Find the remainders when 2^50 and 41^65 are divided by 7?

Answer:

unfortunately tdudeyiutddj try Zurich etu

Answer:

The movie theater sold 85 large bags of popcorn and 204 small bags of popcorn.

Step-by-step explanation:

Let's use the following variables to represent the number of large and small bags of popcorn sold:

L: the number of large bags of popcorn sold

S: the number of small bags of popcorn sold

We can then write a system of equations based on the information given in the problem:

L + S = 289 (the total number of bags sold is 289)

4L + S = 544 (the total revenue from popcorn sales is $544)

To solve for L and S, we can use the method of substitution. Rearrange the first equation to solve for one variable in terms of the other:

L = 289 - S

Substitute this expression for L in the second equation and solve for S:

4(289 - S) + S = 544

1156 - 4S + S = 544

3S = 612

S = 204

Now that we know that 204 small bags of popcorn were sold, we can use the first equation to solve for L:

L + S = 289

L + 204 = 289

L = 85

Therefore, the movie theater sold 85 large bags of popcorn and 204 small bags of popcorn.

The limit of the given function f(x,y) as (x,y) approaches (0,0) is 0.

What is function ?
Function can be defined in which it relates an input to output.

To find the limit of the given function[tex]f(x,y) = sin(2(x^2 + y^2))/(2(x^2 + y^2))[/tex]as [tex](x,y)[/tex] approaches (0,0), we can use the squeeze theorem.

First, note that [tex]sin(2(x^2 + y^2))[/tex]is bounded between -1 and 1 for all (x,y), since the sine function is bounded between -1 and 1. Therefore, we have:

[tex]-1/(2(x^2 + y^2)) < = sin(2(x^2 + y^2))/(2(x^2 + y^2)) < = 1/(2(x^2 + y^2))[/tex]

Next, we can take the limit as (x,y) approaches (0,0) of both sides of this inequality using the squeeze theorem. The left-hand side approaches 0, and the right-hand side approaches 0 as well. Therefore, by the squeeze theorem, we have:

lim (4/3)π(21.03)³- (4/3)π(20.97)³

Hence, the limit of the given function f(x,y) as (x,y) approaches (0,0) is 0.

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Answer:

Step-by-step explanation:

We can conclude that the hypotheses of the Existence and Uniqueness Theorem are satisfied in any rectangular region in the ty-plane that does not contain the curve t² + y² = -1.

The Existence and Uniqueness Theorem for first-order ordinary differential equations states that if a differential equation of the form y' = f(t, y) satisfies the following conditions in some rectangular region in the ty-plane:

1. f(t, y) is continuous in the region.

2. f(t, y) satisfies a Lipschitz condition in y in the region, i.e., there exists a constant L > 0 such that |f(t, y₁) - f(t, y₂)| ≤ L|y₁ - y₂| for all t and y₁, y₂ in the region.

then there exists a unique solution to the differential equation that passes through any point in the region.

In the case of the differential equation y' = (y cot(2t)) / (t² + y² + 1), we have:

f(t, y) = (y cot(2t)) / (t² + y² + 1)

This function is continuous everywhere except at the points where t² + y² + 1 = 0, which is the curve t² + y² = -1 in the ty-plane. Since this curve is not included in any rectangular region, we can say that f(t, y) is continuous in any rectangular region in the ty-plane.

To check if f(t, y) satisfies a Lipschitz condition in y, we can take the partial derivative of f with respect to y and check if it is bounded in any rectangular region. We have:

∂f/∂y = cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²

Taking the absolute value and simplifying, we get:

|∂f/∂y| = |cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²|

= |cot(2t) / (t² + y² + 1)| * |1 - (2y² / (t² + y² + 1)))|

Since 0 ≤ (2y² / (t² + y² + 1)) ≤ 1 for all t and y, we have:

1/2 ≤ |1 - (2y² / (t² + y² + 1)))| ≤ 1

Also, cot(2t) is bounded in any rectangular region that does not contain the points where cot(2t) is undefined (i.e., where t = (k + 1/2)π for some integer k). Therefore, we can find a constant L > 0 such that |∂f/∂y| ≤ L for all t and y in any rectangular region that does not contain the curve t² + y² = -1.

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In formally proving that lim (x² + x) = 42

m = ⌈√ε⌉ - 1

It is shown that for any ε > 0, there exists a δ > 0 such that if 0 < |x - c| < δ, then |(x^2 + x) - 42| < ε.

|(x^2 + x) - 42| = |x^2 + x - 42| = |(x - 6)(x + 7)|

Since |x - c| < δ, we have:

|x - 6| < δ + 6 < δ(m+2)

|x + 7| < δ + 7 < δ(m+2)

Since δ = ε/(m+1), we can solve for m:

m+1 = ε/δ

m+1 = ε/ (ε/(m+1) )

(m+1)^2 = ε

m^2 + 2m + 1 = ε

m^2 + 2m + (1-ε) = 0

Using the quadratic formula, we get:

m = (-2 ±  ⌈√ε⌉ - 1 (4 - 4(1-ε)))/2 = -1 ± √(ε)

Therefore, in conclusion  m =  ⌈√ε⌉ - 1

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Therefore, the cylinder stretch in the new 6.00 m length of steel pipe is 0.094% of its original length, or about 5.64 mm.

The cylinder, which is frequently a three-dimensional solid, is one of the most primitive curved geometric forms. In simple geometry, it is known as a prismatic with a circular as its basis. The term "cylinder" is also used to refer to an infinitely curved surface in a number of modern domains of geometry and topology. A "cylinder" is a three-dimensional object made up of curved surfaces with round tops and bottoms.

Here,

The total weight supported by the new 6.00 m length of pipe is the weight of the pipe and drill bit beneath it, which is:

W = (20.0 kg/m)(3.00 km) + 100 kg

W = 60,100 kg

The equivalent diameter of the solid cylinder is 5.00 cm, or 0.05 m, so its radius is 0.025 m. The cross-sectional area of the steel pipe is therefore:

A = πr^2 = π(0.025 m)^2 = 0.0019635 m^2

The modulus of elasticity for steel is typically around 200 GPa (gigapascals), or 200,000,000 N/m^2. Using the formula for the stretch of a rod under tension, which is:

ΔL/L = F/(AE)

ΔL/L = (Wg)/(AE)

where g is the acceleration due to gravity (9.81 m/s^2).

Substituting the values we have calculated, we get:

ΔL/L = [(60,100 kg)(9.81 m/s^2)]/[(0.0019635 m^2)(200,000,000 N/m^2)]

ΔL/L = 0.0009397 or 0.094%

Therefore, the stretch in the new 6.00 m length of steel pipe is 0.094% of its original length, or about 5.64 mm.

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The percentage of the decrease in the value of the XYZ Company stock is 16%.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
The decrease in the value of the stock is $25 - $21 = $4.

To find the percent decrease, we need to divide the decrease by the original value and then multiply by 100:

Percent decrease = (Decrease / Original value) x 100

In this case, the original value is $25, so:

Percent decrease = (4 / 25) x 100 = 16%

Therefore, the percentage of the decrease in the value of the XYZ Company stock is 16%.

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The equation that shows  the damping ratio for a mass-spring-damper system which is defined in terms of the mass, m, stiffness, k, and damping, b is  ζ = b / (2sqrt(mk)).

The damping ratio ζ is defined as the ratio of the damping coefficient b to the critical damping coefficient b_c, which is the minimum damping required to prevent the system from oscillating.

The damping ratio is a dimensionless quantity that represents the amount of damping in the system relative to the critical damping needed to prevent oscillations. A higher damping ratio indicates a more heavily damped system, while a lower damping ratio indicates a less damped system that may oscillate more.

The motion of a mass-spring-damper system can be described by a second-order linear ordinary differential equation (ODE) of the form:

md²x/dt² + bdx/dt + kx = F(t)

where m is the mass of the system, b is the damping coefficient, k is the spring constant, x is the displacement of the mass from its equilibrium position, and  the external force applied to the system is F(t).

The critical equation will be -

b_c = 2√(mk)

Therefore, the damping ratio can be expressed as:

ζ = b / b_c

Substituting the expression for b_c into the above equation, we get:

ζ = b / (2√(mk))

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Answer:320000

Step-by-step explanation:

that in the second year, we use the beginning book value of $639,900

a. Sum-of-the-years’-digits method:

To compute the depreciation using the sum-of-the-years’-digits method, we first need to determine the total number of years of the asset's useful life. We do this by subtracting the salvage value from the cost and dividing by the estimated yearly depreciation.

Cost of asset = $711,000

Salvage value = $60,000

Useful life = 20 years

Yearly depreciation = (Cost - Salvage value) / Useful life

Yearly depreciation = ($711,000 - $60,000) / 20 = $32,550

To calculate the sum-of-the-years’-digits (SYD) for this asset, we add up the digits of the useful life in descending order. For a 20-year useful life, the SYD would be:

SYD = 20 + 19 + 18 + ... + 1 = 210

Using the SYD and the number of remaining years, we can calculate the depreciation expense for each year as follows:

Year 2020:

Depreciation expense = (20/210) x ($711,000 - $60,000) = $64,286

Year 2021:

Depreciation expense = (19/210) x ($711,000 - $60,000) = $60,952

b. Double-declining-balance method:

To compute the depreciation using the double-declining-balance (DDB) method, we first need to determine the asset's straight-line depreciation rate, which is calculated as follows:

Straight-line depreciation rate = 1 / Useful life

Straight-line depreciation rate = 1 / 20 = 0.05

The DDB depreciation rate is twice the straight-line rate, or 0.10. We can then calculate the depreciation expense for each year as follows:

Year 2020:

Depreciation expense = Beginning book value x DDB rate

Beginning book value = Cost of asset

Depreciation expense = $711,000 x 0.10 = $71,100

Year 2021:

Depreciation expense = Beginning book value x DDB rate

Beginning book value = Cost of asset - Accumulated depreciation from previous years

Accumulated depreciation (2020) = $71,100

Beginning book value (2021) = $711,000 - $71,100 = $639,900

Depreciation expense = $639,900 x 0.10 = $63,990

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Kenny need to buy 4 quarts.

It cost $14.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The mailbox is splitted into two shapes.

One is rectangle and the other is hemisphere.

Length of the rectangle = 2.4 ft

Width of the rectangle = 1.5 ft

Height of the rectangle = 3 ft

Surface area of the given rectangle

                  = 2(lw + wh + lh) – lw

                  = 2(2.4 × 1.5 + 1.5 × 3 + 2.4 × 3) – (2.4 × 1.5)

                  = 2(3.6 + 4.5 + 7.2) – 3.6

                  = 2(15.3) – 3.6

                  = 27

Surface area of the given rectangle = 27 square feet

Radius of the hemisphere = 1.2 ft

Curved surface area of hemisphere

                 = 2*pi*r^2

                  = 9.0432 square feet

Curved surface area of hemisphere = 9.0432 square feet                                      

Total surface area of the mailbox  = 27 + 9.0432

                                                        = 36.0432 square feet

To find how many quarts are needed to cover the mailbox.

1 Quart covers = 10 square feet

36.0432 sq. ft = 36.0432 ÷ 10

                      = 3.60432 quarts

                      ≈ 4 quarts (approximately)

Hence Kenny need to buy 4 quarts.

Cost of 1 quart = $3.50

Cost of 4 quart = 4 × 3.50

                        = 14

Hence it cost $14.

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The height of the triangle is h = 2A/6.

Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the point is. For example, a person's height is typically measured using a stadiometer and is recorded in centimeters or feet and inches. The height of a mountain is usually measured in meters or feet. In aviation, height is measured from the surface of the earth, either above ground level (AGL) or above mean sea level (AMSL).


To find the height of a right triangle given the base, we can use the area formula A = 1/2bh. Rearranging this equation gives us the height: h = 2A/b. In this case, the base is 6 inches and the area is given as A. Therefore, the height of the triangle is h = 2A/6.

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Answer:

Step-by-step explanation:

To solve for b, we can use the law of sines, which states that in any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

Here, we are given B = 150°, C = 20°, and c = 21 inches. We can solve for the remaining angle A by using the fact that the angles of a triangle add up to 180°:

A + B + C = 180°

A = 180° - B - C

A = 180° - 150° - 20°

A = 10°

Now we can use the law of sines to solve for b:

a/sin(A) = b/sin(B)

a = c * sin(A)/sin(C) = 21 * sin(10°)/sin(20°)

b = a * sin(B)/sin(A) = 21 * sin(10°)/sin(20°) * sin(150°)/sin(10°)

b = 21 * sin(150°)/sin(20°)

Using a calculator, we get:

b ≈ 41 inches (rounded to the nearest whole number)

Therefore, the length of side b is approximately 41 inches.

The collection, description, analysis, and drawing of conclusions from quantitative data are all included in the area of statistics, which is a branch of applied mathematics. Probability theory, linear algebra, and calculus of differential and integrals are some of the core mathematical concepts in statistics.

Descriptive statistics were used in the statement.

Descriptive statistics is a branch of statistics that deals with the collection, presentation, and summary of data. It is used to describe and summarize the main features of a data set, such as measures of central tendency (e.g., mean, median, mode) and measures of dispersion (e.g., range, variance, standard deviation).

In this case, the statement is simply reporting a single value, the average credit card debt for college students in 2008. This is an example of a descriptive statistic because it is a summary measure that describes a characteristic of the population or sample under study.

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Descriptive statistics were used in the statement.

Descriptive statistics is a branch οf statistics that deals with the analysis, descriptiοn, and summarizatiοn οf data. It invοlves the use οf variοus statistical measures, such as measures οf central tendency (mean, median, and mοde), measures οf dispersiοn (standard deviatiοn, variance, range), and graphical representatiοns (histοgrams, bοx plοts, scatter plοts, etc.) tο describe the features οf a dataset.

Descriptive statistics were used in the statement. The statement is simply describing the average credit card debt fοr cοllege students in 2008. Descriptive statistics are used tο describe οr summarize a dataset οr pοpulatiοn, while inferential statistics are used tο draw cοnclusiοns οr make predictiοns abοut a larger pοpulatiοn based οn a sample οf data. Since the statement οnly prοvides infοrmatiοn abοut a specific grοup οf cοllege students in 2008, it dοes nοt invοlve making any inferences οr predictiοns beyοnd this grοup.

Hence, Descriptive statistics were used in the statement.

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Answer: y = 2x - 7

Step-by-step explanation:

Slope-intercept form is y=mx+b

Substitute variables with their given values.

 y = 2x + b

In order to find the y-intercept, or b, we can plug the point provided, (4,1) , into y = 2x + b and solve for b.

 1 = 2(4) + b

 1 = 8 + b

-7 = b

Now we can put the y-intercept into the equation, and get y = 2x - 7 .

The required least common denominator for the given expression is  4x³(x + 3). Option C is correct.

A rational expression is a mathematical expression that is the ratio of two polynomial expressions. That is, a rational expression is formed by dividing one polynomial expression by another polynomial expression.

Here,
The given rational expression,
= 1/x²  - 1/4x² + 12x

In the question, we have been asked to determine the least common denominator for the given rational expression.

Since least common denominator is given expression,
= x² (4x² + 12x)
= 4x³(x + 3)

Thus, the required least common denominator for the given expression is  4x³(x + 3). Option C is correct.

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Answer:

43% * 258 = 110.94 (£110.94 is 43% of £258) 258 + 110.94 = 368.94

Step-by-step explanation:

(-7, 4).

[tex]x=-2y+1\\ \\3x+8y=11[/tex]

Most of the times you solve a systems of equations, you'll have to solve one of the equations for one of the variables (x or y), since the first equation is already solved for "x", we may use that and skip this first solving step.

[tex]x=-2y+1[/tex]

[tex]3(-2y+1)+8y=11[/tex]

Chech attached image 1.

[tex](3)(-2y)+(3)(1)+8y=11\\ \\(-6y)+(3)+8y=11\\ \\-6y+3+8y=11[/tex]

[tex]-6y+3+8y-3=11-3\\ \\-6y+8y=8[/tex]

[tex]2y=8[/tex]

[tex]\frac{2y}{2} =\frac{8}{2} \\ \\y=4[/tex]

[tex]x=-2(4)+1\\ \\x=-8+1\\ \\x=-7[/tex]

Now that weëve found a value for both "x" and "y", write the solution as an ordered pair:

(x, y)

(-7, 4).

To algebraically verify your answer, you must use the value of either "x" or "y" on both of the equations and it should return the other value of the missing variable.

Since we already checked with the first equation, go ahead and plug in any of the values on the second equation and check if it returns the correct value.

For example, if we use y=4 in equation 2, it should return an "x" value of -7. Let's test it!

[tex]3x+8(4)=11\\ \\3x+32=11\\ \\3x=11-32\\ \\3x=-21\\ \\\frac{3x}{3} =\frac{-21}{3} \\ \\x=-7[/tex]

That's correct! Answer is (-7, 4).

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Answer:

₹ 2,001.20

Step-by-step explanation:

We can consider the grassy plot as a circle with radius = 42/2 = 21 m

The grassy plot and the path together form another circle with radius = 21 + 3.5 = 24.5 m

Area of a circle = πr² where r is the radius

Area of grassy plot = π x 21² = 441π m²

Area of outer circle (grassy plot + path) = π x (24.5)² = 600.25π m²

Area of the outer path alone = 600.25π - 441π = 159.25π = 500.30 sq meters

Cost of paving 1 square meter = ₹ 4

Cost of paving  500.3 sq m = 500.3 x 4 = ₹ 2,001.20

Answer:

below

Step-by-step explanation:

[ 2.13 * 13   +  2.34 * 12  +  3.00 * 17 ] / ( 13 + 12 + 17) = 2.54 GPA

The domain of the function is  (-∞, -2) ∪(-2, ∞) and it's range is (-∞, 1) ∪ (1, ∞). The function has vertical and horizontal asymptotes as x = -2 and y = 1

In mathematics, the domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined. The range of a function is the set of all possible output values (also known as the dependent variable) that the function can produce.

To determine the domain and range of a function, it's important to consider the nature of the function, its graph or formula, and any restrictions that may apply.

The function f(x) = - (2/ x + 2) + 1

The domain of the function is (-∞, -2) ∪(-2, ∞)

The range of the function is (-∞, 1) ∪ (1, ∞)

The vertical asymptote is x = -2

The horizontal asymptotes y =  1

The y-intercept is (0, 0)

The x - intercept is (0, 0)

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Answer: D.

Step-by-step explanation: It's just a cylinder how can you not see

Answer: 3.14 ft

Step-by-step explanation:

★Given,→ Diameter = 2 feet → Circumference = 2/2 = 1 feet

★Now,→Area of a circle = πr²→ = 3.14 × 1 × 1→ = 3.14 feet

Hence , the circumference is 3.14 ft.  

The solution to inequality is -2/3 ≤ x ≤ 2. The value of x lies between -2/3 and 2.

What is inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the expression on the left should be greater or less than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols.

Given inequality is

|3x-2| ≤ 4

Applying the formula |x| ≤ a → -a ≤ x ≤ a:

-4 ≤ 3x-2 ≤ 4

Add 2 on both sides:

-4 + 2 ≤ 3x-2 + 2 ≤ 4 + 2

-2 ≤ 3x ≤ 6

Divide both sides by 3:

-2/3 ≤ x ≤ 2

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Answer A: Construct a two-sample z-interval for the difference between population proportions.

What is fraction?

A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. It is written as a/b, where a is called the numerator and b is called the denominator. The numerator represents the number of parts or units being considered, while the denominator represents the total number of parts or units in the whole.

According to given conditions:

The best method for the researcher to use to estimate the true difference between the population proportions would be to:

Answer A: Construct a two-sample z-interval for the difference between population proportions.

This is the most appropriate method for estimating the difference between population proportions, as it takes into account the variability of the sample proportions and provides a confidence interval for the true difference between the two populations. The formula for calculating the two-sample z-interval for the difference between population proportions is:

(p₁−p₂) ± z x √[(p₁(1−p₁))/₁ + (p₂(1−p₂))/₂]

Therefore, Answer A: Construct a two-sample z-interval for the difference between population proportions.

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The relationship between hours worked and money is not proportional.

Regina would be able to buy her shoes first after working an additional 50 minutes.

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

To determine if the relationship between hours worked and money is proportional, we need to calculate the hourly rate for each person and see if it is the same.

For Regina, she earned $120 per hour and worked for 5 hours, so she earned a total of 5 x 120 = $600.

This means her hourly rate is $120.

For Abby, she earned $320 for 5 hours of work, so her hourly rate is 320/5 = $64.

Since the hourly rates are different, the relationship between hours worked and money is not proportional.

Now let's see who would be able to buy their shoes first.

Regina needs $100 more to be able to buy her shoes, and she earned $600 from working 5 hours.

Therefore, she can buy the shoes after working for an additional $100/$120 = 0.83 hours, which is approximately 50 minutes.

On the other hand, Abby needs $270 more to buy her shoes, and she earned $320 from working 5 hours.

Therefore, she can buy the shoes after working for an additional $270/$64 = 4.22 hours, which is approximately 4 hours and 13 minutes.

Therefore, Regina would buy her shoes first.

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Answer: 1/64 cubic inch

Step-by-step explanation:

Side of cube = 1/4

Volume = s^3 = 1/4^3

= 1/64

Hope this helps!!

Answer:

4(9+3) = 48

Step-by-step explanation:

To simplify the expression 4(9+3), we need to perform the addition inside the parentheses first and then multiply the result by 4.

9+3 = 12, so we can substitute this into the expression as follows:

4(9+3) = 4(12)

Now we can perform the multiplication:

4(12) = 48

Therefore, the equivalent expression to 4(9+3) is simply 48.

If a 4-yard dumpster cost $95.00 monthly, the total cost for the year is $1,140.

The total cost for the year of the dumpster is the product of the multiplication of the monthly cost and 12.

Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.

In any multiplication, there must be the multiplicand (the number being multiplied), the multiplier (the number multiplying the multiplicand), and the product (or the result).

The monthly cost of the 4-yard dumpster = $95.00

1 year = 12 months

The total annual cost = $1,140 ($95 x 12)

Thus, using the multiplication operation, we can find that none of the options is correct as the total annual cost but $1,140.

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