Solve the inequality for x and identify the graph of its solution. |x+2l <2
Choose the answer that gives both the correct solution and the correct graph.
(I attached an image)

a)The given expression is; x + 9/2

b) The smallest number is  0.104

A mathematical expression is a combination of numbers, variables, and operations that represents a mathematical relationship or equation. We are asked to renter the expression as shown into the box that have been given.

If we arrange the numbers in order, we can see that the decreasing order of the numbers would take the form;

104 > 10.4 > 1.04 > 0.104

Thus we can see that the number that is smallest is  0.104.

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Note that for WKST to be a parallelogram, y must be equal to 8 and m∠S must be equal to 126°. Thus the correct option is (Option C).

A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure.

To justify the above answer, note that:

Since Opposite angles of a parallelogram are congruent, we have

∠W = ∠T

That is:

 3x -18 = 2x +6

Collecting like terms over the equation sign, we have:

3x - 2x = 6 + 18

x = 24

Substituting x into the equation for ∠W = ∠T, we have:

3x -18 = 2x +6

3(24)-18 = 2(24) +6 =54

72-18 = 48 +6 = 54

Thus, the above expression is True. That is:

3x -18 = 54°; and

2x +6 = 54°.

Since The adjacent angle, W is supplementary to either of these, it means that:
∠W = 180° -∠E

⇒ 15y +6 = 180 -54

⇒ 15y = 120

y = 8

Thus, it is correct to state that the value of y and m∠S required to classify WKST as a parallelogram are:

y-8; ∠126° (Option C)

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Full Question:

See the attached image.

The solution of the complex numbers are

a. 3+j(5j/2+3j) = j * (3 + 8i)

b. (4+2j)([tex]3e^{j.2\pi/4}[/tex])+1/3+2j+5[tex]e^{j0.5}[/tex] = 12j² + 12j³ + 1/3 + 2j + 5 * cos(0.5) + 5 * j * sin(0.5)

Complex arithmetic involves working with complex numbers, which are numbers that have both real and imaginary parts.

a. 3+j(5j/2+3j)

To perform this operation, we first need to simplify the expression inside the parentheses: 5j/2 + 3j. We can simplify this expression by adding the two imaginary parts together:

5j/2 + 3j = (5 + 3)j = 8j

Next, we substitute this result back into the original equation:

3 + j(8j) = 3 + j(8 * j) = 3 + j * 8i

Now we can simplify this expression by multiplying the real part 3 with j, and adding it to the real part of the expression:

3 + j * 8i = 3j + j * 8i = j * (3 + 8i)

So the final result is: j * (3 + 8i)

Next, let's look at the second part of the problem:

b. (4+2j)([tex]3e^{j.2\pi/4}[/tex])+1/3+2j+5e^j0.5

We can simplify this expression by using the properties of complex numbers and exponential functions:

(4 + 2j) * ([tex]3e^{j.2\pi/4}[/tex]) = (4 + 2j) * (3 * (cos(2π/4) + j * sin(2π/4)))

= (4 + 2j) * (3 * (cos(π/2) + j * sin(π/2)))

= (4 + 2j) * (3 * j)

= (4 + 2j) * 3j

= 12j² + 6j³ * 2j

= 12j² + 12j³

Next, we substitute this result back into the original equation:

12j² + 12j³ + 1/3 + 2j + [tex]5e^{j0.5}[/tex]

Next, we simplify the remaining terms:

=> 3 + 2j + [tex]5e^{j0.5}[/tex] = 1/3 + 2j + 5 * (cos(0.5) + j * sin(0.5))

=>  1/3 + 2j + 5 * cos(0.5) + 5 * j * sin(0.5)

So the final result is: 12j² + 12j³ + 1/3 + 2j + 5 * cos(0.5) + 5 * j * sin(0.5)

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Person A's optimal choices are x1 = x2 and person B's optimal choices are x1 = x22. Also Demand(x1,x2) = 2x1 + x1 + x22 represents the market demand for x1 and x2.

In order to find the optimal choices of person A and person B, we need to find the values of x1 and x2 that maximize their respective utility functions.

For person A, their utility function is ua = min{x1,x2}, which means their satisfaction is equal to the minimum value of x1 and x2. The optimal choice for x1 and x2 would be the values that make x1 = x2, because if one value is higher, the minimum will always be the lower value. Hence, person A's optimal choices are x1 = x2.

For person B, their utility function is ub = min{x1,x22}, which means their satisfaction is equal to the minimum value of x1 and x22. The optimal choice for x1 and x2 would be the values that make x1 = x22, because if x1 is higher, x22 will be even higher and the minimum will always be x1. Hence, person B's optimal choices are x1 = x22.

To find the market demand, we need to find the aggregate demand of both person A and person B. The aggregate demand is the sum of the individual demands. The demand for x1 and x2 can be found by adding the individual demands.

Person A's demand for x1 and x2 is the same, x1 = x2, hence the total demand for x1 and x2 is 2x1.

Person B's demand for x1 and x2 is x1 = x22, hence the total demand for x1 and x2 is x1 + x22.

The aggregate demand for x1 and x2 is the sum of both individual demands:

Demand(x1,x2) = 2x1 + x1 + x22

This represents the market demand for x1 and x2.

Therefore, Person A's optimal choices are x1 = x2 and person B's optimal choices are x1 = x22. Also Demand(x1,x2) = 2x1 + x1 + x22 represents the market demand for x1 and x2.

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Step-by-step explanation:

what do you not understand here ?

you got the formula, the numbers for the formula.

since you should use 3 for pi, this is a very simple calculation :

3×15² = 3×225 = 675 ft²

that's it.

Based on the expanded the expression (2 - 3x)², the student who got the answer 4 – 12 x + 9x² is the first student.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two (2).

In Mathematics, the standard form of a quadratic function is given by ax² + bx + c = 0.

By applying the following binomial expression to the given quadratic function, we have:

(a - b)² = a² - 2ab + b²

(2 - 3x)² = 4 - 2(2)(3x) + 3x²

4 - 2(2)(3x) + 3x² = 4 - 12x + 9x².

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Step-by-step explanation:

To find the longest time that Ian has to wait to fill the tank, we need to find the total time it takes to fill the tank from its current level of 20 gallons to its maximum level of 125 gallons.

First, we need to find the amount of water that needs to be added to the tank by subtracting the current water level from the maximum water level:

125 gallons - 20 gallons = 105 gallons

Next, we need to divide the amount of water that needs to be added by the rate at which Ian is filling the tank to find the time it will take:

105 gallons / 8 gallons per minute = 13.125 minutes

So the longest time that Ian has to wait to fill the tank is 13.125 minutes.

The required maximum and minimum points of the function y = 2 sin 2(x + π) + 3 is (-3π/4, 5) and (-π/4, 1). Option A is correct.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,

Maximum and minimum points of the function y = 2 sin 2(x + π) + 3. can be determined by drawing the graph of the function, from the graph maximum of point of the function is (-3π/4, 5) and the minimum point is (-π/4, 1).

Thus, the required maximum and minimum points of the function y = 2 sin 2(x + π) + 3 is (-3π/4, 5) and (-π/4, 1). Option A is correct.

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Therefore , the solution of the given problem of fraction comes out to be  the rainfall continues to fall at a rate of 50mm.

Any number of equal amounts or fractions can be used to represent a whole. In standard English, the quantity of a certain size is stated as a fraction. 8, 3/4. Wholes also include fractions. Numbers are represented in mathematics by the fraction to numerator ratio. These are all straightforward integer fractions. There is a fraction in the denominator of a difficult fraction. because the calculations, numerators, and numerators of actual fractions vary.

Here,

the amount of rainfall in Miami over s two hour period. If the rain continues to fall at this rate,

=> Radius

=>  fraction = 127/2 =63.5 mm

=> 2 hours rainfall

Per hour rainfall = 10 mm

=> After 5 hours

=> 50 mm

So,

the rainfall continues to fall at a rate of 50mm.

Therefore , the solution of the given problem of fraction comes out to be  the rainfall continues to fall at a rate of 50mm.

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Answer:

4c+20

Step-by-step explanation:

In total, there are 5 non-congruent triangles with integer sides that have a perimeter of 12.

The number of such non-congruent triangles can be found by considering all possible combinations of sides that add up to 12.

We can start by finding all possible combinations of two sides, and then adding the third side to make the perimeter equal to 12.

For example, for the two sides with lengths 1 and 11, the third side must be equal to 0, which is not allowed in a triangle.

The combinations of two sides are:

(1, 11), (2, 10), (3, 9), (4, 8), (5, 7), (6, 6).

For the combination (1, 11), the third side cannot be greater than 10, so it is not a valid triangle.

For the combination (2, 10), the third side can have lengths 0, 1, or 2, but none of these values result in a valid triangle.

For the combination (3, 9), the third side can have length 0, 1, 2, or 3. The only value that results in a valid triangle is 3, so there is 1 such triangle.

For the combination (4, 8), the third side can have length 0, 1, 2, or 4. The only value that results in a valid triangle is 4, so there is 1 such triangle.

For the combination (5, 7), the third side can have length 0, 1, 2, 3, or 5. The only value that results in a valid triangle is 5, so there is 1 such triangle.

For the combination (6, 6), the third side can have length 0 or 6. The only value that results in a valid triangle is 6, so there is 1 such triangle.

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Answer:

1 point

Step-by-step explanation:

if each question is worth twice as much as the question before it , then the question before each question is half the value, then

5th question = 16

4th question = 16 ÷ 2 = 8

3rd question = 8 ÷ 2 = 4

2nd question = 4 ÷ 2 = 2

1st question = 2 ÷ 2 = 1

the first question is worth 1 point

The solution for the given problem is X= -4, Y= -5.

First we will substitute into one of the equations: 2(3x-1)-6x=4

Then reduce the greatest common factor on both sides:3x-1-3x=2(i.e divide the above equation by 2)

The sum of two opposites equals 0: -1 =2

Rearrange unknown terms to the left side of the equation:

                                   2y+x=6

                                   4y+2x=12

Reorder the equation: x+2y=6

                                    4y+2x =12

Again reorder the equation by taking x variable first : x+2y = 6, 2x+4y= 12

Reduce the greatest common factor on both sides of the equation:

Subtract the two equations:2y-(x+2y)=6-6

Remove parentheses:

Cancel one variable:0=6-6

The sum of two opposites equals 0:0=0

The system of equations has: infinte solutions

Substitute into one of the equations: :x+2x+3=-9

Rearrange unknown terms to the left side of the equation:

Combine like terms:3x=-9-3

Calculate the sum or difference:

Divide both sides of the equation by the coefficient of variable:x=-12/3

Cross out the common factor:x=-4

Substitute into one of the equations:-4+y=-9

Rearrange unknown terms to the left side of the equation: y=-9+4

Calculate the sum or difference: y=-5

Therefore, the solution of the given problem is x=-4, y=-5.

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The missing side, which is 8.2 (rounded to the closest tenth), is indicated by the provided statement.

The leading edge that connects two vertices of a form or two-dimensional object is referred to as a side in geometry. To put it another way, in mathematics, a side is the vector that joins two points on a form. Here, the term "shape" refers to a two-dimensional (flat) form, such as a triangle, rectangle, or square.

Your hypotenuse is present. You require the inverse.

Sin = x/Hypotenuse

Sin27° = x/18

x = Sin27° * 18

x = 0.45 * 18

x = 8.17

x ≈ 8.2

As a result, side 8.2 is missing.

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The class section with the larger standard deviation will be the one with the larger variance.

The standard deviation is a measure of how much variation exists in a set of data. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. To calculate the standard deviation for Joseph and Nichole's class sections, we need to first calculate the variance for each class. To do this, we need to subtract the mean of each class from each data point, square the result, and then average the squared differences. The larger the variance, the larger the standard deviation will be. Therefore, the class section with the larger standard deviation will be the one with the larger variance.

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When the length of 2 section combined is 18 in

width is 12 in

When the length of 2 section combined is 24 in

width is 9 in  

A quadrilateral with four right angles is a rectangle. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.

Rectangles have the following basic characteristics:

The length of the poster is 24 in

The width of the poster is 18 in

The area of the poster = 24*18 = 432 in²

The area of each section of the poster is 432/4 = 108 in².

Length of each section is 24/2 = 12 in

Width of each section is 18/2 = 9 in

The total length when 2 sections are combined is 9 + 9 = 18 in

or, 12 + 12 = 24 in

When the length of 2 section combined is 18 in

width is (108*2)/18 = 12 in

When the length of 2 section combined is 24 in

width is (108*2)/24 = 9 in  

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The five values which are required to graphed a box plot are as follow:

Option 1. Minimum , Quartile 1, Median, Quartile 3 , Maximum

The five values required to represent on the graph of box plot are :

Therefore, the five values used to graphed on a box plot are:

Option 1. Minimum , Quartile 1, Median, Quartile 3 , Maximum

The above question is incomplete , the complete question is :

Which five values are graphed on a boxplot?

1.  Min, Quartile 1, Median, Quartile 3. Max

2.  Min. Quartile 1, Mean Quartile 3, Max

3. Min. Quintile 1, Median, Quintile 3. Max

4. Min. Quintile 1. Mean, Quintile 3, Max

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Answer:

2 green

Step-by-step explanation:

The ratio of blue to green is 4 to 1  <===== there is 1/4th asmany green as blue.... so if there are 8 blue, there are only   2 green

Answer:

None

Step-by-step explanation:

[tex]1-\frac{7}{12}-\frac{1}{6}-\frac{1}{4}=1-\frac{7}{12}-\frac{2}{12}-\frac{3}{12}=1-\frac{12}{12}=0[/tex]

Answer:

Step-by-step explanation:

an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?

The total number of newspapers sold each day is: 200 + 2 + 16 + 128 + 22 = 368.

To find the total number of newspapers sold each day, we need to find the sum of the daily sales of each variety:

English language newspapers: 25 * 8 = 200

French language newspapers: 1 * 2 = 2

Korean language newspapers: 16 * 1 = 16

Japanese language newspapers: 16 * 8 = 128

Russian language newspapers: 22 * 1 = 22

Addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

In mathematics, addition is the process of joining two or more integers. The numbers being added are known as addends, and the result or final response obtained after the procedure is known as the total.

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Functional continuity and derivative continuity (slope smoothness) between the device saturated and device active segments is the value of V12, VOL and Vhr, Vih and Get the NM2 & NmH

What is Functions?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Suppose the threshold vintage of N- mas is VTO

(i) Vin < VTO – Cat of f

(ii) VTO < Vin < V out – Saturation

(iii) Vin > V out + VTO – Liniar

When N-Nos is in Liniar

IR = Kn/2 { 2.(Vin-VTO). V out – V2out }

Cat calculation of VOH,

V out = V Do – RL- IR

When Vin is Low, i.p. Vin <Vto, the M mess is Off Home ID = IR = O

Calculation of VOL,

Let us assume Vin = VoH

= VDo

Since Vin – VTO > V Out, the Transitar is in Lininers,

IR= VDo – V out

Off have IO = IR = o

Calculation of VOL,

Let us assume Vin = VOH = VDO

Since Vin – VTO > V out, the Transifar is in Linears,

IR= VDO – V Out / R2

Using KCL – IR = IO

VDO – VOL / R2 = Kn/2 { 2(VOD  - VTo ) . Vo2 – VOL2}

Vol2 – 2 .{ VOD – VTO + 1/KnR2 } VOL + 2/KnRL . VDD = 0

On Solving for VOL,

VOL = VDD = VTO + 1/KnRL - /- ( VDD – VTO + 1/KNR2 ) 2 – 2VDD/KnR2

D Vot/DVin = 1

For VOCD > Vin – VTO; The N-Mas in Saturation

VDD – V Out /R2 = Kn/2 ( Vin – VTO ) 2

-1/R2 . D V out / D Vin = Kn( Vin – Vto )     put Vin = Vin

-1/RL ( -1) = Kn( Vin – Vto )

Calculation of Visit :-

Put D V out / D Vin = -1

When V Out  < Vin – Vto: M- mas Linier

Vdd – V out / RL = Kn/2 { 2- ( Vin –Vto ) Vout – V2 out }

Differtatyboth side  by d Vin:

-1/RL – D Vout/D Vin = kn/2 { 2.( Vin – Vto) D v out /d Vin

= 2 vat . Dat/dxt

Vdd – V out /R2 = Kn/2 { 2. ( Vin – VTO) V out – V2 Out }

Diffent Both side by D Vin .

-1/RL. DV out/DVin = Kn/2 {2. (Vin – Vto) Dv out / D vin + 2 vat .dat/Dithal      ------- ( i)

Put  dV out/D vin = -1

                                         Put Vin = VTT

-1/RL (-1) = Kn{( Vin – Vto ) – (-1) +2 V out }

VTH = Vto +2 V out -1 / Kn RL ----------(II)

Now Put the Value of Vin From ( II ) in ( I) in the Place of Vin.

Then

Vin = Vto + 8/3 VDo/KnRL – 1/knRL

Now ,Nasie Margin :-

NM2 = V12 – Vol

NMH = Vas – Vin

Substitute the value of V12, VOL and Vhr, Vih and Get the NM2 & NmH.

The value of V12, VOL and Vhr, Vih and Get the NM2 & NmH between the device saturated and device active segments is functional continuity and derivative continuity (slope smoothness).

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The area of the given circle is 36π square meters.

What is the area of a circle?

The region encircled by a circle is known as the area of a circle in geometry. The area of a circle is π multiplied by the square of the radius r. Here, the Greek letter π stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.

Given,

 Diameter of the circle = 12 metres

Radius of the circle = Diameter/2 =12/2 = 6 metres

Area of circle = πr² = π ×6² = 36 π square meters

Therefore the area of the given circle is 36π square meters.

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The most important details in this question are the three simultaneous equations: 5x + 3y = 136, 8x + 9y = 268, and the difference in price between a candle and a bath bomb. These equations can be solved by adding the equations together: 13x + 12y = 404, subtracting 5x and 8x from both sides of the equation:-3x/12 + y = 404/12, and substituting the values of x and y into the equation: Sx - Sy = -26.472.

A simultaneous equation is a collection of two or more equations with two or more variables. Because they share variables, these equations must be solved together. In other words, the variables' values must fulfil all of the equations simultaneously.

(a) 5x + 3y = 136

Substitute the values given in the equation:

5(25) + 3(15) = 136

125 + 45 = 136

Simplify:

170 = 136

This equation is not true.

(b) 8x + 9y = 268

Substitute the values given in the equation:

8(16) + 9(18) = 268

128 + 162 = 268

Simplify:

290 = 268

This equation is not true.

(c) Solve these simultaneous equations.

5x + 3y = 136

8x + 9y = 268

Add the equations together:

13x + 12y = 404

Subtract 5x and 8x from both sides of the equation:

-3x + 12y = 404

Divide both sides of the equation by 12:

-3x/12 + y = 404/12

Simplify:

-1/4x + y = 33.67

Substitute this equation into the original equation:

5x + 3y = 136

5x + 3(33.67) = 136

Simplify:

5x + 100.01 = 136

Subtract 100.01 from both sides of the equation:

5x = 35.99

Divide both sides of the equation by 5:

x = 7.198

Substitute this value into one of the original equations:

5(7.198) + 3y = 136

Simplify:

35.99 + 3y = 136

Subtract 35.99 from both sides of the equation:

3y = 100.01

Divide both sides of the equation by 3:

y = 33.67

(d) Calculate the difference in price between a candle and a bath bomb.

Substitute the values of x and y into the equation:

Sx - Sy = 7.198 - 33.67

Simplify:

Sx - Sy = -26.472

Therefore, the difference in price between a candle and a bath bomb is Sx - Sy = -26.472.

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Answer:none of the above

Step-by-step explanation:

The maximum Z is 1800 and the value of X₁ and X₂ at the optimal solution : X₁ = 5 and X₂ = 3.

The constraints for the linear programming problem:

30X₁ + 70X₂ ≤ 210

20X₁ + 10X₂ ≤ 100

X₁, X₂ ≥ 0

First we draw the graph for equations 30X₁ + 70X₂ = 210 and 20X₁ + 10X₂ = 100

Consider equation 30X₁ + 70X₂ = 210

For X₁ = 0,

70X₂ = 210

X₂ = 3

For  X₂ = 0,

30X₁ = 210

X₁ = 7

This means, the line 30X₁ + 70X₂ = 210 passes through (0, 3) and (7, 0) as shown in the following graph.

So, 30X₁ + 70X₂ ≤ 210  includes the region below the line.

Consider equation 20X₁ + 10X₂ = 100

For X₁ = 0,

10X₂ = 100

X₂ = 10

For  X₂ = 0,

20X₁ = 100

X₁ = 5

This means, the line 20X₁ + 10X₂ = 100 passes through points (0, 10) and (5, 0) as shown in the following graph.

so, an inequality 20X₁ + 10X₂ ≤ 100 includes the region below the line.

From the figure, (0, 3) and (5,0) are feasible corner points.

Thus the optimal solution is:  X₁ = 5 and X₂ = 3

For X₁ = 5 and X₂ = 3,

Z = 300X₁ + 100X₂

Z = 300(5) + 100(3)

Z = 1500 + 300

Z = 1800

Therefore, the maximum value of Z is 1800

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The required complete table regarding the distance traveled has been shown.

From the given condition, let y be the distance left and x be the time,
According to the question an equation model is given as,

Distance traveled = 5x
Distance remaining to travel = y = 5000 - 250x

Now,
Put x = 5
Distance traveled = 250x
                           = 250(5) = 1250

Distance remaining to travel = y
y = 5000 - 1250
y = 3750 ft

Similarly,
At
x = 20
Distance traveled = 5000

X = 10
Distance remaining = 2500

Thus, the required complete table has been shown.

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The mean absolute deviation of the number in the list is 8.8

Mean absolute deviation (MAD) is a measure of the average absolute distance between each data value and the mean of a data set. The formula for MAD is:

MAD =∑|x-m|/n

∑ is known as Sigma and means to sum up

| | are vertical bars that mean absolute value

x is each value

m is the mean

n is the total number of data points in your data set

Given: 35,47,52,40,21

n = 5

m = (35 + 47 + 52 + 40 + 21) /5 = 195/5 = 39

∑|x-m| = |35-39| + |47-39| + |52-39| + |40-39| + |21-39|

          = 4 + 8 + 13 +  1 + 18 = 44

MAD =∑|x-m|/n = 44/5 = 8.8

Therefore, the mean absolute deviation of the number in the list is 8.8

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Answer:

0.12698412698

Step-by-step explanation:

The rate of change is -2.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the table,

(0, 42), (1, 40) and (2, 38)

Rate of change of drone A.

= (40 - 42) / (1 - 0)

= -2/1

= -2

Thus,

-2 is the rate of change.

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The values of x and y are the same with x = 3√2 and y = 3√2 derived using the trigonometric ratio of sine and cosine of the angle 45°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

sin 45° = √2/2 and cos 45° = √2/2

considering the right triangle;

sin 45° = x/6 {opposite/hypotenuse}

√2/2 = x/6

x = 6 × √2/2

x = 3√2

cos 45° = y/6 {adjacent/hypotenuse}

√2/2 = y/6

y = 6 × √2/2

y = 3√2

Therefore, the values of x and y are the same with x = 3√2 and y = 3√2 derived using the trigonometric ratio of sine and cosine of the angle 45.

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