A 354​-inch board is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.

(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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The tail is 764 inches tall.

Unit conversion is the process of changing measurement value of one form to another e.g. changing minutes to seconds, or liters to cubic meter. This is done using a conversion factor.

In this case, the conversion factor is:

1 foot = 12 inches

Since the tail of the jet airliner is 63 2/3 feet tall. The tail of a jet airliner in inches will be:

Tail in inches =  (63 2/3) * 12 = 764 inches

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No, these two events cannot be disjoint. Disjoint events, also known as mutually exclusive events, are events that cannot occur simultaneously.

In other words, if events A and B are disjoint, it means that the occurrence of one event excludes the possibility of the other event occurring.

However, in this case, we are given that P(A) > 0 and P(B) > 0. This means that both events A and B have non-zero probabilities of occurring. Since both events have a positive probability, they cannot be disjoint because there is a possibility of their intersection, where both events occur simultaneously.

Disjoint events would have the property that P(A ∩ B) = 0, indicating that their intersection is an empty set. But given that P(A) > 0 and P(B) > 0, it implies that there is some non-zero probability for the events A and B to occur together, making them not disjoint.

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Answer:

-2

Step-by-step explanation:

The x value is 1, and the y value is 0. Substitute these values into the equation.

y=2x-2

Hope this helps :-)

$484,835 is the amount that separates the lowest 20% of the means of retirement accounts from the highest 80% of the means of retirement accounts.

Given Information:

Mean of retirement accounts = μ = $490,000

Standard deviation of retirement accounts = σ =  $55,000

Sample size = n = 80

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.  

The amount of money that separates the lowest 20% of the means of retirement accounts from the highest 80% is given by

\(P\frac{( \bar x - \alpha )}{\frac{\sigma}{\sqrt{n} } }\)

The z-score corresponding to 0.20 is -0.84

\(\bar x = \alpha + z.\frac{\sigma }{\sqrt{n} } \\\\\bar x = 490,000 - 0.84 .\frac{55,000}{\sqrt{80} } \\\\\bar x = 490,000 - 5165.32\\\\\bar x = 484,834.68\)

Rounding off to the nearest whole number

\(\bar x = $484,835\)

Therefore, $484,835 is the amount that separates the lowest 20% of the means of retirement accounts from the highest 80% of the means of retirement accounts.

How to use z-table?

In the z-table find the probability of 0.20

Note down the value of that row, it would be -0.8.

Note down the value of that column, it would be 0.04.

So the z-score is -0.84

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Answer:

Option C

Step-by-step explanation:

As we can see here, the sum of AB and BC is equivalent to AC. Therefore, we obtained the following equation.

We are given the following measures:

When we plug the values into the equation, we get;

To determine the length of BC, we need to determine the measure of "x". This can be done by simplifying the equation obtained above. Once we determined the value of "x", we can plug the value of "x" into the expression that represents the length of BC (3x + 5) to obtain the length of BC.

As stated above, let's substitute the value of "x" into the expression of BC.

Therefore, Option C is correct.

BC

Answer:

Slope = -5/3

Step-by-step explanation:

Parallel lines have the same slope, so the slope will be -5/3.

Hope this helps!!

Answer:

-5/3x

Step-by-step explanation:

its the same slope

Answer:

44m

Step-by-step explanation:

A = \(\pi\)r² = 154

   = 22/7 * r² = 154

   = r²  = 154 * 7/22

   = r²  = 49

   = r = √49

   = r = 7m

Perimeter of circle = 2\(\pi\)r

                               = 2 * 22/7 * 7

                               = 44/7 * 7

                               = 44 m

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Answer:

44m

Step-by-step explanation:

Area of circular field=154m²

Perimeter of the field=?

At first,

Area =22/7×r²

154m²= 22/7×r²

154×7/22=r²

49=r²

7×7=r²

7=r

Now,

Perimeter = 2×22/7×7

= 44m

Answer:

equiangular -right -obtuse -acute.

Answer:

5.4

Step-by-step explanation:

5^2+2^2=29

square root of 29=5.4

Let X and Y be two matrices in A. We can write X = ((x,0),(0,y)) and Y = ((z,0),(0,w)). If we add X and Y, we get((x+z,0),(0,y+w)). The sum is in A if and only if x+z+y+w=5.

Subset of M2x2:A subset of M2x2 is a set that contains some elements of M2x2.

A subset of M2x2 can be considered as a subspace if it meets the following conditions:

To determine if A is a subspace of M2x2, we need to verify that A meets the following conditions:

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Answer:

y=10

Step-by-step explanation:

Answer:

y = ± 10

Step-by-step explanation:

The absolute value function always gives a positive value, that is

| - a | = | a | = a

Given

| y | + 8 = 18 ( subtract 8 from both sides )

| y | = 10 , then

y = 10 or y = - 10

Answer:

y=-\frac{2}{5}x+\frac{19}{5}y=−52x+519

Further explanation:

We have to find the equation of the line first to graph the line.

The general form of slope-intercept form of equation of line is:

y=mx+by=mx+b

Given

m=-\frac{2}{5}m=−52

Putting the value of slope in the equation

y=-\frac{2}{5}x+by=−52x+b

To find the value of b, putting the point (-3,5) in equation

\begin{gathered}5=-\frac{2}{5}(-3)+b\\5=\frac{6}{5}+b\\5-\frac{6}{5}+b\\b=\frac{25-6}{5}\\b=\frac{19}{5}\end{gathered}5=−52(−3)+b5=56+b5−56+bb=525−6b=519

Putting the values of b and m

y=-\frac{2}{5}x+\frac{19}{5}y=−52x+519

explanation

above shows total explanation by set theory,

answer

2

, t

Answer:

25........................

Time-series Plot graph is the best choice for determining the change in the stock market over time.

The term stock exchange refers to several exchanges where shares of publicly traded companies are bought and sold. Such financial activities are conducted through formal stock exchanges and over-the-counter (OTC) markets that operate under a specific set of regulations.

Other major stock exchanges in the world are Tokyo Stock Exchange (Japan), Shanghai Stock Exchange (China) and London Stock Exchange (UK). Stock exchanges are considered capital markets as they provide long-term financing for companies.

A time series chart, also known as a time series chart or time series graph, is a data visualization tool that plots data points at successive time intervals. Each point on the chart corresponds to both time and quantity being measured.

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Answer:

the answer is graph 1

Step-by-step explanation:

The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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The amount of cherrries that Dahlia has in stock at the end of the day is 69.

The first step is to determine the number of cherries that were remaining after 19 were sold.

Cherries remaining = 22 - 19 = 3

Number of cherries in the shipment == 22 x 3 = 66

Total number of cherries at the end of the day = 66 + 3 = 69

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The volume of the prism shown is equal to 145.89 cubic inches.

In Mathematics and Geometry, the volume of a triangular prism can be determined or calculated by using the following formula:

Volume of triangular prism, V = 1/2 × b × h.

Where:

By substituting the given dimensions (side lengths) into the formula for the volume of a triangular prism, we have;

Volume of triangular prism, V =  1/2 × 5.27 × 8.13 × 6.81

Volume of triangular prism, V = 291.775131/2

Volume of triangular prism, V = 145.89 cubic inches.

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The volume of the prism is 145.89 cubic inches.

To find the volume of a prism, multiply the area of the base by the height of the prism.

We know the formula for the volume of a triangular prism is:

\(V = \frac{1}{2}\times b \times h\)

Where:

b represent the base area of a triangular prism.

h represent the height of a triangular prism.

Therefore, we can calculate the volume of the prism by cubing the length of one of its sides:

\(V = \frac{1}{2}\times 5.27\times 8.13 \times 6.81\)

\(V= \frac{291.775131}{2}\)

\(V = 145.89\) cubic inches.

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Answer:

27º

Step-by-step explanation:

complementary angle is equal to 90º

90 - 63 = 27

Hello Human <3

Here is the answer:

X ∈  { 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 206, 312, 318, 324, 330, 336, 342, 348, 354, 360, 366, 372, 378, 384, 390, 396, 402, 408, 414 }

Step-by-step explanation:

Answer:

The correct answer is A

Step-by-step explanation:

2 is exactly 7 units away from -5.

The linear functions are \(y = -2x\) and \(3x - 4y = 12\), while the non-linear function is \(y =z^2 + 11\)

A linear function is a function that has a constant slope/rate, and it is represented by any of the following forms

Other functions that do not take any of the above forms are non-linear functions.

So, we can conclude that:

\(y = -2x\) and \(3x - 4y = 12\) are linear functions, while \(y =z^2 + 11\) is a non-linear function

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The percent of the dispicable me lovers also like mcdonald's is 71%.

As the question stated-

The percent of the dispicable me = 12 + 7 + 9 = 28%.

The number of mcdonald's lovers = 20%.

Thus, percent of the dispicable me lovers who also like mcdonald's;

= 20 /28

= 20/28

= 0.71

= 71%

Thus, the percent of the dispicable me lovers also like mcdonald's is 71%.

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Answer:

from looking at it it seems the answer is d

Step-by-step explanation:

Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

The -value of the test is 1.90. This indicates that the mean processing time is significantly greater than 5.5 hours, supporting the manufacturer's desire to set a standard time required by employees to complete a certain process

The t-value will be equal to 1.39 for the given statistics.

To test if the mean processing time exceeds 5.5 hours, we can use a one-sample t-test.

The null hypothesis is that the mean processing time is less than or equal to 5.5 hours:

H0: µ ≤ 5.5

The alternative hypothesis is that the mean processing time is greater than 5.5 hours:

Ha: µ > 5.5

We will use a significance level of 0.05.

The formula for the t-test statistic is:

t = (X - µ) / (s / √n)

Where:

X = sample mean

µ = hypothesized population mean

s = sample standard deviation

n = sample size

Substituting the given values, we get:

t = (6 - 5.5) / (2 / √21) = 1.386

The degree of freedom for the t-test is n-1 = 20.

Using a t-table or calculator, the p-value associated with a t-value of 1.386 and 20 degrees of freedom is 0.093.

Since the p-value (0.093) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to suggest that the mean processing time exceeds 5.5 hours.

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Answer:

1115.49 feet

Step-by-step explanation:

To convert meters to feet, multiply 340 meters by 3.281 because there are approximately 3.281 feet in 1 meter.

340*3.281= 1115.49