a company owns two dealerships, both of which sell cars and trucks. the first dealership sells a total of 164 cars and trucks. the second dealership sells twice as many cars and half as many trucks as the first dealership, and sells a total of 229 cars and trucks. an equation for the total cars and trucks for dealership a: an equation for the total cars and trucks for dealership b: how many cars did dealership a sell? how many trucks did the dealership b sell?

To determine the solution of the question, we can divide the total number of tangerines, which is 168, by the number of boxes, which is 9. When we perform this division, we get 18, with a remainder of 6 as the number of tangerines that can be placed in each box.

To understand the answer better, let's go through an explanation of the same. Since the division of 168 by 9 leaves us with a remainder of 6 and a quotient of 18, it implies that 9 boxes shall contain 18 tangerines in each of them and 6 tangerines are leftover after the distribution.

Therefore, the farmer can distribute his 168 tangerines in numbers of 18 in each of the 9 boxes and be left with 6 tangerines.

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The marketing section of a business plan is completed once the market has been analyzed, and goals and objectives have been established.

The marketing section of a business plan is a crucial component that outlines the strategies and tactics to reach the target market effectively. It encompasses various aspects, including market research, target audience identification, competitive analysis, marketing goals, positioning, and promotional strategies. Before completing this section, thorough market analysis is conducted to understand the industry landscape, customer needs, market trends, and competitive dynamics. Once this analysis is complete, the business can establish clear goals and objectives based on their understanding of the market and their desired positioning. These goals can include market share targets, revenue projections, customer acquisition goals, or brand awareness objectives. The marketing section also outlines the marketing mix, including product or service offerings, pricing strategies, distribution channels, and promotional activities. By completing the marketing section, the business can articulate its marketing strategies and plans, which will guide its efforts to attract and retain customers, differentiate itself from competitors, and achieve its overall business objectives.

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The value of angle x is in the intersecting chord, is determined as 1 by applying the theorem.

The value of angle x is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

m∠x = ¹/₂ ( arc 6x - 2 ) - ( arc 2x) )

x = ¹/₂ (6x - 2 - 2x )

The value of x is calculated by simplifying the equation as follows;

2x = 4x - 2

2x - 4x = -2

-2x = - 2

2x = 2

x = 1

Thus, the value of angle x is in the intersecting chord, is determined as 1 by applying the intersecting chord theorem.

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C. Age is a probably lurking variable in this study.

What is variable?

In general, a variable refers to a characteristic, attribute, or quantity that can take on different values or vary from one individual, object, or situation to another.

Based on the given information that there is a strong positive correlation (r = 0.83) between measures of physical coordination and math scores in elementary school children, we can draw the following conclusion:

C. Age is a probably lurking variable in this study.

The conclusion suggests that age might be a potential confounding variable or a lurking variable that is influencing both physical coordination and math scores. In this case, the strong positive correlation observed between physical coordination and math scores could be partially or wholly attributed to the age of the children. As children grow older, both their physical coordination and math skills tend to develop and improve, so age could be a common underlying factor contributing to the correlation.

It's important to note that correlation does not imply causation. While the correlation suggests a relationship between physical coordination and math scores, it does not necessarily mean that one variable directly causes the other. Therefore, it would be inappropriate to conclude that physical coordination directly improves arithmetic (Option A) or that requiring exercise like running will improve arithmetic scores (Option B) based solely on this correlation.

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Answer:

about 11.598 meters

Step-by-step explanation:

For this situation, we will primarily rely on the Pythagorean theorem.
We can draw a (straight) 10-meter line between Tim and the tree in order to further understand the problem. Since Tim and the tree are both standing straight, a perceived line will be parallel to the ground. Another line can be drawn between Tim's eyes and the top of the tree. Please view the attached image for reference. Using the Pythagorean theorem   ([tex]a^{2} +b^{2}=c^{2}[/tex]), we can substitute 10 for a and 14 for c ---> giving us [tex]a^{2} +10^{2}=14^{2}[/tex] or [tex]a^{2} =14^{2}-10^{2}[/tex]. We then subtract--->[tex]a^{2} =96[/tex] and square root both sides to get a, which is equal to about 9.798 meters. However, this is only the height from Tim's eye level; therefore, to it, we must add 1.8 meters.
Our final solution is: about 11.598 meters.

The determinant of the general rotation matrix is indeed 1.

To prove that the determinant of a rotation matrix, specifically the general rotation matrix, must be 1, we can compute the determinant of the given matrix:

Det(cos(x) -sin(x))

   (sin(x)  cos(x))

Expanding the determinant using the first row, we get:

Det = cos(x) * cos(x) - (-sin(x)) * sin(x)

   = cos^2(x) + sin^2(x)

Using the trigonometric identity: cos^2(x) + sin^2(x) = 1, we have:

Det = 1

Therefore, the determinant of the general rotation matrix is indeed 1.

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The correct answers are:

If m AB = 120°, then the following angles have measures of 60° are,

a)∠ADB; and c)∠BCA.

Here, we have,

we know that,

The measure of an intercepted arc is twice as much as the measure of its inscribed angle.

i.e. If the intercepted arc is twice the size of the inscribed angle, then the inscribed angle is half the size of the intercepted arc.

So if the intercepted arc is 120 degrees,

the inscribed angle is 120 / 2 = 60 degrees.

so, we have,

AB corresponds with both ∠ADB and ∠BCA.

Since the arc is 120°, each angle would be half of that, or 60°.

Hence, The correct answers are:

If m AB = 120°, then the following angles have measures of 60° are,

a)∠ADB; and c)∠BCA.

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Answer:

  233 in²

Step-by-step explanation:

You want the area of the composite figure shown.

The area is the sum of the areas of the parts. The parts include a triangle, and a rectangle with a missing corner.

The area of the triangle is given by the formula ...

  A = 1/2bh

where b is the base and h is the height.

Here, we need to figure the missing dimension contributing to the height. The sum of right-side vertical line segments is 4 + 5 + 17 = 26. The bottom left vertical line segment is 6, so the height of the triangle is 26 -6 = 20.

The area of the triangle is ...

  A = 1/2(12 in)(20 in) = 120 in²

The overall dimensions of the rectangle at lower right are 17 in wide by (4+5) = 9 in tall. From that, a piece is removed that is 8 in wide by 5 in tall. The remaining area is ...

  A = LW

  A = (17 in)(9 in) -(8 in)(5 in) = (153 -40) in² = 113 in²

The area shaded blue is the sum of the triangle area and the area of the notched rectangle:

  total area = 120 in² +113 in² = 233 in²

The area of the figure is 233 square inches.

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'The group of cells in the hypothalamus that is stimulated by food intake is known as the Satiety center.

The hypothalamus is mainly for the brain regions. It effects on the brain central region and its control of feeding and expenditure.  The structure of hypothalamus is deep within your brain.

It is link between the endocrine system and your nervous system.

The hypothalamus is a key brain region in the regulation of energy balance as it controls food intake and both energy storage and expenditure through integration of humoral, neural, and nutrient-related signals and cues.

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The most appropriate hypothesis test to determine whether there is support for the claim that the average of the predicted charges is more than $500 greater than the average actual charges would be: c. Two-sample T-test assuming unequal variances (upper-tailed).

In this case, we have two independent samples: one for the predicted charges and another for the actual charges. We want to compare the means of these two samples to determine if there is a significant difference.

Unequal variance refers to the situation where the variances of two groups or populations being compared are not assumed to be equal. In statistical hypothesis testing, it is important to consider the assumption of equal variances, as violating this assumption can affect the accuracy of the results.

Since we are specifically interested in whether the average of the predicted charges is more than $500 greater, we would perform an upper-tailed test.

Assuming unequal variances is appropriate when the variances of the two samples are not assumed to be equal. This test allows for a more accurate assessment of the difference between the means when the variances differ between the groups.

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The area of the figure given after dividing it to known figures is 58 mm².

Given a figure.

We have to find the area of the figure.

The given figure can be divided in to two rectangles by drawing a horizontal line where the length is increased.

Then we get two rectangles of dimensions,

Length = 6 mm and width = 5 mm

Length = 7 mm and width = 4 mm

Area of the figure = Total area of the two rectangles.

Area of a rectangle = length × width

Area of the figure = (6 × 5) + (7 × 4)

                              = 30 + 28

                              = 58 mm²

Hence the area is 58 mm².

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Favorite Art Form​ is drawing 40% of randomly selected people like drawing.

Out of the randomly chosen 50 people, if 20 of them are interested in drawing, it means that the percentage of people interested in drawing can be calculated by dividing the number of interested people by the total number of randomly chosen people and multiplying by 100.

Percentage of people interested in drawing = (Number of interested people / Total number of randomly chosen people) × 100

In this case

Number of people interested in drawing = 20

Total number of randomly chosen people = 50

Percentage of people interested in drawing = (20 / 50) × 100 = 40%

Therefore, 40% of the randomly chosen 50 people are interested in drawing so most people are interested in drawing.

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The question is incomplete the complete question is :

You ask 50 randomly chosen artists in your town about their favorite art form. Determine whether your conclusion is valid. Favorite Art Form​

The 90% confidence interval for the plant's growth is given as follows:

(10.2, 11.8).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 6 - 1 = 5 df, is t = 2.0150.

The parameters for this problem are given as follows:

[tex]\overline{x} = 11, s = 1, n = 6[/tex]

The lower bound of the interval is given as follows:

[tex]11 - 2.0150 \times \frac{1}{\sqrt{6}} = 10.2[/tex]

The upper bound of the interval is given as follows:

[tex]11 + 2.0150 \times \frac{1}{\sqrt{6}} = 11.8[/tex]

The complete problem is:

"The additional growth of plants in one week are recorded for 6 plants with a sample standard deviation of 1 inches and sample mean of 11 inches. What is the 90% confidence interval for the plant's growth?".

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True. Newer models of community organizing and community building emphasize a fluid approach that combines collaboration and advocacy while focusing on community strengths.

In recent years, community organizing and community building have evolved to embrace more dynamic and inclusive approaches. These newer models recognize the importance of collaboration and advocacy as complementary strategies for effecting positive change within communities. Rather than viewing collaboration and advocacy as mutually exclusive, they emphasize the need to strike a balance between the two.

This fluidity allows community organizers and builders to engage in collaborative efforts that bring together diverse stakeholders, including community members, organizations, and institutions. By working together, these stakeholders can pool their resources, expertise, and perspectives to address shared challenges and work towards common goals. Collaboration fosters cooperation, relationship-building, and collective decision-making, enabling the community to tap into its inherent strengths and assets.

Advocacy involves speaking up for community needs, raising awareness about systemic issues, and promoting policy changes that can improve the overall well-being of the community. By combining collaboration and advocacy, community organizers and builders can create a more holistic and comprehensive approach that leverages community strengths, engages a broader range of stakeholders, and promotes sustainable change.

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Fauvist artists extended the visual vocabulary of Post-Impressionism by making their primary subject matter Color

Fauvist artists, a group of early 20th-century painters, indeed extended the visual vocabulary of Post-Impressionism primarily through their innovative use of color. The Fauvist movement emerged in France in the early 1900s and was characterized by bold, vibrant colors and expressive brushwork.

Prior to the Fauvists, Post-Impressionist painters, such as Vincent van Gogh and Paul Cézanne, had already begun to break away from the naturalistic color palette of Impressionism. They explored new ways of using color to convey emotion and form, but it was the Fauvists who took this exploration to new levels.

Fauvist artists, including Henri Matisse, André Derain, and Raoul Dufy, embraced intense, non-naturalistic colors. They used bold, contrasting hues that were often unrelated to the actual appearance of their subjects. This departure from traditional color usage was a radical departure from the subdued, more subdued palettes of earlier movements.

By focusing on color as their primary subject matter, the Fauvists aimed to evoke powerful emotional responses from the viewers. They believed that color had the ability to express emotions and convey meaning on its own, without being limited to realistic representations of objects. Instead of relying on naturalistic color schemes, they used vivid and arbitrary colors to create a sense of energy and vitality.

The Fauvists also liberated color from its traditional role as a means to depict light and shadow. They applied colors freely and spontaneously, often using broad brushstrokes, without concern for accurate representation. This allowed them to create highly expressive and subjective interpretations of their subjects, whether they were landscapes, portraits, or still lifes.

In summary, Fauvist artists extended the visual vocabulary of Post-Impressionism primarily through their revolutionary use of color. By breaking away from the naturalistic color palette and embracing bold, vibrant hues, they explored the expressive potential of color itself, going beyond traditional notions of representation. Their approach opened up new avenues for artistic expression and paved the way for further experiments in color by future generations of artists.

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we can use the proportion: (Number of votes received by the candidate) / (Total number of votes) = 43% / 100%. the candidate received approximately 37.41 votes.

In the given local election, the candidate received 43% of the votes. To determine the number of votes they obtained, we need to use a proportion. A proportion is an equation that states that two ratios are equal.

Let's represent the number of votes received by the candidate as "x." The total number of votes cast in the election is stated as 87.

We can set up the proportion:

x / 87 = 43% / 100.

To solve for "x," we can cross-multiply:

100 * x = 43% × 87.

Simplifying further, we have:

x = (43/100) × 87.

By multiplying the fraction (43/100) by 87, we can determine the number of votes received by the candidate. Evaluating this expression, the candidate received approximately 37.41 votes.

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Answer:

-3/4

Step-by-step explanation:

rise/run

goes down -3

goes to the right 4

slope = -3/4

Reject the H0, there is enough evidence at 94% confidence level to support the claim that the mean is different than 1450.

Sample size refers to the number of observations or individuals included in a sample from a larger population. In statistical analysis, the sample size is an important factor that can affect the reliability and generalizability of the results.

The given information as follows:

sample size = n = 51

sample mean = X =858.13

standard deviation =S = 1064.5

we have to test the claim that the mean number of text student send or receive = 1450

So, null and alternative hypothesis:

Họ : A = 1450

H :p + 1450

this is a two tailed test

since population standard deviation is not known so we use t distribution

degree of freedom = df = n-1 = 51-1 = 50

confidence level = 94% = 0.94

given significance level = α= 1 - 0.94 = 0.06

critical value from t table:

te = t1-0.06.50df £1.924

test statistics:

X - t= o/vn 858.13 – 1450 1064.5/V51 = = -3.97

since t =-3.97 < -1.924, so  reject the null hypothesis (H0).

Conclusion: reject the H0, there is enough evidence at 94% confidence level to support the claim that the mean is different than 1450.

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The amount of gas which is required to travel 200 miles is 10 gallons.

Given that Jason's car uses 20 gallons of gas to travel 400 miles and remaining amount of gas in his car is 7 gallons.

To calculate the gas needed to travel 200 miles by using the concept of proportion.

Gallons of gas/ miles = Gallons of gas / miles.

Let x amount of gas be needed to travel 200 miles.

That implies, 20 gallons/ 400 miles = x gallons / 200 miles.

By cross-multiplication, solve for x gives,

400x = 200 × 20.

On multiplication on RHS gives,

400x = 4000.

By dividing with 400 on both sides gives,

x = 10.

Therefore, the amount of gas which is required to travel 200 miles is 10 gallons.

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The p-value, decision to reject or fail to reject p-value = 0.002, RH₀.

What is the standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.

Here, we have

Given: quart cartons of milk should contain at least 32 ounces. a sample of 20 cartons contained the following amounts in ounces.

In order to calculate the p-value, we need to find t from the data:

t = (mean-μ)[tex]/\sqrt{\frac{sd^2}{n} }[/tex]

Where mean is the average of the data set, u is the comparative value (32), sd is the standard deviation and n is the number of elements.

And the standard deviation is:

∑[tex]\sqrt{\frac{(x-mean)^2}{n-1} }[/tex]

Mean = 604.6/20 = 30.23

Standard deviation  = 2.2

t = [tex]\sqrt{\frac{30.23 - 32}{2.2^2/20} }[/tex]

t = -3.59

From the t-table with degrees of freedom= df = n-1 = 19 we get a p-value of 0.002.

We have a significance level of 5%, or α=0.05

So we have two options:

If p-value ≤α RHo

If p-value >α FRHo

In this case 0.002<0.05.

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An argument in which the reasons support the conclusion so that the conclusion follows from the reasons offered is called a valid argument.

In logic and critical thinking, an argument consists of two main components, premises and a conclusion.

The premises are statements or reasons put forth as evidence or support for the conclusion.

The conclusion is the statement that is being asserted or inferred based on the premises.

A valid argument is one in which the logical relationship between the premises and the conclusion is such that if the premises are true.

Then the conclusion must also be true.

In other words, the conclusion logically follows from the premises.

When an argument is valid, it means that the truth or validity of the premises guarantees the truth or validity of the conclusion.

It does not necessarily mean that the premises are true in reality, but rather that if they were true, the conclusion would be true as well.

Here is an example to illustrate a valid argument,

Premise 1

All mammals are warm-blooded animals.

Premise 2

Dogs are mammals.

Conclusion,

Therefore, dogs are warm-blooded animals.

In this example, if we assume that the premises are true, the conclusion logically follows.

The truth of Premise 1 establishes that all mammals are warm-blooded, and Premise 2 identifies dogs as mammals.

This implies, the conclusion that dogs are warm-blooded animals logically follows from the given premises.

A valid argument can still have false premises or a false conclusion.

The validity of an argument simply relates to the logical relationship between the premises and the conclusion.

Rather than the truth or accuracy of the statements themselves.

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The correct answer is "line of best fit." A regression line is also called the line of best fit as it represents the best approximation of the relationship between the independent and dependent variables in a scatterplot.

In statistics and data analysis, a regression line is a straight line that represents the best-fitting relationship between two variables. It is often referred to as the "line of best fit" because it minimizes the overall distance between the line and the actual data points.

When plotting data points on a scatterplot, the regression line is used to approximate the trend or pattern in the data. It helps in understanding the relationship between the independent variable (usually denoted as "x") and the dependent variable (usually denoted as "y"). The goal is to find a line that is as close as possible to all the data points, capturing the general trend or direction of the relationship.

The line of best fit is determined by using a statistical technique called regression analysis. This technique calculates the optimal values for the slope and intercept of the line based on the data. The most common method for fitting a regression line is known as ordinary least squares (OLS), which minimizes the sum of the squared differences between the observed data points and the predicted values on the line.

By fitting a regression line, we can make predictions or estimations about the dependent variable based on the values of the independent variable. The line of best fit provides a visual representation of the relationship between the variables and allows for easier interpretation and analysis of the data.

It's important to note that the line of best fit is an estimation based on the given data, and it may not perfectly pass through every data point. However, it provides a useful summary of the overall trend and can be used for making predictions or drawing conclusions about the relationship between the variables.

Therefore, the correct answer is "line of best fit." A regression line is also called the line of best fit as it represents the best approximation of the relationship between the independent and dependent variables in a scatterplot.

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Answer:

One real-world example of an object/scenario where a limit exists is the concept of a car approaching a maximum speed.

Let's consider a car accelerating on a straight road. As the car continues to accelerate, there may be physical or engineering limitations that prevent it from reaching an infinite speed. These limitations could be factors like engine power, aerodynamic resistance, or speed limits imposed by laws or safety considerations.

In this case, we can approximate the limit of the car's speed as it approaches the maximum achievable speed. As the car accelerates, its speed increases, but it eventually reaches a point where the increase in speed becomes negligible. At this point, the car is said to have approached its maximum speed or reached its speed limit.

For example, let's say a car is accelerating from 0 km/h and its maximum speed is 200 km/h. As the car accelerates, it gradually gets closer to its maximum speed. At some point, the incremental increase in speed becomes very small, and the car's speed stabilizes around 200 km/h. This indicates that the car has approached its limit or maximum speed.

In this scenario, we can approximate the limit of the car's speed as it approaches 200 km/h. However, it's important to note that the actual limit may depend on various factors and may vary in different real-world situations.

Step-by-step explanation:

The value of tan C is simplest form is,

⇒ tan C = 3 / 4

We have to given that;

A right triangle CDE is shown in figure.

Now, We know that,

⇒ tan θ = Opposite / Base

Here, we have in triangle CDE,

Opposite = 12

Base = 16

Hence, By substituting, we get;

⇒ tan θ = Opposite / Base

⇒ tan C = 12 / 16

⇒ tan C = 3 / 4

Therefore, The value of tan C is simplest form is,

⇒ tan C = 3 / 4

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Hamlet's perspective on the traditional ways of celebrating in Scene 4 reveals his cynicism, introspection, and disillusionment with the world around him.

Scene 4 of Shakespeare's play "Hamlet" takes place in the Elsinore castle, where Hamlet encounters a group of soldiers led by Fortinbras, the Norwegian prince.

In this scene, Hamlet reflects on the traditional ways of celebrating and compares them to his own melancholic state of mind. His perspective on these traditional festivities sheds light on his character and provides insight into his disillusionment and discontentment with the world around him.

Hamlet's soliloquy in this scene reveals his cynical and introspective nature. He observes the soldiers engaging in drinking, dancing, and singing, which are common activities during celebrations.

However, Hamlet criticizes these festivities, stating that they are "a custom / More honor'd in the breach than the observance" (1-2). In other words, he believes that the traditions are better off ignored or abandoned than followed blindly without any true meaning or purpose.

This perspective on traditional celebrations reflects Hamlet's overall disillusionment with life and his contempt for superficiality. Throughout the play, Hamlet is depicted as a deeply introspective and philosophical character, prone to questioning the true nature of existence and the motives of others.

He often sees through the facades and pretenses of the world around him and is particularly critical of the artificiality and shallowness of social conventions.

Hamlet's dissatisfaction with traditional celebrations also ties into his grief and mourning over his father's death and his mother's hasty marriage to his uncle, Claudius.

His deep sense of loss and betrayal colors his perception of the world, making him question the authenticity and sincerity of human relationships. The revelry and merrymaking of the soldiers seem trivial and insignificant to him in the face of his personal anguish.

Furthermore, Hamlet's perspective on celebrations highlights his sense of isolation and alienation. He feels disconnected from the joyous activities and the people partaking in them. His soliloquy emphasizes his feelings of being an outsider, detached from the general spirit of merriment and unable to engage in the traditional ways of celebrating.

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The density of the 359.1 grams silver statue with a volume of 38cm³ is approximately 9.45 g/cm³.

Density is simply the substance's mass per unit of volume.

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given the data in the question:

Plug the given values into the above formula and solve for density of the silver statue:

density p = m / v

density p = 359.1 / 38

density p = 9.45 g/cm³

Therefore, the value of the density is 9.45 g/cm³.

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Step-by-step explanation:

7x + 63 = 3x - 18

4x = -81

x = -81/4

Answer: x = -81/4 or -20.25

Step-by-step explanation:

Step 1.  7x + 63 = 3x - 18

Step 2. -3x  -63   -3x -63

Step 3.  4x = -81

            4       4

Answer: x= -81/4 or -20.25

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The experimental probability of John passing the quiz is 1.

To find the experimental probability that John passed the quiz, the recorded results are used.

Given:

John answered the questions randomly.

He generated random numbers from 1 to 100 using a calculator.

Odd numbers represent True (T) and even numbers represent False (F).

The correct answers are T, T, F, F, and T.

The recorded results are given below:

Recorded Results:

True (T)

False (F)

True (T)

False (F)

True (T)

From the recorded results, John answered 3 out of 5 questions correctly.

Since John needs at least 3 correct answers to pass the quiz, it can e concluded that he passed the quiz based on the experimental data.

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The farm for sale measures 1120 acres.  

How many acres are equivalent to one square mile?

1 square mile= 640 acres.

To convert square miles to acres, we need to know that there are 640 acres in one square mile.

Given that the farm for sale measures one and three-quarter square miles, we can calculate the number of acres as follows:

1 and 3/4 square miles = 1.75 square miles  

Number of acres = 1.75 square miles * 640 acres/square mile

Number of acres = 1120 acres

Therefore, the farm for sale measures 1120 acres.

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There are 164 possibilities that are available for this specific selection.

To calculate the number of selections in which either Alice or Dolph, or both are officers, we can consider the different possibilities separately.

First, let's calculate the number of selections where Alice is an officer and Dolph is not. In this case, we have 4 remaining candidates (Ben, Connie, Egbert, and Francisco) to choose from for each position.

Therefore, there are 4 choices for the chairperson, 4 choices for the secretary, and 4 choices for the treasurer, resulting in a total of 4 * 4 * 4 = 64 selections.

Next, let's calculate the number of selections where Dolph is an officer and Alice is not. Similar to the previous case, we have 4 candidates to choose from for each position. So, there are also 64 selections.

Lastly, let's calculate the number of selections where both Alice and Dolph ar the third position since Alice and Dolph have already been assigned positions.

So, there are 4 choices for the treasurer, but only 3 choices each for the chaie officers. In this case, we have 4 remaining candidates (Ben, Connie, Egbert, and Francisco) to choose from chairperson and secretary. Therefore, there are 3 * 3 * 4 = 36 selections.

To find the total number of selections, we sum up the selections from each case: 64 + 64 + 36 = 164 selections.

To know more about number of selection, refer know :

https://brainly.com/question/30317894#

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