The correct option is Option 1 - 3520.
A farmer owns 3520 acres in which three full sections, four half-sections, and two quarter-sections are there.
Three of a farmer's sections were full. Let's say a full section is 640, which is
=3 x 640,
= 1,920.
He had four half portions as well. Divide 640 by two to get 320 (640/2), which is
= 4 X 320
= 1,280.
He had three quarter portions as well. Divide 640 by 4 to create a quarter piece (640/4 = 160)
= 2 X 160
= 320.
Now we have to add all these,
Three full sections = 1920
Four half-sections = 1280
Two quarter-sections = 320
= 1,920 + 1,280 + 320
= 3,520.
Therefore the acres a farmer had is 3520.
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The following question may be like this:
A farmer owns three full sections, four half-sections, and two quarter-sections. How many acres is this?
3520324044404020Fill in the table using this function rule.
y=2x-3
X Y
-6 ?
-3 ?
0 ?
3 ?
The table is filled considering the numeric values of the function, as follows:
x = -6, y = -15.x = -3, y = -9.x = 0, y = -3.x = 3, y = 3.How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The numeric value in this problem is found replacing the lone instance of x by it's value, hence the numeric value at x = -6 is given as follows:
y = 2(-6) - 3
y = -12 - 3
y = -15.
The same procedure is applied for x = -3, x = 0 and x = 3.
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Tank A has a capacity of 9.5 gallons. 6 1/3 gallons of the tanks water are poured out. How many gallons of water are left in the tanks
The volume of water that are left in the tank is equal to 3.2 gallons.
How to calculate the volume of a geometric figure?Mathematically, the volume of a cuboid tank is a measure of its capacity and it can be calculated by using this following formula:
Volume of a tank = L × W × H
Where:
L represents the length of a cuboid tank.W represents the width of a cuboid tank.H represents the height of a cuboid tank.In order to determine the quantity (volume) of water that are left in the tank, we would use this mathematical expression:
Volume of water left = capacity of tank A - volume of water poured
Volume of water left = 9.5 gallons - 6 1/3 gallons
Volume of water left = 9.5 gallons - 6.3 gallons
Volume of water left = 3.2 gallons.
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the average weekly work hours of full-time u.s. workers have approximately a normal distribution with mean 37 hours and standard deviation hours. suppose 200 u.s. citizens are randomly chosen. find an approximate probability that less than 10 of them are working more than 50 hours a week on average (round off to third decimal place).
The approximate probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average is 0.019
We can use the normal distribution to approximate the probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average.
To do this, we have to standardize the variable by subtracting the mean and dividing by the standard deviation.
In this case, X = (50 - 37) / hours = 1.83
We know that for a standard normal distribution, the probability of X being less than a certain value can be found using a standard normal table or a calculator with a built-in standard normal cumulative distribution function (CDF).
Now, we will use the cumulative distribution function to find the probability of less than 10 out of 200 working more than 50 hours a week on average. Using a standard normal table or calculator, we can find the probability of having X < -2.04.
P(X < -2.04) = 0.0188
So the approximate probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average is 0.0188 which rounding it off to the third decimal place we get 0.019.
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Californians use 75 BTU of energy per home per year which is 25% less than the national average.
How many BTU does an average American household use? Show Work
Proportionately, an average American household uses 100 BTU of energy per home per year while Californians use 75 BTU, which is 25% less than the national average.
What is the proportion?Proportion refers to the ratio or relative size of a value or number compared to another.
Proportions are fractional values equated to each other.
Generally, proportions may be depicted as fractions, decimals, or percentages.
The level of energy per home per year in California = 75 BTU
The national average of BTU use = 100%
California's use = 75% (100 - 25)
Proportionately, if 75% = 75 BTU, 100% = 100 BTU (75/0.75)
Thus, the national average use of energy is expected to be 100 BTU.
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A polynomial function is represented by the data in the table.
Choose the function represented by the data.
f(x) = −14x − 11
f(x) = −12x + 1
f(x) = 2x2 + 1
f(x) = x2 − 6x + 1
Mrs. Norris is planting a vegetable garden with tomatoes and beans. She wants to have 20 more potato plants than beat plants. She will plant 100 plants altogether. How many bean plants should she plant?
Solve using system of equations by elimination. Show your work
PLEASE help me with this question. Will name the BRAINLIEST for whoever gets it right!
The number of bean plants should she plant will be 60
t = tomato plants
b = beans
To Solve by using system of equations
Clear any fractional coefficients if there are any. Alternate the coefficients of a single variable. Select the variable you want to remove. Multiply one or both equations to make the variable's coefficients opposite.
Total plants = 100
t + b = 100 {equation 1}
20 more tomatoes than beans
t = b + 20 {equation 2}
b + 20 + b = 100
2b + 20 = 100
Finish solving for b to find a number of beans.
Then tomatoes will be b+20
Putting this in equation 1
b+20+b=100
2b+20=100
b=40
then t= b+20 {equation 2}
t=60
Hence the number of bean plants should she plant will be 60
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The Chess Club president brought donuts to the club meeting each week. As the club grew, more donuts were needed so that each member could have a donut. The table below shows the ratios of boxed donuts to the cost.
Donuts 2 4 B 8
Cost A 31.60 39.50 C
Determine which table has the correct values for A, B, and C.
Donuts 2 4 5 8
Cost 15.80 31.60 39.50 63.20
Donuts 2 4 6 8
Cost 7.90 31.60 39.50 63.20
Donuts 2 4 7 8
Cost 7.09 31.60 39.50 56.72
Donuts 2 4 6 8
Cost 15.80 31.60 39.50 56.72
The table that has the correct values for A, B, and C will be:
D. Donuts 2 4 6 8
Cost 15.80 31.60 39.50 56.72
How to calculate the ratio?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
Since we know that 4 donut cost 31.60, the.vost for 2 donut will be:
= 31.60 / 4 × 2
= 15.80
Therefore, we can see that the correct table for this is D.
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The scale drawing of the rectangular garden has an area of `2` ft². If Mai used a scale factor of `\frac{1}{3}`, what is the actual area of the garden?
The actual area of the garden without the scale factor is 6 square feet.
What is scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.
What is area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. Depending on the size and number of sides, different forms have varying areas.
Let the original area of the garden be x.
Given that the scale factor used is 1/3, thus we have:
x (1/3) = 2
x = (2)(3)
x = 6
Hence, the actual area of the garden without the scale factor is 6 square feet.
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Convert 4 liters into gallons. Round your answer to the nearest hundredth.
*Note: you must use these exact conversion factors to get this question right.
1 cup (cup) = 8 fluid ounces (fl oz)
1 liter (L) 1000 milliliters (mL)
1 pint (pt) = 2 cups (cups)
1 cubic meter (m³) = 1000 liters (L)
1 quart (qt) = 2 pints (pt)
1 gallon (gal) = 3.785 liters (L)
1 gallon (gal) = 4 quarts (qt)
1 fluid ounce (fl oz) = 29.574 milliliters (ml)
1 cubic foot (ft³) = 7.481 gallons (gal)
Answer:
= (blank) gallons
An airplane is headed for the airport, 15 miles away. If the airplane is at an altitude of 5000 feet, what is the angle of depression, to the nearest tenth of a degree, from the airplane to the airport? (1 mile = 5280 feet)
The angle of depression of the airplane is 3.6⁰.
What is the angle of depression of the airplane?
The angle of depression of the airplane is calculated by forming a triangle with base displacement of the airplane and the altitude.
base of the right triangle = 15 miles = 79,200 ft
height of the right triangle = 5,000 ft
The angle of depression is calculated as follows;
θ = arc tan ( h / b )
θ = arc tan ( 5000 / 79,200 )
θ = 3.6⁰
Thus, the angle of depression of the airplane is a function of the altitude and base displacement of the airplane.
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The post office’s human resources manager wants to determine an optimal hiring plan. Day Number of full-time employees required 1 = Monday 17 2 = Tuesday 13 3 = Wednesday 15 4 = Thursday 19 5 = Friday 14 6 = Saturday 16 7 = Sunday 11 Union rules state that each full-time employee must work 5 consecutive days and then receive 2 days off. Formulate an IP to minimize the number of fulltime employees who must be hired, and solve it using Excel Solver to find the optimal solution
Here is a simple framework to model the problem as an Integer Programming (IP) problem and solve it using Excel Solver:
Define decision variables:Let x(i,j) be the number of full-time employees assigned to work on day i (1 <= i <= 7) and given day off on day j (1 <= j <= 7).
Set constraints:a. Work days constraint: For each day i, the number of employees working must meet the demand:
∑(j=1 to 7) x(i,j) = demand(i) (1 <= i <= 7)
b. Availability constraint: Each employee can work only 5 consecutive days, so for each day j (1 <= j <= 7), the number of employees given day off on day j must be less than or equal to the number of employees working on day j-5:
∑(i=1 to 7) x(i,j) <= ∑(i=j-5 to j-1) x(i,j-5) (1 <= j <= 7)
Set objective:The objective is to minimize the total number of full-time employees hired, so the objective function is:
minimize: ∑(i=1 to 7) ∑(j=1 to 7) x(i,j)
Solve using Excel Solver:Excel Solver can be used to find the optimal solution to the IP problem. The constraints and objective function should be set up in the spreadsheet, and Solver should be configured to use the integer constraint option. The solution will give the optimal number of full-time employees hired and their assignment on each day.
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how to graph y=2x+1
-2x=y=-2
Answer:
For y=2x+1
The line y=2x+1 has a y-intercept of +1, so begin with a point at (0,1)
and its slope is 2/1, which means from there you go Up 2 and Right 1.
Follow that pattern until you can draw a straight line through all the points.
For -2x=y=-2
In this point it only passes (0,2) and (1.0)
Have a wonderful day! :-)
translate the image (x+7,y-19)
The translation rule (x + 7, y - 19) has the meaning given as follows:
Translation 7 units right.Translation 19 units down.What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.The meaning of each translation in this problem is given as follows:
x + 7: 7 units right.y - 19: 19 units down.Missing InformationThe problem asks for the meaning of the translation (x + 7, y - 19).
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Andrew goes to the school by bus.
The probability that the bus is late is 0.1.
If the bus is late, the probability that the Harris is late to the school is 0.8.
If the bus is not late, the probability that Andrew is late to school is 0.05.
i) Draw a tree diagram to show the above information with all the probabilities.
Answer: I am not able to create images such as tree diagrams. But I can explain to you how it could be done.
A tree diagram is a visual representation of the possible outcomes and their probabilities.
The tree diagram to show the above information would have two branches: one representing the event that the bus is late and the other representing the event that the bus is not late.
The first branch, "Bus is Late", would have a probability of 0.1 and would split into two further branches: one representing the event that Andrew is late to school (with a probability of 0.8) and the other representing the event that Andrew is not late to school (with a probability of 0.2).
The second branch, "Bus is not Late", would have a probability of 0.9 and would split into two further branches: one representing the event that Andrew is late to school (with a probability of 0.05) and the other representing the event that Andrew is not late to school (with a probability of 0.95).
This tree diagram will help you to understand the relationship between the different events and their probabilities, as well as the overall probability of Andrew being late to school.
Step-by-step explanation:
Rectangle URST undergoes a dilation centered at the origin. The result is rectangle U'R'S'T'. Which rule describes the dilation? A) (x, y) → (2x, 2y) B) (x, y) → (3x, 3y) C) (x, y) → ( 1 2 x, 1 2 y) D) (x, y) → (− 1 2 x, − 1 2 y)
Option A, (x,y) → (2x,2y) This rule describes an origin-centered stretch with a factor of 2. That is, the image doubles its original size in both the x and y directions.
The new rectangle is similar to the original, but with larger dimensions, so the correct rule is A) (x, y) → (2x, 2y).
In this case, the rule described in option A) (x, y) → (2x, 2y) specifies that the image is twice the size of the original rectangle in both the x and y directions increase. This means that the scale factor is 2. This will result in a similar shape but with larger dimensions. This is the correct rule describing stretching the rectangle URST to the rectangle U'R'S'T'.
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8112 equals 2 ^ 4 times 3 times 13 ^ 2 find the value of the smallest square number that is a mutiple of 8112
The factor 3 does not occur in pair. Thus, ‘3’ is the smallest number by which 8112 should be divided to get a perfect square.
What is the lowest square number?The LCM of 8, 15, and 20 is 120. Prime factors 2, 3, and 5 do not have a pair in this case. To construct a perfect square, 120 must be multiplied by 2 x 3 x 5. As a result, the least square number divisible by 8, 15, and 20 is 3600.
The smallest square matrix is 2 2 2 2 ; there is no theoretical limit to the highest size square matrix, however anything larger than 10 10 10 10 becomes impossible to manage numerically.4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, and 961
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URGENT!! HOMEWORK DUE SOON!!
The difference between two positive numbers is 50. One number is four times the other number. What are the two numbers?
The two missing positive numbers are; 50/3 and 200/3
How to solve algebra word problems?The difference between two positive numbers is 50. Let the two numbers be x and y and as such we have;
x - y = 50 -----(1)
One number is four times the other number. Thus;
x = 4y -----(2)
Put 4y for x in eq 1 to get;
4y - y = 50
3y = 50
y = 50/3
Thus;
x = 4(50/3)
x = 200/3
We conclude that x and y above are the two positive numbers.
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What is the perimeter of parallelogram WXYZ?
W
X
Y
Z
34
34
34
34
60
Answer: The perimeter of a parallelogram is the sum of all its sides.
In this case, since all sides of the parallelogram WXYZ are given as 34 units, the perimeter of parallelogram WXYZ is the sum of all its four sides.
So the perimeter of parallelogram WXYZ = 34 + 34 + 34 + 34 = 136 units
It's important to notice that the given value of perimeter = 60 is not correct.
The perimeter of parallelogram WXYZ is 136 units, not 60 units.
Step-by-step explanation:
find the measure of each interior angle and each exterior angle of a regular 45-gon.
The measure of each interior angle is calculated to be 172° and each exterior angle is calculated to be 8°.
Each interior angle in a polygon can be calculated using the formula, (n - 2) ×180°/n
where, n is the polygon's number of vertices.
So, each exterior angle can be calculated as, 180 - (n - 2) 180°/n
Now, let us put the number of vertices into these formulae,
Each interior angle = (45 - 2)×180°/45 = 43×180°/45 = 172°
Each exterior angle = 180 - (45 - 2) 180°/45 = 8°
So, the interior angle is 172° and the exterior angle is 8°.
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Step by step. Integrated 2 Checkpoint 4 Picture Below
The value of 'x' in the equation 8 - x/x = 3/2 is x equal to [tex]3\frac{1}{5}[/tex].
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, An equation in 8 - x/x = 3/2 fractions.
Now, The LCM of both the denominators is 2x, So we'll multiply each term by 2x.
2(8 - x) = 3x.
16 - 2x = 3x.
- 2x - 3x = - 16.
- 5x = - 16.
5x = 16.
x = 16/5.
x = [tex]3\frac{1}{5}[/tex].
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43 centigrams ? 31.7 milligrams
>. <. =. Please pick a symbol for the question mark
Answer:
43 centigrams > 31.7 milligrams
Step-by-step explanation:
Since 43 centigrams is equal to 430 milligrams, it is therefore greater that 31.7 milligrams.
on a drive from your home to town, you wish to average 64 mph. the distance from your home to town is 88 miles. however, at 44 miles (half way), you find you have averaged only 48 mph. what average speed must you maintain in the remaining distance in order to have an
The average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph is 50.39 mph.
We have to find the average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph.
Let the speed be x.
The total average we want = 33.6 mph
The distance from your home to town = 90 miles
Time = Distance/Speed
Time = 90/33.6
At 45 miles (half way), you find you have averaged only 25.2 mph. So
Time first leg = 45/25.2
Time second leg= 45/x
Now the average speed;
45/25.2 + 45/x = 90/33.6
Subtract 45/25.2 on both side, we get
45/x = 90/33.6 - 45/25.2
After solving the ratio, we get
45/x = 0.893
Multiply by x on both side, we get
0.893x = 45
Divide by 0.893 on both side, we get
x = 45/0.893
x = 50.39 mph
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The complete question is:
On a drive from your home to town, you wish to average 33.6 mph. The distance from your home to town is 90 miles. However, at 45 miles (half way), you find you have averaged only 25.2 mph. What average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph?
a hardware store sells toolboxes. The table shows the types of tools in each toolbox. Becca says that for every 14 tools in a toolbox, there are 2 hammers. Is Becca correct? EXPLAIN
Type l # of tools
Hammer l 2
Plies l 5
Screwdriver l 6
Wrench l 3
Becca is not correct because her probability of 2/14 is not equal to the true experimental probability of 2/16.
How to find the probability of selection?We are given the tools in the box as;
Hammer = 2 nos
Pliers = 5 nos
Screw drivers = 6 nos
Wrench = 3 nos
Thus;
Total number of tools in the box = 2 + 5 + 6 + 3
= 16
Probability of selecting a hammer = 2/16
Now, Becca says that for every 14 tools in a toolbox, there are 2 hammers. This means she is suggesting a probability of 2/14.
This is wrong because it is different from the experimental probability that we got.
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(not
1. If & D is 42, find the measurements of the following angles:
& A-
B-
& C-
4 D-42
E-
4. F-
G-
& H-
If two of the angles of an oblique triangle are equal, the Law of Sines can be used to fill in the remaining lengths or angle measurements.
How do you find the measure of an angle A and B?In the accompanying diagram, two crossing lines are shown, with the angles 1 and 3 being vertical and congruent. In addition, the angles 2 and 4 are vertical and coincide. Vertical angles are two angles that are in opposition to one another, such as D and B in the illustration above.
The sum of the subsequent angles of a ||gm is A+B=180. To view an infinite number of solutions, download the app. Estimating ratios of a particular quantity is what it is. It is created by contrasting a given quantity with the reference unit. These are used to determine something's dimensions, including length, area, perimeter, volume, and amount. Measurement There are formulas for calculating length, area, surface area, volume, circumference, density, mass, etc.
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Complete question:
Which trigonometric law can be used if two of the angles of an oblique triangle are equal?
please help me with this.
Answer:
1: 5/10, square root of 2, 2.5, square root of 25 3: 4.5
Step-by-step explanation:
2.5
5 divided by 10 comes to 0.5
25 square rooted is 5
2 square rooted is 1.4
the biggest number is 5 and the smallest is 0.5
subtract 0.5 from 5 and you get 4.5
In the parallelogram above, AE = 7x+4, BE=15x-12, and DE= 9x. What is the length of BD?
Answer:
BD = 36
Step-by-step explanation:
• the diagonals of a parallelogram bisect each other , so
BE = DE , that is
15x - 12 = 9x ( subtract 9x from both sides )
6x - 12 = 0 ( add 12 to both sides )
6x = 12 ( divide both sides by 6 )
x = 2
Then
BD = BE + ED
= 15x - 12 + 9x
= 24x - 12 ( substitute x = 2 )
= 24(2) - 12
= 48 - 12
= 36
∠TWP≅
∠HGD
∠DGH
∠GHD
∠GDH
Work out the area and perimeter of the shape.
Answer:
area 202.93, perimeter 62.78
Step-by-step explanation:
the triangle:
18² +14² = 520
√520 = 22.8
the curve, without further info, we'll have to assume it's 1/2 circle.
so circumference = 2πr =2 π (14/2) = 14 π = 43.96, 1/2 of it is 21.98
so perimeter of the whole thing is 18+22.8 +21.98 = 62.78
area: 1/2 circle = 1/2 π r² = 1/2 * 3.14*7² = 76.93
triangle area + 1/2 *18*14 = 126
total 202.93
Area of semi circle
πr²/2π(7)²/249π/2Area of Triangle
1/2BH1/2(18)(14)14(9)126Total area
126+49π/2202.9 m²Perimeter
7π+18+14+√18²+14²21.9+22.8+1862.7mhow many 6-digit numbers (leading zeros are allowed) contain exactly one 3, one 4, and one 5 as digits? g
246960 6-digit numbers contain exactly one 3, one 4, and one 5 as digits.
There are a total of 6 digits that make up any of the numbers in 0 to 999999 with the given condition
The total numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
This can be represented as UVWXYZ
Digit 3 can occupy any of the 6 positions
Digit 4 can occupy any of the (6 - 1) positions
Digit 5 can occupy any of the (6 - 2) positions
The remaining 7 digits will occupy the last 3 positions in the following ways:
The first of the 7 digits can be selected from any of 7 ways
The second can be selected from any of 7 ways
The third can be selected from any of 7 ways
So, the total number of selection is:
= 6 × 6 × (6 - 1) × (6 - 2) × 7 × 7 × 7
= 36 × 5 × 4 × 343
= 246960
Therefore there are 246960 numbers.
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Answers for this problem?
Note that the square feet of carpet that will be required for this area is: 42 Square Feet of Carpet.
This is solved using the knowledge of the area of rectangles and right-angled triangles.
What is a right-angled triangle?A right-angled triangle is a triangle in which one of the angles is 90 degrees. The total of the other two angles is 90 degrees.
Note that the area of a right-angled triangle is given as:
A = (½)×b×h square units
Where b is breath and h is height.
Note as well that the area of the rectangle is given as Lx B
To solve the above problem, we must create one more right-angled triangle beside the one already created, then solve for the areas of the respective shapes.
Now that the shape has been divided in to two Right-angled Triangles and one rectangle (See the attached) their respective dimensions are given as follows:
1) Right Angled triangled A
B = 2ft
H = 3ft
Area = 1/2 2 * 3 = 3ft
2) Right-Angled Triangle B
B = 4ft
H = 3ft
A = 1/2 * 4 * 3
A = 6ft
3) Rectangle - C
L = 11ft
B= 3ft
A = 11 * 3 = 33 Ft.
Thus total square feet of outdoor carpet required is:
3 + 6 + 33
= 42 Square Feet of Carpet.
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