Create trig ratios to solve for the variables. Round your answers to the thousandth place: x= and y=

The domain of fog is: Domain of fog = {x ∈ R | 3 ≤ g(x) ≤ 9}

The range of fog is:  Range of fog = {1, 2, 5}

The domain of a function is the set of all possible input values (usually denoted by x) for which the function is defined.

The range of a function is the set of all possible output values (usually denoted by y) that the function can produce for its corresponding inputs in the domain.

(a) Domain of fog:

The domain of fog is the set of all inputs for which the composition is defined. Since g is defined for all values in its domain, and f is defined for all values in the range of g, the domain of fog is the set of all values in the domain of g for which g(x) is in the domain of f.

(b) Range of fog:

The range of fog is the set of all possible outputs of the composition. Since g is defined for all values in its domain, and f is defined for all values in the range of g, the range of fog is the set of all possible outputs of f when its input is an output of g.

Range of fog = {f(g(x)) | x ∈ R, 3 ≤ g(x) ≤ 9}

To determine the values in the range of fog, we need to evaluate f(g(x)) for each x in the domain of fog. We can do this by first determining the outputs of g for each value in its domain, and then evaluating f at those outputs.

The outputs of g for x = 4, 5, 7 are:

g(4) = 6

g(5) = 8

g(7) = 9

Since f is defined for all values in the range of g, we can evaluate f at each of these outputs to get:

f(g(4)) = f(6) = 5

f(g(5)) = f(8) = 2

f(g(7)) = f(9) = 1

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As a result, the company produced number of rods are **56** rods.

What exactly is radius?

A radius is a section of a straight line in geometry that connects a circle's or sphere's center to its edge or surface Its length is divided by the circle's diameter by two.

Each rod has a diameter of 6 centimeters, hence the radius is 3 centimeters. Each rod has a 20-centimeter height.

The following formula can be used to determine a cylinder's volume:

V = πr²h

where V stands for volume, r for radius, which is equal to half of the diameter, and h for height.

Adding these values to the formula yields the following results:

V = π(3)²(20) (20)

V = 180π

The volume of each rod is therefore 180 cubic centimeters.

30520.8 cubic centimeters of steel were used to make how many rods?

To find out,

divide the total volume of steel by the volume of each rod:

30520.8 / (180π) ≈ **56** rods

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The best choice is B. Saving Bonds, Stock Market, Mutual

Investments are defined as assets bought or invested in with the goal of increasing wealth and setting aside funds from salary or capital gains. The main goal of an investment is to generate extra income or to make money on an investment over a certain amount of time.

Generally speaking, the following is the order of investments from the lowest risk to the greatest risk:

Bonds for savings, mutual funds, and the stock market

As a result, list B is the one that runs from investment with the lowest risk to investment with the greatest risk. Stock market, mutual funds, and savings bonds.

The sequence of mutual fund investments, Savings Bonds, and Stock Market in Option A is not in decreasing order of danger.

Savings Bonds, the stock market, and mutual funds are listed in Option C's order, and this is also not from lowest to greatest risk.

Stock markets, mutual funds, and savings bonds are listed in Option D's order of greatest to lowest risk.

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(A)  the annual rate of change between 1992 and 2006 was 0.0804

(B) r = 0.0804 * 100% = 8.04%

(C) value in 2009 = $11,650

What is the rate of change?

The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.

A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.

Using the formula for an annual rate of change (r):

final value = initial value * [tex](1 - r)^t[/tex]

where t is the number of years and r is the annual rate of change expressed as a decimal.

Substituting the given values, we get:

$15,000 = $44,000 * (1 - r)¹⁴

Solving for r, we get:

r = 0.0804

So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.

B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:

r = 0.0804 * 100% = 8.04%

C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.

Substituting the known values, we get:

value in 2009 = $15,000 * (1 - 0.0804)³

value in 2009 = $11,628.40

Rounding to the nearest $50, we get:

value in 2009 = $11,650

Hence, (A)  the annual rate of change between 1992 and 2006 was 0.0804

(B) r = 0.0804 * 100% = 8.04%

(C) value in 2009 = $11,650

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The pοlynοmial functiοn with a fifth degree, 2 as a zerο οf multiplicity 4, −3 as the οnly οther zerο, and a leading cοefficient οf 2 is:

[tex]f(x) = 2(x-2)^4(x+3) = 2x^5 - 32x^4 + 192x^3 - 384x^2 + 216x + 1080[/tex]

What is Polynomial Function?

A pοlynοmial functiοn is a mathematical functiοn οf the fοrm [tex]f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0[/tex], where the coefficients[tex]a_n, a_{n-1}, ..., a_1, a_0[/tex] are constants, x is the variable, and n is a non-negative integer. It is a functiοn that can be graphed as a smοοth curve with nο breaks οr jumps.

If 2 is a zerο οf multiplicity 4, then the pοlynοmial functiοn must have the factοr[tex](x-2)^4[/tex].

If −3 is the οnly οther zerο, then the pοlynοmial functiοn must alsο have the factοr (x+3).

The pοlynοmial functiοn with these properties and a leading cοefficient οf 2 can be written as:

[tex]f(x) = 2(x-2)^4(x+3)[/tex]

Expanding this polynomial gives:

[tex]f(x) = 2x^5 - 32x^4 + 192x^3 - 384x^2 + 216x + 1080[/tex]

Therefore, the polynomial function with a fifth-degree, 2 as a zero of multiplicity 4, −3 as the only other zero, and a leading coefficient of 2 is:

[tex]f(x) = 2(x-2)^4(x+3) = 2x^5 - 32x^4 + 192x^3 - 384x^2 + 216x + 1080[/tex]

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The solution for the equation √(x-1) = x - 13 is x = 17, the correct option is C.

We have the following equation.

√(x-1) = x - 13

If we apply the square exponent in both sides, we will get:

x - 1 = (x - 13)²

x - 1 = x² - 26x + 169

x² - 27x  + 170 = 0

Using the quadratic formula we get:

[tex]x = \frac{27 pm \sqrt{(-27)^2 - 4*170*1} }{2} \\\\x = \frac{27 pm 7}{2}[/tex]

We only care for the positive solution, which is:

x = (27 + 7)/2 = 17

The correct option is C.

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The solution to the given equation is 14 by squaring both sides of the equation and simplifying. Therefore, the solution to the equation is option A.

To solve the equation √x-1=x-13, we first square both sides to eliminate the square root.

That results in the equation x - 2*x +1 = x - 13. Simplify this to get -x + 14 = 0. Further simplifying, x = 14 is the solution. Therefore, the solution to the equation is 14 (option A).

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Therefore, the distance between the pilot and the home is roughly 5,348.2 feet.

The height of the balloon divided by the neighboring side yields the tangent of the angle of depression (the distance from the balloon to the house).

Tan(32°) is therefore equal to 2828/x,

where x is the distance between the balloon and the home.

The answer to the x equation is

x = 2828/tan(32°)

Value of tan 32° = 0.6610060414

x=  5,348.2 feet.

The height of the balloon divided by the neighboring side yields the tangent of the angle of depression (the distance from the balloon to the house).

Tan(45°) is therefore equal to 2828/x, where x is the distance between the balloon and the home.

The answer to the x-problem is x = 2828/tan(45°) 2828 feet.

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Based on the given information, Yelena jumped the highest with a jump of 74 inches (6.17 feet).

Measurement is the process of assigning a numerical value to a physical quantity, such as length, mass, time, temperature, or volume. It is a fundamental aspect of science, engineering, and everyday life. In order to measure something, we need a unit of measurement, which is a standard reference quantity that is used to express the measurement. For example, meters or feet are commonly used units for length, while grams or pounds are used for mass.

To compare the high jumps of the four athletes, we need to convert all the measurements to the same unit.

Anna: 2.1 yards = 6.3 feet

Javier: 72 inches = 6 feet

Charles: 5 feet 11 inches = 71 inches = 5.92 feet

Yelena: 74 inches = 6.17 feet

So, Yelena jumped the highest with a jump of 74 inches (6.17 feet).

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Answer:

27 million dollars

Step-by-step explanation:

Let x be the total amount of the charity's donated funds. We know that the donation of 15.2 million represents 56% of x.

We can set up the following equation to solve for x:

15.2 million = 0.56x

Dividing both sides by 0.56, we get:

x = 15.2 million / 0.56 = 27.14 million

Therefore, the total amount of the charity's donated funds is approximately 27 million dollars.

Answer:

27 million

Step-by-step explanation:

create the equation

[tex]\frac{15200000}{x} =\frac{56}{100}[/tex], where x is equivalent to the total amount of donation funds

solve the equation by cross multiplying

[tex]x=2714285 \frac{5}{7}[/tex],

this can be simplified to 27 million

the length of EF is 11 units.

How to solve similar triangles?

Since triangles DEF and GHF are both right triangles, we can use the Pythagorean theorem to find the length of EF.

Let's first find the lengths of DE and EF.

DE = DF + FE = 13 + x, where x is the length of FE.

GF = DE - DG = (13 + x) - 4 = 9 + x.

GH = 4.

Now, using the Pythagorean theorem in triangle GHF, we have:

GH² + HF² = GF²

4²+ HF² = (9 + x)²

16 + HF² = 81 + 18x + x²

And in triangle DEF, we have:

DE²+ EF² = DF²

(13 + x)² + EF² = 13²

169 + 26x + x²+ EF² = 169

Simplifying the above equation, we get:

EF²= -26x - x²

Substituting this into the equation we got from the GHF triangle, we have:

16 + HF² = 81 + 18x + x² - EF²

16 + HF² = 81 + 18x + x²+ 26x + x²

HF² = 97 + 44x + 2x²

Now, using the fact that HE + EF = HF, we have:

8 + x = √(97 + 44x + 2x²)

Squaring both sides and simplifying, we get:

4x² + 16x - 225 = 0

Solving this quadratic equation, we get:

x = (-16 ± √(16² - 44(-225)))/(2*4) = (-16 ± 34)/8

Since x has to be positive, we take the positive solution:

x = 3

Therefore, EF = HE + FE = 8 + 3 = 11.

So the length of EF is 11 units.

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The correct option is B. 5/14, which is equivalent to approximately 0.357 or 35.7%

The probability of selecting a chocolate ice cream bucket is calculated by dividing the number of chocolate ice cream buckets by the total number of buckets:

P(chocolate) = number of chocolate ice cream buckets / total number of buckets

P(chocolate) = 5 / 14

P(chocolate) = 0.35714285714285715

To simplify the fraction, we can express it as a decimal or a percentage:

P(chocolate) ≈ 0.357 or P(chocolate) ≈ 35.7%

Therefore, the probability of selecting a chocolate ice cream bucket is approximately 0.357 or 35.7%. The probability of selecting a chocolate ice cream bucket can be calculated by dividing the number of chocolate ice cream buckets by the total number of buckets. The number of chocolate ice cream buckets is 5, and the total number of buckets is 14. Therefore, the probability of selecting a chocolate ice cream bucket is: 5/14

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Quotient ➔ 2x² - 7x + 18

Remainder ➔ - 37

━━━━━━━━━━━━━━━━━━━━━━

SolutioN ::

ㅤ

[tex]\begin{gathered} \\ \\ \qquad{\rule{120pt}{7pt}} \\ \\ \end{gathered}[/tex]

VerificatioN ::

ㅤ

[tex]\begin{gathered} \\ \\ \; \; :\longmapsto \; \sf {x(2x^{2} - 7x + 18) + 2(2x^{2} - 7x + 18) + ( - 37)} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf {2x^{3} - 7x^{2} + 18x + 4x^{2} - 14x + 36 - 37} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf {2x^{3} - 7x^{2} + 4x^{2} + 18x - 14x - 1} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf \pink{2x^{3} - 3x^{2} + 4x - 1} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ \\ \; \; :\longmapsto \; \sf \pink{2x^{3} - 3x^{2} + 4x - 1} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf {LHS = RHS} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ \; \; :\longmapsto \; \underline{\boxed{\sf{Verified}}} \; \pmb{\red{\bigstar}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ {\underline{\rule{150pt}{10pt}}} \end{gathered}[/tex]

[tex]\blue{\huge {\mathrm{DIVIDING \; POLYNOMIALS}}}[/tex]

[tex]\\[/tex]

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}[/tex]

[tex]{===========================================}[/tex]

[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}[/tex]

[tex]\qquad\begin{aligned}\sf \blue{2x^2 - 7x + 18} \:\:\:\:\:\:\:\:\:\: &\\\sf x + 2 \: \: ) \overline{2x^3 - 3x^2+4x-1} \quad&\\\sf \: \: \underline{ - 2x^3 - 4x^2 \qquad\qquad \: \: \: \: } \\\sf - 7x^2 + 4x \qquad \: \: \: \\\sf \:\:\: \underline{ - 7x^2 + 14x \qquad \: } \\ \sf 18x - 1 \: \: \: \\ \underline{ \sf{ - 18x - 36 \: }} \\ \sf \red{ - 37} \end{aligned}[/tex]

[tex]{===========================================}[/tex]

[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\qquad\qquad\qquad\tt 04/02/2023[/tex]

Answer: The length of the prism is 8 yards

Step-by-step explanation:

First, take the volume of the prism, divide it by the width (2 1/2). Once you get that divide that answer by height (5 3/4) getting you the length of the prism (8 yards)

Answer:

Certainly, here's an illustration:

       ----------------------

       |                    |

 2cm   |                    |

       |                    |  12cm

       |                    |

       ----------------------

           <---- ¾ of 12cm --->

             (9cm - 2cm)

               = 7cm

In this illustration, the rectangle is represented by a box with a length of 12cm and a width of 7cm. The width is calculated by taking ¾ of the length (which is 9cm) and subtracting 2cm from it. The dimensions of the rectangle are shown inside the box, with the length indicated by the vertical line and the width indicated by the horizontal line.

Answer: Let the total number of students in the class be x.

Then the number of boys in the class is 60% of x, or 0.6x.

And the number of girls in the class is 16.

We can write an equation based on the information given:

0.6x + 16 = x

Solving for x:

0.4x = 16

x = 40

Therefore, there are 0.6x = 24 boys in the class.

Step-by-step explanation:

The expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

The standard deviation is a measurement of how widely apart a set of numbers or statistics are from their mean.

The expected value for the amount of money made selling all of the candy in one bag can be found by;

Expected value = mean number of candy bars per bag x price per candy bar

Expected value = 12 x $1.25 = $15

Formula for the standard deviation of a product of random variables:

[tex]SD (XY) = \sqrt{((SD(X)^2)(E(Y^2)) + (SD(Y)^2)(E(X^2)) + 2(Cov(X,Y))(E(X))(E(Y)))}[/tex]

where X and Y are random variables, SD is the standard deviation, and Cov is the covariance.

X is the number of candy bars in a bag, which has a mean of 12 and a standard deviation of 2. Y is the price per candy bar, which is a constant $1.25. So we have:

E(Y²) = $1.25² = $1.5625

E(X²) = (SD(X)²) + (E(X)²) = 2² + 12² = 148

Cov (X,Y) = 0 (because X and Y are independent)

Using these values, we can calculate the standard deviation for the amount of money made selling all of the candy in one bag:

[tex]SD = sqrt((2^{2} )(148) + (0)(12)(1.25)^{2} + 2(0)(2)(12)(1.25))[/tex]

SD = √(592)

SD ≈ $24.33

Therefore, the expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

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The height of the cliff diver after 1.25 seconds is 35 feet.  

The concept used is evaluating a function at a given input or value. In this case, we are evaluating the height function H(t) at t = 1.25 to find the height of the cliff diver after 1.25 seconds. The formula for the height function is given as H(t) = -16t^2 + 32t + 20.

Here we have

A cliff diver's height (in feet) after t seconds is given by the model

H(t)=-16t² +32t +20  

Given time t = 1.25 seconds

To find the height after 1.25 seconds, we simply need to evaluate H(1.25) using the given formula:

H(1.25) = -16(1.25)² + 32(1.25) + 20

On Simplifying the expression we get:

H(1.25) = -16(1.5625) + 40 + 20

H(1.25) = -25 + 60

H(1.25) = 35

Therefore,

The height of the cliff diver after 1.25 seconds is 35 feet.  

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14 because 14+28=42.

Step-by-step explanation:

Two ends' area = 2 * pi r^2       r is radius = 1/2 diameter = 4m

                            2 * 3.14 * (4^2) = 100.48 m^2

Sidewall is   cicumfernce ( = pi *d)  times the height ( =7m)

      3.14 * 8 *7=175.84 m^2

Cost = (100.48 +175.84) m^2   *   $ 29 /m^2 = $ 8013.28

Answer:

(4x - 5) years old

Step-by-step explanation:

Nick = x years old

Matt = (3 x X)

=3x years old

Oscar = (x - 5) years old

total age = x + 3x + (x - 5)

= (4x - 5) years old

The fourth root of -81 is not a real number is 3√i.

A number that can be represented in the form a + bi is an imaginary number. In this case, a and b are real numbers, while I is the imaginary unit, which is equal to the square root of -1. In mathematics, imaginary numbers are used to expand on the real number system and to describe values that cannot be stated using real numbers.

Complex numbers, which are numbers of the type a + bi, where a and b are real numbers, are one of the principal applications for imaginary numbers. Several mathematical and scientific disciplines, such as electrical engineering, signal processing, and quantum physics, require complex numbers.

The value of -81 can be written as i²(3)⁴.

Taking the fourth root of the number we get 3√.

Hence, the fourth root of -81 is not a real number is 3√i.

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About 25% of students ride the bus for less than 13 minutes.

About 75% of students ride the bus for less than 27 minutes.

Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude.

In this case, the median is 21 minutes. This means that half of the students ride the bus for less than 21 minutes and half of the students ride the bus for more than 21 minutes.

The lower quartile (Q1) is the value that separates the lowest 25% of the data from the other 75%. In this case, the lower quartile is 13 minutes. This means that 25% of the students ride the bus for less than 13 minutes and 75% ride the bus for more than 13 minutes.

The upper quartile (Q3) is the value that separates the highest 25% of the data from the other 75%. In this case, the upper quartile is 27 minutes. This means that 75% of the students ride the bus for less than 27 minutes and 25% ride the bus for more than 27 minutes.

So, to answer the statement about the data set:

About 25% of students ride the bus for less than 13 minutes. (this is because the lower quartile separates the lowest 25% of the data from the other 75%)

About 75% of students ride the bus for less than 27 minutes. (this is because the upper quartile separates the highest 25% of the data from the other 75%)

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Answer:

A 1x3 matrix only has one entry, so there is only one minor, which is the determinant of the matrix itself.

For example, if A = [a, b, c], then the minor of A is simply:

|A| = det(A) = a

Since the determinant of a 1x1 matrix is just its single entry.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Reflecting a point across the x-axis negates the y-coordinate, so the point (-5, 7) reflected across the x-axis becomes (-5, -7).

Reflecting a point across the y-axis negates the x-coordinate, so the point (-5, -7) reflected across the y-axis becomes (5, -7).

Therefore, the third point is (5, -7).

After plotting the points A (-5, -2), B (-3, -2), and D (-5, -4) in the 4th quadrant as shown in the attached graph, we can see that to make the square we have to plot point C, at (-3, -4).

Simply said, the graph is a structured representation of the data. Because of this, it is simpler for us to understand the facts. Data is the term used to describe the numerical information obtained through observation.

The word data is derived from the Latin word datum, which meaning "something delivered."

After developing a research question, data are progressively obtained through observation. The information is then organised, categorised, and visually shown.

Here in the question,

After plotting the points A (-5, -2), B (-3, -2), and D (-5, -4) in the 4th quadrant as shown in the attached graph, we can see that to make the square we have to plot point C, at (-3, -4).

And the coordinate rule that will rotate the rectangle to the fourth quadrant, with vertex C’ at point (4, -3) is known as reflection.

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Answer:

B is greater than A by 1/4 of A

Step-by-step explanation:

Let's use the information given in the problem to write expressions for the values of a and b:

a = b - (1/5)b = (4/5)b

b is greater than a by the difference:

b - a = b - (4/5)b = (1/5)b

To express this difference as a fraction of a, we divide by a:

(b - a)/a = ((1/5)b)/((4/5)b) = 1/4

Therefore, b is greater than a by 1/4 of a.

The solution to the problem is that the number "x" must be less than or equal to -3.9 in order for the sum of "a number times 10 and 20" to be at most -19.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.

Let's use algebra to solve this problem.

Let's call the number we're trying to find "x".

The sum of "a number times 10 and 20" can be written as "10x + 20".

So, we can translate the statement "the sum of a number times 10 and 20 is at most -19" into an equation:

10x + 20 ≤ -19

Now we can solve for x:

10x + 20 ≤ -19

Subtract 20 from both sides:

10x ≤ -39

Divide both sides by 10:

x ≤ -3.9

Therefore, the solution to the problem is that the number "x" must be less than or equal to -3.9 in order for the sum of "a number times 10 and 20" to be at most -19.

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(D) |k - 7| < - 6 has no solution is not a true statement because an absolute value can never be negative, so the inequality has no solution.

Inequality refers to the state of being unequal or not equal in some respect. It can refer to various forms of disparities or differences, such as differences in income, wealth, education, opportunities, health, or social status, among others. Inequality can occur between individuals, groups, communities, or nations, and it can be caused by various factors, such as discrimination, historical legacies, social structures, policies, or economic systems. Inequality is often considered a social problem because it can lead to social tension, unrest, and injustice, as well as undermine economic growth and human development.

(D) |k - 7| < - 6 has no solution is not a true statement because an absolute value can never be negative, so the inequality has no solution.

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Buzz earned $65 - $55 = $10 more than Woody for his pink bear.

How to calculate earnings?

Woody sold his bear for $50 + 10% of $50 = $55.

Buzz sold his bear for $50 + 30% of $50 = $65.

Therefore, Buzz earned $65 - $55 = $10 more than Woody for his pink bear.

To determine how much more money Buzz earned than Woody for their pink bears, we first needed to calculate the selling price for each of them.

We know that both of them bought their bears for $50. Woody sold his bear for 10% more, which means his selling price was $50 + 10% of $50 = $55. Buzz sold his bear for 30% more, which means his selling price was $50 + 30% of $50 = $65. Therefore, Buzz earned $65 - $55 = $10 more than Woody for his pink bear.

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