The circumference of a circle is 23π cm.
What is exact the area of the circle?
Do not round. Include correct units.
Show your process

The exact dimensions (in inches) of the cylindrical mailing tube that may be mailed using the postal service is 7 inches radius and a length of 14 inches.

To find the maximum volume of the mailing tube, maximize the function:

V = πr²L

subject to the constraint:

C = 2πr + L = 84

where C is the girth.

Using Lagrange multipliers, we need to solve the system of equations:

∇V = λ∇C

2πrL = λ(2π)

πr² = λ

2πr + L = 84

Taking the ratio of the first two equations:

L = 2r

Substituting this into the third equation:

4πr + 2r = 84

Simplifying:

r = 7

Substituting this into the equation L = 2r:

L = 14

Therefore, the cylindrical mailing tube of greatest volume that may be mailed using the postal service has a radius of 7 inches and a length of 14 inches.

Find out more on Lagrange multipliers here: https://brainly.com/question/17227640

#SPJ1

Image transcribed:

A package to be mailed using a certain postal service may not measure more than 84 inches in length plus girth. (Length is the longest dimension and girth is the largest distance around the package, perpendicular to the length.)

length

girth

Use Lagrange multipliers to find the exact dimensions (in inches) of the cylindrical mailing tube of greatest volume that may be mailed using the postal service.

radius ______ in

length ______ in

a) General solution of the system is (x, y, z) = (2, 0, 1).

b) There are no multiple solutions, and we cannot find two specific solutions.

The given system of linear equations is:
1) x - y + z = 3
2) 3x + 2z = 7
3) x - 4y + 2z = 5

The reduced matrix for this system is:
1 0 1
0 1 0
0 0 1

Using the reduced matrix, we can rewrite the system of linear equations as:
1) x + z = 3
2) y = 0
3) z = 1

Now we can solve the system step by step:

From equation (3), we know that z = 1.

Next, we can use the value of z in equation (1) to find x:
x + 1 = 3
x = 3 - 1
x = 2

Finally, from equation (2), we know that y = 0.

So, the general solution of the system is (x, y, z) = (2, 0, 1).

(b) Since there is only one solution to this system, there are no multiple solutions, and we cannot find two specific solutions.

Learn more about linear equations.

brainly.com/question/11897796

#SPJ11

Answer:

(4n+3)(2n-5)

Step-by-step explanation:

1) Split the second term [tex]8n^2-14n-15[/tex] into two terms.

1- Multiply the coefficient of the first term by the constant term.

[tex]8\times-15=-120[/tex]

2- Ask: Which two numbers add up to -14 and multiply to -120?

6 and -20

3- Split -14n  as the sum of 6n  and -20n.

[tex]8n^2+6n-20n-15[/tex]

2) Factor out common terms in the first two terms, then in the last two terms.

[tex]2n(4n+3)-5(4n+3)[/tex]

3) Factor out the common term [tex]4n+3[/tex].

[tex](4n+3)(2n-5)[/tex]

The area of the given shape is 22 square tiles. The given shape consists of two rectangles and a square.

To find the area of the shape, we need to find the area of each of these three shapes and then add them up.

First, we can see that the length of the longer rectangle is 6 tiles and the width is 2 tiles. Therefore, the area of this rectangle is 6 × 2 = 12 tiles.

Next, the length of the shorter rectangle is 3 tiles and the width is 2 tiles. Thus, the area of this rectangle is 3 × 2 = 6 tiles.

Finally, the square has a side length of 2 tiles, so its area is 2 × 2 = 4 tiles.

Adding up the areas of the three shapes, we get 12 + 6 + 4 = 22 tiles.

Find out more about the area at

brainly.com/question/26473539

#SPJ4

Answer:

379.94

Step-by-step explanation:

Area of a circle given radius is really easy! The equation for area of a cicle is pi x r^2. So just plug in. Assuming pi is 3.14 your equation would be

3.14x11^2. 11 squared is 121. Then multiply by 3.14 and thats your answer.

Answer:

x² +4x + 3

Step-by-step explanation:

Area = length x width

Area = (x + 3)( x + 1)

Area = x² + X + 3x +3

Area = x² + 4x +3

Answer: y=4

Step-by-step explanation:

you would plug in 10 wherever x would be so your new equation would be 10-7y=-18.

subtract 10 from both sides.

-7y=-28

then divide by -7

y=4

The area of 2.5 by 2.5 square is given as follows:

6.25 square units.

The area of a square of side length s is given by the square of the side length, as follows:

A = s².

For this problem, we have 2.5 by 2.5 square, hence the side lengths are given as follows:

s = 2.5.

Then the area of 2.5 by 2.5 square is obtained applying the formula as follows:

A = 2.5²

A = 6.25 square units.

This means that the entire 2.5-by-2.5 square can be divided into 6.25 unit squares, in which each of them would have a side length of one unit.

More can be learned about the area of a square at brainly.com/question/25092270

#SPJ1

The value of x is 7, and NM and OL are both equal to 37.

Since LMNO is a parallelogram, its opposite sides must be parallel and equal in length. Therefore, we have,

NM = OL

We also have the following information:

NM = x + 30

OL = 4x + 9

Substituting the first equation into the second equation, we get:

x + 30 = 4x + 9

Simplifying this equation, we get:

3x = 21

Therefore, x = 7.

Substituting this value back into the original equations, we get:

NM = x + 30 = 7 + 30 = 37

OL = 4x + 9 = 4(7) + 9 = 37

Learn more about parallelogram here

brainly.com/question/24212888

#SPJ4

Esther missed including the surface area of the square sides of the pyramid. The correct surface area is found by adding the surface area of the four triangular faces, base, and sides. The total surface area is 104cm².

Esther's error was that she only considered the surface area of the triangular faces and the base of the pyramid. She failed to include the surface area of the pyramid's square sides.

To find the correct surface area of the pyramid, we need to add the surface area of the four triangular faces and the surface area of the square base and sides. The surface area of the square base is 4² = 16cm², and the surface area of each triangular face is (1/2)bh = (1/2)(4)(7) = 14cm². The surface area of each square side is 4 x 4 = 16cm².

Therefore, the correct surface area of the square pyramid is:

4 x 14cm² (for the four triangular faces) + 16cm² (for the base) + 4 x 16cm² (for the four square sides) = 104cm².

Learn more about square pyramid here: brainly.com/question/27350043

#SPJ4

The sum of the first 48 terms of the following series, to the nearest integer is 4632.

An computation progression( AP) is a sequence of figures where the differences between every two successive terms are the same. In this progression, each term, except the first term, is attained by adding a fixed number to its former term. This fixed number is known as the common difference and is denoted by'd'. The first term of an computation progression is generally denoted by' a' or' a1'.

We have series as,

5,9,13,....48

so we have

First term = a = 5

Last term T = 48

Interval between them as d = 9 - 5 = 4

To find the sum of the first 48 terms we have formula as,

[tex]S = \frac{n}{2} [a+(n-1)d]\\[/tex]

putting the value of the values in the equation,

[tex]S = \frac{48}{2} [5+(48-1)4]\\\\S = 24[5+188]\\\\S = 4632\\[/tex]

Therefore,  the sum of the first 48 terms is 4632.

Learn more about Sum of the terms:

https://brainly.com/question/29778981

#SPJ4

a. The revenue function, r(x), is given by the product of the price x and the demand function d(x):

[tex] \sf r(x) = x \times d(x) = x \times (400 - 4x) = 400x - 4x^2[/tex]

The domain of this function is the set of possible prices that can be charged for the jeans, which is typically a positive real number, or in interval notation: (0, infinity).

b. If the price is $40, we can find the revenue by plugging in x = 40 into the revenue function:

[tex] \sf r(40) = 400(40) - 4(40)^2 = 16,000 - 6,400 = 9,600[/tex]

Therefore, the company will earn $9,600 in revenue if they sell their jeans at a price of 40

The number of driving lessons you need to take with a professional instructor before your parents can teach you varies depending on the regulations in your area. In some regions, a specific number of driving lessons is required by law before you can apply for your driver's license. As a result, you should check with your local Department of Motor Vehicles (DMV) or other regulatory agency to learn more about the specific requirements in your area.

In general, however, it is usually beneficial to take as many driving lessons as possible with a professional instructor. Professional driving instructors have been educated in how to teach driving skills safely and effectively. They have also assisted many other people in learning how to drive, and as a result, they have a wealth of knowledge and expertise to draw on.

The more driving lessons you take with a professional instructor, the more chances you'll have to learn and improve your driving abilities. You may be able to practice with your parents after only a few lessons, but it's generally a good idea to take as many as possible with an instructor before doing so. This will give you the best chance of success while you learn to drive safely and confidently.

To learn more about driving :

https://brainly.com/question/2619161

#SPJ11

The probability that a bat does not consume any mosquitoes in a 30-second interval is 0.0067379 or 0.67%.

In this case, the average rate of mosquitoes consumed by a bat is 10 per minute.

To find the rate for a 30-second interval, calculate the rate for 1 minute and then adjust it for the 30-second interval:

Average rate for 1 minute = 10 mosquitoes

Rate for 30 seconds = [tex]\dfrac{10 \,mosquitoes}{1 \,minute} \times \dfrac{1}{2}[/tex]

                                  = 5 mosquitoes

The Poisson distribution probability mass function is given by:

[tex]\[ P(X = k) = \dfrac{e^{-\lambda} \cdot \lambda^k}{k!} \][/tex]

Where:

[tex]\(\lambda\)[/tex] is the average rate of events.

In this case, to find the probability that k = 0.

So, let's plug in the values:

[tex]\(\lambda = 5\)[/tex]

[tex]\(k = 0\)[/tex], back to the formula as

[tex]\[ P(X = 0) = \dfrac{e^{-5} \cdot 5^0}{0!} \][/tex]

Calculating the probability as

[tex]\[ P(X = 0) = e^{-5}[/tex]

                [tex]= 0.0067379[/tex]

Therefore, the probability is 0.0067379 or 0.67%.

Learn more about Probability here:

https://brainly.com/question/34689735

#SPJ12

The probability of drawing a diamond from a deck of cards is 1/4. So, the odds in favor of drawing a diamond from an ordinary deck of cards are 1/3.

A deck of cards has 52 cards in it, and there are 13 cards of diamonds in it. So, the probability of drawing a diamond is 13/52. Simplifying 13/52, we get 1/4. The odds of an event happening are the ratio of the probability of an event happening to the probability of an event not happening. It's expressed in the form of x:y.

The probability of an event happening is the probability of success. The probability of an event not happening is the probability of failure. In the current scenario, the probability of drawing a diamond is 1/4. So, the probability of not drawing a diamond is 3/4. Therefore, the odds in favor of drawing a diamond are:

=1/3

The odds in favor of drawing a diamond from an ordinary deck of cards are 1/3.

To learn more about odds refer :

https://brainly.com/question/5816909

#SPJ11

Answer:

The correct order of the steps of eukaryotic DNA replication from when a germ cell enters gap 1 (G1) phase to the cell cycle termination is : G1-> S Phase ->G2 ->Mitosis ->Cytokinesis ->Cell cycle termination

Step-by-step explanation:

The correct order of the steps of eukaryotic DNA replication from when a germ cell enters gap 1 (G1) phase to the cell cycle termination is as follows:

Step 1: G1 phase - During this phase, the germ cell is growing and preparing for DNA synthesis.

Step 2: S phase - DNA replication occurs during this phase. The chromosomes duplicate to form two identical chromatids, which remain attached at the centromere.

Step 3: G2 phase - During this phase, the cell checks for any errors in DNA replication and prepares for cell division.

Step 4: Mitosis - The cell divides its replicated DNA and organelles into two identical daughter cells. This process ensures that each daughter cell has the same amount of genetic material as the parent cell.

Step 5: Cytokinesis - The cytoplasm divides, creating two identical daughter cells.

Step 6: Cell cycle termination: After successful completion of mitosis and cytokinesis, the cell cycle is terminated, and the daughter cells may enter a new cycle or enter a non-dividing state (G0 phase).

Learn more about DNA replication,

https://brainly.in/question/46455393

#SPJ11

The following conditions must be met to conduct a two-proportion significance test:

the populations are independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.

The two-proportion significance test is a hypothesis test that compares the proportions of two independent populations.

To conduct the two-proportion significance test, the following conditions must be met:

Populations must be independent.

Sample sizes are greater than 30.

The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.

The sample size should be large enough so that the sampling distribution of the sample proportion is nearly normal. The sample sizes should be large enough so that the central limit theorem can be applied.

In short, to conduct a two-proportion significance test, the populations must be independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.


To know more about two-proportion significance test refer here:

https://brainly.com/question/30255520#

#SPJ11

From the same starting point, two cyclists ride in different directions. The speed of one cyclist is twice that of the other. They will be 72 miles apart in 2 hours. The rate of each cyclist is 12 miles per hour and 24 miles per hour

Let’s call the rate of the slower cyclist “r”. Then, according to the problem, the rate of the faster cyclist is “2r”.

We can use the formula distance = rate x time to set up two equations, one for the distance traveled by the slower cyclist and one for the distance traveled by the faster cyclist. The sum of these distances is the total distance they are apart after 2 hours, which we know is 72 miles:

2r x 2+r x 2=72

Simplifying this equation, we get:

4r+2r=72

Combining like terms, we get:

6r=72

Dividing both sides by 6, we get:

R=12

So the rate of the slower cyclist is 12 miles per hour. Using the fact that the faster cyclist rides at twice the rate of the slower cyclist, we can find the rate of the faster cyclist:

2r=2 x 12=24

So the rate of the faster cyclist is 24 miles per hour.

Therefore, the two cyclists ride at rates of 12 miles per hour and 24 miles per hour, respectively.

To learn more about distance, refer:-

https://brainly.com/question/2734924

#SPJ4

Answer:

31cm

Step-by-step explanation:

14 + 8 + 9 = 31

Make sure to add the cm on the end!

The perimeter of the triangle is 31cm.

The perimeter of the triangle with sides of length 14 cm, 8 cm and 9 cm is 31 cm. This can be calculated by simply adding up the length of each side. To explain, the perimeter of a triangle is the sum of the lengths of all three sides.

In this particular triangle, the length of side 1 is 14 cm, the length of side 2 is 8 cm and the length of side 3 is 9 cm. When we add these three lengths, we get the perimeter of the triangle: 14 cm + 8 cm + 9 cm = 31 cm.

In general, to calculate the perimeter of any triangle, we first have to identify the lengths of all three sides. Then, we simply add these lengths together to get the perimeter.

For example, if the triangle had sides of lengths 4 cm, 5 cm and 6 cm, then the perimeter would be 4 cm + 5 cm + 6 cm = 15 cm.

In conclusion, the perimeter of any triangle can be calculated by adding together the length of each side. In the case of the particular triangle in question, the perimeter is 31 cm.

To know more about  perimeter refer here:

https://brainly.com/question/6465134

#SPJ11

Joelle has a total of 32 yards of ribbon in all, the correct option is A.

Let's use x to represent Joelle's total amount of ribbon. We know that 24 yards of the ribbon represent 86% of her total amount of ribbon, which can be expressed as:

24 = 0.86x

We can solve for x by dividing both sides by 0.86:

x = 27.91

The response options are all integers, thus we must round to the closest whole number because of this. Since 0.91 is greater than or equal to 0.5, we round up to 28.

Therefore, Joelle has a total of

x = 27.91 / 0.86

= 32.44 yards of ribbon.

Once again, we round to the nearest whole number, which is 32.

To learn more about yards follow the link:

https://brainly.com/question/28365360

#SPJ1

The complete question is:

To wrap gift boxes, Joelle uses 24 yards of ribbon, which is 86 of her total amount of ribbon. How many yards of ribbon does she have in all?

A 32

B 192

C 300

D 1920​

The cost to ship a box containing 5 laptops, weighing a total of 11 kg (including the empty box), is $58.90, with a cost of $40.00 for the first 5 kg and $3.15 for each additional kilogram.

The total mass of the packed shipping box can be found by adding the mass of the laptops (5 * 1.65 kg = 8.25 kg) to the mass of the empty box (2.75 kg) for a total mass of 11 kg.

Since the cost to ship the box is $40.00 for the first 5 kg and $3.15 for each additional kilogram over 5 kg, we can split the total mass into two parts: the first 5 kg and the additional weight above 5 kg.

The cost to ship the first 5 kg is $40.00, and the remaining weight is 11 kg - 5 kg = 6 kg.

The cost to ship the additional 6 kg is $3.15 per kilogram, so the total cost to ship the packed box is:

$40.00 + $3.15 * 6 kg = $58.90

Therefore, the cost to ship the packed box is $58.90.

To know more about Cost of shipping:

https://brainly.com/question/29364736

#SPJ4

The ratio of the heights is 5, the ratio of the surface areas is 25, and the ratio of the volumes is 125

Step-by-step explanation:

We can use the fact that similar pyramids have the same shape, but possibly different sizes. Let's denote the height of pyramid a by h_a, the height of pyramid b by h_b, and the scale factor between the two pyramids by k. Then, we have:

The ratio of the heights is k, since the height is scaled up by the same factor as the base length. That is, k = h_b / h_a.

The ratio of the surface areas is k^2, since the surface area is proportional to the square of the base length and the height. That is, k^2 = (side length of b / side length of a)^2 = (25 / 5)^2 = 5^2 = 25.

The ratio of the volumes is k^3, since the volume is proportional to the cube of the base length and the height. That is, k^3 = (side length of b / side length of a)^3 = (25 / 5)^3 = 5^3 = 125.

Therefore, the ratio of the heights is 5, the ratio of the surface areas is 25, and the ratio of the volumes is 125.

To learn more about proportional visit:

https://brainly.com/question/30657439

#SPJ11

Answer:

height ratio- 1:5   surface area- 1:25  volume- 1:125

Step-by-step explanation:

Variable b represents the number of hours Kevin spends watching television each week.

A statement proving the equality of two mathematical expressions is known as an equation.

Given equation a + b = 15 relates the number of hours.

If here Kevin spends doing homework each week (represented by the variable "a") and the number of hours he spends watching television each week (represented by the variable "b").

Since the total number of hours Kevin spends doing homework and watching television each week is 15, we can write:

homework + watching television = 15 hours

a + b = 15

To find out what b represents, we can rearrange the equation to solve for b:

b = 15 - a

This means that b represents the number of hours Kevin spends watching television each week, given that he spends a hours doing homework each week and the total number of hours spent on both activities is 15.

To know more about equation, visit:

https://brainly.com/question/2228446

#SPJ1

Complete question-

The equation is a + b = 15

There are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.

The total number of ways to form the delegation from five pairs of dance partners can be calculated using the combination formula. The combination formula is used to calculate the number of different combinations of n objects taken r at a time without repetition.

In this question, n is the total number of dance partners (5) and r is the number of people on the delegation (4).

Therefore, the calculation is as follows:

total number of ways = nCr

                    = 5C4

                    = 5! / 4!(5-4)!

                    = 5! / 4!1!

                    = 5 x 4 x 3 x 2 x 1 / 4 x 1 x 1

                    = 5 x 4 x 3 x 2

                    = 120

Hence, there are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.

Learn more about combination here:

https://brainly.com/question/20211959

#SPJ4

Answer:

4x^{3} ÷ 8 = x^{3}/2

The answer based on debt to assets ratio for east and west company are,

East company debt to assets ratio is equal to 0.44.

West company debt to assets ratio is equal to 0.28.

After comparing both the company debt to assets ratio East company is at higher level of financial risk.

Assets = Liabilities + Equity

For East company,

206,000 =  91,000 + 115,000

Assets = 206,000

liabilities = 91,000

Equity = 115,000

For West company,

603,000 =  169,000 + 434,000

Assets = 603,000

liabilities = 169,000

Equity = 434,000

Debt-to-assets ratio = Total liabilities divided by the total assets.

Debt-to-assets ratio for East

= 91,000 / 206,000

= 0.44

Debt-to-assets ratio for West

= 169,000 / 603,000

= 0.28

Comparing the two ratios,

0.44 > 0.28

This implies,

Company East has a higher debt-to-assets ratio is greater than the compared to Company West.

This represents that Company East has a higher level of financial risk.

As larger proportion of their assets are financed through debt.

This shows it is difficult to repay if the company experiences financial difficulties.

Company West has a lower level of financial risk as smaller proportion of their assets are financed through debt.

Therefore, the answer of the following questions are,

Debt to asset ratio of east company = 0.44

Debt to asset ratio of west company = 0.28

Company east has a higher financial risk level .

learn more about debt to asset ratio here

https://brainly.com/question/18648883

#SPJ4

Answer:

The answer is six eighths

There's 8 letters in all and 6 of them are consonants (M, T, H, C, L, B)

Step-by-step explanation:

so all you have to do is take out all the vowel and count the letters that are consonant then you make that your top number than you put that over the amount of numbers in total

Plot the x-intercept of (-0.5,0) Plot the y-intercept of (0,-2) Draw a line passing through both intercepts.

To graph 4x + 2y = 8, we'll first look at the x-intercept and y-intercept.

The x-intercept occurs when y is zero, and the y-intercept occurs when x is zero.

0 = 4x + 2y => x = -0.5y = 4x + 2(0) => y = -2

From the two equations, we get the ordered pairs(-2,0), and (-0.5,0) as our intercepts.

The line defined by these two points and that represent all solutions to the equation is:

y = -2x + 4

The table would show different values of x for different values of y, but since there are no specific values to solve, you

just have to use the slope-intercept formula to determine the points on the graph.

Here's how to plot the ordered pairs on a graph:

Plot the x-intercept of (-0.5,0)

Plot the y-intercept of (0,-2)

Draw a line passing through both intercepts.

for such more question on x-intercept

https://brainly.com/question/11989858

#SPJ11