Help please:))

2. When shipping ice cream, melting is understandably a big concern. You will notice that ice cream is not generally packaged in a cube-shaped container. A standard container of ice cream contains 1 L, or 1000 cm3 of ice cream,

a. What would be the optimal dimensions (radius and height) to minimize surface area?

b. What would the surface area be?

C. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.​

Answers

Answer 1

Answer:

a) Because this asks about the radius and height, I assume that we are talking about a cylinder shape.

Remember that for a cylinder of radius R and height H the volume is:

V = pi*R^2*H

And the surface will be:

S = 2*pi*R*H + pi*R^2

where pi = 3.14

Here we know that the volume is 1000cm^3, then:

1000cm^3 = pi*R^2*H

We can rewrite this as:

(1000cm^3)/pi = R^2*H

Now we can isolate H to get:

H = (1000cm^3)/(pi*R^2)

Replacing that in the surface equation, we get:

S = 2*pi*R*H + pi*R^2

S = 2*pi*R*(1000cm^3)/(pi*R^2) + pi*R^2

S = 2*(1000cm^3)/R + pi*R^2

So we want to minimize this.

Then we need to find the zeros of S'

S' = dS/dR = -(2000cm^3)/R^2 + 2*pi*R = 0

So we want to find R such that:

2*pi*R = (2000cm^3)/R^2

2*pi*R^3 = 2000cm^3

R^3 = (2000cm^3/2*3.14)

R = ∛(2000cm^3/2*3.14) = 6.83 cm

The radius that minimizes the surface is R = 6.83 cm

With the equation:

H = (1000cm^3)/(pi*R^2)

We can find the height:

H = (1000cm^3)/(3.14*(6.83 cm)^2) =  6.83 cm

(so the height is equal to the radius)

b) The surface equation is:

S = 2*pi*R*H + pi*R^2

replacing the values of H and R we get:

S = 2*3.14*(6.83 cm)*(6.83 cm) + 3.14*(6.83 cm)^2 = 439.43 cm^2

c) Because if we pack cylinders, there is a lot of space between the cylinders, so when you store it, there will be a lot of space that is not used and that can't be used for other things.

Similarly for transport problems, for that dead space, you would need more trucks to transport your ice cream packages.


Related Questions

An industrial psychologist consulting with a chain of music stores knows that the average number of complaints management receives each month throughout the industry is 4, but the variance is unknown. Nine of the chain's stores were randomly selected to record complaints for one month; they received 2, 4, 3, 5, 0, 2, 5, 1, and 5 complaints. Using the .05 significance level, is the number of complaints received by the chain different from the number of complaints received by music stores in general?
1. Use the five steps of hypothesis testing.
2. Sketch the distributions involved
3. Explain the logic of what you did to a person who is familiar with hypothesis testing, but knows nothing about t tests of any kind. Be sure to explain how this problem differs from a problem with a known population variance and a single sample.

Answers

Answer: See explanation

Step-by-step explanation:

1. Use the five steps of hypothesis testing.

Step 1: The aim of the research is to conduct the five steps of hypothesis testing.

Step 2:

Null hypothesis: H0 u= 4

Population mean: H1 u = 4

Alternate hypothesis: u ≠ 4

Population mean: u ≠ 4

Step 3 and step 4 are attached.

Step 5: Based on the calculation, the calculated value of t is less than the t critical value, therefore, the null hypothesis will be failed to be rejected.

2. Sketch the distributions involved

This has been attached.

3. Explain the logic of what you did to a person who is familiar with hypothesis testing, but knows nothing about t tests of any kind.

The distribution is "t".

The means is tested by using T-test.

Chi-square is used to test the single variance.

A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within with ​% confidence if ​(a) she uses a previous estimate of ​? ​(b) she does not use any prior​ estimates?

Answers

Answer:

732 samples ;

752 samples

Step-by-step explanation:

Given :

α = 90% ; M.E = 0.03 ; p = 0.58 ; 1 - p = 1 - 0.58 = 0.42

Using the relation :

n = (Z² * p * (1 - p)) / M.E²

Zcritical at 90% = 1.645

n = (1.645² * 0.58 * 0.42) / 0.03²

n = 0.65918769 / 0.0009

n = 732.43076

n = 732 samples

B.)

If no prior estimate is given, then p = 0.5 ; 1 - p = 1 - 0.5 = 0.5

n = (Z² * p * (1 - p)) / M.E²

Zcritical at 90% = 1.645

n = (1.645² * 0.5 * 0.5) / 0.03²

n = 0.67650625 / 0.0009

n = 751.67361

n = 752 samples

The average cost when producing x items is found by dividing the cost function, C(x), by the number of items,x. When is the average cost less than 100, given the cost function is C(x)= 20x+160?
A) ( 2, infinit)
B) (0,2)
C) (-infinit,0) U (2,infinit)
D) (- infinit,0] U [2,infinit)

Answers

9514 1404 393

Answer:

  A)  (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don't think about it

Step-by-step explanation:

We want ...

  C(x)/x < 100

  (20x +160)/x < 100

  20 +160/x < 100 . . . . . separate the terms on the left

  160/x < 80 . . . . . . . subtract 20

  160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0

  x > 2 . . . . . . simplify

In interval notation this is (2, ∞).   matches choice A

__

Technically (mathematically), we also have ...

  160/80 > x . . . . and x < 0

which simplifies to x < 0, or the interval (-∞, 0).

If we include this solution, then choice C is the correct one.

_____

Comment on the solution

Since we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.

HELPPPP

what is this

Answers

Answer:

Pls be specific with your question

Which ratio expresses the scale used to create this drawing?
1 square=10 yards

Answers

Answer:

option B

Step-by-step explanation:

option B

gdyfudjfjghfhguftduc

The theoretical mean of a distribution is also known as its ______________.

Answers

Answer:

skewness

Step-by-step explanation:

Average.

The average of a set of observations is the most important and useful measure of statistics and is a position measure, as it shows the positions of the numbers to which it refers. The average value is involved in several types of statistics and is examined in almost all statistical distributions. It is generally defined as the sum of the observations by their number. That is, it is the mathematical operation of finding the "mean distance" between two or more numbers.

Learn more about averages in https://brainly.com/question/22390452

i’ll make brainliest
look at the photo and check my work?
also tell me the answer to the ones i didn’t do
thanks :)

Answers

First of all, your work all seems to be correct.

2. =, this is because in decimals 100% and 1 are the same.

3. Measure of center is the mean, median, and mode, as they are all ways to interpret the center of the data.

5. The lines do not appear to be congruent as they are of different lengths.


Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
The person above is correct but gives me Brainliest because I’m want it mores then they can, but I don’t want too do wrk

wrote the terms below.

–8, –4, 0, 4, 8, 12

What do these terms represent?
an arithmetic series
an arithmetic sequence
a geometric series
a geometric sequence

Answers

Answer:

an arithmetic sequence

Step-by-step explanation:

an arithmetic series is wrong also heres an example i found of an arithmetic sequence

The terms in the given sequence represents an arithmetic sequence.

What is Arithmetic Sequence?

Arithmetic sequence is a sequence of numbers where the numbers are arranged ion a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.

Given sequence of numbers is,

-8, -4, 0, 4, 8, 12, ......

We have to find which sequence does it represent.

This is not a series since they are not represented as the sum.

If the sequence is a geometric sequence, then the ratio of consecutive numbers will be same.

If it is arithmetic sequence, then the difference of consecutive numbers will be same.

Here, ratio is not same.

Difference are same.

-4 - -8 = 4, 0 - -4 = 4, 4 - 0 = 4, 8 - 4 = 4, ........

Common difference is 4.

Hence it is an arithmetic sequence.

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A drinking container is shaped like a cone and must hold at least 10 ounces of fluid. The radius of the top of the container is 2.25 inches. The steps for determining the height of the cone-shaped container are shown below.

Answers

9514 1404 393

Answer:

  C.  h ≥ 1.9 in

Step-by-step explanation:

As the final step, divide both sides of the inequality by 5.3:

  (5.3h)/5.3 ≥ 10/5.3

  h ≥ 1.9

f(x) = 2x2 + 4x - 5
g(x) = 6x3 – 2x2 + 3
Find (f + g)(x).

Answers

Answer:

4x-5=4x-5

(f+g) (x)=6x³+3

Step-by-step explanation:

The wholesale price of 6 oz plastic bottles is 6 cents how many plastic bottles can be purchased for $98.41

Answers

Answer:

1640

Step-by-step explanation:

Take the total amount and divide by the amount for one

Make sure to write 6 cent in dollar form (.06)

98.41 / .06

1640.1666

Round down since we need to buy whole bottles

1640

a soft drink vendor at a popular beach analyzes his sales recods and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by

Answers

Complete Question:

A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x² + 3x - 1800.

a. What is his maximum profit per day?

b. How many cans must be sold in order to obtain the maximum profit?

Answer:

a. $450

b. 1500 cans

Step-by-step explanation:

Given the following quadratic function;

P(x) = -0.001x² + 3x - 1800  ......equation 1

a. To find his maximum profit per day;

Since P(x) is a quadratic equation, P(x) would be maximum when [tex] x = \frac {-b}{2a} [/tex]

Note : the standard form of a quadratic equation is ax² + bx + c = 0  ......equation 2

Comparing eqn 1 and eqn 2, we have;

a = -0.001, b = 3 and c = -1800

Now, we determine the maximum profit;

[tex] x = \frac {-b}{2a} [/tex]

Substituting the values, we have;

[tex] x = \frac {-3}{2*(-0.001)} [/tex]

Cancelling out the negative signs, we have;

[tex] x = \frac {3}{2*0.001} [/tex]

[tex] x = \frac {3}{0.002} [/tex]

x at maximum = 1500

Substituting the value of "x" into equation 1;

P(1500) = -0.001 * 1500² + 3(1500) - 1800

P(1500) = -0.001 * 2250000 + 4500 - 1800

P(1500) = -2250 + 2700

P(1500) = $450

b. Therefore, the soft-drink vendor must sell 1500 cans in order to obtain the maximum profit.

What is the derivative of x^2?

Answers

Answer:

[tex]\displaystyle \frac{d}{dx}[x^2] = 2x[/tex]

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = x^2[/tex]

Step 2: Differentiate

Basic Power Rule:                                                                                         [tex]\displaystyle \frac{dy}{dx} = 2x^{2 - 1}[/tex]Simplify:                                                                                                         [tex]\displaystyle \frac{dy}{dx} = 2x[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

PLEASE i need the answers!!!!!!!!!
I have no time please if you know the answer please tell MEEE!!!!!!!!!!!

Answers

Answer:

5x^2(2-3x)

(n+4)(x+y)

Step-by-step explanation:

please help me its timed -H.M​

Answers

Answer:

f(3) = g(3)

General Formulas and Concepts:

Algebra I

Functions

Function NotationGraphing

Step-by-step explanation:

We can see from the graph that the lines intersect at (3, 6). If this is the case, then that means that when x = 3 for both functions, it outputs f(x) = 6.

Rewriting this in terms of function notation:

f(3) = 6, g(3) = 6

∴ f(3) = g(3)



Suppose 50.7 liters of water came out of a faucet today. If 2.6 liters of water come out each minute, for how many minutes was the faucet on?

Answers

I believe the answer is 19.5 (or 19m 30s), 50.7/2.6=19.5, 2.6x19.5=50.7

A trough has ends shaped like isosceles triangles, with width 2 m and height 5 m, and the trough is 18 m long. Water is being pumped into the trough at a rate of 8 m3/min. At what rate (in m/min) does the height of the water change when the water is 2 m deep

Answers

9514 1404 393

Answer:

   5/9 m/min

Step-by-step explanation:

The depth of the water is 2/5 of the depth of the trough, so the width of the surface will be 2/5 of the width of the trough:

  2/5 × 2 m = 4/5 m

Then the surface area of the water is ...

  A = LW = (18 m)(4/5 m) = 14.4 m²

The rate of change of height multiplied by the area gives the rate of change of volume:

  8 m³/min = (14.4 m²)(h')

  h' = (8 m³/min)/(14.4 m²) = 5/9 m/min

can someone help me out with this question??? ​

Answers

Answer:

a

Step-by-step explanation:

A television stand at Wiles' Discount Mart is $187, and the sales tax is 6%. What is the amount of tax to be paid for the TV?

Answers

Answer:

$11.22

Step-by-step explanation:

100% = 187

1% = 187/100 = $1.87

6% = 1%×6 = 1.87×6 = $11.22

Answer:

In this case, you need to calculate the 6% of the price, which is 187 $.

We only need to multiply the price (187) by the percentage (6%):

187 * 0.06 = 11.22

So the tax would be $11.22

Find the range from the ordered pair {(1, 2), (2, 3), (3, 4), (4, 5)}

Answers

Answer:

Range { 2,3,4,5}

Step-by-step explanation:

The range is the output values

Range { 2,3,4,5}

A car travels 1/8 mile in 2/13 minutes. What is the speed in terms of miles per minute?

Answers

Answer:

13/16 miles per minute

Step-by-step explanation:

Take the miles and divide by the minutes

1/8 ÷ 2/13

Copy dot flip

1/8 * 13/2

13/16 miles per minute

Not sure how to do this

Answers

Answer:
Scale factor of 2

Explanation:
I compared the lengths of AC to DF. AC is one unit long, whereas DF is two units long, so DF is dilated by a scale factor of 2.

Find x on this triangle

Answers

Answer:

3 sqrt(3) =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos 30 = x/6

6 cos 30 = x

6 ( sqrt(3)/2) = x

3 sqrt(3) =x

Answer this please~!!!!

Answers

Answer:

12

Step-by-step explanation:

113.04=3.14 x 3^2 x h/3

find m∠H
What does m∠H happened to equal​

Answers

Answer:

[tex]m\angle H = 30^o[/tex]

Step-by-step explanation:

Given

See attachment

Required

Find [tex]m\angle H[/tex]

To calculate [tex]m\angle H[/tex], we make use of:

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

So, we have:

[tex]\cos(H) = \frac{GH}{HI}[/tex]

This gives:

[tex]\cos(H) = \frac{10\sqrt3}{20}[/tex]

[tex]\cos(H) = \frac{\sqrt3}{2}[/tex]

Take arccos of both sides

[tex]m\angle H = cos^{-1}(\frac{\sqrt3}{2})[/tex]

[tex]m\angle H = 30^o[/tex]

Which graph represents y = |xl?
A
B
C
D

Answers

Answer:

B

Step-by-step explanation:

The equation represented in the question is the parent absolute value question. If you know the different parent functions, then the answer is obvious because absolute value equations always form a V. However, if you do not do this then you can create a table and plugin values. Plugin numbers like 0, -1, and 1 for X and solve for Y. Finally, graph these points and see what graph best fits. If needed you can also plug in more points.

Answer:

B.

Step-by-step explanation:

I got it correct on the warm up

Draw clearly the graph of the linear equation. y=1/2x, where x= (-4 -2, 0, 2, 4)​

Answers

Answer:

(in attachment)

Step-by-step explanation:

you can find the points by inputting the x-values into the equation to solve for the y-values, then connecting the plotted points to create the line.

When x=-4

y=1/2(-4)

y=-2

(-4,-2)

Repeat for all values.

Select the correct statement about what data scientists do during the Data Preparation stage.

a. During the Data Preparation stage, data scientists define the variables to be used in the model.
b. During the Data Preparation stage, data scientists determine the timing of events.
c. During the Data Preparation stage, data scientists aggregate the data and merge them from different sources.
d. During the Data Preparation stage, data scientists identify missing data.
e. All of the above statements are correct.

Answers

Answer:

e. All of the above statements are correct.

Option e is correct. All of the above statements are correct.

What is Data science?

Data science is an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processes, algorithms and systems to extract or extrapolate knowledge and insights from noisy, structured and unstructured data

Data Scientist makes value out of data, he is expert in various tools and technologies like machine learning, deep learning, artificial intelligence and he solve business problems by presenting a model to predict business future.

During data preparation, data scientists and DBAs aggregate the data and merge them from different sources. During data preparation, data scientists and DBAs define the variables to be used in the model.

Hence, All of the above statements are correct, Option e is correct.

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The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds. For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23. Find the P-value of the test statistic.

Answers

Answer:

The p-value of the test statistic is 0.2019.

Step-by-step explanation:

Test if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds.

At the null hypothesis, we test if it relieves pain in at most 384 seconds, that is:

[tex]H_0: \mu \leq 384[/tex]

At the alternative hypothesis, we test if it relieves pain in more than 384 seconds, that is:

[tex]H_1: \mu > 384[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

384 is tested at the null hypothesis:

This means that [tex]\mu = 384[/tex]

For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23.

This means that [tex]n = 41, X = 387, \sigma = 23[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{387 - 384}{\frac{23}{\sqrt{41}}}[/tex]

[tex]z = 0.835[/tex]

P-value of the test:

The p-value of the test is the probability of finding a sample mean above 387, which is 1 subtracted by the p-value of z = 0.835.

Looking at the z-table, z = 0.835 has a p-value of 0.7981.

1 - 0.7981 = 0.2019

The p-value of the test statistic is 0.2019.

a study of patients who were overweight found that 53% also had elevated blood pressure. If 3 overweight patients are selected find the probability that all three have elevated blood pressure

Answers

Answer:

14.8%

Step-by-step explanation:

53/100*53/100*53/100

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