-5x + 6y = 13: solve for x.

The Fourier transform of \(y(t)\) is \(-\frac{2}{1+j\omega} e^{-j6\omega}\).

Answer: \(Y(\omega) = -\frac{2}{1+j\omega} e^{-j6\omega}\)

To find the Fourier transform of the signal \(y(t) = x(-3t+6)\), where the Fourier transform of \(x(t)\) is given as \(X(j\omega) = \frac{2}{1+j\omega}\), we can follow these steps:

1. Start with the inverse Fourier transform formula:

\[x(t) = \frac{1}{2\pi} \int X(\omega) e^{j\omega t} d\omega \quad \text{(1)}\]

2. Obtain the inverse Fourier transform of \(X(j\omega)\):

\[x(t) = 2\pi e^{t/2} u(-t)\]

3. Substitute \(-3t+6\) for \(t\) in equation (1):

\[y(t) = x(-3t+6)\]

4. Perform the variable substitution:

\(-3t + 6 = u\)

5. Find \(\frac{dt}{du}\):

\(\frac{dt}{du} = -\frac{1}{3} \Right arrow dt = -\frac{1}{3} du\)

6. Substitute the values of \(t\) and \(dt\) in equation (1):

\[y(t) = \int x(u) e^{-j\omega(-3t/3+6)} \left(-\frac{1}{3}\right)du\]

7. Replace \(u\) with \(-3t/3\):

\[y(t) = -\frac{1}{3} e^{j\omega(6)} \int x(u) e^{j\omega u} du\]

8. Substitute \(X(-\omega)\) in place of \(x(u)\), as \(X(\omega)\) represents the Fourier transform of \(x(t)\):

\[y(t) = -\frac{1}{3} e^{j\omega(6)} X(-\omega) = -\frac{2}{1+j\omega} e^{-j6\omega}\]

Therefore, the Fourier transform of \(y(t)\) is \(-\frac{2}{1+j\omega} e^{-j6\omega}\).

Answer: \(Y(\omega) = -\frac{2}{1+j\omega} e^{-j6\omega}\)

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Given the expression:

You can find its value by following these steps:

1. You have to solve the operation that is inside the parentheses. Then, you need to add 14 and 6:

2. Finally, you must solve the Multiplication. Then, you get this result:

Hence, the answer is:

Answer:

60

Step-by-step explanation:

1) Add 14 + 6 which gives you 20

2) Multiply 20 x 3 which gives you 3

Your welcome :)

The addition of the polynomials \(\rm (2x^4 +x^3-4x^2 +3)\) and \(\rm (4x^4-2x^3-x^2 +10x +2)\) is \(\rm 6x^4 -x^3-5x^2 +10x +5\\\).

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

The polynomials are shown below.

\(\rm (2x^4 +x^3-4x^2 +3)\ and \ (4x^4-2x^3-x^2 +10x +2)\).

We have to find the addition of the polynomials.

On adding the polynomials, we have

\(\rm (2x^4 +x^3-4x^2 +3) + (4x^4-2x^3-x^2 +10x +2)\\\\2x^4 +x^3-4x^2 +3 + 4x^4-2x^3-x^2 +10x +2\\\\6x^4 -x^3-5x^2 +10x +5\\\)

Thus, the addition of the polynomials is \(\rm 6x^4 -x^3-5x^2 +10x +5\\\).

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The graphs of the quadratic expressions are added as attachment

Function 5

Given that

y = -x² + 8x - 14

The graph is added as an attachment and the solution is x = 2.59 and x = 5.41

Function 6

Given that

y = 1/2x² - x - 3

The graph is added as an attachment and the solution is x = -1.65 and x = 3.65

Function 7

Given that

y > x² + 6x + 5

The graph is added as an attachment and the solution is x values between -5 and -1 (exclusive)

Function 8

Given that

y ≤ 2x² - 4

The graph is added as an attachment and the solution is x values outside -1.414 and 1.414 (inclusive)

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The given information indicates that the average speed on the 405 freeway follows a normal distribution with a mean of 50 mph and a standard deviation of 12 mph. To find the probability that someone is driving slower than 35 mph, we need to calculate the deviation from the mean using the z-score formula:

z = (x - μ) / σ

where x is the value we are interested in (35 mph), μ is the mean (50 mph), and σ is the standard deviation (12 mph).

z = (35 - 50) / 12
z = -1.25

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than -1.25. The probability is approximately 0.1056 or 10.56%.

Therefore, the probability that someone is driving slower than 35 mph on the 405 freeway is about 10.56%.

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Answer:

Step-by-step explanation:

\(-2x+9 < x-9\)           (now add 9 to both sides of inequality)

     \(-2x < x-18\)         (now subtract \(x\) to both sides of inequality)

     \(-3x < - 18\)             (now divide both sides of inequality by -3)

          \(x > 6\)                 (REMEMBER: swap directions when dividing or

                                     multiplying by a negative)

SOLUTION:  A

Answer:

The answer is below

Step-by-step explanation:

The equation x² - 3x - 2 cannot be factorized, I think the correct question is:

factorize x² - 3x + 2​

Solution:

A quadratic equation is a polynomial equation of the second degree (that is there is at least one term with a degree of 2).

The standard form of a quadratic equation is given by the equation:

ax² + bx + c = 0

Where a, b, and c being constants and x is the unknown variable.

Given:

x² - 3x + 2

= x² - 2x - x + 2

= x(x - 2) -1(x - 2)

= (x - 1)(x - 2)

Answer:

x

Step-by-step explanation:

Answer:

12 divided by 1 can be 12. If thats what you mean and if not, just tell me by explaining with more detail

Step-by-step explanation:

Answer:

I’m guessing that you want to know how much is in the container so it’s 56 ounces

Step-by-step explanation:

if 64 is the max just do 64 - 8 and you’ll get whats left

Complete question :

A man has a garden measuring 40m by 24m. He wants to divide it equally into the minimum number of square plots. what is the length of each square plot?

Answer:

8 m

Step-by-step explanation:

Given that :

Dimension of garden = 40m by 24m

Length of garden = 40m

Width of garden = 24m

To Obtain the length of each square plot if the garden is divided into minimum number of square plots ; we take the highest common factor of the dimension:

Length (40) = 1, 2, 4, 5, 8, 10, 20, 40

Width (24) = 1, 2, 3, 4, 6, 8, 12, 24

The highest common factor here is 8 ;

Thus, the length of each square plot is 8m

Alex can make a total of 180 different sandwiches by choosing one kind of meat from 10 options and two kinds of cheese from 9 options.

To determine the number of different sandwiches Alex can make, we need to consider the combinations of meat and cheese. Since Alex can choose one kind of meat from 10 options, there are 10 choices for the meat component of the sandwich. For the cheese component, Alex can choose two kinds of cheese from 9 options.

To calculate the total number of combinations, we can use the formula for combinations without repetition. The formula is nCr = n! / (r!(n-r)!), where n is the total number of options and r is the number of choices. In this case, n is 9 (number of cheese options) and r is 2 (number of cheese choices). Thus, the number of combinations of two kinds of cheese is \(9C2\)= 9! / (2!(9-2)!) = 36.

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Answer:

m= r-n/2

Step-by-step explanation:

2m+n=r

2m=r-n

m=r-n/2

Answer:

One

Step-by-step explanation:

y = 3 x - 5.

y = -x + 4.

x=9/4 and y=7/4

1 solution (9/4 , 7/4)

For a system of the equation to be an Independent Consistent System, the system must have one unique solution. The system of the equation has only one solution. Thus, the correct option is A.

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

Given the two equations y=3x -5 and y=-x+4. If the two of the equations are plotted on the graph. Then it can be observed from the graph that there is only one intersection between the two lines.

Hence, the system of the equation has only one solution. Thus, the correct option is A.

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Answer:

The answer to this is B, $135.

Step-by-step explanation:

I took the test.

Answer:

$135 is the correct answer, I took the test and got it right

Step-by-step explanation:

The probability of obtaining a sample mean between 4.1 and 4.11 in a random sample of size 511 is 0.

To calculate the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in a discrete uniform population with x = 2.4, we can use the properties of the sample mean and the given population.

In a discrete uniform population, all values are equally likely. Since the mean of the population is x = 2.4, it implies that each value in the population is 2.4.

The sample mean is calculated by summing all selected values and dividing by the sample size. In this case, the sample size is 511.

To find the probability, we need to calculate the cumulative distribution function (CDF) for the sample mean falling between 4.1 and 4.11.

Let's denote X as the value of each individual in the population. Since X is uniformly distributed, P(X = 2.4) = 1.

The sample mean, denoted as M, is given by M = (X1 + X2 + ... + X511) / 511.

To find the probability P(4.1 < M < 4.11), we need to calculate P(M < 4.11) - P(M < 4.1).

P(M < 4.11) = P((X1 + X2 + ... + X511) / 511 < 4.11)
           = P(X1 + X2 + ... + X511 < 4.11 * 511)

Similarly,
P(M < 4.1) = P(X1 + X2 + ... + X511 < 4.1 * 511)

Since each value of X is 2.4, we can rewrite the probabilities as:

P(M < 4.11) = P((2.4 + 2.4 + ... + 2.4) < 4.11 * 511)
           = P(2.4 * 511 < 4.11 * 511)

Similarly,
P(M < 4.1) = P(2.4 * 511 < 4.1 * 511)

Now, we can calculate the probabilities:

P(M < 4.11) = P(1224.4 < 2099.71) = 1 (since 1224.4 < 2099.71)
P(M < 4.1) = P(1224.4 < 2104.1) = 1 (since 1224.4 < 2104.1)

Finally, we can calculate the probability of the sample mean falling between 4.1 and 4.11:

P(4.1 < M < 4.11) = P(M < 4.11) - P(M < 4.1)
                 = 1 - 1
                 = 0

Therefore, the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in the given discrete uniform population is 0.

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Converting the given decimal numbers to hexadecimal and then to binary, we find that

(a) 757.1710 is equivalent to 2F5.2E16 in hexadecimal and 1011110101.001011002 in binary.

(b) 356.2510 is equivalent to 164.4016 in hexadecimal and 101100100.01000011012 in binary.

To convert a decimal number to hexadecimal, we divide the whole number part and the fractional part separately by 16 and convert the remainders to hexadecimal digits.

For the whole number part of (a) 757, dividing it by 16 gives us a quotient of 47 and a remainder of 5, which corresponds to the hexadecimal digit 5.

Dividing the fractional part 0.17 by 16 gives us a hexadecimal digit of 2. Combining these digits, we get the hexadecimal representation 2F5.

To convert (b) 356 to hexadecimal, we divide it by 16, obtaining a quotient of 22 and a remainder of 4, which corresponds to the hexadecimal digit 4.

For the fractional part 0.25, dividing by 16 gives us a hexadecimal digit of 1. Combining these digits, we get the hexadecimal representation 164.

To convert hexadecimal numbers to binary, we simply replace each hexadecimal digit with its equivalent four-digit binary representation. Converting (a) 2F5 to binary, we get 1011110101.

Similarly, converting (b) 164 to binary, we get 101100100.

For the fractional parts, converting 0.2E to binary gives us 0010, and converting 0.401 to binary gives us 01000011.

Therefore, (a) 757.1710 is equivalent to 2F5.2E16 in hexadecimal and 1011110101.001011002 in binary, while (b) 356.2510 is equivalent to 164.4016 in hexadecimal and 101100100.01000011012 in binary.

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The following can be shown about the diagonals of parallelogram PQRS to compare the proof that diagonals of a parallelogram bisect each other: B. PR and SQ have the same midpoint.

In Mathematics and Geometry, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

In order for any quadrilateral to be considered as a parallelogram, two pairs of its parallel opposite sides must be equal (congruent). This ultimately implies that, the diagonals of a parallelogram would bisect one another only when their midpoints are the same:

(Line segment PR)/2 = (Line segment SQ)/2

Line segment PR = Line segment SQ

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The mass of 1 liter (1000 mL or 1000 cm(^3)) of Argon would be 1.78 grams.

To determine the number of atoms of Argon required to make a line 1 inch long, we need to calculate the number of atoms that can fit within that length.

First, we convert the atomic radius of Argon from picometers (pm) to inches.

1 inch = 2.54 cm = 2.54 * 10^7 pm (since there are 10^12 picometers in a meter)

The atomic radius of Argon is 188 pm, we can convert it to inches:

188 pm * (1 inch / 2.54 * 10^7 pm) = 7.40157 * 10^(-6) inches

Next, we calculate the number of atoms that can fit in 1 inch:

Since the atomic radius represents half the length of an atom, we double it to get the length of a single atom:

2 * 7.40157 * 10^(-6) inches = 1.48031 * 10^(-5) inches

To find the number of atoms that can fit in 1 inch, we divide the length of 1 inch by the length of a single atom:

1 inch / (1.48031 * 10^(-5) inches) = 6.751 * 10^4 atoms

Therefore, approximately 67,510 atoms of Argon must be lined up to make a line 1 inch long.

B. To calculate the mass of 1 liter (1000 (cm^3)) of Argon, we need to use its density:

Density = mass / volume

Rearranging the equation, we can solve for mass:

Mass = Density * Volume

Since the volume is given in cm(^3) and the density is given in g/cm^3, the resulting mass will be in grams.

Given that the density of Argon is 1.78 * 10^(-3) g/cm^3 and the volume is 1000 cm^3, we can calculate the mass:

Mass = 1.78 * 10^(-3) g/cm^3 * 1000 cm(^3) = 1.78 grams

Therefore, the mass of 1 liter (1000 mL or 1000 cm(^3) )of Argon would be 1.78 grams.

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Answer:

225 coins

Step-by-step explanation:

9----------4%

x------------100%

Cross multiplication

4x = 900

x=225

Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In △RST;

The vertices are, R(4, 1), S(7, 3), and T(6, 4)

Here, Translation: (x, y) → (x, y−1)

And, Reflection in the y-axis.

Hence, New coordinate of the image of △RST are,

⇒ R' = (- 4, 1 - 1) = (- 4, 0)

⇒ S' = (- 7, 3- 1) = (- 7, 2)

⇒ T' = (- 6, 4 - 1) = (- 6, 3)

Thus, Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

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Answer:

Exact Form:

2√7/7

Decimal Form:

0.75592894…

I believ this is right sry if it's not

The simplest radical form of the number \(\sqrt{\dfrac{4}{7}}\) is, \(\dfrac{2\sqrt{7} }{7}\)

Used the concept of the square root of a number that states that,

The square root of a number is the number that, when multiplied by itself, gives the original number.

Given that the number is,

\(\sqrt{\dfrac{4}{7}}\)

Simplify the expression by taking the square root of numbers as

Since, \(\sqrt{4} = \sqrt{2^2}\)

= \(2\)

Hence, the simplest radical form is,

\(\sqrt{\dfrac{4}{7}} = \sqrt{\dfrac{2^2}{7}}\)

\(= \dfrac{2}{\sqrt{7}}\)

Multiply and divide by \(\sqrt{7}\);

\(= \dfrac{2\times \sqrt{7} }{\sqrt{7}\times \sqrt{7}}\)

\(= \dfrac{2\sqrt{7} }{7}\)

Therefore, the simplest form is, \(\dfrac{2\sqrt{7} }{7}\)

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Answer:

$90

Step-by-step explanation:

To find commission, you multiply the amount made by the rate of which they can earn.

300*.3 (As this is a 30 percent commission)

The definition of SSS, SAS, and AAS congruency conditions is shown.

SSS condition:

In accordance with the SSS rule, two triangles are considered to be congruent if their corresponding three sides are equal on both triangles.

SAS condition:

The two triangles are congruent if two sides and the included angle of one triangle match those of a second triangle by two sides and the included angle.

AAS condition:

The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Therefore, the definition of SSS, SAS, and AAS congruency conditions is shown.

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Histogram for the test scores of different students is represented in the Image attached.

A histogram is a bar graph type of data representation in this representation the width of the class size is represented by the rectangle shapes reaching a particular height which describes the the number of frequency distribution.

We have to draw the histograms for the data set that scores the test scores of different students which follows 85, 90, 82, 65, 75, 96, 72, 90, 98, 70, 86, 92.

The histogram is represented in the x and y axis. The number of students is represented on the y axis while the range of the marks obtained by the students is represented on the x-axis.

Their are a total of four classes defined ranging from 60-69, 70-79, 80-89, 90-99. All classes are represented by different colors.

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c ans

...................

As the sample size rises, the sample distribution approaches a normal distribution.

The sample distribution approaches a normal distribution as the sample size grows. The sampling distribution's mean equals the population's mean if the number of consecutive samples is "infinite".

The Gaussian distribution is the official name for the normal distribution. However, the word "normal" was coined in the nineteenth century after a scientific inquiry revealed that numerous natural events appeared to "deviate from normal" from their typical values.

In his 1889 work Natural Inheritance, naturalist Sir Francis Galton popularized the notion of normal variability as the standard curve.

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Hello! :)

\(y = -\frac{cos^{4}(x)}{4} + C\)

Use u-substitution to solve for the indefinite integral:

\(\int cos^{3}(x)sin(x)dx\)

Allow "u" to be the expression with an exponent:

\(u = cos(x)\\\\du = -sin(x)dx\)

\(-du = sin(x)dx\)

In the integral, we are missing a negative symbol (du = -sin(x)), so we can adjust the integral to accommodate this.

Substitute "u" for cos(x) and du for -sin(x):

\(-\int u^{3}du\)

Use the integral power rule to solve:

\(\int x^{n} = \frac{x^{n + 1}}{n + 1}\)

\(-\int u^{3}du = -[\frac{u^{4}}{4} ]\)

Add the constant "C" as this is an indefinite integral:

\(= -[\frac{u^{4}}{4} ] + C\)

Substitute in the value of u (cos(x)) into the equation:

\(= -\frac{cos^{4}(x)}{4} + C\)

And you're done!

Answer:

yes there is a multiple of 27491

Janet cut a total of 6.6 meters of ribbon by combining 9 pieces measuring 0.4 meters each and 5 pieces measuring 0.6 meters each.

Janet cut a total of 9 pieces of ribbon, each measuring 0.4 meters, and 5 pieces of ribbon, each measuring 0.6 meters.

To find the total length of ribbon Janet cut, we need to calculate the sum of the lengths of all the individual pieces.

For the 9 pieces of ribbon measuring 0.4 meters each, we can multiply the length of each piece by the number of pieces: 9 * 0.4 = 3.6 meters.

Similarly, for the 5 pieces of ribbon measuring 0.6 meters each, we can calculate the total length: 5 * 0.6 = 3 meters.

To find the total length of ribbon Janet cut, we add the lengths of the two sets of ribbons together: 3.6 + 3 = 6.6 meters.

Therefore, Janet cut a total of 6.6 meters of ribbon by combining the 9 pieces of 0.4-meter ribbon and the 5 pieces of 0.6-meter ribbon.

In summary, Janet cut a total of 6.6 meters of ribbon by combining 9 pieces measuring 0.4 meters each and 5 pieces measuring 0.6 meters each.

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