The amount that should be invested today is $544.56.
How much should be invested today?
Continous compounding is when the amount invested and the interest that has already been earned increase infinitely over a period of time. Continous compounding means that the value of the investment increases at every moment of the investment period.
The formula that can be used to determine the amount to be invested today is:
A = FV / ( e^r x N)
Where:
A= amount e = 2.7182818N = number of years r = interest rate$5000 / [(2.718^0.02) X 9] = $544.56
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i really need help this is overdue
Answer:
I can help you.
Step-by-step explanation:
so, you have to write in a)
2•5=10, 4÷2=2, 6+10=16, 16+2=18, 18-3=15. so answer is 15
And then, u have to write in b) 6+2=8, 8•5=40, 40+4=44, 44÷2=22, 22-3=19. so answer is 19.
1. Yale economist Robert J. Shiller and Wellesley economist Karl Case created the Case-Shiller
index of American housing prices that tracks the value of housing back to 1890 in consistent
terms, factoring out the effects of inflation. The 1890 benchmark is 100 on the chart. If a
standard house sold in 1890 for $100,000 (inflation-adjusted to today's dollars), an equivalent
house would have sold for $66,000 in 1920 (66 on the index scale) and $220,000 in 2006 (220 on
the index scale).
Use the following graph, based on the Case-Shiller index, to write a 60-second summary about
home values in the United States since 1890. You can use the Internet to find the current value
of homes and see if these projections are accurate.
A History of Home Values
130
120
110
100
90
80
70
60
PROJECTION
WORLD
GREAT WORLD
WARI DEPRESSION WAR II
for
1890
1900
1910
1920
1930
1940
1950
CURRENT JULY 2006
BOOM
1970'S 1980'S
BOOM BOOM
M
200
190
180
170
160
150
140
130
120
110
100
According to the chart, homes in the United States have fluctuated between $90,000 and $130,000 most of the time between 1890 and 2010 and then rise to more than $200,000.
What does the graph show?The graph shows the changes in the value of homes in the United States from the year 1890 to the year 2010. An important aspect of this graph is the influence that international events such as the world wars, the great depression, the boom of the 70s and 80s and the great boom.
How do home prices change?According to the graph, the price of houses varies as follows:
In 1890 it starts with a standard value of $100,000.Between 1890 and 1900 it has had two moments of increase in which it reached prices of 125,000 and 110,000. On the other hand, in 1900 it reaches the lowest point of this period with 90,000.Between 1900 and 1910 it peaks at 110,000, but closes the decade with a price of 95,000.Between 1910 and 1920, the effects of the First World War caused its value to fall to 65,000.Between 1920 and 1930 the Great Depression causes prices to not exceed 80,000 and closes the decade with a value of 75,000.Between 1930 and 1940 prices increase until reaching 80,000 at the end of the decade.Between 1940 and 1950 the effects of World War II cause prices to fall again to 70,000. However, the second half of the decade marks a recovery that reaches 110,000.Between 1950 and 1960 prices increase in the middle of the decade but close the period at 110,000.Between 1960 and 1970 prices remain stable. However, they close the decade with a minimal decrease.Between 1970 and 1980 there is a significant increase that raises prices to 120,000 at the end of the decade.Between 1980 and 1990 prices fall again in the middle of the decade to 105,000 but at the end of the period they exceed 120,000.Between 1990 and 2000 prices fall below 110,000.Between 2000 and 2010 prices increase exorbitantly and reaches more than 200,000.Learn more about house prices in: https://brainly.com/question/17021793
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The angles of a quadrilateral are in the ratio 1:2:2:4. What is the measure, in degrees, of the largest angle?
A. 40 degrees
B. 60 degrees
C. 80 degrees
D. 160 degrees
Below are graphs of functions over the interval [−4, 4]. Find the following for each function: The domain Zeros of the function (the values of x where the value of the function is zero) Intervals where the function is positive and intervals where it is negative
From the graph of a function over the interval [-4,4]. the following are found for each function
The domain is x ≥ -4, -4 ≤ x ≤ 4, x ≤4the zeros of the function is ( 0, 0 ), ( 0, 0 )The function is positive at 0 ≤ x ≤ 4, x ≥ 4. The function is negative at x ≥ -4, -4 ≤ x ≤ 0What is domain of a function?The domain of a function refers to the input variables, often times the domain comprises of the x axis. for the given graph the domain is -4 ≤ x ≤ 4.
How to get the domain of a function.This would be through the points in the function. We are given [-4,4]
-4 is the negative side while 4 is the positive. We have to write this out as
-4 ≤ x ≤ 4.
The positive part part of the function is at 4. This is because we can assume a +4 sign.
The negative part is the point -4.
Hence we can say that the domain is -4 ≤ x ≤ 4 with the positive and negative at 4 and -4 respectively
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Seven subtracted from seven times a number is 147
Answer: x = -20
Find x▬▬▬▬▬▬▬
[tex]7-7(x)-7=147-7\\-7(x)=140\\= \frac{-7x}{-7}=\frac{140}{-7}\\=-20\\= x = -20[/tex]
▬▬▬▬▬▬▬
Answer Explained:
Using phrases such as subtracted, times, a number, we make an equation using the integers in the equation, and make a variable for the unknown number, x. We then subtracted 7 from both sides, and for the division, substituted 7 as absolute number, |-7|.
Therefore,
7 - 7 × -20 = 147
PLEASE HELP ME I WILL GIVE YOU 100 POINT PLEASE HELP AND MARK BRAINLETS AND STOP REPORTING ME I ALREADY LOST 100 POINTS
Answer:
Step-by-step explanation:
1.
Only the graph on the left is a function, due to the one on the right failing the vertical line test.
2.
This is asking for a positive x-value of the two functions, we can find that by setting them equal to a common value and then equal to each other.
Lets set them both equal to x.
First equation:
[tex]y=x^2\\\sqrt{y}=x[/tex]
Second equation:
[tex]y^2=x[/tex]
Now we set them equal to each other:
[tex]y^2=\sqrt{y}[/tex]
Then solve for y by squaring both sides:
[tex]y^4=y[/tex]
Now we solve by factoring:
[tex]y^4=y\\y^4-y=0\\y(y^3-1)=0\\y^3-1=0\\y^3=1\\y=\sqrt[3]{1}\\ y=1[/tex]
Can someone help me solve this?
Answer:
1 = 34°
2 = 52°
3 = 38°
4 = 94°
5 = 56°
6 = 38°
What is true about the angles in the diagram shown below? A D E (31) The value of x is B C Enter the correct answers in the boxes.
Answer:
x = 22.5
∠ADE = 67.5
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180° and the given is a right triangle so we can find the value of x easily:
90 + x + 3x = 180 add like terms
90 + 4x = 180 subtract 90 from both sides
4x = 90 divide both sides by 4
x = 22.5
To find the measure of angle ADE we use the same equation:
90 + 22.5 + ∠ADE = 180 add like terms
112.5 + ∠ADE = 180 subtract 112.5 from both sides
∠ADE = 67.5
Are the functions of g(x)=(x-4)^2 and h(x)=x^2-4 equivalent? Explain your reasoning.
Answer:
[tex]g(x) = (x-4)^2\; and \;h(x)= x^2-4 \;are\;\bold{not}\;equivalent[/tex]
Step-by-step explanation:
For two functions g(x) and h(x) to be equivalent, they must have the same domain and range.
Domain is the set of all values of x(inputs) that result in a real and defined value for the function
Range is the set of all values of the function that it can take given the values of x in the domain
[tex]g(x)=(x-4)^2=16-8x+x^2\\[/tex]
Can be rewritten as
[tex]g(x) = x^2 -8x + 16[/tex] The domain of g is unrestricted, g can be any value so the
Domain of g: [tex]-\infty < x < \infty[/tex]
Range of g: Since [tex](x-4)^2[/tex] is always positive including 0, the range of g(x) is g(x) ≥ 0
[tex]h(x) = x^2 - 4[/tex]
Domain of h : [tex]-\infty < x < \infty[/tex] since x can be any value and we will still get a real number as function output
However x² is always zero or a positive number so we have the restriction
x² ≥ 0
Subtract 4 on both sides
x²-4 >= -4
But the above is nothing but the outputs of h(x)
So h(x) >= -4 and can be written as -4 ≤ x ≤ ∞
So we can see that, while the domains of the two functions are the same, their ranges are different
Hence the two functions g(x) and h(x) are not equivalent
Tip
If you have difficulty determining domain and range, take a specific value of x for both functions and check if the function output values are the same. It may not always be easy choosing an appropriate x value depending on the function
For x = 0
g(0) = (0-4)² = (-4)² = 16
h(0) = 0^2 -4 = 0-4 = -4
So we get different output values for the same input value for both functions and therefore they are not equivalent
You can this latter explanation to the above explanation
Hope that helps and is understandable :)
What is the rectangular equivalence to the parametric equations?
x(θ)=3cosθ+2, y(θ)=2sinθ−1 , where 0≤θ<2π .
Drag a term into each box to correctly complete the rectangular equation.
The rectangular equivalence to the parametric equations is;
(x - 2)²/9 + (y + 1)²/4 = 1
How to Interpret Parametric Equations?
We want to find the rectangular equivalence to the parametric equations;
x(θ) = 3cosθ + 2
y(θ) = 2sinθ − 1
where 0 ≤ θ < 2π .
Making the trigonometric ratio the subject gives us;
cosθ = (x - 2)/3
sinθ = (y + 1)/2
Now, from trigonometric identities, we know that;
cos²θ + sin²θ = 1
Thus;
((x - 2)/3)² + ((y + 1)/2)² = 1²
(x - 2)²/9 + (y + 1)²/4 = 1
Thus, the rectangular equivalence to the parametric equations is;
(x - 2)²/9 + (y + 1)²/4 = 1
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A certain number is 7 less than
the product of 18 and 4. what is
the value of that number?
Answer:
Step-by-step explanation:
um first add 7+11 u get 18 and so yeah
I NEED THE ANSWERS TO 3, 4 and 5 PLEASEEE:))
Answer:
3. (d) y = 2x + 2
4. (c) 10
5. See attachment.
Step-by-step explanation:
Slope formula
[tex]\boxed{\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
where (x₁, y₁) and (x₂, y₂) are points on the line.
Slope-intercept form of a linear equation
[tex]\boxed{y=mx+b}[/tex]
where m is the slope and b is the y-intercept.
Question 3Given points on the line:
(x₁, y₁) = (1, 4)(x₂, y₂) = (-2, -2)Substitute the given points into the slope formula to find the slope, m:
[tex]\implies \textsf{slope}\:(m)=\dfrac{-2-4}{-2-1}=\dfrac{-6}{-3}=2[/tex]
Substitute the found slope and one of the points into the slope-intercept equation and solve for b:
[tex]\implies 4=2(1)+b[/tex]
[tex]\implies b=2[/tex]
Therefore, the equation of the line is:
[tex]\boxed{y=2x+2}[/tex]
Question 4Given equation:
[tex]y=10x-6[/tex]
Upon comparing the given equation with the slope-intercept formula, the slope of the given line is: [tex]\boxed{10}[/tex]
Question 5The equation y = 2 means that y is 2 for all values of x.
Therefore, to graph y = 2, draw a straight, horizontal line at y = 2.
(See attached graph).
Find the equation of the linear function represented by the table below in slope-intercept form.
x y
1 0
2 1
3 2
4 3
Answer:
y=1x-1
Step-by-step explanation:
The wavelength of a seventh wave is recorded. The wavelength is greater than 4/100 nanometer, but less than 4 x 10^-1 nanometer. write the answer with a denominator of 100 is it possible to have more than 1 correct answer
Using inequalities, we can say that Yes, there are more than 1 possible ways to get the answer of inequalities.
What are inequalities?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Given,
the wavelength is greater than 4/100 nanometer and
less than 4 x 10^-1 nanometer
Let wavelength = λ
4/100 ≤ λ ≤ 4/10
0.04 ≤ λ ≤ 0.4
or
1/50 ≤ λ ≤ 2/5
So, from the above three equations, we can conclude that there can be more possible ways to have more than 1 correct answer.
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the cost of one scoop sundae is 2.75 and a cost of a two scoop sundae is 4.25 write and evaluate an expression to fine the total cost of 3 one scoop sundaes and 2 two scoop sundaes
The total cost of 3 one scoop sundaes and 2 two scoop sundaes by evaluating an expression 2.75(3)+ 4.25(2) is 16.75.
What is an expression in two variable?An expression in two variables is a combination of numbers and two variables using mathematical operation +,-,/,*. It will a linear expression when the maximum power of variables is only one in the expression.
Let x and y are two variables and a, b, c are some numbers. Then a linear two expression can be given by ax+ by+ c
Given the cost of one scoop sundae is 2.75 and a cost of a two scoop sundae is 4.25
Let the number of sundaes of one scoop sundae be x and the numbers of sundaes be y
Then the total cost of these sundaes is given as by expression 2.75x + 4.25y
Given that there are 3 one scoop sundaes and 2 two scoop sundaes
Thus, x= 3 and y = 2
Total cost is given by expression= 2.75(3)+ 4.25(2)= 16.75
Therefore, he total cost of 3 one scoop sundaes and 2 two scoop sundaes is 16.75
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on december 31 the company purchases equipment for 10,000 and pays cash of $10,000
The journal entry will be:
Date General Debit Credit
$ $
Dec 31 Equipment 10000
Cash 10000
We know that:
1) The $10,000 will be posted to the debit side of the Equipment Account as the equipment is an asset and it is being bought in the company. So, purchasing an asset is being debited in the account.
2) The $10,000 will be posted to the credit side of the Cash Account as cash is also an asset which is being given. Since, the asset is going out from the company, it is being credited in the company's account.
The journal entry then will become as:
Date General Debit Credit
$ $
Dec 31 Equipment 10000
Cash 10000
Therefore, the journal entry will be:
Date General Debit Credit
$ $
Dec 31 Equipment 10000
Cash 10000
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Your question was incomplete. Please refer the content below:
On December 31, the company purchases equipment for $10,000 and pays cash of $10,000. Complete the necessary journal entry by selecting the account names from the pull-down menus and entering dollar amounts in the debit and credit columns.
Lindsay invests $80 in an account that pays 1% annually interest, compounded monthly. Michele invests $60 in an account that pays 2% annual interest, compounded weekly
Lindsay has the greater balance after one year and also had the greater balance in investment account after 12 years
What does monthly compounding mean?
The monthly compounding means that the interest is computed every month , 12 months a year rather than once a year.
Monthly compounding?
FV=PV*(1+r)^N
FV=future worth
PV=initial investment=$80
r=monthly interest rate=1%/12=0.000833333333333333
N=number of months in one year=12
FV(1 year)=$80*(1+0.000833333333333333)^12
FV(1 year)=$80.80
FV(year 12)=$80*(1+0.000833333333333333)^(12*12)
FV(year 12)=$90.20
Weekly compounding:
weekly interest rate=2%/52=0.000384615384615385
FV(1 year)=$60*(1+0.000384615384615385)^52
FV(1 year)=$61.21
FV( year 12)=$60*(1+0.000384615384615385)^(52*12)
FV(year 12)=$76.27
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Concluding part of the question:
a. Whose balance is greater after one year?
b. Whose balance is greater after twelve years?
five less than six times a number
Answer: 6x-5
5 less is just subtract 5 from whatever follows
N/12 = 300 N=? what is the answer please
Answer:
3600
Step-by-step explanation:
N = 300 x 12 =3600
<
In 2
5600
The amount of carbon 14 present after t years is given by the exponential equation A(t) = A, et, with k = -- Using carbon 14 dating of charcoal found
along with fossilized leaf fragments, botanists arrived at an age of 41,000 years for a plant. What percent of the original carbon 14 in the charcoal was present?
% of the original carbon 14 in the charcoal was present.
(Round to the nearest tenth as needed.)
Using an exponential function, it is found that 0.6% of the original carbon 14 in the charcoal was present.
What is the exponential function?The exponential function for the amount of the substance after t years is given by:
[tex]A(t) = A(0)e^{-kt}[/tex]
k is the exponential decay rate, given by:
k = ln(2)/5600 = 0.00012377628.
Hence:
[tex]A(t) = A(0)e^{-0.00012377628t}[/tex]
The amount after 41,000 years is given as follows:
[tex]A(41000) = A(0)e^{-0.00012377628 \times 41000}[/tex]
A(41000) = 0.006A(0).
Hence:
0.6% of the original carbon 14 in the charcoal was present.
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A small plant is 212 inches tall. How tall will it be in 3 weeks if it grows 34 inch each week? Which method will NOT give the correct number of inches?
The method that will not give the correct number of inches is that the total length of the plant in a week is 19/4 inches.
How to calculate the value?Length of the small plant = 2 1/2 = 5/2 inches
Rate of growth = 3/4 inches
Increase in length in 3 weeks will be:
= 3 × 3/4 = 4
Total length = 5/2 + 9/4
= 19/4 inches.
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Here are weights (in pounds) of sample of 12 male eleventh graders. 152, 175, 148, 175, 155, 175, 163, 166, 174, 164, 165
The mean weight of the male graders will be 151 pounds.
How will you calculate the mean?It should be noted that from the information, the sample of 12 male eleventh graders are: 152, 175, 148, 175, 155, 175, 163, 166, 174, 164, 165.
We will add the values together and this will be 1812. Also, there are 12 students.
Therefore, the mean will be:
= Total weight / Number of students
= 1812 / 12
= 151 pounds.
Therefore, the mean weight will be 151 pounds.
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Here are weights (in pounds) of sample of 12 male eleventh graders. 152, 175, 148, 175, 155, 175, 163, 166, 174, 164, 165. Calculate the mean weight.
will give brainliest if correct
Answer:
d
Step-by-step explanation:
as x→-∞ , y→+∞
as x→∞ , y→-∞
What is 5y if y= 983
Answer:
4915
Step-by-step explanation:
y= 983 so multiply 983 by 5
5x983 = 4915
Answer: 4915
Step-by-step explanation: Pls brainliest.
HURRY PLS ILL GIVE BRANALIEST
The elevation of city A is 96 feet below sea level; the elevation of city C is 24 feet below sea level. The elevation of city D is 1 over 4 of the elevation of city C.
Part A: Write an expression to represent the elevation, in feet, of city D. (5 points)
Part B: Solve the expression and explain why the answer is negative or positive. (5 points)
Answer:
(A) -24 × 1/4 ft
(B) -6 ft
A negative times a positive is a negative
Step-by-step explanation:
Sea level is 0, therefore the elevation of city (A) is -96 , and the elevation of city (C) is -24 . The elevation of city (D) is 1/4 of city (C).
Expression = - 24 × 1/4
Part (B)
-24 × 1/4 = -6
Explanation A negative times a positive gives a negative product.
5 friends went out to a tapas restaurant and ordered from the menu that included $4, $6 and $7 options. They ordered a total of 24 items. The number of $4 items was twice the $6 and $7 items combined. When they split the bill at the end, they each owed $23. How many of each type of item did they order?
The 5 friends ordered 16 items of $4 , 5 items of $6 , 3 items of $7 .
How to find solution of system of equations in two variables by substitution?Let p and q be two variables and
a₁p+ b₁q=c₁
a₂p+ b₂q =c₂
Where a₁, a₂, b₁, b₂, c₁, c₂ are constants then we can solve these simultaneous equations by substitution take value of p from equation (1) and then put it in (2) to get an equation for q only and then solve for q. Put value of q in equation (1) to get value of p.
Let the 5 friends ordered x number of $4 items , y number of $6 and z number of $7 items
They ordered total a total of 24 items.
Then, x+ y + z = 24 ....(1)
Given that $4 was twice the $6 and $7 items combined
Then, x =2( y+ z )
Put this expression of x in (1),we get
2(y+ z)+ y + z =24
3y + 3z =24
y + z =8 ....(2)
Also given that they split the bill at the end, they each owed $23
Therefore total bill will be 5 times $23 = 5*23 = $ 115
Total money spent on bill = $ 4x+6y+7z
Thus, 4x+6y+7z = 115
Again put x =2(y+ z) here and get
8(y+ z) +6y+ 7z =115
8y +8z + 6y +7z = 115
14y +15z = 115 ....(3)
Therefore, (2) and (3) is the system of equations we have to solve.
From (2) we get y =8 -z
Put this value of y into (3) and get
14(8-z)+15z =115
112 - 14z +15z =115
z= 115-112 = 3
Then, y = 8-z = 8-3 = 5
x = 2(y+ z)= 2(3+5) =16
Therefore x= 16 , y = 5, z=3 from system of equations generate by (2) and (3)
The 5 friends ordered 16 items of $4 and 5 items of $6 and 3 items of $7.
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Fill in the blank of any operations and make sure to use ().
4 ? 2 ? 3 = -2
Answer:
4-2*3=-2 At first we have to do multiple of2 and 3
then subtract with 4
Convert R57 894 to dollars if the exchange rate is R7,30 = 1 dollar.
Main answer:R57 894 is 79.3 dollors.
Concept and definitions should be there:
The formula for calculating exchange rates is: Starting Amount (Original Currency) / Ending Amount (New Currency) = Exchange Rate. For example, if you exchange 100 U.S. Dollars for 80 Euros, the exchange rate would be 1.25.
Given data
Convert R57 894 to dollars if the exchange rate is R7,30 = 1 dollar.
Soving part
The formula for exchanging rates
R (57894/730)
now dividing the starting amount and ending amount we get exchange rate.
Final Answer : 79.3 dollers.
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A rectangle has a perimeter of 104 cm and it’s length is 1 cm more than twice its width.
A. Find the definition of perimeter write an equation for P in terms of L and W
B. Using the relationship given in the problem statement write an equation for L in terms of W.
C. The Width is ____ cm
D. The Length is ____ cm
The equation for L in terms of W is ( 1 + 2w) where length and width of the rectangle is 35 cm and 17 cm respectively
Perimeter of rectangleLength of the rectangle, l = 1 + 2wWidth of the rectangle = wPerimeter = 104 cmPerimeter of rectangle = 2(L + W)
104 = 2{(1 + 2w) + w}
104 = 2(1 + 2w + w)
104 = 2(1 + 3w)
104 = 2 + 6w
104 - 2 = 6w
102 = 6w
w = 102 / 6
w = 17 cm
Recall,
Length of the rectangle, l = 1 + 2w
= 1 + 2(17)
= 1 + 34
= 35 cm
Therefore, the equation for L in terms of W is ( 1 + 2w) where length and width of the rectangle is 35 cm and 17 cm respectively
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5,14,15,12,14,10,6,16 round to the nearest tenth
The required solution is 5,14,15,12,14,10,6,16 respectively.
It is required to find round to the nearest tenth.
What is rounded number?A number that is easily multiplied, divided, etc., and especially a number that ends in zero.
Given:
The tenth number is the first digit after decimal point. If the second digit is greater than or equal to 5 add 1 to calculate rounding to nearest tenth.
Rounding to the nearest tenth means adjusting the given number to an approximate value without changing the whole part of the number.
5.0 the nearest tenth is 5.
14.0 the nearest tenth is 14.
15.0 the nearest tenth is 15.
12.0 the nearest tenth is 12.
14.0 the nearest tenth is 14.
10.0 the nearest tenth is 10.
6.0 the nearest tenth is 6.
16.0 the nearest tenth is 16.
Therefore, the required solution is 5,14,15,12,14,10,6,16 respectively.
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