Consider a causal continuous time LTI system whose input x(t) and output y(t) are related by the following differential equation d/dt y(t) + 4y(t) = x(t) Find the Fourier series representation of the output y(t) for each of the following inputs: A. x(t) = cos(3 pi T) B. x(t) = sin(3 pi t) + cos(6 pi t+pi/4)

Answer:

Step-by-step explanation:

An inequality which represents all possible values for x in -2x>-48 is: B. x < 24.

In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data such as integers, and variables in an equation based on any of the following inequality symbols:

Next, we would find the solution and possible values to this given inequality as follows:

-2x > -48

Dividing both sides of the inequality by -2, we have:

-2x/-2 > -48/-2

x < 48/2

x < 24.

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Answer:

ya  poop in the coffee and then ya see how  many pounds there is find the the type urself

Step-by-step explanation:

The percent of medical residents less than 28 years old is 69.15%.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 28

μ = mean = 27

σ = standard deviation = 2

z-score = (28 - 27) / 2

z-score = (1) / 2

z-score = 0.5

Find the probability that corresponds to the z-score in the z-table. (see attached images)

at z = 0.5,     p = 0.6915

Multiply the probability by 100 to get the percentage.

% = p x 100

% = 0.6915 x 100

% = 69.15

Hence, the percent of medical residents that are less than 28 years old is 69.15%.

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$57 is the amount of the tip the server hopes to receive.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

A server at a restaurant is hoping for a 15% tip from a large party.

The party's bill at the end of the night was $312.00.

Now we need to find 15% of $312

15% is converted to decimal by dividing with 100

15/100=0.15

Now multiply 0.15 with 380

0.15×380

57

Hence $57 is the amount of the tip the server hopes to receive.

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Answer:

x= -2

Step-by-step explanation:

-2 = 3x + 8/2

-2+2=3x+4+2          (add 2 to both sides)

0=3x+6                          

-6=3x+6-6

3x=-6

x=-6/3

x= -2

The rate written in miles per hour is 2.67 mph.

What is constant rate?

A rate of change is constant when, at any given point along the function, the ratio of the output to the input remains constant. The slope is another name for the rate of change that is constant. A linear function will change at a constant rate.

Let, John walks at a constant rate of 8 miles every 3 hours.

Therefore, the rate per hour is,

[tex]\frac{8}{3} = 2.6666\\ = 2.67 miles per hour.[/tex]

Therefore, the rate written in miles per hour is 2.67 miles per hour.

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Answer:

y=2x-2

Step-by-step explanation:

2.5y=5x-5

 /2.5. /2.5

y=2x-2

Hopes this helps please mark brainliest

Answer:

y=2x−2

Step-by-step explanation:

The slope-intercept form is

y=mx+b, where m

is the slope and b

is the y-intercept.y =mx+b

Divide each term in 2.5y=5−5 by 2.5

and simplify. y=2x−2

Probability that the dealership will be fined is 0.157

Probability  that the dealership will be dissolved is 0.158

the management decides to evaluate the satisfaction surveys = 62 customers

the sample mean is 0.84

we solve this using sampling distribution of the proportion

standard deviation of the sample is [tex]\sqrt{\frac{PQ}{n} }[/tex]  P = 0.84  Q= 0.16 n= 62

[tex]\sqrt{\frac{0.84*0.16}{62} }[/tex] =  0.04

mean(P) = 0.84

standard deviation = 0.04

45/62 = 0.72

50/62 = 0.80

(a) the probability that the dealership will be fined

p(45 < x < 50) = p(x< 50) - p(x<45)

Z-value for 50 is (0.80- 0.84)/0.04 = -1

p(x<50)= 0.1586

Z-value for 45 is (0.72-0.84)/0.04 = -3

p(x<45) = 0.0013

p(45 < x < 50) = 0.1586-0.0013 = 0.1573

(b) the probability that the dealership will be dissolved

p(x<45) = 0.1586

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[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 5.8\%\to \frac{5.8}{100}\dotfill &0.058\\ t=\textit{hours}\dotfill &2\\ \end{cases} \\\\\\ ~\hfill A=100(1 - 0.058)^{2} ~\hfill[/tex]

The equation represents the grams of the compound will remain after 2 hours will be;

⇒ C = 100 (1 - 0.058)²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A radioactive compound with mass 100 grams decays at a rate of 5.8% per hour.

And, Time = 4 hours

Now,

Since, We know that;

Amount for Exponential Decay is,

⇒ [tex]C = P (1 - r)^t[/tex]

Where, C is current amount, P is initial amount, r is rate and t is timeeee

Substitute all the values, we get;

The equation represents the grams of the compound will remain after 2 hours will be;

⇒ C = 100 (1 - 0.058)²

Thus, The equation represents the grams of the compound will remain after 2 hours will be;

⇒ C = 100 (1 - 0.058)²

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Answer:

you can do the favour of marking the answer brainlest pls

Answer:  After 5 Years Alex will receive 90 Dollar.

Step-by-step explanation 5 x 6% of 300 = 30% is 90 Dollar.

Answer:

x = 20

Step-by-step explanation:

Expanding the bracket on the right gives us :

2.5x + 20 = 3.5x - 4

Subtract 2.5x from both sides :

20 = x - 4

Add 4 to both sides :

20 = x

x = 20

Hope this helped and have a good day

Using multiplication or division, we can have either of the numbers from the operation.

multiplication is the repeated addition of numbers. But the rules for multiplication of integers are different from that of addition. It includes three possibilities. They are:

The product of two integers with similar sign numbers will always be positive. This means the product of two positive numbers or two negative numbers will always be positive. While the product of a positive number and a negative number (integers with different signs) will always be negative.

In this case, the three numbers are interconnected via arithmetic operation.

135 ÷ 15 = 9

9 × 15 = 135

135 ÷ 9 = 15

So, which ever way we go with, these numbers are connected to each other.

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Answer:

it is 3 0 o 90 not up okbg 56

The image of A(3, 7) under a translation along the vector (-4, 2) is A'(-1,9).

Given:

A(3,7) under a translation along the vector (-4, 2).

A' = A + (-4,2)

= (3,7) + (-4,2)

= (3+(-4), 7+2)

= (3-4, 9)

= (-1, 9)

Therefore the image of A(3, 7) under a translation along the vector (-4, 2) is A'(-1,9).

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The ratios of the right triangle to solve for x is as follows;

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sides of a right angle triangle can be named base on the position of the angles.  

The sides of a right angle triangles are hypotenuse sides, opposite and adjacent side. The hypotenuse side is the longest side of the right triangle.

Therefore, let's find the ratio that can be used to find the angle x.

Triangle PNM

sin x = opposite / hypotenuse

sin x = 6 / 10

Triangle ABC

cos x = adjacent / hypotenuse

cos x = 5 / 10

Triangle DEF

tan x = opposite / adjacent

tan x = 4 / 6

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Using scientific notation, the number 1240000 can be expressed as 1.24×10⁶

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form. As we know, the whole numbers can be extended till infinity, but we cannot write such huge numbers on a piece of paper. Also, the numbers which are present at the millions place after the decimal needed to be represented in a simpler form. Thus, it is difficult to represent a few numbers in their expanded form. Hence, we use scientific notations.

Converting the number 1,240,000 to scientific notation, we will get

1,240,000 = 1.24×10⁶

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The slope of the linear equation of the entire data set is -720.98

1. Bring data in to excel sheet

2.Select both x and y variable and insert scatter plot chart. Select any data point in the chart and add trend line. In the format trend line option choose "Linear" and also select "Display an equation on chart" & "Display R-squared value on chart"

To find: What is the slope of the linear equation of the entire data set? Round to nearest hundredth.

Regression equation : y = -720.98x + 15,90,277.32

Slope = -720.98 (Round to nearest hundredth.)

Intercept = 15,90,277.32

So, the slope of the linear equation of the entire data set is -720.98

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Answer:

56

Step-by-step explanation:

Number with two digits = 10y + x

x > y

x-y = 1

10y + x = 5(x+y) + 1

x = y + 1

10y + y + 1 = 5(y+1 +y) + 1

11y + 1 = 5(2y+1) + 1

11y + 1 = 10y + 5 + 1

11y - 10y = 5

y = 5

x = 5 + 1 = 6

Answer:

n=7

Step-by-step explanation:

-6n-9=25-8n

2n=34

n=17

The greatest total area, length will be 300 ft. and width will be 200 ft.

Given,

In the question:

A rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of the playground. 1200 feet of fencing is used.

Now, According to the question:

Lets assume, the length of the playground is l ft. and width is w ft.

Suppose, the playground is divided into two parts by a fence parallel to width. That means the length of the divider fence will be w ft.

So, the total length of the fence needed = (2l+ 3w)ft.

It is given in the question that 1200 feet of fencing is used.

2l + 3w = 1200

2l = 1200 - 3w

l = 600 - [tex]\frac{3}{2}w[/tex]  ......(1)

Now, the area of the playground....

A = l × w

A = ( 600 - [tex]\frac{3}{2}w[/tex]  ) × w

A = 600w - [tex]\frac{3}{2}w^2[/tex]

Taking derivative on both side in respect of "w" ,

we will get:

dA/dw = 600 - [tex]\frac{3}{2} (2w)[/tex]

dA/dw = 600 - 3w

A will be maximum when dA/dw = 0

600 - 3w = 0

600 = 3w

w = 600/3

w = 200

Now plugging this w = 200 into equation (1)...

l = 600 - [tex]\frac{3}{2}[/tex] × 200

l = 600 - 300

l = 300

Hence, for the greatest total area, length will be 300 ft. and width will be 200 ft.

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Deepak will work for at-least 4 hours in each job

Linear Inequality in one variable:

                                       A linear inequality in one variable that can be written either in the form of,

a+bx<0

a+bx≤0

a+bx>0

a+bx≥0  

             where,

                   where a and b are real numbers and a≠0 a ≠ 0

For the given question,

          Deepak charges $30 for each job he does plus an additional $15 for each hour he works.

He only accepts jobs if he will earn at least $90 per job.

If,

     x is number of hours Deepak works in each job then,

      required inequality can be written as,

             30 + 15x  [tex]\geq[/tex] 90

                 15x ≥ 90 - 30

                  15x ≥ 60

                    x ≥ 60/15

                    x ≥ 4

thus,

      we conclude that Deepak will work for at-least 4 hours in each job.

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The area of the semi circle with radius 2mm is 2[tex]\pi[/tex][tex]mm^{2}[/tex]

A semicircle is formed when a lining passing through the centre touches the two ends on the circle. Thus, by joining two semicircles we get a circular shape.

When a circle is cut into two halves or when the circumference of a circle is divided by 2, we get a semicircular shape.

Area of a semi-circle = [tex]\frac{\pi r^{2} }{2}[/tex]

but radius r = 2mm

substitute r into the area equation, we have

Area of semicircle = [tex]\frac{\pi 2^{2} }{2}[/tex]

Area of semicircle is = 2[tex]\pi[/tex][tex]mm^{2}[/tex]

In conclusion the area of the semicircle is  2[tex]\pi[/tex][tex]mm^{2}[/tex]

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Answer:

X=-2

Step-by-step explanation:

5+0.1x=3(1-0.3x)

5+0.1x=3-0.9x

    +0.9x         +0.9x

5+x=3

-5.   -5

x=-2

Hopes this helps

Answer:

the answer is B

Step-by-step explanation:

5+0.1x=3(1-0.3x)=}

5+0.1x=3-0.9x=}

0.1x+0.9x=3-5=}

x= - 2

The minimal cost of the box is $96.

Given data;

The volume of the box (v) = x²y

Given that, volume = 16 m³

So, 16 = x²y

y = 16/x² → (I)

Material for the base costs $8 per square meter, and material for the sides costs $2 per square meter.

Total cost (C) = 8 (x²) + 2*(xy)(4)

                      = 8x² + 8xy

Using (I),

C(x) = 8x² + 8x(16/x²)

C (^) = 8x² + 128/x

Now find critical points from

∴ [tex]\frac{d}{dx} = [8x^2+\frac{128}{x} ]=0[/tex]

  x³ = 8

  x = 2

So, the minimal cost will be given by x= 2,

Now, y = 16/x²

            = 16/4

            = 4

Dimension of the box that minimizes the cost is;

height = 4m, width=2m and breadth = 12m

Now,

Minimum cost = 8 (2)² + 128/2 = 32 + 64

                        = 96

Hence, The minimal cost of the box is $96.

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The area of the triangle ΔHIJ is 42805 square centimeters.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the area of a given ΔABC can be obtained by (1/2)×a×c×sin(∅/2)

where sin(Ф/2) is the included angle.

Given,  ΔHIJ, h = 730 cm, i = 390 cm and ∠J=35°.

∴ The area of the ΔHIJ is (1/2)×730×390×sin(35/2) square centimeter.

= 142,350×sin(17.5) square centimeter.

= 42805 square centimeters.

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Answer: 17.9

Step-by-step explanation:

Answer: 17.9

Step-by-step explanation:

[tex]a^{2} +b^{2} =c^{2} \\b^{2}=c^{2}-a^{2} =21^2-11^2=441-121=320\\b=\sqrt{320} =17.8885438[/tex]

Rounded to the nearest tenth would be 17.9.

At that particular critical point, the second derivative needs to be negative in order to obtain the dimensions of the cylinder with the maximum volume. The values of the function that contain both variables are then substituted to obtain the dimensions.

A right circular cone with a height of 2.5 and a base radius of 7.5 inscribes the given cylinder.

Assume that h is the height and r is the radius of the cylinder. Using triangles that are similar, express h in terms of r as follows:

2.5/7.5 = 2.5-h/r

2.5r = 18.75 x 7.5 x 2.5 h = 2.5 x 1/3r

V= πr²h is the formula for the cylinder's volume.

As a result, only write the volume in terms of r.

V= r2h V= r2(2.5-1/3r)

V= 2.5πr² - 1/3πr³

As a result, the cylinder must have dimensions of r=5 and h=0.83.

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