4: (12), (21), (13)(24), (24)(13).

The group S4 is the symmetric group on 4 elements and has 24 elements. We can list all of its subgroups as follows:

Now, let's consider the sets (a) and (b) and see if they are subgroups of S4:

(a) {σ ∈ S4 : σ(1) = 3}

This set contains the following elements of S4: (13), (23), (34), (24), (14), (12)(34), (13)(24), (14)(23). We can check that this set is not a subgroup of S4 because it is not closed under composition. For example, (13)(14) = (134) is not in the set.

(b) {σ ∈ S4 : σ(2) = 2}

This set contains the following elements of S4: (12), (21), (13)(24), (24)(13). We can check that this set is a subgroup of S4. It is closed under composition, inverses, and contains the identity element e. Therefore, it is a subgroup of S4 and is isomorphic to the cyclic group of order 2.

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In order to run a successful charity event for 6 people, it is important to ensure that everyone has something to enjoy.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


One way to do this is to provide cupcakes to one out of every three people. This will ensure that some people get a special treat while the others still have a chance to get one if they come to the event again. It also allows for a sense of fairness and equality, as everyone has an equal chance of receiving a cupcake. Additionally, it helps to build a sense of community and fellowship among the participants, as they can share the cupcakes and enjoy the experience together. It is also a great way to raise awareness about the charity and its cause, as people can talk about it while enjoying the cupcakes. To make sure that the event runs smoothly, it is important to have plenty of cupcakes on hand and to make sure that everyone is aware of the rules for receiving one.

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The equation of the ellipse in standard form is 16x² + 25y² = 400.

The standard form of the equation of an ellipse centered at the origin is:

x²/a² + y²/b² = 1

where a is the distance from the center to a vertex along the x-axis, and b is the distance from the center to a co-vertex along the y-axis.

In this case, we know that the center of the ellipse is at (0,0), a vertex is at (-5,0), and a co-vertex is at (0,4).

The distance from the center to a vertex along the x-axis is the absolute value of the x-coordinate of the vertex, which is 5. So, a = 5.

The distance from the center to a co-vertex along the y-axis is the absolute value of the y-coordinate of the co-vertex, which is also 4.

So, b = 4.

Substituting these values into the standard form equation, we get:

(x²/5²) + (y²/4²) = 1

Simplifying and multiplying by 5² and 4², we get the standard form equation of the ellipse:

16x² + 25y² = 400

Therefore, the equation of the ellipse in standard form is 16x² + 25y² = 400.

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The student's claim is incorrect, and SAS information is sufficient to prove the congruence of the triangles.

What is triangle ?

A triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and has various properties and formulas associated with it, such as its area, perimeter, angles, and side lengths. Triangles can be classified into different types based on their angles and side lengths, such as acute, right, obtuse, isosceles, and equilateral triangles. Triangles also have applications in various fields, including engineering, architecture, and physics.

The error in the student's reasoning is that they have misunderstood the SAS (Side-Angle-Side) congruence criterion. SAS criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. The order of the vertices of the triangle does not matter.

In the given case, if we have AJ = AR and KL = QP, and the included angle JAK is congruent to the included angle RAQ, then we have the SAS information to prove that triangles AJK and ARQ are congruent. The student's argument that the triangles are not congruent because J does not map onto R and L does not map onto P is incorrect, as the order of the vertices does not matter. The correct mapping is to move J to R and L to P by using a translation, and the triangles will coincide.

Therefore, the student's claim is incorrect, and SAS information is sufficient to prove the congruence of the triangles.

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Answer:

a. The sequence x_n = n^-2 converges quadratically to zero as n approaches ∞.

b. The sequence x_n = 2^-n converges linearly to zero as n approaches ∞.

c. The sequence x_n = 2^-2n converges quadratically to zero as n approaches ∞.

d. The sequence x_n = 2^-a_n with a_0 = a_1 = 1 and a_n+1 = a_n+a_n-1 for n≥2 converges superlinearly to zero as n approaches ∞.

Step-by-step explanation:

a. The sequence {x_n} = {n^(-2)} converges quadratically to zero as n approaches ∞.

To see this, we can calculate the limit of the ratio between consecutive terms:

lim_{n -> ∞} (x_{n+1} / x_n) = lim_{n -> ∞} ((n+1)^(-2) / n^(-2)) = lim_{n -> ∞} ((n / (n+1))^2) = 1

Since the limit is equal to 1, we know that the convergence rate of {x_n} is at least quadratic. This can also be seen from the fact that the error in the nth term is O(n^(-3)), which is smaller than the error in a linearly converging sequence (which is O(n^(-1))).

b. The sequence {x_n} = {2^(-n)} converges linearly to zero as n approaches ∞.

To see this, we can calculate the limit of the ratio between consecutive terms:

lim_{n -> ∞} (x_{n+1} / x_n) = lim_{n -> ∞} (2^(-(n+1)) / 2^(-n)) = lim_{n -> ∞} (1/2) = 1/2

Since the limit is strictly less than 1, we know that the convergence rate of {x_n} is linear.

c. The sequence {x_n} = {2^(-2n)} converges quadratically to zero as n approaches ∞.

To see this, we can calculate the limit of the ratio between consecutive terms:

lim_{n -> ∞} (x_{n+1} / x_n) = lim_{n -> ∞} (2^(-(2(n+1))) / 2^(-2n)) = lim_{n -> ∞} (1/4) = 1/4

Since the limit is equal to 1/4, we know that the convergence rate of {x_n} is at least quadratic. This can also be seen from the fact that the error in the nth term is O(n^(-2)), which is smaller than the error in a linearly converging sequence (which is O(n^(-1))).

d. The sequence {x_n} = {2^(-a_n)}, where a_0 = a_1 = 1 and a_{n+1} = a_n + a_{n-1} for n >= 2, converges superlinearly to zero as n approaches ∞.

To see this, we can use the fact that a_n grows exponentially with n. We can prove by induction that a_n >= phi^n, where phi is the golden ratio. Since the terms of {x_n} are decreasing and bounded below by 0, they must converge to a limit L. Taking the limit of the ratio of consecutive terms, we get:

lim_{n -> ∞} (x_{n+1} / x_n) = lim_{n -> ∞} (2^(-a_{n+1}) / 2^(-a_n)) = lim_{n -> ∞} (2^(-a_n - a_{n-1})) = 0

This shows that the convergence rate of {x_n} is superlinear.