The dimensions of the plot that would enclose the most area are (width, length) = (125/6, 125/3).
We have,
Let's assume that the barn wall is located on the south side of the rectangular plot, and the fencing is required on the remaining three sides (east, north, and west).
Let's denote the width of the plot as x and the length of the plot as y.
Then, the length of fencing required can be expressed as:
L = x + y + x/2
where x/2 is the length of the shared fencing with the neighbor.
The cost of fencing can be expressed as:
C = 24L
Substituting the value of L, we get:
C = 24(x + y + x/2)
Since the farmer is not willing to spend more than $6000, we have:
24(x + y + x/2) ≤ 6000
Simplifying this inequality, we get:
3x + 4y ≤ 500
Now, we need to maximize the area of the rectangular plot, which is given by:
A = xy
Using the inequality constraint, we can express y in terms of x as:
y ≤ (500 - 3x)/4
Substituting this value of y in the expression for A, we get:
A = x((500 - 3x)/4)
Simplifying this expression, we get:
A = (125/4)x - (3/4)x^2
To find the value of x that maximizes A, we can take the derivative of A with respect to x and set it equal to zero:
dA/dx = 125/4 - (3/2)x = 0
Solving for x, we get:
x = 125/6
Substituting this value of x in the expression for y, we get:
y = (500 - 3(125/6))/4 = 125/3
Therefore,
The dimensions of the plot that would enclose the most area are (width, length) = (125/6, 125/3).
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30 POINTS ANSWER FOR BRAINLIST
Solve m^2 − 6m = 3. Use the Quadratic Formula. Leave your answers as simplified radicals.
Answer:
To solve m^2 - 6m = 3 using the quadratic formula, we first need to put the equation in standard form, which is ax^2 + bx + c = 0.
m^2 - 6m - 3 = 0
Now we can identify a, b, and c:
a = 1, b = -6, c = -3
Next, we can plug these values into the quadratic formula:
m = (-b ± sqrt(b^2 - 4ac)) / 2a
m = (-(-6) ± sqrt((-6)^2 - 4(1)(-3))) / 2(1)
m = (6 ± sqrt(48)) / 2
Simplifying the square root of 48, we get:
m = (6 ± 4sqrt(3)) / 2
Now we can simplify by factoring out a 2 from the numerator:
m = 3 ± 2sqrt(3)
So the solutions to the equation are:
m = 3 + 2sqrt(3) or m = 3 - 2sqrt(3)
Step-by-step explanation:
Answer: 3±2√3
Step-by-step explanation:
see image for explanation
Let me know if you more explanation with simplifying the root. That is a whole lesson in itself.
An appropriate tip for a waiter at a restaurant is at least 15%. For a tab of $20, how much money should be left, including tip?
An appropriate tip for a waiter at a restaurant is at least 15% of the total bill. For a tab of $20, the tip would be:
Tip amount = 15% of $20
Tip amount = 0.15 x $20
Tip amount = $3
Therefore, the total amount of money that should be left, including tip, is:
$20 (tab) + $3 (tip) = $23.
Triangle ABC shown below has m∠B=36∘, a=5, and c=13. Find the area of the triangle.
Answer: 19.1 is correct
Step-by-step explanation:
where a and c are the lengths of two sides of the triangle and C is the angle between them. To use this formula, we need to find side b and angle A.
We can use the Law of Cosines to find side b:
Michael checked several websites and stores around town for the television he wanted to purchase. He saw eight different prices: $273 $267 $276 $297 $264 $294 $264 $269 What is the mean, median, and mode of this data set?
The mean is 270.75 and the median is 271. While there is no single mode, then we conclude that our mode is 264 and 294 respectively.
Understanding how to calculate mean, median, modeBy definition:
Mean is the sum of all the numbers in the set divided by the total number of numbers.
Median is the middle value in the set when the numbers are arranged in order.
Mode is the number that appears most frequently in the set.
If we re-arrange the data given in ascending order, we have:
264 264 267 269 273 276 294 297
To calculate Mean:
Add up all the numbers and divide by the total number of numbers:
Mean = (264 + 264 + 267 + 269 + 273 + 276 + 294 + 297) / 8
Mean = 270.75
To calculate Median:
We need to find the middle number in the set. Since there are 8 numbers in the set, the median is the average of the 4th and 5th numbers:
Median = (269 + 273) / 2
Median = 271
To calculate Mode:
We need to determine which number appears most frequently in the set. In this case, there are two numbers that appear twice (264 and 294), and the rest of the numbers appear only once. Therefore, there is no single mode for this data set.
Mode = 264 and 294
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A manufacturer cuts a piece of metal for a microscope. The resulting piece of metal can be
represented in a coordinate plane by a triangle with vertices A (8,8), B(5, 3), and C(11,3)
. One unit in the coordinate plane represents one millimeter.
Prove that AABC is isosceles.
Find the exact length of each side.
AB =
BC =
AC =
We can actually see here that the triangle ABC is an isosceles triangle. This is because two sides of the triangle are equal.
What is an isosceles triangle?An isosceles triangle is actually a geometric shape having three sides, two of which are equal in length. Consequently, two of the angles that are across from those sides are also equal.
In order to prove that the triangle is an isosceles triangle, we will find the following:
Distance between vertices A and B:
AB = √((8-5)² + (8-3)²) = √(3² + 5²) = √34 = 5.83mm
Then, we also find the distance between vertices B and C:
BC = √((11-5)² + (3-3)²) = 6mm
Finally, we find the distance between vertices A and C:
AC = √((11-8)² + (3-8)²) = √(3² + 5²) = √34 = 5.83mm
Thus, we see here that AB and AC are actually equal which makes the triangle an isosceles.
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A company has recently been hiring new employees. Today the company has 33% more employees than it did a year ago. If there are currently
66,500 employees, how many employees did the company have a year ago?
employees
If the company has 33% more employees than it did a year ago and there are currently 66,500 employees, the number of employees the company had a year ago was proportionately, 50,000 employees.
What is proportion?Proportion refers to the ratio of one quantity or value compared to another.
Proportions are fractional values, representing using fractions, decimals, or percentages.
The current population of a company's employees = 66,500
The percentage increase in the population from last year's = 33%
Proportionately, last year's population = 100%, while this year's population is 133% (100 + 33).
If 66,500 = 133% (1.33), then 100% = 50,000 (66,500 ÷ 1.33)
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Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run?
A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by.
Select all that apply.
You know the difference in the distances the boys ran, so this is a subtraction problem.
You are finding the total distance the boys ran, so this is an addition problem.
Dean ran part of the distance Sam ran, so this is a multiplication problem.
The correct equation is s + 2.3 = 6.8.
The correct equation is s – 2.3 = 6.8.
The correct equation is 2.3s = 6.8.
Answer:
A,E
Step-by-step explanation:
Operation: Minus
To find how far Sam ran, we need to subtract 2.3 from Dean's distance of 6.8 km.
6.8 km - 2.3 km = 4.5 km
Therefore, Sam ran 4.5 km, since Dean ran 2.3 km fewer than Sam.
Answer:
a and e
Step-by-step explanation:
got it right on homework
The histogram displays the ages of 50 randomly selected users of an online music service. Based on the data, if the service has 25,000 users, how many of them are 30 and older?
The number of users that are 30 and older is 10,500.
We have,
From the histogram,
The number of users that are 30 and older.
= 7 + 9 + 3 + 2
= 21
Now,
The percentage of 30 and older users.
= 21/50 x 100
= 21 x 2
= 42%
Now,
Total users = 25,000
So,
The percentage of 30 and older users.
= 42% of 25,000
= 42/100 x 25,000
= 42 x 250
= 10500
Thus,
The number of users that are 30 and older is 10,500.
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Question 2
Plot the coordinates on the number line provided and then find the coordinate of the indicated point
on a number line that partitions the segment into the given ratio.
(The numbers are not aligned properly to the marks, so redraw the number line.)
A is at -2 and B is at 14. Find the point, T, so that T is three-fourths of the distance from A to B.
-10
5
10
Note that in the line graph presented, 3/4 the distance from A to B is 12, thus, t = 12.
what is the explanation about this?
Given:
A (- 2 , 0) and B(14, 0)
Using distance formula, we can determine the distance between coordinates given:
d = √ ( (x2 - x1)² + ( y2 - y1) ²)
In this case, x1 = -2 y1 = 0,
x2 = 14, and y2 = 0.
Substituting these values into the formula, we get:
d = √( (14 - (-2 ) ) ² + (0 - 0) ²)
= √((16)² + (0)² )
= √(256)
= 16
The distanc between the points (-2,0) and (14,0) is 16 units.
Recall that we need to find the position of t which is 3/4 the distance between A and B.
That is:
3/4 x 16
t = 12.
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Each week, Nursen saves $5 and shares $3.75. She also spends $4.95 on bus fare to get home from music lessons. This week she earned $24 babysitting. How much money does Nursen have left that she can spend?
Answer: In one week, Nursen saves $5 and shares $3.75, so she has $5 + $3.75 = $8.75 per week.
She spends $4.95 on bus fare, so she has $8.75 - $4.95 = $3.80 per week to spend.
This week, Nursen earned $24 babysitting, so she has an additional $24 to spend.
Therefore, Nursen has $3.80 + $24 = $27.80 to spend.
Step-by-step explanation:
Why is it essential to maximize the volume for a fixed surface area for cost and material waste?
It is essential to maximize the volume for a fixed surface area for cost and material waste.
Because it can help to optimize the efficiency of material usage and minimize the cost of production.
In many manufacturing and construction processes, the cost of materials is a significant expense.
By maximizing the volume of an object for a fixed surface area, we can reduce the amount of material needed to construct the object.
This means that we can save money on material costs and reduce waste by using fewer materials overall.
In addition, minimizing the surface area of an object for a fixed volume can also help to reduce production costs.
This is because the surface area of an object is often a factor in determining the time and labor required to produce it.
By minimizing the surface area, we can reduce the amount of time and labor needed to produce the object.
Which can help to reduce production costs.
Therefore, maximizing volume for fixed surface area is an essential consideration in many manufacturing and construction processes.
It help to optimize material usage, minimize waste, and reduce production costs.
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Help please!! I need help!!! I will mark you brainlest!
Answer:
2(4.5) + (1/2)(4)(2) = 9 + 4 = 13 square feet
PLEASE HELP ( WILL GIVE BRAINLIEST)
The amount of money Laurie would pay to have the pond cleaned is equal to $3,161.85.
How to calculate the volume of a hemisphere?In Mathematics and Geometry, the volume of a hemisphere can be calculated by using the following mathematical equation (formula):
Volume of a hemisphere = 2/3 × πr³
Where:
r represents the radius.
Note: Radius = diameter/2 = 13/2 = 6.5 feet.
By substituting the given parameters into the formula for the volume of a hemisphere, we have the following;
Volume of a hemisphere = 2/3 × 3.14 × (6.5)³
Volume of a hemisphere = 574.881 ft³
Cost = 5.50 × 574.881 ft³
Cost = $3,161.85
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Select the correct answer. What is the solution to 4|x − 3| + 1 = 1? A. x = 3 B. x = 3 or x = 4 C. x = 3 or x = 6 D. No solutions exist.
Answer:
a
Step-by-step explanation:
Please help its due soon
The ratio of sec θ is determined as 5/3.
option A.
What is the ratio of secθ?The ratio is sec θ is calculated by applying the following method;
sec θ = 1/cosθ
Given that tanθ = -4/3 = oppo/adjacent
The hypotenuse side is calculated by applying Pythagoras theorem as shown below;
h = √ 4² + 3²
h = 5
The ratio of sec θ is calculated as follows;
sec θ = 1/cosθ
1/cosθ = 1/(3/5)
1/cosθ = 5/3
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What is 3/10 + 1/4 + 4/5 enter your answer in the box as a mixed number in simplest form
Answer:
[tex]1 \frac{7}{20} [/tex]
Step-by-step explanation:
Well you should find a common denominator for 10, 4 and 5 first to be able to mix them. Let's take 20 because it's the smallest number we can convert 10, and 4 and 5 to.
So
[tex] \frac{3 \times 2}{10 \times 2} + \frac{1 \times 5}{4 \times 5} + \frac{4 \times 4}{5 \times 4} [/tex]
And you get
6/20 + 5/20 + 16/20 (now you can add them because they all have 20 as denominator) so = 27/20 = 1 7/20
A 138 foot antenna is on top of the top of a tall building. From a point on the ground, the angle of elevation to the top of the antenna is 30.5ﾟ while the angle of elevation to the bottom of of the antenna from the same point is 23.5ﾟHow tall is the building
Answer:
289
Step-by-step explanation:
Let's call the height of the building "h" and the distance from the point on the ground to the base of the building "d".
From the point on the ground, the distance to the top of the antenna is d + 138, and the distance to the bottom of the antenna is d.
Using trigonometry, we can set up two equations:
tan(30.5°) = (d + 138) / h (1)
tan(23.5°) = d / h (2)
We can solve equation (2) for d:
d = h tan(23.5°)
Substituting this into equation (1), we get:
tan(30.5°) = (h tan(23.5°) + 138) / h
Simplifying:
tan(30.5°) = tan(23.5°) + 138/h
tan(30.5°) - tan(23.5°) = 138/h
h = 138 / (tan(30.5°) - tan(23.5°)) ≈ 289.12 feet
Therefore, the height of the building is approximately 289.12 feet.
Find the values of x and y
Answer:
x = 8.4
y = 23.6
Step-by-step explanation:
tan31 = x/14
x = tan31(14) = 8.412
y² = (8.412)² + (22)² = 554.7626
y = √554.7626 = 23.55
Abdoulaye is planning to drive from City X to City Y. The scale drawing below shows the distance between the two cities with a scale of 1 inch = 5 miles. City X and City Y are 11/2 between
City X ---------- 11/2 ------------- City Y
What is the actual distance between the two cities?
The actual distance between the two cities is [tex]7\frac{1}{2}[/tex] miles .
What is the actual distance?A scale drawing is the reduced version of a larger image. The scale drawing is reduced at a constant proportion to the original image using a scale. An example of a scale drawing is a map of the city.
Actual distance between the cities can be determined by multiplying the distance in the scale drawing by the scale.
Actual distance = 1[tex]\frac{1}{2}[/tex] x 5
= [tex]\frac{3}{2}[/tex] x 5 = [tex]\frac{15}{2}[/tex] = [tex]7\frac{1}{2}[/tex] miles
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Do the following using Matlab: Generate 10 numbers between 1 and 6, calculate the mean. Generate 100 numbers between 1 and 6. calculate the mean. Generate 1000 numbers between 1 and 6, calculate the mean. There is a command in Matlab to generate numbers. Do not include the numbers when you submit the project. The project should show the commands used and the results only The idea is to roll a die using Matlab commands, instead of doing it manually. Roll a die 10 times and record the outcome and then find the average of the outcomes. Then compare the means for the cases of 10, 100 & 1000. On page 2 of lecture 10, we found that the mean of rolling a die to be 3.5. Therefore, your answer will be close to 3.5 every time you repeat the experiment for larger numbers.
We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.
We have,
To generate numbers between 1 and 6 in Matlab, we can use the "randi" command.
To generate 10 numbers, we can use:
```matlab
numbers10 = randi([1, 6], [1, 10]);
mean10 = mean(numbers10);
disp(mean10);
```
To generate 100 numbers, we can use:
```matlab
numbers100 = randi([1, 6], [1, 100]);
mean100 = mean(numbers100);
disp(mean100);
```
To generate 1000 numbers, we can use:
```matlab
numbers1000 = randi([1, 6], [1, 1000]);
mean1000 = mean(numbers1000);
disp(mean1000);
```
After running these commands, we will get the means for generating 10, 100, and 1000 numbers between 1 and 6.
As mentioned in the question, the mean of rolling a die is 3.5.
Therefore,
We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.
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Hurry up please time limit
State the domain and range and tell if the graph is a function yes or no?
What’s the domain and range ?
Answer:No, X=-3, yly =-4,0,4
Step-by-step explanation:
∠A and ∠B are vertical angles. If m ∠ A=(2x−2) ∘ and B=(3x−15) ∘ , then find the value of x
The value of x is 13°
What are Vertical Angles?When two lines intersect, four angles are formed. There are two pairs of nonadjacent angles. These pairs are called vertical angles.
In a coordinate plane, a line parallel to the Y-axis is called Vertical Line. It is a straight line which goes from top to bottom and bottom to top. Any point in this line will have the same value for the x-coordinate.
We have:
The angles are:
m ∠ A=(2x−2) ∘ and ∠ B=(3x−15) ∘
We have to find the value of x
Now, We know that :
m ∠A = m ∠B (Def. of Vertical Angles)
(2x−2) = (3x−15)
Combine the like terms:
2x - 3x = -15 + 2
-x = -13
x = 13
The value of x is 13°
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Male 16 15 2 33
Female 14 11 18 43
Total 30 26 20 76
If one student is chosen at random,
Find the probability that the student was female:
Find the probability that the student was female AND got a "C":
Find the probability that the student was female OR got a "C":
If one student is chosen at random, find the probability that the student was female GIVEN they got a 'C':
a) The probability that the student was female is 43/76
b) The probability that the student was female AND got a "C" is 9/38
c) The probability that the student was female OR got a "C" is 45/76
We have,
A B C
Male 16 15 2 33
Female 14 11 18 43
Total 30 26 20 76
a) The probability that the student was female
= 43/76
b) The probability that the student was female AND got a "C"
= 18/76
= 9/38
c) The probability that the student was female OR got a "C"
= 43 /76 + 20/76 - 18/76
= 45/76
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In this circle, mQR = 72°.
What is m/QPR?
A. 18°
B. 24°
C 36°
D. 72°
Please show work or give an explanation please
Answer:
< QPR = 36
Step-by-step explanation:
Inscribed Angle = 1/2 Intercepted Arc
< QPR = 1/2 ( 72)
< QPR = 36
Which number line shows a graph of the inequality x < 6
The number line that shows the inequality x < 6 is given by the following option:
Option D.
What are the inequality symbols?The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:
> x: the amount is greater than x -> the number is to the right of x with an open dot at the number line. -> points above the dashed horizontal line y = x on the coordinate plane.< x: the amount is less than x. -> the number is to the left of x with an open dot at the number line. -> points below the dashed horizontal line y = x on the coordinate plane.≥ x: the amount is at least x. -> the number is to the right of x with a closed dot at the number line. -> points above the solid vertical line y = x on the coordinate plane.≤ the amount is at most x. -> the number is to the left of x with a closed dot at the number line. -> points above the dashed vertical line y = x on the coordinate plane.The inequality for this problem is given as follows:
x < 6.
Which is composed by the numbers to the left of x = 6, with an open circle, due to the open interval.
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Find the missing angle
Answer:
I Think 62°
Step-by-step explanation:
Write in terms of x and y only.
Result:
sin(tan⁻¹(x) - tan⁻¹(y)) in terms of x and y only = (x - y) / (1 + xy).
How do we express the equation in term of x and y?For us to write the expression, we shall use this formular formula:
tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))
where:
a = tan⁻¹(x)
b = tan⁻¹(y)
Next, we have:
tan(tan⁻¹(x) - tan⁻¹(y)) = (tan(tan⁻¹(x)) - tan(tan⁻¹(y))) / (1 + tan(tan⁻¹(x))tan(tan⁻¹(y)))
= (x - y) / (1 + xy)
From both sides, we have sine:
sin(tan⁻¹(x) - tan⁻¹(y)) = sin(tan(x - y / 1 + xy))
So, sin(tan⁻¹(x) - tan⁻¹(y))
= sin(tan⁻¹(x) - tan⁻¹(y))
= (x - y) / (1 + xy) in terms of x and y.
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I REALLY NEED THIS IMMEDIATELY PLEASE HELP !
(Use The Image)
Patrica is building a garden in her backyard that is shaped like a triangle. She has already built two sides of the garden and they have lengths of 6 feet and 7 feet.
Answer:
Step-by-step explanation:
The third side of Patricia's garden should be approximately 10.64 feet long.
To determine the length of the third side of Patricia's garden, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we have two known side lengths (6 feet and 7 feet) and the angle between them (110 degrees).
The Law of Cosines states that for a triangle with side lengths a, b, and c, and angle C opposite side c:
c² = a² + b² - 2ab*cos(C)
We want to find the length of the third side, so let's call it c. Plugging in the known values:
c² = 6² + 7 - 267*cos(110°)
Simplifying the equation:
c² = 36 + 49 - 84*cos(110°)
Now, we can calculate the value of cos(110°) using a calculator or trigonometric tables. Once we have that value, we can substitute it back into the equation to find c². Taking the square root of c² will give us the length of the third side.
Note: The value of cos(110°) is approximately -0.342.
c² = 36 + 49 - 84*(-0.342)
c² ≈ 36 + 49 + 28.248
c^2 ≈ 113.248
Taking the square root:
c ≈ √113.248
c ≈ 10.64
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PLEASEEEE HELP MEMEMEMEM PLESSEEE I WILL GIVE U BRAINLIST QUICK
The numeric value of the function graphed is given as follows:
f(-8) = 6.
How to obtain the numeric value of the function?The expression for the numeric value of the function in this problem is given as follows:
f(-8).
This means that the input is given as follows:
x = -8.
Passing a vertical line through x = -8, the value of y in which the vertical line crosses the graph is given as follows:
y = 6.
Hence the numeric value is given as follows:
f(-8) = 6.
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A circular arc of length 9 feet subtends a central angle of 65 degrees. Find the radius
of the circle in feet.
The radius of the circle is approximately 7.9 feet.
What is the radius of the circle?The arc length formula (if θ is in degrees) is expressed as:
s = 2πr × (θ/360°)
Where r is radius and θ is the central angle subtended by the arc.
Given that:
Arc length s = 9ft
Central angle subtended by the arc = 65°
Radius r = ?
Plug the given values into the above formula.
s = 2πr × (θ/360°)
9ft = 2 × 3.14 × r × (65/360°)
r = 9ft / 1.133888
r = 7.9 ft
Therefore, the radius is 7.9 ft.
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