Read the conclusion below.
The ancient Greeks devised a way to help audience members find their correct seats.

Which sentence from the article provides the BEST support to the statement above? A) Your admission ticket, a bronze or lead disk, probably had letters telling you which section to sit in. B) Priests and other important citizens sat in the front row, often in throne-like stone seats. C) Girls and women, if admitted at all, probably sat high up in the back rows, nearly 200 feet from the stage. D) But no matter where you sat, you could have heard the actors speak, because acoustics were perfect.​

The difference between the lightest bag of grapes that has been recorded by Colton will be 3/2 or 1 - 1/2.

\(2 - \frac{1}{2} \)

\( = \frac{4}{2} - \frac{1}{2} \)

\( = \frac{3}{2} or \: 1 - \frac{1}{2} \)

Data gathering, analysis, interpretation, presentation, and organization are all topics covered in the study of statistics. In other words, gathering and summarizing data is a mathematical discipline. Additionally, statistics can be considered a subfield of applied mathematics.

Uncertainty and variation are two crucial and fundamental concepts in statistics. Only statistical analysis can be used to determine the uncertainty and variation in various fields. Probability, which has a significant impact on statistics, essentially determines these uncertainties.

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Answer:

C

Step-by-step explanation:

using the pythagorean theorem,

a²+b²=c²

8²+7²=c²

64+49=c²

113=c²

\( \sqrt{113 = \sqrt{c}² } \)

10.63=c

A sample size of at least 109 GPAs to estimate the population mean with a 90% confidence level

Confidence level = 90%

Standard deviation = 0.88

Mean = 0.1

Calculating the sample size -

\(n = [(zα/2σ) / E]^2\)

The crucial value for a confidence level of 90%, denoted by z/2, may be determined using a typical normal distribution table or calculator, where n is the required sample size. The value of z/2 at a 90% degree of confidence is around 1.645. The problem statement specifies that the population standard deviation at 0.88 and that E is the most significant error of the sample mean from the population mean at 0.1.

Therefore, substituting the values -

\(n = [(1.645 x 0.88) / 0.1]^2\)

n = 108.25

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Answer:

3/4

Step-by-step explanation:

sin^2(240°)

=sin^2(360-120)

=sin^2(-120)

={-sin^2(120)}

=(-\(\sqrt({3} /2)^2\)

=3/4

Step-by-step explanation:

i hope so u can see sorry

and it is correct

Every year, 1800 units crossover point. The process focus is less expensive for volumes over 1800.

When all tax credits have been used up by a limited partnership and the limited partners are left with a tax burden, that moment is known as the crossover point.

When both projects have positive values, the crossover point is formed by the intersection of two IRR curves.

The weighted average cost of capital, also known as the crossover rate, is the rate of return at which the net present values (NPV) of two projects are equal.

The rate of return at which the net present value profiles of two projects cross each other is what this term denotes.

So, annual crossover sales are 1800 units.

Process emphasis is less expensive and less important for volumes under 1800 units; repeated manufacturing concentration is less expensive and less important for volumes exceeding 1800 units.

Fixed cost ÷ variable cost

$90000÷50 =$1800

$9,000÷5=$1800

Therefore, every year, 1800 units cross over. The process focus is less expensive for volumes over 1800.

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Correct question:

A product is currently made in a process-focused shop, where fixed costs are $9,000 per year and variable costs are $50 per unit. The firm is considering a fundamental shift in process, to repetitive manufacturing. The new process would have fixed costs of $90,000, and variable costs of $5. The cross over is at 1800 units annually. for volumes over 1800, the process focus is cheaper.

Answer:

c = 8

Step-by-step explanation:

Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = \(\frac{adjacent}{hypotenuse}\)

=> cos x = \(\frac{25}{40}\)

=> cos x = \(\frac{5}{8}\)

=> x = \(cos^{-1}\frac{5}{8}\)

=> x = 51.3°

Hence the value of x is 51.3°.

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Answer:

(i) The complement of the intersection of Sets A and B, denoted by (A∩B)', is the set of all elements that are not in the intersection of Sets A and B. It can be found by taking the union of the complements of Sets A and B, denoted by A' and B'. Hence, (AnB)' = A' U B'.

(ii) The complement of the union of Sets A and C, denoted by (A U C)', is the set of all elements that are not in the union of Sets A and C. It can be found by taking the intersection of the complements of Sets A and C. Hence, (A U C)' = A' ∩ C'.

(iii) The complement of the union of Sets A, B, and C, denoted by (A U B U C)', is the set of all elements that are not in the union of Sets A, B, and C. It can be found by taking the intersection of the complements of Sets A, B, and C. Hence, (A U B U C)' = A' ∩ B' ∩ C'.

Answer:

See explanation.

Step-by-step explanation:

The arc BX, central angle BCX, and inscribed angle BNX are connected through the following relationships:

1. The central angle BCX subtends the arc BX. This means that the central angle is formed by two radii connecting the center of the circle to the endpoints of the arc BX.

2. The inscribed angle BNX subtends the same arc BX. This means that the inscribed angle is formed by two chords connecting a point on the circumference of the circle to the endpoints of the arc BX.

3. The relationship between the central angle BCX and the inscribed angle BNX is given by the Inscribed Angle Theorem, which states that the measure of an inscribed angle is half the measure of the central angle subtending the same arc. In other words, if θ is the measure of the central angle BCX and α is the measure of the inscribed angle BNX, then:

\(\alpha =\frac{1}{2}\) θ

The equation of the exponential function is 2ˣ with the given properties.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

An exponential function of base e has the form f(x) = \(ae^{(bx)}\), where a and b are constants.

The horizontal asymptote of this function is at y=1, which means that a=1.

The y-intercept is the point where the graph crosses the y-axis, which is at x=0. The value of f(0) is the y-intercept of the graph, and since it is less than 2, we have \(f(0) = 1\times e^{(b\times0)}\) = 1 < 2.

The graph also contains the point (-1, 2), which means that f(-1) = 2. Substituting the values we have found for a and f(0) into the equation for f(x), we get \(f(-1) = 1\times e^{(b\times(-1))}\) = 2.

Solving this equation for b, we find that b = ln(2).

Substituting this value for b into the equation for f(x), we get f(x) = \(e^{(ln(2)x)} = 2^x\).

This is the equation of the exponential function with the given properties.

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490

472 <490<500

it fits the criteria

Answer:

1/a^2 is the answer to this question

The surface area of the cone is 180 pi square feet

Surface area of a cone

The formula for calculating the surface area of a cone is expressed as shown below;

SA = πr(r+l)

where

r is the radius

l is the slant height.

From the given diagram

radius r = 24/2 =12ft

For the slant height

Using the Pythagoras theorem;

l^2 = 9^2 + 12^2
l^2 = 81 + 144
l^2 = 225
l = 15ft

Substitute

Surface area = 3.14 * (12) * 15
Surface area = 3.14 * 180

Surface area  = 180pi square feet

Hence the surface area of the cone is 180 pi square feet

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Answer:B

Step-by-step explanation:55 divided by 100 will give you 0.55

Given: A function-

Required: To determine the point where the function starts.

Explanation: To determine where the function starts, we need to determine the domain and range of the function. The domain of a function is the set of x values for which the function is defined.

The square root is not defined for negative values. Hence the domain of the function is the set of all x values greater than or equal to zero as follows-

And the range for a function of the type-

is-

Hence, the range of the function is-

Hence, the function starts at the point (1/2,3).

Final Answer: Option D is correct.

Answer:

Mean: 7

Median: 8

Range: 9

Mode: 3

Step-by-step explanation:

First, to find the mean of a set of numbers you need to add up all of the numbers and divide that by the total amount of numbers. In this case that makes this equation, \(\frac{3+3+4+8+9+10+12}{7}\), which is \(\frac{49}{7}\), which is 7.

To find a median you need to find the middle number. A handy trick I use for this is to place my fingers on the first and last number, and then move them towards the middle, at the same time by one number until there is just one number left in the middle. If there are no numbers left after doing this, meaning there are an even amount of numbers given, the median is the mean of the last two numbers that were covered. In this case, this is not necessary, so the median is 8.

The range is the difference between the maximum and minimum of a data set. In this case that would give you the equation Range=12-3, which means the range is 9.

Finally, the mode is the number that occurs the most in a given data set. In this case the number that occurs the most is 3, which occurs twice compared to every other number which only occurs once.

Hey there!

‘‘Find the mean median range and mode for 3, 3, 4, 8, 9, 10, and 12’’

• Mean is known as your AVERAGE number. You have to ADD all of your NUMBERS the DIVIDE it by the TOTAL numbers in your given set

• We have the total of SEVEN numbers in your set

“3 + 3 + 4 + 8 + 9 + 10 + 12 / 7”

6 + 4 + 8 + 9 + 10 + 12/7

10 + 8 + 9 + 10 + 12/7

18 + 9 + 10 + 12/7

27 + 10 + 12/

37 + 12/7

49/7 = 7

Answer: Mean = 7 ✔️

• Median is the number you see in the center (the middle) of the problem. You can solve for this by putting your numbers from least to greatest

• If you have an ODD number in your given set then your middle number will be the single number)

• If you have an EVEN number then you have to average your TWO middle number

“ 3, 3, 4, 8, 9, 10, 12”

• you still have 3 on both sides of your 8 (3 is an ODD number, so we have to let it be be a single number)

Answer: mean = 8 ✔️

• Mode is your number than you see repeated OR more than once

• We “3” repeated so it is your Mode

Answer: Mode = 3 ✔️

Answers ⬇️

• Mean: 7 ☑️

• Median: 8 ☑️

• Mode: 3 ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

For this problem, we are given the mean and standard deviation for the height of men. We need to calculate the minimum height to be considered in the top 10% of tallest men, and the maximum height to be considered in the shortest 15% of men.

The first step we need to solve this problem is to calculate the z-score. The z-score can be found by using the following expression:

For the first situation, we want a z-score for the top 10% of tallest men. This means that we need to go on the z-table and find the z-score that represents 90% of probability to the left because this will give us the minimum height to be at the 10% tallest. From the z-table we have:

Now we can use the z-score expression to find the value of x. We have:

The man should be at least 71.85 inches tall to be considered among the 10% of tallest men.

For the second situation, we have something similar. We need to find the maximum height for a man to be considered between the 15% of men. We need to go into the z-table and find the z-score that produces a result close to 0.15. We have:

Now we need to use the z-score expression to determine the height:

In order to be considered among the smallest men, someone needs to be 64.88 inches tall.

The degree of financial leverage for Foggy Futures Weather Forecasters

is 1.06

Degree of Financial leverage (DFL) = (EBIT) / (EBT)

Earnings Before Interest and Taxes (EBIT) = $750,000

Amount to be given as loan on $1000000

$1,000,000 x 4.5% = $1,000,000 x 4.5/100

= $45000

To find EBT ( Earnings Before Tax),

EBT = EBIT - 45000

       = 750000 - 45000

EBT = 705000

∴ DFL =  (EBIT) / (EBT)

          = 750000/705000

 DFL = 1.06

The DFL is a percentage that accountants and financial professionals use to show changes in a company's net income due to changes in its profits before interest and taxes (EBIT).

Earnings before interest and taxes (EBIT) is a measurement of a company's profit in accounting and finance that takes into account all revenues and costs (both operating and non-operating), with the exception of interest costs and income tax costs.ve

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The measure of VU is 16 units

The given parameters are:

\(OV = 7x + 2\)

\(VU = 3x + 10\)

Given that, lengths OV and VU are congruent, we have:

\(OV =VU\)

Substitute values for OV and VU

\(7x +2 =3x + 10\)

Collect like terms

\(7x -3x = 10 -2\)

Evaluate like terms

\(4x = 8\)

Divide both sides by 4

\(x = 2\)

Substitute 2 for x in \(VU = 3x + 10\)

\(VU = 3 \times 2 + 10\)

\(VU = 6 + 10\)

Evaluate like terms

\(VU = 16\)

Hence, the measure of VU is 16 units

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Answer:

Its gonna be a 50/50 on the coin and 20/100 chance for the spinner

Answer:

5 outcomes for the spinner and a 50/50 chance for the coin

Step-by-step explanation:

for the spinner, there are five numbers, 1,2,3,4, and 5. so, there is a 1/5 chance or you could also say there is a 20/100 chance.   For the coin, there are two sides and 100 divided by 2 is 50 therefore, there is a 50/50 chance

Hope this helps!!

Answer:

$2,950

Step-by-step explanation:

Interest earned (I) = Principal x Interest rate x Time

Total Amount (A) = Interest Earned + Principal

I = 2500(.03)(6)

I = 450

A = 450 + 2500

A = 2950

The function of Car A is an exponential function.

The function that describes the value is g(x) = \(18,000(0.94^{x})\).

The value of f(x) in 9 years is $10,313.91.

The function of Car B is a linear function.

The function that describes the value is  g(x) = 18,500 -750x.

The value of f(x) in 9 years is $11,750.

The value of the car declines with the passage of time. Thus, the value of the car depreciates with the passage of time.

A linear function is a function that has a single variable raised to the power of 1. A linear function increases or decreases by a constant value.  

The general form of a linear function is f(x) = a + bx

Where:

Rate of change = value of the car B in year 2 - value of the car B in year 1

17,000 - 17,750 = - 750

g(x) = 18,500 -750x

Value of g(x) when x is 9:

g(x) = 18,500 -750(9)

g(x) = 18,500 - 6,750

g(x) = $11,750

An exponential function can be described as an equation with exponents. The exponent is usually a variable.

The general form of exponential function is f(x) = \(e^{x}\)

Where:

• x = the variable

• e = constant

Constant = (Value of the car in year 2 / value of the car in year 1) - 1

Constant = (16,346.60 / 17,390) - 1 = -0.06 = -6%

g(x) = \(18,000(0.94^{x})\)

Value of the car in 9 years =  \(18,000(0.94^{9})\) = $10,313.91

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The given triangles are obtuse = 36 m, right angled = 225 m and right angled = 2500 m.

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

7.) This triangle is obtuse.

To see this, we can use the Pythagorean theorem:

4*4 + 5*5 = 16 + 25 = 41

6*6 = 36 m

Since 41 > 36, we know that the triangle is obtuse.

8.) This triangle is right.

To see this, we can again use the Pythagorean theorem:

11*11 + 12*12 = 121 + 144 = 265

15*15 = 225 m

Since 265 = 225 + 40, we know that the triangle is right.

9.) This triangle is also right.

We can use the same method as before:

30*30 + 40*40 = 900 + 1600 = 2500

50*50 = 2500 m

Since 2500 = 2500, we know that the triangle is right.

Therefore, The given triangles are obtuse , right angled and right angled.

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The percentage of people playing basketball is approximately 86.67%.

To determine the percentage of people playing basketball, we need to find the number of people playing basketball.

Given that there are 14 people who play football, 5 people who play both football and basketball, and a total of 30 people playing one sport, we can use this information to calculate the number of people playing basketball.

Let's denote the number of people playing basketball as 'B'.

From the given information, we know that:

The number of people playing football only = 14 - 5 = 9

The number of people playing basketball only = 30 - 9 = 21

The number of people playing both football and basketball = 5

To find 'B', we sum up the number of people playing basketball only and those playing both sports:

B = 21 + 5 = 26

Now, to calculate the percentage of people playing basketball, we divide the number of people playing basketball by the total number of people and multiply by 100:

Percentage of people playing basketball = (26 / 30) \(\times\) 100 = 86.67%

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Let the amount of pizza be 1:

Amount ate by devon = 0.25 = 1/4

Amount ate by his friends = 3/8 + 1/8 = 4/8

The total fraction consumed = 1/4 + 4/8

The total fraction consumed = (2+4)/8

The total fraction consumed = 6/8

The fraction of the pizza left unconsumed = Total amount of pizza - amount consumed

The fraction of the pizza left unconsumed = 1 - 6/8

The fraction of the pizza left unconsumed = (8-6)/8

The fraction of the pizza left unconsumed = 2/8

The fraction of the pizza left unconsumed = 1/4

Hence the amount of pizza left is 1/4

Hello, the graph sould be like this. Just remember, if you want to draw a graph, you should know the x and y state. x is from left and y is from right.