The function that completely describes the condition is a piecewise function;
[tex]\begin{cases}c=8n\text{ }\mleft\lbrace1\leq n\leq5\mright? \\ c=0\text{ }\mleft\lbrace n>5\mright?\end{cases}[/tex]what is the domain of the relation shown below?
The correct option C { -3, 1, 2, 6} is the domain of the relation given.
What is described as the domain?A function's domain is the set of the all the values within which the function is defined, and its range is the set of all values which f takes.The domain of such a function is indeed the set of values that can be plugged into it. This set contains the x values together in function like f(x). A function's range is the set of values which the function can take. This is the set of values that function returns after we enter an x value.For the given relation in the question;
The values which are input in the function is called domain.
In put values are - { -3, 1, 2, 6}
Thus, domain of the given relation is { -3, 1, 2, 6}.
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Solve the equation 4 > lxl + 1
Answer:A) 3
Step-by-step explanation:
8. Rectangle R's perimeter remains 180 feet when
the length is halved and the width is doubled.
What are the dimensions of rectangle R?
(Hint: Perimeter = 2(l+w)
rectangle
The perimeter of 180, the length and width of the rectangle with maximum area are 45 and 45.
What is the maximum-area rectangle?The difference in length and breadth of any rectangle must be minimal for the area to be maximum. As a result, the length must be ceil (perimeter / 4) and the breadth must be floor (perimeter /4). As a result, the maximum area of a rectangle with a given perimeter is ceil(perimeter/4) * floor(perimeter/4). As a result, the area is greatest when the rectangle is square.Let x= the length and y= the width of the rectangle.
The area of the rectangle A=x y
2 x+2 y=180 because the perimeter is 180.
Solve for y
[tex]$&2 y=180-2 x \\[/tex]
[tex]$&y=90-x[/tex]
Substitute for y in the area equation.
[tex]$&A=x(90-x) \\[/tex]
[tex]$&A=90 x-x^2[/tex]
This equation describes a parabola that extends down. The maximum value of the area is at the vertex.
Rewriting the area equation in the form [tex]$a x^2+b x+c$[/tex]
[tex]$A=-x^2+90 x \quad a=-1, b=90, c=0$[/tex]
The formula for the x coordinate of the vertex is
[tex]$x=\frac{-b}{2 a}=\frac{-90}{2 \cdot-1}=45[/tex]
The maximum area exists found at x=45
and [tex]$y=90-x=90-45=45$[/tex]
Given a perimeter of 180, the proportions of the rectangle with the maximum area are 45 × 45
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Which expression is equivalent to one third times the quantity 2 times x plus 12 end quantity minus 14 over 15 times x?
one and three fifths times x plus four
four fifteenths times x minus 4
negative four fifteenths times x minus four
negative 4 over fifteen times x plus four
Option Negative 4 over fifteen times x plus four is equivalent to expression one third times the quantity 2 times x plus 12 end quantity minus 14 over 15 times x.
Firstly writing the mentioned expression in mathematical form -
Expression = 1/3(2x + 12) - 14x/15
Simplifying the expression by performing multiplication
Expression = 2x/3 + 12/3 - 14x/15
Taking LCM of these three denominator, we get 15
Expression = 2x×5 + 12×5 - 14x/15
Performing multiplication in numerator of the Right Hand Side of the expression
Expression = 10x + 60 - 14x/15
Performing subtraction
Expression = - 4x + 60/15
Rewriting the expression
Expression = - 4x/15 + 60/15
Performing division on extreme Right Hand Side of the expression
Expression = - 4x/15 + 4
Thus, the correct equivalent expression is option negative 4 over fifteen times x plus four.
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13. A number line is shown below. Which of the following expressions represents the distance between -4and 5 on the number line?-4-3-2-1012345A. 1-4+51B. 14-51C. |-5-(-4)D. |-4-51
Remember that to find a distance between two numbers, we have to subtract the least number from the greater one. So, in this case, we have -4 and 5, where 5 is greater than -4.
[tex]5-(-4)=5+4=9[/tex]Therefore, the distance between the numbers is 9.The answer is C.7. If f(x) = -x + 7, what is f(15)?Of(15) = 22f(15) = -22Of(15) = -8f(15) = 8
the fuction f(x) is equal to:
[tex]f(x)=-x+7[/tex]now, to evaluate f(15) we have to replace x=15 so the equation is going to be equal to:
[tex]f(15)=-15+7=-8[/tex]If it laptop computer right now because $1549 and is on sale for $1149 what percentage discount is being given round your answer to the nearest hundredth when necessary
Okay, here we have this:
Considering the following equation:
Sale Price=Original Price*(100%-Percentage discount)
Replacing we obtain:
$1149=$1549*(100%-Percentage discount)
$1149/$1549=(100%-Percentage discount)
0.7417=100%-Percentage discount
Percentage Discount=100%-0.7417
Percentage Discount=1-0.7417
Percentage Discount=0.2583
Percentage Discount=25.83%
Finally we obtain that the discount percentage is 25.83%.
40% of the airplanes were hydroplanes. If 660 were hydroplanes, how many were not hydropons?
40% of the airplanes were hydroplanes.
If 660 were hydroplanes, how many were not hydroplanes?
SOLUTION
If 40% of the airplanes were hydroplanes.
Let x represents the total number of Hydroplanes.
So that 40 % of X = 660
40/ 100 x X = 660
2 / 5 x X = 660
2X / 5 = 660
cross- multiply, we have:
2X = 660 X 5
2 X = 3300
Divide oth sides by 2 , we have :
X = 3300 / 2
X = 1650
Total number of Hydrophones = 1650
Those that are Hydrophones = 660
Those that are not Hydrophones = 1650 - 660
= 990
The following shows the allowances before a tax of 25% is applied;
•Personal allowance = $40 000
•Spousal allowance = $10 000
•Dependent allowance = $8 000 for each dependent
Tom earns $180 000 per year in his position at a company. He is married with two kids.
Solomon earns $200 000 per year at the same company. He is single.
(a) What are the total allowances for each of the men?
(b) What is Tom’s net income?
(c) What is Solomon’s net income?
Considering the given allowances, it is found that:
a) Tom's allowances are of $66,000, while Solomon's are of $40,000.
b) Tom's net income is of $151,500.
c) Solomon's net income is of $160,000.
What is the effect of an allowance on taxes?An allowance is an exemption in the taxable income of a person, meaning that taxes are not paid over this amount.
Solomon is single, hence he only has the personal allowance of $40,000, and his net income will be of:
Solomon's net income = 0.75 x 160,000 + 40,000 = $160,000. (75% because 25% of the amount not claimed in allowances is paid in taxes).
Tom's allowances are given as follows:
Personal: $40,000.Spousal: $10,000, as he is married.Dependent: 2 x $8,000 = $16,000, one for each kid.Hence his total allowances are of:
$40,000 + $10,000 + $16,000 = $66,000.
His net income will be of:
Tom's new income = 0.75 x 114,000 + 66,000 = $151,500.
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Write .242424... as a
fraction in lowest terms
Answer: 8/33
Step-by-step explanation:
r = 0.242424....
100r= 24.2424....
100r - r = 99r
99r = 24
r = 24/99 = 8/33
Please show work THANK YOU
The net force acting on the object is 12.44 N.
In this problem, we are dealing with the magnitude of a vector, where A vector is an object that has both a magnitude and a direction. Geometrically, able to picture a vector as a directed line segment, whose length is the magnitude of the vector, and with an arrow showing the direction. A vector's magnitude is the length of the vector. The magnitude of the vector a is signified as ∥a∥. Since we are provided with magnitudes of the three forces acting on the object which are (-8,5), (0,1), and (4, -7) So we can represent them in terms of vectors which are :
F₁= -8i+5j
F₂= j
F₃ = 4i-7j
The magnitude of a vector is basically to add the individual horizontal and vertical components to get the horizontal and vertical components of the resultant force, then sum up the square of the vertical components and horizontal of the resultant force and take the square root of the result.
F(net) =[tex]\sqrt{}[/tex]( F₁²+ F₂²+ F₃²)
=[tex]\sqrt{}[/tex] ((-8)²+(0)²+(4)²) +((5)²+ (1)²+(-7)²)
=[tex]\sqrt{}[/tex](64+16)+(25+1+49)
= 12.44 N
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I need help help with this geometry question
Solution:
Given the a figure;
The figure is a square with the unshaded region is a semi circle.
The measure of the side lengths of the square is 25 ft
To find the area, A, of the shaded region, the formula is
[tex]\begin{gathered} A=Area\text{ of Square}-Area\text{ of a semi circle} \\ A=(l^2)-(\frac{\pi r^2}{2}) \end{gathered}[/tex]Where
[tex]\begin{gathered} l=25\text{ ft} \\ d\text{ is the diameter of the semi circle} \\ d=l=25\text{ ft} \\ r\text{ is the radius of the semi circle} \\ r=\frac{d}{2}=\frac{25}{2}=12.5\text{ ft} \\ r=12.5\text{ ft} \end{gathered}[/tex]Substitute the values of the variables into the formula above
[tex]\begin{gathered} A=25^2-(\frac{\pi\cdot12.5^2}{2}) \\ A=625-245.4369 \\ A=379.5631\text{ ft}^2 \\ A=379.56\text{ ft}^2\text{ \lparen nearest hundredth\rparen} \end{gathered}[/tex]Hence, the answer is 379.56 ft² (nearest hundredth)
What i5 divided by 312
The value derived when 5 is divided by 312 is 62.40.
What is the value of the division?Division is the process of putting a number into distinct equal groups using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. Other mathematical operations include addition, subtraction and multiplication.
312 ÷ 5 = 62.40
The long division is:
62.4
5[tex]\sqrt{312}[/tex]
- 30
12
- 10
20
- 20
00
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Chris and Beth Micelli made a $235,000 offer for the purchase of a new home, which was accepted. They made a 30% down payment and financed the rest. Using the closing cost table below, find the mortgage total if they include the closing costs in the mortgage amount.
The amount of mortgage will be the remaining amount after they made a downpayment.
Since the downpayment is 30%, the mortgage will be 70% of the purchased amount
So mortage will be :
mortgage = 0.70 x $235,000 = $164,500
From the closing cost table :
There are charges related to the mortgage (Points, Document stamp and Processing fee)
Adding these charges will be :
=2% + 0.30% + 1.10% = 3.4% of the mortgage
So this will give us :
= 0.034 x $164,500 = $5,593
Now to find the total mortgage, add the values in the closing cost table including the mortgage itself.
Total mortgage = 164500 + 5,593 + 252 + 65 + 325 + 212 + 410 + 350 + 450
Answer :
Total mortgage = $172,157
Triangle pqr is rotated clockwise. The image is a pqr.
A rotation is a rigid transformation, this means that the shape changes location but does not change its size. So even if triangle PQR was rotated to P'Q'R', the side lengths remain the same so that
PQ=P'Q'= 9
QR=Q'R'= 12
RP=R'P'= 7
The same happens with the angles
Q=∠Q'=35°
R=∠R'=48|°
180-()35+48= 97°
So
P'Q'=9
P'=97|°
on a coordinate plane, point a is located (-2,2) and point b is located at (6,-1). determine the coordinates of the point that is 7/8 of the distance from a to b
The coordinates of the point between points a to b are (5, -5/8)
How to determine the coordinate of the point on the line segment?We have the following endpoints on the segment
A = (-2, 2)
B = (6, -1)
The line ratio is given as the following fraction
Ratio, m : n = 7/8
Express the fraction as a ratio
So, we have
m : n = 7 : 8 - 7
Evaluate the difference
So, we have
m : n = 7 : 1
The coordinate of the point is then calculated as
Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)
Substitute the known values in the above equation
Point = 1/(7 + 1) * (7 * 6 + 1 * -2, 7 * -1 + 1 * 2)
Evaluate the products in the above equation
So, we have
Point = 1/8 * (42 -2, -7 + 2)
Evaluate the sum and the difference
So, we have
Point = 1/8 * (40, -5)
Evaluate the products
So, we have
Point = (5, -5/8)
Hence, the coordinates of the point that is 7/8 of the distance from a to b are (5, -5/8)
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f(x) = -x +2^x+8
Find f(-2)
Value of f(-2) is 12.25.
What is equation?Equation, also known as a statement of equivalence between two expressions with variable- and/or number-based components. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
Given Data
Expression
f(x) = -x +2ˣ+8
f(-2)
Equating -2 in the place of x
= -(-2) + 2⁻² + 8
= 4 + 8 +[tex]\frac{1}{4}[/tex]
= [tex]\frac{16+32+1}{4}[/tex]
= [tex]\frac{49}{4}[/tex]
= 12.25
Value of f(-2) is 12.25.
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A project is budgeted for 1200 hours and will last 4 weeks. A labor covered 30% of the workload in the first two weeks and then covered 60% for the final two weeks. If a labor normally works 50 hours per week, how many total hours will the labor cover?
Thus total number of labor is 15.6
What is basic algebra ?Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical formulas. Mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z are needed to construct a valid mathematical expression. Coordinate geometry, calculus, and trigonometry are just a few of the mathematics topics that involve algebra. Basic algebraic expressions like 2x + 4 = 8 are created by performing operations on variables and constants, such as addition, subtraction, multiplication, and division. These algebraic expressions serve as the mathematical statements.
1 st week:
30% of 1200 hour = 360 hour
1 labor = 50 hour
y =360 hour
y= [tex]\frac{360}{50}[/tex]=7.2 technicians
Final two weeks : 2nd and 3rd week
50% of (1200hr - 360hr)= 50% of 840hr=420hr
1 labor = 50 hr
2 labor = 100hr
x = 420 hr
x = 420×[tex]\frac{2}{100} =\frac{420}{50}[/tex]
=8.4 technicians
Thus total number of labor = x+y
= 7.2 +8.4
=15.6
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Please help I don’t know how to solve this
(a) 291/2020
Divide the total for the 10-14 year column by the total.
(b) 77/465
There are 465 people from the east, 77 of which were loyal for 10 to 14 years
(c) 437/1010
There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.
(d) 145/376
376 people are from the West, (45+100)=145 of which are at least 10.
(e) 32/157
157 people were loyal for less than a year, 32 of which were from the East.
(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.
(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.
(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.
How far can a woman drive into the tiwnif she drives out at 40 miles per hour,return over the same rod at 30 miles per hour, and spends 8 hours away from home, including a 1 hour stop for luch
Given the time, the distance that the.womn drives will be 240 miles.
How to calculate the distance?From the information illustrated, the woman drives out at 40 miles per hour, return over the same road at 30 miles per hour, and spends 8 hours away from home.
It should be noted that the average speed will be illustrated as:
= (2 × r1 × r2) / +r1 + r2)
= (2 × 40 × 30) / (40 + 30)
= 240/7
Since she drive for 7 hours, the distance will be:
= 240/7 × 7
= 240 miles.
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The length of a parking lot is 4 yards more than the width. If the area of the parking lot is 117 square yards, find the dimensions of the parking lot.
A parking lot's length is 4 yards longer than its width. The dimensions of the parking lot are width=9 and length =12.
Given that,
A parking lot's length is 4 yards longer than its width.
We have to determine the parking lot's measurements if the area is 117 square yards.
Let us take the width as x and we get the length as x+4.
We can write as,
x(x+4)=117
x²+4x=117
x²+4x-117=0
x²+13x-9x-117=0
x(x+13)-9(x+13)=0
(x+13)(x-9)=0
x+13=0 and x-9=0
x=-13 and x=9
Therefore, The dimensions of the parking lot are width=9 and length=12.
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Graph using slope-intercept form.
3x-2y<10
Answer:
3x-2y=10
2y=3x-10
Y=(3/2)x-5
Slope m=3/2
Answer:
See attachment.
Step-by-step explanation:
Slope-intercept form:
[tex]\boxed{y=mx+b}[/tex]
where:
m = slopeb = y-intercept-----------------------------------------------------------------------------------
Given inequality:
[tex]3x-2y < 10[/tex]
Rearrange the given inequality to make y the subject:
[tex]\implies 3x-2y+2y < 10+2y[/tex]
[tex]\implies 3x < 10+2y[/tex]
[tex]\implies 3x-10 < 10+2y-10[/tex]
[tex]\implies 3x-10 < 2y[/tex]
[tex]\implies 2y > 3x-10[/tex]
[tex]\implies \dfrac{2y}{2} > \dfrac{3}{2}x-\dfrac{10}{2}[/tex]
[tex]\implies y > \dfrac{3}{2}x-5[/tex]
Compare this with the slope-intercept form.
Therefore:
slope = ³/₂y-intercept = (0, -5)When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.To graph the given inequality using its slope and y-intercept:
Plot the y-intercept → point (0, -5). As the slope is ³/₂, plot another point 3 units up and 2 units right from (0, -5) → point (2, -2). Draw a dashed straight line through the two points.Shade above the line.Learn more about graphing inequalities here:
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2x-9/x-7 + x/2 = 5/x-7
So the answer is X1 = 5.51 and X2 = -0.85
Please help I give points
Answer:
[tex]y=\frac{1}{5}x^2+\frac{9}{5}x+4[/tex] or y = 1/5x^2+9/5x+4 (they are the same just different formats)
Step-by-step explanation:
In this case we are given the intercepts of the parabola (aka another name for a quadratic function). Since the intercepts are given, it makes the most sense to use intercept form.
The basic formula for intercept form is:
y=a(x-b)(x-c) where a, b, and c are all constants
b and c are the x intercept values.
plug in the values:
y=a(x-(-4))(x-(-5))=a(x+4)(x+5)
y=a(x+4)(x+5) let's call this equation 1
unfortunately, there is still an "a" at the beginning, but that's where the y intercept is used.
Since (0,4) is a solution to the equation: y=a(x+4)(x+5), the values can be plugged into this equation to solve for a.
In this case, x = 0 and y = 4, so plug in those values
4=a(0+4)(0+5) = a(4)(5) = 20a
a = 1/5
Now, plug "a" back into equation 1
y=1/5(x+4)(x+5) this is the intercept form. However, the question ask for standard form, so it must be expanded
FOIL the parentheses (expand it) to get:
y=1/5(x^2+9x+20) = [tex]\frac{1}{5}x^2+\frac{9}{5}x+4[/tex]
(1/8) raised to -x ppwer= 64 raised to x powerI'll upload a picture
x = 0
Explanation:[tex](\frac{1}{8})^{-x}=64^x[/tex][tex]\begin{gathered} \frac{1}{8\text{ }}\text{ = }\frac{1}{2^3}\text{ } \\ \text{Rule: }\frac{1}{a^b}=a^{-b} \\ so,\text{ }\frac{1}{2^3}=2^{-3} \\ (\frac{1}{8\text{ }})^{-x}=(\frac{1}{2^3})^{-x}\text{ = }(2^{-3})^{-x} \\ =2^{3x} \end{gathered}[/tex][tex]\begin{gathered} 64=2^6 \\ 64^x=(2^6)^x=2^{6x} \\ (\frac{1}{8})^{-x}=64^x \\ 2^{3x}\text{ = }2^{6x} \\ \text{base cancels out:} \\ 3x\text{ = 6x} \end{gathered}[/tex][tex]\begin{gathered} 3x\text{ - }6x\text{ = 0 } \\ -3x\text{ = 0} \\ \text{divide both sides by -3:} \\ \frac{-3x}{-3}\text{ = }\frac{0}{-3} \\ x\text{ = 0} \end{gathered}[/tex]The graph below shows the relationship between population density and pollution per person for 36 Japanese cities.what is the best description of this relationship?____________________* Positive linear association* Negative linear association* Nonlinear association* No association
Answer:
No association
Explanation:
If there is a positive linear association, the graph would show something close to a straight line with a positive slope.
In the same way, if there is a negative linear association, the graph would be a straight line with a negative slope
If there is a nonlinear association we would see a curve.
Since all the data is dispersed in the graph, we can say that the best description of this relationship is No association.
One number is 16 more than two times another. Their sum is 58. Find the numbers.
The larger number is 44 and the smaller number is 14.
What are the numbers?The first step is to develop a system of equations using the information provided in the question.
y = 2x + 16 equation 1
x + y = 58 equation 2
Where:
y = larger number
x = smaller number
The next step is to substitute for y in equation 2 using equation 1.
x + 2x + 16 = 58
Combine similar terms:
x + 2x = 58 - 16
Add similar terms together:
3x = 42
Divide both sides of the equation by 3:
x = 42 / 3
x = 14
Substitute for x in equation 2:
14 + y = 58
y = 58 - 14
y = 44
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Jaya's monthly bank statement showed the following deposits and withdrawals:
$31.87, -−$34.19, -−$58.47, $48.57, -−$13.16
If Jaya's balance in the account was $94.42 at the beginning of the month, what was the account balance at the end of the month?
If Jaya's balance in the account was $94.42 at the beginning of the month, then account balance at the end of the month is $69.04 .
In the question ,
it is given that Jaya's account balance at beginning of month was $94.42 ,
first transaction +$31.87 ,
means Jaya deposited $31.87
So Account balance = $94.42+$31.87 = $126.29
Second transaction -$34.19 ,
means Jaya withdraw $34.19
So Account balance = $126.29-$34.19 = $92.10
third transaction -$58.47 ,
means Jaya withdraw $58.47
So Account balance = $92.10-$58.47 = $33.63
fourth transaction +$48.57,
means Jaya deposited $48.57
So Account balance = $33.63+$48.57 = $82.20
fifth transaction -$13.16 ,
means Jaya withdraw $13.16
So Account balance = $82.20-$13.16 = $69.04
Therefore , if Jaya's balance in the account was $94.42 at the beginning of the month, then account balance at the end of the month is $69.04 .
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Hello I need help please :)
The steps of finding the line that best fits a data set are the following:
1.- Draw and label the axes of a graph
2.- Plot the data points
3.- Choose two points that best fit the data set
4.- Find the slope of the line through the points
5.- Substitute one point in the equation y = mx+b
6.- Solve for b
7.- Write the complete linear equation
5. Suppose that 25 acres of land is purchased, but because of roads and wetland concerns, 6 2/3 acres can not be developed into lots. How many 5/6 acre lots can the rest of the land be divided into?
22 lots of 5-6 acres each can be created from the remaining area.
What is acres?
The imperial and US customary systems both utilise the acre as a unit of land area. One chain by one furlong (66 by 660 feet) is the traditional definition, which is exactly equal to 10 square chains, 1/640 of a square mile, 4,840 square yards (43,560 square feet), and 4,047 m² (or around 40% of a hectare). An acre may be stated to be exactly 4,046.8564224 square metres based on the international yard and pound agreement of 1959.
Out of 25 acres of land 6 2/3 acres can not be developed into lots.
Therefore land that is left = 25 - 6 2/3 acres
= 25 - 20/3 acres
= 55/3 acres
No.of 5/6 acre lots can the rest of the land be divided into = 55/3 / 5/6 lots
= 22 lots
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