A box is to be made where the material for the sides and the lid cost $0.20 per square foot and the cost for the bottom is $0.05 per square foot. Find the dimensions of a box with volume 20 cubic feet that has minimum cost.
Please answer in length , width and height in ft
Answer:
Let x represent the edge dimension of the square base in feet. Then the area of the base or lid is x², and the height of the box is 5/x². Total cost is then ...
... cost = cost of lid + 4×(cost of one side) + cost of bottom
... cost = 0.2x² + 4×(0.2x(5/x²)) + 0.5x²
... cost = 0.7x² + 4/x
We can differentiate this with respect to x and set that derivative to zero. This will give us the x-value at which the cost is a minimum.
... d(cost)/dx = 1.4x -4/x² = 0
... x³ = 4/1.4
... x = ∛(20/7) ≈ 1.419
Then the height of the box is
... height = 5/x² ≈ 5/2.01351 ≈ 2.483
The box is 1.491 ft square and 2.483 ft high.
______
The average cost of the top and bottom is (0.2 +0.5)/2 = 0.35 per square foot. The overall cost will be minimized when the average cost of each face is the same. That is, the areas of the lateral faces will be equal and must be 0.35/0.2 = 1.75 times the area of the top or bottom to make the average cost of a lateral face equal to that of the top or bottom. Hence, the base will be square, and the box will be 1.75 times as high as it is wide or deep. The base edge dimension is then ∛(5/1.75) ≈ 1.419 ft.
Step-by-step explanation:
All of the factory workers in a steel mill either purchased their breakfast in the company cafeteria, or brought their breakfast from home on Wednesday. • 26% of the factory workers purchased their breakfast. • 148 brought their breakfast from home. How many factory workers are employed at the steel mill?
Answer:
There are 200 factory workers employed still mill
HOPE IT'S HELPS YOUQuestion 5(Multiple Choice Worth 5 points)
(8.02 LC)
The coordinate grid shows the graph of four equations:
A coordinate grid is shown from negative 12 to positive 12 on the x axis and also on the y axis. Line A passes through the ordered pairs negative 3, 4 and 9, negative 2. Line B passes through the ordered pairs 2, 8 and 8, negative 8. Line C passes through the ordered pairs negative 3, negative 4 and 4, 6. Line D passes through the points 2, negative 2 and 5 and 6.
Which set of equations has (1, 2) as its solution?
A and D
C and D
A and C
B and D
Answer:
I think it is A and C
can you do these two pls
PLZZZ help with this
Answer:
I D K A and C but B is 776 and 29 D is 101 and 8 I hope i helped
Step-by-step explanation:
(b) 5x^2+1
5(5)^2+1
25^2+1
775+1
776
x^2+4
5^2+4
25+4 29
(d) 5x^2+1
5(2)^2+1
10^2+1
100+1
101
x^2+4
2^2+4
4+4
8
ugh helpme plz i need to turn dis in now
Answer:
By using the 90 degree clockwise rotation formula, we are able to determine that the answer is (7, 6)
Step-by-step explanation:
The formula for 90 degree clockwise rotation is
(x,y)--->(y,-x)
The reason why our -6 turns into a positive is because the negative was replacing that negative therefore making it positive.
Hope this helps!
I'll leave the rest of the formulas I have in my notes for you!
180 degree rotations
(x,y)--->(-x,-y)
90 degree counterclockwise
(x,y)--->(-y,x)
270 degree rotation
(x,y)--->(y,-x)
coach cliffman made an deposit of$1,800 into and account that earns 2% annual simple interest. find the amount of interest that coach cliffman earned after 3 years
Answer:
5508$
Step-by-step explanation:
10 points help me pls
ONLY ANSWER IF YOU KNOW THE ANSWER. Today only, a sofa is being sold at a 72% discount. The sale price is $151.20.
What was the price yesterday?
Answer:
42.336 or 42.34 if you round
Step-by-step explanation:
Answer:
270
Step-by-step explanation:
I hope this helps!
Let me know if I am wrong
20 points
How do you convert mass to volume without density?
Answer:
Well, you could always just put it onto a scale to find the mass. But assuming you aren't talking about a laboratory setting. sorry if its all werid i cant really put it into how it supposed to be
The general formula is:
ρ
=
m
V
where
ρ
is density in
g/mL
if mass
m
is in
g
and volume
V
is in
mL
.
So to get the mass...
m
=
ρ
V
Or to get the volume...
V
=
m
ρ
When you have the volume and not the density, and you want to find mass, you will need to find the density yourself. It's often readily available on the internet.
Just replace "[...]" with the object you want, and if it's not exactly what you need, consider it an estimate.
These days, you should be able to search for the density of any common object.
When you have the density and volume but not the mass, then just make up a mass.
You shouldn't need specific numbers to do a problem. You can always solve a problem in general and get a solution formula. If you need to, just make up some numbers that you know how to use.
I need the correct answer for this it says incorrect?????
Answer:
x-13
Step-by-step explanation:
why you may ask?
subtracted=being taken away from
13 is *being taken away from* x
so if using numbers, 13 is being taken away from 20
or 13 is being subtracted from 20 would be 7, so x-13 would be your expression
The table shows the number of bottles of different kinds of juice sold at a cafeteria on Monday.
If the cafeteria has 80 customers on Tuesday, which prediction for Tuesday is NOT supported by the data in the table?
Pls answer ASAP
Dont guess!
I will mark brainliest if its correct!
Also no links!
Answer:
I know you said no guessing, but I'm assuming it's the first one, F.
Answer:
The second graph as per my best guess LOL
Step-by-step explanation:
LMK if I'm wrong please
HELP ASAP RN (do not send links)
_______________________________________________________
Sophia has $6 to spend on lunch during a basketball tournament. The concession stands sell sodas for $0.75 and all of their food items for $1.50. What is the maximum number of food items Sophia can purchase if she buys one drink?
Important info:
- Sophia has $6 to spend on lunch
- Concession stands sell sodas for $0.75
- All of their food items for $1.50
- Pretend she buys one drink
- Find the maximum amount of food she can buy now.
Process:
Subtract 600 and 75 since $6 = 600 cents
600 - 75 = 525
So Sophia has $5 and 25 cents left
Each food item is worth $1.50 which is 150 cents and she currently has $5.25 which is 525 cents
So divided 525 and 150
525 / 150 = 3.5
Unfortunately she can't buy half of a food item so the answer would be 3
Final Answer:
3, Sophia can buy 3 food items after buying 1 drink
Eve wants to buy a balance beam. The original price is $388. How much will Eve pay if she buys it during the sale? It was on sale for 75%!
Answer:
Eve will pay $97 if she buys it during the sale.
Step-by-step explanation:
price during sale = original price - (original price * discount percentage)
disc. % = 75%
75% = 0.75
pr. = 388 - (388 * 0.75)
pr. = $97
Answer:
97$
Step-by-step explanation:
Don't guess!
I will mark brainliest if its correct!
Don't answer if you don't know!
Also no links!
And show your work plz!
POD: 4 (2a + 3) = 28
Answer:
a = 2
Step-by-step explanation:
4 (2a + 3) = 28
4 * 2
= 8
4 * 3
= 12
8a + 12 = 28
28 - 12
= 16
8a = 16
16 / 8
= 2
a = 2
PLSSS HELPPPPPPP CORRECT ANSWERS PLSSSS
Answer:
-4. (x+4)(x-4)
Step-by-step explanation:
Answer:
-4 x+4 x-4
Step-by-step explanation:
CHARGE YOUR PHONE
(08.03)Heather recorded the different types of music her friends like in the table below:
Type of Music Number of Friends
Country
3
Hip-hop
2
Pop
4
Rock
1
Which of the following plots represents the data in the table?
A: A dot plot line labeled Types of Music and titled Music. Four tick marks labeled Country, Hip-hop, Pop, and Rock. There are 3 dots above Country, 2 above Hip-hop, 4 above Pop, and 1 above Rock.
B: A dot plot line labeled Types of Music and titled Music. Four tick marks labeled Country, Hip-hop, Pop, and Rock. There is 1 dot above Country, 2 above Hip-hop, 3 above Pop, and 4 above Rock.
C: A dot plot line labeled Types of Music and titled Music. Four tick marks labeled Country, Hip-hop, Pop, and Rock. There are 3 dots above Country, 4 above Hip-hop, 1 above Pop, and 2 above Rock.
D: A dot plot line labeled Types of Music and titled Music. Four tick marks labeled Country, Hip-hop, Pop, and Rock. There are 2 dots above Country, 4 above Hip-hop, 4 above Pop, and 3 above Rock
answer:
a)
step-by-step explanation:
the explanation is the picture
**edit** i didn't realize that the words got 'deleted' but here's the order i put them in country, hip-hop, pop, and rock i'm sorry about the inconvinence
good luck :)
i hope this help
brainliest would be highly appreciated
have a nice day!
Answer:
The answer is A.
I took the test and got it right. Hope this helps!
Have a good day :)
~Amy❤
The ratio of apples to oranges in Maria's basket was 1:4. There were 8 apples. How many fruits were in the basket?
Answer:
40 fruits
Step-by-step explanation:
apples:oranges
1 : 4
8 : ?
If 1 = 8 then 4 = 32
8 : 32
Total fruits: 8 + 32 = 40
40 fruits
A triangle has one angle that measures 34 degrees, one angle that measures 47 degrees, and one angle that measures 99 degrees.
What kind of triangle is it?
A.
equilateral triangle
B.
scalene triangle
C.
right triangle
D.
isosceles triangle
Answer: Scalene
Step-by-step explanation:
None of the angles equals the other so no isosceles or equilateral and a right triangle had a right angle and all right angles equal 90 degrees.
start at 200. create a pattern that multiplies each number by 2. stop when you have 5 numbers
Answer:
200 → 400 → 800 → 1600 → 3200
Step-by-step explanation:
starting at 200 and multiplying by 2 until you have 5 numbers.
Answer:200,400,800,1600,3200
Step-by-step explanation:
Thats the questions for my other problem
are there any answer choices??
PLS HELP ILL GIVE BRAINLIEST!
Answer:
B
Step-by-step explanation:
-the base angles are 34, so the total value of both base angles is 68
-an isosceles triangle is equal to 180
-subtract 68 from 180 for the answer, so the equation is 68+x=180
hope this helps, comment in you have a question :)
Answer:
i think its b
Step-by-step explanation:
A train drove the distance of 440 feet in 20 seconds. Select ALL the unit rates that are equivalent to the speed of the model airplane.
Answer:
22 feet/s
Step-by-step explanation:
Answer:
Step-by-step explanation:
The units of measurement listed below are suitable:
ft/sec
ft/min
miles/hr
Weren't there more choices?
please HELP ME omg istggg plsss im begging yalll
HELP ASAP WILL GIVE BRAINLIEST!
Answer:it a
Step-by-step explanation:
the answer is c because the definition of multiplicative inverse is :
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number.
Emma had p marshmallow peeps, and Ana gave 3 more marshmallow peeps to Emma. Which expression represents the number of marshmallow peeps that Emma has now?
Answer:
am I to find the p? are there any multiple question answers ?
Answer:
y=p+3
Step-by-step explanation:
please help me asap! also please prove how you got your answer
What is the surface area of the triangular prism below?
Answer:
Let me figure it out rq hold on
how to find the surface area:
The surface area of the triangular prism is the sum total of the areas of its bases and its lateral faces,