find the equation that is parallel to the line y=x+9 and passes through the point (-6,7).Write the equation in slope intercept form

Answer:

Acute or Acute Scalene triangle to be exact

Answer:

Step-by-step explanation:h

If a quiz has 20 multiple choice questions, then the expected number of correct answers is 5.

For each question, there are 4 possible choices, and only 1 of them is correct.

So, the probability of randomly guessing the "correct-answer" for any  question is = 1/4 = 0.25,

Each question is an independent event, we use the concept of linearity of expectation to calculate the expected number of correct answers for all 20 questions.

The "Expected" number of correct answers for a "single-question" is  probability of guessing it correctly, which is 0.25,

The "Expected-Number" of correct answers for 20 questions is the sum of the expected number of correct answers for each question,

⇒ Expected number of correct answers = (Probability of guessing a single question correctly) × (Number of questions),

Substituting the values,

We get,

⇒ Expected number of correct answers = 0.25 × 20,

⇒ Expected number of correct answers = 5

Therefore, the expected number of correct answers when making "random-guesses" on all 20 multiple choice questions is 5.

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For a branch that is taken with 80% frequency, the "predict taken" scheme is the best choice as it provides the highest accuracy of 80% compared to the "predict not taken" scheme (20%) and dynamic predictor with 90% accuracy (82%).

For a branch that is taken with 80% frequency, the "predict taken" scheme will be the best choice, as it will provide an accuracy of 80%. The "predict not taken" scheme would only provide an accuracy of 20%, while the dynamic predictor with 90% accuracy would provide an accuracy of 82% ((90% x 0.8) + (10% x 0.2)).

Thus, even though the dynamic predictor has a high average accuracy, it may not always be the best choice for specific branches. In this case, the "predict taken" scheme is the most suitable option, as it provides the highest accuracy for this particular branch.

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The amount of fencing, dirt and sod for the baseball field are;

Length of fencing ≈ 1410.5 feet

Area of the sod ≈ 118017.13 ft²

Area of of the field covered with dirt ≈ 7,049.6 ft²

The fencing of a baseball field is the outer enclosure of the field, which typically, is located along the outfield boundary.

The amount of fencing, dirt, and sod can be found using the formula for finding the circumference of a circle and the area of a circle as follows;

Area of a circle = π × r²

Circumference of a circle = 2 × π × r

Where r is the radius of the circle

The area of a quarter of a circle is therefore; Area of a circle ÷ 4

The perimeter of a quarter of a circle is; The perimeter of a circle ÷ 4

Fencing = (1/4) × 2 × π × 380 + 2 × 15 + 2 × 380 + (1/4) × 2 × π × 15

Fencing = 190·π + 790 + 7.5·π = 197.5·π + 790 ≈ 1410.5

Grass = π/4 × (380 - 6)² + 87² - π/4 × (87 + 30)² + 2 × 380 × 15 + π/4 × 15² - (3/4) × π × 10² - 25·π = 31528·π + 18969 ≈ 118017.13

Dirt; π/4 × 380² - π/4 × (380 - 6)² + π/4 × (87 + 30)²- 87² + π·100 = (18613·π - 30276)/4 ≈ 7049.6

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By using the unitary method, we found that 60 items were sold at $25 each, while 90 items were sold at $5 each at the charity's craft fair.

In this problem, we know the total number of items sold and the total revenue earned. Let's assume that the number of items sold at $5 each is x, and the number of items sold at $25 each is y. Therefore, we can write two equations based on this information:

x + y = 150 (Equation 1)

5x + 25y = 1950 (Equation 2)

Equation 1 represents the total number of items sold, while Equation 2 represents the total revenue earned from the sale. Now, we can use the unitary method to find the value of y, which represents the number of items sold at $25 each.

Let's rearrange Equation 2 to solve for y:

5x + 25y = 1950

25y = 1950 - 5x

y = (1950 - 5x)/25

Now, we can substitute this expression for y into Equation 1:

x + (1950 - 5x)/25 = 150

Simplifying this equation, we get:

25x + 1950 - 5x = 3750

20x = 1800

x = 90

Therefore, we know that 90 items were sold at $5 each. Now, we can use Equation 1 to find the number of items sold at $25 each:

y = 150 - x

y = 150 - 90

y = 60

Hence, 60 items were sold at $25 each.

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1. The x intercept is 0 or 6

x-cordinate vertex = 3 , y-cordinate vertex = 9

2. x intercepts are 4 and -5

x-cordinate vertex = -1 and y-cordinate vertex = -20

What is intercept and vertex of a quadratic graph?

The x intercept of a quadratic graph are the roots of the quadratic equation. The vertex of a quadratic equation is the maximum or minimum point on the equation's parabola.

To find the x coordinate of the vertex , we use

x = -b/2a

and the y cordinate is found by substituting the value of -b/2a for x

1. y = x( x -6)

when y = 0

the roots of the equation = x = 0 or 6

and the x coordinate vertex = -(-6)/2 = 6/2 = 3

the y cordinate vertex = y = 3(3-6) = 3 × 3 = 9

2. y = (x-4)(x+5)

when y = 0

x = 4 or -5

and the x coordinate vertex = -1/1 = -1

y cordinate vertex = (-1-4)(-1+5)

= -5× +4 = -20

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3. The area of the shaded region is 5x² + 2x - 3

4. The area of the shaded region is 18x² + 21x + 6

From the question, we are to determine the area of the shaded region in the given diagrams.

3.

Area of the shaded region = {[(x - 1) + (2x - 1)] × [(x + 1) + (x + 1)]} - (x + 1)(x - 1)

Area of the shaded region = [(x - 1 + 2x - 1) × (x + 1 + x + 1)] - (x + 1)(x - 1)

Area of the shaded region = [(3x - 2) × (2x + 2)] - [(x + 1)(x - 1)]

Area of the shaded region = [(3x - 2)(2x + 2)] - [(x + 1)(x - 1)]

Area of the shaded region = (6x² + 6x - 4x - 4) - (x² - x + x -1)

Area of the shaded region = 6x² + 6x - 4x - 4 - x² + x - x + 1

Area of the shaded region = 6x² + 2x - 4 - x² + 1

Area of the shaded region = 6x² - x² + 2x - 4  + 1

Area of the shaded region = 5x² + 2x - 3

4.

Area of the shaded region = [(6x + 4)(4x + 2)] - [1/2(1/2(6x +4) × (4x + 2))]

Area of the shaded region = [(6x + 4)(4x + 2)] - [1/2((3x + 2)(4x + 2))]

Area of the shaded region = [24x² + 12x + 16x + 8] - [1/2(12x² + 6x + 8x + 4)]

Area of the shaded region = (24x² + 12x + 16x + 8) - (6x² + 3x + 4x + 2)

Area of the shaded region = (24x² + 28x + 8) - (6x² + 7x + 2)

Area of the shaded region = 24x² + 28x + 8 - 6x² - 7x - 2

Area of the shaded region = 24x² - 6x² + 28x - 7x + 8 - 2

Area of the shaded region = 18x² + 21x + 6

Hence, the area is 18x² + 21x + 6

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Answer:

undefined

Step-by-step explanation:

hope this helps

Answer:

-5y * 77

Step-by-step explanation:

The largest number we can factor out is 5. Therefore:

-385y

= -5y * 77

The 16 factors of -385 are:

1, 5, 7, 11, 35, 55, 77, 385

-1, -5, -7, -11, -35, -55, -77, -385

The factor pairs of -385 are:

1 × -385 = -385

5 × -77 = -385

7 × -55 = -385

11 × -35 = -385

35 × -11 = -385

55 × -7 = -385

77 × -5 = -385

385 × -1 = -385

Hope my answer helps you✌️

Mark BRAINLIEST

Answer:

6 inches

Step-by-step explanation:

To interpret the residual plot, we need to understand that the residuals are the differences between the actual values and the predicted values from the regression model.

I. The residual plot can give us an indication of the linearity of the relationship between the two variables. If the plot shows a clear pattern or curvature, it suggests that the relationship is non-linear. From the given information, we cannot see the residual plot and thus cannot determine if the relationship between the number of employees at Microsoft and the year is non-linear.

II. If the regression equation overestimates the number of employees at Microsoft in 1982, it means that the actual number of employees in 1982 was lower than what the regression equation predicted. Looking at the residual plot, if the residuals for the year 1982 are mostly positive (i.e., above the horizontal line), it suggests that the regression equation overestimated the number of employees in 1982. We cannot see the residual plot from the given information to determine if this statement is true.

III. If the number of employees at Microsoft decreased from 1976 through 1982, it means that the actual number of employees in 1982 was lower than the number of employees in 1976. Looking at the residual plot, if the residuals for the years from 1976 to 1982 are mostly negative (i.e., below the horizontal line), it suggests that the regression equation overestimated the number of employees during those years, which would be consistent with a decrease in the number of employees. Therefore, this statement could be true based on the residual plot.

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Your answer will be 35

If the revenue-function, in dollars, is R(x)= -2x² + 421x, then the profit function is P(x) = -2x² + 410x - 13448.

The "Profit-Function" is defined as the difference between the "revenue-function" and the "cost-function".

To find the "profit-function", we subtract the cost function from the revenue function.

The cost function is given as a "fixed-cost" of $13448 plus a "variable-cost" of $11 per tub of ice cream.

So the cost function can be expressed as : C(x) = 11x + 13448,

where x = number of tubs of ice-cream produced.

The "revenue-function" is : R(x) = -2x² + 421x,

To find "profit-function", we subtract "cost-function" from the "revenue-function":

⇒ P(x) = R(x) - C(x),

Substituting the expressions for R(x) and C(x),

We get,

⇒ P(x) = (-2x² + 421x) - (11x + 13448),

⇒ P(x) = -2x² + 421x - 11x - 13448,

⇒ P(x) = -2x² + 410x - 13448,

Therefore, the profit function is P(x) = -2x² + 410x - 13448.

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The given question is incomplete, the complete question is

The unit cost, in dollars, to produce tubs of ice cream is $11 and the fixed cost is $13448. The revenue function, in dollars, is R(x)= -2x² + 421x.

Find the profit function.

The probability of Laura missing 3 free throws before making 12 is approximately 0.0037 or 0.37%.
The basketball free throw.

A success would be considered when Laura makes a free throw.

A failure would be when Laura misses a free throw.
The negative binomial distribution is a probability distribution that calculates the probability of obtaining a certain number of failures before a specified number of successes occur.

The specified number of successes is 12, and the number of failures is represented by the variable x.
To calculate the probability of x failures, we need to know the probability of a single failure.

Since Laura is an 82% free throw shooter, the probability of her missing a free throw is 18%.
We can use the formula for negative binomial distribution to determine how many failures are required before 12 successes are achieved.

The formula is:
[tex]P(X = x) = (r+x-1)C(x) \times p^r \times (1-p)^x[/tex]
Where:
P(X = x) is the probability of having x failures before achieving 12 successes
r is the number of successes required (in this case, 12)
p is the probability of a single success (in this case, 0.82)

[tex](r+x-1)C(x)[/tex]is the combination of r+x-1 choose x

For example, if we want to find the probability of Laura missing 3 free throws before making 12, we will plug in x = 3, r = 12, p = 0.82 into the formula:

[tex]P(X = 3) = (12+3-1)C(3) \times 0.82^1^2\times (1-0.82)^3[/tex]
[tex]P(X = 3) = 14C3 \times 0.082^1^2 \times 0.18^3[/tex]
[tex]P(X = 3) = 364 \times 0.000018 \times 0.005832[/tex]
P(X = 3) = 0.000037
Overall, the trial in this scenario is each individual attempt at a free throw, the success is making a free throw, and 12 successes are required before the shooting session is considered complete.

The negative binomial distribution is used to calculate the probability of obtaining a certain number of failures before achieving the specified number of successes.

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'x' follows a negative binomial distribution with 'r' being 12 successes.

In this scenario, a trial refers to each individual attempt at shooting a free throw. A success is when Laura successfully makes a free throw. To achieve her goal of making 12 free throws, she needs to have 11 successes (since she will miss on the final attempt). Therefore, r = 11.

In this context, a "trial" refers to each individual attempt Laura makes to shoot a basketball free throw. A "success" is when Laura makes a free throw (hits the basket), while a "failure" (not mentioned in the question) would be when Laura misses a free throw. Since Laura keeps shooting free throws until she makes 12, the number of successes required, denoted as 'r', is 12.

Therefore, 'x' follows a negative binomial distribution with 'r' being 12 successes.

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The angles in the triangle are as follows:

A = 32 degrees

B = 58 degrees

The sum of angles in a triangle is 180 degrees. The triangle ABC is a right angle triangle. A right angle triangle has one of its angles as 90 degrees.

Therefore, let's find the angle A and B as follows:

Using trigonometric ratios,

sin A = opposite / hypotenuse

Therefore,

sin A = 8 / 15

A = sin⁻¹ 0.53333333333

A = 32.2286948935

A = 32 degrees

Let's find angle B

B = 180 - 90 - 32(sum of angles in a triangle)

B = 90 - 32

B = 58 degrees

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Answer: The estimated probability is 0.76.

Step-by-step explanation:

When dividing 80,543 by 176, the quotient is 458 with a remainder of 15.

What is the process of 80,543 divided by 176?

We start by dividing the first digit of the dividend (8) by the divisor (176). Since 8 is smaller than 176, we need to look at the first two digits of the dividend 80.

We divide 80 by 176. The result is 0, with a remainder of 80.

We bring down the next digit of the dividend to the remainder, making it 805.

We divide 805 by 176. The result is 4, with a remainder of 111.

We bring down the next digit of the dividend to the remainder, making it 1114.

We divide 1114 by 176. The result is 6, with a remainder of 58.

We bring down the next digit of the dividend to the remainder, making it 583.

We divide 583 by 176. The result is 3, with a remainder of 55.

We bring down the next digit of the dividend (the final digit, in this case) to the remainder, making it 555.

We divide 555 by 176. The result is 3, with a remainder of 27.

Since there are no more digits in the dividend, the quotient is the combination of all the individual results we got from each step. In this case, the quotient is 458, and the remainder is 15.

Therefore, 80,543 divided by 176 is 458 with a remainder of 15.

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Correct question is "What is remainder and quotient when 80,543 divided by 176?"

Angle relationship and algebra are closely related in geometry, as we often use algebraic expressions to represent angle measures and their ratios.

For example, if we are given that angle A and angle B are complementary (meaning that their sum is 90 degrees), we can write an algebraic equation:

Similarly, if we know that angle A is three times larger than angle B, we can write:

We can use algebraic equations to solve for unknown angle measures or to find relationships between angles.

For example, let's say we are given that angle A is complementary to angle B, and that angle B is twice as large as angle C. We can write:

We can substitute the second equation into the first equation to get:

This equation relates the three angles A, B, and C. We can use algebra to solve for any of the unknown angles, given the measures of the others.

Therefore, algebraic equations and expressions are an important tool in understanding and analyzing angle relationships in geometry.

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The probability that they run or bike for exercise is 0.91

The probability that a randomly selected executive runs or bikes for exercise can be calculated by adding the probability of running and biking for exercise, subtracting the probability of running and biking for exercise simultaneously (which would be double counted).

This can be expressed mathematically as:

A recent poll of 300 executives revealed how they exercise.

95 reported running, 127 reported biking and 49 reported that they both bike and run for exercise.

If one of these executives is randomly selected, the probability that they run or bike for exercise is 0.91.

This can be calculated by adding the probability of running and biking for exercise, subtracting the probability of running and biking for exercise simultaneously (which would be double counted).

This shows that the majority of executives prefer to exercise by running or biking.

P(Run or Bike for exercise) = P(Run) + P(Bike) - P(Run and Bike)

Plugging in our given values, we get:

P(Run or Bike for exercise) = P(Run) + P(Bike) - P(Run and Bike)

P(Run or Bike for exercise) = 95/300 + 127/300 - 49/300

P(Run or Bike for exercise) = 0.91

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The central limit theorem tells us that under certain conditions.

The sampling distribution of the means will approximate a normal distribution.

Regardless of the shape of the population distribution.

Building a sampling distribution through simulation, each dot in the graph represents a simulated sample.

Calculated from a sample of a fixed size (usually denoted as "n") drawn randomly from a population.

To create a sampling distribution.

Multiple simulated samples of the same size are drawn randomly from the population.

The mean of each sample is calculated.

Each dot on the graph represents the mean of one of these simulated samples.

By plotting the distribution of these sample means on a graph.

Visualize the behavior of the sample means and infer about the population mean.

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Answer:

Step-by-step explanation:

3(2x+1) = 6x+3

5x+x+3 = 6x+3

3(2x+3) = 6x+3

so the answer is 3(2x=3)[tex]\neq \neq[/tex]

Answer:

Identify the expression that is not equivalent to 6x + 3.

Step-by-step explanation:

In the hexagon,

a) side length = 11.56 unit , radius = 11.56 unit.

b) Area = 346.8 square unit.

What is area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Here the given hexagon apothem a= 10 units.

We know that central angle = 360° and number of sides n=6

Then apothem bisect the angle. Then, [tex]\theta = \frac{360}{12}=30\textdegree[/tex]

Now using cosine ratio then cos30° = [tex]\frac{a}{radius} = \frac{10}{radius}[/tex]

=> radius = [tex]\frac{10}{cos30\textdegree}[/tex] = 11.56 unit.

Now using sine ratio then,

=> sin30° = [tex]\frac{\frac{s}{2}}{radius}[/tex]

=> s = sin 30°× 2radius  = 11.56  unit

Now using area formula then,

Area A = [tex]\frac{1}{2}aP[/tex]

=> A = [tex]\frac{1}{2}\times10\times6\times11.56[/tex]

=> A = 346.8 square unit.

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A rule that could represent this dilation of a hexagon on a coordinate grid with the origin as the center is: (x, y) → (kx, ky), where k is the dilation factor (0 < k < 1) for creating a smaller hexagon.

The rule that could represent this dilation is to multiply the coordinates of each vertex of the original hexagon by the scaling factor (the factor by which the hexagon is being dilated) and the distance from the origin. Since the origin is the center of the dilation, the distance from the origin to any point on the hexagon remains constant. Therefore, the rule for dilating a hexagon with the origin as the center of dilation can be written as:
New Vertex = Scaling Factor x Distance from Origin x Old Vertex

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The rule that represents the dilation of the hexagon with the origin as the center of dilation is:
[tex](x\prime, y\prime) = (xr, yr)[/tex]
r is the ratio of the side lengths of the image to the pre-image, and (x, y) are the coordinates of a point on the pre-image.

A hexagon means to scale it up or down in size while maintaining its shape.

The hexagon will be made smaller.

The center of the dilation is the origin, which means that the hexagon will be scaled equally in all directions from the center.
To find the rule that represents this dilation, we can use the formula for dilation.

The formula for dilation is:
[tex](x\prime, y\prime) = k(x, y)[/tex]
(x, y) are the coordinates of a point on the pre-image (the original hexagon), [tex](x\prime, y\prime)[/tex] are the coordinates of the corresponding point on the image (the smaller hexagon), and k is the scale factor.
The center of dilation is the origin, which means that the coordinates of the center of the pre-image and the image are both (0, 0). Since the hexagon is being scaled down, the scale factor k must be less than 1.
To find the value of k, we need to know the ratio of the side length of the image to the side length of the pre-image. Let's say that the side length of the pre-image is s, and the side length of the image is [tex]s\prime[/tex].

The scale factor k can be found using the formula:
[tex]k = s\prime / s[/tex]
Since the hexagon is being scaled down, we know that[tex]s\prime < s.[/tex]

Let's say that the ratio of the side lengths is r, where:
[tex]r = s\prime / s[/tex]
Then we can rewrite the formula for k as:
[tex]k = r / 1[/tex]
The center of dilation is the origin, the coordinates of each point on the pre-image are equal to the length of their respective sides.

The vertices of the pre-image using the following coordinates:
A = (0, s)
[tex]B = (s\sqrt 3/2, s/2)[/tex]
[tex]C = (s\sqrt 3/2, -s/2)[/tex]
[tex]D = (0, -s)[/tex]
[tex]E = (-s\sqrt3/2, -s/2)[/tex]
[tex]F = (-s\sqrt3/2, s/2)[/tex]
The coordinates of the corresponding vertices on the image, we can substitute these coordinates into the formula for dilation:
[tex]A\prime = k(0, s) = (0, rs)[/tex]
[tex]B\prime = k(s\sqrt3/2, s/2) = (s\sqrt3/2 r, s/2 r)[/tex]
[tex]C\prime = k(s\sqrt3/2, -s/2) = (s\sqrt3/2 r, -s/2 r)[/tex]
[tex]D\prime = k(0, -s) = (0, -rs)[/tex]
[tex]E\prime = k(-s\sqrt3/2, -s/2) = (-s\sqrt3/2 r, -s/2 r)[/tex]
[tex]F\prime = k(-s\sqrt3/2, s/2) = (-s\sqrt3/2 r, s/2 r)[/tex]

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The solution to the system of equations is (3, -2). Therefore, the correct answer is A) (3, -2).

To solve this system of equations using substitution, we need to isolate one of the variables in one of the equations and substitute it into the other equation. We can choose to isolate x in the second equation:

x = 2y + 7

Now we can substitute this expression for x in the first equation:

3x + 2y = 5

3(2y + 7) + 2y = 5

6y + 21 + 2y = 5

8y = -16

y = -2

Now that we know the value of y, we can substitute it back into either of the original equations to find the value of x. We'll use the second equation for this:

x = 2y + 7 = 2(-2) + 7 = 3

Therefore, the correct answer is A) (3, -2).

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The correct choice is To control voluntary response bias.

Random assignment helps to control voluntary response bias by icing that individualities are assigned to the treatment and control groups fully arbitrarily, without any input or influence from the individualities themselves.

Voluntary response bias occurs when individuals tone-elect into a particular group, frequently because they have a particular interest or opinion on the content being studied. This can lead to prejudiced results because the individuals who choose to share may not be representative of the larger population.

Random assignment helps to control for voluntary response bias by icing that individualities are assigned to the treatment and control groups fully at arbitrarily, without any input or influence from the individualities themselves. This helps to insure that the groups are representative of the larger population and that any observed differences between the groups are due to the treatment itself, rather than other factors that may be associated with certain individualities or groups.

thus, arbitrary assignment helps to minimize the implicit impact of voluntary response bias on the results of a trial.

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The correct question is given below-

What is the purpose of random assignment in an experiment? Check all that apply.

Group of answer choices

To select a sample that is representative of the population

To create similar treatment groups

To eliminate the effects of the explanatory variable

To control voluntary response bias

Control for confounding variables

Applying the, Intersecting Chords Theorem, the value of x is calculated as: x = 16.

The Intersecting Chords Theorem is a geometric principle that states that when two chords intersect within a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

Thus, we would apply this theorem to find the value of x in the image given as explained below:

(x - 6)(8) = (x)(5)

8x - 48 = 5x

8x - 5x = 48

3x = 48

Divide both sides by 3

3x/3 = 48/3

x = 16

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Therefore , the solution of the given problem of equation comes out to be x = π/2 and x = 3*π/2 are the answers to the above equation in the range [0, π].

In intricate algorithms, variable words are typically employed to demonstrate consistency between two opposing arguments. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider the specifics associated with the x + 7 suggestions.

Here,

The equation is as follows:

=> Cscx+Csc² = 2.

Remember this formula: csc(2x) = 1/sin(2x)

=>  1/sin(2x)+csc(2x) = 2

=>  cscxsin2x + 1 = 2sin2x

We may enter this number into the equation since cscx = 1/sinx:

=>  2(1/cscx)² = 1 + (1/cscx)(1/cscx)

If we simplify, we get:

=>  1/(cscx) + 1 = 2/(cscx)

Eliminating the fraction requires multiplying both sides by cscx2:

=>  cscx² + 1 = 2

=>  cscx² = 2 - 1

=>  cscx² = 1

=>  |cscx| = 1

Situation 1: cscx = 1

=>  Sinx = 1/cscx = 1/1 = 1 if cscx = 1.

In the range [0, π], this happens when x = π/2.

Case 2: Cscx equals 1.

=>  Sinx = 1/cscx = 1/-1 = 1 if cscx = -1.

This happens when x in the range [0, pi] = 3*π/2.

So, x = π/2 and x = 3*π/2 are the answers to the above equation in the range [0, π].

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Answer:

1/x^2 = x^-2

x^4/x^3 = x

(x^2)^2 = x^4

x^3 * x^3 * x^3 = x^9

Step-by-step explanation:

The answer is: The answers will vary from person to person.

The statement that is true about statistical questions is that the answers will vary from person to person. Statistical questions are questions that can be answered using data and statistics. These questions involve gathering information from a population or a sample of that population, analyzing the data, and making conclusions based on the results. Since different people may have different data and different ways of analyzing that data, the answers to statistical questions can vary. This is why it is important to consider the sample size, the sample method, and the statistical methods used to analyze the data when interpreting the results of statistical questions. A well-designed study can help minimize variability and improve the accuracy of the results, but some degree of variability is still expected due to natural differences in the data collected by different individuals or groups

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