Answer:
hence the required minimum production level is 12units
Step-by-step explanation:
Given the cost function expressed as c(x) = x^3 - 24x^2 + 30,000x
The average cost function will be c(x)/x
Dividing the cost function through by x
Average cost function = c(x)/x = x³/x - 24x²/x + 30,000x/x
Average cost function = x²-24x + 30,000
A(x) = x²-24x + 30,000
If the average cost is minimized, hence dA/dx = 0
dA/dx = 2x - 24
0 = 2x - 24
-2x = -24
Divide both sides by -2
-2x/-2 = -24/-2
x = 12
For the second deriviative
d²A/dx² = 2 which is greater than zero
Hence a production level that will minimize the average cost per item of making x items is 12
The production level that will minimize the average cost per item of making x items is x = 12
How to obtain the minimum value of a function?To find the minimum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.
Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.
For this case, the function in consideration is: [tex]c(x) = x^3 - 24x^2 + 30000x[/tex]
This is cost function for x items' manufacturing.
The average cost per item would be c(x) / x
This gives us a function a(x) as:
[tex]a(x) = c(x)/x = x^2 -24x + 30000[/tex]
For finding the minimum of a(x), getting its first two derivatives as:
[tex]a'(x) = 2x - 24\\a''(x) = 2 > 0[/tex]
Equating first rate to 0,
[tex]a'(x) = 2x - 24 = 0[/tex] critical point.
Since second rate is positive, the point x = 12 is point of minima, and since only one critical point is there, it is the point on which a(x) is minimum.
Thus, the production level that will minimize the average cost per item of making x items is x = 12
Learn more about minima and maxima of a function here:
https://brainly.com/question/13333267
Ordan is cutting a 2 m 2 m2, start text, space, m, end text by 1 1 4 m 1 4 1 m1, start fraction, 1, divided by, 4, end fraction, start text, space, m, end text piece of rectangular paper into two pieces along its diagonal. Find the area of each of the pieces. m 2 m
Answer:
5/4 m²
Step-by-step explanation:
Jordan is cutting 2 m by 1 1/4 m piece of rectangular paper into 2 pieces along its diagonal.What is the area of each of the pieces.
Length of the rectangular paper = 2m
width of the rectangular paper = 1 1/4m
Area of a rectangle = Length × width
= 2 × 1 1/4
= 2 × 5/4
= (2 * 5)/4
= 10/4 m²
Area of a rectangle = 10/4 m²
Diagonal divides the rectangle into 2 equal pieces
Divide area of the rectangle by 2
Area of each piece of the diagonal = Area of the rectangle / 2
= 10/4 m² / 2
= 10/4 ÷ 2
= 10/4 × 1/2
= (10*1) / (4*2)
= 10/8
= 5/4 m²
Area of each piece of the diagonal = 5/4 m²
FASST PLEASE ANSWER NO LINKS!!!!!
Answer:
180
Step-by-step explanation:
Answer: 180 is the correct answer. Hope this helps!!!!
Step-by-step explanation:
Why is a negative times a negative always a positive?
Answer: A negative times a negative is always positive because the two negative signs are canceled out.
Step-by-step explanation:
If you seek a more in-depth explanation, Khan Academy actually has a video available on this topic!
Delilah and a group of friends had an excellent service at a restaurant. They would like to give the server a 25 percent gratuity on their $140 bill. Use the diagram to identify the amount of the tip.
Answer:
The answer is $35
what is 5.823 rounded to the nearest whole
what is 3.147 rounded to the nearest whole
Answer:
6 and 3
Step-by-step explanation:
5.8 to the nearest whole is 6
3.147 to the nearest whole is 3
Not sure if i got this right?
Answer:
The effect it will have on the volume is;
The volume will be 8 times larger
Step-by-step explanation:
The dimensions of the given prism are;
The length of the prism, l = 5 in.
The breadth of the prism, b = 5 in.
The slant height of the prism, = 4 in. by 5 in.
The height of the prism, h = 7 in.
The shape of the prism = Parallelepiped
The volume of a parallelepiped = Area of Base × Height of the prism
The base area of the parallelepiped = The length × Breadth of the parallelepiped
∴ The base area of the given parallelepiped = 5 in. × 5 in. = 25 in.²
The volume of the given parallelepiped, V₁ is found as follows;
V₁ = 5 in. × 5 in. × 7 in. = 25 in.² × 7 in. = 175 in.³
When a scale factor of 2 in applied to the dimensions of the prism, we have;
The new volume, V₂ = 2 × 5 in. × 2 × 5 in. × 2 × 7 in.
∴ V₂ = 2 × 2 × 2 × 5 in. × 5 in. × 7 in. = 8 × 5 in. × 5 in. × 7 in. = 8 × V₁
Therefore;
V₂ = 8 × V₁
The volume of the image of the object, V₂ after applying a scale factor of 2 is 8 times larger than the volume of the object, V₁.
Is 7/8 bigger than one or greater or equal to one
Answer:
7/8 is less than 1, sure it is close to one but not 1.
The graph of F(x), shown below, has the same shape as the graph of G(x) = x2, but it is shifted to the left 2 units. What is its equation?
Answer: F(x)=(x+2)²
Step-by-step explanation:
Factorise full the following x squared +2x
Answer:
x(x+2) is the answer please
Step-by-step explanation:
x²+2x
x(x+2)
what does 41 = w - 4
Rose cuts 3 feet from a 9-foot length of rope. Then she cuts 13 inches from the rope. How many inches of rope are left?
Answer:
uh hajsjdjjfhdbdjdjjdjvjjvjfjrbdbjfhxbfjxj
Step-by-step explanation:
ok
In ΔKLM, k = 5.1 cm, l = 6.4 cm and m=3.6 cm. Find the area of ΔKLM to the nearest 10th of a square centimeter.
Answer:
eIn ΔKLM, k = 5.1 cm, l = 6.4 cm and m=3.6 cm. Find the area of ΔKLM to the nearest 10th of a square centimeter.
Step-by-step explanation:
ee
Answer:
9.2
Step-by-step explanation:
Can you please help me on #12 pls
And also no links
Answer:
12) Well follow the orders of operations
Parentheses
Exponents
Mulitpacation - division (left to right)
Addition - subtraction (left to right)
Well we see an exponents lets do that first
6^2=36
And basically theres these parenthesis on the side for each so really its
(8+36) / (11)
This only occurs if the number is presented like this as diviosn or a fraction.
Now we solve that
8+36= 44
44/11=4
4+7*2
Thats the final equation
Well multiply first
7*2=14
14+4=18
The answer would be 18
What is the domain and range for the function below:
y = log2 (x - 1)+4
Answer:
I smell gas
Step-by-step explanation:
can somebody please just explain to me how to do this, it says solve for x in each diagram. I already answered the first question and I just want to make sure that I'm doing it
Answer:
u did it right
Step-by-step explanation:
solve it like this
2x -7 = 47
2x = 47 + 7
2x = 54
54/2
x= 27
Please mark as brainliest
Have a great day, be safe and healthy
Thank u
XD
find the value of b if triangles are similar
Answer:
9 because the constant of proportianlity is 3/4 and 3/4 of 12 is 9.
Marsha deposited $7,500 into a savings account 5 years ago. The simple interest rate is 3%. How much money did Marsha earn in interest? What would be her new account balance?
they made $1125 and the new balance is $8625
Answer:
earned in intrest would be 450.
Step-by-step explanation:
i did the assingment
Please help me y’all i’m begging!!!!
Answer:
212
Step-by-step explanation:
0.5*11*10=55
3.14*10*10/2=157
157+55= 212
an alloy contains nickel and chromium in 3:2 ratio, find the mass of each metal in 540g of alloy.
Answer:
Let the mass of nickle be 3x
And the mass of chromium be 2x
According to question,
3x+2x = 250
5x = 250
x =250/5
x = 50
What is the expanded form of 54,582? *
1 point
5 x 100,000 + 4 x 1,000 + 5 x 100 + 8 x 10 + 2 x 1
5 x 10, 000 + 4 x 1,000 + 5 x 1/10 + 8 + 1/100
5 x 1,000,000 + 4 x 10,000 + 5 x 100 + 8 x 10 + 2 x 1
5 x 10,000 + 4 x 1,000 + 5 x 100 + 8 x 10 + 2 x 1
Answer:
5 x 10,000 + 4 x 1,000 + 5 x 100 + 8 x 10 + 2 x 1
Step-by-step explanation:
all the other ones are incorrect
Which expression is equivalent to: -3a-7a+4b
A: -10a-7+4b
B: -10a+4b
C: -14ab
D: -4a+4b
Answer:
-10a+4b
hope this answer helps you.....
1. What is the area of the trapezoid? The diagram is not drawn to scale.
When rolling a number cube 500 times, how many times can you expect to roll a number divisible by 2?
Answer:
You can expect to roll a number divisible by 2, 167 times
Step-by-step explanation:
In the picture,...
what is the range of the data set on this dot plot
A.
B.
C.
D.
Answer:
B
Step-by-step explanation:
Subtract the minimum number from maximum number.
[tex]10 - 2 = 8[/tex]
The rectangle below has an area of x^2-15x+56x
−15x+56x, squared, minus, 15, x, plus, 56 square meters and a length of x-7x−7x, minus, 7 meters.
What expression represents the width of the rectangle?
Width= meters
Answer:
x-8
Step-by-step explanation:
HELP OMGGGGGGGGG PLSSS
Step-by-step explanation:
find the area of the big rectangle [ 8 * 18]
find the area of the small triangle [½ * 8 * 8]
calculate the difference of the 2 areas.
that's Ur answer
Answer:
B. [tex] 112 \: {in}^{2} [/tex]
Step-by-step explanation:
Area of the shaded region = Area of rectangle with dimensions 18 in and 8 in - Area of triangle with base 8 in and height 8 in
[tex] = 18 \times 8 - \frac{1}{2} \times 8 \times 8 \\ \\ = 144 - 32 \\ \\ = 112 \: {in}^{2} [/tex]
Beth has 50 blueberry scones and 75 cranberry scones. She wants to make as many identical bags as possible. Each bag should have an equal number of cranberry and blueberry scones. What is the greatest number of bags she can fill?
Answer:
The greatest number of bags she can fill is 50.
Step-by-step explanation:
If each bag must have an equal number of cranberry and blueberry scones, she is limited to 50 bags by only having 50 blueberry scones.
A tennis court for singles play is 78 feet long and 27 feet wide. Part 1 out of 3 The court for doubles play is 9 feet wider than the court for singles play. How much more area is covered by the tennis court used for doubles play? The tennis court used for doubles play covers square feet more area than the court used for singles play.
Answer:
702 ft^2
Step-by-step explanation:
Steps to answering this question
1. determine the area of the singles court
area of a rectangle = length x width
27 x 78 = 2106 ft^2
2. Determine the width of the doubles court
27 + 9 = 36FT
3. Calculate the area of the doubles court
area of a rectangle = length x width
78 x 36 = 2808 ft^2
Find the difference in areas
2808 - 2106 = 702 ft^2
Students standing in line for a theme park were surveyed about their favorite ride. Their responses are shown below. If one student is picked randomly, then which of the following is true?
Answer:
H is the answer
Step-by-step explanation:
14 is 1/2 of 28
help!? me please help mee
Answer:
X=7
Step-by-step explanation:
in order to get everything out of the square root, just square both sides.
This will give you x + 1 = 2x - 6
move like terms to each side and you’ll end up with x = 7