how many ways are there to seat four of a group of ten people around a circular table where two seatings are considered the same when everyone has the same immediate left and immediate right neighbor?

Answer:

Step-by-step explanation:

Move 6a to the other side

Subtract 7a and 6a

use inverse operations. So add 3 on both sides

Answer:

a = 6

Step-by-step explanation:

The given equation is,

→ 7a - 3 = 3 + 6a

Now the value of a will be,

→ 7a - 3 = 3 + 6a

→ 7a - 6a = 3 + 3

→ a = 3 + 3

→ [ a = 6 ]

Hence, the value of a is 6.

Answer:

c

Step-by-step explanation:

To find a perpendicular line, you must compare the slopes. With the equation y=2x-5, we're looking for the inverse/opposite slope of -1/2.

Option A still has a slope of 2. Option B, when everything is in the format of mx+b = y format is -x-4=-2y. which gives us 1/2 but not -1/2. C when everything is on the right side gives us -2y=x-6. Divide both sides by -2 to get the y by itself and you're left with y = -1/2x+3. Now we found the equation that gives us the -1/2 slope we were looking for.

The largest area that can be enclose in straight wall is 2450 m².

Let 'x' be the length of rectangle.

Let 'y' be the width rectangle.

Perimeter =  140 meters

2x + y = 140      

y = 140 - 2x

Area = xy

Put the value of y in area.

Area = x(-2x + 140)

Area = -2x² + 140x

Differentiating the area with respect to x.

dA/dx = -4x + 140

Put dA/dx = 0 to get the critical point.

-4x + 140 = 0

x = 140/4

x = 35

Largest area at x = 35.

y = 140 - 2x

y = 140 - 2×35

y = 70

Area = xy

Area = 70×35

Area = 2450 m²

Thus, the largest area that can be enclose in straight wall is 2450 m².

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Answer:

B and D

Step-by-step explanation:

A is wrong because x has a negative exponent

C is wrong because x is a denominator

The equation of the line passing through

(1) point (-6, -3) and m = -1 is y = -x -9  .

(2) point (-7 , 6) and m = 0 is  y = 6 ,

(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3  .

the graph of the line is shown below .

In the question ,

point on the line and slope of the line is given

So , equation will be

Part(1)

(-6, -3), m = -1

(y -(-3)) = -1(x -(-6))

y + 3 = -1(x + 6)

y + 3 = -x - 6

y = -x -6 -3

y = -x -9

the equation is y = -x -9  .

Part(2)

(-7, 6), m = 0

(y - 6) = 0(x -(-7))

y - 6 = 0(x + 7)

y - 6 = 0

y = 6

the equation is y = 6

Part(3)

(-2, 11), m=4/3

(y - 11) = (4/3)(x -(-2))

y - 11 = (4/3)x + 8/3

y = (4/3)x + 8/3 + 11

y = (4/3)x + 41/3

the equation is y = (4/3)x + 41/3

the graph of all the three equations are shown below .

Therefore , The equation of the line passing through

(1) point (-6, -3) and m = -1 is y = -x -9  .

(2) point (-7 , 6) and m = 0 is  y = 6 ,

(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3  .

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The total amount paid in dollars per hour is $19.

Unitary Method:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

It is given that the total amount given by the uncle is $133 for the work done by Barn for 7 hours.

We have to find the amount paid per hour.

Total amount given = $133

Number of hour Barn work = 7 hours

Amount paid per hour = 133/ 7

= $ 19

Therefore the amount paid per hour is $19.

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If the equation 2(x-7) = 36, then the value of x is 13 and 1

The equation is

[tex](x-7)^2[/tex] = 36

The equation is defined as the statement the connect the two expression with an equal sign.

We know the square of 6 is 36

[tex]6^2[/tex] = 36

Substitute the value in the equation

[tex](x-7)^2=6^2[/tex]

Apply square root in the both side of the equation

[tex]\sqrt{(x-7)^2} = \sqrt{6^2}[/tex]

Then the equation will become

x - 7 = ± 6

If the value is +6

x - 7 = 6

Add both side of the equation by 7

x - 7 +7 = 6+7

x = 13

If the value is -6

x - 7 = -6

Add both side of the equation by 7

x - 7 + 7 = -6 + 7

x = 1

Hence, If the equation 2(x-7) = 36, then the value of x is 13 and 1

The complete question is:

Given [tex](x-7)^2=36[/tex], find the value of x.

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The probability that both Rachel and Robert are in the picture is 3/16.

The terms probability and possibility are interchangeable. It is a mathematical branch concerned with the occurrence of a random event. The value is between 0 and 1. In mathematics, the probability was introduced to predict the likelihood of events occurring.

Given that

Rachel and Robert both begin at the same point

Rachel completes a lap every 90 seconds.

Robert completes a lap every 80 seconds.

The photographer captures 1/4th of the track, centered on the starting line.

As a result, the photo captures 1/8th of the track on either side of the starting line.

The photographer captures it between 10 and 11 minutes, or 600 and 660 seconds.

Let us calculate the time interval between 600 and 660 seconds during which Rachel and Robert will be running in the quarter-length region of the track centered on the starting line. Specifically, 1/8th of the track length on each side of the starting line.

Robert will complete 1/8th of a lap in 10 seconds. So, between 630 and 650 seconds, Robert will be in the area of the ground captured by the photographer.

Rachel finishes one lap in 90 seconds. As a result, Rachel will take the starting line at the 630th second (after 7 laps).

Rachel will complete 1/8th of a lap in 90/8 seconds. So, Rachel will be in the area of the ground captured by the photographer from (630 - 90/80) seconds to (630 + 90/80) seconds.

i.e., for a duration of 90/80 seconds out of the 60 seconds both of them are in the frame captured by the photographer.

Required probability = {time window in which both Rachel and Robert are in the favorable zone}/{time window in which the photographer captures the picture}

= {90/8}/60

= 3/16

Therefore the probability that both Rachel and Robert are in the picture is 3/16

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Answer:

weight = 57 Kg

Step-by-step explanation:

We require to find the length of the diagonal (d) piece of metal

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

d² = 8² + 6² = 64 + 36 = 100 ( take square root of both sides )

d = [tex]\sqrt{100}[/tex] = 10

the length of the 5 pieces is then

8 + 8 + 6 + 6 + 10 = 38 m

the total weight of the 5 pieces is then

weight = 38 × 1.5 Kg = 57 Kg

The number of dime and the number of quarters that Aiden have are 10 and 8 respectively.

Aiden ha $3 worth of dime and quarter. Aiden has 2 more dime than quarter. The number of dime and the number of quarter that Aiden has can be calculated as follows:

let

x =  number of quarter

y = number of dime

Therefore,

y = 2 + x

y - x = 2

0.1y + 0.25x = 3

Multiply equation(ii) by 10

y - x = 2

y + 2.5x = 30

subtract equation(i) from equation(ii)

3.5x = 28

x = 28 / 3.5

x = 8

Hence,

y = 2 + 8

y = 10

Therefore,

number of dime  = 10

number of quarters = 8

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Ella answer makes sense because the value of  ? is 4

Given: the equation 32 divided ? =8 she says the value of ? is 4

32 / ? = 8    

Let x represent ? in the equation, thus:

32 / x = 8         cross multiply

8x = 32

x = 32/8

x = 4

Since x = 4. This implies ? = 4

Also, the value that divides 32 to give is 4

Since the value of ? is 4. Therefore, Ella's answer makes sense

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Each of Aaron's pals receives nine (9) rocks in total.

The question states that,

Aaron collects a total of 54 rocks at the beach.

He wants to give an equal number of rocks to six (6) of his friends.

It is given that let 'r' be the number of rocks each of his friends gets.

The required equation is;

Rock's Aaron's friends get,

→ 6*r = 54

   r = 54/6

   r = 9

The total number of rocks each of Aaron's friends get is 9.

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The correct option ; Quadrilateral, has the given information describing quadrilateral UVWX.

For the given values in the question;

In the quadrilateral UVWX

As, none of the sides are equal to other and none of the angles are equal to the other.

Thus, the this information shows the values are given for quadrilateral.

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The expected value of the bet if the odds that the horse will win are 3 to 12 is $18.8

What is expected value?

Expected value is the predictive value of all the possibilities that occur by multiplying the value by the probability.

Winning probability = odds / total outcomes

= 3 / (3 + 12)

= 3 / 15

= 0.2

Now, we need to calculate expected value.

= winning probability x amount won - losing probability x amount lost

= 0.2 x 110 - (1 - 0.2) x 4

= 22 - 3.2

= 18.8

Thus, the expected value of the bet if the odds that the horse will win are 3 to 12 is $18.8

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The value of k is 4.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Volume= 16

Width = 4

So, we can write the relation as

Volume= k (width)

k = Volume/ width

k= 16/4

k = 4

Hence, the value of k is 4.

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The inequality that represents the the possible numbers of x pairs of socks you can buy when you buy 2 pairs of sneakers, using a system of equations, is of:

y ≤ 7.

A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of the problem from which the system was built.

For this problem, the variables are given as follows:

You have a $250 card to use at a sporting goods store. Each pair of sneakers is worth $80 and a pair of socks costs $12, hence the inequality regarding the total spending is:

80x + 12y ≤ 250.

When two pairs of sneakers are bought, we have that:

x = 2.

Hence the inequality regarding how many pairs of socks can be bought is:

80(2) + 12y ≤ 250.

160 + 12y ≤ 250.

12y ≤ 90

y ≤ 90/12

y ≤ 7. (rounded down, as you can buy 7 pairs of socks but not 8).

The cost of a pair of socks is of $12.

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Solve for 12 - h(7)

First find h(7)

h(7) = 7^2+3(7)-2

h(7) = 49 + 21 - 2

h(7) = 68

12 - 68 = - 56

12 - h(7) = -56.

I'm not sure if the question wants h(-56) as well, but just plug that in.

H(-56)=2966

hope this helps :)

The difference between an independent sample and a dependent sample is that the dependent sample for one set of items is paired measurement while measurements made on two samples are termed an independent sample.

In statistics, while considering two samples and conducting a hypothesis test, one should be aware of which type of test should be conducted based on samples whether they are dependent or independent. If the value of another sample is affected by any one sample then the samples are dependent. If no information can be deduced from the other sample using one sample then the samples are independent.

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The length and width of a rectangle that maximises the enclosed area are 800 yards. The maximum area is 640,000 square yards.

In the given question we have to find the maximum area of the rectangular area.

Liana has 3200 yards of fencing to enclose a rectangle.

As we know that the perimeter of rectangle

P= 2(l+b)

Let length of the rectangle is x yards and width is y yards.

So the equation should be

2(x+y) = 3200

Divide by 2 on both side we get

x+y = 1600................(1)

From the area of rectangle is

A = xy

From the equation the value of y is 1600-x.

Now putting the value of y

A = x(1600-x)

A = 1600x-x^2

On differentiating

dA/dx = 1600-2x

Putting dA/dx=0

1600-2x=0

Subtract 1600 on both side we get

-2x= -1600

Divide by -2 on both side we get

x = 800 yards

Now putting the value of x in the y=1600-x

y=1600-800

y=800 yards

So the maximum area is

A= 800*800

A= 640,000 square yards

Hence, the length and width of a rectangle that maximises the enclosed area are 800 yards. 640,000 square yards is the maximum area.

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Answer:

A. $760

Step-by-step explanation:

Price: $8

Amount of goods; 95

revenue = price x total units

$8 x 95 = $760 revenue

Answer:

Side BC is congruent to side YZ

Answer:

y = - 2x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 11) and (x₂, y₂ ) = (6, - 11) ← 2 points on the line

m = [tex]\frac{-11-11}{6-(-5)}[/tex] = [tex]\frac{-22}{6+5}[/tex] = [tex]\frac{-22}{11}[/tex] = - 2

the line crosses the y- axis at (0, 1 ) ⇒ c = 1

y = - 2x + 1 ← equation of line

The equation of the line parallel to the equation y = - 2 / 3 x + 5 is 2x - 3y = 21

The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.

Lines are parallel when they have the same slope.

Using slope intercept form,

y = mx + b

where

Therefore,

y = - 2 / 3 x + 5.

The slope of the equation is - 2 / 3.

Hence, let's find the equation that has the same slope as - 2 / 3. First, we will have to represent the equation in slope intercept form.

2x - 3y = 21

add 2x to both sides of the equation

2x + 2x - 3y = 21 + 2x

- 3y = 2x + 21

divide both ides by - 3

- 3y  / - 3 = 2x / -3 + 21 / - 3

y = - 2 / 3 x - 7

Therefore, the slope is - 2 / 3 , the equation is 2x - 3y = 21

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8.77 ft/sec  is the tip of her shadow moving with a speed of 6 ft/sec .

What is speed, for instance?

Let H = the height of the pole.

h = the height of the woman.

x = the length of the woman's shadow.

s = the distance from the pole to the woman.

By similar triangles,  H/h = (s + x)/x  or  Hx = h(s + x).

Differentiating, H dx/dt = h(ds/dt + dx/dt)

19 dx/dt = 6(6 + dx/dt) = 36 + 6 dx/dt

13 dx/dt = 36

dx/dt = 36/13 ft/sec = 2.77 ft/sec for how fast her shadow is lengthening.

The speed of the tip of her shadow would be this speed added to her traveling speed: 2.77 + 6 = 8.77 ft/sec.

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The length of the table is 1.51 meters.

Allan is measuring his dining room table to make a tablecloth. The table is 0.45 meter longer than it is wide. The width of the table is 1.06 meter. We need to find out the length of the table.

Let the length of the table be represented by the variable "L". In the context of a mathematical problem or experiment, a variable is a quantity that may vary. The length of the table is the sum of the width of the table and the difference between the two quantities.

L = 1.06 + 0.45

L = 1.51

Hence, the length of the table is 1.51 meters.

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The capital invested by q is $60,000 when p invested capital of $40,000.

According to the question,

We have the following information:

The ratio of the profits earned by by p and q is 2:3.

Amount invested by p = $40,000

Now, let's take the amount invested by p to be $2x and the amount invested by q to be $3x.

So, we have the following expression:

2x = 40000

x = 40000/2

x = $20000

Now, putting the value of x in 3x in order to find the amount invested by q:

3*20,000

$60,000

Hence, the amount invested by q is $60,000 when p invested capital of $40,000.

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Answer:

29

Step-by-step explanation:

1+3= 4

3+4=7

4+7=11

7+11=18

11+18=29

The measure of width of given figure is 2 units. Therefore, option B is the correct answer.

From the given figure, the length is 9 units and the width is 1 unit.

Length is defined as the measurement or extent of something from end to end. In other words, it is the larger of the two or the highest of three dimensions of geometrical shapes or objects. For example, a rectangle has its dimensions as length and breadth.

From the figure, the width is 1+1=2 units

The measure of width of given figure is 2 units. Therefore, option B is the correct answer.

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The nature of the roots for y=2x²- 5 is there are 2 distinct real roots.

What is the nature of roots?

The nature of the roots of the quadratic can fall into one of three categories depending on the value of the discriminant

Δ > 0 means there are 2 distinct real roots.

Δ = 0 means there are 2 equal real roots or 1 distinct real root.

Δ < 0 means there are no real roots, but 2 complex roots.

Here,

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

b² - 4ac

Substitute the values of a, b, and c.

Evaluate the given equation to find the discriminant, we get

= 0 - 4×2×(-5)

= 41

> 0

Since the discriminant is greater than 0

Hence, there are 2 distinct real roots.

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