A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $20 per linear foot to install and the farmer is not willing to spend more than $7000, find the dimensions for the plot that would enclose the most area. (Enter the dimensions as a comma separated list.)
Answers
Answer:
The dimensions for the plot that would enclose the most area are as follows:
Width = 116.67 ft
Length = 175 ft.
Step-by-step explanation:
Note: Kindly refer to the attached diagram where:
x = Length of the rectangular area
y = Width of the rectangular area.
The fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. This implies that it is $10 per foot. Otherwise, it will be $20 per foot. Since no fencing is needed along the barn, it implies that there is no fence along the northern length.
Since the farmer is not willing to spend more than $7000, we have:
10y + 20x + 20y = 7000
20x + 30y = 7000
Divide through by 20, we have:
x + 1.5y = 350
x = 350 - 1.5y …………………………. (1)
The fenced area is
A = x * y ………………………………….. (2)
Substituting equation (1) into (2), we have:
A = (350 - 1.5y)y
A = 350y - 1.5y^2 ……………. (3)
To maximize A, equation (3) is differentiated with respect to y and equated it to 0 as follows:
That is,
A'(y) = 350 - 3y = 0
Solving for y, we have:
y = 350/3
y = 116.67 ft
Substituting y = 116.67 for y in equation (1), we have:
x = 350 - (1.5 * 116.67)
x = 175ft
Therefore, the dimensions for the plot that would enclose the most area are as follows:
Width = 116.67 ft
Length = 175 ft.
Related Questions
Find cot 0, sec 0, and cos 0, where is the angle shown in the figure. Give exact values, not decimals approximations.
Answers
Answer:
Cot 0 = undefined
Sec0 = cos0 = 1
Step-by-step explanation:
According to trig identity
Cot theta = 1/sin theta
Sec theta = 1/cos theta
Hence
Cot 0 = 1/tan0
Cot 0 = 1/0
Since a/0 is undefined, hence cot 0 will be undefined
Sec 0 = 1/cos 0
Sec0 = 1/1 = 1
Cos 0 = 1
In circle A below, chord BC and diameter DAE intersect at F. If arc CD = 46° and arc BE = 78°, what is m_BFE? D B А
Answers
Given:
Consider the below figure attached with this question.
In circle A below, chord BC and diameter DAE intersect at F.
The arc CD = 46° and arc BE = 78°.
To find:
The measure of angle BFE.
Solution:
According to intersecting chords theorem, if two chords intersect inside the circle then the angle on the intersection is the average of intercepted arcs.
Using intersecting chords theorem, we get
[tex]m\angle BFE=\dfrac{1}{2}(m(arcCD)+m(arcBE))[/tex]
[tex]m\angle BFE=\dfrac{1}{2}(46^\circ+78^\circ)[/tex]
[tex]m\angle BFE=\dfrac{1}{2}(124^\circ)[/tex]
[tex]m\angle BFE=62^\circ[/tex]
Therefore, the measure of angle BFE is 62°.
please help I'm not good with word problems
Answers
Answer:
7 5/8
Step-by-step explanation:
5+2= 7 3/8+2/8=5/8 7+5/8=7 5/8
7 ⅝ miles is the answer
how can i answered this
Answers
Answer:
hope it is helpful to you
Question 8 of 10
The linearized regression equation for an exponential data set is
log y = 0.23x + 0.8, where x is the number of years and y is the population
What is the predicted population when x - 10? Round your answer to the
nearest whole number.
A. 81,963
B. 200
C. 3
D. 1259
.
Answers
Answer:
log y = 3
Step-by-step explanation:
Substitute 10 for x, obtaining the following:
log y = 0.23(10) + 0.8, or
log y = 2.3 + 0.8, or 3.10, or (to the nearest whole number):
log y = 3
An animal shelter has enough pens for x small dogs and y large dogs, and can hold up to 36 dogs at a time. It costs the shelter $12 a week to keep a large dog and $7 a week to keep a small dog. The shelter must keep its weekly costs under $350. Which system of inequalities can be used to represent this situation?
Answers
Answer:
7x+12y<350
Step-by-step explanation:
7 times each small dog (x) plus 12 times each large dog (y) needs to be less than (<) 350
Get brainiest if right!!
Mark has 1.5 times more collectible cards than Jacob. If Mark
gives Jacob 11 cards, they will have the same number of
collectible cards. How many cards do they have?
Answers
Answer:
17.5 cards
Step-by-step explanation:
11 x 1.5 = 16.5
16.5 + 11 = 17.5 cards
Answer:
110
Step-by-step explanation:
Let us take Jack cards as x
Then Mark cards will be 1.5 * x
Mark gives 11 cards to Jack...the equation is
1.5 * x - 11 = x + 11
Adding +11 on both sides
1.5*x -11 + 11 = x + 11 + 11
1.5*x = x + 22
Subtracting x on both sides
1.5*x - x = x + 22 - x
.5*x = 22
x = 22 * 1/.5 = 220/5 = 44
Now go back to the initial equation
Mark >> 1.5 * x = 66
Jack >> 1 * x = 44
Total >> 110.
Find the solution of the system of equations.
6x+2y = 16
20 - 2 = 32
HELP PLSSSS
Answers
From a standard deck of 52 cards (containing the spades, diamonds, clubs, and hearts suites), what is the probability that you draw the three of squares?
Answers
Answer:
1/52
Step-by-step explanation:
theres 52 cards and there is only one three of squares so there is a 1/52 chance
Answer:
3/52
Step-by-step explanation:
What is a statistical error?
Answers
Answer:
Statistical error is the difference between the estimated or approximated value and the true value.
Two Possible Types of Statistical Error
Type I Errors occur when we reject a null hypothesis that is actually true; the probability of this occurring is denoted by alpha (a).
Type II Errors are when we accept a null hypothesis that is actually false; its probability is called beta (b).
Example
You test whether a new drug intervention can alleviate symptoms of an autoimmune disease.
A Type I error happens when you get false positive results: you conclude that the drug intervention improved symptoms when it actually didn’t. These improvements could have arisen from other random factors or measurement errors.
A Type II error happens when you get false negative results: you conclude that the drug intervention didn’t improve symptoms when it actually did. Your study may have missed key indicators of improvements or attributed any improvements to other factors instead.
How to solve the inequality 8x + 10 ≤ 60
Answers
Answer:
x ≤ 6.25
Step-by-step explanation:
8x + 10 ≤ 60
Subtract 10 from both sides
8x ≤ 50
Divide both side by 8
x ≤ 6.25
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
5/6 multiples by 10/11
Answers
Answer:
0.757... (recurring)
Step-by-step explanation:
5 10 50
_ x _ = _
6 11 66
50/66 = 0.757...
:D
Answer:
50/66
Step-by-step explanation:
[tex](\frac{5}{6})(\frac{10}{11}) = \frac{50}{66}[/tex]
Have a great day!
.
6.EE.2c
1. Evaluate the following algebraic expression when x = 3
2xexponet2 + 5x - 10
Answers
Answer:
the answer is 23
Step-by-step explanation:
2x9+15-10
18+15-10
33-10
23
Plz show work, this is a test. NO LINKS!!!
Answers
Answer:
surface area of the square pyramid
=(32×32)+(2×32×20)
=1024+1280
=2304 square feet
Idek how to explain this but please help me
Answers
Answer:
Put 4 in the place of x then you'll get
[tex] \frac{10}{22} [/tex]
Answer:
[tex]\frac{5}{11}[/tex]
Step-by-step explanation:
→ Substitute 4 for x
[tex]\frac{4^{2}-6 }{(3*4)+10} =\frac{16-6}{12+10} =\frac{10}{22} =\frac{5}{11}[/tex]
question : Suppose you have VND 100 million to save orspend. If you lend, you will receive 112 million after a year. Inflation is 14% / year.
a. What is the nominal interest rate you get?
b. What is the real interest rate?
c. Should you save or spend that money?
d. Question (c) how will be answered if inflation is 10% / year, nominal interest rates do not change?
Answers
Answer:
Step-by-step explanation:
a.-2
b.2
c.1
d.-1
e.-6
plz help being timed will mark brainliest
Answers
Answer:
-2 and -1
Step-by-step explanation:
The range would be inside the red half circle and since it is below the horizontal middle line, it is negative. Both -1 and -2 are in the range of the red half circle, both of them are the answer
`Please help me with this 4/5v = - 8/7
Answers
Explanation: Simply both sides of the equation then isolate the variable.
Please help.
A: 4/7
B: 3/7
C:5/7
D: 2/7
Answers
D: 2/7
Step-by-step explanation:
The probability of an event x is how likely the event will occur. It is given as;
P(x) = number of expected outcomes / number of possible outcomes
Given:
Event A = The place is a city.
Therefore,
P(A) is the probability that the event A happens. i.e the probability that a place is a city.
P([tex]A^c[/tex]) is the probability that the event A does not happen. i.e the probability that a place is not a city
Also,
The sum of the probability that an event happens and the probability that the event does not happen is equal to 1. i.e
P(A) + P([tex]A^c[/tex]) = 1
From the table,
P([tex]A^c[/tex]) is found by counting the number of places that does not have a tick on the "is a city" column, then divide the result by the total number of places. i.e
P([tex]A^c[/tex]) = 2 ÷ 7
P([tex]A^c[/tex]) = 2/7
Therefore P([tex]A^c[/tex]) which is the probability that the place is not a city is 2/7
If the mean of a normal distribution is 26, what is the median of the distribution? O A. 22 O B. 14 C. 26 D. 18 SUB
Answers
Answer:
B
Step-by-step explanation:
26 divides by 2 = 13
13+2=14
Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it is 20 cm
How far did Chubby run?
Round your answer to the nearest cm
PLEASE HELP ILL GIVE BRAINLIEST
Answers
9514 1404 393
Answer:
6283 cm
Step-by-step explanation:
The circumference of the wheel is given by ...
C = πd
C = π(20 cm) ≈ 62.83185 cm
100 turns of the wheel will be a distance 100 times this value, or ...
race = 100C = 100(62.83185 cm) = 6283.185 cm
Chubby ran about 6283 cm.
__
Additional comment
To get the required 4 significant figures in the answer, we used the "pi button" on the calculator. Alternatively, you could use the ratio π ≈ 355/113, which is good for 6 significant figures.
A bookstore helppppppoo
Answers
30% fewer mysteries means it has 70% of the quantity of science fiction:
Mysteries = 120 x 0.70 = 84
They have 84 mystery books.
They have 25 % more biographies than mysteries:
Multiply the number of mysteries by 1 + 25%:
84 x 1.25 = 105
They have 105 biographies
I’ll give brainliest
Answers
Answer:
C. C = 3P
Step-by-step explanation:
C = total costs
P = number of popsicles
Unit price of 1 popsicle = $3
To get the total cost of popsicles, we need to multiply the number of popsicles bought by the price of each popsicles
Total cost of popsicles = number of popsicles × unit price
Thus, the question would be written as:
C = 3P
Determine the value of x.
1) 14.75
2)15.25
3)11.92
4)18.56
Answers
6x+10+81.5=180
Combine like terms:
6x+91.5=180
Subtract 91.5 to both sides:
6x=88.5
Divide 6 to both sides:
x=14.75
The answer is 1) 14.75
Hope this helped!
can someone please help me solve?
Answers
Answer:
0.75
Step-by-step explanation:
d = FE = 4
e = DF = 3
f = ED = 5
f/sin(F) = e/sin(E)
5/sin(90) = 3/sin(E)
5 = 3/sin(E)
sin(E) = 3/5 =0.6
E = asin(0.6) = 36.869898... degrees
tan(E) = tan(36.869898...) = 0.75
A union of restaurant and foodservice workers would like to estimate the mean hourly wage, , of foodservice workers in the U.S. The union will choose a random sample of wages and then estimate using the mean of the sample. What is the minimum sample size needed in order for the union to be confident that its estimate is within of
Answers
Answer: the minimum sample size needed = 145
Step-by-step explanation:
Formula for sample size:
[tex]Sample \ size =(\dfrac{z^*\times standard\ deviation}{margin \ of \ error})^2[/tex]
, where z* = Critical z-value
Given: Standard deviation = 2.15
Margin of error = 0.35
Z* for 95% confidence = 1.96
Sample size = [tex](\frac{1.96\times2.15}{0.35})^2[/tex]
[tex]=(12.04)^2\\\\=144.9616\approx145[/tex]
Hence, the minimum sample size needed = 145
Ralph’s classroom measures 12 meters in length. What is the length of the classroom in millimeters?
A. 11,000 mm
B. 12,000 mm
C. 12,500 mm
D. 13,000 mm
Answers
Answer:
b. 12 000 mm
Step-by-step explanation:
multiply by 1 000
(select all the correct answers) Which function are correctly graphed
Answers
9514 1404 393
Answer:
A, D
Step-by-step explanation:
The first and last functions are correctly graphed here. The others suffer from misplaced solid/open dots. When the inequality is < or > and does not include the "or equal to" bar (as in ≤ or ≥), then the corresponding end dot is an open circle.
if the average of 6 numbers is 60, what is their sum?
Answers
Answer:
10
Step-by-step explanation:
The average of a dataset is the mean value of the dataset. It is calculated by dividing the sum of the dataset by the number of items in the dataset. The sum of the 6 numbers is 360.
Given that:
[tex]Average = 60[/tex]
[tex]n = 6[/tex] --- the number of data in the dataset
The average of a dataset is represented as:
[tex]Average = \frac{Sum}{n}[/tex]
Make Sum the subject
[tex]Sum = Average * n[/tex]
This gives:
[tex]Sum = 60 * 6[/tex]
[tex]Sum = 360[/tex]
Hence, the sum of the 6 numbers is 360.
Read more about averages at:
https://brainly.com/question/16480181
Does someone know the answer too: 10 less than s? Ty
Answers
Answer:
s-10
hope this helps
have a good day :)
Step-by-step explanation: