1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Katyanochek1 [597]
3 years ago
10

A carpenter wants to build a rectangular box with square sides in which to put round things. the material for the bottom costs $

20/ft^2, material for the sides costs $10/ft^2 and the material for the top costs $50/ft^2
If the volume of the box must be 5 ft^3, then find the dimensions that will minimize the cost (and find the minimum cost).
Mathematics
1 answer:
alexira [117]3 years ago
5 0

Answer:1.627\times 1.627\times 1.88\ ft^3

Step-by-step explanation:

Given

Suppose side face have a dimension of l\times l

and width of h

volume V=l^2\cdot h

h=\frac{V}{l^2}

volume V=5 ft^3

Area of side wall is A_s=l^2

Area of top Wall A_t=l\times h

Area of bottom A_b=l\times h

Cost of bottom wall c_b=20\times l\times h=20lh

Cost of top wall c_t=50\times l\times h=50lh

Cost of side walls c_s=4\times l^2\times 10=40l^2

total cost C=c_s+c_t+c_b=20lh+50lh+40l^2

C=70lh+40l^2

C=70\times l\times \frac{5}{l^2}+40l^2

differentiate C w.r.t l to get minima or maxima

\frac{\mathrm{d} C}{\mathrm{d} l}=0

-\frac{350}{l}+80l^2=0

l^3=\frac{350}{80}

l=1.627 ft

h=\frac{5}{2.648}

h=1.88 ft

Dimension of Box is 1.627\times 1.627\times 1.88\ ft^3

You might be interested in
Your teacher gives you a number cube with numbers 1-6 on its faces. You are asked to state a theoretical probability model for r
butalik [34]

The missing part of the question is show in bold format.

Your teacher gives you a number cube with numbers 1-6 on its faces. You are asked to state a theoretical probability model for rolling it

once. Your probability model shows a probable outcome of 1/6 for each of the numbers on the cube, 1 chance for all any of the 6 numbers.

You roll it 500 times and get the following data:

Outcome 1 2 3 4 5 6

Frequency 77 92 75 90 76 90

Exercises 1–2

1. If the equality model was correct, about how many of each outcome

would you expect to see if the cube is rolled 500 times

2. Based on the data from the 500 rolls, how often were odd numbers observed? How often were even numbers observed?

Answer:

Step-by-step explanation:

1.

If the equally likely model was correct,  about how many of each outcome

would you expect to see if the cube is rolled 500 times.

The probability of rolling any of the numbers from 1 to 6 is  p(1/6)

The number of each of the outcomes expected to be seen in 500 rolls of the number cube is np

= 500 * \frac{1}{6}  \\ \\ = \frac{500}{6} \\ \\  = 83.333 \\ \\ \approx 83

2.  From the given data in the roll;

The odd numbers 1, 3 and 5, were obtained at  77, 75 and 76 times respectively.

Thus, the total number of times odd number were rolled = 77 + 75 + 76 = 228

Probability of an odd number turning up = \frac{ number \ of  \ required  \ outcome}{ total \  number  \ of  \ possible \ outcome}

= \frac{228}{500}

= 0.456

= 45.6%

The even numbers, 2, 4 and 6, were obtained 92, 90 and 90 times respectively.

The total number of times even number were rolled = 92 + 90 + 90 = 272

Probability of an even number turning up  = \frac{ number \ of  \ required  \ outcome}{ total \  number  \ of  \ possible \ outcome}

= \frac{272}{500}

= 0.544

= 54.4%

4 0
3 years ago
Aaliyah is starting her own lawn mowing business. Aaliyah has calculated that she needs to earn $721 per week to support her fam
Roman55 [17]

Answer:She will have to charge her customers at least 21 dollars an hour to help her family.

Step-by-step explanation:

7 0
3 years ago
When Nayeli goes bowling, her scores are normally
Ber [7]

Using the normal distribution, it is found that she scores less than 128 in 28.1% of her games.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

In this problem, the mean and the standard deviation are given, respectively, by \mu = 135, \sigma = 12.

The proportion of games in which she scores less than 128 is the <u>p-value of Z when X = 128</u>, hence:

Z = \frac{X - \mu}{\sigma}

Z = \frac{128 - 135}{12}

Z = -0.58

Z = -0.58 has a p-value of 0.281.

She scores less than 128 in 28.1% of her games.

More can be learned about the normal distribution at brainly.com/question/24663213

#SPJ1

3 0
2 years ago
How much larger is the circumference of circle A than the circumference of circle B?
Rzqust [24]

Answer:

Circumference of Circle A is about 16 units larger than the Circumference of Circle B

Step-by-step explanation:

Formula for Circumference of a circle = πd

Where, d = diameter of circle

Thus:

Circle A diameter = 13

Circle B diameter = 8

Therefore:

Circumference of Circle A = π*13 = 40.8407045 ≈ 41 unit (nearest whole number)

Circumference of Circle B = π*8 = 25.1327412 ≈ 25 unit (nearest whole number)

✔️Difference between circumference of Circle A and Circle B = 41 - 25 = 16

Therefore the Circumference of Circle A is about 16 units larger than the Circumference of Circle B

3 0
3 years ago
What is the frequency of the function f(x)?
Readme [11.4K]

Answer:

The frequency = 5/2π

Step-by-step explanation:

* Lets revise some facts about the trigonometry function

- If the function is f(x) = A sin (B x + C) + D  

* A is the amplitude  

- The amplitude is the height from highest to lowest points and  

 divide the answer by 2  

* The period is 2π/B  

- The period is the distance from one peak to the next peak

- Period and Frequency are related where frequency = 1/period

* C is the horizontal shift  

- The horizontal shift is how far the function is shifted to left  

 (C is positive) or to right (C is negative) from the original position.  

* D is the vertical shift  

- The vertical shift is how far the function is shifted vertically up

  (D is positive) or down (D is negative) from the original position.  

* Lets solve the problem

∵ f(x) = 3 cos (5x) + 2

∵ f(x) = A sin (B x + C) + D  

∴ A = 3 , B = 5 , C = 0 , D = 2

∵ The period = 2π/B

∴ The period = 2π/5

∵ The frequency = 1/period

∴ The frequency = 1/(2π/5) ⇒ multiply up and down by 5

∴ The frequency = 5/2π

4 0
3 years ago
Other questions:
  • Solve S = 2πrh for r
    6·1 answer
  • A meteor crater is 4200 feet in diameter. Approximate the distance around
    10·1 answer
  • Divide 132kg in a ratio of 3:3:5
    10·1 answer
  • You are building a toothpick fort for class. Each wall must be 1 1⁄3 feet long. Each toothpick is 2 inches long. How many toothp
    12·1 answer
  • Simplify –2x3y × xy 2.
    8·1 answer
  • Can someone tell me if this is correct and if not tell me how to put it plzzzzzzzz
    10·1 answer
  • H e l p m e p l z ! ! ! !
    8·2 answers
  • If you are 6’1 and someone else is 5,1 what is your height difference by inches? :&gt;
    6·2 answers
  • Your two day pass to a theme park is $76.50. this is 31.41 less than your uncle's two day pass. what is the price of
    12·1 answer
  • If it is 8:50 a.m., what will the time be 4 hours and 20 minutes later?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!