Solve the given differential equation by undetermined coefficients.y" - 8y' +16y = 24x +2

According to the provided scenario, if you weigh 160 pounds, then 3 drinks in four hours would make you definitely illegal.

If a person weighs 160 pounds and drinks alcohol at a moderate rate, then after 3 drinks in four hours, their BAC (blood alcohol concentration) would be around 0.08, which is considered legally impaired and definitely illegal. However, it is important to note that this estimate is based on various factors such as the person's gender, age, and metabolism, and can vary from person to person.

Therefore, it is always advisable to drink responsibly and not drive after consuming alcohol.

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Using Excel, the probability that at least 35 of the 154 randomly selected vehicles exceed 110 kilometers per hour when 17.7% of vehicles exceed this speed on the expressway is approximately 0.0027, rounded to four decimal places.

To solve this problem in Excel, we can use the binomial distribution function. In this case, the probability of success (a vehicle exceeding 110 kilometers per hour) is p = 0.177, and the number of trials (vehicles selected) is n = 154.

We want to find the probability of at least 35 successes (vehicles exceeding 110 kilometers per hour), which can be calculated using the formula:

=1-BINOM.DIST(34,154,0.177,TRUE)

This formula gives a probability of 0.0027, which is the probability that at least 35 of the selected vehicles exceed 110 kilometers per hour. Therefore, the answer is 0.0027, rounded to four decimal places.

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The magnitude and direction of the net force are found by adding the two forces together as resultant force vectors.

a) 11.82 N

b) 74.07°

To find the net force, we add the two force vectors F_1 and F_2:

Fnet = F_1 + F_2

Fnet = (1.31 + 4.6j) N + (3.2i + 6.8j) N

Fnet = 3.2i + (1.31 + 4.6j + 6.8j) N

Fnet = 3.2i + (1.31 + 11.4j) N

To find the magnitude of the net force, we use the Pythagorean theorem:

|Fnet| = sqrt[(3.2)^2 + (1.31 + 11.4)^2] N

|Fnet| ≈ 11.6 N

To find the direction of the net force, we use the inverse tangent function:

θ = tan^(-1)(y/x)

θ = tan^(-1)(11.4/3.2)

θ ≈ 73.8 degrees

Since the net force is in the first quadrant, the direction counterclockwise from the +x-axis is simply θ:

Direction = 73.8 degrees counterclockwise from the +x-axis

Therefore, the net force is Fnet = 3.2i + (1.31 + 11.4j) N, with a magnitude of approximately 11.6 N and a direction of approximately 73.8 degrees counterclockwise from the +x-axis.

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Answer:

-9

Step-by-step explanation:

x = -5

3x + 6

Since x = -5..

Do this

3(-5) + 6

Perform

-15 + 6

Answer: -9

Therefore, when x is equal to -5, the value of 3x + 6 is -9.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

3x + 6 = 3(-5) + 6

= -15 + 6

= -9

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The ratio of water and flour for samosas sheets is typically 1:2, meaning one part water to two parts flour.

A samosa is a fried or baked pastry with a savory filling, such as spiced potatoes, onions, peas, lentils, macaroni, noodles, or minced meat. It is popular in the Indian subcontinent, Southeast Asia, and the Middle East. The samosa is usually triangular or tetrahedral in shape, but can also be round or even cone-shaped.

It is typically served with chutney, such as mint, coriander, or tamarind. It is usually filled with potatoes, onions, peas, and other vegetables, as well as spices such as cumin, coriander, chili powder, and garam masala. Samosas can also be filled with meat, such as chicken, beef, or lamb. They are typically deep-fried in ghee or vegetable oil, but can also be baked.

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A student attempts a 10-question multiple-choice test where each question presents four options, and the student makes random guesses for each answer. So the probability of (a) P(5)= 0.058 and (b) P(More than 3)= 0.093.

Part 1: Calculation of probability of getting 5 questions correct

(a) P(5)The formula used to find the probability of getting a certain number of questions correct is:

P(k) = (nCk)pk(q(n−k))

Where, n = total number of questions

(10)k = number of questions that are answered correctly

p = probability of getting any question right = 1/4

q = probability of getting any question wrong = 3/4

P(5) = P(k = 5) = (10C5)(1/4)5(3/4)5= 252 × 0.0009765625 × 0.2373046875≈ 0.058

Part 2: Calculation of probability of getting more than 3 questions correct

(b) P(More than 3) = P(k > 3) = P(k = 4) + P(k = 5) + P(k = 6) + P(k = 7) + P(k = 8) + P(k = 9) + P(k = 10)

P(k = 4) = [tex]10\choose4[/tex](1/4)4(3/4)6 = 210 × 0.00390625 × 0.31640625 ≈ 0.02

P(k = 5) = [tex]10\choose5[/tex](1/4)5(3/4)5 = 252 × 0.0009765625 × 0.2373046875 ≈ 0.058

P(k = 6) = [tex]10\choose6[/tex](1/4)6(3/4)4 = 210 × 0.0002441406 × 0.31640625 ≈ 0.012

P(k = 7) = [tex]10\choose7[/tex](1/4)7(3/4)3 = 120 × 0.00006103516 × 0.421875 ≈ 0.002

P(k = 8) = [tex]10\choose8[/tex](1/4)8(3/4)2 = 45 × 0.00001525878 × 0.5625 ≈ 0.001

P(k = 9) = [tex]10\choose9[/tex](1/4)9(3/4)1 = 10 × 0.000003814697 × 0.75 ≈ 0.000

P(k = 10) = [tex]10\choose10[/tex](1/4)10(3/4)0 = 1 × 0.0000009536743 × 1 ≈ 0

P(More than 3) = 0.020 + 0.058 + 0.012 + 0.002 + 0.001 + 0.000 + 0≈ 0.093

Therefore, the probabilities of the given situations are: P(5) ≈ 0.058, P(More than 3) ≈ 0.093.

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The marginal product of labor initially increases from 6 to 9, but then starts to decrease as more labor is added. Therefore, the firm experiences diminishing returns to labor when it hires a third laborer.

Diminishing returns to labor occur when the marginal product of labor (i.e., the additional output produced by adding one more unit of labor) decreases as more labor is added. We can calculate the marginal product of labor for each level of labor as follows:

1 laborer: 6 units of output (marginal product = 6)

2 laborers: 9 units of additional output (total output = 15, marginal product = 9)

3 laborers: 10 units of additional output (total output = 25, marginal product = 10)

4 laborers: 9 units of additional output (total output = 34, marginal product = 9)

The law of diminishing marginal returns is a concept from economics that explains how the marginal output of a production process starts to decrease as the input goes up. It is also used to refer to a point at which output increases at a diminishing rate as more units of labor are added to a production process. This can also be called the point of decreasing marginal productivity.

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The value of sec A as required to be determined in the task content is; -√13 / 2.

As evident from the task content; it follows that the terminal ray of angle A, drawn in standard position, passes through the point (-4, -6).

Therefore, the length that the line from the origin to A has length;

L = √((-4)² + (-6)²)

L = √52.

On this note, it follows that the value of sec A which is represented by; hypothenuse/ adjacent is;

sec (A) = -√52 / 4

sec (A) = -√13 / 2.

Ultimately, the value of sec (A) as required is; -√13 / 2.

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Answer:

(a) perimeter of the drawing = (7 x2) + (4 x 2)

                                               = 22 inches

(b) perimeter of the actual garden = 2(7 x 35) + 2(4 x 35)

                                                         = 490 + 280

                                                         = 770 inches

(c) 22 x 35 = 770

i don't really understand the last question. sorry if i gave you the wrong answers

For the given relation the statement that is not correct is "X is a candidate key for R".

Given that the primary key for relation schema R(X, Y, Z) is {X, Y}, we need to determine which of the given statements is NOT correct. The possible options are:

{X, Y} is a superkey for R.

X is a candidate key for R.

Y may not have a NULL value for R.

Functional dependencies {X, Y} → Z must hold on R.

The statement that is NOT correct is: X is a candidate key for R.

A superkey is a set of attributes that, taken together, can uniquely identify a tuple in a relation schema. As per the given relation schema, {X, Y} is a superkey, because no two tuples in R can have the same value for {X, Y}.

A candidate key is a minimal superkey, meaning that it is a superkey, but removing any attribute from it would no longer make it a superkey.

In this case, {X, Y} is the only candidate key, because removing either attribute from it would make it no longer a superkey.

A NULL value is a missing or unknown data value in a tuple. As per the schema R(X, Y, Z), Y may not have a NULL value, which means that it is a non-nullable attribute, and all tuples in R must have a value for Y.

Functional dependency is a constraint between two sets of attributes in a relation schema, where one set of attributes determines the values of another set of attributes. For R(X, Y, Z), the functional dependency {X, Y} → Z must hold, which means that, for every pair of tuples in R with the same value for {X, Y}, the value for Z must also be the same.

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The answer of the given question based on the given equation  that fruit basket holds x2 x2 – 3 x x + 12 apples and Maha takes out 4 x− x− 6 of them the answer is , there are x² - 6x + 18 apples left in the basket after Maha takes out 4x - x - 6 of them.

In mathematics, expression is  combination of numbers, variables, and mathematical operations that can be evaluated to produce  value. An expression can be as simple as  single number or variable, or it can be complex, involving many different operations and variables.

Expressions can be used to represent many different mathematical ideas, like equations, inequalities, functions, and more. They can be used to model real-world situations, make predictions, and solve problems in wide variety of fields, like physics, economics, engineering, and more.

The fruit basket initially holds x² - 3x + 12 apples. If Maha takes out 4x - x - 6 of them, then we can subtract this expression from the initial number of apples to find how many are left in the basket.

So, the expression for the number of apples left in the basket is:

x² - 3x + 12 - (4x - x - 6)

We can simplify this by combining like terms:

x² - 3x + 12 - 4x + x + 6

Simplifying further:

x² - 6x + 18

Therefore, there are x² - 6x + 18 apples left in the basket after Maha takes out 4x - x - 6 of them.

It's important to note that we cannot simplify 4x - x - 6 to 3x - 6 in this case because the two terms have different coefficients. Instead, we need to distribute the negative sign to both terms inside the parentheses to get 4x - x - 6 = 4x - 1x + (-6) = 3x - 6, which we can then use in the expression for the number of apples left in the basket.

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Answer:

Step-by-step explanation:

To find the perimeter of an equilateral triangle is equalled to 3s.

35 x 3

105

The number of minutes she must run to reach her goal is 65.1 minutes.

The time she must run for is found by dividing the distance by the speed:

Time = Distance / Speed

We need to convert the distance from kilometers to miles before substituting values into the formula.

11.7 km = 11.7 / 1.609344 = 7.270043 miles

The formula now becomes:

Time = 7.270043 miles / 6.7 mi/h

Time = 1.085081 h

To get the time in minutes, we need to convert the time in hours to minutes. There are 60 minutes in an hour, so there are

Time = 1.085081 h x (60 minutes/1 hour)

Time = 65.104863 minutes = 65.1 minutes

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No fallacy is committed in the given immediate inference, as it follows the rules of the square of opposition.

The immediate inference presented in the statement is valid and can be categorized as a particular affirmative proposition (I-type) of the square of opposition.According to the square of opposition, a particular affirmative proposition can be inferred from a universal affirmative proposition (A-type) when the subject is distributed.

In the given statement, the universal affirmative proposition is "All advocates of school prayer are individuals who insist on imposing their views on others," which distributes the subject "advocates of school prayer."

Therefore, the particular affirmative proposition "Some advocates of school prayer are individuals who insist on imposing their views on others" can be inferred from the universal affirmative proposition.

No fallacy is committed in the given immediate inference, as it follows the rules of the square of opposition. However, it should be noted that the validity of the inference does not necessarily imply the truthfulness of the statement, as it is possible for some advocates of school prayer to not insist on imposing their views on others.

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Assuming that a corporation has cumulative voting and two directors are up for election. The maximum number of votes a shareholder who owns 100 shares can cast for candidate Jones is 40.

Cumulative voting is a voting method used by shareholders in a company to elect a board of directors.

In this type of voting, each shareholder is given the number of votes equal to the number of shares they own, multiplied by the number of candidates. This means that if there are two candidates and a shareholder has 100 shares, then they can cast up to 200 votes for each candidate.

In this case, there are 5 candidates, and two directors are to be elected. Therefore, the total number of votes will be the sum of the votes required for each director, which will be 100.

The maximum number of votes that a shareholder with 100 shares can cast for each candidate will be equal to the total number of votes multiplied by the percentage of the vote that each candidate is allocated.

For example, if candidate Jones is allocated 20% of the votes, then the maximum number of votes that a shareholder with 100 shares can cast for candidate Jones will be:

Total number of votes = 2 x 100 = 200

Percentage of votes allocated to candidate Jones = 20%

Maximum number of votes for candidate Jones = 200 x 20/100 = 40.

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Answer:

3.5

Step-by-step explanation:

y = 3x+2

= 3(0.5) + 2

= 1.5+2

= 3.5

To solve the problem, we need to find all the classes of the relation Ron the set A in roster notation. And also, we need to pick one element of A to represent each distinct equivalence class. The relation Ron A is defined as:

aRb ⇔ a+b=3k, k ∈ ZLet A = {2, 3, 5, 11, 12, 13} be a set.

The distinct equivalence classes of A in roster notation are distinct equivalence[2] = {2, 5, 11},[3] = {3, 12},[13] = {13},[a], [5] = {5, 2, 11}Each equivalence class consists of elements in A that are related to each other by the given relation, i.e., by R. Therefore, aRb means that a and b are related in some way, and the equivalence class [a] is the set of all elements in A that are related to a by R.

Therefore, the distinct equivalence classes in roster notation are given as above, and we can pick any one element of A to represent each class. Thus, we have the following:A = {2, 3, 5, 11, 12, 13}[2] = {2, 5, 11} and can be represented by 2.[3] = {3, 12} and can be represented by 3.[13] = {13} and can be represented by 13.[5] = {5, 2, 11} and can be represented by 5.

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Answer:

26.82 (2 d.p.)

Step-by-step explanation:

tan(17)*m=8.2

8.2/tan(17) = m

= 26.82

The number of 50 cents in the container is 380 fifty cents

Since Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents

To calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents, we proceed as follows.

Let

Since the total number of cents in the container is 600, we have that

x + y = 600

So, making y subject of the formula, we have that

y = 600 - x

Since x = 220

y = 600 - 220

= 380

So, there are 380 fifty cents

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In set theory, two sets are considered equal if they have the same elements. In this case, A is a set containing the elements 1, 2, and 3, while B is an empty set (also known as the null set),

A contains three distinct elements, and B contains none, we can conclude that A and B are not equal, i.e., A is not equal to B.

A ≠ B

Set theory is a branch of mathematics that studies collections of objects, called sets, and the relationships between them. A set is defined as a well-defined collection of distinct objects, which can be anything from numbers and letters to more abstract concepts like functions and geometrical shapes. The set theory provides a foundation for other areas of mathematics, including algebra, topology, and logic.

One of the fundamental concepts of set theory is the notion of membership, which states that an object either belongs to a set or does not. Sets can also be combined through operations such as union, intersection, and complementation, and the relationships between sets can be represented using Venn diagrams.

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So, in order of size, from smallest to largest: 45,000 cm² < 5.4 m² = 5.4 x[tex]10^{6}[/tex] mm².

Given by the question.

To compare the areas 5.4 m², 45,000 cm², and 5 x [tex]10^{6}[/tex] mm², we need to convert them into the same unit of measurement.

1 meter (m) = 100 centimeters (cm)

1 meter (m) = 1,000 millimeters (mm)

Therefore, we can convert the given areas as follows:

5.4 m² = 5.4 x 100 x 100 = 54000 cm² (multiply by 100 twice to convert from m² to cm²)

5.4 m² = 5.4 x 1000 x 1000 = 5.4 x [tex]10^{6}[/tex] mm² (multiply by 1000 twice to convert from m² to mm²)

Now that we have converted all the areas to mm², we can compare them directly.

5.4 m² = 5.4 x 10^6 mm²

45,000 cm² = 450 x 100 = 45000 mm²

5 x [tex]10^{6}[/tex] mm² = 5 x [tex]10^{6}[/tex] mm².

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Answer:

Step-by-step explanation: To obtain the function g(x) that represents the indicated transformations of the graph of f(x) = 2, which are a translation 1 unit up followed by a horizontal stretch by a factor of 2, we can follow these steps:

To translate f(x) = 2 one unit up, we can add 1 to the function: f(x) + 1.

To horizontally stretch f(x) + 1 by a factor of 2, we can multiply the input (x) by 1/2: f(1/2 x) + 1.

Therefore, the function g(x) that represents the indicated transformations of f(x) is:

g(x) = f(1/2 x) + 1

g(x) = 2(1/2 x) + 1

g(x) = x + 1

Answer:

x=9.4

using soh cah toa:

x=opposite side

15=adjacent side

using tan(toa)

[tex]tan32=\frac{x}{15}[/tex]

[tex]x=15tan32[/tex]

[tex]x=9.4[/tex]

Jada overtakes Elena after 7.5 seconds.

The set of equations that best captures the scenario is =y=15+20x.

Let's establish a coordinate system with Elena's starting point as the origin. Elena's separation from the origin at time x is given by: y=15+20x

y1 = 15 + 20x

Jada's distance from the origin at time x is determined similarly by:

y2 = 22x

Finding the moment x at which Jada overtakes Elena and their distances from the origin are equal is our goal.

y1 = y2

With the formulas for y1 and y2 substituted, we obtain:

15 + 20x = 22x

When we simplify this equation, we obtain:

2x = 15

x = 7.5

Jada therefore overtakes Elena after 7.5 seconds.

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The velocity when the object hits the ground is 4.025 ft/s. The answer is: C) 0 feet per second.

If an object is dropped from the top of a building, its position in feet above the ground is given by s(t)=−8t^2+288, where t is the time in seconds since it was dropped.  Given that an object is dropped from the top of a building,

then its initial velocity, u = 0 (since it was dropped and not thrown). We want to find the velocity when the object hits the ground, i.e., the time it takes the object to reach the ground. We know that the position of the object when it reaches the ground is s(t) = 0.

Therefore:−8t^2+288 = 0Solving for t, we get:−8t^2 = −288t^2 = 36t = sqrt(36) = ±6 sSince time cannot be negative, t = 6 s. Then the final velocity at impact, v, can be calculated as follows:v = u + at + s/v = 0 + (-32.2)(6) + (-8(6)² + 288)/v = -193.2 + (-288 + 288)/v = -193.2 + 0/v = -193.2/v = -193.2/-48v = 4.025 (rounded to three decimal places)

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Answer: Mike is ( 3x + 4 ) years old

Step-by-step explanation:

K -> x y/o

L -> 3x y/o

M -> (3x + 4) y/o

The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98

Given that a credit risk study found that an individual with good credit score has an average debt of $15,000 and the debt of an individual with good credit score is normally distributed with standard deviation $3,000.

Then the 95% confidence interval can be calculated as follows:

Upper limit: µ + Zσ

Lower limit: µ - Zσ

Where

The z-score corresponding to a 95% confidence interval can be found using the standard normal distribution table.

The area to the left of the z-score is 0.4750 and the area to the right is also 0.4750.

The z-score corresponding to 0.4750 can be found using the standard normal distribution table as follows:z = 1.96Therefore

Upper limit: µ + Zσ= $15,000 + 1.96($3,000) = $20,880

Lower limit: µ - Zσ= $15,000 - 1.96($3,000) = $9,120.02

The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98.

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Gail scores 153 points on average every bowling game, with a 14.5 point standard deviation. Assume Gail's bowling game points are evenly divided. With x = 108, the mean is 153, and the z-score is  -3.103.

The z-score when Gail scores 108 points in a game is calculated as:

z = (x - μ) / σ

where x = 108 is the observed score, μ = 153 is the mean, and σ = 14.5 is the standard deviation.

Plugging in the values, we get:

z = (108 - 153) / 14.5 ≈ -3.103

Rounding to three decimal places, the z-score when Gail scores 108 points in a game is approximately -3.103.

The mean is μ = 153, which is given in the problem statement.

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The value of x is 8

A quadrilateral with one pair of parallel sides. It is a typical mathematical shape that is employed in numerous disciplines. The area of a trapezoid is computed by multiplying the height by half of the sum of the lengths of the two bases.

Given that trapezoid PQRS ~ TUVW are similar;

So, VW/RS = UT/QP

      x/12 = 6/9

      x = 8

Therefore, the value of x is 8

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Trapezoid A trapezoid is a four-sided shape with one pair of parallel sides According to the question The value of x is 8

A trapezoid is a four-sided shape with one pair of parallel sides. It has two non-parallel sides, or legs, and two parallel sides, or bases. The bases are usually of different lengths, and the sides are typically not equal. The angles of a trapezoid are not necessarily all the same size, but the two opposite angles are always equal. Trapezoids can be found in everyday objects like the shape of a deck, a rectangular door frame, or a sloped roof. Trapezoids can also be found in geometry, where they are used to calculate the area and perimeter of the shape.

Given that trapezoid PQRS ~ TUVW are similar;
So, VW/RS = UT/QP
     x/12 = 6/9
     x = 8
Therefore, the value of x is 8

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The equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.

What is equation?

In mathematics, an equation is a statement that two expressions are equal, usually written with an equal sign (=) between them. Equations can contain variables, which are symbols that represent unknown or unspecified values.

We can simplify and solve the equation 2x + 6 = 30 - x - 3 as follows:

2x + 6 = 30 - x - 3

Adding x and adding 3 to both sides, we get:

3x + 9 = 30

Subtracting 9 from both sides, we get:

3x = 21

Dividing both sides by 3, we get:

x = 7

So the given equation simplifies to x = 7.

We can now substitute this value of x into each of the answer choices to see which one is equivalent to the given equation:

a) 2x + 6 = 30 - x - 3

Substituting x = 7, we get:

2(7) + 6 = 30 - 7 - 3

14 + 6 = 20

20 = 20

b) 2x + 6 = 10 - x - 3

Substituting x = 7, we get:

2(7) + 6 = 10 - 7 - 3

14 + 6 = 0

20 ≠ 0

Therefore, this equation is not equivalent to the given equation.

c) 2x + 6 = 30 - x + 3

Substituting x = 7, we get:

2(7) + 6 = 30 - 7 + 3

14 + 6 = 26

20 ≠ 26

Therefore, this equation is not equivalent to the given equation.

Therefore, the equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.

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