The function f(x) = 12,000(1.036)x, represented in the table, shows the population of a certain town where x is the number of years after 2008.

Year 2008 2011 2014 2017 2020
Population 12,000 13,343 14,836 16,498 18,344

Find the average rate of change from 2014 to 2017 and interpret its meaning in terms of the context.

−831; represents the average depreciation in the population from 2014 to 2017
831; represents the average growth in the population from 2014 to 2017
−554; represents the average depreciation in the population from 2014 to 2017
554; represents the average growth in the population from 2014 to 2017

The amount of gravel needed to cover the floor of the cube shaped tank to a depth of 1 inch is 0.38 ft^3.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Various forms have various volumes.

Given that the fish tank is a cube that holds 10 ft^3 of water.

The volume of the cube is given by:

V = a³

Substituting the value of 10 in V we have:

a³ = 10

a = 2.15

Now, to gravel at the bottom of the tank will have the following dimensions as height will be 1 inch.

1 inch = 0.083

V = (a)(a)(a)

V = (2.15) (2.15) (0.083)

V = 0.38 ft^3

Hence, the amount of gravel needed to cover the floor of the tank to a depth of 1 inch is 0.38 ft^3.

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Answer: $840

If it's 20% off, it's 80% of it's original price.

80% = 0.8

$1,050 x 0.8 = $840

The use of x^2^k is a more efficient way to multiplying than starting with x and successively squaring.

according to question,

real number = x

positive integer = k

x^2^k

Starting with x and squaring to find x², x⁴, xⁿ

The efficient way of multiplying is

x^2^k

where, k = 1, 2, 3, 4,.....…

check:

when k = 1

x^2^1

= x²

when k = 2

x^2^2

= x⁴

when k = 3

x^2^3

= x^2*2*2

= x^8

Therefore,

x^2^k

is a more efficient way to multiplying.

Integer

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

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If a red balloon costs $0.80, then 9 red balloons costs would be $7.20.

What is an algebraic manipulation?

Algebraic manipulation is the process of rearranging mathematical expressions in order to solve equations or to make them easier to understand. It involves the use of mathematical operations and properties such as addition, subtraction, multiplication, division, and the commutative, associative, and distributive properties.

To find out how much 9 red balloons cost, you need to multiply the cost of one red balloon by the number of red balloons.

So 9 red balloons cost $0.80 * 9 = $7.20

Hence, If a red balloon costs $0.80, then 9 red balloon costs would be $7.20.

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The graph of the polynomial function is given by the following option:

Not C or D.

At z = -3, the function has a zero with an even multiplicity of 2, meaning that the graph of the function turns at z = -3, due to the even multiplicity.

At z = 2, the function has a zero with an odd multiplicity of 3, meaning that the graph of the function crosses the x-axis at z = 2, due to the odd multiplicity.

At z= -4, the function is negative, hence it becomes positive at z = 2 and goes towards infinity.

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If a bicycle is of worth $500 and decreases in value by 7.8% per year , then the function to model this situation is P(n) = 500(0.922)ⁿ  and the value of bicycle after 5 years is  $333.14    .

The price of  bicycle is = $500 ;

the percent decrease in the value per year is = 7.8% = 0.078   ;

let number of years be = "n" years ;

So , the Price of bicycle after "n" years is written as :

⇒ P(n) = 500(1 - 0.078)ⁿ ;

⇒ P(n) = 500(0.922)ⁿ ;

to find the value of bike after 5 years , we substitute n = 5 ;

⇒ P(5) = 500(0.922)⁵  ;

⇒ P(5) = 500 × 0.66627

⇒ P(5) = 333.138334052816

⇒P(5) ≈  $333.14

Therefore , the value of bike after 5 years is $333.14   .

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The y-intercept of the line 11x + 10y = 2 is equal to 1/5.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Based on the information provided about the line, it is represented by this equation;

11x + 10y = 2

By making "y" the subject of formula in the above equation, we have the following:

10y = -11x + 2

By dividing both sides of the equation by 10, we have the following:

y = -11x/10 + 2/10

y = -11x/10 + 1/5.

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The scale factor of a model is, 30 feet in a inch.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

A model of Seattle, Washington space Needle is 20 inches tall The actual Space Needle is approximately 600 feet tall.

Hence, The scale factor of a model is,

⇒ 600 feet / 20 inches

⇒ 30 feet per inches

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Answer: C 150-99

Step-by-step explanation:

The ratio of x:y in simplest form is 5 : 2

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

3.5y = 1.4x

Divide both sides of the equation by 1.4

So, we have

3.5y/1.4 = x

Divide both sides of the equation by y

So, we have

3.5/1.4 = x/y

Express as ratio

x : y = 3.5 : 1.4

Divide by 0.7

x : y = 5 : 2

Hence, the ratio is 5 : 2

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The measure of the longer leg of the triangle is given as follows:

6.93 cm.

The three trigonometric ratios are defined as follows:

The longer leg is opposite to the angle of 60º, hence the sine relation is used to find the length, as follows:

sin(60º) = x/8

x = 8 x sine of 60 degrees

x = 6.93 cm.

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Answer:

6931.73

Step-by-step explanation:

π =3

cone base diameter = 6 so r=3

it's given height is 11

so use formula given V = π/3*3²*11 =99

sphere r =3

so use formula given V = 4/3*π*3³ = 4*81 = 324

total 99+324 =423 cubic INCHES!!!

1" = 2.54 cm

so you'll have to multiply 2.54³ to covert it to

cubic CMS = 6931.73 cubic CMS

The volume of the cabinet where Samantha stores all her important documents would be given as = 7.2 ft

A cabinet is defined as an equipment usually located in offices or laboratory which is used for the storage of documents that are of high importance to an organisation.

The shape of the cabinet is the shape of a cube and the volume of a cube is the product of all the sides given

That is = 2⅙ × 1¼ × 2⅔ ( change to single fraction)

= 13/6 × 5/4 × 8/3

= 520/72

= 7.2 ft

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Answer:

0.02

Step-by-step explanation:

hope it helped

Answer:

0.0266666667 or 0.02

Step-by-step explanation:

The step that can be used to draw an Inscribed Circle of A ABC is to draw the perpendicular bisectors of AB, BC, and AC that pass through point D

Inscribed Circle is a circle that touches each of the three sides of the triangle at exactly one point. Inscribed Circle is the largest circle that can be made in a triangle. The center of the Inscribed Circle is also the center of the triangle, that is, the point where the angle bisectors of the triangle meet.

Steps to draw an Inscribed Circle:

a. construct an angle bisector of each vertex (<ABC, <BAC, <ACB) of the triangle to determine the center of the triangle.

b. draw a line perpendicular to one side of the triangle that passes through its center.

c. draw an Inscribed Circle that passes through the point where the sides of the triangle intersect and the perpendicular from above.

As in the question, it was stated that the center of the Inscribed Circle is point D, so the step that can be used to draw an Inscribed Circle of A ABC is to draw the perpendicular bisectors of AB, BC, and AC that pass through point D

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The shape of the histogram is expected to be symmetric.

A histogram is a graphical representation of the distribution of a dataset. It is an estimate of the probability distribution of a continuous variable. The histogram is plotted with bin ranges on the x-axis and the frequency (count) of data points that fall within each bin on the y-axis.

The shape of the histogram can give you a sense of the underlying distribution of the data, such as whether it is symmetric or skewed.

Standardized test scores, like the SAT, are typically designed to have a normal distribution, meaning that the majority of scores fall in the middle range, with fewer scores at the extremely high or low ends.

Additionally, because the data is being collected from a large and diverse population of students from one state, it is unlikely that there would be a significant skew in one direction or another.

However, some factors such as socioeconomic status, family background, school district, and student ethnicity may affect the distribution.

Therefore, The shape of the histogram is expected to be symmetric.

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Answer: We can start by solving for one variable in one of the equations and then substituting that value into the other equation.

Solve for y in the first equation: y = 1 - 3x

Substitute this value of y into the second equation: 4(1 - 3x) + 4x = -20

Solve for x: -4x = -24

x = 6

Substitute this value of x into the first equation to find the value of y: y = 1 - 3(6) = -17

So the solution is x = 6 and y = -17.

Step-by-step explanation:

The given statement about the stake holders of DMAIC is false.

The term DMAIC stands for Define, Measure, Analyze, Improve, and Control and it represents the five phases that make the process,

Here we have given that generally, all stakeholders agree that there is a problem and on what the problem is before beginning the DMAIC process.

And we need to check whether the statement is true or not.

Here we know that in DMAIC process we have to follow the following steps they are listed as,

=> Define the problem

=> Improve activity

=> To determine opportunities for improvement

=> Identify the project goals

=> To analyze project goals and customer requirements.

Hence through this we have identified that the main purpose of DMAIC is to improve the effectiveness and efficiency of an organization's existing processes.

And here we have also know that DMAIC is a core data-driven improvement methodology of Six Sigma.

So, here the given statement is false.

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The quotient of the expression is 7x² + 8x +  1

From the question, we have the following expression that can be used in solving the quotient

(7x^3-13x^2-23x-5)/(x-3)

Express properly

So, we have

(7x³ - 13x² - 23x - 5)/(x-3)

Set the divisor to 0

x - 3 = 0

So, we have

x = 3

Using a synthetic setup, we have

3 | 7 - 13 - 23 - 5

The synthetic division is then carried out as follows

3 | 7 - 13 - 23 - 5

        21   24    3

    7   8     1    -2

So, we have

Quotient = 7   8   1

Remainder = 2

Introduce the variable

Quotient = 7x² + 8x +  1

Remainder = 2

Hence, the result is 7x² + 8x +  1 remainder 2

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Answer:

10 Slices

Step-by-step explanation:

6x5=30

30 slices in total

We are trying to find 2/3 of 30 slices so we multiply them.

(2x30)/3

=60/3

=20

20 slices were sold out of 30 total slices

This means that 10 slices are left

30-20=10

The probability of an even number is twice as likely to occur as an odd number is 2/9 and 1/9 respectively.

Probability in math term is defined as  a number that reflects the chance or likelihood that a particular event will occur.

Here we have given that an unfair/biased die is considered as an even number is twice as likely to occur as an odd number.

And here we need to find the probability of the event.

Here let us consider that probability of getting an even number = x and let probability of getting odd number = y

Then it can be written as

=> 3x+3y=1

Here we write it as because probability of getting even number or odd number = 1 since those two are the only possibilities.

Then we have to apply the value of x=2y (given)

Now, we have to solve these two, then we get,

=> x=2/9 and y=1/9

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The solution is Option B.

The rotation of the line JK around the point P by 180° will be J'K'

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the rotation angle be represented as A

Now , the value of A is 180°

Let the points be represented as J and K

Let the rotated point be represented as J'K'

And , when a point is rotated by and angle 180° , the x and y coordinates of the point will become their additive inverse

For a 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

And , the figure which represents the coordinates of the point J' and K' is when K' is below and J' is above

Hence , the solution is Option B.

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The measure of one interior angle in the regular polygon is 180° degrees.

Polygon:

A polygon is a shape that is made of straight line segments that are connected to each other.

The polygons are named according to their properties and the number of sides they have which have a minimum of three sides.

A polygon cannot have curved sides they are all straight line segments and can measure each side equal to one other.

The formula to find the interior angles of a regular polygon is required.

The required formula is     [tex]\frac{(n-2)*180}{n}[/tex]

where n = Number of sides of the polygon.

given to measure one interior angle n=1

Substitute the n value in the above formula, and we get

[tex]A=\frac{(2-1)*180}{1}[/tex]

A=180°

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The correct option is C. ((6, 5), (3,2), (2, 4), (6, 3), (1, 0))

Reason: This relation has two y-values of 6 which violates the vertical line test and therefore is not a function.

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Answer:

$560

Step-by-step explanation:

if 25% is the discount than the total of the item after the discount is .75x. So to find the original total we need the equation 420=.75x

first we need to isolate x so we divide both sides by .75, doing this will give us 560= x

to check our answer you need to multiply 560 by .75 (which I got by subtracting the discount, .25, from 1) which gives us our discounted total of $420

The equation to represent the coldest temperature recorded at Vostok Station in °F is 4*(−22.3)°F = 89.2°F.

The solution is obtained by using the arithmetic operations.

What are arithmetic operations?

In mathematics, mainly there are four basic operations upon which all the calculations are done. The operations are:

1. Addition(‘+’) wherein the sum of the numbers is obtained.

2. Subtraction(‘-’) wherein the difference of the numbers is obtained.

3. Multiplication(‘×’) wherein the product of the numbers is obtained.

4. Division(‘÷’) wherein the quotient of the numbers is obtained.

We are given that the coldest temperature recorded in a city in Texas was −22.3°F and the coldest temperature recorded at Vostok Station in Antarctica was 4 times as cold.

This means that the coldest temperature recorded at Vostok Station in Antarctica was

4*(−22.3)°F = 89.2°F

Hence, the equation to represent the coldest temperature recorded at Vostok Station in °F is 4*(−22.3)°F = 89.2°F.

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Answer: 33.93 in

Step-by-step explanation:

we can see it is a right angle there. h is oppsite line of the right triangle and 70in is Hypotenuse. So, we can use the formula sin29 = h/70. Then sin29*70=h. h=33.93 in.

The measure of PQ is approximately 57.8 units.

Now, According to the question:

A proportion is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.

Quadrilateral JKLM is similar to quadrilateral NOPQ .

We have the sides are:

JK = 9, LM = 13.7, NO = 38,

and To find the measure of PQ.

Corresponding sides in similar figures are proportional in length:

PQ/LM = NO/JK

PQ/13.7 = 38/9

PQ = 13.7(38/9) = 2603/45 ≈ 57.8

Hence, The measure of PQ is approximately 57.8 units.

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