The area of the circular flower bed is approximately 78.54 square feet.
The circular flower bed's 10 foot diameter corresponds to a radius of 5 feet, or half the diameter. The area and circumference of the circular flower bed can be determined using the following data:
Circumference:
The formula for calculating a circle's circumference is:
C = 2πr
where the mathematical constant is roughly equivalent to 3.14159 and r is the circle's radius.
Using the values we were provided as replacements, we obtain:
C = 2π(5) \sC = 10π
We may calculate a rough estimate of the circumference using a calculator:
C ≈ 31.42 feet
As a result, the flower bed's circumference is approximately 31.42 feet.
Area:
The area of a circle is determined using the following formula:
A = πr²
Using the values we were provided as replacements, we obtain:
A = π(5)² \sA = 25π
We can calculate the area's value using a calculator as follows:
A area of 78.54 square feet.
Thus, the circumference of the flower bed is about 78.54 square feet.
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Suppose a university raises its tuition from $3,000 to $3500. As a result, student enrollment falls from 5,000
to 4,500. Calculate the price elasticity of demand using the mid-point formula. (Round to three decimal places). Is the demand elastic, unitary elastic or inelastic?
For full credit please tell me the following:
1. What is the numerator
2. What is the denominator?
3. What is the numerator divided by the denominator?
4. Is the demand is elastic, unit elastic or inelastic.
Hint: When calculating the midpoint formula start by determining the starting quantity Q1 and the starting
price P1. Next, determine the ending quantity Q2 and the ending price P2.
Answer: The numerator is the percentage change in quantity demanded, which is (Q2 - Q1)/[(Q2 + Q1)/2] = (4500 - 5000)/[(4500 + 5000)/2] = -0.1818
The denominator is the percentage change in price, which is (P2 - P1)/[(P2 + P1)/2] = (3500 - 3000)/[(3500 + 3000)/2] = 0.1429
The numerator divided by the denominator is -0.1818/0.1429 = -1.2727
The price elasticity of demand is greater than 1 in absolute value, which means the demand is elastic.
Using the midpoint formula, we can calculate the price elasticity of demand as:
[(Q2 - Q1)/((Q1 + Q2)/2)] / [(P2 - P1)/((P1 + P2)/2)]
Substituting the given values, we get:
[(-500)/((5000 + 4500)/2)] / [(3500 - 3000)/((3500 + 3000)/2)]
Simplifying, we get:
-0.1818 / 0.1429 = -1.2727
Since the price elasticity of demand is greater than 1 in absolute value, the demand is elastic. This means that the percentage change in quantity demanded is greater than the percentage change in price, and the university can expect a relatively large decrease in enrollment due to the tuition increase.
Step-by-step explanation:
Before a renovation, a movie theater had 127 seats. After the renovation, the theater has 188 seats. What is the approximate percentage increase of the number of seats in the theater? If necessary, round to the nearest tenth of a percent.
Answer:
48% hope this helps!
Step-by-step explanation:
188-127= 61 <--(increase)
divide increase by original( 61/127= 0.480)
Multiply by 100 to get percent (0.480x100= 48%)
A traffic light cycles through red, yellow, and green every 2 minutes. How many seconds does the cycle last? Show your work?
Answer:
Step-by-step explanation:
number of minuties for whole cycle
green time+yellow time+ orange time
2+2+2=6
min to seconds==> 1min=60 seconds
so 6*60=360 seconds
Enjoy:)
is 9/18 a rational number?
Therefore , the solution of the given problem of rational numbers comes out to be that 9/18 is a rational number
What are rational numbers, exactly?Rational numbers are those that can be written as the ratio (not the fraction) of two integers. A fraction with a nonzero denominator is considered sensible. Examples of rational numbers include 1/2, 1/5, but it also 3/4. Additionally, "0" can be written in many different ways as a real purpose, such as 0/1, 0/2, as well as 0/3. But 1/0, 2/0, 3/0, and so forth. The number of seven is reasonable. Two parameters can be divided to produce a rational figure.
Here,
Because 9/18 can be written as a ratio of two numbers, it is a rational number. By dividing the numerator and denominator by their largest common factor, which is 9 in this instance, we can simplify the expression 9/18:
=> 9/18
=> (9 ÷ 9) / (18 ÷ 9) = 1/2
We can see that 9/18 is a rational number because 1/2 is also a ratio of two numbers.
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At a local bed and breakfast, guests have a choice of 3 themes for their room, 2 sizes of rooms, and 4 breakfast options. How many choices are available to guests when booking their stay?
Answer:
there are 24 different choices available to guests when booking their stay at the bed and breakfast.
Step-by-step explanation:
To find the total number of choices available to guests at the bed and breakfast, you can use the multiplication principle of counting.
According to the multiplication principle, if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.
Using this principle, we can calculate the total number of choices available to guests by multiplying the number of choices for each option:
Choice of 3 themes for their room: 3 options
Choice of 2 sizes of rooms: 2 options
Choice of 4 breakfast options: 4 options
Total number of choices = 3 x 2 x 4 = 24
Therefore, there are 24 different choices available to guests when booking their stay at the bed and breakfast.
What is the period of the graph of y = 5 sin (4pi x) + 3?
A. 4pi
B. 1/2
C. 3
D. 5
Answer:
Step-by-step explanation:
Equate whats inside (arguments) \sin with base period of sine function 2\pi and solve for x to get period,
\pi x=2\pi\implies x=2
So the period of the graph of the given function is precisely 2.
Hope this helps :)
Which statement is NOT true about the dot plot the right?
A statement is not true about the dot plot to the right include the following: A. the French Club has a greater mean than the Spanish Club.
What is a dot plot?In Mathematics, a dot plot is a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.
How to calculate the mean for a data set?Mathematically, the mean for this set of scores can be calculated by using the following formula:
Mean = [F(x)]/n
Mean of French Club = 1/12(18 + (19 × 4) + (20 × 4) + (21 × 2) + 22)
Mean of French Club = 1/12(238)
Mean of French Club = 119/6 = 19.83.
Mean of Spanish Club = 1/12(18 + (19 × 2) + (20 × 3) + (21 × 3) + (22 × 3))
Mean of Spanish Club = 1/12(246)
Mean of Spanish Club = 123/6 = 20.5.
Therefore, 19.83 is less than 20.5.
Median of French Club = 20
Median of Spanish Club = (20 + 21)/2 = 20.5.
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Quadrilateral NOPQ is dilated by a scale factor of to form
quadrilateral N'O'P'Q'. What is the measure of side Q'N'?
18
Z
20.1
20.1
18
0
K
The measure of side Q'N' after a dilation of quadrilateral NOPQ by a scale factor of 2/3 is 12 units
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
Scale factor is the ratio of new side to original side. It is given as:
Scale factor = new side / original side
Given that the scale factor is 2/3 and the side QN is 18, hence:
QN * scale factor = Q'N'
Substituting:
18 * 2/3 = Q'N'
Q'N' = 12
The measure of side Q'N' is 12 units
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Alison saved 15% on the cost of her computer software, which was $355. How much did Alison save?
Answer:
$53.25
Step-by-step explanation:
$[tex]\frac{355}{100}= 1[/tex]%
$[tex]15\frac{355}{100} = 15[/tex]%[tex]= 53.25[/tex]$
Answer:
53.25
Step-by-step explanation:
Calc for business!
Please help!
A chemical substance has a decay rate of 8.8% per day. The rate of change of an
dN
amount N of the chemical after t days is given by =-0.088N
dt
(i) Let No represent the amount of the substance present at to. Find the exponential function
that models the decay.
(ii) Suppose that 400g of the substance is present at to. How much will remain after 3 days?
(iii) What is the rate of change of the amount of the substance after 3 days?
(iv) After how many days will half of the original 400 g of the substance remain?
(i) N(t) = No e^(-0.088t) (ii) approximately 323.3 g of the substance(iii) the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.(iv) approximately 7.88 days.
Describe Rate of change?The rate of change can be positive, indicating an increase in the value of the variable, or negative, indicating a decrease. It can also be constant, indicating a steady increase or decrease, or it can vary over time, indicating a more complex pattern of change. Understanding the rate of change of a variable is important in many fields, including engineering, economics, and finance, among others.
(i) Since the decay rate is given by -0.088 per day, the exponential function that models the decay is:
N(t) = No e^(-0.088t)
where No is the initial amount of the substance present at t=0.
(ii) If 400g of the substance is present at t=0, then we have No = 400. Substituting this value into the exponential function, we get:
N(t) = 400 e^(-0.088t)
To find how much will remain after 3 days, we need to evaluate N(3):
N(3) = 400 e^(-0.088*3) ≈ 323.3 g
Therefore, approximately 323.3 g of the substance will remain after 3 days.
(iii) The rate of change of the amount of the substance after t days is given by:
dN/dt = -0.088N
To find the rate of change after 3 days, we need to evaluate dN/dt at t=3:
dN/dt | t=3 = -0.088N(3) = -0.088(323.3) ≈ -28.4 g/day
Therefore, the rate of change of the amount of the substance after 3 days is approximately -28.4 g/day.
(iv) We want to find the value of t such that half of the original 400 g of the substance remains. In other words, we want to solve the equation:
N(t) = 200
Substituting No = 400 into the exponential function, we get:
400 e^(-0.088t) = 200
Dividing both sides by 400, we get:
e^(-0.088t) = 0.5
Taking the natural logarithm of both sides, we get:
ln(e^(-0.088t)) = ln(0.5)
Simplifying, we get:
-0.088t = ln(0.5)
Solving for t, we get:
t ≈ 7.88 days
Therefore, after approximately 7.88 days, half of the original 400 g of the substance will remain.
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Lena bought 2 CDs that were each the same price. Including sales tax, she paid a total of $23.40. Of that total, $1.80 was tax. What was the price of each CD
before tax?
Therefore , the solution of the given problem of unitary method comes out to be each Disc cost $10.80 before taxes.
What is an unitary method?The measurements taken from this nanosecond subset must be multiplied by two in order to complete the task using the unitary technique. In essence, the characterised by a group and the colour sections are both removed from the unit method when a desired object is present. For example, 40 pens with a variable price would pay Inr ($1.01).
Here,
Let's name the CDs' pre-tax cost "x" for simplicity. The overall cost of the CDs before tax is two times because Lena purchased two of them for the same price. The cost of the Discs, with the addition of the $1.80 sales tax, is:
=> 2x + $1.80
Given that we know the final price, including tax, was $23.40, we can create the following equation:
=> 2x + $1.80 = $23.40
By deducting $1.80 from each half, we arrive at:
=> 2x = $21.60
When you divide both parts by 2, you get:
=> x = $10.80
As a result, each Disc cost $10.80 before taxes.
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In figure AB and CD are two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD respectively. If ∠POQ = 140°, then (∠APQ + ∠CQP) is equal to
(i)120 (ii)130 (iii) 140 (iv)150
The answer is (iv) 150. This result can be obtained by applying the alternate segment theorem.
What is circle?A circle is a shape with all points at an equal distance from the center. It has no sides or angles and is the only two-dimensional shape with this property. It is also the most basic of all shapes, and is found in nature in many forms, such as raindrops, the sun, and even the human pupil. Circles are often used in art, design, and architecture, and are sometimes even used to represent infinity.
This theorem states that if two chords of a circle intersect at right angles, then the angles in the alternate segments of the circle are equal. In this case, the alternate segments are APQ and CQP. Hence, ∠APQ + ∠CQP = 150°.
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A new employee at a woodworking repair shop is asked to remove some minor stains from a wooden patio table. He decides to use grade 1 steel wool thinking that a higher grade of steel wool will be most effective in quickly removing the stains.
What faulty inference did the employee use to make this decision?
There is little difference between grade levels of steel wool.
The coarser the steel wool grade, the less steel wool needed.
The higher the steel wool grade, the less muscle power required.
The coarser the steel wool, the better for all woodworking repair jobs
The higher the steel wool grade, the less muscle power required.
What faulty inference did the employee use to make this decision?The faulty inference the employee used to make this decision is that a higher grade of steel wool will be more effective in quickly removing stains. In reality, higher grade steel wool is more abrasive and can actually damage the wood surface, leaving behind scratches and making the problem worse.
Grade 1 steel wool is the finest grade and is typically used for finishing and polishing wood. It is not suitable for removing stains, as it is not abrasive enough to remove the outer layer of the wood where the stain is located. To remove stains from wood, it is recommended to use a lower grade of steel wool or a non-abrasive cleaning solution specifically designed for wood.
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Plot the following points in the plane: (2, 1), (-1/2, 0), (π, -3). Is there a point in the plane for which you need exactly three numbers to specify its location?
There is no such point that requires exactly three numbers to specify its location.
What is the Euclidean plane?A mathematical notion known as the Euclidean plane symbolizes a two-dimensional environment in which points, lines, and forms may be specified and altered. The Greek mathematician Euclid, who originally described the geometry of the plane in his book Elements, is honoured by the name of the object. The Pythagorean theorem is used to calculate distance in the Euclidean plane, while degrees or radians are used to calculate angles.
The plane doesn't have any points that can be precisely located by three integers. Each point in the Euclidean plane may be found using only two integers, namely its x- and y-coordinates.
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XPO Corporation has a minimum tax credit of $51,000 from 2017. XPO’s 2018 tax liability before any MTC carryover is $30,500. What is XPO’s minimum tax credit carryover to 2019, if any?
XPO's minimum tax credit carryover to 2019 is $20,500.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants. An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
XPO's minimum tax credit from 2017 is $51,000. This means that they are allowed to reduce their 2018 tax liability by up to $51,000 using this credit.
Since their 2018 tax liability before any MTC carryover is $30,500, they have not used the entire minimum tax credit for 2017. Therefore, they can carry over the remaining credit to 2019.
To calculate the minimum tax credit carryover to 2019, we need to subtract the amount of the minimum tax credit that XPO used in 2018 from the total minimum tax credit of $51,000:
Minimum tax credit carryover = $51,000 - $30,500 = $20,500
Therefore, XPO's minimum tax credit carryover to 2019 is $20,500.
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There are 100 students in a band. Ninety percent of the students are either 12 or
13 years old. The number of 13-year-olds is 125% of the number of 12-year-olds. The rest of
the students are 14 years old. Write the portion of the band for each age as a fraction and a
percent.
12-year olds: fraction: *blank*, percent: *blank*
13-year olds: fraction: *blank*, percent: *blank*
14-year olds: fraction: *blank*, percent: *blank*
Answer:
Step-by-step explanation:
Let's first find the number of 12-year-olds and 13-year-olds in the band:
Let x be the number of 12-year-olds.
Then the number of 13-year-olds is 1.25x (125% of x).
The total number of students in the band is 100, so we know that x + 1.25x = 0.9(100).
Solving for x, we get x = 40, so there are 40 12-year-olds and 50 (1.25x) 13-year-olds.
The number of 14-year-olds is the remainder after we count the 12 and 13-year-olds:
The total number of students in the band is 100, and we know that 90% of them are 12 or 13 years old, so 10% are 14 years old.
10% of 100 is 10, so there are 10 14-year-olds.
Now we can find the portion of the band for each age group:
12-year olds: fraction = 40/100 = 2/5, percent = 40%
13-year olds: fraction = 50/100 = 1/2, percent = 50%
14-year olds: fraction = 10/100 = 1/10, percent = 10%
Graph the following functions and determine where F(x) = G(x). State the x values only. Select all that apply.
f(x)= -x^2+8x-13 and g(x)= x+3
a. 4
b. no solution
c. all real numbers
d. -13
For the specified functions, there is no answer. By graphing the functions, the answer has been discovered.
What does graphing a function mean?The method of graphing a function begins with creating the graph of a pertinent function. The function equation will be satisfied at a point on a curve if it reflects the function at that location.
According to the given information:We are given two functions as f(x) = -x² + 8x - 13 and g(x) = x + 3
The graph of the given functions has been plotted and attached below.
In the graph, the red function represents the f(x) function and the blue line represents the g(x) function.
From the graph, we can see that the two does not meet.
Hence, there is no solution for the given functions.
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Pilots can make quick calculations by solving one-step equations. For instance: the distance in miles from the airport that a plane should begin descending, divided by 3, equals the plane's height above the ground in thousands of feet. If an aircraft is 10,000 feet above the ground, write and solve an equation to find the distance the pilot should begin descending.
Let d be the distance in miles from the airport that a plane should begin descending. According to the problem statement, we can write the equation:
d/3 = 10
To solve for d, we can isolate it by multiplying both sides of the equation by 3:
d = 3 * 10
Therefore, the pilot should begin descending when the plane is 30 miles from the airport.
The length of a gulf park is 2.5km long is represented on a map by a line 250mm long.What is the scale of the map.
The scale of the map is 1/10,000.
The formula used to find the formula to find the scale is
scale = length on the map / actual length
Given,
Actual length of the golf park = 2.5 km
length on map = 250 mm
Here, we need to convert both lengths into the same units
2.5 km = 2.5 x 1000 m/km x 1000 mm/m = 2,500,000 mm
we know that,
scale = length on the map / actual length
= 250 mm / 2,500,000 mm
= 1/10,000.
Therefore, the scale of the map is 1/10,000.
i.e, one unit on the map is equal to 10,000 units of length in reality.
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nework activity 8.1 Calculate the perimeter of a wall in a classroom where the length is 10 m and the height of the vall is 3 m. A computer desk has a length of 70 cm and a breadth of 40 cm. Work out the perimeter of the computer desk. The length of a wall in a computer classroom is 15 m. How many computer desks can be placed side-by-side along the wall?
The perimeter of the wall in a classroom is 26 meters.
What is the perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.
Given that, a wall in a classroom measures, the length is 10 m and the height is 3 m.
So, the perimeter of wall is 2(Length+Height)
= 2(10+3)
= 2×13
= 26 meters
A computer desk has a length of 70 cm and a breadth of 40 cm.
Now, the perimeter of a computer desk is 2(Length+Breadth)
= 2(70+40)
= 220 cm
220 cm can be written as 220/100 = 2.2 meters
Number of computers v=can be placed along wall =15/2.2
= 6.8
≈ 7
Therefore, approximately 7 computers desks place along the wall.
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In the given equation, b is a positive constant.
The sum of the solutions of the equation is 5.
What is the value of b?
x²(x+3)(x - b) = 0
Answer: b = 8
Step-by-step explanation:
From the equation, we can see that x = 0 is one of the solutions. This means that the remaining solutions must add up to 5.
Let's factor the equation and set each factor equal to zero:
x²(x+3)(x - b) = 0
x = 0 or x + 3 = 0 or x - b = 0
Solving for x in each case, we get:
x = 0 or x = -3 or x = b
Since the sum of the solutions is 5, we can write:
0 + (-3) + b = 5
Simplifying, we get:
b - 3 = 5
Adding 3 to both sides, we get:
b = 8
Therefore, the value of b is 8.
Hello, I need help with this problem. Thanks
Solve the indicated quantity.
In order to start a small business, a student takes out a simple interest loan for $7000.00 for 3 months at a rate of 7.25%.
a. How much interest must the student pay?
b. Find the future value of the loan.
The interest to be paid by the student is $126.875 and the amount is $7126.875
What is simple interest?The simple interest is the interest amount for a particular principal amount of money at some rate of interest.
Given that, a student takes a loan on SI on $7000 for 3 months and the rate of interest is 7.25%
SI = PRT / 100
Putting the values,
SI = 7000 x 3 x 7.25 / 1200
= 126.875
Amount = Principal + Interest
Amount = 7000 + 126.875
= 7126.875
Hence, the interest to be paid by the student is $126.875 and the amount is $7126.875
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A right circular cylinder has a height of 1934 ft and a diameter 125 times its height.
What is the volume of the cylinder?
Enter your answer as a decimal in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.
Answer: 545,884,646.36 ft3.
Step-by-step explanation:
The volume of the cylinder is calculated using the formula V=πr2h, where r is the radius of the cylinder and h is the height. The radius of the cylinder can be calculated by dividing the diameter (125 times the height) by 2.
Therefore, the radius = (125 * 1934) / 2 = 118,550 / 2 = 59,275 ft
Plugging in the values of radius and height into the formula, the volume of the cylinder is V = 3.14 * (59,275)2 * 1934 = 545,884,646.36 ft3
Rounding to the nearest hundredth, the volume of the cylinder is 545,884,646.36 ft3.
State whether each investment below realized a profit or loss. Compute the percent of increase or decrease.
Purchase Price: $12.00
Selling Price: $8.25
The given investment realized a loss of $3.75 with 31.25% decrease.
What is profit?The amount made by selling a product, which should be greater than the product's cost price, is generally referred to as the profit. It is the profit generated by all business activities. In other words, a product is deemed to have made a profit if its selling price (SP) exceeds its cost price (CP). It explains the financial gain realised when the revenue from a company activity outpaces the costs, like as taxes and expenses, involved in maintaining a business activity.
Given : Purchase Price: $12.00
Selling Price: $8.25
Since the purchase price is more than the selling prize, So the investment has been sold at a loss.
The loss on investment = Purchasing price - Selling price
= $ 12 - 8.25
= $3.75.
% of decrease = (loss/ purchasing price) × 100
= 3.75/12 × 100
= 31.25 %
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Find the value of the angle θ rounded to 1 DP.
The diagram is not drawn accurately.
Check the picture below.
[tex]\sin(24^o )=\cfrac{\stackrel{opposite}{y}}{\underset{hypotenuse}{17}}\implies 17\sin(24^o )=y \\\\[-0.35em] ~\dotfill\\\\ \sin(\theta )=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{y}}\implies \theta =\sin^{-1}\left( \cfrac{4}{y} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{4}{17\sin(24^o )} \right)\implies \theta \approx 35.3^o[/tex]
Make sure your calculator is in Degree mode.
A solid right pyramid has a square base with an edge
length of x cm and a height of y cm.
X
y
Which expression represents the volume of the
pyramid?
Oxy cm³
0x²y cm³
Oxy² cm³
0x²y cm³
The volume of the solid right pyramid is, x²y cm³.
What is a pyramid?A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces.
The number of sides on its base is equal to the number of lateral faces.
The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.
We know, Area of a square is a product of it's any two sides.
Now, If we want to determine the volume we have to multiply the height also(another dimension).
Therefore, From the given information and options, A pyramid with square bases(x) and a height of 'y' will have a volume,
= x×x×y cm³.
= x²y cm³.
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A political scientist takes a simple random sample of n = 140 registered voters in Maricopa County, AZ to determine the proportion of registered voters who consider themselves Democrats. Assume the (unknown) true proportion of registered voters who are Democrats is 46%.
Using percentage, the true proportion of registered voters who are Democrats is = 64.
What do you mean by percentage?
A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%.
It is written as 30:100 in ratio form and 30/100 in fraction form. In this context, "%" is read as "percent" or "percentage" to represent a percentage.
In the question,
Sample size, n = 140.
Now 46% of the registered voters are Democrats.
Now the no. of registered voters =
46% of 140
= 46/100 × 140
= 6440/100
= 64.4
≈ 64
Therefore, 64 is the true proportion of registered voters who are Democrats.
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Ben drew a rectangle. The length of his rectangle is the width of the rectangle.
1/3
Let & = length.
Let w = width.
W
Complete the table, and graph
Based on the relationship between the length and width of the rectangle, the length of the rectangle for the various values of the width is given below:
when width, W = 1, Length, l = 1/3when width, W = 3, Length, l = 1when width, W = 7, Length, l = 7/3What is the relationship between the length and the width of the rectangle?The relationship between the length and the width of the rectangle is a linear relationship given by the linear equation below:
l = w/3
where;
l is the length of the rectangle
w is the width of the rectangle
When w = 1
l = 1/3
When w = 3
l = 3/3
l = 1
when w = 7
l = 7/3
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