A sheet of paper 54 cm-by-54 cm is made into an open box (i.e. there's no top), by cutting x-cm squares out of each corner and folding up the sides. Find the value of x that maximizes the volume of the box.
Give your answer in the simplified radical form/
x = ... is the max

Answer:

23/54 meters

Step-by-step explanation:

Assuming that the scale model is smaller, then the scale model should be 1/27th of the actual thing. Therefore:

11.5/27

= 23/54 meters tall

The value of the double integral  ∫∫ (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1] is  11.77

In this question we need to calculate the double integral. {8x}/{1 + xy} dA ; R = 0, 8 0, 1

i.e., to find ∫∫ (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1]

First we integrate the function (8x)/(1 + xy)  as a function of y, treating the variable x as a constant.

G(x) = ∫_[0, 8] ((8x)/(1 + xy) ) dy

G(x) = 8 ln(8x + 1)

Now we calculate the integral of the previous result as a function of x.

i.e., ∫_[0, 1] G(x) dx

= ∫_[0, 1] [8 ln(8x + 1)] dx

= 9 ln(9) - 8

= 11.77

Therefore, the solution to the double integral (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1] is 11.77

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Answer:-4 is your answer

Step-by-step explanation: When x = 8 your y = –4 (which is the function)

The sum of the remainders is 10. This result is independent of the value of x and holds true for any five consecutive positive integers.

Arbitrary positive integer is any positive integer that is chosen without any particular reasoning or pattern. This can also refer to any number that is randomly chosen or assigned.

Let the original numbers be x, x+1, x+2, x+3, and x+4, where x is an arbitrary positive integer.

Then, their modulo 5 values are x mod 5, (x+1) mod 5, (x+2) mod 5, (x+3) mod 5, and (x+4) mod 5.

Now, let's calculate the sum of these modulo 5 values.

x mod 5 + (x+1) mod 5 + (x+2) mod 5 + (x+3) mod 5 + (x+4) mod 5

= x mod 5 + x mod 5 + 1 + x mod 5 + 2 + x mod 5 + 3 + x mod 5 + 4

= 5x mod 5 + 10

= 0 + 10

= 10

Hence, the sum of the remainders is 10.

This result is independent of the value of x and holds true for any five consecutive positive integers.

This is because when modulo 5 is applied to any set of five consecutive numbers, each number in the set will have an entry in the modulo 5 table, and the sum of the entries in the table is 10.

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Answer:

it will be A. good buddy

Step-by-step explanation:

The data represented by given stem and leaf display is 25, 26, 27, 53, 58, 62, 67, 69, 96, 96, 123. The correct option is B.

A stem-and-leaf display, also known as a stem-and-leaf plot, is a technique used to visualize the shape of distribution by displaying data in a graphical fashion, similar to a histogram.

The data represented by the different rows of stem-and-leaf display is,

First row → 25, 26, 27

Second row → 53, 58

Third row → 62, 67, 69

Fourth Row → 96, 96

Fifth Row → 123

Hence, the data represented by given stem and leaf display is 25, 26, 27, 53, 58, 62, 67, 69, 96, 96, 123.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

Firstly, let's get the fractions out of mixed form.

2 1/5 = 11/5

(To do this, multiply 2 times 5 and add to the 1.)

1 5/6 = 11/6

(To do this, multiply 1 times 6 and add to the 5.)

Next, let's get the common denominator. When making a common denominator, keep in mind you must multiply/divide both the numerator and denominator

The Mean Absolute Deviation (MAD) for the five-month moving average method, using the given patient data (749, 739, 779, 749, 546, 374, 610), is approximately [rounded MAD value with at least 4 decimal places].

To calculate the MAD using the five-month moving average method, we first need to calculate the moving averages for each group of five consecutive months. We start by taking the average of the first five months (749, 739, 779, 749, 546) and place the average as the first moving average. Then we shift the window by one month and calculate the average of the next five months (739, 779, 749, 546, 374) and continue this process until we reach the last group of five months (546, 374, 610).

Next, we calculate the absolute differences between each actual value and its corresponding moving average. For example, the absolute difference for the first month is |749 - moving average 1|, and so on. We sum up all these absolute differences and divide the total by the number of data points to obtain the MAD.

Performing these calculations using the given patient data will yield the MAD value, rounded to at least 4 decimal places. This MAD value represents the average absolute deviation from the moving averages and indicates the overall variability or dispersion of the data points around the moving averages.

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Answer:

3.89

Step-by-step explanation:

To find the price per quart of the window cleaner, we need to first determine how many quarts the 3-gallon container contains. We can do this by converting the number of gallons to quarts using the conversion factor that 1 gallon is equal to 4 quarts.

3 gallons * 4 quarts/gallon = 12 quarts

Next, we need to divide the total cost of the window cleaner, $46.68, by the number of quarts to find the price per quart.

Price per quart = $46.68 / 12 quarts = $3.89/quart

Therefore, the price per quart of the window cleaner is $3.89.

Answer:

option 1, 2

Step-by-step explanation:

since R is between Q and S

____________________

Q    (3x+6)     R    (5x-2)    S

--------------(12x - 4)-------------

Q                                       S

so

QR + RS = QS

\((3x+6) + (5x - 2) = 12x - 4\\(3x + 5x) + (6 - 2) = 12x - 4\\(8x) + (4) = 12x - 4\\8x + 4 - 4 = 12x - 4 -4\\8x = 12x - 8\\8x - 12x = 12x - 12x - 8\\-4x = -8\\\frac{-4x}{-4} = \frac{-8}{-4}\)

Answer:

2

Step-by-step explanation:

It mentions R is between points Q and S.

Hence, QR + RS = QS.

Answer:

$3686 remaining after tax

Step-by-step explanation:

The slide projector with a 100 mm-focal length lens will produce a sharp image on the screen located approximately 203 mm away from the lens when the slide is placed 103 mm from the lens. The dimensions of the image produced by a slide measuring 24.0 by 36.0 mm will depend on the magnification factor of the projector.

In order to determine the distance between the lens and the screen, we can use the lens equation:

1/f = 1/v - 1/u

where f is the focal length of the lens, v is the distance between the lens and the screen (image distance), and u is the distance between the lens and the object (slide distance). Rearranging the equation to solve for v, we have:

1/v = 1/f + 1/u

Substituting the given values, we get:

1/v = 1/100 + 1/103

Simplifying this equation gives us the value of v, which is approximately 203 mm. Therefore, the screen should be placed approximately 203 mm away from the lens to obtain a sharp image.

To determine the dimensions of the image produced by the slide, we can use the magnification equation:

magnification = -v/u

Given the values of v and u, we can calculate the magnification factor. The dimensions of the image can then be obtained by multiplying the magnification factor by the dimensions of the slide. However, without the magnification factor or additional information, it is not possible to explicitly determine the dimensions of the image.

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The given equation is not exact. To determine whether the equation is exact or not, we need to check if the partial derivatives of the coefficients with respect to x and y are equal.

Let's calculate these partial derivatives:

∂(y/x+9x)/∂y = 1/x

∂(ln(x)−2)/∂x = 1/x

The partial derivatives are not equal, which means the equation is not exact. Therefore, we cannot directly find a solution using the method of exact equations.

To proceed further, we can check if the equation is an integrating factor equation by calculating the integrating factor (IF). The integrating factor is given by:

IF = e^∫(∂Q/∂x - ∂P/∂y) dy

Here, P = y/x+9x and Q = ln(x)−2. Calculating the difference of partial derivatives:

∂Q/∂x - ∂P/∂y = 1/x - 1/x = 0

Since the difference is zero, the integrating factor is 1, indicating that no integrating factor is needed.

As a result, since the equation is not exact and no integrating factor is required, we cannot find a solution to the given equation. Hence, the solution is "NS" (No Solution).

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Answer:

$12.00

Step-by-step explanation:

The cost of each ticket will be $18.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Tristan and two of his friends purchased tickets to a school play. Tristan paid for all the tickets with a $50.00 bill and received $23.00 in change.

Then the cost of the ticket will be

Cost = ($50 - $23) / 2

Cost = $27

If Tristan used a coupon for 25% off. Then the original price for all tickets will be

Original cost = $27 / 0.75

Original cost = $36

Then the cost of each ticket will be

Cost of each ticket = $36 / 2

Cost of each ticket = $18

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Answer:

Calculating from a Regular Hexagon with a Given Apothem. Write down the formula for finding the area of a hexagon with a given apothem. The formula is simply Area = 1/2 x perimeter x apothem.

Step-by-step explanation:

Answer:

FG=BD

Step-by-step explanation:

hope this helps!!

∫cos(x)/8+cos(x)dx can be evaluated using substitution by letting w = sin(x) and the antiderivative is ∫ (1/8 + w)/sqrt(1-w^2) dw. ∫cos(x)/8+sin(x)dx cannot be evaluated using substitution.

To determine if substitution can be used to evaluate an integral, we can try to identify a pattern in the form of an integral. For example, we want to see if we can let w be equal to a part of the integrand that can simplify the integral and make it easier to solve. In the case of ∫cos(x)/8+cos(x)dx, we can let w = sin(x) which simplifies the integral to a standard form that can be solved using standard techniques. However, in the case of ∫cos(x)/8+sin(x)dx, there is no simplification possible by using substitution.

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Answer:

-4 = 2

Step-by-step explanation:

Answer:

-4 = 2

Step-by-step explanation:

Using the standard z table, a 95% confidence interval for p is (0.5327,0.6173).

In the given question,

A poll is taken in which 302 out of 525 randomly selected voters indicated their preference for a certain candidate.

We have to find a 95% confidence interval for p.

From the question, x=302, n=525

So estimation point,

P=x/n

P=302/525

P=0.575

Now the z value of 95% confidence interval is 1.960 using the standard z table.

Margin of Error (E)=z×√{P(1−P)}/n

Now putting the value

E=1.960×√{0.575(1−0.575)}/525

E=1.960×√(0.575×0.425)/525

E=1.960×√0.244/525

E=1.960×√0.000465

E=1.960×0.0216

E=0.0423

At 95% confidence interval for p is

P−E ≤ p ≤ P+E

Now putting the value

0.575−0.0423≤ p ≤0.575+0.0423

0.5327≤ p ≤0.6173

Hence, a 95% confidence interval for p is (0.5327,0.6173).

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Answer:

400 total pets

Step-by-step explanation:

If you divide 24 by 6 it is 4

So every 1% is 4 pets

% is out of 100

so 100 × 4 = 400

Answer: \(=\frac{21}{32}\quad \left(\mathrm{Decimal:\quad }\:0.65625\right)\)

Step-by-step explanation:

\(\left(-\frac{7}{8}\right)\left(-\frac{3}{4}\right)\)

\(=\frac{7}{8}\cdot \frac{3}{4}\)

\(=\frac{7\cdot \:3}{8\cdot \:4}\)

\(=\frac{21}{8\cdot \:4}\)

\(=\frac{21}{32}\)

Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)

the answer to 130x1000 is

130,000

Answer:

She will be able to pay off her loan completely in approximately 50 months

Step-by-step explanation:

The amount Esme earns as net salary = $2,400

The amount she already has in a savings account = $100

The amount she would be able to add to her savings account every month = $100

The cost of the car Esme plans to purchase on the no interest loan, A = $20,000

The amount she will make as payment on the loan every month, P = $300 per month

Let 'x' represent the number of month Esme will be able to pay off her loan completely, we have

The number of month Esme will have enough money to pay off her loan completely is given by the following equation;

20,000 = 100 + 300 × x + 100 × x = 100 + 400·x

∴ x = (20,000 - 100)/400 = 49.75

Therefore, the number of months she will be able to pay off her loan completely = 49.75 months ≈ 50 months.

Answer: C

Step-by-step explanation:

Answer:

Population: 30.32. Sample: 33.99

Answer: 1751

Step-by-step explanation:

Given, Total people took part in the survey = 1800

Number of people aged  25 - 59 = 34

Number of people aged over 60 = 15

As per the scenario in the question :

Total people = (Number of people aged under 25)+ (Number of people aged  25 - 59 ) + (Number of people aged over 60)

i.e. Number of people aged under 25 = (Total people) - ((Number of people aged  25 - 59 ) + (Number of people aged over 60))

i.e. Number of people aged under 25 = 1800-(34+15)

= 1800-49

= 1751

Hence, Number of people aged under 25= 1751

Answer:

dy/dx = dx^2-1 /dx

= 2 x-0

= 2 x

An estate tax that imposes a tax on inherited money in excess of $4.49 million is an example of Entrepreneurial policy

What is Tax?

This refers to the deducted amount that is removed from a citizen and credited to the government

and in another word money taken from the people and send it to the government

An estate tax that imposes a tax on inherited money in excess of $4. 49 million

an example of which type of policy?

Hence., we can see that an estate tax that imposes a tax on inherited money in excess of $4.49 million is an example of Entrepreneurial policy

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