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The value of x is 43.2

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

25/40 = 27/x

cross multiply.

25*x = 25x

40*27 = 1080

25x = 1080

divide by 25 both sides.

25/25 = 0

1080/25 = 43.2

x = 43.2

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The box and whisker plots and the IQR for each of the data set is given below.

A box and whisker plot has a rectangular box and two lines that connect from it on both sides, where:

The above stated values are referred to as the five-number summary of a data.

The interquartile range (IQR) = Q3 - Q1.

6. The five-number summary for the data set, 32, 34, 36, 37, 36, 37, 38, 37, 38 are:

The IQR is: 37.5 - 35 = 2.5

7. The five-number summary for the data set, 52, 52, 55, 55, 53, 56, 57, 57, 58 are:

The IQR is: 57 - 52.5 = 4.5

8. The five-number summary for the data set, 50, 51, 52, 58, 58, 59, 49, 50, 49 are:

The IQR is: 58 - 49.5 = 8.5

9. The five-number summary for the data set, 18, 16, 15, 19, 11, 14, 12, 14, 16 are:

The IQR is: 17 - 13 = 4

The box and whisker plot for each of the data set given is shown in the diagram below.

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Answer:

Both angles are 56°

Step-by-step explanation:

These angles are vertical angles and vertical angles are congruent

5x + 1 = 6x -10  Subtract 5x from both sides

1 = x -10  Add 10 to both sides

11 = x  Plug this back into one of the expressions to find the measurement of the angels

5x + 1

5(11) + 1

55 + 1

56  or

6x - 10

6(11) -10

66 - 10

56

In the parallelogram ABCD, the side BC would be 4.8 units.

One particular type of quadrilateral that is created by parallel linesAB, BC, CD, DA is a parallelogram ABCD. The angle between the adjacent sides of a parallelogram can vary, but the opposite sides must be parallel for it to be a parallelogram. If two opposite sides of a quadrilateral are congruent and parallel, the shape is a parallelogram. So a quadrilateral with both pairs of opposite sides being parallel and equal is described as a parallelogram.

How to solve?

The parallelograms ABCD and A1B1C1D1  are similar.

Now, AB = 8 (Given in the figure), so CD = 8.

Now, we can write,

BC/B1C1=CD/C1D1

BC/3=8/5

{Since, given that B1C1=3 andC1D1=5 }

BC=4.8 units

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As we dilate rectangle ABCD by a scale factor of 1/2 and use E as the center, the coordinates of the point D' = (2, -1).

A rectangle is a quadrilateral in Euclidean plane geometry with four right angles.

The coordinates of the rectangle's points A'B'C'D' are as follows:

A' = the point's coordinates (-2, -1)

B' = the coordinates of the point (-2, 1)

C' = the coordinates of the point (2, 1)

D' = the coordinates of the point (2, -1)

Using the point P as the chart's origin, we get;

The coordinates of point B are (-4, 2), and the coordinates of point C are (4, 2).

Given that the sides are parallel to each other, the coordinates of point A = (-4, -2) The coordinates of point D = (4, -2)

We have; given that the sides are parallel to the axis.

The segment length AB = 2 - (-2) = 4

The segment length BC = 4 - (-4) = 8

The segment length CD = 2 - (-2) = 4

The segment length AD = 4 - (-4) = 8

As a result, a 1/2 dilation yields;

The segment length A'B' = AB/2 = 4/2 = 2

The segment length B'C' = BC/2 = 8/2 = 4

The segment length C'D' = CD/2 = 4/2 = 2

The segment length A'D' = AD/2 = 8/2 = 4

Point A' coordinates = Point A/2 coordinates = (-4, -2)/2 = (-2, -1)

= (-4, 2)/2 = (-2, 1) (-2, 1)

The coordinates of the point B' = (-2, 1) The coordinates of the point C' = (4, 2)/2 = (2, 1)

C' = the coordinates of the point (2, 1)

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The line integral ∫CF⋅dr = ∫(df/dx)dx + ∫(df/dy)dy + ∫(df/dz)dz

A gradient fiield is a function of the form F = ∇f where f is a scalar field and

∇= gradient function = (d/dx)i + d/dyj + d/dzk.

So, F =  [(d/dx)i + d/dyj + d/dzk]f

A line integral is the integral along a line. It is given by ∫F⋅dr = ∫Fxdx + ∫Fydy + ∫Fzdz

Since F=F(x,y,z) is a gradient field with F=∇f, S is a level surface of f, and C is a curve on S.

We desire to find the line integral ∫CF⋅dr.

Since the gradient field = ∇f, we have that

F =  [(d/dx)i + d/dyj + d/dzk]f

F(x, y, z) =  (df/dx)i + df/dyj + df/dzk

Now, the line integral along the curve C is ∫CF⋅dr

Since ∫F⋅dr = ∫(Fxi + Fyj + Fzk).(dxi + dyj + dzk)

= ∫[(df/dx)i + df/dyj + df/dzk].(dxi + dyj + dzk)

= ∫(df/dx)dx + ∫(df/dy)dy + ∫(df/dz)dz

So, we see that the line integral ∫CF⋅dr = ∫(df/dx)dx + ∫(df/dy)dy + ∫(df/dz)dz

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Half plane is both open and closed.

A half-plane is a section of a plane with all of its points on one side and none on the other of an endless straight line.

An inequality of half plane is: a boundary that divides the coordinate plane in half results from graphing an inequality on the coordinate plane. They are each referred to as half-planes.

Y > X is the equation for the upper-half plane. The y-coordinate of C is smaller than its x-coordinate in a similar manner. Y X is the equation for the lower-half plane.

A half-plane is a section of a plane with all of its points on one side and none on the other of an endless straight line. It is referred to as a closed half-plane if the points along the line are included. It is referred to as an open half-plane if the line's points are not taken into account.

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By solving the question, The equation has 2 valid solutions; no extraneous solutions that are x = 2,5

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Equation is -

[tex]\sqrt{x - 1} - 5 = x-8[/tex]

adding 5 to both of the sides,

[tex]\sqrt{x - 1} = x-8+5[/tex]

[tex]\sqrt{x - 1} = x - 3[/tex]

squaring,

[tex]( x- 1) = (x-3)^{2}\\ x - 1 = x^{2} + 9 - 6x\\x^{2} - 7x + 10 = 0\\x(x-2)-5(x-2)=0\\x=2, 5\\[/tex]

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The equation (x - 3)² / 144 + (y - 5)² / 196 = 1 is the standard form of the ellipse.

Herein we know the main features of a vertical ellipse, that is, the center and the lengths of its axes. The standard form of the equation of the ellipse:

(x - h)² / a² + (y - k)² / b² = 1, b > a

Where:

If we know that (h, k) = (3, 5), a = 12, b = 14, then the standard form of the equation of the ellipse is:

(x - 3)² / 12² + (y - 5)² / 14² = 1

(x - 3)² / 144 + (y - 5)² / 196 = 1

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If we model the situation with a discrete dynamical system, with time interval

one day, we obtain the following:

[tex]\[x_{n+1} =\[x_{n}- \frac{3}{50}\[x_{n}[/tex]    ---------(1)

[tex]\[y_{n+1} =\[y_{n}+\frac{3}{50}\[x_n}-\frac{3}{100} \[y_{n}[/tex]

The amount of pollutant in Upper Lake tomorrow, [tex]\[x_{n+1}[/tex], is equal to the

amount of pollutant in Upper Lake today,[tex]\[x_{n}[/tex], minus the amount of pollutant which has flown into Lower Lake, via the river. The concentration of pollutant in Upper Lake today is [tex]\frac{\[x_{n}m^3}{50km^3}[/tex] The amount of water carried by the river to Lower Lake during the day is [tex]3km^3[/tex] This water contains

                                           [tex]3km^3\frac{\[x_{n}m^3}{50km^3}[/tex] [tex]=\frac{3}{50} {\[x_{n}m^3}[/tex]

of the pollutant. So the decrease of pollutant in Upper Lake is equal to [tex]=\frac{3}{50} {\[x_{n}}[/tex]  (measured in m3 , which are the correct units for the components of the state vector). This justifies Formula (1).

The change in the pollutant in Lower Lake consists of the inflow from

Upper Lake, which is [tex]\frac{3}{50}[/tex] , minus the outflow, which is [tex]{3}\frac{{\[y_{n}}}{100}[/tex] , because the concentration of the pollutant in Lower Lake is  [tex]\frac{{\[y_{n}}}{100}[/tex].

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The value  of x and y is  3

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equals sign =. [2] [3] In other languages, the word equation and its cognates may have slightly different meanings; for example, in French, an équation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.

Let the equations be

x + 3y = 8    ..............(1)

x + y = 2    ..............(2)

substracting equation 1 from 2

(x + 3y) - (x + y ) = 8 - 2

x + 3y - x + y = 6

3y - y = 6

2y =6

y = 6/2

y = 3

multiply the equation 2  with value of 3

x + y=2*3

x+y =6

x+3 = 6

x = 6 - 3

x = 3

Therefore the value of x and y is both are 3

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The value of (r + s) in the given equation, (x+r)(x+s) = x² + 3x - 10, is (r + s) = 3

From the question, we are to determine the value of the given expression.

The expression we are to determine its value is

(r + s)

To do this, we will compare the terms of the given equation.

From the given equation

(x+r)(x+s) = x² + 3x - 10

First, we will expand the left-hand side of the equation

Expanding the left-hand side of the equation

(x+r)(x+s)

x(x + s) + r(x + s)

x² + xs + xr + rs

Factor the middle expressions

x² + x(s + r) + rs

x² + x(r + s) + rs

x² + (r + s)x + rs

Now, compare the resulting expression to the expression on the right-hand side

x² + 3x - 10

By comparison,

r + s = 3

Hence, the value is 3

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The all the possibilities and combination for the x - intercepts , of the roots of the polynomial with degree 4 are :  

0 x-intercepts and 4 imaginary roots   ,

4 distinct x-intercepts  ,  

1 x-intercept with multiplicity 4  and

2 distinct x-intercepts each with multiplicity 2   .

In the question ,

it is given that ,

there is polynomial of degree 4 ,

and some statements about the roots of the polynomial is given ,

we have to find the suitable options that are for the roots .

We know that the fourth degree polynomial will have theoretically four roots .

So , the possible situations for the roots are

it can have ,

0 x intercepts and 4 imaginary roots ( where imaginary roots must occur in pairs )   OR

it can have 4 distinct x intercepts .    OR

1 x intercept that have multiplicity 4 ,     OR

2 distinct x intercepts that have multiplicity 2 .

Therefore  , the possibilities options are (b) , (d) , (e) and (h) .

The given question is incomplete , the complete question is

Below are several options for the roots of a polynomial with degree 4. Consider all possibilities and combinations for the x- intercepts .

(a) 2 distinct x-intercepts of which one has a multiplicity of 3 ,

(b) 0 x-intercepts and 4 imaginary roots

(c) 3 distinct x-intercepts of which one has a multiplicity of 2

(d) 4 distinct x-intercepts

(e) 1 x-intercept with multiplicity 4

(f) 1 x-intercept with 3 imaginary roots

(g) 3 distinct x-intercepts and 1 imaginary root

(h) 2 distinct x-intercepts each with multiplicity 2

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Trigonometric functions have the same maximum value y = arcsinx and y = arccosx.

What is Trigonometric Function?

Trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. It implies that these trig functions provide the relationship between a triangle's angles and sides.

Arcsin, Arccos, Arcsec, and similar symbols are used to represent inverse trigonometric functions.

Inverse functions refer to the trigonometric operations that are used to determine an angle from any of the angle's trigonometric ratios.

When solving inverse trigonometric equations, the following formula is used:

Arcsinx = Arcsinx -

arccosx = pi-arccosx.

Arctan = Arctan - Arctan

arsecx = pi - arsecx

The maximum values we obtain from the following equations are:

arcsinx = -1 to 1

arccosx = -1 to 1

arctanx = -pi/2 to pi/2

arcsecx = ∞

So the trigonometric functions which have the same maximum value is arcsinx and arccosx.

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The half-life of vanadium-48 is 16 days.

What is half life?

The half-life formula is used to determine the half-life of a material whose quantity is degrading or decreasing. When a substance degrades, the rate of decay varies depending on the quantity present. It is exceedingly challenging to determine the life of a decaying substance since when the quantity of the chemical decreases, the pace of decay likewise slows down. In order to offer the appropriate metrics to quantify the life of decomposing material, the half-life formula is applied.

According to law of radio active decay, IN=N

N-- amount of sample present

N1--- initial amount of sample

Decay 0 constant

Half life = 16 days

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Answer:

2^2

Step-by-step explanation:

(2^7)/(2^5) = 2^(7 - 5) = 2^2

Answer:

Step-by-step explanation:

Ok:

1. Use PEMDAS to solve equations(Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

First parentheses:

4(x−5)=20

4x-20=20

Second add subtract from both sides by isolating variable x!

4x-20=20

4x=40

4*x=40

x=40/4

x=10

3. Answer: x=10

The ratio of a:b is 3:16

What is Ratio?

Ratio ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division. That is, a:b = a/b

To find the ratio a:b

[tex]\frac{a+3b}{5}[/tex] = [tex]\frac{a-2b}{2}[/tex]

Cross multiply

2(a+3b) = 5(a-2b)

Open bracket

2a + 6b = 5a - 10b

Collect like terms

2a - 5a = -10b - 6b

-3a = -16b

Divides through by -1

-3a/-1 = -16b/-1

3a = 16b

The Ratio a:b is 3:16

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The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .

In the question,

few statements about Correlation is given ,

we need to find the statement that is True .

we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,

the correlation can be negative , positive or 0 ,

and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .

So , from the above information about Correlation ,

we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "

Therefore , the statement in option (c) is True  .

The given question is incomplete , the complete question is

Select the statement below that is true about correlations.

(a) Correlations can only be negative

(b) Correlations are a measure of how much one variable changes as the other variable changes

(c) Correlations are a measure used to determine the degree to which two variables are related.

(d) Correlations are a measure of causation between two variables

(e) A negative correlation implies no relationship between variables

(f) Correlations can only be positive .

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The roots of the quadratic equation are x = (3±2i)/2

The meaning of quadratic formula is a formula that gives the solutions of the general quadratic equation ax² + bx + c = 0

Given a quadratic equation, 4x²+13 = 12x

4x²-12x + 13 = 0

Quadratic formula =

x = [-b ± (√b²-4ac)]/2a

a = 4, b = -12 and c = 13

x = [12 ± (√(-12)² - 4*4*13)]/2*4

x = (12 ± 8i)/8

x = (3 ± 2i)/2

Hence, The roots of the quadratic equation are x = (3±2i)/2

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-3 is less than 2

< is the symbol

Answer:

Step-by-step explanation:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

[tex]A=5300(1+\frac{.08}{12} )^{12\times6[/tex]

[tex]A=5300(1.00666666667)^{72}[/tex]

[tex]A=5300\times1.613502[/tex]

[tex]A=8551.561489[/tex]

Now, it is up to you to round to the nearest cent.

Thanks,

Eddie

The mean and the standard deviation of the sampling distribution of x are given as follows:

The mean and the standard deviation of the sampling distribution of x are defined according to the Central Limit Theorem, which states that:

The parameters for this problem are given as follows:

Hence the standard deviation for the sampling distribution of x is given as follows:

s = 60/sqrt(10) = 19 seconds.

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Answers:

Domain = {12, 10, 8, 6}

Range = {1, 3, 5, 7}

============================================

Explanation:

The domain is the set of allowed x inputs. Simply list the x coordinates of each point.

The range will have us list the y coordinates of each point. This shows the list of possible outputs.

Use curly braces for the domain and range because each is a set of values.

Optionally you can sort the values. I decided not to sort them to keep the same order of coordinates mentioned from left to right.

{12,10,8,6} sorts to {6,8,10,12}

If there were any duplicate items, in either domain or range, then you would erase them. Simply list each unique item once.

-------------------

Extra info:

1. Both segments have the slopes = 1/2.

2. Slope of CD = -1/3.

Slope of CD = -1/3.

Slope of zipline = -1/3.

3. ΔAHE, ΔBID, and ΔCGF are the slope triangles.

Slope of the line = 1/2.

4. See attachment for the slope triangles drawn.

The slope of the line = 3/5

A slope triangle can be described as an imaginary triangle that is drawn on a coordinate plane, whereby, the hypotenuse of the triangle is the line we are interested in finding the slope, and the legs represent the rise and run of the line that is used to calculate the slope.

The slope formula = rise/run.

1. Slope of segment RT = rise/run = 2/4 = 1/2

Slope of segment TV = rise/run = 1/2

The slopes of both segments are equal.

2. Choosing points C and D, the slope of CD = rise/run = -1/3.

Choosing points B and C, the slope of CD = rise/run = -2/6 = -1/3.

The slope of the zipline is: -1/3.

3. The slope triangles are ΔAHE, ΔBID, and ΔCGF.

Slope of the line = rise/run = 2/4 = 1/2.

4. The slope triangles drawn is in the image attached below.

The slope of the line = rise/run = 3/5

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If he has $2.34 to spent on oranges, then he can buy 6 oranges

Total number of oranges in a bag = 4 oranges

The cost of 4 oranges = $1.4

The total amount that he spent = $2.34

Here we have to use the unitary method

The cost of 1 orange = The cost of 4 oranges / 4

Substitute the values in the equation

= 1.4/4

= $0.35

Then the number of oranges that he bought =  The total amount that he spent / The cost of 1 orange

Substitute the values in the equation

= 2.34 / 0.35

Divide the terms

= 6.68

≈ 6

Hence, he can buy 6 oranges with $2.34

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The correct option is [tex]6x^2+3x[/tex] which is the area of triangle. It can be obtained by the formula of area of triangle and algebriac multiplication.

What is the are formula of area of a triangle?

Area of any shape is the measure of the 2 dimentional space occupied by that shape. Its SI unit is [tex]m^2[/tex].  Area of the triangle is given by the following formula:

[tex]A=\frac{1}{2}bh[/tex]

Here, A is the area, b is the base, and h is the height.

Substitute 4x+2 for b and 3x for h in the above equation.

[tex]A=\frac{1}{2}(4x+2)(3x)[/tex]

Now, multiply using algebriac multiplication as follows:

Initially, use distributive property as follows:

[tex]A=\frac{1}{2}[(4x)(3x)+(2)(3x)][/tex]

Now, multipliy and again open brackets as follows

[tex]A=\frac{1}{2}(12x^2+6x)\\=6x^2+3x[/tex]

This gives the area of the triangle is [tex]6x^2+3x[/tex]. Hence, the correct option is the last option.

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Answer:

d

Step-by-step explanation: