A cereal box is designed to hold a volume of 4096 cubic centimetres of cereal.
What dimensions will minimize the cost of producing the box?

Answers

Answer 1

Answer:

Refer to the step-by-step

Step-by-step explanation:

To minimize the cost of producing the box, we would want the box to be a cube.

Where the volume, [tex]V=s^{3}[/tex], where s is the length of one side of the box.

We were given the value, [tex]V=4096 cm^{3}[/tex], plug this into the equation above so we can find the dimensions of the box...

[tex]4096=s^{3} = > s=\sqrt[3]{4096} = > s=16[/tex]

Thus the dimensions to minimize the cost of the production of the box would be 16cm by 16cm by 16cm.


Related Questions

52 > 43 + w

is it a solution?
7 yes or no
4 yes or no
13 yes or no
9 yes or no
answer yes or no for EACH one

Answers

Answer:

Step-by-step explanation:

Is the first side “SW=XW” or “ST=XU”?

Answers

Answer:

SW =XW and ST=XU and UW=TW

Step-by-step explanation:

All are true and correct since the two triangles are congruent

Sides SW=WX are congruent
Angle S=X are congruent
Sides UW=WT are congruent

i have no idea pls help

Answers

Answer:

Q1. Radius = 3 cm

Diameter = 6 cm

Circumference = 18.84 cm

Area = 28.26 cm²

Step-by-step explanation:

Hello! Let us solve Q.1 together and you can solve Q2 and 3 by how we did in Q1. First, you will need to know what diameter, radius, and circumference means.

Definitions:

Diameter - It is a line that passes through the center of the circle and the line's end (known as endpoints) touches the opposite to each other (basically there are two endpoints).

Radius - It is a line which is half of the diameter.

Circumference - It is the circle.

Now that we know the definitions, let us solve it.

Q1. Radius = 3 cm

Diameter = 6 cm

Circumference = 18.84 cm

Area = 28.26 cm²

Looking at the circle, we are already given the radius which is 3 cm. Now let us find the diameter. We know that the radius is half of the diameter, so we would multiply the radius (3 cm) by 2.

3 × 2 = 6 cm ---> diameter

Lastly let us find the circumference. If you look above the questions, you are given an example and gives you the formula of circumference. We will use that formula to find the circumference of Q1. circle.

Circumference formula:-

[tex]c \: = \: \pi \: \times \: d[/tex]

C = 3.14 × 6

C = 18.84 cm

Same goes with finding the area. You are already given the formula, so you will use it to find the area of Q1.

Area of circle formula:-

[tex]a \: = \: \pi \: \times \: r {}^{2} [/tex]

a = 3.14 × 3²

a = 3.14 × 9

a = 28.26 cm²

Hope this helps and if you need help I would be glad to help you, thank you :) !!

Find the value of
5x? if x =
- 3

Answers

Answer:

-15

Step-by-step explanation:

5x-3=-15

Step-by-step explanation:

On amazon, you found the same shoe for $108. What is the percent difference between the price of the original and the price of the amazon shoe

Answers

Answer:

Step-by-step explanation:

Here's the complete question:

It cost Nike $55.00 to make the Kyrie 5, but it is selling for $130.19. Calculate the markup/percent Increase for the shoe. On Amazon, you found the same shoe for $108. What is the percent difference between the price of the original shoe and the price of the amazon shoe

The percentage Increase of the shoe will be:

= Selling price - Cost/ Cost × 100

= (130.19 - 55.00) / 55.00 × 100

= 75.19 / 55.00 × 100

= 136.71%

The percent difference between the price of the original shoe and the price of the amazon shoe will be:

= (130.19 - 108)/130.19 × 100

= (22.19 / 130.19) × 100

= 17%


Apply In Bhutanese architecture, the faces of
buildings are trapezoids. If the row of decorative
brick shown is 28.5 feet wide, what is the width
of the base of the building?

Answers

Answer:

Understand Given kite ABCD and isosceles trapezoid WXYZ, complete a two-​column proof to show that ... 9. △ADW ≅ △CDZ. 9. SAS. 9. Apply In Bhutanese architecture, the faces of buildings are trapezoids. If the row of decorative brick shown is 28.5 feet wide, what is the width of the base of the building? 25 ft. 16 ft. 16 ft.

Step-by-step explanation:

Limx→0 e^x -e^5/ x-5

Answers

Answer:e5

Step-by-step explanation:

Here you go

Refer to the attached image.

ind the Average Rate of Change of the table below for the interval 0 < x < 4

Answers

The average rate of change is equivalent to 2.

What is expression?

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is the table as shown below -

[x] :  0  1  2  3  4

[y] :  -2 -3 1  3  6

The rate of change in the interval 0 < x < 4 is -

AROC = (6 + 2)/(4 - 0)

AROC = 8/4

AROC = 2

Therefore, the average rate of change is equivalent to 2.

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Given triangle ABC, which equation could be used to find the measure of ∠C?

a
tan m∠C = one half

b
sin m∠C = square root of 5 over 5

c
sin m∠C= square root of 5 over 2

d
tan m∠C = 2

Answers

The measure of the angle ∠C in the triangle ABC can be gotten using tan m∠C = 2

What is an equation?

An equation shows how two or more numbers and variables are related to each other.

On the other hand, trigonometric ratios are used to show the relationship between the sides and angles of a right angled triangle.

The basic equations of the trigonometry ratios are

sinФ = opposite/hypotenuse; cosФ = adjacent/hypotenusetanФ = opposite/adjacent

Using the above as a guide, and the given triangle:

We have:

tan m∠C = opposite/adjacent

Substitute the known values in the above equation, so, we have the following representation

tan m∠C = 6/3

Evaluate

tan m∠C = 2

Hence, the true equation is (d) tan m∠C = 2

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HELP PLEASE IVE BEEN STUCK ON THIS PROBLEM ALL DAY

Answers

The table that is a justification for the given solution to the system of equations is table 1

How to determine the table that bears the correct values?

The two linear equations are

y=4x-9 and

y=2x-5

We that the following points for x : -1, 0, 1, 2, 3

When we substitute the values in the two equations we will have

x           y₁              y₂

-1         -13             -9

0           -9             -5

1             -5            -3

2            -1              - 1

3            3                1

Conclusively the values of y₁, and y₂ are shown in the table above

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Can anyone help me asap!?<3

Answers

Answer:

(3,-5).

Explanation:

Can u pls help me, pls

Answers

Answer: C
i believe it’s c because it’s long enough to be equal to 85

Answer:

The answer is A.

Step-by-step explanation:

○Lets Angle 1 and the angle with in a linear pair.

○Now we have 53+42+Angle x = 180° (Angle sum property of triangle)

= 53+42+x= 180

= 95+x= 180

= x= 180-95

= x= 85°

○Now that we found x, we can take angel x and angel 1 in linear pair again.

= Angelx + Angel 1= 180° (Linear Pair)

= 85 + Angel 1= 180°

= Angel 1= 180-85

= Angel 1= 95°

Therefore, option A is correct.

Six toilet rolls cost $1.99. Nine toilet rolls cost $2.69. Is cost directly proportional to number of toilet rolls? Explain your reason!​

Answers

Answer:

not directly proportional

Step-by-step explanation:

if the cost is directly proportional to number of rolls , then the unit cost for both will be equal.

first

one roll costs $1.99 ÷ 6 = $0.33 ( to 2 decimal places )

second

one roll costs $2.69 ÷ 9 = $0.30 ( to 2 decimal places )

since the unit costs are different there is not a directly proportional relationship.

Answer:

No because to buy nine rolls would be $2.69 but to buy six and then three to make nine then it would be $2.985 which is more expensive.

Step-by-step explanation:

$1.99 divided by 2 = 0.995

$1.99 + 0.995 = $2.985

$2.985 > $2.69

Hope this helps!!! :)

Can some one help me with this question its hard :( down below ill give brainliest

Answers

Exponent law:
m^x * m^y = m^(x + y)
In other terms, when multiplying same bases, the exponents add
m^(2 + 2) = m^4

Solution: A. m^4

Given the parent functions f(x) = 5x - 1 and g(x) = 3^x-
9, what is g(x) - f(x)?

Answers

Answer:

g(x) - f(x) = 3^x - 9 - (5x - 1) = 3^x -5x - 8

What is the Volume of this Prism?

Answers

Answer:

240

Step-by-step explanation:

Elizabeth buys 50 meters of ribbon to make bows for the cheer squad. Each bow uses 1.3 meters of ribbon. How many bows can Elizabeth make? *

Answers

Bum bum girl yea okay huh

Answer:

38 bows

Step-by-step explanation:

50 ÷ 1.3 ≡ 38 6/13

38 × 1.3 = 49.4

Since you cant make 6/13 of a ribbon, Elizabeth would be able to make 38 bows.

Which expression is equivalent

Answers

Answer:

10^14

Step-by-step explanation:

The expression (10^2)^7 uses an exponent rule known as power raised to a power.

The rule states that when you multiply a base and its exponent to a power, you multiply the inner exponent and the outer exponent:

[tex](a^m)^n\\a^m^n[/tex]

Thus, we have

[tex](10^2)^7\\10^2^*^7\\10^1^4[/tex]

URGENT!!!
The number of customers that come to a certain clothing store each day follows a normal distribution. The mean number of customers is 428, and the standard deviation is 32. What is the probability that more than 524 customers will come to the store on a given day?

Answers

Answer: 0.15%

Step-by-step explanation: edmentum

Answer:

Step-by-step explanation:

the answer is 0.15

Consider the differential equation dy/dx=xy^4.
(b) Find ⅆ2yⅆx2 in terms of x and y. Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.
(c) Find the particular solution y=f(x) to the given differential equation with initial condition f(4)=−1.

Answers

The differential equation [tex]\frac{dy}{dx} = xy^{4}[/tex] is considered and the solutions for the following questions are found.

What is a differential equation?

A differential equation is an equation that links the derivatives of one or more unknown functions. Differential equations contain derivatives, which might be either partial derivatives or ordinary derivatives.

The differential equation describes a relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.

Given,

    [tex]\frac{dy}{dx} = xy^{4}[/tex]

a) Now finding [tex]\frac{d^{2} y}{dx^{2} }[/tex] = [tex]y^{4} + 4xy^{3} \frac{dy}{dx}[/tex] = [tex]y^{4} + 4xy^3 (xy^4) = y^4 + 4x^2y^7[/tex]

In quadrant II, the values of x < 0 and the values of y >0.

So  [tex]\frac{d^{2} y}{dx^{2} }[/tex] =  [tex]y^4 + 4x^2y^7[/tex] > 0 for all values of x and y in quadrant II.

Therefore the concavity is up for of all solution curves of the given differential equation.

b)

         [tex]\frac{dy}{dx} = xy^{4}\\\\\frac{dy}{y^4} =x dx\\\\\int {\frac{dy}{y^4} } \, = \int {x} \, dx \\\\\frac{y^{-4+1} }{-4+1} = \frac{x^{2} }{2} + c\\\\\frac{y^{-3} }{-3} = \frac{x^{2} }{2} +c[/tex]

      Now it is given that initial condition is f(4) = -1

   So substituting x =4 and y = -1 is the above equation to find c, we get

        [tex]\frac{-1^{-3} }{-3} = \frac{4^2}{2} +c \\\\\frac{1}{3} = 8 + c\\\\c = \frac{1}{3} - 8 = \frac{-23}{8}[/tex]

Therefore the solution y = f(x) is to the given differential equation with initial condition f(4)=−1.

  [tex]\frac{y^{-3} }{-3} = \frac{x^{2} }{2} -\frac{23}{8}\\ \\ \frac{1}{3y^3} = \frac{46 - 8x^2 }{16} = \frac{23 - 4x^2 }{8}\\\\y = \sqrt[3]{\frac{8}{3(23-4x^2)} }[/tex]

 

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Can anyone help with these 2 problems explain how you got the answer please I’ll give brainleist.

Answers

Answer:

It is best it you guess. What grade are you in

Step-by-step explanation:

Answer:

I think <BCH would also be 108 since its corresponding angles

and with <MNJ would also be 97 since its alternate exterior angles

Which of the parabolas has a maximum?
(1) y = 8x² + 6x + 6
(2) y = -2x² + 6x - 6
(3) y = 2x² - 6x + 6
(4) y = 6x² - 6x-6

Answers

Answer:

(2) y = -2x² + 6x - 6

Step-by-step explanation:

Notice that the only leading coefficient that is negative is in the 2nd equation. Hence, the shape of the parabola will be upside down, making it have a maximum.

thats not evan an answer choise

Answers

What are you talking about?

What do you mean? I’m confused

How do you write 4 7/8 as a decimal

Answers

Answer:

4.88

Step-by-step explanation:

Turn 4 7/8 as an improper fraction  Divide The FractionDone!

Hops This Helps!

To convert 4 7/8 into a decimal, we first need to turn the mixed number into an improper fraction.

In order to turn the mixed number into an improper fraction, we need to multiply the whole number by the denominator and add it up with the numerator.

[tex]4\dfrac{7}{8}[/tex]

[tex]4\times8=32+7=39[/tex]

Now, put that sum over the denominator:

[tex]\dfrac{39}{8}[/tex] (improper)

Now, to turn the improper fraction into a decimal, we need to divide the numerator by the denominator:

[tex]39\div8[/tex]

[tex]=\fbox{4.875}[/tex]  (final answer)

Juanita changed $20 into euros when the exchange rate was €1=$1.2685.
How many euros did she receive?
Give your answer correct to 2 decimal places.

Answers

245 euro is the wright answer to 2 decimal places

Please Help me find the area of the figure round to the nearest hundredth nessary

Answers

Answer:

912 cm²

Step-by-step explanation:

Formula for area of triangle: 1/2bh

So you'll first multiply the base by the height of the triangle

48 x 38 = 1,824

Then you'll multiply 1,824 by 1/2(which is the same as dividing it by 2)

1,824 ÷ 2 = 912

if y varies jointly as x and the inverse of z and y = -5 and x = -5 and z = 6, find y when x = 5 and z = -8

Answers

Step-by-step explanation:

y varies inversely as x=

y= k/xz

-5= k(-5)/6

k= 6

y=6/xz

y=6/5×-8

y= -3/20

AABC~ ADEF. What is the scale factor?

Help please

Answers

Answer:

3:1 or 3

Step-by-step explanation:

the left triangle is scaling up to the right triangle. 5/15 is 1/3

7/21 is 1/3

4/14 is 1/3

since it is scaling UP, the scale factor is 3:1

a dealer sold printing machine for 47460 including 13% vat. find the original price(excluding vat).

Answers

Answer:

42000

Step-by-step explanation:

Original price (before VAT) is 100% of price.

VAT is 13%, of the original price so final price is 113% of original price.

113% = 1.13

original price = 47460/1.13 = 42000

(100 points)A catering company offers meal pairings that include an appetizer of either salad or soup and an entree of either chicken or fish. At one event, they serve a total of 78 meals. Of the 46 meals that include salads, 21 also include fish. There are 35 meals with fish as the entree. Determine which two-way frequency table represents this situation. Jk

Answers

Two-way table showing meal pairings with frequency of salad, soup, chicken and fish.

Meal Pairing Salad Soup Chicken Fish

Frequency  46.          32.           ?. 35

To calculate the frequency of chicken, subtract the frequency of salad and fish from the total of 78 meals.

Frequency of chicken

= 78 - 46 - 35

= 27.

Meal Pairing Salad Soup Chicken Fish

Frequency 46.           32.            27. 35

The total number of meals served is 78. Of the 46 meals that included salads, 21 also included fish. This means that the frequency of fish is 35. The frequency of chicken can be calculated by subtracting the frequency of salad and fish from the total number of meals. The frequency of chicken is 27. The two-way frequency table representing this situation is as follows: Meal Pairing, Salad, Soup, Chicken, Fish; Frequency, 46, 32, 27, 35. This table shows that there were 46 meals with salad, 32 meals with soup, 27 meals with chicken, and 35 meals with fish.

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