i. The payback period for the project is 6 years.
ii. The accounting rate of return (ARR) using the average investment method is 21.18%.
iii. The net present value (NPV) of the project is -165,143.
iv. The internal rate of return (IRR) of the project is approximately 19.61%.
i. The payback period for the project:
To calculate the payback period, we need to determine how long it takes for the cumulative net cash flows to equal or exceed the initial investment of 350 million + 150 million.
Year 1: 70,000, Year 2: 70,000, Year 3: 80,000, Year 4: 100,000, Year 5: 100,000, Year 6: 120,000.
Cumulative Cash Flow:
Year 1: 70,000
Year 2: 70,000 + 70,000 = 140,000
Year 3: 140,000 + 80,000 = 220,000
Year 4: 220,000 + 100,000 = 320,000
Year 5: 320,000 + 100,000 = 420,000
Year 6: 420,000 + 120,000 = 540,000.
The cumulative cash flows exceed the initial investment of 500 million (350 million + 150 million) in Year 6.
So, the payback period for the project is 6 years.
ii. The accounting rate of return (ARR) using the average investment method:
ARR = Average Annual Profit / Average Investment
Average Annual Profit = Sum of Net Cash Flows / Number of Years
Average Annual Profit = (70,000 + 70,000 + 80,000 + 100,000 + 100,000 + 120,000) / 6
Average Annual Profit = 540,000 / 6
Average Annual Profit = 90,000
Average Investment = (Initial Investment + Residual Value) / 2
Average Investment = (500 million + 350 million) / 2
Average Investment = 425 million.
ARR = 90,000 / 425,000 = 0.2118 or 21.18%
iii. The net present value (NPV) of the project:
To calculate NPV, we discount each cash flow to its present value using the cost of capital of 12%.
NPV = (Net Cash Flow1 / [tex](1 + r)^1)[/tex] + (Net Cash Flow2 / [tex](1 + r)^2)[/tex] + ... + (Net Cash Flow6 / (1 + r)^6) - Initial Investment.
[tex]NPV = (70,000 / (1 + 0.12)^1) + (70,000 / (1 + 0.12)^2) + (80,000 / (1 + 0.12)^3) + (100,000 / (1 + 0.12)^4) + (100,000 / (1 + 0.12)^5) + (120,000 / (1 + 0.12)^6) -[/tex] (350 million + 150 million)
Calculating each term and summing them up:
NPV = 54,017 + 48,234 + 54,497 + 62,313 + 55,631 + 60,165 - 500 million
NPV = -165,143
Therefore, the net present value (NPV) of the project is -165,143.
iv. The internal rate of return (IRR) of the project:
To calculate the IRR, we find the discount rate that makes the NPV equal to zero. Using a financial calculator or Excel, we can determine that the IRR for this project is approximately 19.61%.
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PLEASE HELP AS SOON AS POSSIBLE
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 f(x)=/x-7 and g(x) - 4x - 8
which statement is true
1 is in the domain
1 isnt in the domain of f(0) g
ANSWERED: 1 is NOT in the domain.
The statement "1 is NOT in the domain" is true because for the function f(x), the expression x - 7 results in division by zero when x equals 1, which makes 1 not a valid input for the function.
To determine if a value is in the domain of a function, we need to consider any restrictions or limitations on the input values.
For the function f(x) = √(x - 7), the square root function is defined only for non-negative values.
Therefore, the expression (x - 7) inside the square root must be greater than or equal to zero. In other words, x - 7 ≥ 0.
Solving this inequality, we find x ≥ 7.
This means that any value of x that is greater than or equal to 7 is in the domain of f(x).
However, the statement is asking specifically about the value 1.
Since 1 is less than 7, it does not satisfy the inequality x ≥ 7 and is therefore not in the domain of f(x).
Similarly, for the function g(x) = 4x - 8, there are no restrictions on the domain.
Any real number can be substituted into the function, including the value 1.
Therefore, the statement "1 isn't in the domain of f(0) g" is not accurate.
It is true that 1 is not in the domain of f(x), but it is in the domain of g(x).
In summary, the correct statement is that "1 is not in the domain."
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Drag each shape and value to the correct location on the image. Not all labels will be used.
The tower has a base that is 24 meters wide. The height is shown for the separate sections of the tower.
What is an appropriate shape to model each section of the tower? What is an approximate surface area if each of those shapes?
The appropriate shape to model each section of the tower are the cone and the cylinder.
The approximate surface area of each shape would be =
For cone = 1,041.27m²
For cylinder = 3,543.72m².
How to calculate the surface area of each shape given above?The first shape is a cone and the formula for the surface area = A = πr(r+√h²+r²)
where;
Radius = 24/2 = 12
height = 10m
Area = 1,041.27m²
For cylinder:
A = 2πrh+2πr²
where:
r = 12m
h = 35m
A = 3,543.72m²
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Find y" by implicit differentiation.
cos(y) + sin(x) = 1
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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Rewrite 9 2/7 as an improper fraction. 25/2 65/7 25/7 23/7 Rewrite 2 4/5 as an improper fraction. 10/4 13/5 14/5 22/5 Find the product of 9 2/7 and 2 4/5. Express your answer in simplest form. 26 130/5 910/35 15
Answer:
1. 9 2/7 = (63+2)/7 = 65/7
2. 2 4/5 = (10+4)/5 = 14/5
3. 65/7 * 14/5 = 910/35 = 26
0.059 and 0.01 which is greater?
A rocket is launched from 168 feet above the ground at the time t=0. The function that model thsi situation is given by h =-16t^2+96t+168 where t is the time in seconds and h is the height of the position of the rocket above the ground level in feet. what is the reasonable domain restriction for t in this context?
The domain for the time in this context is (0, 7.4)
What is an equation?An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.
Let h represent the height of the ball after spending t seconds. A ball is thrown straight up from the top of a building that is 168 ft high with an initial velocity of 96 ft/s.
Given the equation:
h(t) = -16t² + 96t + 168
The reasonable domain restriction for t, is when the height of the rocket is above the ground. Hence the domain for the time in this context is (0, 7.4)
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Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −1.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−5, 5), M′(−2, 3), O′(−3, 7)
N′(3, 2), M′(0, 1), O′(1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
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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Find the equation of the line in slope-intercept form, parallel to a line joining the points (1,-2) and (-4,3) and passing through (-4,-5).
I
The equation of the line parallel to a line joining points (1,-2) and (-4,3) and passing through (-4,-5) is
(Simplify your answer. Type your answer in slope-intercept form.)
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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find the value of x and the measure of angle axc
Answer:
x = 4
m<AXC = 150
Step-by-step explanation:
m<1 + m<2 = m<AXC
102 + 10x + 8 = 6(6x + 1)
10x + 110 = 36x + 6
26x = 104
x = 4
m<AXC = 6(6x + 1)
m<AXC = 6(24 + 1)
m<AXC = 150
7. At age 20, Heather began investing $3000 annually
into an account earning 7.5% interest compounded
annually. Lesley invested $6000 annually into a similar
account but began at age 40. They both stopped
contributing at age 65.
a) How much money did Heather and Lesley contribute
to their account?
b) What is the value of each of their investments when
they are 65 years old?
c) At age 65, when the investments mature, who has
more money and by how
much?
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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Natalie is selling fruit at the Saturday market. She has a
otal of 48 pears that she wants to sell. She makes bags of
pears and sells them for $5 per bag. In which equation
oes b represent the number of bags of pears?
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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What is the solution to x – 5 + 2 < 20? –7 < x < 15 –13 < x < 23 x < –7 or x > 15 x < –13 or x > 23
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 :)
Two cyclists, 54 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
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.
Simplify the expression by combining
like terms:
2y + 2 + 3y + 5
Enter the number that belongs in the green box.
[?]y + [ ]
Toula owns the Pita Pan restaurant. She needs to order supplies for the upcoming weekend rush. She needs 150 bags of pita bread. The bread come in crates of 50, and each crate costs $15.00. She also needs 65 containers of hummus dip. There are 5 containers in a box, and each box costs $20.00 What expressions can Toula use to determine how much the pita bread and hummus dips will cost? What will the total be?
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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Determine the period.
NAV
8 10 12 14
3
2
1
-1
-2
-3
2
Answer:
7
Step-by-step explanation:
V looking shape has ends at 1 & 8
8 - 1 = 7
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there are 50 people in a coffee shop fourteen are tourist.what percent of people in the shop are tourist and non tourist
Answer:
tourist: 28%
non-tourist: 72%
Step-by-step explanation:
total: 50
tourists: 14
non-tourists:50 - 14 = 36
tourist percentage: 14/50 × 100% = 28%
non-tourist percentage: 36/50 × 100 = 72%
Jade decided to rent movies for a movie marathon over the weekend. The function g(x) represents the amount of money spent in dollars, where x is the number of movies. Does a possible solution of (6.5, $17.50) make sense for this function? Explain your answer.
Yes. The input and output are both feasible.
No. The input is not feasible.
No. The output is not feasible.
No. Neither the input nor output is feasible.
The output value is feasible. The input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.
Jade decided to rent movies for a movie marathon over the weekend.
The function g(x) represents the amount of money spent in dollars, where x is the number of movies.
The given function is g(x) which represents the amount of money spent in dollars, where x is the number of movies.
The solution given is (6.5, $17.50).
We need to find whether the solution makes sense for the given function or not.
The input is given as 6.5 and the output is given as $17.50.
This means that Jade rented 6.5 movies and spent $17.50 on renting those movies.
To check whether the solution makes sense or not, we need to see if the input and output values are feasible or not.
The input value 6.5 is not a feasible value because it is not possible to rent half a movie.
Jade can rent 6 movies or 7 movies but not 6.5 movies.
Therefore, the input value is not feasible.
On the other hand, the output value $17.50 is a feasible value because it is possible for Jade to spend $17.50 on renting 6 movies.
The output value is feasible.
Since the input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.
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Find the area of the parallelogram
The area of the parallelogram is 189 square units
How to determine the areaFirst, we have the determine the length of the base and height.
The distance between the lines x = 9 and f(x) = 9 + 2x is the height
We have that the line parallel to f(x) passes through (4, 11)
The equation in point-slope form is;
y - 11 = 2(x - 4
y = 2x + 3
Substitute x = 9 in the equation, y = 2x + 3.
y = 2(9) + 3 = 21
The points are then (9, 21) and (9, 0).
The distance between the y-axis and the line x = 9 is the base.
Base = 9 units.
The formula for calculating area of a parallelogram is given by ;
= base × height
= 9 × 21
= 189 square units.
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(12²-15+17)+16= what is the answer
162
Step-by-step explanation:
(12 square - 15 + 17) + 16
=(144 - 15 + 17) + 16
=146 + 16
=162
quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 62
minutes with a mean life of 606
minutes.
If the claim is true, in a sample of 99
batteries, what is the probability that the mean battery life would be greater than 619
minutes? Round your answer to four decimal places.
Answer:
Step-by-step explanation:
See picture dfown below for refgerecnce
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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What is the measure of angle jnk?
The hourly wage, the number of hours and the number of days Jaxon works indicates that the amount Jaxon gets paid is $192
What is the formula for calculating hourly wage?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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Which linear equation shows a proportional relationship?
y equals negative one sixth times x
y equals one sixth times x minus 8
y = −6x + 1
y = 6
Answer:
y = (-1/6)x represents a proportional relationship.
Select the correct answer.
Omar has a gift card for $40.00 at a gift shop. Omar wants to buy a hat for himself for $13.50. For his friends, he would like to buy souvenir bracelets, which are $3.25 each. All prices include taxes.
Which inequality can be used to solve for how many bracelets Omar can buy?
A.
3.25x + 13.50 ≤ 40
B.
3.25x + 13.50 ≥ 40
C.
13.50x + 3.25 ≤ 40
D.
13.50x + 3.25 ≥ 40
Answer:
A.
3.25x + 13.50 ≤ 40
Step-by-step explanation:
The value v of a tractor purchased for $13,000 and depreciated linearly at the rate of $1,300 per year is given by v= -1,300t+13,000, where t represents the number of years since the
purchase. Find the value of the tractor after (a) two years and (b) six years. When will the tractor have no value?
a) the value of the tractor after two years is $10,400.
b) the value of the tractor after six years is $5,200.
To find the value of the tractor after a certain number of years, we can substitute the value of t into the equation v = -1,300t + 13,000.
a) After two years:
Substituting t = 2 into the equation, we get:
v = -1,300(2) + 13,000
v = -2,600 + 13,000
v = 10,400
Therefore, the value of the tractor after two years is $10,400.
b) After six years:
Substituting t = 6 into the equation, we get:
v = -1,300(6) + 13,000
v = -7,800 + 13,000
v = 5,200
Therefore, the value of the tractor after six years is $5,200.
To find when the tractor will have no value, we need to find the value of t when v = 0. We can set the equation v = -1,300t + 13,000 equal to 0 and solve for t:
-1,300t + 13,000 = 0
-1,300t = -13,000
t = -13,000 / -1,300
t = 10
Therefore, the tractor will have no value after 10 years.
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A gaming system costs $600 and is on sale for 15% off. After the discount, there is a 5% tax. What is the final price of the gaming system?
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
What is the volume of the triangular prism?
3 in.
15 in.
13 in.
Arc BC on circle A has a length of 115,
- inches. What is the radius of the circle?
115/6 pi
138°
The radius of the circle is 25 inches. The length of arc with a central angle of 138° is 115π/6 in
What is an equation?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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