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Answer:

13

Step-by-step explanation:

18-5 = 13

X-5=18

Add 5 to both sides

X=23

Answer:

[tex]A=38.47\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of a quarter circle is equal to

[tex]A=(1/4)\pi r^{2}[/tex]

we have

[tex]r=7\ cm[/tex]

substitute the values

[tex]A=(1/4)(3.14)(7)^{2}=38.47\ cm^{2}[/tex]

The circumference is found by multiplying the diameter by PI.

Circumference = 13 inches x 3.14 = 40.82

Rounded to the nearest tenth = 40.8 inches.

Answer:13.3

Step-by-step explanation:

Answer:

  45° or π/4 radians

Step-by-step explanation:

You want the angle whose tangent is 1.

Your calculator can evaluate the inverse tangent function for you.

  arctan(1) = 45° = π/4 radians

Answer:

B

Step-by-step explanation:

Answer with explanation:

We will use [tex]\frac{28}{36}[/tex], rule here,which states that , 28% of your gross income should be used for housing finances and 36% of your income , should be used for debt purposes.

Total monthly income of Brenda = $ 1700

→28% of 1700

  [tex]=\frac{28}{100}\times 1700\\\\=28 \times 17\\\\=476[/tex]

⇒Total Housing finances, which includes , housing, food and transportation = $ 476

→Option C:

She has allotted more than 36% of her income for housing.

Answer:

4 + 12 + 36 + ...

Step-by-step explanation:

4, 12, 36, ... is a geometric sequence, it has a common ratio of [tex]r=\frac{36}{12}=\frac{12}{4}=3[/tex]

When we add the terms of a geometric sequence we get a geometric series.

4+12+36+ ... is a geometric series, it has a common ratio of [tex]r=\frac{36}{12}=\frac{12}{4}=3[/tex]

4 + 12 + 20 + ... is not a geometric series because it has no common ratio

[tex]\frac{20}{12}\ne \frac{12}{4}[/tex]

The second choice is correct

Answer:

b.[tex]x=1,3,\:or\:5[/tex]

Step-by-step explanation:

The given equation is;

[tex]x^3-9x^2+23x-15=0[/tex]

To solve by the x-intercept method we need to graph the corresponding function using a graphing tool.

The corresponding function is

[tex]f(x)=x^3-9x^2+23x-15[/tex]

The solution to [tex]f(x)=x^3-9x^2+23x-15=0[/tex] is where the graph touches the x-axis.

We can see from the graph  that; the x-intercepts are;

(1,0),(3,0) and (5,0).

Therefore the real solutions are:

[tex]x=1,3,\:or\:5[/tex]

Answer:

A statistic is a number that describes a sample and a parameter is a number that describes a population.

Step-by-step explanation:

The definition of "statistic" is:

A piece of data from a portion of a population.

The definition of "parameter" is:

A value that tells you something about a population.

Using these definitions, the correct answer to the question is that a statistic is a number that describes a sample and a parameter is a number that describes a population.

The correct option is A statistic is a number that describes a sample and a parameter is a number that describes a population.

A parameter is a number that describes the entire population (for example, the population mean).

A statistic is a number that describes a sample (e.g., sample mean).

A few examples of statistics are:

Hence, the correct option is A statistic is a number that describes a sample and a parameter is a number that describes a population.

Learn more about Parameter and statistics:

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Answer:B:There is no overlap between the two distributions hope this helps

Answer: There is no overlap between the two distributions

Answer:

The answer in the procedure

Step-by-step explanation:

Let

x-----> amount corresponding to 75%

we know that

using proportion

[tex]\frac{100}{84}\frac{\%}{\$} =\frac{75}{x} \frac{\%}{\$}\\ \\ x=84*75/100\\ \\ x=\$63[/tex]

Answer: $33.80

Step-by-step explanation: If Hector’s account was overdrawn by $22.80 and then he deposited $56.60 his balance would be $33.80

The formula to solve this is -22.80 + 56.60 = 33.80

Answer:

$33.80

Step-by-step explanation:

i did it on my test got it right

Here is your answer

[tex]\bold{x= 6}[/tex]

REASON:

Theorem used: The diagonals of a parallelogram bisect each other.

Let diagonals AC and BD bisect each other at O

So, OA=OC

Now,

3x=4x-6 [OA=3x and OC=4x-6]

4x-3x= 6

x= 6

HOPE IT IS USEFUL

Answer:

Step-by-step explanation:

Parallelogram's diagonals theorem states that the diagonals in a parallelogram must bisect each other.

So for ABCD to be a parallelogram, the two diagonals must be divided in equal sections.

That is given for BD already.

For AC, 3x = 4x - 6

Rearranging, 4x - 3x = 6

x = 6

Answer:

B.

Step-by-step explanation:

Because the graph shown is not constant, if you look at when it hits a whole unit. It is increasing because it is moving right.

The true statement is:

B.  

The function indicates that the number of members is increasing at a rate that is not constant.

We could write the data points as is given on the graph as follows:

  x       y

  0      40

  1       50

  2      60

  3      80

  4      100

  5      120

  6      150

  7      190

  8      240

  9      300

  10     370

Hence, the rate of change from x=0 to x=1 is:

[tex]Rate=\dfrac{50-40}{1-0}\\\\\\Rate=\dfrac{10}{1}\\\\\\Rate=10[/tex]

Rate of change from x=3 to x=5 is:

[tex]Rate=\dfrac{120-80}{5-3}\\\\\\Rate=\dfrac{40}{2}\\\\\\Rate=20[/tex]

Hence, the rate is not constant.

Also we could see that with the increasing value of x the y-value also increases.

                  Hence, option: B is the correct answer.

Answer:

[tex]V=36 \pi h\ ft^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a cylinder (sculpture) is equal to

[tex]V=\pi r^{2}H[/tex]

In this problem we have

[tex]r=12/2=6\ ft[/tex] ----> the radius is half the diameter

[tex]H=h\ ft[/tex]

substitute the values

[tex]V=\pi (6^{2})(h)=36 \pi h\ ft^{3}[/tex]

Answer:

36πh cubic feet

Step-by-step explanation:

To find the volume of a cylinder  with a diameter of 12 feet and a height of h feet, we must know the formula for finding the volume of  a cylinder.

The volume V of a cylinder with a radius r and a height h is given as

V = πR^2h

where π = 22/7

Given that the radius of the given cylinder is 12 feet, the radius r

= 12/2 feet

= 6 feet

The volume v

= π * 6^2 * h

= 36πh cubic feet

[tex] \frac{55}{11} - \frac{13}{11} = \frac{42}{11} \: or \:3 \frac{9}{11} [/tex]

Answer:

0.731 < p < 0.775

Step-by-step explanation:

We have a sample proportion of 753/1000 = 0.753

We need to construct a 90% confidence interval for the population proportion.  Since n > 30, we use the corresponding z-value of 1.645.  

See attached photo for the formulas and construction of the confidence interval.

The 90% confidence interval for the proportion of American adults who think exercise is an important part of daily life is 0.749 to 0.757.

To find the 90% confidence interval for the proportion of American adults who think exercise is an important part of daily life, we can use the formula for the confidence interval of a proportion. The formula is: CI = p ± Z * sqrt((p * (1-p))/n), where p is the sample proportion, Z is the z-score corresponding to the desired confidence level, and n is the sample size.

First, we need to calculate the sample proportion: p = 753/1000 = 0.753.

Next, we need to find the z-score for a 90% confidence level. Looking up the z-score in the standard normal distribution table, we find that the z-score for a 90% confidence level is approximately 1.645.

Now we can plug in the values into the formula: CI = 0.753 ± 1.645 * sqrt((0.753 * (1-0.753))/1000).

Calculating the expression inside the square root gives us approximately 0.0027. Plugging this value into the formula gives us the 90% confidence interval for the proportion: CI = 0.753 ± 1.645 * 0.0027.

Calculating this expression gives us the lower and upper bounds of the confidence interval: CI = 0.753 ± 0.0044.

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Answer:

(u)^{2}+7(u)-8=0

Step-by-step explanation:

Answer:

The equivalent quadratic equation corresponding to (3x + 2)² + 7(3x + 2) – 8 = 0 is y² + 7y – 8 = 0  

Step-by-step explanation:

Here given (3x + 2)² + 7(3x + 2) – 8 = 0

Substitute 3x + 2 as y

Solving

          y² + 7y – 8 = 0  

The equivalent quadratic equation corresponding to (3x + 2)² + 7(3x + 2) – 8 = 0 is y² + 7y – 8 = 0  

1.45÷5=0.29

0.29×3=0.87

1.13-0.87=0.26

0.26÷2=0.13

One banana costs 0.13

Final answer:

By setting up two equations based on the cost of apples and the combined cost of apples and bananas, we can calculate that the cost of one banana is \'0.13.

Explanation:

To solve the question about the cost of one banana, we need to set up two equations based on the given information. Let's denote the cost of one apple as 'A' and the cost of one banana as 'B'.

We are given that 5 apples cost \'1.45, which can be written as an equation: 5A = 1.45. We are also given that 3 apples and 2 bananas cost \'1.13, which can be expressed as the equation 3A + 2B = 1.13. By solving these two equations simultaneously, we can find the value of 'B', the cost of one banana.

First, we solve the first equation for A: A = 1.45/5. We get A = 0.29. Now, we substitute this value into the second equation: 3(0.29) + 2B = 1.13. This simplifies to: 0.87 + 2B = 1.13. Solving for B, we get: 2B = 1.13 - 0.87, hence B = (1.13 - 0.87)/2. After performing the subtraction and division, we find that B = 0.13.

Therefore, the cost of one banana is \'0.13.

Answer:

The answer is

D.16

Step-by-step explanation:

Answer:

Step-by-step explanation:

You would do this question like this.

4 meats * 2 cheeses * x breads = 24 different kinds of  sandwiches.

8x = 24

8x/8 = 24/8

x = 3

There are 3 different kinds of breads.

Answer:

y = 5

Step-by-step explanation:

-7 (5 - 3) = -14

y = 5

I took the test.

Answer:

see explanation

Step-by-step explanation:

If (x + 2) is a factor then x = - 2 is a root and p(- 2) = 0

p(- 2) = -4[tex](-2)^{4}[/tex] + 6(- 2)³ + 8(- 2)² + 2(- 2) - 1

         = - 64 - 48 + 32 - 4 - 1 = - 85

Hence remainder R = - 85

Since p(- 2) ≠ 0 then (x + 2) is not a factor of p(x)

Answer:

1) x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60

2) x² + y² + 6x - 8y - 10 = 0 ⇒ No choice

3) 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18

4) 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ No choice

5) 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56

6) x² + y² + 2x - 6y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46

Step-by-step explanation:

- The general form of the equation of the circle is:

* x² + y² + Dx + Ey + F = 0

 where D , E and F are constant

- The standard form of the equation of the circle is:

* (x - h)² + (y - k)² = r²

 where (h , k) is the center of the circle, r is the radius of it

- To chose the circle equations in general form with their

  corresponding equations in standard form lets do that

1) x² + y² - 4x + 12y - 20 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(-4)/2(1) = 2

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(12)/2(1) = -6

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (2)² + (-6)² - (-20) = 4 + 36 + 20 = 60

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x - 2)² + (y + 6)² = 60 ⇒ x² + y² - 4x + 12y - 20 = 0

2) x² + y² + 6x - 8y - 10 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(6)/2(1) = -3

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(-8)/2(1) = 4

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (-3)² + (4)² - (-10) = 9 + 16 + 10 = 35

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x + 3)² + (y - 4)² = 35 ⇒ there is no choice

3) 3x² + 3y² + 12x + 18y - 15 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(12)/2(3) = -2

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(18)/2(3) = -3

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (-2)² + (-3)² - (-15/3) = 4 + 9 + 5 = 18

- We divide F by 3 because the coefficient of x² and y²

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x + 2)² + (y + 3)² = 18 ⇒ 3x² + 3y² + 12x + 18y - 15 = 0

4) 5x² + 5y² - 10x + 20y - 30 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(-10)/2(5) = 1

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(20)/2(5) = -2

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (1)² + (-2)² - (-30/5) = 1 + 4 + 6 = 11

- We divide F by 5 because the coefficient of x² and y²

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x - 1)² + (y + 2)² = 11 ⇒ there is no choice

5) 2x² + 2y² - 24x - 16y - 8 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(-24)/2(2) = 6

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(-16)/2(2) = 4

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (6)² + (4)² - (-8/2) = 36 + 16 + 4 = 56

- We divide F by 2 because the coefficient of x² and y²

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x - 6)² + (y - 4)² = 56 ⇒ 2x² + 2y² - 24x - 16y - 8 = 0

6) x² + y² + 2x - 12y - 9 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(2)/2(1) = -1

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(-12)/2(1) = 6

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (-1)² + (6)² - (-9) = 1 + 36 + 9 = 46

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x + 1)² + (y - 6)² = 46 ⇒ x² + y² + 2x - 6y - 9 = 0

Answer and Step-by-step explanation:

Answer:

# x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60

# 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18

# 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56

# x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46

Step-by-step explanation:

* Lets study the problem to solve it

- Use the terms of x and y in the general form to find the standard form

∵ x² + y² - 4x + 12y - 20 = 0

- Use the term x term

∵ -4x ÷ 2 = -2x ⇒ x × -2

∴ (x - 2)²

- Use the term y term

∵ 12y ÷ 2 = 6y ⇒ y × 6

∴ (y + 6)²

∵ (-2)² + (6)² + 20 = 4 + 36 + 20 = 60

∴ x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60

∵ x² + y² + 6x - 8y + 10 = 0

- Use the term x term

∵ 6x ÷ 2 = 3x ⇒ x × 3

∴ (x + 3)²

- Use the term y term

∵ -8y ÷ 2 = -4y ⇒ y × -4

∴ (y - 4)²

∵ (3)² + (-4)² - 10 = 9 + 16 - 10 = 5

∴ x² + y² + 6x - 8y + 10 = 0 ⇒ (x + 3)² + (y - 4)² = 5 ⇒ not in answer

∵ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ divide all terms by 3

∴ x² + y² + 4x + 6y - 5 = 0

- Use the term x term

∵ 4x ÷ 2 = 2x ⇒ x × 2

∴ (x + 2)²

- Use the term y term

∵ 6y ÷ 2 = 3y ⇒ y × 3

∴ (y + 3)²

∵ (2)² + (3)² + 5 = 4 + 9 + 5 = 18

∴ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18

∵ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ divide both sides by 5

∴ x² + y² - 2x + 4y - 6 = 0

- Use the term x term

∵ -2x ÷ 2 = -x ⇒ x × -1

∴ (x - 1)²

- Use the term y term

∵ 4y ÷ 2 = 2y ⇒ y × 2

∴ (y + 2)²

∵ (-1)² + (2)² + 6 = 1 + 4 + 6 = 11

∴ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ (x - 1)² + (y + 2)² = 11 ⇒ not in answer

∵ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ divide both sides by 2

∴ x² + y² - 12x - 8y - 4 = 0

- Use the term x term

∵ -12x ÷ 2 = -6x ⇒ x × -6

∴ (x - 6)²

- Use the term y term

∵ -8y ÷ 2 = -4y ⇒ y × -4

∴ (y - 4)²

∵ (-6)² + (-4)² + 4 = 36 + 16 + 4 = 56

∴ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56

∵ x² + y² + 2x - 12y - 9 = 0

- Use the term x term

∵ 2x ÷ 2 = x ⇒ x × 1

∴ (x + 1)²

- Use the term y term

∵ -12y ÷ 2 = -6y ⇒ y × -6

∴ (y - 6)²

∵ (1)² + (-6)² + 9 = 1 + 36 + 9 = 46

∴ x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46

Answer:

D

Step-by-step explanation:

We would need to understand 2 rules of translation in order to figure this out.

1. The graph of f(-x) is the graph of f(x) reflect about the y-axis

2. The graph of f(x+a) is the graph of f(x) shifted horizontally a units LEFT and the graph of f(x-a) is the graph of f(x) shifted horizontally a units RIGHT

We are comparing [tex]ln(5-x)[/tex] with the parent graph of [tex]lnx[/tex]. Firstly, there is -x in place of x, this means the graph is reflected about y-axis. Next, there is +5 added with -x, so it means the graph is shifted horizontally 5 units to the LEFT

Looking at the answer choices, D is the correct answer.

Answer:

Option d

Step-by-step explanation:

Let f(x) be a logarithmic function of the form [tex]f(x) = log(x)[/tex]. So:

[tex]y = f(-x)[/tex] represents a reflection of f(x) on the y axis.

[tex]y = f(-x) = log(-x)[/tex]

Then:

[tex]y = f(x + 5)[/tex] represents a displacement of [tex]f(x)[/tex] 5 units to the left.

[tex]y = f(x + 5) = log(x + 5)[/tex]

Therefore, the operation:

[tex]y = f(-x + 5) = log(5-x)[/tex]

Represents a reflection on the y axis and a translation of 5 units to the left

Answer:

1/9.

Step-by-step explanation:

There is a total of 15 cards in the stack.

Prob( Queen is chosen) =  5/15 = 1/3.

The probability of a second queen being chosen is also 1/3

Required probability = 1/3 * 1/3 = 1/9.

Answer:

4.6 Or 4.60

Step-by-step explanation:

Like the other person said, 4.56. The question says "round to the nearest tenth" so 4.56 rounds to 4.60

Hope it helps~

To determine how many kilometers east Santos walked, we can use the Pythagorean theorem to find the distance traveled for each leg of the journey.

To determine how many kilometers east Santos walked, we need to use the Pythagorean theorem to find the distance traveled for each leg of the journey. Since he ends up 5 kilometers away from his starting position, we can form a right triangle with the hypotenuse representing the total distance walked.

Let's assume Santos walked x kilometers east. The other leg of the triangle represents the 2 kilometers south he walked. Using the Pythagorean theorem, we have x2 + 22 = 52.

This simplifies to x2 + 4 = 25. Subtracting 4 from both sides gives us x2 = 21. Taking the square root of both sides, we find that x ≈ 4.58. Therefore, Santos walked approximately 4.58 kilometers east.

Answer:

ln(1.225)/0.1

Step-by-step explanation:

The credit all goes to @lucic , but the answer is expressed as a natural log

Answer:

x = 13.

Step-by-step explanation:

Because it is an isosceles trapezoid the 2 marked angles are equal, so

5x + 15 = 7x - 11

15 + 11 = 7x - 5x

2x = 26

x = 13.

2 time legal assistant = 900,000 x 2 = 1,800,000

school teacher = 1,850,000

Difference = 1,850,000 - 1,800,000 = $50,000

Master degree for 26 weeks = 1326 x 26 = 34,476

Associates degree for 42 weeks: 792 x 42 = 33,264

Difference = 34,476 - 33,264 = $1,212

For 20 years she earned: $900,000

Twice that would be $1,800,000

So for 30 years the schoolteacher earns the same amount.

Answer:

The difference between the school teacher and the legal assistant is $50,000. The school teacher earns about twice as much in thirty years. The next answer is $1,212.  

Step-by-step explanation:

The legal assistant makes $1,800,000 in 40 year. The school teacher in 30 years makes 1,850,000. 1,850,000 - 1,800,000= $50,000.

A person with the masters degree mages $34,476 in 26 weeks.The person with the Associates degree make $33,264 in 42 weeks.  

Answer:

43.75 ft²

Step-by-step explanation:

     Let r = the radius of the semicircle

   and h = the height of the rectangle

Then 2r = the width of the window

The formula for the perimeter of a circle is C = 2πr,

so, πr = the perimeter of the semicircle

The perimeter of the window is

P = πr + 2h + 2r = 25

      2h + (π +2)r = 25

                       h = ½[25 - (π + 2)r]

(1)                   h = 12.5 - (π/2 +1)r

The formula for the area of a circle is A= πr²,  so

½πr² = the perimeter of the semicircle

The area of the window is

(2) A = ½πr² + 2rh

Substitute (1) into (2).

    A = ½πr² + 2r[12.5 - (π/2 +1)r] = ½πr² + 25r - (π +2)r²

    A = 25r - (π + 2 - π/2)r²

(3) A =  -(π/2 + 2)r² + 25r

This is the equation for a downward opening parabola.

One way to find the vertex is to set the first derivative equal to zero.

dA/dr = -2(π/2 + 2)r + 25 = 0

               -(π    + 4)r  + 25 = 0

               -(π     + 4)r        = -25

                                     r = 25/(π + 4)

(4)                                 r ≈ 3.50 ft

The maximum area occurs when r = 3.50 ft.  

Substitute (4) into (1).

h = 12.5 - (π/2 +1)(3.50) = 12.5 - (2.571× 3.50) = 12.5 - 9.00 = 3.50  

(4) h = 3.50 ft

Substitute (4) into (2)

A =  1.571(3.50)² + 2×3.50×3.50 = 19.25 + 24.50

A = 43.75 ft²

The area of the largest possible Norman window with a perimeter of 25 ft is 43.75 ft².

The maximum area of a Norman window with a given perimeter of 25 feet can be found by creating an equation for the area, taking its derivative, setting it equal to zero and solving for the window's dimensions. This involves calculus, namely the method for optimization problems.

The problem involves maximizing the area of a Norman window given a certain perimeter. The Norman window is composed of a rectangle and a semicircle, where the diameter of the semicircle equals the width of the rectangle. First, let's denote the width of the rectangle or the diameter of the semicircle as x. The radius of the semicircle will then be x/2. The height of the rectangle can be represented as 25 - x (since the perimeter of the window should equal 25 feet).

The area of a rectangle is height multiplied by width. The area of a semicircle is (1/2)πr2. So to find the area A of the Norman window, we add the area of the rectangle and the semicircle: A = x(25-x) + (1/2)π*(x/2)2.

To find the maximum area, we need to take the derivative of A with respect to x, set it equal to zero, and solve for x. We find x approximates to around 7.64 feet (after using calculus concepts). Then substitute x = 7.64 into the area function A and solve for A, which gives us the maximum area of the Norman window.

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