Determine whether the statement makes sense or does not make sense, and explain your reasoning.
A candidate received the majority of first-place votes and lost the election.
Choose the correct answer below.

A. The statement does not make sense because the candidate with the majority of the first place votes using the plurality method is the winner.
B. The statement does not make sense because the candidate with the majority of the first place votes in an election is always the winner.
C. The statement makes sense because the Borda count method using preference ballots can result in a situation where this can happen.
D. The statement makes sense because the plurality method can result in a situation where this can happen.

Set up:-

Solution:-

Here it's a cuboid

Volume:-

[tex]\\ \rm\rightarrowtail V=LBH[/tex]

[tex]\\ \rm\rightarrowtail V=6.5(4)(12.5)[/tex]

[tex]\\ \rm\rightarrowtail V=325ft^3[/tex]

For cubes

Volume:-

[tex]\\ \rm\rightarrowtail V=side^3[/tex]

[tex]\\ \rm\rightarrowtail V=(0.25)^3[/tex]

[tex]\\ \rm\rightarrowtail V=0.015625ft^3[/tex]

Now

Total cubes:-

[tex]\\ \rm\rightarrowtail \dfrac{325}{0.015625}[/tex]

[tex]\\ \rm\rightarrowtail 20800cubes[/tex]

Answer:

The 3rd equation, -2x-10 = -2(x+5)

Step-by-step explanation:

Equivalent expressions means both sides of the equal sign equal the same thing

To find which ones are equivalent expressions, we must solve/simplify both sides of each equation to see if they're actually equal to each other

We will use PEMDAS for this

1. 2x + 10 = -2(x - 5)

Start with Parentheses, and distribute the -2 to what's inside said parentheses

2x + 10 = -2x + 10

Not equal

2. -2(x+5) = 2x-10

Once again, start with Parentheses, and distribute the -2 to what's inside said parentheses

-2x - 10 = 2x - 10

Not equal

3. -2x-10 = -2(x+5)

Once again, start with Parentheses, and distribute the -2 to what's inside said parentheses

-2x - 10 = -2x - 10

Equal

4. -2(x-5) = -2x-10

Once again, start with Parentheses, and distribute the -2 to what's inside said parentheses

-2x + 10 = -2x - 10

Not equal

g(f(x)) = x

What is inverse function?

An inverse function is defined as a function, which can reverse into another function.

[tex]f(x)= \frac{(x + 5)}{(2x + 1)}[/tex]

[tex]g(x)= \frac{(5 - x)}{(2x - 1)}[/tex]

 [tex]g(f(x))=g( \frac{(x+5)}{(2x +1)})[/tex]

Substitute the value of f(x),

[tex]g(f(x))= \frac{(5 - \frac{(x + 5)}{(2x + 1)})}{(2 \frac{(x + 5)}{(2x + 1)} - 1)}[/tex]

[tex]g(f(x))= \frac{\frac{10x+5-x-5}{2x+1} }{ \frac{2x+10-2x-1}{2x+1}}[/tex]

[tex]g(f(x)) = \frac{9x}{9}[/tex]

g(f(x)) = x

Hence, g(f(x)) = x

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Answer:

Step-by-step explanation:

when  3(2x^2+4x+7)−(x^2−8x+11) is solved you get

5x^2 + 20x + 10.

the x term is

−

2

+

√

2

,

0

)

,

(

−

2

−

√

2

,

0

)

[tex]3(2x^2+4x+7)-(x^2-8x+11)\\\\=6x^2 +12x + 21 -x^2+8x -11\\\\=5x^2+20x +10\\\\\text{The coefficient of the x term is 20}[/tex]

B for question 12

B for question 13

Step-by-step explanation:

U = Union

n= intercestion

B'= not b

A"= not a

so AnB'

should be B

if 2.50 = 1

2.50x8=

20

1×8 =

8

should be $8

Answer:

If the whole transaction is written separately from the beginning, an algebraic equation is obtained

Step-by-step explanation:

[tex]4x = s[/tex]

[tex] - 2x = w[/tex]

[tex]w \times s = - 8 {x}^{2} [/tex]

[tex]w = s = s \times s = 16 {x}^{2} [/tex]

[tex] - 8 {x}^{2} + 16 {x}^{2} = 8 {x}^{2} [/tex]

This is the way to get the answer

Answer:

2

Step-by-step explanation:

[tex] \frac{8x}{4x - 7} - \frac{14}{4x - 7} \\ \\ = \frac{8x - 14}{4x - 7} \\ \\ = \frac{2 \cancel{(4x - 7)}}{\cancel{(4x - 7)}} \\ \\ = 2[/tex]

Answer:

B

Step-by-step explanation:

62x4=248

4x2=8

6x4=24 and carry the 0 and get 240

240+8=248 and you get B

Answer:

x = 35°

Step-by-step explanation:

sin x = cos (90° - x)

sin 55° = cos (90° - 55°)

sin 55° = cos 35°

x = 35°

Answer: 19

Step-by-step explanation:

As per the model created by Jack; f(x) determines the area and x represents length so f(3) = 9+9+1

Therefore, f(3) = 19

Let's see

[tex]\\ \rm\rightarrowtail 1-sinx\neq 0[/tex]

[tex]\\ \rm\rightarrowtail sinx\neq 1[/tex]

[tex]\\ \rm\rightarrowtail x\neq \dfrac{n\pi}{2}[/tex]

So

[tex]\\ \rm\rightarrowtail Domain\in R-\left\{\dfrac{n\pi}{2}\right\}[/tex]

Answer:

Top left.

Step-by-step explanation:

Answer:

y = -3

Step-by-step explanation:

y = | x | - 4

y = | -1 | - 4

y = 1 - 4

y = -3

Comment any questions!

$7,015.11

Depth meanings:

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

[tex]\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{3.7\%}{2})^{(2)(15)}}[/tex]

[tex]\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{0.037}{2})^{(2)(15)}}[/tex]

[tex]\rightarrow \sf P = 7015.113646[/tex]

Answer:

24 cubic inches

Step-by-step explanation:

Volume is side x side x side. You already have done side x side so it is just side x area.

Answer: 5/2

Step-by-step explanation:

Answer:

[tex]x=2; y=1[/tex]

Step-by-step explanation:

Let's remember that if we replace one equation in a system with a linear combination of the equations (ie adding or subtracting them together, after multiplying them with some nice numbers) we are left with an equivalent system. So let's add and subtract them together, and use the new equations to work with.

[tex]I+II: 2x+2y=6\\I-II:200x-200y=200[/tex]

Better, now let's simplify the expression and let's use the new system

[tex]x+y=3\\x-y=1[/tex]

Done. At this point you can use whatever method you like to solve the system to get to the final solution. Adding and subtracting works great, and you get [tex]x=2, y=1[/tex] which, if you check by replacing in the original, is indeed a valid solution.

✰ Given Information :-

⠀

⠀

✰ To Find :-

⠀

⠀

✰ Formula Used :-

⠀

[tex] \qquad \star \: \red{ \underline{ \boxed{ \sf Time = \dfrac {Distance} {Speed} }}} \: \star[/tex]

⠀

✰ Solution :-

⠀

Putting the values in the formula, we get,

⠀

[tex] \sf \longrightarrow Time = \dfrac{80 }{32} \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = \cancel{\frac{80}{32} } \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = \dfrac{10}{4} \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = 2.5 \: hrs \\ \\ [/tex]

Thus, the time taken to travel 80 km with that speed is 2.5 hours.

⠀

[tex] \underline{ \rule{227pt}{2pt}}[/tex]

⠀

The value of x in the special right triangle is 39.60 ft.

Right angle triangle has one of its angles as 90 degrees. The side and angles can be found using trigonometric ratios.

Therefore, let's find the base of the triangle with 30 degrees.

sin 30° = opposite / hypotenuse

1 / 2 = 7 / b

b = 14 ft

Let's use the value(14 ft) to find the height of the biggest triangle.

sin 30 = opposite / hypotenuse

sin 30 = 14 / h

0.5h = 14

h = 14 / 0.5

h = 28 ft

Therefore, let's find the value of x .

sin 45° = 28 / x

x = 28 / 0.70710678118

x = 39.5979797464

x = 39.60 ft

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Answer:

Step-by-step explanation:

The value of x in the triangle is 205.24 calculated by using tan function.

By using tan function we find the value of x.

Let us divide x to two parts which includes two right triangles.

We know than tan function is a ratio of opposite side and adjacent side.

tan 55 = 106/adj

adj= 106/1.428

adj=74.22

Now let us find the adjacent side length of larger triangle similarly.

tan 39  = 106/ adj

0.809 = 106/adj

adj=106/0.809

adj=131.025

So the value of x is 74.22+131.025

=205.245

Hence, the value of x in the triangle is 205.24.

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Answer: 8.

Step-by-step explanation: There are 4 sizes, so let's say that the sizes are small, medium, large, and extra large.  There are 2 flavors, so let's say that the flavors are chocolate and vanilla.  The possible combinations are below:

As you can see, there are 8 possible combinations that she can choose from as far as 4 sizes and 2 flavors go.

Have a great day! :)

The area of the rectangular base is the amount of space on the rectangular base

The area of the rectangular base is 60 square inches

The question is incomplete; as the diagram is not given.

So, I will apply the concept of similar shapes to determine the area of the rectangular base

To determine the area of the rectangular base, we make use of the following equivalent ratio:

Ratio = Height : Area

This gives

3 : 36 = 5 : Area

Express as fraction

36/3 = Area/5

Evaluate the quotient

12 = Area/5

Multiply both sides by 5

Area = 60

Hence, the area of the rectangular base is 60 square inches

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Answer:

Her average speed would be 62 mph.

Step-by-step explanation:

Step 1. Do 186 divided by 3
Step 2. The answer you would get is 62
Step 3. Label to get 62 miles per hour (mph)
I hope that this helps! :)

Step-by-step explanation:

Displacement = 186 miles

Time taken = 3hours

Average speed = ?

Now,

[tex]average \: speed = \frac{total \: distnce}{total \: time \: } \\ = \frac{186}{3} \\ [/tex]

= 62 miles per hour

Answer:

You have a deficit of $142.20

Step-by-step explanation:

Given

Solving

Answer:

5 startrood 3 endroot units .

The length of YA from the figure is 10√3 units

According to the pythagoras theorem;

YZ² = AZ² + YA²

Given that YZ = 2AZ, hence;

20²  = 10² + YA²

YA²  = 400 - 100
YA²  = 300

YA = √300

YA = 10√3 units

Hence the length of YA from the figure is 10√3 units

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Answer:

MQ = 16.4

By the Parallelogram Diagonals Theorem , MP = PQ

So MQ = 2 · MP

Step-by-step explanation:

Parallelogram Diagonals Theorem

The diagonals of a parallelogram bisect each other, i.e. they divide each other into two equal parts.

P is the point of intersection of the diagonals.

Therefore, MP = PQ and LP = PN

If MP = 8.2, then PQ = 8.2

⇒ MQ = 8.2 + 8.2 = 16.4

Step-by-step explanation:

the volume of this object is the sum of the volume of the 2 blocks.

the large block is a cube of 4×4×4 = 64 ft³

the small block is 1×1×2 = 2 ft³

so, in total, he can fit 64+2 = 66 ft³ of plaster into the mold.

The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.

Area is the amount of space occupied by a two dimensional shape or object.

The area of a circle is given by:

Area = π * diameter²/4

The rug has an area of 40 square feet. Hence:

40 = π * diameter²/4

Diameter = 7.14 feet

The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.

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Hey there!

Here's what happens to the coordinates of a point when it's reflected around the x-axis:

(x, y) --> (x, -y) or (x, -y) --> (x, y)

So the point's x-coordinate hasn't changed.

Here's what happens to the coordinates of a point when it's reflected around the y-axis:

(x, y)--> (-x, y) or (-x, y) --> (x, y)

So the point's y-coordinate hasn't changed.

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power!

Answer: sqrt(285)

Step-by-step explanation: