An elf, a dwarf, a hobbit, a wizard, and a man are sitting in a line.How many different ways can they sit if the elf and the dwarf insist on sitting next to each other

Term limits have been approved almost everywhere they’ve been on the ballot.

However, the evidence suggests that at the margin, term limits are helpful to the cause of individual liberty. Elhauge’s report showed that term limits lessen the influence of seniority. His research demonstrated that long-term lawmakers from both major parties vote for more bureaucracy than do lawmakers who have been in office for shorter times.

Therefore, term limits have been approved almost everywhere they’ve been on the ballot

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If the farmer plotted a straight line graph of how many goats he had left over time, the slope of the line would be -14.

To find the slope of the line representing the number of goats the farmer has over time, we need to use the formula:

Where y2 and y1 are the number of goats the farmer has at the end of two different months, and x2 and x1 are the number of months that have passed since he started selling the goats.

In this case:

So the slope of the line is:

The slope of the line is -14, which means that the number of goats the farmer has decreases by 14 goats per month.

It's important to note that when the value of the slope is negative, it means that the line is going down; this means that the farmer is selling goats at a constant rate.

This question is incomplete and should be written as:

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Answer:

Interest is $4185.00

Please give me brainliest

Step-by-step explanation:

[tex]i = \frac{p \: r \: t}{100} \\ i = \frac{6750 \times \frac{62}{3} \times 3 }{100} \\ i = \frac{418500}{100} \\ i = 4185[/tex]

Answer:

Step-by-step explanation:

Formula for simple interest =S= (P*R*T)/100

Here P=$6750,R=62/3% T=3Years

Simple interest for given is S= 41.85

The quadratic equation in standard form that has an axis of symmetry of x=-2 and y-intercept of (0,6) is x² + 4x - 6 = 0.

A quadratic equation in standard form is of the form ax² + bx + c, where a, b, and c are constants.

The axis of symmetry of a quadratic equation is given by the line x = -b/2a, so if the axis of symmetry is x=-2, we can set -b/2a = -2, which gives b = 4a.

To find the y-intercept of the quadratic equation, we can set x = 0 and substitute that into the equation: y = a(0)² + b(0) + c = c
So, if the y-intercept is (0,6) then c = 6.

By using above two information, we can write the quadratic equation in standard form as:

a(x+2)² + 4a(x+2) + 6 =0
=> a(x²+4x+4) + 6 = 0
=> a(x²+4x+4) = -6
=> a(x²+4x+4) = -6
=> x² + 4x + 4 = -6/a
=> x² + 4x + 4 = -6/a +10
=> x² + 4x - 6 = 0

So, the quadratic equation in standard form that has an axis of symmetry of x=-2 and y-intercept of (0,6) is x² + 4x - 6 = 0.

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A "full table of 5" refers to a multiplication table that includes all of the products of the number 5 multiplied by the integers from 1 to some maximum value.

Here is an example of a full table of 5:

5 x 1 = 5

5 x 2 = 10

5 x 3 = 15

5 x 4 = 20

5 x 5 = 25

5 x 6 = 30

5 x 7 = 35

5 x 8 = 40

5 x 9 = 45

5 x 10 = 50

In this example, the maximum value for the multiplier is 10, but a full table of 5 can continue with any number of rows. This table is useful for memorizing the multiplication facts of 5, and also to see the pattern of the multiples of 5.

It's worth to mention that if you are looking for a way to calculate the products you could use a loop or a function that takes the maximum value of the multipliers as an input and prints the full table of 5.

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So, on solving the provided question we can say that coordinates are -

(6, -4.) and T (-1,2) y-y1 = m(x - x1) => 2x - y -16 =0

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.

here,

coordinates are -

(6, -4.) and T (-1,2)

y-y1 = m(x - x1)

y +4 = 2(x -6)

y+ 4 = 2x - 12

2x - y -16 =0

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A function y = 10 a not linear function

We know that the general form of linear function is f(x) = a + bx

A linear function has one independent variable (for above function x) and one dependent variable(here, f(x)).

The graph of linear function is always a straight line.

Let y = f(x)

So, y = a + bx

where b is the slope of line

and a is the y-intercept

here, the independent variable is x and the dependent variable is y.

We have been given a function y = 10

The graph of y = 10 is a horizontal line parallel to x -axis and intersects y-axis at (0, 10)

There is no y-intercept and the slope is undefined.

Therefore, given function is not a linear function

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Mary is mistaken in her conclusion that the two triangles are not similar because size does not determine similarity. Similarity is determined by the proportionality of corresponding sides and the congruence of corresponding angles. Congruence is the equality of all the measures of the corresponding parts of two figures.

In order to determine if two triangles are similar, we must compare the ratios of corresponding sides. If the ratios of corresponding sides are equal, then the triangles are similar. In the diagram, it is not specified what the measures of the sides of the triangles are, so it is not possible to determine if the triangles are similar based on the information given. However, if the ratio of corresponding sides are same, then the triangles are similar.

It is important to note that similarity and congruence are different concepts. Congruence refers to the equality of all measures of corresponding parts of two figures, including side lengths and angles. Similarity refers to the proportionality of corresponding parts, including side lengths and angles. A triangle can be similar to another triangle without being congruent, and congruent triangles are always similar.

In summary, Mary is mistaken because the size of the triangle does not determine similarity, it is determined by the proportionality of corresponding sides and congruence of corresponding angles. Without knowing the measures of the sides of the triangles, it is impossible to determine if the triangles are similar based on the information given.

The vertices of the new polygon A'B'C'D' is A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1) (optionB)

A vertex is a corner point of a polygon, polyhedron, or other higher-dimensional polytope, formed by the intersection of edges, faces or facets of the object.

The vertices of the polygons are given as B(−2, 2), C(4, −2), D(4, 4) . The polygon is reduced by using a scale factor one fourth. i.e 1/4.

This means that each coordinates of the vertices will be reduced by 4 to give the vertices of the new polygon.

A = (-4,6) , A' = ( -1, 1.5)

B = ( -2,2) B' = ( -0.5, 0.5)

C = ( 4, -2) C' = ( 1, -0.5)

D = ( 4,4) , D' = ( 1, 1)

Therefore the vertices of the new polygon is A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)

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Answer:

its not b i tried and it was wrong

Step-by-step explanation:

The linear regression equation is y = 22.086x + 898.620 and the year for 1171 cases is 2024

From the question, we have the following parameters that can be used in our computation:

The table of values

Using a graphing calculator, we have the following summary

The regression equation is represented as

Regression Equation = ŷ = bX + a

Where

b = SP/SSX = 386.5/17.5 = 22.08571

a = MY - bMX = 953.83 - (22.09*2.5) = 898.61905

So, we have

ŷ = 22.08571X + 898.61905

Approximate

y = 22.086x + 898.620

When the new cases is 1171, we have

22.086x + 898.620 = 1171

This gives

x = 12

i.e. year = 2012 + 12 = 2024

Hence, the year is 2024

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The equation of the line perpendicular to 2x + 3y = 12 will be y = 3x/2 + c where c ∈ R.

The equation of the line given here is 2x + 3y = 12

Now rearranging it to the slope-intercept form we get

3y = -2x + 12

or, y = -2x/3 + 4

Now any 2 lines are perpendicular when the product of their slopes results in -1.

Hence, let the equation of the line perpendicular to the given line be

y = mx + c, where m is the slope of the line and c is the intercept.

Hence,

-2m/3 = -1

or, m = 3/2

Hence the equation of the line will be

y = 3x/2 + c where c ∈ R

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Answer:

The following equations are equivalent:

2 + x = 5

x + (negative 4) = 7

Negative 5 + x = negative 2

All of these three equations are equivalent because they all represent the same mathematical relationship between x and other numbers. The variable x is the same in each equation. We can see this by applying the same operation on both sides of the equations, and the variable x will cancel out and the two sides will be equal.

Answer:

45 cents

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

y=3x13

2x=y-9

2x=3x+13-9

2x=3x+13-9

2x=3x+4

-3  -3

-x=4

-x/ -x/

x=-4

(You said "3x13" so i'm going to guess you meant to say "3x+13").

(If you meant "3x-13" I can also help you with that too)!

The point that lies in the fourth quadrant is (1, -2).

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates are:

(1,−2), (1, 8), (-5, -4), and (-5, 2).

(1, -2) is in the fourth quadrant.

(1, 8) is in the first quadrant.

(-5, -4) is in the third quadrant.

(-5, 2) is in the second quadrant.

Thus,

(1, -2) lies in the fourth quadrant.

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Answer:   (5,−2) is the only point in the fourth quadrant.

Step-by-step explanation:

Answer:

Step-by-step explanation:

H=456,533/pier^2

H=456533×7/22×7×7*. Here 7 as radius

H=29.645cm

Therefore , the solution of the given problem circle comes out to be

straight line distance from Sydney to Capetown ≈11139 km

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is axis of rotation equal about the center at every angle. Every set of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetrical about the center at every angle.

Here,

The distance between Sydney and Cape Town's longitudes is 151.13° and 18.22°, respectively, for the little circle, which equals 533.669 km. Sydney to Capetown distance in a straight line is

151.13∘−18.22∘=132.91∘

Straight line distance from Sydney to Capetown

d= √53372+53372−2×5337×5337× cos132.91∘

= 9785 km

θ=cos⁻¹ (6400²+6400²−9785² / 2 x 6400×6400)=99.72∘

Great Circle route from Sydney to Cape Town

=>πR / 180∘ ×θ

=> 6400π180∘×99.72∘

=> 11138.831…≈11139 km

Therefore , the solution of the given problem circle comes out to be

straight line distance from Sydney to Capetown ≈11139 km

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To find the coordinates of the midpoint of two points in a plane, you can use the midpoint formula. The midpoint formula is:

(x,y) = ((x1 + x2) / 2, (y1 + y2) / 2)

Where (x1, y1) and (x2, y2) are the coordinates of the two points, and (x,y) are the coordinates of the midpoint.

For example, if you have two points (3, 4) and (7, 10), you can use the midpoint formula to find the coordinates of the midpoint:

(x,y) = ((3 + 7) / 2, (4 + 10) / 2)

(x,y) = (5, 7)

The midpoint of points (3,4) and (7,10) is (5,7).

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1. steps to find the value of x

The first step is to equalize the form of the equation.

y = 6x-11 = -6x+y= -11

-2x-3y = -7

thus becoming:

-6x+y= -11

-2x-3y = -7

Then eliminate y:

-6x+y= -11 | times -3| becomes 18x-3y=33

18x-3y=33

-2x-3y = -7

y in the equation can be eliminated to become:

20x=40

x=40/20

x=2

steps to find the value of y:

The first step is to equalize the form of the equation.

y = 6x-11 = -6x+y= -11

-2x-3y = -7

thus becoming:

-6x+y= -11

-2x-3y = -7

Then eliminate x:

-2x-3y = -7 | multiplied by 3| becomes -6x-9y=-21

-6x+y= -11

-6x-9y=-21

x in the equation can be eliminated to become:

10y=10

y=-10/10

y=1

2.

1. steps to find the value of x

The first step is to equalize the form of the equation.

2x-3y = -1

y = x-1 becomes -x+y=-1

thus becoming:

-2x-3y = -1

-x+y=-1

Then eliminate y:

-x+y=-1| times -3| to 3x-3y=3

-2x-3y = -1

3x-3y=3

y in the equation can be eliminated to become:

-5x=-4

x=4/5

Steps to find the value of y:

The first step is to equalize the form of the equation.

2x-3y = -1

y = x-1 becomes -x+y=-1

thus becoming:

-2x-3y = -1

-x+y=-1

Then eliminate x:

-x+y=-1| multiplied by 2| becomes -2x+2y=-2

-2x-3y = -1

-2x+2y=-2

x in the equation can be eliminated to become:

-5y=1

y=-1/5

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Answer:

a)   Length of the parking lot: 98 m

b)   Width of the pool: 89 m

Step-by-step explanation:

a)   The formula for the area of a rectangle is [tex]A=lw[/tex].

We need to evaluate the length. Lets solve for [tex]l.[/tex]

[tex]A=lw[/tex]

Divide both sides of the equation by [tex]w[/tex].

[tex]\frac{A}{w} =l[/tex]

We are given

[tex]A=8428\\w=86[/tex]

Lets evaluate [tex]l[/tex].

[tex]\frac{8428}{86}=l[/tex]

[tex]l=98[/tex]

b)   The formula for the perimeter of a rectangle is [tex]P=2l+2w[/tex].

We need to evaluate the width. Lets solve for [tex]w[/tex].

[tex]P=2l+2w[/tex]

Subtract [tex]2l[/tex] from both sides of the equation.

[tex]P-2l=2w[/tex]

Divide each term by 2.

[tex]\frac{P}{2} -\frac{2l}{2} =\frac{2w}{2}[/tex]

Simplify.

[tex]w=\frac{P}{2}-l[/tex]

We are given

[tex]P=376\\l=99[/tex]

Lets evaluate [tex]w[/tex].

[tex]w=\frac{376}{2}-99[/tex]

[tex]w=188-99[/tex]

[tex]w=89[/tex]

Answer:

a) 98m , b) 89m

Step-by-step explanation:

(a) Given,

To Find : Length of the Parking lot

Length of a rectangle shape can be derived by the formula,

[tex]l = \frac{A}{w}[/tex]

[tex]l = \frac{8428}{86}[/tex]

[tex]l = 98m[/tex]

Hence , the length of a rectangular parking lot is 98m

(b) Given ,

To Find : The width of the rectangular pool

We take the width as variable 'x'

Now we plug it into the perimeter of a rectangle equation

[tex]376 = 2(99 + x)[/tex]

Using distributive property we,

[tex]376 = 198 + 2x[/tex]

We now flip the equation

[tex]2x + 198 = 376[/tex]

[tex]2x = 376 - 198[/tex] ( Transposing into the right hand side)

[tex]2x = 178[/tex]

[tex]x = \frac{178}{2}[/tex]

[tex]x = 89[/tex][tex]m[/tex]

Hence , the width of the rectangular swimming pool is 89m

The probability that the 2 marbles taken from the bag are the same color is 25/49.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of red marbles = 3

Number of blue marbles = 4

Total marbles = 7

Now,

The probability of taking two blue marbles consecutively with replacement.

= 4/7 x 4/7

= 16/49

The probability of taking two red marbles consecutively with replacement.

= 3/7 x 3/7

= 9/49

Since the two marbles of the same color can be blue or red.

The probability that the 2 marbles taken from the bag are the same color.

= 16/49 + 9/49

= 25/49

Thus,

The probability that the 2 marbles taken are the same color is 25/49.

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Using the concept of ratios, the constant of proportion between middle school and high school is 3/4

Proportionality is a fundamental concept in mathematics and physics. It is a relationship between two or more variables where a change in one causes a proportional change in the other. In other words, the ratio between the two remains constant. Proportionality is an important concept in mathematics because it is used to make predictions and solve problems. The constant of proportionality is the ratio between the two variables that remain constant in a proportional relationship.

To determine the constant of proportionality in this relationship, we can write an equation in the form

y = kx

Or we can easily use ratio to find the constant of proportion

Number of girls in middle school = 6

Number of girls in high school = 8

The ratio = 6/8 = 3 / 4 = Option B

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The following statements are true for all the numbers. The proof is shown as follows.

A real number is multiplied by an imaginary unit, I whose feature i2 = 1 defines it as an imaginary number. Bi is an imaginary number, while b2 is its square. For instance, the square of the fictitious integer 5i is 25. Zero is regarded as both real and fictitious by definition.

We know z₁ = a + bi and zbar= a-bi

z1+z1bar=2a that is purely real. Similarly with z2 +z2bar

z1-z1bar=-2bi that is purely imaginary. Similarly with z2-z2bar

Again

z1bar+z2bar= a-bi+c-di

z1+z2(whole bar)=a+c-(b+d)i

Hence Z₁ + Z₂ = Z₁ + Z₂

Similarly

z1bar.z2bar=z1.z2(whole bar)

Hence proved

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The midpoint formula helps us to find the midpoint of a line given to us on a coordinate system.

The coordinate system in geometry is a plane space in which points are located using paired numerical values called coordinates. It is of two types Cartesian coordinate system and polar coordinate system

The cartesian coordinate system is further divided into majorly two parts i.e., 2-Dimensional and 3- dimensional systems. A 2-D system has 2 axis X and Y whereas a 3-D system has X, Y, and Z axes. The plane is divided into 4 quadrants

The midpoint formula is used to find the center of a line or a figure. It is a mathematical equation used in geometry and economics. On a line from point (x1,y1) to (x2,y2) the midpoint P= (x1+y1)/2 , (x2+y2)/2. It divides the line in a 1:1 ratio.

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The required translation of the given statement into an equation is given as 38 = 2d.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
38 is the product of Della's score and 2.
Let the variable d to represent Della’s score,
2 × d = 38

2d = 38

Thus, the required translation of the given statement into an equation is given as 38 = 2d.

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Answer: y = 8x

Step-by-step explanation:

The line passes through points (1,8) and (2,16).

Using this, we can first find the slope.

Slope = Δy/Δx = 8/1 = 8

So the slope is 8.

The equation is now

y = 8x + b

Let's use the point (1,8) to find the value of b now.

8 = 8 +b

b = 0

Therefore, y = 8x is the answer.

(you can skip the last step by noticing that the graph passes through the origin)

Answer:

y = 8x

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

From inspection of the given graph, two points on the line are:

Substitute the points into the slope formula to find the slope of the line:

[tex]\implies m=\dfrac{16-0}{2-0}=\dfrac{16}{2}=8[/tex]

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

The y-intercept is the y-value of the point where the line crosses the y-axis. From inspection of the given graph, the y-intercept is zero. So b=0.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

[tex]\implies y=8x+0[/tex]

[tex]\implies y=8x[/tex]

Therefore, the equation for the line in slope-intercept form is: