What is a group of objects that share common characteristics and are well-defined?​

The shape of the swimming pool is modeled by the equation of an ellipse, given by 9\(x^{2}\) + 4\(y^{2}\) = 36. To find the volume, we integrate the area of each cross section over the range of y values that the ellipse covers.

The cross sections of the pool, cut perpendicular to the y-axis, are semi-circles. Since the cross sections are semi-circles, we know that the area of each cross section is (1/2) \(\pi\) \(r^{2}\), where r is the radius of the semi-circle. In this case, the radius of each semi-circle is given by the equation r = \(\sqrt{(9x^2 + 4y^2).}\) To find the limits of integration for y, we solve the equation of the ellipse for y:

\(9x^{2} +4y^{2}\) = 36

4\(y^{2}\) = 36 - 9\(x^{2}\)2

\(y^{2}\) =\(\frac{ 36 - 9x^{2} }{4}\)

y = ±\(\sqrt{\frac{(36 - 9x^2) }{4} }\)

Now we can integrate the area of each cross section from y = \(-\sqrt{\frac{ 36 - 9x^{2} }{4}}\) to y = \(\sqrt{\frac{ 36 - 9x^{2} }{4}}\)with respect to x, and multiply the result by 2 to account for the semi-circles on both sides of the y-axis. The integral of (1/2) π  \((\sqrt{(9x^2 + 4y^2))} )^{2}\)with respect to x will give us the volume of water the pool can hold in cubic yards.

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Answer:

2/3

Step-by-step explanation:

Simplify

\(26=6\cdot \left(5-a\right)\\26=6\cdot 5+6\cdot -a\\26=30+6\cdot -a\\26=30+\left(6\cdot -1\right)a\\26=30-6a\\30-6a=26\)

Group constants

\(30-6a=26\\30-6a-30=26-30\\-6a+30-30=26-30\\-6a=26-30\\-6a=-4\\\)

Isolate the term, a

\(-6a=-4\\\frac{-6a}{-6}=\frac{-4}{-6}\\\frac{6a}{6}=\frac{-4}{-6}\\a=\frac{-4}{-6}\\\\\frac{-a}{-b} = \frac{a}{b}\\\\a=\frac{4}{6}\\a=\frac{2\cdot 2}{3\cdot 2}\\a=\frac{2}{3}\)

The equations that represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the point (5, -4) are:

y + 4 = (-2/5)(x - 5)2x + 5y = -10y = (-2/5)x - 2

To find the equations that represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the point (5, -4),

we first need to put the equation in slope-intercept form, y = mx + b.5x - 2y = -6-2y = -5x - 6y = 5/2 x + 3

The slope of the given line is 5/2.

To find the slope of the line perpendicular to this line, we can use the following formula:

slope of the perpendicular line = -1/m

where m is the slope of the given line.

So, the slope of the perpendicular line is:-1/(5/2) = -2/5

Thus, the equation of the line that is perpendicular to the given line and passes through the point (5, -4) is:

y - y_1 = m(x - x_1),

where m = -2/5, and

(x_1, y_1) = (5, -4).

y + 4 = (-2/5)(x - 5)

y + 4 = (-2/5)x + 2y = (-2/5)

x - 4 - 5y = 2x + 10y = (2/5)x - 4

Thus, the equations that represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the point (5, -4) are:y + 4 = (-2/5)(x - 5)2x + 5y = -10y = (-2/5)x - 2

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75m/60=1.25

1.25=1 1/4 hours

So the answer Is 1 1/4 hours.

hope this helps

The balanced scorecard approach can be utilized as a strategic control system to ensure the organization pursues long-term profitability by aligning financial objectives with key performance indicators across multiple perspectives.

The balanced scorecard approach is a strategic control system that enables organizations to effectively measure and manage performance across various dimensions. It provides a holistic view of the organization's activities by incorporating financial and non-financial indicators, and it serves as a valuable tool to ensure strategies are aligned with long-term profitability goals.

One key aspect of the balanced scorecard approach is the inclusion of multiple perspectives. Instead of focusing solely on financial metrics, the balanced scorecard incorporates additional perspectives such as customer, internal processes, and learning and growth. This ensures a comprehensive evaluation of the organization's performance, taking into account both short-term financial results and the long-term drivers of profitability.

By utilizing the balanced scorecard approach, organizations can set clear objectives and identify relevant key performance indicators (KPIs) for each perspective. This allows for a more balanced and well-rounded assessment of performance, ensuring that strategies are not solely focused on financial outcomes but also consider customer satisfaction, operational efficiency, and employee development.

Furthermore, the balanced scorecard approach facilitates the translation of the organization's strategy into actionable initiatives. By establishing cause-and-effect relationships between the different perspectives, organizations can develop a clear understanding of how their strategic objectives will lead to long-term profitability. This enables better resource allocation, effective monitoring of progress, and timely adjustments to ensure strategies remain aligned with the pursuit of maximum profitability.

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Answer:

17/21

Step-by-step explanation:

Because i had that question and it was 17/21

The first term of the arithmetic sequence is -5. The common difference of the arithmetic sequence is -2.

In an arithmetic sequence, each term is obtained by adding a constant value, known as the common difference, to the previous term. To find the first term and the common difference, we can use the given information about the 7th and 20th terms.

Let's denote the first term as "a" and the common difference as "d". We are given that the 7th term is -17 and the 20th term is -43. Using this information, we can write the following equations:

For the 7th term: a + 6d = -17   (since the 7th term is obtained by adding 6d to the first term)

For the 20th term: a + 19d = -43 (since the 20th term is obtained by adding 19d to the first term)

To solve these equations, we can use a method such as substitution or elimination. Let's use the substitution method here.

From the first equation, we can express "a" in terms of "d":

a = -17 - 6d

Substituting this value of "a" into the second equation, we have:

(-17 - 6d) + 19d = -43

Simplifying the equation:

-17 + 13d = -43

13d = -26

d = -2

Now that we know the common difference "d" is -2, we can substitute it back into the first equation to find the first term "a":

a = -17 - 6(-2)

a = -17 + 12

a = -5

Therefore, the first term of the arithmetic sequence is -5 and the common difference is -2.

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Answer:

The most likely outcome is exactly 4 free throws

Step-by-step explanation:

Given

\(n = 5\) --- attempts

\(p = 82.6\%\) ---- probability of a successful free throw

\(p = 0.826\)

Required

A histogram to show the most likely outcome

From the question, we understand that the distribution is binomial.

This is represented as:

\(P(X = x) = ^nC_x * p^x * (1 - p)^{n-x}\)

For x = 0 to 5, where x represents the number of free throws; we have:

\(P(X = x) = ^nC_x * p^x * (1 - p)^{n-x}\)

\(P(X = 0) = ^5C_0 * 0.826^0 * (1 - 0.826)^{5-0}\)

\(P(X = 0) = ^5C_0 * 0.826^0 * (0.174)^{5}\)

\(P(X = 0) = 1 * 1 * 0.000159 \approx 0.0002\)

\(P(X = 1) = ^5C_1 * 0.826^1 * (1 - 0.826)^{5-1}\)

\(P(X = 1) = ^5C_1 * 0.826^1 * (0.174)^4\)

\(P(X = 1) = 5 * 0.826 * 0.000917 \approx 0.0038\)

\(P(X = 2) = ^5C_2 * 0.826^2 * (1 - 0.826)^{5-2}\)

\(P(X = 2) = ^5C_2 * 0.826^2 * (0.174)^{3}\)

\(P(X = 2) = 10 * 0.682 * 0.005268 \approx 0.0359\)

\(P(X = 3) = ^5C_3 * 0.826^3 * (1 - 0.826)^{5-3}\)

\(P(X = 3) = ^5C_3 * 0.826^3 * (0.174)^2\)

\(P(X = 3) = 10 * 0.5636 * 0.030276 \approx 0.1706\)

\(P(X = 4) = ^5C_4 * 0.826^4 * (1 - 0.826)^{5-4}\)

\(P(X = 4) = 5 * 0.826^4 * (0.174)^1\)

\(P(X = 4) = 5 * 0.4655 * 0.174 \approx 0.4050\)

\(P(X = 5) = ^5C_5 * 0.826^5 * (1 - 0.826)^{5-5}\\\)

\(P(X = 5) = ^5C_5 * 0.826^5 * (0.174)^0\)

\(P(X = 5) = 1 * 0.3845 * 1 \approx 0.3845\)

From the above computations, we have:

\(P(X = 0) \approx 0.0002\)

\(P(X = 1) \approx 0.0038\)

\(P(X = 2) \approx 0.0359\)

\(P(X = 3) \approx 0.1706\)

\(P(X = 4) \approx 0.4050\)

\(P(X = 5) \approx 0.3845\)

See attachment for histogram

From the histogram, we can see that the most likely outcome is at: x = 4

Because it has the longest vertical bar (0.4050 or 40.5%)

Step-by-step explanation:

3=4y+x => x+4y = 3

4y=−x+3 => x+4y = 3

the systems are dependent equations

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer: 3172

Step-by-step explanation:

The equation of the tangent line to f-1(x) at the point (3, -1) is y = 1/(-2) x - 1/2.

This is because the slope of the tangent line to f(x) at (-1,3) is -2, and since f(x) and f-1(x) are inverse functions, the slopes of their tangent lines are reciprocals.

Therefore, the slope of the tangent line to f-1(x) at (3,-1) is -1/2. To find the y-intercept, we can use the fact that the point (3,-1) is on the tangent line. Plugging in x=3 and y=-1 into the equation y = -1/2 x + b, we get b = 1/2. Therefore, the equation of the tangent line to f-1(x) at (3,-1) is y = 1/(-2) x - 1/2.

In summary, to find the equation of the tangent line to f-1(x) at a point (a,b), we first find the point (c,d) on the graph of f(x) that corresponds to (a,b) under the inverse function.

Then, we find the slope of the tangent line to f(x) at (c,d), take the reciprocal, and plug it into the point-slope formula to find the equation of the tangent line to f-1(x) at (a,b).

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9514 1404 393

Answer:

  3x -4y = -9

Step-by-step explanation:

Multiply by 4 to clear the fraction.

  4(y -6) = 3(x -5)

Subtract the left-side term to get variables on the same side, with a positive x-coefficient.

  0 = 3(x -5) -4(y -6)

Eliminate parentheses and collect terms.

  0 = 3x -15 -4y +24

  0 = 3x -4y +9

Subtract 9 and swap sides to get standard form.

  3x -4y = -9

_____

Standard form is ...

  ax +by = c

where a ≥ 0, and a, b, c are mutually prime integers. If a=0, then b > 0.

__

The attached graph shows the equations give the same line. The original line is shown dotted so that you can see they overlap.

The function f(theta) is:

f(theta) = sin(theta) + cos(theta) + 3

To find the function f, we will integrate the given second derivative with respect to theta twice, and use the initial conditions to determine the constants of integration.

First, integrating f ''(theta) = sin(theta) + cos(theta) with respect to theta gives:

f '(theta) = -cos(theta) + sin(theta) + C1

where C1 is a constant of integration.

Next, integrating f '(theta) = -cos(theta) + sin(theta) + C1 with respect to theta gives:

f(theta) = sin(theta) + cos(theta) + C1*theta + C2

where C2 is another constant of integration.

To determine the values of C1 and C2, we use the initial conditions:

f(0) = 4 gives us:

4 = sin(0) + cos(0) + C1*0 + C2

4 = 1 + C2

so C2 = 3.

f '(0) = 1 gives us:

1 = -cos(0) + sin(0) + C1

1 = 1 + C1

so C1 = 0.

Therefore, the function f(theta) is:

f(theta) = sin(theta) + cos(theta) + 3

Note that there are other ways to express this function, such as using trigonometric identities to simplify the expression, but this is the most general form.

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The present ages of the father and son are 36 and 9, respectively.

The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the father's age at that time. To find the present ages of the father and son, we can set up a system of equations.

Let's denote the present ages of the father as "F" and the present age of the son as "S".

From the information given, we have two equations:

Equation 1: F + S = 45 (The sum of their ages is 45)
Equation 2: (F - 5)(S - 5) = 4(F - 5) (Five years ago, the product of their ages was four times the father's age at that time)

To solve this system of equations, we can use substitution or elimination method.

Let's solve it using the substitution method:

From Equation 1, we can express F in terms of S: F = 45 - S

Now, substitute F in Equation 2 with 45 - S:

(45 - S - 5)(S - 5) = 4(45 - S - 5)

Simplify the equation:

(40 - S)(S - 5) = 4(40 - S)

Expand and simplify:

40S - 5S - 200 + 25 = 160 - 4S

Combine like terms:

35S - 175 = 160 - 4S

Add 4S to both sides:

35S + 4S - 175 = 160

Combine like terms:

39S - 175 = 160

Add 175 to both sides:

39S = 335

Divide both sides by 39:

S = 335/39

Simplify:

S ≈ 8.59

Since age cannot be in decimal places, we can approximate the son's age to the nearest whole number:

S ≈ 9

Now, substitute S = 9 into Equation 1 to find the father's age:

F + 9 = 45

Subtract 9 from both sides:

F = 45 - 9

F = 36

Therefore, the present ages of the father and son are 36 and 9, respectively.

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If a > b, then |a - b| = a - b if a - b is positive. This means that the distance from a - b to zero on the number line is equal to a - b itself. If a - b is negative, then |a - b| is equal to the opposite of a - b.

The absolute value of a - b is equal to a - b if a - b is positive because the absolute value of a number is the distance from that number to zero on the number line. So, if a is greater than b, then a - b is a positive number. Therefore, the distance from a - b to zero on the number line is equal to a - b.

The absolute value of a number is the distance from that number to zero on the number line. For example, the absolute value of 5 is 5 because the distance from 5 to 0 on the number line is 5 units. The absolute value of -5 is also 5 because the distance from -5 to 0 on the number line is also 5 units.
Now, let's look at the expression |a - b|. This means the absolute value of the difference between a and b. If a is greater than b, then a - b is a positive number. For example, if a = 10 and b = 5, then a - b = 5. So, |a - b| = |10 - 5| = |5| = 5.
However, we are looking for the condition under which |a - b| = a - b. This means that the absolute value of a - b is equal to a - b itself. This only happens when a - b is positive. Let's use the same example as before. If a = 10 and b = 5, then a - b = 5. In this case, a - b is positive, so |a - b| = |10 - 5| = |5| = 5, which is equal to a - b.

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The requried there are 192,000 different ways to choose one teacher, one girl, and one boy to represent the school.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
To work out the number of different ways to choose one teacher, one girl, and one boy, we can use the multiplication principle of counting.

First, we need to choose one teacher out of 16. This can be done in 16 ways. Next, we need to choose one girl out of 120. This can be done in 120 ways. Finally, we need to choose one boy out of 100. This can be done in 100 ways.

By the multiplication principle of counting, the total number of ways to choose one teacher, one girl, and one boy is,

16 × 120 × 100 = 192,000

Therefore, there are 192,000 different ways to choose one teacher, one girl, and one boy to represent the school.

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Answer:

1308

Step-by-step explanation:

PEMDAS has us do 6^4 first which is 1296. Then we can do 6*2 which is 12 then 12 + 1296 is 1308.

Answer:

the numbers are 20, 21 and 22

Step-by-step explanation:

x+(x+1) + (x+2) = 63

3x +3 = 63

3x = 60

x = 20

doing this for ponits

Answer:

the numbers are 20, 21 and 22

Step-by-step explanation:

x+(x+1) + (x+2) = 63

3x +3 = 63

3x = 60

x = 20

Answer:

a) 1

b)I would like to help u but i don't understand the question I think something is missing there plus sign or minus sign sry

Step-by-step explanation:

2.5x + 1.25 < 3.75

2.5x < 3.75 - 1.25

2.5x < 2.5

\( \frac{2.5x}{2.5} = \frac{2.5}{2.5} \)

x = 1

I hope u like it ‍❤️‍‍❤️‍

For any question comment me

Really sorry for the second question

Answer:

Actually...It's really easy

Step-by-step explanation:

All you have to do is put the numbers in order like this

                422

            x     18

_________________

             7,596

There you go! Hope it helps!

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The nth term of the arithmetic series can be defined as hₙ = 4n - 2.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

The nth term of an arithmetic sequence is given by the formula,

aₙ = a₁ + (n-1)d

Since the first term of the arithmetic sequence is 2, while the difference is 4. Therefore, the definition for the nth term of arithmetic sequence,h can be written as,

hₙ = 2 + (n-1)4

hₙ = 2 + 4n -4

hₙ = 4n - 2

Hence, the nth term of the arithmetic series can be defined as hₙ = 4n - 2.

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Answer:

Solution

1cm=60 cm

4.5cm=4.5×60

=270m (breadth)

3.7cm=3.7×60

=222m (length)

Perimeter of rectangle=2(l+b)

=2(222+270)

=2×492

=984m

hope it helps you

make me brainliest if u r satisfied

The perimeter of the rectangular park is P = 984 m

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the scale of the rectangular park be 1 cm = 60m

Now , the Perimeter P of rectangle = 2 ( Length + Width )

The length of the rectangular park L = 4.5 cm = 4.5 x ( 60 )

The length of the rectangular park L = 270 m

And ,

The width of the rectangular park W = 3.7 cm = 3.7 x ( 60 )

The width of the rectangular park W = 222 m

Now , the perimeter of rectangular park = 2 ( 270 + 222 )

The perimeter of rectangular park P = 984 m

Hence , the perimeter of the rectangular park is 984 m

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Answer:

Step-by-step explanation:

BD is geometric mean

BD² = 5 × 13 = 65

BD = √65

We can be 95% confident that the true mean concentration of THMs in your drinking water lies within the range [2.9584 ppb, 3.0416 ppb]. This was calculated using a confidence interval formula for the mean.

The confidence interval for the mean concentration of THMs can be calculated using the formula x ± z * (s/√n), where x is the sample mean, z is the z-score for a given confidence level, s is the sample standard deviation and n is the sample size.

In this case, we have x = 3 ppb, s = 0.3 ppb, and n = 200. To calculate the confidence interval at a certain confidence level (e.g. 95%), we need to find the corresponding z-score. For a 95% confidence level, the z-score is approximately 1.96.

Substituting these values into the formula above gives us:

3 ± 1.96 * (0.3/√200) = [2.9584, 3.0416]

So we can be 95% confident that the true mean concentration of THMs in your drinking water lies within the range [2.9584 ppb, 3.0416 ppb].

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SOLUTION:

Step 1:

we are to find the measure of minor arc cut off by one of the diagonals;

The sum of interior angles in a pentagon is:

Each interior angle of a regular pentagon is

So the size of the major arc can be gotten by the circle theorem; the angle at the centre is twice the angle at the circumference.

Then recall,

Step 2:

We are to find the length of the same minor arc in problem;

Where our angle (titan) is 144 and radius is 10

So the length of the minor arc, given that the radius is 10 cm is 8 pi

Answer:

Second option 168= 18.X + 12.2X

Step-by-step explanation:

Area of the shape is in two parts,

Are of the larger rectangle is Lenght x width

Lenght is 12cm and width is x +2x

Area = 12 x 3x = 36x cm²

Area of the smaller rectangle = 6 x X = 6xcm²

Total area 36x + 6x = 168cm²

Another method

Find the area of the big rectangle including the cut off area

Lenght x width = 18 x (2x + X)

Area =18 x 3x or 18.3x

Calculate the white area

Length x width = 6 x 2x = 12x

Deduct the white area from the larger area

168= 18.3x - 12x

Third method

Divide the rectangle from top down

First rectangle length x width = 18x X or 18x

Second rectangle length x width = 12 x 2x

168= 18. x + 12 . 2x

The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The figure shown has a total area of 168 cm².

Now, We can find as;

Area of rectangle = Length x width

Hence, We can formulate;

⇒ 18 × x + 12 × 2x = 168

Thus, The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

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The values of the variable are:

x is 45.

y is 18.

z is 18.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

From the figure,

Sin 45 = z / (18√2)

Sin 45 = 1 /√2

So,

1/√2 =z / 18√2

z = 18

Cos 45 = y / (18√2)

1/√2 = y/18√2

y = 18

Tan x = y / z

Tan x = 18/18

Tan x = 1

x = \(tan^{-1}\)1
x = \(tan^{-1}\) tan 45

x = 45

Thus,

x is 45.

y is 18.

z is 18.

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Answer:

256

Step-by-step explanation:

23:9      

9x8=72

23x9=184

184+72

It says in total