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The steps used in the solution of the equation -6 = -2/3(x + 12) + 1/3x are based on the principles of the Distributive Property, combining like terms, addition property of equality, symmetric property, subtraction property of equality, and multiplication property of equality.

Let's analyze the steps of the solution for the given equation -6 = -2/3(x + 12) + 1/3x:

Step 1: Distributive Property

The equation begins with the Distributive Property, which states that you can distribute a factor to each term inside parentheses. In this case, we distribute -2/3 to (x + 12), resulting in -2/3 * x and -2/3 * 12.

Step 2: Simplification

We simplify the expression -2/3 * 12 to -8, as multiplying -2/3 by 12 gives us -24, and simplifying the fraction -24/3 yields -8.

Step 3: Combine Like Terms

We combine the like terms -2/3x and -8. The equation becomes -2/3x - 8 + 1/3x.

Step 4: Combine Like Terms

We combine the like terms -2/3x and 1/3x by adding their coefficients. The sum of -2/3x and 1/3x is -1/3x.

Step 5: Addition Property of Equality

We add -1/3x to both sides of the equation to isolate the constant term. The equation becomes -6 - 1/3x = -1/3x.

Step 6: Symmetric Property

Since the equation has a form of -1/3x = -6 - 1/3x, we can rearrange the terms using the Symmetric Property.

Step 7: Addition Property of Equality

We add 1/3x to both sides of the equation to isolate the constant term. The equation becomes -6 = 0.

Step 8: Subtraction Property of Equality

We subtract 0 from both sides of the equation to simplify it further. The equation remains -6 = 0.

Step 9: Multiplication Property of Equality

We multiply both sides of the equation by any non-zero number to check for consistency. In this case, there is no need for multiplication as the equation is already in its simplified form.

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The modal sizes of shoes in the family's cupboard are 8 and 7.

To determine the modal size of shoes in the family's cupboard, we need to find the shoe size that appears most frequently in the given data. Let's analyze the sizes:

8, 7, 8, 8.5, 7, 8.5, 7

To find the mode, we can create a frequency table by counting the number of occurrences for each shoe size:

8     |     3

7     |     3

8.5 | 2

From the frequency table, we can see that both size 8 and size 7 appear three times each, while size 8.5 appears two times. Since both size 8 and size 7 have the highest frequency of occurrence (3), they are considered modal sizes. In this case, there is more than one mode, and we refer to it as a bimodal distribution.

To determine the mode, we performed a frequency count of each shoe size in the given data. We counted the number of occurrences for sizes 8, 7, and 8.5. Based on the frequency counts, we identified the sizes with the highest frequency, which turned out to be 8 and 7, both occurring three times. Thus, they are the modal sizes in the data set.

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Answer:

Step-by-step explanation:

The period of oscillation is 3 seconds

A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.

The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds

Oscillation can also be vibration or revolution or cycle.

Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.

This means that the period of the particle is 3 seconds.

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Anna ran the fastest with a speed of approximately 4.67 miles per hour.

To find the speed at which each person ran, we can use the formula: Speed = Distance / Time.

Let's calculate the speed for each person:

Noah:

Distance = 2 1/2 miles

Time = 3/5 hour

Speed = (2 1/2) / (3/5)

= (5/2) / (3/5)

= (5/2) [tex]\times[/tex] (5/3)

= 25/6 ≈ 4.17 miles per hour

Emily:

Distance = 3 3/4 miles

Time = 5/6 hour

Speed = (3 3/4) / (5/6)

= (15/4) / (5/6)

= (15/4) [tex]\times[/tex] (6/5)

= 9/2 = 4.5 miles per hour

Anna:

Distance = 3 1/2 miles

Time = 3/4 hour

Speed = (3 1/2) / (3/4)

= (7/2) / (3/4)

= (7/2) [tex]\times[/tex] (4/3)

= 14/3 ≈ 4.67 miles per hour

Based on the calculations, Noah ran at a speed of approximately 4.17 miles per hour, Emily ran at a speed of 4.5 miles per hour, and Anna ran at a speed of approximately 4.67 miles per hour.

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The purchasing power in five years will be $15,476.

To predict the purchasing power in five years, we can substitute the value of X as 5 into the equation y = 20000(0.95)^X.

Plugging in X = 5, we have:

[tex]y = 20000(0.95)^5[/tex]

Calculating the expression, we find:

[tex]y ≈ 20000(0.774)[/tex]

Simplifying further, we get:

[tex]y ≈ 15480[/tex]

Rounding the result to the nearest dollar, the predicted purchasing power in five years would be approximately $15,480.

Therefore, the closest option to the predicted purchasing power in five years is $15,476.

So the correct answer is:

$15,476.

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Rounding to the nearest dollar, the predicted purchasing power in five years is approximately $15,480.

To predict the purchasing power in five years using the given equation, we substitute the value of x (representing the number of years) as 5 and calculate the result.

The equation provided is: y = 20000(0.95)^x

Substituting x = 5 into the equation, we have:

y = 20000(0.95)⁵

Now, let's calculate the result:

y ≈ 20000(0.95)⁵

≈ 20000(0.774)

y ≈ 20000(0.774)

≈ 15,480

This means that, according to the given equation, the purchasing power of $20,000, with an inflation rate of five percent, would be predicted to be approximately $15,480 after five years.

By changing the value of x (representing the number of years) to 5, we can use the preceding equation to forecast the buying power in five years.

The example equation is: y = 20000(0.95)^x

When x = 5 is substituted into the equation, we get y = 20000(0.95).⁵

Let's now compute the outcome:

y ≈ 20000(0.95)⁵ ≈ 20000(0.774)

y ≈ 20000(0.774) ≈ 15,480

This indicates that based on the equation, after five years, the purchasing power of $20,000 would be estimated to be around $15,480 with a five percent inflation rate.

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The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)

Let's break down the information given:

Height of the rectangular box = 7 ft

Length of the rectangular box = 1 ft longer than thrice the width (x)

Volume of the rectangular box = 798 ft³

To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.

The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.

Given that the height is 7 ft, we can substitute this value into the equation.

Volume = (Length) * (Width) * (7)

Now, let's focus on the length. It is described as 1 ft longer than thrice the width.

Length = 1 + (3x)

Substituting this value into the equation, we have:

Volume = (1 + (3x)) * (Width) * (7)

Since the volume is given as 798 ft³, we can set up the equation as follows:

798 = (1 + (3x)) * (Width) * 7

Simplifying further, we get:

798 = 7 * (1 + 3x) * (Width)

Dividing both sides of the equation by 7, we have:

114 = (1 + 3x) * (Width)

Therefore, the equation in terms of x that represents the given relationship is:

114 = (1 + 3x) * (Width)

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El supplemento y el complemento de cada ángulo son, respectivamente:

Caso A: m ∠ A' = 43°

Caso B: m ∠ A' = 31°

De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:

Ángulo y su complemento

m ∠ A + m ∠ A' = 90°

Ángulo y su suplemento

m ∠ A + m ∠ A' = 90°

Donde:

Ahora procedemos a determinar cada ángulo faltante:

Caso A: Complemento

47° + m ∠ A' = 90°

m ∠ A' = 43°

Caso B: Suplemento

149° + m ∠ A' = 180°

m ∠ A' = 31°

El enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.

The statement is written in Spanish and its answer is written in the same language.

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The length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."

The Pythagorean theorem, which asserts that given a right triangle, the sum of the squares of the two shorter sides (a and b), is equal to the square of the hypotenuse (c), can be used to determine the length of the triangle's hypotenuse (c).

a = 10 feet

b = 20 feet

Using the Pythagorean theorem, we can calculate c as follows:

c^2 = a^2 + b^2

c^2 = 10^2 + 20^2

c^2 = 100 + 400

c^2 = 500

To find c, we take the square root of both sides:

c = √500

c ≈ 22.36

Rounding the answer to the nearest whole number, we get c ≈ 22.

Therefore, the length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."

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a. For a score of X = 70, a standard deviation of σ = 4 would give a better grade.

b. For a score of X = 80, both standard deviations would give the same grade.

a. To determine which standard deviation would give a better grade for a score of X = 70, we can compare the z-scores associated with each standard deviation.

The z-score measures the number of standard deviations a given value is from the mean.

For σ = 4:

Z = (X - μ) / σ

Z = (70 - 78) / 4

Z = -2  

For σ = 8:

Z = (X - μ) / σ

Z = (70 - 78) / 8

Z = -1

The z-score for σ = 4 is -2, while the z-score for σ = 8 is -1. A higher z-score indicates a better grade since it represents a score that is further above the mean.

Therefore, in this case, a standard deviation of σ = 4 would give a better grade.

b. Similarly, for a score of X = 80:

For σ = 4:

Z = (X - μ) / σ

Z = (80 - 78) / 4

Z = 0.5

For σ = 8:

Z = (X - μ) / σ

Z = (80 - 78) / 8

Z = 0.25.

The z-score for σ = 4 is 0.5, while the z-score for σ = 8 is 0.25.

Again, a higher z-score indicates a better grade.

Therefore, in this case, a standard deviation of σ = 4 would give a better grade.

In both scenarios, a standard deviation of σ = 4 would result in a better grade compared to σ = 8.

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Answer:

D

Step-by-step explanation:

to find the coterminal angles add/ subtract 360° to the given angle

- 255° + 360° = 105°

- 255° - 360° = - 615°

The graph that displays the line of best fit for the data is the one where the line with the best fit goes through the points.

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The resulting matrix after the rows are interchanged is given as follows:

[tex]\left[\begin{array}{cccc}2&9&4&5\\8&-2&1&7\\1&4&-4&9\end{array}\right][/tex]

The matrix for this problem is defined as follows:

[tex]\left[\begin{array}{cccc}8&-2&1&7\\2&9&4&5\\1&4&-4&9\end{array}\right][/tex]

The row 1 is given as follows:

[8 -2 1 7].

The row 2 is given as follows:

[2 9 4 5].

Interchanging the rows means that the elements of the row 1 in the matrix is exchanged with the elements of row 2, hence the resulting matrix is given as follows:

[tex]\left[\begin{array}{cccc}2&9&4&5\\8&-2&1&7\\1&4&-4&9\end{array}\right][/tex]

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Answer:

hope you understand it and please follow me

Answer:

be more clear of what u mean edit the question to explain more

Step-by-step explanation:

no explanation

Answer:

Step-by-step explanation:

To simplify the expression, we can combine the square roots and simplify the exponents.

Starting with the expression:

3√(16x^7) * 3√(12x^9)

Let's simplify each term separately:

Simplifying 3√(16x^7):

The index of the radical is 3, so we need to group the terms in sets of three. For the variable x, we have x^7, which can be grouped as x^6 * x.

Now, let's simplify the number inside the radical:

16 = 2^4, and we can rewrite it as (2^3) * 2 = 8 * 2.

So, 3√(16x^7) becomes:

3√(8 * 2 * x^6 * x) = 2 * x^2 * 3√(2x)

Simplifying 3√(12x^9):

Again, the index of the radical is 3, and we group the terms in sets of three. For the variable x, we have x^9, which can be grouped as x^6 * x^3.

Now, let's simplify the number inside the radical:

12 = 2^2 * 3.

So, 3√(12x^9) becomes:

3√(2^2 * 3 * x^6 * x^3) = 2 * x^2 * 3√(3x^3)

Now we can multiply the simplified terms together:

(2 * x^2 * 3√(2x)) * (2 * x^2 * 3√(3x^3))

Multiplying the coefficients: 2 * 2 * 3 = 12.

Multiplying the variables: x^2 * x^2 = x^4.

Now, let's combine the square roots:

3√(2x) * 3√(3x^3) = 3√(2x * 3x^3) = 3√(6x^4).

Therefore, the simplified expression is:

12x^4 * 3√(6x^4)

Answer:

15 coins, d + q coins

Step-by-step explanation:

If asking for the amount (in $)

5(.10) + 10(.25) = 2.5+.5 = $3

He would have 0.1d + 0.25q for d dimes and q quarters.

The value of the required arc in the figure is solved to be

The inscribed angle is given in the problem as 40 degrees. This is the angle formed at the circumference of the circle

The relationship between inscribed angle and the intercepted arc is  

intercepted arc = 2 * inscribed angle

in the problem, we have that

intercepted arc = ?

inscribed angle = 40

plugging in the values

intercepted arc = 2 * 40

intercepted arc = 80 degrees

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Answer:

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

Angles ABD and DBC form a linear pair, hence their sum is 180°.

Set up an equation and solve for x:

Substitute 40.5 for x and find the measure of ∠DBC:

Angle C can be found by subtracting the sum of angles A and B from 180 degrees:

b. A = 34.1°; B = 44.4°; C = 101.5°

To solve a triangle with side lengths a = 4, b = 5, and c = 7, we can use the law of cosines and the law of sines.

First, let's find angle A using the law of cosines:

[tex]cos(A) = (b^2 + c^2 - a^2) / (2\times b \times c)[/tex]

[tex]cos(A) = (5^2 + 7^2 - 4^2) / (2 \times 5 \times 7)[/tex]

cos(A) = (25 + 49 - 16) / 70

cos(A) = 58 / 70

cos(A) ≈ 0.829

A ≈ arccos(0.829)

A ≈ 34.1°

Next, let's find angle B using the law of sines:

sin(B) / b = sin(A) / a

sin(B) = (sin(A) [tex]\times[/tex] b) / a

sin(B) = (sin(34.1°) [tex]\times[/tex] 5) / 4

sin(B) ≈ 0.822

B ≈ arcsin(0.822)

B ≈ 53.4°

Finally, angle C can be found by subtracting the sum of angles A and B from 180 degrees:

C = 180° - A - B

C = 180° - 34.1° - 53.4°

C ≈ 92.5°.

b. A = 34.1°; B = 44.4°; C = 101.5°

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The correct answer is A- A model with 12 squares labeled exact value and 3 squares labeled error.

To determine which model represents a percent error of 25%, we need to compare the number of squares labeled "exact value" and "error" in each model and calculate the ratio between them.

Let's calculate the ratio for each model:

Model A: 3 squares labeled error / 12 squares labeled exact value = 0.25 or 25%.

Model B: 5 squares labeled error / 10 squares labeled exact value = 0.5 or 50%.

Model C: 3 squares labeled error / 9 squares labeled exact value ≈ 0.3333 or 33.33%.

Model D: 4 squares labeled error / 8 squares labeled exact value = 0.5 or 50%.

From the calculations, we can see that only Model A represents a percent error of 25%. The other models have ratios of 50% and 33.33%, which do not match the desired 25% error.

Consequently, the appropriate response is A- A model with 12 squares labeled exact value and 3 squares labeled error.

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An equation representing a line perpendicular to y = -6/5 [tex]\times[/tex] x - 7 would be y = 5/6 [tex]\times[/tex] x + c, where c is any constant.

To determine a line that is perpendicular to the given line y = -6/5 [tex]\times[/tex] x - 7, we need to consider the slope of the given line.

The given line has a slope of -6/5.

For two lines to be perpendicular, their slopes must be negative reciprocals of each other.

The negative reciprocal of -6/5 can be found by flipping the fraction and changing the sign, which gives us 5/6.

Therefore, the equation of a line perpendicular to y = -6/5 [tex]\times[/tex] x - 7 will have a slope of 5/6.

To find the equation of this perpendicular line, we can use the point-slope form of a line, using a known point on the line.

Let's assume the line passes through the point (x1, y1).

The equation of the perpendicular line can be written as: y - y1 = (5/6) [tex]\times[/tex] (x - x1).

Since we do not have a specific point given, we cannot determine the exact equation of the perpendicular line without additional information.

In summary, the equation of a line perpendicular to y = -6/5 [tex]\times[/tex] x - 7 will have a slope of 5/6, but the specific equation depends on the point it passes through.

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A suitable delta (δ) for ε = 0.01 is any positive value smaller than √6.

To find a suitable delta (δ) for the given limit, we need to consider the epsilon-delta definition of a limit.

The definition states that for a given epsilon (ε) greater than zero, there exists a delta (δ) greater than zero such that if the distance between x and the limit point (2, in this case) is less than delta (|x - 2| < δ), then the distance between the function (√x + 7) and the limit (3) is less than epsilon (|√x + 7 - 3| < ε).

Let's solve the inequality |√x + 7 - 3| < ε:

|√x + 7 - 3| < ε

|√x + 4| < ε

-ε < √x + 4 < ε

To remove the square root, we square both sides:

(-ε)^2 < (√x + 4)^2 < ε^2

ε^2 > x + 4 > -ε^2

Since we're interested in the interval around x = 2, we substitute x = 2 into the inequality:

ε^2 > 2 + 4 > -ε^2

ε^2 > 6 > -ε^2

Since ε > 0, we can drop the negative term and solve for ε:

ε^2 > 6

ε > √6

Please note that this solution assumes the function √x + 7 approaches the limit 3 as x approaches 2. To verify the solution, you can substitute different values of δ and check if the conditions of the epsilon-delta definition are satisfied.

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There is a 53.33% chance of drawing a piece of paper with a number less than 9 from the jar.

To calculate the probability of drawing a piece of paper with a number less than 9 written on it, we need to determine the number of favorable outcomes (pieces of paper with a number less than 9) and divide it by the total number of possible outcomes (all 15 pieces of paper).

In this case, the favorable outcomes are the numbers 1 through 8, as they are less than 9. There are 8 favorable outcomes.

The total number of possible outcomes is 15 since there are 15 pieces of paper in the jar.

Therefore, the probability of drawing a piece of paper with a number less than 9 is:

Probability = Number of favorable outcomes / Total number of possible outcomes

= 8 / 15

Simplifying the fraction, we find that the probability is approximately:

Probability ≈ 0.5333 or 53.33%

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The result of the row operation on the matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

The matrix in this problem is defined as follows:

[tex]\left[\begin{array}{cccc}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

The row operation is given as follows:

[tex]R_1 \rightarrow \frac{1}{2}R_1[/tex]

The meaning of the operation is that every element of the first row of the matrix is divided by two.

Hence the resulting matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation: