Choose the correct name for the set of numbers.
{-₁ √11, 21.6555..., 16,

If this trend continues, the total books the author would have sold over the first 12 months is 157,810 books.

In this scenario, we would calculate the total books sold by this author over the first 12 months as follows;

First month = 19,000 books.

Second month; 19,000 × (1 - 7)% = 19,000 × 93/100 = 17,670 books.

Third month; 17,670 × (1 - 7)% = 17,670 × 93/100 = 16,433 books.

Fourth month; 16,433 × (1 - 7)% = 16,433 × 93/100 = 15,283 books.

Fifth month; 15,283 × (1 - 7)% = 15,283 × 93/100 = 14,213 books.

Sixth month; 14,213 × (1 - 7)% = 14,213 × 93/100 = 13,218 books.

Seventh month; 13,218 × (1 - 7)% = 13,218 × 93/100 = 12,293 books.

Eigth month; 12,293 × (1 - 7)% = 12,293 × 93/100 = 11,432 books.

Ninth month; 11,432 × (1 - 7)% = 11,432 × 93/100 = 10,632 books.

Tenth month; 10,632 × (1 - 7)% = 13,218 × 93/100 = 9,888 books.

Eleventh month; 11,432 × (1 - 7)% = 11,432 × 93/100 = 9,196 books.

Twelveth month; 9,196 × (1 - 7)% = 9,196 × 93/100 = 8,552 books.

Next, we would add all of the books sold in each month together;

Total books sold = 19,000 + 17,670 + 16,433 + 15,283 + 14,213 + 13,218 + 12,293 + 11,432 + 10,632 + 9,888 + 9,196 + 8,552

Total books sold = 157,810 books.

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The ratio of the original height of candle x to the original height of candle y is 13:8. This means that candle x is 13/8 times taller than candle y.

The ratio of the original height of candle x to the original height of candle y can be found by considering their burning rates and the time it takes for them to reach the same length. Based on the given information, candle x burns at a rate of 1/13 of its height per hour, while candle y burns at a rate of 1/24 of its height per hour. After burning for 9 hours, both candles have the same length.

Let's assume the original height of candle x is Hx and the original height of candle y is Hy. Candle x burns at a rate of 1/13 of its height per hour, so after burning for 9 hours, its remaining height would be (1 - 9/13)Hx = (4/13)Hx. Similarly, candle y burns at a rate of 1/24 of its height per hour, so after burning for 9 hours, its remaining height would be (1 - 9/24)Hy = (15/24)Hy.

Given that both candles have the same length after burning for 9 hours, we can equate their remaining heights:

(4/13)Hx = (15/24)Hy

To find the ratio of the original heights, we divide both sides of the equation by Hy:

(4/13)Hx / Hy = (15/24)

Simplifying the equation, we get:

Hx / Hy = (15/24) * (13/4) = 13/8

Therefore, the ratio of the original height of candle x to the original height of candle y is 13:8. This means that candle x is 13/8 times taller than candle y.

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In a cubic polynomial function f is defined by f(x) = 4x³ + ax² + bx + k, where a, b, k, are constants and has a local minimum at x = -2 and a local maximum at x = 0, then values of a and b is 12 and 0 respectively. If integrate of f(x)dx = 32 from 0 to 1, then value of k is 27.

The given cubic polynomial function is

f(x) = 4x³ + ax² + bx + k

f'(x) = 12x² + 2ax + b

f''(x) = 24x + 2a

At local maximum f' = 0

f'(0) = 12×(0)² + 2a×(0) + b = 0

b = 0

At local minimum, f' = 0

That is f'(-2) = 0 and f''(-2) > 0

f'(-2) = 12×(-2)² + 2a×(-2) + b = 0

48 - 4a + b = 0

4a - b = 48  

a = 12

Therefore, f(x) =  4x³ + 12x² + k

Integrate f(x)dx = 32 from 0 to 1, that is

∫₀¹ f(x)dx = 32

∫₀¹ (4x³ + 12x² + k) dx = 32

[ x⁴ + 4x³ + kx ]₀¹ = 32

(1⁴ - 0⁴) + 4(1³ - 0³) + k(1 - 0) = 32

1 + 4 + k = 32

k = 27

-- The question is incomplete, answering to the question below--

"A cubic polynomial function f is defined by f(x) = 4x³ + ax² + bx + k, where a, b, k, are constants. The function f has a local minimum at x = -2 and a local maximum at x = 0.

A. Find the values of a and b

B. If you integrate f(x)dx = 32 from 0 to 1, what is the value of k?"

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Scott pays his nephew $10 per hour, and he initially had $900 for extra labor. Then the correct option is C.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The graph below illustrates how much Scott must spend on additional labor to hire someone to assist him as he works on his property. He recruited his nephew to work on weekends and after school.

From the graph, the two points are (0, 900) and (800, 10). Then the slope of the line is given as,

m = (900 - 800) / (0 - 10)

m = - 100 / 10

m = - 10 dollars per hour

Then the equation is given as,

y = - 10x + 900

Scott pays his nephew $10 per hour, and he initially had $900 for extra labor. Then the correct option is C.

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The slant height of the pyramid is approximately 5.657 cm.

Let's denote the side length of the square base of the pyramid as 's'.

According to the given information, the height of the pyramid is half the side length of the pyramid's base. This means the height (h) is equal to (1/2) * s.

To find the slant height (l) of the pyramid, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.

In our case, the slant height (l) is the hypotenuse, and the height (h) and half the side length of the base (s/2) are the other two sides.

Using the Pythagorean theorem:

l^2 = h^2 + (s/2)^2

l^2 = [(1/2) * s]^2 + (s/2)^2

l^2 = (1/4) * s^2 + (1/4) * s^2

l^2 = (1/2) * s^2

Taking the square root of both sides:

l = √[(1/2) * s^2]

l = (1/√2) * s

Substituting the value of s = 8cm into the equation:

l = (1/√2) * 8

l ≈ 5.657 cm

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Answer:

n=3 then open bracket

Step-by-step explanation:

3n-(2+n)

=3x4-(2+4)

=12-6

=6

A continuous variable does allow fractional amounts. a discrete variable  does not allow fractional amounts.

Which variables require boundaries, also known as real limits, in their measurement scales?

A researcher must utilize genuine limits, which are boundaries that are exactly halfway between adjacent categories, to specify the units for a continuous variable.

What distinguishes a ratio scale from an ordinal scale?

For continuous data, what kind of data would you use?

Line graphs, skews, and other data analysis techniques are used to measure continuous data. One of the most popular kinds of continuous data analysis is regression analysis.

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Answer:0 = 3x - 21

Step-by-step explanation:

From this given function we can take an  

x

common from its expression

i.e  

x

2

−

6

x

=

x

(

x

−

6

)

As we know that the product of two numbers is zero,when either one of them is zero

then in the above expression that we just factorised

the function can be zero when either  

x

=

0

or when  

x

=

6

i.e when  

x

=

0

,  

0

(

0

−

6

)

=

0

when  

x

=

6

,  

6

(

6

−

6

)

=

6

(

0

)

Finally, our prize of all that math, the zeroes of the function are  

0

and  

6

these numbers are called the zeroes of the function because when you put these values in  

x

the function gives zero.

Answer:

1/1

Step-by-step explanation:

up 1 over 1

Answer:

the slope in the graph is m=1

Step-by-step explanation:

m=1

Transformation includes changing the size and position of a shape.

The transformations that produce triangle U from triangle T, are:

(c) Dilation by a scale factor of 2, and a reflection over the x-axis

From the graph that shows the relationship between both triangles (see attachment), we have the following observations.

This means that: the transformations from triangle T to triangle U, are:

Option (c) Dilation by a scale factor of 2, and a reflection over the x-axis

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Answer:

Dilate by a scale factor of 2 and reflect over the x-axis

Step-by-step explanation:

Correct on i-ready :)

Chris and Mary, who live 14 miles apart, will meet after apart, will meet after a certain number of hours. Chris walks at a rate of 3 mph, and Mary walks at a rate of 4 mph.

To determine the number of hours it takes for Chris and Mary to meet, we can use the concept of relative speed. The relative speed is the sum of their individual speeds, which is 3 mph + 4 mph = 7 mph.

Since they are walking towards each other, their combined speed of 7 mph represents the rate at which the distance between them is decreasing. The distance between them is initially 14 miles. We can use the formula: time = distance / speed to find the number of hours it takes for them to meet.

Applying the formula, time = 14 miles / 7 mph = 2 hours. Therefore, Chris and Mary will meet after 2 hours of walking.

The concept of relative speed helps us determine how the distance between two objects changes over time when they are moving towards each other.

By considering their individual speeds and using the formula for time, we can calculate the time it takes for Chris and Mary to meet. In this case, their combined speed of 7 mph allows them to cover the initial distance of 14 miles in 2 hours, resulting in their meeting point

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The value of x is 17

The congruent arcs are (b) PQ and SR

The radius is 12 units

The value of PQ is 4

The length YZ is 19 units

In this question, we make use of the property of congruent sides

So, we have

3x - 24 = x + 10

When evaluated, we have

2x = 34

Divide by 2

x = 17

By the definition of congruent arcs, congruent arcs are arcs that have equal measures

In this figure, the congruent arcs are PQ and SR i.e. (b) PQ and SR

The radius of the circle is calculated as

r² = (25 + r)² - 35²

When expanded, we have

r² = 625 + 50r + r² - 1225

So, we have

50r = 600

Divide both sides by 50

r = 12

In this question, we make use of the property of congruent sides

So, we have

PQ = SR

Where

SR = 4

When evaluated, we have

PQ = 4

The length of YZ in the circle is calculated as

YZ² = (9 + 8)² + 8²

So, we have

YZ² = 17² + 8²

When expanded, we have

YZ² = 289 + 64

So, we have

YZ² = 353

Take the square root of both sides

YZ = 19

Hence, the length YZ is 19 units

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If the gradient of AB is 0, the coordinates of point A and B are (-4, 2) and (6, 2) respectively.

If the gradient of line AB is 0, it means that the line is horizontal. In this case, we can determine the coordinates of points A and B using the information given.

Since the midpoint of line AB is (1,2), we can infer that the average of the x-coordinates of A and B is 1, and the average of the y-coordinates is 2.

Let's assume that point A has coordinates (x₁, y₁) and point B has coordinates (x₂, y₂).

Since the midpoint of line AB is (1,2), we can write the following equations:

(x₁ + x₂) / 2 = 1 (1)

(y₁ + y₂) / 2 = 2 (2)

We also know that the length of line AB is 10 units.

Using the distance formula, we can express this as:

√((x₂ - x₁)² + (y₂ - y₁)²) = 10 (3)

Since the gradient of line AB is 0, the y-coordinates of points A and B must be the same. Therefore, y₁ = y₂. We can substitute this into equations (1) and (2):

(x₁ + x₂) / 2 = 1 (1')

y₁ = y₂ = 2 (2')

Now, let's substitute y₁ = y₂ = 2 into equation (3):

√((x₂ - x₁)² + (2 - 2)²) = 10

√((x₂ - x₁)²) = 10

(x₂ - x₁)² = 100

Taking the square root of both sides, we get:

x₂ - x₁ = ±10

Now, we have two cases to consider:

Case 1: x₂ - x₁ = 10

From equation (1'), we have:

(x₁ + x₁ + 10) / 2 = 1

2x₁ + 10 = 2

2x₁ = -8

x₁ = -4.

Substituting x₁ = -4 into equation (1), we find:

(-4 + x₂) / 2 = 1

-4 + x₂ = 2

x₂ = 6

Therefore, in this case, point A has coordinates (-4, 2), and point B has coordinates (6, 2).

Case 2: x₂ - x₁ = -10

From equation (1'), we have:

(x₁ + x₁ - 10) / 2 = 1

2x₁ - 10 = 2

2x₁ = 12

x₁ = 6

Substituting x₁ = 6 into equation (1), we find:

(6 + x₂) / 2 = 1

6 + x₂ = 2

x₂ = -4

Therefore, in this case, point A has coordinates (6, 2), and point B has coordinates (-4, 2).

To summarize, if the gradient of AB is 0, there are two possible solutions:

A(-4, 2) and B(6, 2)

A(6, 2) and B(-4, 2).

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Answer:  -1 < x < 3

Step-by-step explanation:

\(\dfrac{5}{(x+2)(4-x)}<1\)

Step 1   The denominator cannot equal zero:

x + 2 ≠ 0    and     4 - x ≠ 0

     x ≠ -2                4 ≠ x

Place these restrictive values on the number line with an OPEN dot:

    <----------o-------------------o--------->

                -2                       4

Step 2   Find the zeros (subtract 1 from both sides and set equal to zero):

\(\dfrac{5}{(x+2)(4-x)}-1=0\\\\\\\dfrac{5}{(x+2)(4-x)}-\dfrac{(x+2)(4-x)}{(x+2)(4-x)}=0\\\\\\\dfrac{5-(-x^2+2x+8)}{(x+2)(4-x)}=0\\\\\\\dfrac{5+x^2-2x-8}{(x+2)(4-x)}=0\\\\\\\dfrac{x^2-2x-3}{(x+2)(4-x)}=0\\\\\\\text{Multiply both sides by (x+2)(4-x) to eliminate the denominator:}\\x^2-2x-3=0\\(x-3)(x+1)=0\\x-3=0\quad x+1=0\\x=3\quad x=-1\)

Add the zeros to the number line with an OPEN dot (since it is <):

    <----------o-----o----------o----o--------->

                -2     -1            3      4

Step 3    Choose test points to the left, between, and to the right of the points plotted on the graph. Plug those values into (x - 3)(x + 1) to determine its sign (+ or -):

Left of -2: Test point x = -3: (-3 - 3)(-3 + 1) = Positive

Between -2 and -1: Test point x = -1.5: (-1.5 - 3)(-1.5 + 1) = Positive

Between -1 and 3: Test point x = 0: (0 - 3)(0 + 1) = Negative

Between 3 and 4: Test point x = 3.5: (3.5 - 3)(3.5 + 1) = Positive

Right of 4: Test point x = 5: (5 - 3)(5 + 1) = Positive

          +         +        -          +       +

    <----------o-----o----------o----o--------->

                -2     -1            3      4

Step 4  Determine the solution(s) based on the inequality symbol. Since the original inequality was LESS THAN, we want the solutions that are NEGATIVE.

Negative values only occur between -1 and 3

So the solution is:     -1 < x < 3

Answer:

We can use long division to divide the polynomial (2x³5x² + 3x-6) by the binomial (x+4).

x + 4 | 2x³ + 5x² + 3x - 6

- (2x³ + 8x²)

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

2x² - 3x + 15

____________________

-3x² + 3x

- (-3x² - 12x)

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

15x - 6

- (15x + 60)

----------

-66

Therefore, the quotient is 2x² - 3x + 15, and the remainder is -66.

The 67th term of the arithmetic sequence -17,-23,-29 is -413.

What is the arithmetic sequence?

An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive terms is always the same. This difference is called the common difference, and it can be represented by the variable d.

Given the sequence -17,-23,-29, we can see that the common difference is d = -23 - (-17) = -6

The nth term of an arithmetic sequence can be found using the formula:

a_n = a_1 + (n-1)d

where a_1 is the first term of the sequence, n is the term number and d is a common difference.

For the 67th term, a_1 = -17, n = 67 and d = -6

So the 67th term is:

a_67 = -17 + (67-1) * -6 = -17 + 66 * -6 = -17 - 396 = -413

Hence, the 67th term of the arithmetic sequence -17,-23,-29 is -413.

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Answer: -413

Step-by-step explanation:

Answer:

14 units.

Step-by-step explanation:

Because your trying to find the distance between you add the negative and positive together.

Answer:

y=4x+2

Step-by-step explanation:

Answer:

error= 0.1/2, 0.05

4.8 + 0.05 = 4.85

6.3 + 0.05 = 6.35

4.85 x 6.35 = 30.7975 cm (when rounded, gives 30.80 cm).

Step-by-step explanation:

The approximate mass of air in a typical room with dimensions 5.7m × 3.9m × 3.0m is about 80.14 kg.

To calculate the approximate mass of air in a typical room with dimensions 5.7m × 3.9m × 3.0m, we need to find the volume of the room first. The volume of the room is given by:

Volume = length x width x height = 5.7m x 3.9m x 3.0m = 66.78 cubic meters

Assuming that the air in the room has a density of approximately 1.2 \(kg/m^3\), we can use the formula:

Mass = Density x Volume

where density is in kg/m^3 and volume is in cubic meters.

Substituting the values, we get:

Mass = \(1.2 kg/m^3 x 66.78\) cubic meters

Mass ≈ 80.14 kg

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Therefore, we can see that the UK has a higher population density than Spain.

In mathematics, "square" usually refers to the operation of multiplying a number by itself. When we square a number, we write it as that number raised to the power of 2, or we can use the symbol "^2" to indicate that we are squaring the number.

For example, the square of 3 is. \(3^2\), which is equal to 9. Similarly, the square of -5 is. \((-5) ^2\), which is equal to 25. In general, we can square any real number (positive, negative, or zero) to get a non-negative result.

We can also use the term "square" to refer to a geometric shape that has four equal sides and four right angles, such as a square on a checkerboard or a piece of paper.

by the question.

For the UK:

\(Population density = Population /Area\)

\(= 66,000,000 /95,000\)

\(= 694.74 people per square mile\)

For Spain:

\(Population density = Population / Area\)

\(= 47,000,000 / 195,000\)

\(= 241.03 people per square mile\)

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The correct answer is option A which is y = 25x + 100.

Given the following:

To join a local square dancing group, Jan has to pay a $100 sign-up fee plus $25 per month

We need to write an equation for the cost (y) based on the number of months.

To solve the above problem, the answer is;a. y = 25x + 100

Explanation; Let's break down the problem

The $100 sign-up fee is a fixed cost that is added only once to the monthly fee which is $25. Thus the equation for the cost (y) based on the number of months can be expressed as; y = 25x + 100 where:y is the cost for the number of monthsx is the number of months

Therefore the correct answer is option A which is;y = 25x + 100.

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To join a local square dancing group,

Jan has to pay a $100 sign-up fee plus $25 per month.

The equation for the cost (y) based on the number of months is

y = 25x + 100,

where x is the number of months.

Option A is the correct equation for the cost based on the number of months.

Writing the equation:

y = 25x + 100

Where:

y = Cost based on the number of months

x = Number of months

Therefore, when Jan has been part of the local square dancing group for 1 month, the total cost will be:

$25 * 1 + $100 = $125

And if Jan has been a part of the group for 4 months, then the total cost would be:

$25 * 4 + $100 = $200

Therefore, option A is the correct answer.

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Answer:

792 cm²

Step-by-step explanation:

Surface Area (Cylinder)

⇒ 2πrh + 2πr²

⇒ 2πr (h + r)

Here, r = 9 cm and h = 5 cm.

⇒ 2π × 9 (5 + 9)

⇒ 18π × 14

⇒ 252 x 22/7

⇒ 36 x 22

⇒ 792 cm²

Answer:

A is the correct answer

Answer:

a=2

Step-by-step explanation:

5+14a=9a-5 subtract 9a from both sides

5+5a=-5 subtract 5 from both sides

5a=-10 divide by 5 on both sides

a=-2

hope you do well :)

Answer:

2 hours

Step-by-step explanation: