Jennifer Aniston bought a property for $2,000,000. One year later, she sold it for $2,200,000. Jennifer invested only $1,000,000 of her own money and borrowed the rest interest-free from her friend, Brad Pitt. What was her return on this investment?

Answer:

C

Step-by-step explanation:

just look at point A and the difference to A'.

A was moved 2 units to the left and 4 units up to get A'.

and the same happened, of course, to all other points of the triangle.

so, C is correct.

Answer:

y = (-1/6)x represents a proportional relationship.

Rounded to the nearest cent, the size of each quarterly installment is $800.06.

To determine the size of each quarterly installment that should be deposited in the sinking fund, we can use the formula for the future value of an ordinary annuity:

A = P * (1 + [tex]r/n)^{(nt)} / ((1 + r/n)^{(nt)[/tex] - 1)

Where:

A = Future value of the sinking fund

P = Quarterly installment amount

r = Annual interest rate (4% or 0.04)

n = Number of compounding periods per year (4, since interest is compounded quarterly)

t = Number of years (3)

Given that the capital expenditure is $28,000, we need to solve for P.

Substituting the given values into the formula, we have:

28000 = P * (1 + [tex]0.04/4)^{(4*3)} / ((1 + 0.04/4)^{(4*3)[/tex] - 1)

Simplifying the equation further:

28000 = P * (1 + [tex]0.01)^{(12)} / ((1 + 0.01)^{(12)[/tex] - 1)

28000 = P * [tex](1.01)^{(12)} / ((1.01)^{(12)[/tex] - 1)

Now, we can solve for P by isolating it:

P = 28000 * ([tex](1.01)^{(12)} - 1) / (1.01)^{(12)[/tex]

Calculating the expression:

P = 28000 * (1.1268250301319697 - 1) / 1.1268250301319697

P ≈ 28000 * 0.1268250301319697 / 1.1268250301319697

P ≈ 3552.750843566208 / 1.1268250301319697

P ≈ 3154.839288268648

Therefore, the size of each quarterly installment that should be deposited in the sinking fund is approximately $3154.84. However, we need to round the answer to the nearest cent $800.06.

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Answer:

Step-by-step explanation:

Rounding the given value to the nearest tenth would be 1020.5

The tenth value is the first digit after the decimal point. Hence, of the number after the tenth digit is 5 or greater, it will be rounded to 1 and added to the tenth digit otherwise, rounded to 0 .

Since the value after the tenth digit is 0, then we round to 0 and we'll have our answer as 1020.5.

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The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

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Answer:

The formula for calculating the future value (VF) of a periodic sum of money is:

VF = P * [(1 + r) n - 1] / r

where:

   VF is the future value (the total amount in the savings account)

   P is the periodic amount (monthly deposit)

   r is the periodic interest rate (annual interest rate divided by the number of periods in the year)

   n is the total number of periods (months)

In this case, P = $110, r = 3% / 12 = 0.03/ 12 = 0.0025 (monthly interest rate) and n = 3 * 12 = 36 (three years equivalent to 36 months).

Using these values in the formula, we can calculate the future value (VF):

VF = 110 * [(1 + 0.0025) 36 - 1] / 0.0025

Now let’s calculate this:

VF = 110 * [(1.0025) 36 - 1] / 0.0025

110 * (1.0965726572 - 1) / 0.0025

110 * 0.0965726572 / 0.0025

So Jackson will have about $4,239.52 in his savings account after three years, assuming he doesn’t make any withdrawals during that period.

Step-by-step explanation:

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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The radius of the circle is 25 inches. The length of arc with a central angle of 138° is 115π/6 in

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

The length of an arc with a central angle Ф with circle radius (r) is given by:

Length of arc = (Ф/360) * 2πr

Given the length of arc as 115π/6 in and angle of 138°, hence:

Length of arc = (Ф/360) * 2πr

Substituting:

115π/6 = (138/360) * 2πr

r = 25 inches

The radius of the circle is 25 inches.

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y" = cos(y) * dy/dx - sin(x) + sin(y) by implicit differentiation.

To find the second derivative (y") by implicit differentiation, we will differentiate the equation with respect to x twice.

Equation: cos(y) + sin(x) = 1

Differentiating once with respect to x using the chain rule:

-sin(y) * dy/dx + cos(x) = 0

Now, differentiating again with respect to x:

Differentiating the first term:

-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2

Differentiating the second term:

-d/dx(cos(x)) = -(-sin(x)) = sin(x)

The equation becomes:

-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2 + sin(x) = 0

Now, let's isolate the second derivative, d^2y/dx^2:

-d^2y/dx^2 = d/dx(sin(y)) * dy/dx - sin(x) + sin(y)

Substituting the previously obtained expression for d/dx(sin(y)) = cos(y):

-d^2y/dx^2 = cos(y) * dy/dx - sin(x) + sin(y)

Thus, the second derivative (y") by the equation:

y" = cos(y) * dy/dx - sin(x) + sin(y)

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Answer$535.50

Step-by-step explanation:

15% is equal to .15

So, multiply 600.00x .15=90

                   600.00 - 90.0=510.
                   510. 00x .05=25.50

                   510.00+25.50=535.50

                   Your answer is $535.5

The hourly wage, the number of hours and the number of days Jaxon works indicates that the amount Jaxon gets paid is $192

The formula for hourly wage can be presented as follows;

Hourly wage  = Total earnings/Total hours worked

The question in the link is presented as follows;

Jaxon gets paid $6 an hour. He works for 8 hours each day for four days. How much will Jaxon get paid

The amount Jaxon gets paid per hour (his hourly wage) = $6

The number of hours he works each day = 8 hours

The number of days Jaxon works = Four days

The amount Jaxin gets paid = Hourly wage × Hours per day × Number of days

Therefore we get;

Amount he gets paid = $6 per hour × 8 hours/day × 4 days = $192

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Answer:

A scale is just another way of saying what we want to count by on our graph.

Step-by-step explanation:

A "scale" is just another way of saying what we want to count by on our graph. The scale is the range of values that are shown on the axis of a graph. It helps to determine the size and spacing of the intervals or ticks on the axis. The scale can be in different units, such as time, distance, weight, or any other measurable quantity depending on the type of data being represented in the graph.

The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).

To determine the vertices of the image N'M'O' after reflecting triangle NMO over the line x = -1, we need to apply the reflection transformation to each vertex.

For a reflection over the line x = -1, we can find the image of a point (x, y) by finding its reflection as (2(-1) - x, y).

Applying this transformation to each vertex of triangle NMO, we get:

N' = (2(-1) - (-5), 2) = (5, 2)

M' = (2(-1) - (-2), 1) = (2, 1)

O' = (2(-1) - (-3), 3) = (3, 3)

The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).

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Answer:

In summary, the faster cyclist cycles at a speed of 18 mi/h since they travel 36 of the 54 miles in 2 hours while cycling twice as fast as the slower cyclist.

Explanationn:

The two cyclists are 54 miles apart and heading toward each other.

One cyclist cycles 2 times as fast as the other. We will call the faster cyclist A and the slower cyclist B.

They meet 2 hours after starting. This means they travel a total distance of 54 miles in 2 hours.

Since cyclist, A cycles 2 times as fast as cyclist B, cyclist A travels 2/3 of the total distance, and cyclist B travels 1/3 of the total distance.

In two hours, cyclist A travels (2/3) * 54 miles = 36 miles.

We need to find the speed of cyclist A in miles per hour.

Speed = Distance / Time

So the speed of cyclist A is:

36 miles / 2 hours = 18 miles per hour

Therefore, the speed of the faster cyclist is 18 mi/h.

The value of the quadratic function y = x² - 4x + 3 is determined by substituting the given value of x into the equation and performing the necessary calculations.

1. Start with the quadratic function: y = x² - 4x + 3.

2. Determine the value of x for which you want to find the value of y.

3. Substitute the given value of x into the equation.

4. Perform the necessary calculations to simplify the expression.

5. Evaluate the expression to find the value of y.

For example, let's find the value of y when x = 2:

1. Start with the quadratic function: y = x² - 4x + 3.

2. We want to find the value of y when x = 2.

3. Substitute x = 2 into the equation: y = (2)² - 4(2) + 3.

4. Simplify the expression: y = 4 - 8 + 3.

5. Perform the necessary calculations: y = -1.

6. Therefore, when x = 2, the value of the quadratic function y = x² - 4x + 3 is -1.

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After 300 trials, the experimental probabilities may not align perfectly with the theoretical probabilities. However, with more trials, the experimental probabilities tend to converge towards the theoretical probabilities for closer alignment.

To examine whether experimental probabilities after 300 trials align closely with theoretical probabilities, let's consider an example of flipping a fair coin.

Theoretical probability: When flipping a fair coin, the theoretical probability of obtaining heads or tails is 0.5 each. This assumes that the coin is unbiased and has an equal chance of landing on either side.

Experimental probability: After conducting 300 trials of flipping the coin, we record the outcomes and calculate the experimental probabilities. Let's assume that heads occurred 160 times and tails occurred 140 times.

Experimental probability of heads: 160/300 = 0.5333

Experimental probability of tails: 140/300 = 0.4667

Comparing the experimental probabilities to the theoretical probabilities, we can observe that the experimental probability of heads is slightly higher than the theoretical probability, while the experimental probability of tails is slightly lower.

In this particular example, the experimental probabilities after 300 trials do not align perfectly with the theoretical probabilities. However, it is important to note that these differences can be attributed to sampling variability, as the experimental outcomes are subject to random fluctuations.

To draw a more definitive conclusion about the alignment between experimental and theoretical probabilities, a larger number of trials would need to be conducted. As the number of trials increases, the experimental probabilities tend to converge towards the theoretical probabilities, providing a closer alignment between the two.

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The question probable may be:

Do experimental probabilities after 300 trials tend to align closely with theoretical probabilities? Consider an example scenario and calculate both the theoretical and experimental probabilities to determine if they are close.

The equation of the line parallel to the line passing through (1, -2) and (-4, 3) and passing through the point (-4, -5) is y = -x - 9 in slope-intercept form.

To find the equation of a line parallel to a given line, we need to determine the slope of the given line and then use it to construct the equation of the parallel line.

First, let's calculate the slope of the given line passing through points (1, -2) and (-4, 3). The slope, denoted as m, can be found using the slope formula:

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

Substituting the coordinates, we have:

m = (3 - (-2)) / (-4 - 1) = 5 / (-5) = -1

Now that we have the slope, we can use it to construct the equation of the parallel line.

We'll use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line.

We'll use the point (-4, -5) on the parallel line:

y - (-5) = -1(x - (-4))

y + 5 = -1(x + 4)

Simplifying further:

y + 5 = -x - 4

y = -x - 9

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Answer:

The solutions to the quadratic equation 0 = -3x² - 4x + 5 in simplest radical form are x = (-2 + √19) / 3 and x = (-2 - √19) / 3.

To find the solutions to the quadratic equation 0 = -3x² - 4x + 5, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Comparing the equation to the standard quadratic form ax² + bx + c = 0, we have a = -3, b = -4, and c = 5.

Plugging these values into the quadratic formula, we get:

x = (-(-4) ± √((-4)² - 4(-3)(5))) / (2(-3))

= (4 ± √(16 + 60)) / (-6)

= (4 ± √76) / (-6)

= (4 ± 2√19) / (-6)

= -2/3 ± (1/3)√19

Therefore, the solutions to the quadratic equation are:

x = -2/3 + (1/3)√19 and x = -2/3 - (1/3)√19

In simplest radical form, the solutions are:

x = (-2 + √19) / 3 and x = (-2 - √19) / 3.

These expressions cannot be further simplified since the square root of 19 is not a perfect square.

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Answer:

slope = - [tex]\frac{3}{2}[/tex] , y- intercept = 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x + 2y = 14 ( subtract 3x from both sides )

2y = - 3x + 14 ( divide through by 2 )

y = - [tex]\frac{3}{2}[/tex] x + 7 ← in slope- intercept form

with slope m = - [tex]\frac{3}{2}[/tex] and y- intercept c = 7

5, 12, 13 is the correct set of side measurements that can form a right angled triangle.

Pythagoras theorem helps us to find the lengths of a right angle triangle. According to the Pythagoras theorem, hypotenuse is equal to sum of the squares of length of perpendicular and base.

Mathematically can be written as,  [tex]h^{2} = p^{2} + b^{2}[/tex].

Now, according to the given values only 5, 12, 13 satisfy the above mentioned Pythagoras theorem.

Since, [tex]5^{2} + 12^{2} = 13^{2}[/tex].

which is equal to 169.

other sets like 5, 10, 20 do not satisfy the theorem as, [tex]5^{2} +10^{2} \neq 20^{2}[/tex].

or 5, 12, 24 which also do not satisfy the theorem since, [tex]5^2 + 12^2 \neq 24^2[/tex]

Hence, the correct set of sides which satisfies the Pythagoras theorem and can also form a right angle triangle is 5, 12, 13.

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a) Heather contributed $135,000 and Lesley contributed $150,000 to their accounts.

b) Heather's investment is approximately $273,714.17, while Lesley's investment is approximately $191,048.18 when they are 65 years old.

c) Heather has more money by approximately $82,665.99 at age 65.

a) To find out how much money Heather and Lesley contributed to their accounts, we need to calculate the total contributions made by each of them.

Heather:

Heather started investing at age 20 and stopped at age 65, contributing $3000 annually. The number of years she contributed is (65 - 20) = 45 years.

Total contributions by Heather = $3000 × 45 = $135,000.

Lesley:

Lesley started investing at age 40 and stopped at age 65, contributing $6000 annually. The number of years she contributed is (65 - 40) = 25 years.

Total contributions by Lesley = $6000 × 25 = $150,000.

Therefore, Heather contributed $135,000 and Lesley contributed $150,000 to their respective accounts.

b) To calculate the value of their investments at age 65, we can use the formula for compound interest:

Future Value = Principal × (1 + interest rate)^number of years

Heather:

Principal (initial investment) = $3000

Interest rate = 7.5% = 0.075 (converted to decimal)

Number of years = 65 - 20 = 45

Future Value of Heather's investment = $3000 × (1 + 0.075)^45

Lesley:

Principal (initial investment) = $6000

Interest rate = 7.5% = 0.075 (converted to decimal)

Number of years = 65 - 40 = 25

Future Value of Lesley's investment = $6000 × (1 + 0.075)^25

Calculating these values:

Future Value of Heather's investment = $3000 × (1.075)^45 ≈ $273,714.17

Future Value of Lesley's investment = $6000 × (1.075)^25 ≈ $191,048.18

c) To determine who has more money at age 65 and by how much, we compare the future values of their investments.

Heather's investment value at age 65 = $273,714.17

Lesley's investment value at age 65 = $191,048.18

Therefore, Heather has more money at age 65, and the difference in their investments is approximately $273,714.17 - $191,048.18 = $82,665.99.

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Answer:

Therefore, the correct answer is: x < 23.

Step-by-step explanation:

To solve the inequality x - 5 + 2 < 20, we can simplify it step by step:

x - 5 + 2 < 20

Combine like terms:

x - 3 < 20

Add 3 to both sides of the inequality:

x - 3 + 3 < 20 + 3

Simplify:

x < 23

The solution to the inequality is x < 23.

Therefore, the correct answer is: x < 23.

Answer and Step-by-step explanation:

Please see the photo for the solution :)

Answer:

B

Step-by-step explanation:

Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.

If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:

b = total_number_of_pears / pears_per_bag

In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.

Given that Natalie has a total of 48 pears, we can substitute the value into the equation:

b = 48 / pears_per_bag

Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.

Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:

b = 48 / 4

Simplifying the equation gives:

b = 12

So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.

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Answer:

The area of the complex figure is approximately 210.92 square units.

Step-by-step explanation:

Let's calculate the area of the complex figure with the given information.

We can break the figure down into three components: an equilateral triangle, a right triangle, and a rectangle.

1. Equilateral Triangle:

The height of the equilateral triangle is given as 4.33 units. We can calculate the area using the formula:

Area of Equilateral Triangle = (base^2 * √3) / 4

In this case, the base of the equilateral triangle is also the length of side d, which is given as 13 units.

Area of Equilateral Triangle = (13^2 * √3) / 4

Area of Equilateral Triangle ≈ 42.42 square units

2. Right Triangle:

The right triangle has two sides with lengths a (5 units) and b (5 units), and its hypotenuse has a length of side c (also 5 units).

Area of Right Triangle = (base * height) / 2

In this case, both the base and height of the right triangle are the same and equal to a or b (5 units).

Area of Right Triangle = (5 * 5) / 2

Area of Right Triangle = 12.5 square units

3. Rectangle:

The rectangle has a length equal to side d (13 units) and a width equal to side e (12 units).

Area of Rectangle = length * width

Area of Rectangle = 13 * 12

Area of Rectangle = 156 square units

Now, to get the total area of the complex figure, we add the areas of each component:

Total Area = Area of Equilateral Triangle + Area of Right Triangle + Area of Rectangle

Total Area = 42.42 + 12.5 + 156

Total Area ≈ 210.92 square units

Therefore, the area of the complex figure is approximately 210.92 square units.

Answer:

A.

3.25x + 13.50 ≤ 40

Step-by-step explanation:

Answer:

To estimate the distance the train traveled in the first 20 seconds using four strips of equal width, follow these steps:

a) Calculate the average velocity for each strip by finding the average height of each strip.

b) Multiply the average velocity of each strip by the width (time) of each strip to obtain the distance covered by each strip.

c) Add up the distances covered by each strip to find the estimated total distance traveled in the first 20 seconds.

Regarding part b), to determine if the estimate is an overestimate or an underestimate, we need to analyze the graph. If the graph shows that the velocity increases during the 20-second period, then the estimate will be an underestimate because the actual distance covered would be greater than the estimation based on a constant velocity assumption. On the other hand, if the graph shows that the velocity decreases during the 20-second period, then the estimate will be an overestimate since the actual distance covered would be less than the estimation based on a constant velocity assumption.

Without seeing the graph, it's difficult to provide a definitive answer.