how many ways are there to seat 8 people around a circular table where two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors?

Answer: B

Step-by-step explanation:

The system of equation for the given condition is: 5+0.03x = 0.10x, where x is the number of texts.

There is no certain number of texts for which two plans are equal.

Let the number of texts for which two plans amount to same number be = x

Plan A: $5.00 per month charge along with a charge of $0.03 per text.

So, Plan A: 5+0.03x

Plan B: No per month charge but a charge of 0.10 per text.

Plan B: 0.10x

Since the plans amounted to same for x texts. So, the suitable system of equation is,

5+0.03x = 0.10x

Solving the equation we get,

0.10x - 0.03x = 5

0.07x = 5

x = 5/0.07 = 71.42 (approximately)

Since the number of texts cannot be decimal number so there is no such number of texts for which plans are equal.

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Answer:

j = 0.4

Step-by-step explanation:

hope it helps

To answer this question, you should combine like terms:

Like terms are two or more terms that share the same variable.

J is the variable in this question so add 0.9j to both sides of the equation to get j on one side:

-0.1j + 0.8 = 0.76

Now subtract 0.8 from both sides to isolate j on one side of the equation:

-0.1j = -0.04

Divide both sides by -0.1 to isolate j and your answer should be:

Answer: j = 0.4

a = -2 is the value of linear equation .

What are examples of linear equations?

Step 1 - Write the equation.

3/a + 2 - 6a/a² - 4 = 1/a - 2

Step 2 - rewrite the equation.

3/a + 2 - 6a/a² - 4 = 1/a - 2

Step 3 - Take the LCM.

3(a- 2) - ( a + 2 )/a² - 2² = 6a/a²-4

Step 4 - Further simplify the above expression

3a - 6 - a - 2/a² - 4 = 6a/a² - 4

Step 5 - Cancel out the denominator of both sides and then further simplify.

2a - 8 = 6a

a = -2

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The complete question is -

A student solves the following equation and determines that the solution is −2. Is the student correct? Explain.

3/a + 2 − 6a/a2 − 4 = 1/a − 2

Answer:

9x-4

Step-by-step explanation:

Answer:

458.7 cm

Step-by-step explanation:

to find circumference we multiply diameter by pi

146(pi)

458.673

And we round to 1 d.p.

458.7

Hopes this helps please mark brainliest

The pair of triangles that can be used to show that the slope of line a is same everywhere is upper half triangles

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees

The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h.

The pair of triangles in choice C (shown in the figure below) demonstrates that line a has a constant slope throughout.

Let's investigate:

Rise/run = slope

Regarding the initial lower triangle:

Rise = 3.5

Run = 4.5

Slope = 3.5/4.5 ≈ 0.8

For the upper second traingle:

Rise = 4

Run = 5

Slope = 4/5 = 0.8

As a result, it demonstrates that the graph's line's slope is constant throughout.

The pair of triangles that can be used to show that the slope of line a is same everywhere is upper half triangles

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Answer:

1.90°

2.30°

3.60°

Step-by-step explanation:

calculate it using the distance and angle

which is division

The cost of materials for the least expensive such container is $327.081  .

In the question ,

it is given that

the volume of the container = 10 m³ .

let the width of the container = x

so , the length of the container = 2x

So , base area = 2x*x = 2x²

cost for base = $20

cost for the sides = $12

Since the volume is 10 m³

Volume = base area *  height

10 = 2x² * h

h = 10/2x²

h = 5/x²

The cost of making the container

cost of base = 2x² * (20) = 40x²

cost of sides = [2*2x*(5/x²) + 2*x*(5/x²)](12)

= 360/x

the total cost of the container [tex]=[/tex] cost of base [tex]+[/tex] cost of sides

= 40x² + 360/x

= 40( x² + 9/x)

to get the minimum cost , we differentiate with respect to x and equate to 0

= 40 ( 2x - 9/x²)

2x - 9/x² = 0

2x³ = 9

x³ = 9/2

x³ = 4.5

x = 1.651

Substituting x in the cost equation ,

we get

Cost = 40x² + 360/x

= 40(1.651)² + 360/(1.651)

= 109.032 + 218.049

= 327.081

Therefore , The cost of materials for the least expensive such container is $327.081  .

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The recursive formula for sequence starting with 12, 6 is, [tex]a_1=a_0-\frac{a_0}{2}[/tex].

What is recursive formula?

Any term of a series can be defined by its preceding term in a recursive formula (s).

For instance: An arithmetic series has the recursive formula [tex]a=a_n_-_1+d[/tex] . [tex]a_n=a_n_-_1r[/tex] is the recursive formula for a geometric sequence.

Given two terms are, 12, 6.

The first term is 12, so [tex]a_0=12[/tex].

The second term is 6, which is half of the first term.

So, [tex]a_1=a_0-\frac{a_0}{2}[/tex]

Therefore, the recursive formula for the sequence starting with 12, 6 is

[tex]a_1=a_0-\frac{a_0}{2}[/tex].

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Answer:

The perpendicular slope is the negative reciprocal of the original slope:

For example: the perpendicular slope for y/x is -x/y

In this case, we want the slope from x +4y = 28

x +4y = 28

4y = 28 - x

y = 7 -x/4

so the answer is: 4/x

Box 1 = 8

Box 2 = 2

If he earned $64 in 8 hours then dividing by 64 by 8 will tell us how much he earned in 1 hour. That gives $8

Using that we can then divide the number of dollars by the amount he receives in 1 hour to see how many hours it was.

So $16 / $8 per hour gives 2 hours

Step-by-step explanation:

both roots are square roots.

if we write the 2 or leave the base of the root blank, it both means square root.

so, we have

sqrt(15) / sqrt(3)

we can combine them into

sqrt(15/3) = sqrt(5) = 2.236067977...

Answer: 422.39

Step-by-step explanation:

To find the shaded region (I'm assuming it's the area inside the circle but outside the rectangle), subtract the area of the rectangle from the area of the circle.

The formula for circle area: πr^2

r is the radius, and it is given that r = 12, so the area of the circle is:

π * 12^2    --->    144π    is the area of the circle

Next, find the area of the rectangle: 3 * 10 = 30

Finally, find subtract the area of the rectangle from the area of the circle to find the shaded region:

144π - 30 ≈ 422.39

The coordinates of the point will be (5 , 5).

Section formula is used to find coordinates of a point when a point divides the line segment externally or internally.

For a line segment A ([tex]x_{1} , y_{1}[/tex]) and B ([tex]x_{2} , y_{2}[/tex]) getting divided by point C (x , y) in ratio m : n the formula is given as

x = [tex]\frac{mx_{2} + nx_{1} }{m + n}[/tex]             y = [tex]\frac{my_{2} + ny_{1} }{m + n}[/tex]

Now in the question it is given that C from point A is twice the distance from point B which means ratio of A:B IS 2:1

A = (1 , 3)

B = (7 , 6)

by applying the formula

x = (2*7 + 1*1) / 2+1

x = 15/3

x = 5

y = (2*6 + 1*3) / 2+1

y = 15/3

y = 5

Therefore the coordinates of C will be (5 , 5)

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The equation of the line is - 175 x + 2 y = - 500

From the question, we have

Point 1 :

x-coordinate, x1 = 6

y-coordinate, y1 = 275

Point 2 :

x-coordinate, x2 = 8

y-coordinate, y2 = 450

We know that,

y-275 = (275-450)/(6-8)*(x-6)

y-275 = 175/2*(x-6)

- 175 x + 2 y = - 500

Slope of a Line :

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.

where "m" represents a line's slope.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

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Expression equivalent to log 9⁵ is 5 log9.

Equivalent is not the same as equal in mathematics. While equivalent indicates similar but not the same, equal means the same in all respects. For instance, 1 + 1 is equivalent to 2, even if 2 is said to be equal to 2. Equivalent value or dated value refers to the value of an original sum at any given moment. The original amount and interest accrued up to the dated value date are combined to create the comparable payment. Money amounts are not directly comparable if they are payable or due at separate times.

Given,

Expression equivalent to log 9⁵

a) 5 log9

Expression equivalent to log 9⁵ is 5 log9.

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If a washer and dryer cost $750 and the cost of the washer is two times the cost of the dryer, then the cost of the dryer $250

The total cost of a washer and dryer combined = $750

The cost of the dryer = x

The cost of the washer is two times the cost of the dryer.

The cost of the washer = 2x

Then the equation will be

x + 2x = 750

Add the like terms of the equation

3x = 750

Move 3 to the right hand side of the equation

x = 750/3

x = $250

Hence, if a washer and dryer cost $750 and the cost of the washer is two times the cost of the dryer, then the cost of the dryer $250

The complete question is:

A washer and dryer cost $750 combined the cost of the washer is two times the cost of the dryer what is the cost of the dryer?

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The nth term of this quadratic sequence 3, 8, 15, 24, 35, … is 2n

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.

Confirm if the sequence is quadratic and this is done by finding the second difference

Sequence = 3, 8, 15, 24, 35, …

1st difference = 5, 7, 9, 11

2nd difference = 2, 2, 2

Divide the second difference by 2, and let the value be a

2 ÷ 2 = 1

So the first term of the terms is [tex]n^{2}[/tex]

subtract [tex]n^{2}[/tex] from the sequence gives 2, 4, 6 , 8, 10

the nth term is 2n

Therefore, the nth term is 2n

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Answer:

length = 13 cm and width = 14 cm

Step-by-step explanation:

let n be the length then n + 1 is the width

the perimeter (P) of a rectangle is calculated as

P 2(l + w) ← l is length and w is width

given P = 54 , then

2(n + n + 1) = 54 ( divide both sides by 2 )

2n + 1 = 27 ( subtract 1 from both sides )

2n = 26 ( divide both sides by 2 )

n = 13

n + 1 = 13 + 1 = 14

length = 13 cm and width = 14 cm

Answer:

a number x times by 3

Step-by-step explanation:

yw I hope that helps

The exponential generating function for the sequence of factorials is x! = Γ(x+1) = [tex]\int\limits^{infinity}_0 {t}^{x}{e}^{-t} \, dt[/tex].

We are given a sequence. A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It has members, just like a set. The length of the sequence is defined by the number of elements. The given sequence consists of factorials. The product of all positive integers less than or equal to n, denoted by n!, is the factorial of a non-negative integer n. We need to find the exponential generating function for the given sequence. The sequence is 0!, 1!, 2!, …, n!. The exponential generating function for the sequence of factorials is given below.

x! = Γ(x+1) = [tex]\int\limits^{infinity}_0 {t}^{x}{e}^{-t} \, dt[/tex]

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The equation representing the sum of three consecutive integers as 42 are x [tex]+[/tex] (x [tex]+[/tex] 1) [tex]+[/tex] (x + 2) [tex]=[/tex] 42   and (x - 1) [tex]+[/tex] x + (x [tex]+[/tex] 1) [tex]=[/tex] 42   , the correct option are (a) and (c) .

In the question ,

it is given that ,

the sum of the three consecutive integers = 42

the equations that shows the relationship is only option (a) and option(c) , because

option (a)

x [tex]+[/tex] (x [tex]+[/tex] 1) [tex]+[/tex] (x + 2) [tex]=[/tex] 42

3x + 3 = 42

3x = 39

x = 13

yes , the terms are consecutive and are  13 , 14 , 15 .

option(c)

(x - 1) [tex]+[/tex] x [tex]+[/tex] (x [tex]+[/tex] 1) [tex]=[/tex] 42

3x = 42

x = 14

putting in equation we get 14-1 = 13 , 14 , 14+1 = 15

yes , the terms are consecutive and are  13 , 14 , 15 .

Therefore , The equation representing the sum of three consecutive integers as 42 are x + (x + 1) + (x + 2) = 42   and (x - 1) + x + (x + 1) = 42 .

The given question is incomplete , the complete question is

The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers.

(a) x + (x + 1) + (x + 2) = 42

(b) x + (x + 2) + (x + 4) = 42

(c) (x - 1) + x + (x + 1) = 42

(d) (x - 2) + x + (x + 2) = 42

(e) x + 2 x + 3 x = 42

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The value in dollars of a $3,000 investment after n years is given by f(n) = 3,000(1.05)n.

The value of the investment after 4 years is $12600.

A simple definition of an equation is a mathematical statement that depicts the relationship between two values. In an equation, the equal sign often equates the two values.

From this question we can assume that n = 4.

In the given equation,

F(n)= 3000(1.05)n

After putting the value of n which is 4, it will be:

F(4)= 3000(1.05) × 4 = 12600

Hence, the value of the investment after 4 years in $12600.

There are many different kinds of equations:

• Linear equation

o Equation with one variable

o Equation with two variables

o Equation with three variables

• Polynomial equation

o Monomial equation

o Binomial equation

o Polynomial equation

• Quadratic equation

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The expression that represents the amount of sodium per serving in the new soup is 0.67x milligrams.

The new soup recipe contains 33%, percent less sodium per serving than the old soup recipe. The old soup recipe contained x milligrams of sodium per serving.

The expression that can be used to represent the amount of sodium per serving in milligrams in the new soup can be computed as follows;

Old soup amount of sodium = x milligram

The new soup contains 33% less sodium per serving than the old soup recipe.

Therefore,

amount of sodium per serving in the new soup = x - 33% of x

amount of sodium per serving in the new soup = x - 33 / 100 x

amount of sodium per serving in the new soup = x - 0.33x

Therefore,

amount of sodium per serving in the new soup = x(1 - 0.33)

amount of sodium per serving in the new soup = x(0.67)

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Answer:

BANK A

I=5700.825

T.P=25190.83

BANK B

I=3274.32

P=22764.32

Answer:

x=-4 or x=2

Step-by-step explanation:

2(x+4)(x-2)=0

Subtract 4 from both sides:

(x+4)=0

Simplify:

x=-4

a) The bearing of Wellington from Gisborne is 232°

b) The bearing of Wellington from Auckland is  175.37°

We are given that AW = 410 km and GW = 400 km.

a) AG  is a transversal intersecting two parallel lines N₁A and N₂B and ∠N₁AG = 115°.

Thus;

∠AGN₂ = 180 − 115 = 65°  

since the sum of the interior angles on the same sides of the transversal intersecting two parallel lines are supplementary.

Thus;

∠N₂GW = 65 + 63 = 128°.

The reflex angle;

∠N₂GWW = 360 − 128° = 232°

b) In  △AGW, we can say that by the sine rule;

(sin∠WAG)/WG = (sin∠AGW)/AG  

Plugging in the relevant values;

(sin∠WAG)/400 = (sin∠63°)/410

Solving for ∠WAG gives; ∠WAG = 60.37°

Then;

∠N₁AW = 115 + 60.37

∠N₁AW = 175.37°

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Answer:

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

It has a variable x and its coefficient (-1), the 3 is the constant.

[tex]\Large \boxed{\sf -1}\\\\\\\displaystyle \sf A\ coefficient\ in\ an\ expression\ is\ the\ integer\\ value\ multiplied\ by\ the\ variable.\\\\(-1) \times x + 3[/tex]