Kenney High School's swimming pool is 25 yards long. The pool has 8 lanes, each of which is 3 yards wide. The pool is filled to a depth of 6 feet.

What are the lengths and width in terms of feet?

The length of the side P is 15 cm. And the right option is C.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides.

To calculate the length of side P we use Pythagoras theorem's formula

Pythagoras formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the right option is C 15 cm.

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The firm’s economic value added (EVA), that is, how much value did management add to stockholders’ wealth during 2018 is $0.42 million

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

Net operating profit = (22 million - 19 million)*(1 - 0.36)

                                = $1.92  million

EVA = net operating profit after taxes - invested capital*WACC

       = 1.92 million - 15 million*0.10

       = $0.42 million

Therefore, The firm’s economic value added (EVA), that is, how much value did management add to stockholders’ wealth during 2018 is $0.42 million.

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To solve the inequality 2x < 12, we need to isolate x on one side of the inequality sign. We can do this by dividing both sides by 2:

2x < 12

x < 6

Therefore, the solution to the inequality is x < 6. This means that all values of x that are less than 6 satisfy the inequality. We can represent this graphically on a number line:

<=======()------6-------------->

The open circle () indicates that x cannot be equal to 6, but can be any value less than 6. The arrow indicates that the inequality is true for all values of x to the left of the open circle.

In summary, the solution to the inequality 2x < 12 is x < 6.

I'm 15 BTW

$3,244.21 can be withdrawn each month for 25 years, assuming an interest rate of 7% and a starting principal of $500,000.

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

where:

PV is the present value of the annuity

PMT is the payment amount per period

r is the interest rate per period

n is the total number of periods

In this case, we want to withdraw a fixed amount each month for 25 years, which represents 12 ×25 = 300 periods.

The interest rate per period is 7% / 12 = 0.5833%.

Let's assume that you want to withdraw a fixed amount each month, and you want the withdrawals to last for 25 years. To calculate the amount you can withdraw each month,

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

500,000 = PMT × [1 - (1 + 0.005833)⁻³⁰⁰] / 0.005833

Solving for PMT, we get:

PMT = PV × r / [1 - (1 + r)⁻ⁿ]

PMT = 500,000 × 0.005833 / [1 - (1 + 0.005833)⁻³⁰⁰]

PMT = $3,244.21

Therefore, you can withdraw $3,244.21 each month for 25 years, assuming an interest rate of 7% and a starting principal of $500,000.

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Answer:

A

Step-by-step explanation:

Answer:

\( 16 \: {m}^{2} \)

Step-by-step explanation:

Area of the quadrilateral

\( = \frac{1}{\cancel 2} \times 8 \times \cancel 2 + \frac{1}{\cancel 2} \times 8 \times \cancel 2 \\ \\ = 8 + 8 \\ \\ = 16 \: {m}^{2} \)

Answer:

100

Step-by-step explanation:

100/ 10

= 10

Answers:

Step-by-step explanation:

Part 1.) To solve for the first one:

Replace the variables with the given numbers. 2 x 4 = 8^2 (= 64), and 3 x 8 = 24. (P.S, the carrot symbol ^ means exponent, or to the power of, just to let you know.)

So, 8 - 24 = (-16).

Part 2.) To solve for the second part of the equation:

Replace the variables with the given numbers, and distribute the coefficient (2) into the parentheses. 2 x 8 = 16, 2 x 4 = 8.

Now add the two sides and then place them over a fraction. 16 + 8 = 24, 24/4 = 6.

Part 3.) So, the answer is -16 < 6. Six is the larger number.

I hope this helps.

1) 2x+y=5 ...... It is a linear equation

2) y= x + 6 ....... It is a linear equation

Because they are of first degree and they contain x and y (equations of a line)

Answer: 86

Step-by-step explanation:

This is a cyclic quadilateral in which opposite angles adds upto 180.

Let the unknown angle be x

ATQ

x + 94 = 180

x = 180 - 94

x = 86

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The domain of function f(x) is given as follows:

{x | 1 ≤ x < 5}.

The values of x of the function given at the end of the answer are as follows:

Hence the domain is given as follows:

{x | 1 ≤ x < 5}.

The function is given by the image presented at the end of the answer.

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Answer:

A - {x | 1 < x < 5}

Step-by-step explanation:

took the Quiz

The highest height for the daily rainfall were for 5 and 6 inches

Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.

From the given dot plot, we see the number of times for each height of rainfall.

Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.

Thus, we conclude those were the highest heights for the daily rainfall.

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The correct statement is;

False,  because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be  x = 2π/3 + 2nx and x = 4π/3 + 2nx.

Option D

From the information given, we have that;

All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx

There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx

Such that n is an integer.

This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.

The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.

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Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

  $50,000

Step-by-step explanation:

The given relations can be used to write and solve an equation for the amount invested in stocks.

Let s represent the amount invested in stocks. Then (120,000-s) is the amount invested in bonds. The total earnings by the two investments were ...

  0.18s +0.12(120,000 -s) = 17,400

Simplifying the equation, we have ...

  0.06s +14,400 = 17,400

  0.06s = 3000 . . . . . . . . . . subtract 14,400

  s = 50,000 . . . . . . . . . . . . divide by 0.06

Neal invested $50,000 in stocks.

__

Additional comment

The amount invested in bonds was 70,000. The profit earned was ...

  0.18(50,000) +0.12(70,000) = 9,000 +8,400 = 17,400

The description best compares the graph given by the equations 3x - y = 5 and 2x + 6y = 24 will be intersecting but not perpendicular. Option D is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation of the line is 3x - y = 5 and 2x + 6y = 24.

The graph for the function is plotted on the paper below and it is observed that the lines are intersecting.

Thus, the description best compares the graph given by the equations 3x - y = 5 and 2x + 6y = 24 will be intersecting but not perpendicular. Option D is correct.

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The purpose of data is to provide information and insights that can be used to make informed decisions, draw conclusions, and gain knowledge about a particular subject or phenomenon.

Data plays a crucial role in various fields, including science, business, research, healthcare, and everyday life.One primary purpose of data is to describe and understand the world around us.

By collecting and analyzing data, we can identify patterns, trends, and relationships that exist within a dataset. This helps us gain a deeper understanding of complex systems and phenomena.

For example, in scientific research, data is used to study the behavior of natural processes, investigate the effects of interventions, and formulate theories and models.

Data also serves as a foundation for making informed decisions. By examining relevant data, individuals and organizations can assess the potential outcomes of different choices and select the most optimal course of action.

Data-driven decision-making enables organizations to improve efficiency, identify opportunities, mitigate risks, and enhance overall performance. In fields like marketing and finance, data is extensively used for market research, customer segmentation, trend analysis, and financial forecasting.

Furthermore, data is crucial for monitoring and evaluating performance. By collecting data over time, organizations can track progress, measure outcomes, and identify areas for improvement. Data-driven monitoring allows for evidence-based assessments and adjustments to strategies or interventions.

Overall, the purpose of data is to provide reliable information that can be used to enhance understanding, support decision-making, and drive progress in various domains. It empowers individuals and organizations with the ability to derive insights, solve problems, and make meaningful contributions to society.

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Answer:

Step-by-step explanation:

To determine the monthly payment Amy pays, we can use the formula for calculating the monthly payment on a loan. The formula is:

M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Principal amount (loan amount)

r = Monthly interest rate

n = Number of monthly payments

Given information:

Principal amount (loan amount) = $21,000

Down payment = 10% of $21,000 = $2,100

Remaining balance = $21,000 - $2,100 = $18,900

APR = 3.5%

Number of monthly payments (n) = 36

To calculate the monthly interest rate (r), we divide the annual interest rate by 12 (number of months in a year):

Monthly interest rate (r) = APR / (12 * 100)

Substituting the values into the formula:

r = 3.5 / (12 * 100) = 0.0029167 (rounded to 7 decimal places)

M = (18,900 * 0.0029167 * (1 + 0.0029167)^36) / ((1 + 0.0029167)^36 - 1)

Using a calculator to evaluate the expression within the formula:

M ≈ $539.26

Therefore, the monthly payment that Amy pays is approximately $539.26.

Answer:

AB = 146°

Step-by-step explanation:

The measure of the arc is equal to the angle it subtends at the centre, thus

measure of arc AB = 146°

Answer:

mAB = 214

Step-by-step explanation:

A circle has 360 degree all around

mAB = 360-146 = 214 degree

Simplify:

7/8 - 17/24

To complete the operation, we need to have both denominators with the same value.

One denominator is 8 and the other one is 24

Note 24 is a multiple of 8 (24=8*3).

Thus, to make both denominators be equal, we just multiply the first fraction by 3. This is called amplification

The expression is now:

21/24 - 17/24

Please note the first fraction was amplified by 3: 7*3= 21 and 8*3=24

Now we have both denominators the same, we just subtract the numerators:

(21-17) / 24

Operating:

4 / 24

This fraction can be simplified by 4:

1/6

This is the final result

The cost of 20 T-Shirt will be 2560 when cost of one t-shirt is 128.

When a selling price and profit are provided, cost price equals selling price plus profit. When the selling price and loss are disclosed, cost price equals selling price plus loss.

Profit is calculated as S.P. - C.P. If the selling price is less than the cost price, the difference between the two is the loss incurred. Loss is also equal to C.P. - S.P.

We must divide the gross profit by the entire revenue for the year, multiply by 100, and then find the gross profit margin. We must divide net income (or net profit) by the entire annual revenue before multiplying the result by 100 to get the net profit margin.

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n⁴ - 2n³ - 23n² + 24n + 144 is the standard form of given zeroes.

What is a linear equation in mathematics?

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.

                              A linear equation is an equation that raises a variable to the first power. ax+b = 0 is an example of a 1 variable. x is a variable and a and b are real numbers.  

Roots : -3(mult . 2), 4(mult.2)

the function is given as

     f(n) = (n + 3)² (n - 4)²

         = (n + 3) (n + 3 ) ( n - 4 ) ( n - 4)

        = (n² + 6n + 9) (n² - 8n + 16 )

        = n⁴ - 8n³ + 16n² + 6n³ - 48n² + 96n + 9n² - 72n + 1

collecting like term,

    f(n) = n⁴ - 2n³ - 23n² + 24n + 144

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Answer:

area = 113.04 ft²

Step-by-step explanation:

area = πr²

r = 1/2diameter so:

r = 6 ft

π = 3.14

area = (3.14)(6²) = (3.14)(36) = 113.04 ft²

Answer:

The area is about 113.04 ft² square feet

Step-by-step explanation:

Hope this helps

The percent decrease in the number of ponds that support brook trout would be approximately 47.37%.

To calculate the percent decrease in the number of ponds that support brook trout, we need to determine the difference between the initial number of ponds and the final number of ponds, and then express that difference as a percentage of the initial number of ponds.

Initial number of ponds: 19

Final number of ponds: 10

To calculate the percent decrease, we can use the following formula:

Percent Decrease = (Difference / Initial Value) * 100

Let's apply this formula to the given data:

Difference = Initial number of ponds - Final number of ponds

Difference = 19 - 10

Difference = 9

Percent Decrease = (9 / 19) * 100

Now, let's calculate the percent decrease:

Percent Decrease = (9 / 19) * 100

Percent Decrease ≈ 47.37%

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The probability that the third largest observation in the sample is less than 0.7 is  0.2401 =  24.01%.

The sample size n = 5,

Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.

Probability that X₃ is less than 0.7:

Since X₃ is the third largest observation =  (X₁ and X₂) < 0.7.

The probability that X₃ is less than 0.7 is (0.7)² = 0.49.

.

The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.

We then get the product of both cases:

Probability = 0.49 * 0.49 = 0.2401

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The dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ration.

To determine the amounts of the 70% protein supplement and the 20% protein ratio needed to make a 1900-pound high-grade 55% protein ration, we can set up a system of equations.

Let's assume x represents the pounds of the 70% protein supplement and y represents the pounds of the 20% protein ratio.

The total weight equation is given by:

x + y = 1900

The protein content equation is given by:

(0.70x + 0.20y) / 1900 = 0.55

Simplifying the second equation, we get:

0.70x + 0.20y = 0.55 × 1900

0.70x + 0.20y = 1045

Now, we can solve this system of equations to find the values of x and y.

Rearrange the first equation to solve for x:

x = 1900 - y

Substitute this expression for x in the second equation:

0.70(1900 - y) + 0.20y = 1045

1330 - 0.70y + 0.20y = 1045

1330 - 0.50y = 1045

-0.50y = 1045 - 1330

-0.50y = -285

y = -285 / -0.50

y = 570

Now substitute this value of y back into the first equation to find x:

x + 570 = 1900

x = 1900 - 570

x = 1330

Therefore, the dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ratio.

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Step-by-step explanation:

7! = 5040 ways

Answer:

64°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

let the third angle be x , then

x + 90° + 26° = 180°

x + 116° = 180° ( subtract 116° from both sides )

x = 64°

the other angle is 64°