Answers
Answers:
Min cost = $464.76
Dimensions = 11.619 feet by 5.164 feet
Each value mentioned above is approximate.
========================================================
Explanation:
x = horizontal dimension
y = vertical dimension
xy = 60
y = 60/x
The amount of outer fencing needed is 2x+2y feet, aka the perimeter of the largest rectangle.
There are 5 vertical inner fences, so we need 5y feet of inner fencing.
Let's set up the cost function.
Cost = 10*(amount of outer fencing) + 5*(amount of inner fencing)
C = 10*(2x+2y) + 5*(5y)
C = 20x+20y+25y
C = 20x+45y
Plug y = 60/x into the cost function.
C = 20x+45y
C = 20x+45(60/x)
C = 20x + (2700/x)
Then use either calculus or a graphing calculator to find the lowest point on the cost curve is roughly located at (11.619, 464.758)
Use the x value x = 11.619 to find its paired y value
y = 60/x
y = 60/11.619
y = 5.16395558998192
y = 5.164
The entire enclosure should be roughly 11.619 feet by 5.164 feet
The total cost is minimized at approximately $464.76
Answer:
11.619 by 5.164 feet$464.76 minimum costStep-by-step explanation:
You want the dimensions and cost of a rectangular enclosure with an area of 60 square feet and 5 internal partitions. The cost of outside fence is $10 per foot, and the cost of partition fence is $5 per foot.
SetupLet x represent the length of the enclosure, and y the width (and the partition length). Then we have ...
xy = 60
10(2x) = cost fencing for length
10(2y) +5(5y) = cost of fencing for width
We know the cost will be minimized when the cost of fence for the length is equal to the cost of fence for the width.
20x = 45(60/x)
Solutionx² = 135 . . . . . . . . . . . multiply by x/20
x = 3√15 ≈ 11.619 . . . .square root
y = 60/(3√15) = (4/3)√15 ≈ 5.164 . . . . . find y
Then the cost is ...
2(10(2x)) = 120√15 ≈ 464.76 . . . . minimum cost
The enclosure is 11.619 by 5.164 feet, for a cost of $464.76.
Related Questions
The manufacturer's suggested retail price (MSRP) for a particular car is $25020, and it is expected to be worth $14212 in 4 years.
a) Find a linear depreciation function for this car.
(b) Estimate the value of the car 5 years from now.
(c) At what rate is the car depreciating?
Answers
The linear depreciation function is: Depreciation = [tex]\frac{Cost-scrap value}{Estimated life span}[/tex], (b) the value after five years is $11510 and (c) rate of depreciation is 11%
How to calculate depreciation?We should know that depreciation is a loss on a fixed asset over the accounting period that benefited from it.
The given parameters are
Cost of the asset (MSRP)= $25020
Scrap value = $14212
Estimated life span = 4 years
a. Applying the depreciation model
Deprecation = [tex]\frac{Cost of asset - scrap value}{estimated life span}[/tex]
Depreciation = [tex]\frac{25020-14212}{4}[/tex]
depreciation = 10808/4
Dep. = $2702
(b) Note that the accumulated depreciation after 5 years is 2702*5
=$13510
The value of the car after 5 years is $(25020-13510)
=$11510
(c) The rate of depreciation is determined by the model
% dep. = 1-[tex]\sqrt[n]{\frac{s}{c} }[/tex]
where n= number of years
s=scrap value
c cost of the asset
Applying the formular we have
% dep - 1-[tex]\sqrt[5]{\frac{14212}{25020} } = 1-\sqrt[5]{0.5680}[/tex]
% dep= 1-0.89
=0.11*100
=11%
In conclusion, the linear depreciation function is (Cost - Scrap value)÷Number of years, the value of the car 5 years from now is $11510 and the rate of depreciation is 11%
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Problem Situation:
Eric is adding water to a 60-gallons pool.
The pool already has 12 gallons of water, and he wants to fill it to at least 27 gallons. The water flows at a rate of 6 gallons per minute.
How many minutes, x, will it take for Eric to fill the pool with at least 27 gallons of water?
Inequality that represents this situation:
27≤12+6x
To solve the inequality, you can begin by solving the equation as shown.
Drag a diagram to each row of the table to show which number line represents all of the solutions for the inequality and which number line represents all of the solutions for the problem situation.
Answers
The number line which represents all of the solutions for the problem situation is Number line A.
How to solve an inequality?Volume of the pool = 60-gallonsWater in the pool already = 12 gallonsWater left to fill the pool = 27 gallonsWater flow per minute = 6 gallonsNumber of minutes it takes to fill the pool = xThe inequality:
27 ≤ 12 + 6x
substract 12 from both sides
27 - 12 ≤ 6x
15 ≤ 6x
divide both sides by 6
x ≤ 15/6
x ≤ 2.5 minutes
Therefore, the given inequality has the solution x ≤ 2.5 minutes.
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What is 18 1/2 + 6.6 ?
Answers
Answer:
25.1 i think
Step-by-step explanation:
Answer:
25.1
Step-by-step explanation:
Conversion a mixed number 18 1/2 to an improper fraction: 18 1/2 = 18 1/
2= 18 · 2 + 1/2= 36 + 1/2 = 37/2 2. a) Multiply the whole number 18 by the denominator 2. Whole number 18 equally 18 * 2/2 = 36/2 Conversion a decimal number to a fraction: 6.6 = 66/10 = 33/5
10 points! What is the greatest common factor of 32 and 40? * 1 point
2
4
8
16
I have to explain also!
Answers
Answer:
8
Step-by-step explanation:
Question:
What is the greatest common factor of 32 and 40?
Find the factors of 32 and 40:
The factors are all the numbers the we can divide 32 or 40 by, and the result will be a whole number. Example:32/1= 32, 32/2= 16, yet 32/3 = 10.6 not a whole number so 3 is not a factor of 32.
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Find the greatest factor that is common for both 32 and 40 ( the GCF):
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
GCF is 8
7. Sale price of ear-pads after getting 20% discount is Rs 1600. Then the amount of disccount will be A) 400 C) 1620 B) 2000 D) 3200
Answers
Answer: B) 2000
Step-by-step explanation:
Sale Price: The cost following a discount applied to the initial cost.
Cost Price: The cost price is what we pay to purchase a good.
Discount Price : A price that is lower than the usual price.
Cost price equals selling price plus revenue ( when selling price and profit is given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ).
So, The sale price is Rs 1600 after discount.
Discount =20%
Selling price of the skates = Rs 1600
Discount price = 100/80 × 1600= Rs 2000
Discount price = Rs 2000
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two pounds of flour cost 1.20 .How much flour do you get per dollar?
Answers
1.67 pounds flour we get per dollar.
What does pounds mean in weight?Pound, avoirdupois weight unit equivalent to 16 ounces, 7,000 grains, or 0.45359237 kg, and troy and apothecaries' weight unit equal to 12 ounces, 5,760 grains, or 0.3732417216 kg The symbol lb comes from the Roman predecessor of the contemporary pound, the libra.
Given,
Cost for 2 pounds of flour = $ 1.20
Cost per pound of flour = $ 1.20 /2
= $ 0.20
Now for 2 dollar we get flour = 2 pounds.
for 1 dollar we will get flour = 2/1.20 pounds
= 1.6666 pounds
i.e. for 1 dollar we will get flour = 1.67 pounds.
So, 1.67 pounds flour we get per dollar.
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Lexi is creating beaded jewelry to give to her family and friends. For her family, she assembled 5 bracelets and 9 necklaces, using a total of 922 beads. For her friends, she assembled 9 bracelets and 5 necklaces, using a total of 786 beads. Assuming she uses a consistent number of beads for every bracelet and necklace, how many beads is she using for each?
Answers
The number of Lexi is using for every bracelet and necklace include the following:
For her bracelet =329
For her necklace= 593
What is addition?Addition is defined as one of the arithmetic parameters that can be used to combine various data together to arrive at a particular value.
For the family,
bracelet = 5
necklace = 9
Total jewelry made = 14
total number of beads used = 922 beads
The number of beads used for bracelet;
= 5/14×922
= 4610/14
= 329
The number of beads used for necklace;
= 9/14× 922
= 8298/14
=593
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8x - 3y = 12
-8x+3y=5.
Answers
Answer:
No solution
Step-by-step explanation:
Given :
8x - 3y = 12-8x + 3y = 5Because we have two variables that can cancel out, we can solve the system using elimination as we can easily add the two equations, cancel out one of the variables and solve for the other.
8x - 3y = 12
+ -8x + 3y = 5
-----------------------
0x + 0y = 17
Simplifying this we are left with 0 = 17
Because no variables can be defined there are no solutions to the equation.
Graph the solution to this inequality on the number line.
−18≤−3p
Answers
The solution of the inequality expression −18≤−3p is p ≤ 6.
What is inequality?Inequality, A declaration of an order connection between two integers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).
Hence, to solve for −18≤−3p, let's make P the subject of the formula.
-3p ≥ -18
Using -3, divide both sides
⇒ -3p/-3 ≥ -18/ -3
Hence,
⇒ P ≤ 6
See the graph attached.
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A class measured the radius and circumference of various circular objects. Does there appear to be a proportional relationship between the radius and circumference of a circle explain or show ur reasoning.
Answers
The required given relationship between the radius and circumference of the circle is not a proportional relationship.
Given that,
A class measured the radius and circumference of various circular objects.
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here
For the proportional relationship,
the ratio of y / x should be equal but,
18 / 3 ≠ 25/4
Which implies that the relationship is not proportional.
Thus, the required given relationship of the radius and circumference of the circle is not a proportional relationship.
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The current yield on stock invested in Lynx Corporation is 4.2%. The dividend last year was $3.25 per share. What was the selling price of the stock?
Answers
Answer:
Step-by-step explanation:
77.38$
Find the measure of the supplement of a 10° angle.
Answers
Answer:
170°
Step-by-step explanation:
180 - 10 = 170
508x8 = (500+ 8) × 8
(500x)+(8×______)
=. +64
=
Answers
508
Step-by-step explanation:
After walking 1/4. Mile from home, han is 1/3
Answers
The miles that Han will need to get to school is 2/3 miles
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in
From the information, after walking 1/4 mile from home, Han is 1/3 miles to the school.
The miles that she will need more to get to school will be:
= 1/3 × 2
= 2/3
The miles is 2/3 miles.
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Complete question
After walking 1/4 mile from home, han is 1/3 miles to the school. How many miles more will he need to get to school.
A restaurant offers 4 main courses, 3 desserts, and 5 types of juices. What is the total number of items on the menu? 3 12 9 7
Answers
Answer:
749
Step-by-step explanation:
Would you rather........
have your boss pay
you $10,000 a day
for 3 full weeks
including weekends
or
start working with a savings
account with a quarter in it
and your boss double it each
day you work for 3 full weeks
7
the answer
1. Before working, discuss, make a guess and tell us why you'd rather. Be sure to state you reasons for your
choice.
2. Find out how much you would be making after working 7 days in both scenarios,
3. Find out how much you would be making after working 14 days in both scenarios.
S make sure you have
-a title
-your original choice
-an equation for both scenarios
-a graph
-a full table showing from the first day to the end of 3 weeks (day 21)
-picture and/or written explanations of your findings (what surprised you and how were they
ell us how much money you would be making in each scenario at 7 days and 14 days
Answers
1) I would choose option 2 because I will get more money.
What is a quarter ?
Any one of four identical or nearly identical portions of an item, quantity, amount, etc. Also known as one fourth. the number (1/4) is one divided by four.
I would choose option 2, and I did so because I believe that doubling the amount every day for three weeks will give me more money, even if it starts with a quarter, than option 1, which would give me a bonus of $10,000 and $10,000 per day for three weeks.
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What is the approximate value of 27)976?
Answers
Answer:
26352
Step-by-step explanation:
Answer: 36.1481481481. So approximately 36.1
Step-by-step explanation:
A. The result is a repeated number.
The event is { }
(Use a comma to separate answers as needed. Type an ordered pair.)
The probability is [ ]
(Type an integer or a simplified fraction.)
B. The second number is 9 or 11.
The event is { }
(Use a comma to separate answers as needed. Type an ordered pair.)
The probability is [ ]
(Type an integer or a simplified fraction.)
C. The first number is even and the second number is odd.
The event is { }
(Use a comma to separate answers as needed. Type an ordered pair.)
The probability is [ ]
(Type an integer or a simplified fraction.)
Answers
Answer:
Answer:
A. The event is (2,2), (4,4), (6,6), (8,8), (10,10), (12,12) and the probability is 1/6.
B. The event is (2,9), (2,11), (4,9), (4,11), (6,9), (6,11), (8,9), (8,11), (10,9), (10,11), (12,9), (12,11) and the probability is 2/6.
C. The event is (2,9), (2,11), (4,9), (4,11), (6,11), (8,9), (8,11), (10,9), (10,11), (12,9), (12,11) and the probability is 5/6.
toooooooooooo ezzzzzzzzzzyyyty
Step-by-step explanation:
F and H are sets of real numbers defined as follows.
F = { v l v < 4}
H = { v l v ≥ 7}
Write F ∩ H and F ∩ H using interval notation. If the set is empty, write ∅.
Answers
The final interval notation is F ∩ H = [7, 4] & F ∪ H = [-∞, ∞].
What is the interval notation?
A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.
We have,
F and H are sets of real numbers defined as follows.
F = { v l v < 4}
H = { v l v ≥ 7}
F is the set of all real numbers that are less than or equal to 4. H is the set of real numbers greater than 7.
F U H is the union (or combination) of the two sets, so it is the set of all real numbers that are less than equal to 3 or greater than 6:
F ∩ H is the set of real numbers that are in both sets; but since F is less than or equal to 4 and H is greater than 7, there are no numbers that are in both sets. Hence the answer is the empty set, Ø:
F ∩ H = Ø
F ∩ H = [7, 4]
F ∪ H = [-∞, ∞]
Hence, the final interval notation is F ∩ H = [7, 4] & F ∪ H = [-∞, ∞].
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All the gummy machines at a candy factory work at the same rate. Six machines working simultaneously can complete a big order in 22 hours. How many hours would it take to fill the order if the number of working machines decreased by a factor of 2 ?
Answers
It will take 88 hours to fill the order if the number of machines is; deceased by a factor of 4.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that Six machines working simultaneously can complete a big order in 22 hours.
Since we are decreasing the number of machines by a factor of four and all the machines work at the same rate, then we simply going to increase the work hours by a factor of 4.
Therefore Increasing the work hours by a factor of 4 will
22 x 4 = 88 hours
Hence it will take 88 hours to fill the order if the number of machines is deceased by a factor of 4.
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Answer:
44
Step-by-step explanation:
guys lat asnwer was correct too but she just did 4 instead of 2 so just divided her answer by 2 which sums up to 44
HELP please This is a missing assignment know
Answers
Answer: -4.25
Step-by-step explanation:
subtract -6.75 from 2.5 and you have your answer. This works out because 2.5 and -2.5 cancel out and become 0.
PLEASE HELP ASAP. DUE IN A FEW MINS
Answers
5(k + 2)
(5 * k) + (5 * 2)
= 5k + 10
______________________________
8(4 - 1.2h)
(8 * 4) - (8 * 1.2h)
= 32 - 9.6h
______________________________
3(1 - 7m)
(3 * 1) - (3 * 7m)
= 3 - 21m
______________________________
(b + 9)(6)
(6 * b) + (6 * 9)
= 6b + 54
. Model with Math Dani's neighbors paid
her to take care of their bird during their
vacation. Dani spent $4 of her earnings on
an afternoon snack and $16 on a new book.
Afterward, she had at least $8 left. Write
an inequality to represent how much Dani's
neighbors paid her.
Answers
Answer:
x-4-16≥8
x≥28
Step-by-step explanation:
If you use x to begin with the unknown payment. then take away what you know was spent ($4,$16) and you have at least $8 left, x would have to be greater than or equal to 28
solve sin(2x)cos(6x) - cos(2x)sin(6x) = - 0.8 for the smallest positive solution
Answers
The smallest positive solution is 13.28⁰.
What is trigonometry?Trigonometry is a discipline of mathematics dealing with particular angle functions and their application to computations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names.
Given,
sin (2x)cos(6x) - cos(2x)sin(6x) = - 0.8
Let, assume 2x = A and 6X= B
As we know, sin (A-B) = sin A cos B - cos A sin B
Putting the value of 2x and 6x in the given equation, we get
or, sin A cos B - cos A sin B = -0.8
or, sin (A-B) = -0.8
or, sin (2x-6x) = - 0.8
or, sin (-4x) = - 0.8
or, - sin 4x = - 0.8
or, sin 4x = 0.8
Apply sin on both side we get,
or, sin⁻¹ (sin 4x) = sin⁻¹ (0.8)
or, 4x = 53.13
or, x = 13.28⁰
The smallest positive solution is 13.28⁰.
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21. Select the code that should come next in the sequence below.
the sequence question F2, E4, D8, C16
the answer choose the correct answer carefully
A. B24
B. A24
C. B28
D.B32
Answers
Answer:
Step-by-step explanation:
F,E,D,C,B
2,4,8,16,32
B32
What change should Jazmin make in sentence 11?
Answers
Explain how to do x+7>4
Answers
[tex]x > -3[/tex].
Step-by-step explanation:1. Write the expression.[tex]x+7 > 4[/tex]
2. Subtract 7 from both sides of the inequality.[tex]x+7-7 > 4-7\\ \\x > -3[/tex]
3. Express the final result.[tex]x > -3[/tex].
write a mixed number and a fraction greater than 1 for each point on the number line
Answers
Answer:
Step-by-step explanation:
If a fair die is rolled 5 times, what is the probability, to the nearest thousandth, of getting exactly 0 sixes?
Answers
Answer:
below
Step-by-step explanation:
5/6 th chance of NOT rolling a six EACH time (five rolls)
(5/6)^5 = .402
Given a bag of 20 m&m's with 5 red, 4 blue, 2 green, 4 brown and rest are yellow. What is the probability of pulling a green one and then, without replacing it, pulling a blue? Answer in decimal form
Answers
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
The probability of pulling a green one and then, without replacing it, pulling a blue one is 0.021.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Total number of balls = 20
Red = 5
Blue = 4
Green = 2
Brown = 4
Yellow = 5
The probability of pulling a green one.
= 2/20
= 1/10
Number of balls remaining = 20 - 1 = 19
The probability of pulling a blue without replacing the first green one.
= Number of blue balls / Total number of remaining balls
= 4/19
Now,
The probability of pulling a green one and then, without replacing it, pulling a blue one.
= 1/10 x 4/19
= 4/190
= 2/95
= 0.021
Thus,
The probability of pulling a green one and then, without replacing it, pulling a blue one is 0.021.
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