you are to construct an open rectangular box from 12 ft2 of material. what dimensions will result in a box of maximum volume?
Answers
The dimensions of the open rectangular box that will result in a box of maximum volume using 12 ft^2 of material are 2 ft x 2 ft x unlimited height.
To find the dimensions of the open rectangular box that will result in a box of maximum volume using 12 ft^2 of material, we need to use optimization techniques.
Let's assume that the box has length L, width W, and height H, where L and W are the dimensions of the base and H is the height of the box. Since we are given that the box is open, we can assume that one of the dimensions, say H, is unlimited.
The surface area of the box is given by:
SA = LW + 2LH + 2WH
Since we are given that the total amount of material used is 12 ft^2, we can write:
SA = 12
Substituting H with an unlimited value, we can write the volume of the box as:
V = LW H
To find the dimensions that will result in a box of maximum volume, we can use the method of Lagrange multipliers. We need to maximize the volume function V subject to the constraint that the surface area SA is constant, which gives us the following function to maximize:
F(L, W, H, λ) = LW H + λ(12 - LW - 2LH - 2WH)
We take the partial derivative of F with respect to L, W, H, and λ, and set each to zero:
∂F/∂L = WH - λ(2H + W) = 0
∂F/∂W = LH - λ(2H + L) = 0
∂F/∂H = LW - λ(2L + 2W) = 0
∂F/∂λ = 12 - LW - 2LH - 2WH = 0
Solving these equations simultaneously, we get:
L = W = 2H
Substituting these values into the equation for surface area, we get:
SA = LW + 2LH + 2WH = 12
Substituting L = W = 2H into this equation, we get:
12H + 4H^2 = 12
Simplifying and solving for H, we get:
H = 1 ft
Substituting this value of H into L = W = 2H, we get:
L = W = 2 ft
Therefore, the dimensions of the open rectangular box that will result in a box of maximum volume using 12 ft^2 of material are 2 ft x 2 ft x unlimited height.
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Related Questions
Please answer number 11.
Answers
Where the above parameters are given, Mikayla will need about 5,036.64 in² of paint to finish her project. Note that this is about surface area.
How to go about thisa) determine the surface area of each rectangular prism. The formula for this is:
SA = 2lw + 2lh + 2wh
Where I is the lenght, w is the width, and h is theheight.
For each of the prisms we have:
l = 3ft -= 36in
w = 2.5 ft = 30 inches
h = 3 inches
The surface area of the rectangular prism is:
= 2 (36 )(30) + 2 (36) ( 3) + 2 (30 ) (3)
= 2160 + 216 + 180
= 2556in²
B) Now it's time to compute the surface area of the culindrical hole using the formula:
SA = πdh
Recall that π = 3.14
Since d = 4 inches and
h = 3 inches
The surface area (SA) of the cylindrical hole is:
3.14 x 4 x 3
= 37.68in²
Thus, total surface area to be painted is:
2(2556 - 37.68)
= 2(2518.32)
= 5036.64in²
Thus, the assertion is correct that the total amount of paint required is approximately 5037 in² of paint.
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An elevator has a placard stating that the maximum capacity is 1884 lb-12 passengers. So, 12 adult male passengers can have a mean weight of up to 1884/12=157 pounds. If the elevator is loaded with 12 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 157 lb. (Assume that weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.) Does this elevator appear to be safe? BICICIE The probability the elevator is overloaded is (Round to four decimal places as needed) Does this elevator appear to be safe? OA. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity OB. No, 12 randomly selected people will never be under the weight limit. OC. Yes, there is a good chance that 12 randomly selected people will not exceed the elevator capacity OD. Yes, 12 randomly selected adult male passengers will always be under the weight limit. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275. Round to four decimal places. www OA. 0.4332 OB. 0.9332 OC. 0.5000 OD. 0.0668 Find the value of the linear correlation coefficient r. The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Cost 9 2 3 5 9 10-> 4 2 68 67 Number 52 55 85 A. 0.235 OB. 0.708 OC. 0.246 OD. -0.071 86 83 73
Answers
The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.
Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:
Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.
We can write as below:
Maximum capacity per person=1884/12=157lb.
And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586
Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.
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ANSWER ASAP I GIVE BIG BRAIN; Which table represents a linear funcion?
Answers
Answer: on the screenshot
Step-by-step explanation: linear function should go down or up(straight line)
Find the area of the parallelogram.
Answers
Answer:
35 cm^2
Step-by-step explanation:
a = bh
a = (7)(5)
a = 35 cm^2
Find x and Angle EFG.
Answers
The volume of Solid A is 28m^3 and the volume of solid B is 1,792m^3. If the solids are similar what is the ratio of the surface are of solid A to the surface area of solid B
Answers
The ratio of the surface area of solid A to the surface area of solid B is 1/64
How to calculate the ratio of similar shapesThe volume is the amount of substance an object contains
Given the following parameters
Volume of solid A = 28m^3
Volume of solid B = 1,792m^3.
Calculate the ratio of the surface areaRatio = A/B
Ratio = 28/1792
Ratio = 1/64
Hence the ratio of the surface area of solid A to the surface area of solid B is 1/64
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(1 ÷ 2 3 ⁄ 4 ) + (1 ÷ 3 1 ⁄ 2 ) = _____.
Answers
Answer:
50/77
Step-by-step explanation:
(1÷2 3/4)+(1÷3 1/2)
2 3/4 is same as 11/44
1/2 is same as 7/2
so to divide fraction you have to flip the second number and multiply
so 1 times 4/11=4/11
and 1 times 2/7=2/7
4/11 +2/7=28/77+22/77=50/77
Jane and Abigail measured the lengths of their bedrooms. Jane's was 11.75 feet and Abigail's was 14.5 feet. How much longer was Abigail's room?
Answers
Abigail's room is 2.75 feet longer than Jane's
How to determine how much longer is the length?The lengths of the rooms are given as
Length of Jane's room = 11.75 feet
Length of Abigail's room = 14.5 feet
The length where the length of Abigail's room is greater or longer than Jane's is calculated using
Length = Length of Abigail's room - Length of Jane's room
Substitute the known values in the above equation
So, we have
Length = 14.5 feet - 11.75 feet
Evaluate the difference
Length = 2.75 feet
Hence, the length is 2.75 feet longer
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I need help on this ASAP!! THANKS!
Answers
Use the pythagorean theorem.
\(a^{2} +b^{2} =c^{2}\)
which we can quickly type as a^2+b^2=c^2. (The ^2 means squared.)
C is the hypotenuse, the longest length. It doesn't matter what you call a and b; just use the two shorter lengths.
So we're going to take each set of numbers, and if the square of the hypotenuse (c, the longest side) is equal to the sum of the squares of each length (the other two sides, a and b), then it's a right triangle. If it doesn't equal, then it's NOT a right triangle.
3,4,5:
3^2+4^2 = 9+16 = 25 = 5^2, so this IS a right triangle.
5, 12, 13:
5^2+12^2 = 25+144 = 169 = 13^2, so this IS a right triangle.
6,8,12:
6^2+8^2= 36+64 = 100. 12^2 = 144. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.
6, 9, 12:
6^2+ 9^2 = 36+81 = 117. 12^2 = 144. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.
8, 13, 26:
8^2 + 13^2 = 64+ 169 = 233. 26^2 = 676. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.
8, 15, 17:
8^2+ 15^2 = 64 + 225 = 289. 17^2 = 289, so this IS a right triangle.
9, 12, 14:
9^2 + 12^2 = 81+144 = 225. 14^2 = 196. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.
3, 8, 19:
3^2 + 8^2 = 9 + 64 = 73. 19^2 = 361. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.
0.5, 6, 3:
Oh, your teacher is trying to trick you bc the hypotenuse has been the last number with every other problem! 6 is the longest and that's your hypotenuse (c).
0.5^2 + 6^2 = 0.25 + 36 = 36.25. 6^2 = 36. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.
helppppppppppppppppppppppppppppppppppppp
Answers
Answer:
D. \(x^2 - 4x - 12.\)Step-by-step explanation:
Given expression:
(x - 6)(x + 2) =Solve to get the power:
(x - 6)(x + 2)= (x - 6)\(x^2\)= \(x^2 - 4x - 12\).Your answer is D.
99% of all confidence intervals with a 99% confidence level should contain the population parameter of interest. true or false
Answers
The statement that 99% of all confidence intervals with a 99% confidence level should contain the population parameter of interest is false.
A confidence interval (CI) is essentially a range of estimates for an unknown parameter in frequentist statistics. The most frequent confidence level is 95%, but other levels, such 90% or 99%, are infrequently used for generating confidence intervals.
The confidence level is a measurement of the proportion of long-term associated CIs that include the parameter's true value. This is closely related to the moment-based estimate approach.
In a straightforward illustration, when the population mean is the quantity that needs to be estimated, the sample mean is a straightforward estimate. The population variance can also be calculated using the sample variance. Using the sample mean and the true mean's probability.
Hence we can generally infer that the given statement is false.
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Find the distance (8,-7) (-4,-2)
Answers
Distance = 13 units
Point A: (8, -7)
Point B: (-4, -2)
\(\sqrt{(8 + 4)^{2} + (-7 + 2)^{2} }\)
\(\sqrt{(12)^{2} + (-5)^{2} }\)
\(\sqrt{144 + 25 }\)
\(\sqrt{169}\)
\(13\)
Answer:
\(\boxed {d = 13}\)
Step-by-step explanation:
Use the Distance Formula to help you find the distance between the two following points:
\(d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\)
(where \((x_{1}, y_{1})\) represents the first point and \((x_{2}, y_{2})\) represents the second point)
-Apply the two following onto the formula:
\((x_{1}, y_{1}) = (8, -7)\)
\((x_{2}, y_{2}) = (-4, -2)\)
\(d = \sqrt{(-4 - 8)^{2} + (-2 + 7)^{2}}\)
-Solve for the distance:
\(d = \sqrt{(-4 - 8)^{2} + (-2 + 7)^{2}}\)
\(d = \sqrt{(-12)^{2} + 5^{2}}\)
\(d = \sqrt{144 + 25}\)
\(d = \sqrt{169}\)
\(\boxed {d = 13}\)
Therefore, the distance is \(13\).
After a 15% increase January receives a new salary of R23000. What was his salary before the increase
Answers
Answer:
His salory before Increse is 17250
Old salary x 1.15 = R23000
Old salary = 23000 / 1.15 = R20000
A length is stated as 4 m correct to the nearest m. What is the lower bound?
Answers
The lower bound is the smallest value that rounds up to the given value.
Given value = 4m
The lower bound would be 3.5m
Any number less than .5 rounds down, any number greater to or equal to 0.5 rounds up, so if you have 3.5 or higher it rounds to 4
What is the area of EFG? ILL GIVE BRAINLIEST!!!!
Answers
Answer:
36
Step-by-step explanation:
8*9=72 72/2=36
Help with slope pleaseee
^^
Answers
You have to do to get the answer
Please look at picture answer and explain work
Answers
Answer: The answer is D. 240 grams
Step-by-step explanation:
1. Find the volume.
2cm×3cm×5cm=30 cubic centimeters
2. Find the volume of the other box.
4cm×9cm×5cm=180 cubic centimeters.
3. Divide. 180÷30=6
4. 6 times the amount it can hold, 40=240 grams of clay.
Hope that helped!
Answer:
Step-by-step explanation:
we are told that the box is 2 cm high, 3 cm wide 5 cm long and holds 40 grams of clay
so 2*3*5 = 30 \(cm^{3}\)
so the 30 cubic centimeter volume holds 40 grams ( it would have been nice if they had let the box hold 30 grams but, no :(
40/30 = 1.333333 or 1 and \(\frac{1}{3}\) of a gram okay, sooooo now we know each cubic centimeter holds that much clay, now let's solve for how many cubic centimeters are in the bigger box, you can try to solve it 1st if you'd like to practice, below I solve it
twice the height so 2(2)=4 high
3 times the width , so 3(3) = 9 wide
same length, so 5 long
4*9*5 = 180
180*1.33333333333 = 240 grams of clay in 2nd bigger box :)
I'm sure there is a funny box joke in there some where :DDDD
do you get the math? :)
You are required to: a.Rewrite the formulation above in the standard form by adding the required variables to replace the inequalities. b.Find a solution for the above formulation utilizing the linear programming simplex method.
Answers
Using the simplex method, the optimal solution for the given linear programming problem is x = 2, y = 2, z = 0, with the maximum objective value of P = 10.
a. To rewrite the formulation in standard form, we need to replace the inequalities with equality constraints and introduce non-negative variables. Let's assume x, y, and z as the non-negative variables:
Maximize P = 3x + 2y + 4z
Subject to:2x + y + z + s1 = 8
x + 2y + 3z + s2 = 10
x, y, z ≥ 0
b. Utilizing the linear programming simplex method, we can solve the above formulation. After setting up the initial tableau, we perform iterations by selecting a pivot element and applying the simplex algorithm until an optimal solution is reached. The algorithm involves row operations to pivot the tableau until all coefficients in the objective row are non-negative. This ensures the optimality condition is satisfied, and the maximum value of P is obtained.
To provide a brief solution within 120 words, we determine the optimal solution by applying the simplex method to the above formulation. After performing the necessary iterations, we find that the maximum value of P occurs when x = 2, y = 2, z = 0, with P = 10. Therefore, the maximum value of P is 10, and the solution for the given problem is x = 2, y = 2, and z = 0.
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What is 13 4/5 + 5 1/3
Answers
Step-by-step explanation:
Add the whole numbers
13 +5 = 18
Add the fractions
4/5 +1/3
The LCD is 15
12/15 + 5/15
17/15
Simplify
17/15 = 1 2/15
1 is a while number so, add it to the other whole number
18 +1 = 19
Your final answer will be 19 2/15
Please gimme brainliest
Sarah is trying to fence a rectangular area containing at least 100 sq. ft while using the least amount of material to build the fence. The length of the rectangular area should be 15 ft longer than the width. What should the width, in ft, be
Answers
Answer: 5 ft
Step-by-step explanation:
Area = 100 sq. ft
Length = x + 15ft
Width = x
Area of rectangle= L x W
100= (x + 15) x X
100= X^2 + 15x
X^2 + 15x -100 = 0
X^2 +20x - 5x - 100 = 0
x(x +20) - 5(x +20) = 0
(x+20)(x-5)= 0
solving for x:
x+20 = 0
x= -20
or
x-5 = 0
x = 5
Since width cannot be negative, the width is 5 feet
Hi, can you help me with this question? Thank you.
Answers
SOLUTION
We are asked if
\(m\angle4=m\angle5\)which lines are parallel.
If
\(m\angle4=m\angle5\)then line r and line s are parallel, while line L is a transversal.
A transversal is a line that cuts two parallel lines.
Since line r and line s are parallel, then angle 4 and angle 5 are alternate angles. Alternate angles are always equal and congruent.
Send us rain clouds, Grandfather. They laid the bundle in the back of the pickup and covered it with a heavy tarp before they started back to the pueblo. This quote is located early in the narrative. What does it reveal about Leon? He is more worried about the rain than the death of his grandfather. He is a devout follower of the Roman Catholic Church. He is already planning on asking for holy water from Father Paul. He greatly values the traditional beliefs of the Pueblo people.
Answers
Answer:
D: He greatly values the traditional beliefs of the Pueblo people.
Step-by-step explanation:
E2022. Comment below if you have any questions or comments.
Answer:
d
Step-by-step explanation:
edge 22
Find the solution to the systems of equations using the elimination method.
2x + 3y = 11
5x + 3y = 14
Answers
x=-3/5y+14/5
Answer:
x = 1 ; y = 3
Step-by-step explanation:
5(2x + 3y = 11)
2(5x + 3y + 14)
(distribute)
10x + 15y = 55
10x + 6y = 28
(subtract)
9y = 27
(divided 9 to both sides)
9 divided by 9 cancels out and 27 divided by 9 = 3
so..
y = 3
now, using any equation, (i’ll be using 2x + 3y =11) plug in the y value to find the x value
2x + 3y = 11
2x + 3(3) = 11
(multiply 3 x 3)
2x + 9 = 11
(subtract 9 from 9 and 11)
2x = 2
(divide 2 from both sides)
2 divided by 2 = 1
therefore...
x = 1
Students in a poetry class are writing poems for their portfolios. The teacher wants them to write stanzas with certain numbers of lines each. Megan wrote 10 short stanzas and 2 long stanzas, for a total of 98 lines. Sebastian wrote 3 short stanzas and 7 long stanzas, for a total of 87 lines. How many lines do the two sizes of stanzas contain?
Answers
Found that a short stanza contains 8 lines and a long stanza contains 9 lines.
What is linear equation ?
A linear equation is an equation that describes a straight line in a two-dimensional coordinate system. The general form of a linear equation is:
y = mx + b
Explanation:
Let's use "s" to represent the number of lines in a short stanza and "l" to represent the number of lines in a long stanza.
From the problem, we know that Megan wrote 10 short stanzas and 2 long stanzas, for a total of 98 lines. This can be written as the equation:
10s + 2l = 98
We also know that Sebastian wrote 3 short stanzas and 7 long stanzas, for a total of 87 lines. This can be written as the equation:
3s + 7l = 87
We want to find the values of s and l that satisfy both of these equations. We can use algebra to solve for s and l.
Multiplying the first equation by 3, we get:
30s + 6l = 294
Multiplying the second equation by 2, we get:
6s + 14l = 174
Now we can add the two equations together to eliminate the variable s:
30s + 6l + 6s + 14l = 468
Simplifying and rearranging, we get:
36s + 20l = 468
Dividing both sides by 4, we get:
9s + 5l = 117
Now we have a new equation that relates the values of s and l that satisfy both sets of stanzas. We can use this equation along with one of the original equations to solve for either s or l.
Let's use the first equation, 10s + 2l = 98. We can solve for s in terms of l:
10s + 2l = 98
10s = 98 - 2l
s = (98 - 2l)/10
Now we can substitute this expression for s into the equation 9s + 5l = 117:
9[(98 - 2l)/10] + 5l = 117
Simplifying and solving for l, we get:
l = 9
Now we can substitute this value of l back into either of the original equations to solve for s. Using the first equation:
10s + 2l = 98
10s + 2(9) = 98
10s = 80
s = 8
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Judy has 15 books in her library. She bought some books at a thrift store on Saturday. She now has 85 books in her library. How many books did she buy at the thrift store? Write and solve an equation using a variable for each word problem.
Answers
She bought 70 books at the thrift store.
15+x=85
Answer:
Judy bought 70 books at the thrift store.
Step-by-step explanation:
I got 70 by adding 15+70=a and a= 85
how many cards must be selected from a standard deck of 52 cards to guarantee that at least three cards of the same (matching) suit are chosen
Answers
Answer:
Step-by-step explanation:
17
How many minutes in 420 seconds?
Answers
Answer: 7 minutes
Step-by-step explanation:
There is 1 minute every 60 seconds
So if we divide the amount of seconds by 60 we will get the answer.
Therefore our equation is: 420/60
420/60=7
SO the answer is 7 minutes
Hope this helps! :)
Does the graph show a linear function?
Answers
Answer:
The graph does show a linear function
Step-by-step explanation:
The line is decreasing at a constant rate that keeps the line straight.
Larry has $20 to spend at the store. He plans to purchase five items that cost $5.79, $7.63, $3.46, $2.99, and $3.65. Larry estimated his total cost to make sure he has enough money for his purchases. Is his estimate accurate? Explain why or why not.
Answers
Answer:
he don't have the money
Step-by-step explanation:
5.79+7.63=13.42+3.46=16.88+2.99=19.87+3.65=23.52$
Answer:
does not. 5.79 + 7.63 + 3.46 +2.99 + 3.65 is equivalent to $23.52. And on top of that you don’t know if it’s before or after tax.
Step-by-step explanation:
one container is filled with a mixture that is 30% acid a second container is filled with the mixture that is 50% acid the second container is 50% larger than the first and the two containers are emptied into a third container what percent of acid is in the third container
Answers
Answer:
42%
Step-by-step explanation:
x is for the volume of the container
the amount filled in the first container=0.30x
the volume of the first container + 50% of the second=(x+x*50%)=1.5 x
the amount of acid in the second container= 1.5x * 50%=0.75x
total amount of acid in the third one =0.3x+0.75x=1.05x
total solution : x+1.5x=2.5x
percentage=1.05x/2.5x= 0.42 or 42%