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Mortgage B: 381.93 12-30 = $137.494.80
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Module 2.5 Unders
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Question
Stephen is comparing two mortgage options for his $80, 000 mortgage.
Mortgage A: 15 years at 4.5% with monthly payments of $611.99 and a total payb
$110, 158.20.
Mortgage B: 30 years at 4% with monthly payments of $381.93and a total paybac
$137, 494.80.
Provide your answer below:
Which option requires more interest to be paid over the life of the mortgage? How

The derivative formula for the division of two functions is equal to d [θ(x)] / dx = [g(x) · f'(x) - f(x) · g'(x)] / [g(x)]², where θ(x) = f(x) / g(x).

In this problem we need to derive the formula for the derivative of the division of two functions, that is, the expression θ(x) = f(x) / g(x). First, we write the definition of the derivative for the given expression:

[tex]\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{\theta(x + h) - \theta (x)}{h}[/tex]

Second, substitute and expand the expression by algebra properties:

[tex]\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{\frac{f(x + h)}{g(x + h)} - \frac{f(x)}{g(x)} }{h}[/tex]

[tex]\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} \frac{f(x + h) \cdot g(x) - f(x) \cdot g(x + h)}{h\cdot g(x + h)\cdot g(x)}[/tex]

Third, expand and simplify the expression one more time by algebra properties and limit properties:

[tex]\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{f(x + h) \cdot g(x) - f(x) \cdot g(x) + g(x) \cdot f(x) -f(x) \cdot g(x + h)}{h \cdot g(x + h) \cdot g(x)}[/tex]

[tex]\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} g(x) \cdot \frac{f(x + h) - f(x)}{h\cdot g(x+h)\cdot g(x)} - \lim_{h \to 0} f(x) \cdot \frac{g(x + h) - g(x)}{h\cdot g(x+h)\cdot g(x)}[/tex]

[tex]\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} \frac{g(x)}{g(x + h) \cdot g(x)} \cdot \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} - \lim_{h \to 0} \frac{f(x)}{g(x+ h) \cdot g(x)} \cdot \lim_{h \to 0} \cdot \frac{g(x + h) - g(x)}{h}[/tex]

Fourth, simplify the resulting expression by evaluating the limits:

d [θ(x)] / dx = [g(x) / [g(x)]²] · f'(x) - [f(x) / [g(x)]²] · g'(x)

d [θ(x)] / dx = [g(x) · f'(x) - f(x) · g'(x)] / [g(x)]²

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1. The amount of pizzas which the pizzeria must sell for employees to receive the bonus is 78.

2. The new number of pizzas sold is considered as percent increase of 20%.

The pizzeria sold 65 pizzas yesterday and the owner offers bonus if the number sold increases by 20% today. The number that must be sold, to receive a bonus is computed as follows:

= 65 pizza * (65 pizza * 20%)

= 65 pizza * 13 pizza

= 78 pizza.

It is a percent increase which is computed as follows. The formula for percentage increase is: ((Final value - Initial value)/Initial value * 100).

The Percent increase:

= (78 pizza - 65 pizza) / 65 pizza.

= 13 pizza / 65 pizza

= 0.2

= 20%

Full question "A local pizzeria sold 65 pizzas yesterday. (step 1) The owner offers the employees a bonus if the number of pizzas sold increases by 20% today. How many pizzas must the pizzeria sell for employees to receive the bonus? Explain your reasoning. (Part 2) Suppose the actual number of pizzas sold today was 60. Describe the number of pizzas sold as a percent increase or decrease, rounded to the nearest hundredth. Show your work. Answer:"

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Answer:

Step-by-step explanation:

Since Joe bought six bunches of seedless black grapes for $15, the cost per bunch of grapes is $15 / 6 = $2.50.

Since Anjali has $7.50, she can buy $7.50 / $2.50 = 3 bunches of seedless black grapes.

Step-by-step explanation:

(a) To convert feet to fathoms, we can use the conversion factor 1 fathom = 6 feet. Hence, we can divide the depth in feet by 6 to find the depth in fathoms:

36,078 feet / 6 feet/fathom = 6,013 fathoms

So the depth of the seabed is 6,013 fathoms.

(b) To convert feet to leagues (marine), we can use the conversion factor 1 league (marine) = 5,556 feet. Hence, we can divide the depth in feet by 5,556 to find the depth in leagues (marine):

36,078 feet / 5,556 feet/league (marine) = 6.52 leagues (marine)

So the depth of the seabed is approximately 6.52 leagues (marine).

The x- and y-components of the vector [tex]\mathbf{\hat a}}[/tex] are 8.9 m/s² and -6.4 m/s², respectively.

In mathematics, components are the parts or elements that make up a larger structure or object. In the context of vectors, components refer to the parts of a vector that describe its direction and magnitude in a particular coordinate system.

To find the x-components and y-components of the vector [tex]\mathbf{\hat a}}[/tex] = (11 m/s², 36 degrees left of -y-axis), we need to determine the direction of the vector. The notation "left of -y-axis" means that the vector makes an angle of 36 degrees with the negative y-axis, as measured counterclockwise from the negative y-axis.

The magnitude (or length) of the vector is given by the first component, which is 11 m/s².

The x-component of the vector can be found by multiplying the magnitude by the cosine of the angle:

x-component = magnitude x cos(angle) = 11 m/s² x cos(36°) = 8.9 m/s²

The y-component of the vector can be found by multiplying the magnitude by the sine of the angle:

y-component = magnitude x sin(angle) = 11 m/s² x sin(36°) = -6.4 m/s²

The negative sign indicates that the y-component is in the opposite direction of the negative y-axis.

Therefore, the x- and y-components of the vector [tex]\mathbf{\hat a}}[/tex] are 8.9 m/s² and -6.4 m/s², respectively.

Expressed as an ordered pair, the components are (8.9 m/s², -6.4 m/s²).

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The positive angle which is less than 360 degrees and is co-terminal with -305 as required is; 55°.

It follows from the task content that the position angle which is co-terminal with -305° as required is to be determined.

Let the positive angle in discuss be; x.

Therefore, the angle x = 360 + (-305)

Consequently, it can be calculated as follows;

x = 360 - 305.

x = 55°

Hence, the required value of the positive co-terminal angle is; 55°.

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The scaled dimensions of a kitchen with dimensions 6.3m by 4.8m, if the kitchen plan is drawn to a scale of 1:500, are given as follows:

1.26 cm and 0.96 cm.

The scaled dimensions are obtained applying the proportions in the context of the problem.

The scale is of 1:500, meaning that each dimension is divided by 500, as follows:

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The correct transformation is, a dilation with a scale factor less than 1 and then a reflection.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, a transformation that maps polygon ABCD to polygon A'B'C'D',

We are asked to select the correct composition of similarity transformations,

According to the graph, there is a scale factor of 1/2 which is smaller than 1,

Also, the polygon is dilating and then reflected.

Hence, the correct transformation is, a dilation with a scale factor less than 1 and then a reflection.

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Answer:

  EF = 7

Step-by-step explanation:

You want to know the length of midsegment EF in the triangle with it labeled 43-4x and the parallel base segment labeled 32-2x.

The midsegment is half the length of the base segment, so we have ...

  (43 -4x) = 1/2(32 -2x)

  43 -4x = 16 -x . . . . . simplify

  27 = 3x . . . . . . . . add 4x-16

  9 = x . . . . . . . . divide by 3

  EF = 43 -4x = 43 -4(9) = 43 -36

  EF = 7

This student would receive 10 bag of popcorns.

Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In order to determine the quantity of popcorn, we would make use of the information provided about the unit price for one bag of popcorn by using the following mathematical expression;

Number of bag of popcorns = Cost of one bag of popcorn/Unit price

Substituting the given parameters into the mathematical expression above, we have the following;

Number of bag of popcorns = 5/0.50

Number of bag of popcorns = 10 bag of popcorns.

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a) A linear equation for the total remaining oil reserves, R, in terms of t, the number of years since the current year, is 2,090 - 18t.

b) Based on the above linear equation, 15 years from now, the total oil reserves will be 1,820 billion barrels.

c) Using division operation, the world's oil reserves will be completely depleted approximately 116 years from now.

A linear equation is a mathematical or algebraic equation written in the form of y = mx + b.

A linear equation consists of a constant and a first-order term, where m is the slope, and variable b, the y-intercept.

The current total world oil reserves, R = 2,090 billion barrels

Average decrease per year = 18 billion barrels

a) Linear equation for R is 2,090 - 18t

b) In 15 years, the total oil reserves = 2,090 - 18(15)

= 2,090 - 270

= 1,820

c) The constant rate of decrease = 18 billion barrels per year

The world's oil reserves will be completely depleted approximately 116 years from now (2,090/18).

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d. The logarithmic model can be expressed as y1~alog(x1)+k or y1~aln(x1)+k.

The best fit curve for the given data would be: y1 = 0.2 * log(x1) + k or y1 = 0.2 * ln(x1) + k

a. If you wanted to find a station with a frequency of 93.3 on your radio dial, you would need to use the formula Frequency = 88 + 0.2 * (Channel Number). Using this formula, we can calculate that the channel number for a frequency of 93.3 is:

Channel Number = (Frequency - 88) / 0.2

Channel Number = (93.3 - 88) / 0.2

Channel Number = 5.3

Therefore, a station with a frequency of 93.3 can be found on channel 5.3 on your radio dial.

b. If you turned the radio dial to be 4 centimeters from the left end of the radio, the channel number would be:

Channel Number = 4 / 0.2

Channel Number = 20

Using the formula Frequency = 88 + 0.2 * (Channel Number), we can calculate that the frequency for channel 20 is:

Frequency = 88 + 0.2 * (Channel Number)

Frequency = 88 + 0.2 * (20)

Frequency = 96.0

Therefore, turning the radio dial to be 4 centimeters from the left end of the radio, you will pick up a station with a frequency of 96.0.

Based on the proceeds and effective rate, Wilson should take out the simple discount note, which has a higher proceeds of $5,005 and a higher effective rate of 9.9% compared to the simple interest note's proceeds of $5,995 and effective rate of 9.0%.

To compare the simple discount note and the simple interest note, we can calculate the proceeds and effective rates for each.

For the simple discount note, the interest is deducted upfront and the borrower receives the difference, or the proceeds. The interest on a $5,500 note at 6% for 18 months can be calculated as:

Interest = Principal × Rate × Time

Interest = $5,500 × 6% × 1.5 years

Interest = $495

The proceeds for the simple discount note can be calculated as:

Proceeds = Principal - Interest

Proceeds = $5,500 - $495

Proceeds = $5,005

The effective rate for the simple discount note can be calculated using the formula:

Effective Rate = Interest / Proceeds × 100%

Effective Rate = $495 / $5,005 × 100%

Effective Rate = 9.9%

For the simple interest note, the interest is calculated on the principal amount and added to the principal at the end of the term. The interest on a $5,500 note at 6% for 18 months can be calculated as:

Interest = Principal × Rate × Time

Interest = $5,500 × 6% × 1.5 years

Interest = $495

The total amount due at the end of the term for the simple interest note can be calculated as:

Total Due = Principal + Interest

Total Due = $5,500 + $495

Total Due = $5,995

The effective rate for the simple interest note can be calculated using the formula:

Effective Rate = Interest / Principal × 100%

Effective Rate = $495 / $5,500 × 100%

Effective Rate = 9.0%

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Answer:

27,64,216,64,243

Step-by-step explanation:

Any number raise to power 3

Answer:

Step-by-step explanation:

C. There is a moderate correlation between the scores and grades.

Based on the scatter plot and the calculated correlation coefficient, we can conclude that there is a moderate positive correlation between the pretest scores and the course grades. This means that as the pretest scores increase, the course grades tend to increase as well. However, the correlation is not extremely strong, so other factors may be affecting the course grades besides the pretest scores.

The correlation between two variables describes the relationship between them. The strength of the correlation can be classified into four categories: no correlation, weak correlation, moderate correlation, and strong correlation.

In this case, since the values of X and Y appear to have a moderate association, it might be concluded that there is a moderate correlation between the scores on the pretest and the course grade.

However, correlation does not imply causality, meaning that even if there is a correlation between two variables, it does not mean that one variable causes the other. Further analysis, such as regression analysis, is needed to determine the strength and direction of the relationship and to determine if there is a causal relationship.

a. The profit function is given by P(x) = R(x) - C(x). Substituting the expressions for R(x) and C(x), we have P(x) = 12x + 300√x - 2500.

b. The marginal profit function is the derivative of the profit function with respect to x. To find the marginal profit function, we will differentiate P(x) is dP/dx = 12 + 300/2√x.

c. The marginal average profit function is the derivative of the profit function divided by the number of units sold is dP/dx ÷ x = (12 + 300/2√x) ÷ x.

d. To estimate the profit from the sale of the 201st doll, we will evaluate the profit function at x = 201 is $16.62.

What do you mean by  profit function?

A profit function is a mathematical model that represents the profit made from selling a certain product or service as a function of the number of units sold. The profit function is calculated as the difference between the total revenue and the total cost of producing and selling the product.

Mathematically, if R(x) represents the total revenue from selling x units of a product and C(x) represents the total cost of producing and selling x units of the product, then the profit function can be represented as P(x) = R(x) - C(x).

a. The profit function is given by P(x) = R(x) - C(x). Substituting the expressions for R(x) and C(x), we have:

P(x) = 14x - (2x - 300√x + 2500)

P(x) = 12x + 300√x - 2500

b. The marginal profit function is the derivative of the profit function with respect to x. To find the marginal profit function, we will differentiate P(x):

dP/dx = 12 + 300/2√x

c. The marginal average profit function is the derivative of the profit function divided by the number of units sold.

dP/dx ÷ x = (12 + 300/2√x) ÷ x

d. To estimate the profit from the sale of the 201st doll, we will evaluate the profit function at x = 201:

P(201) = 12 * 201 + 300 * √201 - 2500 = $3347.09

Since we want the profit from the sale of one unit, we divide the profit by 201:

P(201) ÷ 201 = $16.62

So, the estimated profit from the sale of the 201st doll is $16.62.

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Answer:The range rule of thumb states that the standard deviation (s) is approximately equal to the range (R) divided by 4, where the range is the difference between the maximum and minimum values of a data set.

Using this formula, we can estimate the standard deviation of the heights as:

s = R / 4 = (192.5 - 152.0) / 4 = 20.625 / 4 = 5.156 cm

Comparing this estimate to the actual standard deviation of 12.22 cm, we see that the estimate is off by a factor of approximately 2.37.

Since the estimate is not within 1.7 cm of the actual standard deviation, it suggests that the range rule of thumb is not a very accurate way to estimate the standard deviation of this data set. The standard deviation calculated using the full set of data is much larger than the estimate, which means that the spread of the data is greater than what would be expected based on the range rule of thumb.

To find the weight of 2.2 cubic feet of water in pounds, we can use the following formula:

Weight in pounds = Volume in cubic feet x Density of water in pounds per cubic foot

The density of water is 62.4 pounds per cubic foot, so we can substitute the values into the formula:

Weight in pounds = 2.2 x 62.4 = 138.08

So, 2.2 cubic feet of water weighs 138.08 pounds.

To convert this weight to tons, we can divide by 2000, as there are 2000 pounds in a ton:

Weight in tons = 138.08 / 2000 = 0.06904 tons

So, 2.2 cubic feet of water weighs 0.06904 tons.

Answer:

Step-by-step explanation:

First, we need to find how many gallons of water 2.2 cubic feet hold:

2.2 cubic feet * 7.48 gallons per cubic foot = 16.456 gallons

Next, we'll find the weight of the water in pounds:

16.456 gallons * 8.33 pounds per gallon = 136.08 pounds

Finally, we'll convert the weight to tons:

136.08 pounds / 2000 pounds per ton = 0.0680 tons

So 2.2 cubic feet of water weigh 136.08 pounds and 0.0680 tons.

Answer:

[tex]x > 7[/tex]

Step-by-step explanation:

Given the inequality

[tex]x+4 > 11[/tex]

Lets solve the inequality for [tex]x[/tex].

Subtract [tex]4[/tex] from both sides of the inequality.

[tex]x > 11-4[/tex]

Evaluate [tex]11-4[/tex].

[tex]x > 7[/tex]

[tex]x[/tex] is greater than 7

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The volume of the parallelopiped is 4

We have to solve this with the use of matrix system in math

PQ, PR, PS where

P(-3, 3, 2), Q(-1, 6, 5), R(-4, 2, 1), S(3, 1, 4)

we have to find

Q - P

(-1, 6, 5) - (-3, 3, 2)

= (2, 3, 3)

R - P

R(-4, 2, 1) - (-3, 3, 2)

= ( -1 , -1, -1)

S - P

S(3, 1, 4) - (-3, 3, 2)

= (6 , -2, 2)

we would have [tex]\left[\begin{array}{ccc}2&3&3\\-1&-1&-1\\6&-2&2\end{array}\right][/tex]

the determinant of the matrix is the volume

2[(-1 * 2) - 3[(-1x2)-(6x-1)] + 3[(-1x-2) -(6 x -1)]

= -8 - 12 + 24

= 4

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Answer:

A.

Step-by-step explanation:

Since [tex]5[/tex] can rewritten as [tex]\sqrt{25}[/tex] and [tex]6[/tex] rewritten as [tex]\sqrt{36},[/tex] we can see which options go between [tex]\sqrt{25}[/tex] and [tex]\sqrt{36}.[/tex] The only square root that goes between is [tex]\sqrt{29}.[/tex] Therefore the answer is [tex]\boxed{A.}[/tex] (or [tex]\sqrt{29}.[/tex])

Answer:13

Step-by-step explanation:

r = circumference/2pi

81.64/6.28 = 13

The radius of the garden is 13 units.

Answer:

To find the probability of Miko taking a red marble first, then a white marble, we can use the formula for joint probability:

P(red, then white) = P(red) * P(white | red)

Where P(red) is the probability of Miko taking a red marble first and P(white | red) is the probability of Miko taking a white marble second, given that he took a red marble first.

P(red) = 3/12 = 1/4

P(white | red) = 4/12 = 1/3

So,

P(red, then white) = 1/4 * 1/3 = 1/12

Therefore, the probability of Miko taking a red marble first, then a white marble is 1/12.

The number of pieces of candy that will be left on day 4 would be 2, 560 candies .

The number of pieces of candy left on day 8 would be 66 candies .

To find the number of candy left on the fourth day, given that Augustus only gives candies after the pile of 100, 000 candies is reached, the formula is:

= Number of starting candy x ( 1 - Percent given away ) ^ number of days

= 100, 000 x ( 1 - 60 % ) ⁴

= 100, 000 x 40 % ⁴

= 2, 560 candies

On Day 8, this would be:

= 100, 000 x ( 1 - 60 % ) ⁸

= 66 candies

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The question is:

How many pieces of candy will be left on day 4? On day 8?

To get the cash flows from operating activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.39 billion. Rounding to two decimal places, we get -$1.01 billion).

What is algebraic expression ?

An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.

The change in total cash of Rectangle is $0.02 billion (3.59 - 0.59 - 4.18 = -0.98, which is rounded to -$1.00 billion, and then added to the beginning cash amount of $0.69 billion to get $0.69 - $1.00 = -$0.31 billion or -$0.31/100 = -$0.02 billion).

The ending cash amount of Circle is $0.72 billion (1.39 - 0.29 - 1.38 = -0.28, which is added to the beginning cash amount of $0.69 billion to get $0.41 billion or $0.41/100 = $0.72 billion).

The amount of cash flows from financing activities of Pentagon is -$0.55 billion (the change in total cash of $0.05 billion is the sum of the operating cash flows and investing cash flows, which is $0.08 billion + $0.62 billion = $0.70 billion. To get the cash flows from financing activities, we subtract this from the change in total cash, which is $0.05 billion, to get -$0.65 billion. Rounding to two decimal places, we get -$0.55 billion).

The amount of cash flows from investing activities of Square is -$0.40 billion (the change in total cash of $0.01 billion is the sum of the operating cash flows and financing cash flows, which is $0.59 billion + $0.41 billion = $1.00 billion. To get the cash flows from investing activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.99 billion. Rounding to two decimal places, we get -$0.40 billion).

The amount of cash flows from operating activities of Hexagon is -$1.01 billion (the change in total cash of $0.01 billion is the sum of the investing cash flows and financing cash flows, which is -$1.40 billion + $1.02 billion = -$0.38 billion.

Therefore,  To get the cash flows from operating activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.39 billion. Rounding to two decimal places, we get -$1.01 billion).

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Answer:

Bryce is 10 years old

Step-by-step explanation:

The age of Brice is given by B = 10 years old

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as B

Now , the value of B is

Substituting the values in the equation , we get

The age of Aida = 15 years

The age of Brice = 5 years younger than Aida

On simplifying the equation , we get

So , age of Brice = 15 - 5 = 10 years

The age of Henry = three years younger than Aida

So , the age of Henry = 15 - 3 = 12 years

Hence , the age of Brice is 10 years old

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The probability that more than 2 students will attend is 0.9179.

Part (a) List the values that X may take on.

X may take on the values 0, 1, 2, 3, ..., 13.

Part (b) Give the distribution of X.

The distribution of X can be represented as follows: X-0:0, 1:0.23, 2:0.23, 3:0.23, 4:0.23, 5:0.23, 6:0.23, 7:0.23, 8:0.23, 9:0.23, 10:0.23, 11:0.23, 12:0.23, 13:0.23

Part (c) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)

We can expect 3 students to attend the festivities.

Part (d) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.)

The probability that at most 3 students will attend is 0.6923.

Part (e) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)

The probability that more than 2 students will attend is 0.9179.

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The solution to the complex number in rectangular form is; -2 + 2i

The complex number is given as;

2√2(cos 135° + i sin 135°)

The standard form is a + bi.

The value of cos 135° is; -(√2)/2

The value of sin 135° is; (√2)/2

Plugging these values into the given equation is;

2√2(-(√2)/2 + ((√2)/2)i)

Expanding the bracket gives;

-2 + 2i

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