Figure AFigure B

Find the area of Figure B.

225 ft 2
68 ft 2
17 ft 2
315 ft 2

Answer:

x=-2

Step-by-step explanation:

0=4x+8

-4x=8

x=-2

Answer:

true

Step-by-step explanation:

Answer:97

Step-by-step explanation:

Answer:

k = 62

Step-by-step explanation:

x + 97 + 149 + 55 = 360  {sum of all angles of quadrilateral}

x + 301 = 360

x = 360 - 301

x = 59

l // m and AB is transversal.

∠1 = x   {alternate interior angles}

∠1 = 59

ΔABC is an isosceles triangle.

m∠1 =  m∠2 = 59

In ΔABC ,

59 + 59 + k = 180  {angle sum property of triangle}

118 + k = 180

k = 180- 118

k = 62

The linear approximation of sin(5π/12) is approximately 0.9035.

The linear approximation of f(x) = sin(x) at x = π/3 can be found using the formula:

L(x) = f(a) + f'(a)(x-a)

where a =π/3, f(a) = sin(π/3) = √(3)/2, and f'(x) = cos(x), so f'(a) = cos(π/3) = 1/2.

Plugging these values into the formula, we get:

L(x) = √(3)/2 + (1/2)(x-π/3)

L(5π/12) can be approximated using this linear approximation:

L(5π/12) = √(3)/2 + (1/2)(5π/12 - π/3) = √(3)/2 + (1/2)(π/12)

Simplifying this expression gives:

L(5π/12) = √(3)/2 + π/24 ≈ 0.9035

Therefore, the linear approximation of sin(5π/12) is approximately 0.9035.

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The angle measure with a negative cotangent ratio is given as follows:

c) 320º.

The cotangent of an angle is obtained with the division of the cosine of the angle by the sine of the angle, that is:

cot(x) = cos(x)/sin(x).

The cotangent is negative when the sine and the cosine have different signs, hence on these following quadrants:

For this problem, we have that the angle of 320º is on the fourth quadrant, hence it has a negative cotangent and is the answer for this problem.

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Mean reversion is the tendency of prices or variables to return to their average level. The mean-reverting level, x1, is calculated using statistical methods and indicates potential future decreases or increases.

Mean reversion refers to the tendency of asset prices or economic variables to move back to their average or mean level over time. The mean-reverting level, x1, for a time series can be calculated using statistical methods like moving averages or exponential smoothing. These techniques estimate the average value or trend of the data.



The interpretation of x1 depends on the context. If the current value is above x1, it suggests a potential future decrease, reverting back to x1. Conversely, if the current value is below x1, it indicates a potential future increase, also reverting back to x1. The deviation from x1 provides insights into the strength or speed of the mean reversion process.



Therefore, Mean reversion is the tendency of prices or variables to return to their average level. The mean-reverting level, x1, is calculated using statistical methods and indicates potential future decreases or increases.

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Answer:

Step-by-step explanation:

To solve this problem, we need to use the hypergeometric distribution.

Let's first calculate the total number of ways to choose 8 executives from 30 candidates:

Total number of ways = COMBIN (30, 8) = 8,347,680

Now we need to calculate the number of ways to choose 2 executives from each of the four functional areas (finance, marketing, accounting, operations).

Number of ways to choose 2 executives from finance = COMBIN(8, 2) = 28

Number of ways to choose 2 executives from marketing = COMBIN(6, 2) = 15

Number of ways to choose 2 executives from accounting = COMBIN(9, 2) = 36

Number of ways to choose 2 executives from operations = COMBIN(7, 2) = 21

So the total number of ways to choose exactly 2 executives from each functional area is:

Total number of ways = 28 * 15 * 36 * 21 = 1,516,320

Now we can calculate the probability by dividing the number of ways to choose exactly 2 executives from each functional area by the total number of ways to choose 8 executives:

P (exactly 2 from each functional area) = 1,516,320 / 8,347,680 = 0.1813

Therefore, the probability that exactly 2 executives from each of the four functional areas are on the task force is 0.1813 or approximately 18.13%.

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Scientific Notation is the way of writing a number or expressing them in a shorter or more compact way.

No, Taylor's resoning is incorrect because  2,800,000 = \(2.8 * 10^{6}\)

From the question, we are given:

2,800,000 .

2,800,000 in scientific notation is  \(2.8 * 10^{6}\).  

The reason the power is not to the negative 6 is that we are moving from the right-hand side to the left-hand side 6 times.

Therefore, Taylor's reasoning is incorrect.

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x is 280........................

34

It been a while since I've done these, so hopefully it's correct :)

Based on the passage you provided, it seems like you are being asked to apply principles of logic and construct a truth table based on the premises and conclusion presented in the passage. To accomplish this, you need to follow the three steps outlined:

Step 1: Break the premises into several statements (usually denoted by p, q, r, etc.)

From the passage, we can identify the following statements:

- Statement 1: Water is fundamental for life and the environment.

- Statement 2: Water crisis is one of the most important challenges of the 21st century.

- Statement 3: Ensuring that we use water more wisely, more productively, and less profligately will be one of the defining challenges of this century.

- Statement 4: If all public services collaborate to address the water scarcity problem, then the governments will be able to provide a planning framework to manage water usage and boost awareness of the water crisis.

- Statement 5: There is a lack of planning frameworks or there are not enough campaigns to raise awareness of the water crisis.

- Statement 6: Therefore, there is no efficient collaboration among various public sectors to address the water shortage problem.

Step 2: Express the premises and conclusion symbolically.

Using the statements identified above, we can symbolically represent them as follows:

- p: Water is fundamental for life and the environment.

- q: Water crisis is one of the most important challenges of the 21st century.

- r: Ensuring that we use water more wisely, more productively, and less profligately will be one of the defining challenges of this century.

- s: All public services collaborate to address the water scarcity problem.

- t: Governments will be able to provide a planning framework to manage water usage and boost awareness of the water crisis.

- u: There is a lack of planning frameworks or there are not enough campaigns to raise awareness of the water crisis.

- v: There is no efficient collaboration among various public sectors to address the water shortage problem.

Step 3: Construct a truth table.

To construct a truth table, assign truth values (T or F) to each statement and evaluate the truth value of the conclusion based on the truth values of the premises

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Answer:

40/9

$189

Step-by-step explanation:

1 2/3 / 3/8 =

4 4/9 = 40/9

6.85 x 315 - 6.25 x 315 = $189

Hope that helps!

Answer:

ik gonna let u solve this question but I explained what u need to do to solve it

A variable that is changed in the experiment on purpose by the experimenter accurately summarizes a test variable (independent variable) in an experiment.

In an experiment, there are different types of variables that are used to measure the effect of the experiment on the outcome.

The independent variable, also known as the test variable, is the variable that is intentionally changed by the experimenter to measure its effect on the dependent variable, which is the variable that is being measured in the experiment.

Therefore, a variable that is changed in the experiment on purpose by the experimenter accurately summarizes a test variable (independent variable) in an experiment.

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Answer:

domain: all real numbers

range : y ≥ 7

Step-by-step explanation:

The domain is the values that x can take

X can take any value so the domain is all real numbers

The range is the values that y can take

The smallest value  for the absolute value is 0

0+7 =7 so the smallest value for y is 7

range is y ≥ 7

Answer: This is a function

Step-by-step explanation: It passes for the vertical line test.

Answer:

The cylinder's height is 14 cm

Step-by-step explanation:

Recall that the formula for the volume of a cylinder is given by:

\(Volume=\pi\,R^2\,\,H\)

where R is the radius of the cylinder's base, and H the cylinder's height (which we we don't know and need to find)

In order to use this formula to solve for our unknown we need to obtain the radius "R" by using the second piece of information on the length of the base's circumference (22 cm). Recall the formula for the length of a circumference of radius R:

\(length=2\,\pi\,\,R\)

Then, in our case:

\(length=2\,\pi\,\,R\\22=2\,\pi\,\,R\\R=\frac{22}{2\,\pi} \\R=3.50\,\,cm\)

We now use this information in the volume equation to find the cylinder's height:

\(Volume=\pi\,R^2\,\,H\\539\,\,cm^3=\,pi\,(3.5\,\,cm)^2\,\,H\\H=\frac{539}{\pi\,12.25} \,cm\\H=14.0 \,cm\)

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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Statements (1) and (4) are consistent, while statements (2) and (3) are contradictory.

Let's analyze the given statements:

1. f(x) < 0 over the interval (-∞, -4):

This means that for any value of x between negative infinity and -4, the function f(x) yields a negative value.

2. f(x) < 0 over the interval (-∞, -3):

This statement is a subset of the previous one. It implies that for any value of x between negative infinity and -3, the function f(x) yields a negative value.

3. f(x) > 0 over the interval (-∞, -3):

This contradicts the previous statement (2). If f(x) is greater than 0 for any value of x between negative infinity and -3, it means that the function yields positive values in that interval.

4. f(x) > 0 over the interval (-∞, -4):

This statement is a subset of statement (3). It implies that for any value of x between negative infinity and -4, the function f(x) yields positive values.

Therefore, statements (1) and (4) are consistent, while statements (2) and (3) are contradictory.

It's important to note that without specific information about the function f(x), we cannot provide a precise interpretation of these statements. The analysis is based solely on the given conditions.

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A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices, and 12 edges. 

The diagonal of a cube is √3 side.

If the volume of a cube is 4096 cm³ the diagonal of a cube is 16√3 cm.

A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices, and 12 edges. 

The volume of a cube is given as:

Volume = side³

The diagonal of a cube = √3 side.

We have,

The volume of a cube = 4069 cm³

The volume of a cube = side³

4096 = side³

side = ∛4096

side = 16 cm

Now,

The diagonal of a cube:

= √3 side

= √3 x 16

= 16√3 cm

Thus,

The diagonal of a cube is 16√3 cm.

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A square must be a rectangle because it's a four-sided geometric shape with four right angles and congruent sides, but a rectangle doesn't always have congruent sides.

In Mathematics and Geometry, a square can be defined as a type of quadrilateral in which the length of all its four (4) sides are equal in magnitude (congruent) and the sum of all its interior angles is equal to 360 degrees (360°) and it forms a right angle.

In Mathematics and Geometry, a rectangle can be defined as a type of quadrilateral in which its opposite sides are equal and all the angles that are formed are right angles.

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Answer:   (0,-1) (4,4)

Plz mark brainliest:)

Answer:

The top one is (-4,4)

and the other one is (0.-1)

hope this helps :)

Answer:

Step-by-step explanation:

The function y = -2 is a constant function. It means that the output of the function is always equal to -2, regardless of the input value.

Here is a function table that shows the input and output values for y = -2:

x y

1 -2

2 -2

3 -2

4 -2

5 -2

As you can see, for any value of x, the output is always -2, since y = -2 is a constant function

The value of x is approximately 1.91.

Since the shape of Tom's property is a parallelogram, opposite sides are equal in length. Let's denote the length of the shorter sides as y and the longer sides as 2x - 15. Then, we can write:

Perimeter = 2y + 2(2x - 15) = 4x - 30 + 2y

We know that the perimeter is 300 feet, so we can set up an equation:

4x - 30 + 2y = 300

Simplifying this equation, we get:

4x + 2y = 330

We are also given that y = 45x + 75. Substituting this expression for y into the equation above, we get:

4x + 2(45x + 75) = 330

Simplifying and solving for x, we get:

94x = 180

x = 180/94

x ≈ 1.91

Therefore, the value of x is approximately 1.91.

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Jordan was reading 26 pages more than jessica

Step-by-step explanation:

when choosing a sample everyone must have an equal chance of getting picked

The number of terms in geometric series with common ratio 0.5 is 5.

A geometric series is a set of integers where each term following the first is created by multiplying the term before it by a predetermined value called the common ratio. To put it another way, each term in the series is created by multiplying the term before it by a set integer.

The sum of a finite geometric sequence is given by the formula:

\(S = a(1 - r^n)/(1 - r)\)

Where, S is the sum of the series,

a is the first term,

r is the common ratio, and n is the number of terms.\(55.5625 = 28(1 - 0.5^n)/(1 - 0.5)\\\\55.5625(1 - 0.5) = 28(1 - 0.5^n)\\27.5625 = 28 - 28(0.5)^n\\0.4375 = (0.5)^n\\n = log(0.4375)/log(0.5)\\n = 4.17\)

Rounding the numbers, we have n = 5.

Hence, the number of terms in geometric series is 5.

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Answer: An arithmetic sequence has a constant difference between each term.

For example: 2,4,6,8,10,12,…

We can see clearly that all the terms differ by +2.

We call this the common difference, d.

A geometric sequence has a constant ratio (multiplier) between each term.

An example is: 2,4,8,16,32,…

So to find the next term in the sequence we would multiply the previous term by 2.

This is called the common ratio, r.

These sequences are closely related as they both have the same first term, but I hope you can see how different they become if they have a common difference or a common ratio.

We can create a decreasing arithmetic sequence by choosing a negative common difference.

Similarly, a decreasing geometric sequence would have a common ratio of less than 1.

Step-by-step explanation: I think that should answer for you.

Let's start with the expression:

5+i/5-i

The given expression can be rationalized as shown below:

5+i/5-i × (5+i/5+i)5+i/5-i × (5+i)/ (5+i)

Now, we can simplify the expression as shown below:

5+i/5-i × (5+i)/ (5+i)= (25+i²+10i)/(25-i²)

Since i² = -1,

we can substitute the value of i² in the above expression as shown below:

(25+i²+10i)/(25-i²) = (25-1+10i)/(25+1) = (24+10i)/26 = 12/13 + 5/13 i

Therefore, the quotient is 12/13 + 5/13 i which is in standard form.

Answer: The quotient in standard form is 12/13 + 5/13 i.

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The area of the base of the prism would be = 290cm²

To calculate the base area of the prism, the formula that should be used would be given below as follows:

The area of a triangle = 1/2× base × height.

Where;

Base = 20cm

Height = 29

Area = 1/2 × 20 × 29

Area = 290cm²

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