Jasmine can eat 8 goldfish in 3 minutes. How many could she eat in 16 minutes? Round to the nearest tenth if needed.

Our assumption that AC ≤ BC must be false.  To prove that the hypotenuse is the longest side of a right triangle, we will use an indirect proof. We will assume the opposite of what we want to prove and show that it leads to a contradiction.

Assume that AC ≤ BC. This means that the side opposite the acute angle A is shorter than the side opposite the acute angle C.

Now, let's draw a line segment from vertex C perpendicular to AB. This line segment divides the triangle into two smaller triangles, let's call them ΔACD and ΔBCD.

Since the line segment is perpendicular to AB, angle ACD and angle BCD are both right angles. And since angle A is acute, angle ACB must be acute as well.

Now, using the Pythagorean theorem, we can write:
AC² = AD² + CD²
BC² = BD² + CD²

Since AD < BD (because AC ≤ BC), we can substitute BD - AD for BD in the second equation:
BC² = (BD - AD)² + CD²
BC² = BD² - 2AD·BD + AD² + CD²

But now we have a contradiction:
AC² = AD² + CD² < BC² = BD² - 2AD·BD + AD² + CD²

If we simplify the inequality, we get:
0 < BD² - AC² - 2AD·BD

But this cannot be true, because all the terms on the right-hand side are positive (BD > AD, AC < BC, and both sides are squares). Therefore, our assumption that AC ≤ BC must be false.

We have proven that the hypotenuse is the longest side of a right triangle.

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The value of x is 7[tex]\sqrt{3}[/tex] inches

The correct answer is an option (d)

Let us assume that in the attached diagram of right triangle the angle A measures 30 degrees.

Here, the hypotenuse measures 7 in.

We know that in right triangle, the tangent of angle θ is nothing but the ratio of opposite side of angle θ to the adjacent side of angle θ.

Consider the tan of angle A

tan(A) = opposite side of angle A / adjacent side of angle A

tan(30°) =  7 / x

We know that from the standard trigonometric table the value of tan(30°) is [tex]\frac{1}{\sqrt{3} }[/tex]

Substitute this value in above equation we get,

[tex]\frac{1}{\sqrt{3} }[/tex] =  7/x

We solve this equation to find the value of x.

x = 7 × [tex]\sqrt{3}[/tex]

x = 7[tex]\sqrt{3}[/tex] in.

Therefore, the correct answer is an option (d)

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81.06% of people in the 25-34 age group spend less than $2,500 on reading and entertainment per year.

To find the z-score for a person who spends $2,500 on reading and entertainment in the 25-34 age group, we can use the formula:

[tex]z = \frac{(x - μ) }{σ} [/tex]

Where: x = $2,500 μ = $2,080 σ = $480 Substituting these values, we get:

[tex]z = \frac{ (2500 - 2080)}{ 48} \\ z = 0.88[/tex]

This means that a person who spends 2,500 on reading and entertainment is 0.88 standard deviations above the mean. To find the proportion of people who spend less than 2,500 on reading and entertainment, we can use a standard normal table or calculator to find the area to the left of z = 0.88. The area is 0.8106. Therefore, approximately 81.06% of people in the 25-34 age group spend less than $2,500 on reading and entertainment per year.

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Answer:75

Step-by-step explanation:

[tex]\frac{9}{12} =\frac{\frac{9}{3}}{\frac{12}{3} } =\frac{3}{4} \\and percentage is fraction*100\\\frac{3}{4}*100=75[/tex]

The solution to the equation √x = 6 is x = 36.

What is equation?

An equation is a mathematical statement that shows the equivalence of two expressions. It typically includes variables, represented by letters, that can assume different values, as well as constants and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.

To solve the equation √x = 6, we need to isolate x on one side of the equation.

One way to do this is to square both sides of the equation, since squaring both sides will eliminate the square root:

(√x)² = 6²

Simplifying the left side by applying the property that (√a)² = a, we get:

x = 36

Therefore, the solution to the equation √x = 6 is x = 36.

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1.Communism is a political and economic theory that advocates for a society where all property and resources are owned and controlled by the community, without social classes. The theory proposes that the state or community should control the means of production, and individuals should work for the benefit of society, rather than their own gain.

2.Capitalism is an economic and political theory that emphasizes private ownership of the means of production, with wealth being accumulated through free markets and competition. The theory holds that individuals should be free to pursue their own economic interests, while the government's role is limited to protecting property rights and ensuring market efficiency.

3.The proletariat refers to the working class in Marxist theory, who do not own the means of production and must sell their labor to survive. The proletariat is said to be exploited by the bourgeoisie, who extract surplus value from their labor.

4.The bourgeoisie refers to the capitalist class in Marxist theory, who own the means of production and extract surplus value from the labor of the proletariat. The bourgeoisie are motivated by profit, and their accumulation of wealth comes at the expense of the working class.

5.Famine is a situation in which a large number of people are unable to access enough food to meet their basic nutritional needs. Drought, war, government policies, and economic instability are some factors that can contribute to famine.

6.A dictatorship is a form of government in which a single individual or small group holds absolute power, often through the use of force and repression. Dictatorships are characterized by the absence of political freedom and civil liberties, and the subjugation of the populace to the will of the dictator or ruling clique.

7.Ideology refers to a set of beliefs, values, and assumptions that shape an individual's worldview and guide their actions and decisions. Ideologies can take many different forms, from religious and philosophical systems to political and economic theories.

8.In economics, demand refers to the quantity of a good or service that consumers are willing and able to purchase at a given price. The law of demand states that as the price of a good or service increases, the quantity demanded decreases, and vice versa.

9.Overproduction is a situation in which producers manufacture or produce more goods or services than can be consumed or sold in the market. Overproduction can lead to a surplus of goods, which can depress prices and lead to economic downturns.

10.Shareholders are individuals or entities that own shares in a company, entitling them to a portion of the company's profits and a say in its management. Shareholders can exercise their ownership rights through voting on important company decisions and receiving dividends on their investments.

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Exponential growth that shows greater increases with passing time, creating the curve of an exponential function and Arithmetic growth takes place when a constant is being added such that the amount of addition remains constant.

The amounts added grow by a fixed rate of growth, expressed in percentages. Due to the fact that these remain constant while the amounts added rise, growth is then typically measured in doubling times.

Due to the fact that all populations of organisms have the potential to experience exponential growth, the concept of exponential growth is particularly intriguing in the field of population biology.

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24 different 4-digit numbers using all the digits in the number 4129.

The total number of different 4-digit numbers using all the digits in the number 4129, we can use the permutation formula, which is:

nPr = n! / (n - r)!

where n is the total number of items, and r is the number of items taken at a time.

In this case, we have 4 digits to choose from, and we need to choose all 4 of them. Therefore, n = 4 and r = 4.

So, the number of different 4-digit numbers using all the digits in the number 4129 is:

4P4 = 4! / (4 - 4)!

= 4! / 0!

= 24 / 1

= 24

Therefore, there are 24 different 4-digit numbers using all the digits in the number 4129

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged. Put simply, a permutation is a word that describes the number of ways things can be ordered or arranged. With permutations, the order of the arrangement matters..

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The minimum amount of wrapping paper needed for the trapezoidal chocolate is 272 cm².

The minimum amount of wrapping paper that Maria will need to wrap the block of chocolate can be calculated as follows:

Therefore,

Surface area of the trapezoidal prism = (a + b)h + Lateral surface area

Lateral surface area = (a + b + c + d)l

Hence,

Lateral surface area = (5 + 11 + 5 + 5) 8

Lateral surface area = 26(8)

Lateral surface area = 208 cm²

Therefore,

Surface area of the trapezoidal prism = (5 + 11)4 + 208

Surface area of the trapezoidal prism = (16)4 + 208

Surface area of the trapezoidal prism = 64 + 208

Surface area of the trapezoidal prism = 272 cm²

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The null hypothesis for an ANOVA test is that all population means are equal, and the alternative hypothesis is that at least one mean is different from the others.

The p-value for the F-test in this case is 0.064, which is greater than the 5% significance level. Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the mean sulfur dioxide concentrations for the three cities are different.

In other words, it appears that the mean concentration levels are approximately the same for the three city populations.

Therefore, the correct conclusion is that "It appears that the mean concentration levels are approximately the same for the three city populations."

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1.  The opportunity cost of producing 1 ton of grain in Sweden is 0.5 tons of dates.

2. The opportunity cost of producing 1 ton of grain in Libya is 2.5 tons of dates.

3.  Sweden should focus on producing dates, and Libya should focus on producing grain.

4. Both countries can obtain both goods at a lower opportunity cost than if they had tried to produce both goods themselves.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

1. What is the opportunity cost of producing 1 ton of grain in Sweden?

To produce 1 ton of grain in Sweden, a farmer would have to give up producing 0.5 tons of dates (since a farmer in Sweden can produce 10 tons of grain or 5 tons of dates in a season). Therefore, the opportunity cost of producing 1 ton of grain in Sweden is 0.5 tons of dates.

2. What is the opportunity cost of producing 1 ton of grain in Libya?

To produce 1 ton of grain in Libya, a farmer would have to give up producing 2.5 tons of dates (since a farmer in Libya can produce 10 tons of grain or 25 tons of dates in a season). Therefore, the opportunity cost of producing 1 ton of grain in Libya is 2.5 tons of dates.

3. In which country should each good be produced?

Sweden has a comparative advantage in producing dates, since its opportunity cost of producing dates is lower than Libya's. Libya has a comparative advantage in producing grain, since its opportunity cost of producing grain is lower than Sweden's. Therefore, Sweden should focus on producing dates, and Libya should focus on producing grain.

4. Can trade benefit both countries? If so, which good should each country specialize in producing?

Yes, trade can benefit both countries. Sweden should specialize in producing dates and trade them for grain with Libya, which should specialize in producing grain. This way, both countries can obtain both goods at a lower opportunity cost than if they had tried to produce both goods themselves.

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The measure of angle ITE is 44 degrees. In a kite, the diagonals intersect at a right angle and bisect each other. Let's label the points in the kite as follows:

Point P is the intersection of the diagonals.

Point K is at one end of the kite.

Point E is at the other end of the kite, opposite to point K.

Point I is between points K and P.

Point T is between points E and P.

Since the diagonals bisect each other, we know that IP = KP and EP = TP. Let's use this fact to find the measure of angle ITP, which is equal to ITE:

We know that angle KIP = 46 degrees.

Since IP = KP, angle KIP is isosceles, so angle KPI is also 46 degrees.

Similarly, since KEP = 34 degrees, we know that angle KPE is also 34 degrees.

Since EP = TP, angle EPT is also 34 degrees.

We also know that angles KPI and EPT add up to 90 degrees, since they are complementary angles formed by the intersection of perpendicular lines.

Therefore, angle IPT is 90 - 46 = 44 degrees.

Since IP = TP, angles ITP and IPT are congruent, so angle ITP is also 44 degrees.

Therefore, the measure of angle ITE is 44 degrees.

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The sampling method is not specified. The probability a customer spends less than $14 each visit is approximately 0.8413. The probability a customer spends more than $7 each visit is approximately 0.9082. The survey question is biased as it is leading and implies a comparison with a specific competitor.

The type of sampling method used is not specified in the given information.

Using the standard normal distribution, the probability that a customer spends less than $14 can be found as

P(X < 14) = P(Z < (14-11)/3) = P(Z < 1) = 0.8413

Therefore, the probability that a customer spends less than $14 each visit is 0.8413.

Similarly, the probability that a customer spends more than $7 can be found as

P(X > 7) = P(Z > (7-11)/3) = P(Z > -1.33) = 0.9082

Therefore, the probability that a customer spends more than $7 each visit is 0.9082.

The survey question "How does our food compare to PhillyBurger?" may be biased because it suggests a comparison between two specific brands, which may influence the customer's response. A more neutral question would be "How do you rate the quality of our food?"

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The weighted average rating for movie 3285 can be calculated by multiplying each rater's similarity with the given rating and then dividing the sum by the total sum of similarities.

In this case, we have two raters with similarity values of 15 and 30, respectively. For the first rater with an ID of 30, the similarity value is 15 and the given rating for movie 3285 is 7.0. Therefore, the contribution of this rater to the weighted average rating is (15 x 7.0) = 105.0.

For the second rater with an ID of 20, the similarity value is 30 and no rating is given for movie 3285. Therefore, the contribution of this rater to the weighted average rating is 0. The total sum of similarities is 15 + 30 = 45.0. Thus, the weighted average rating for movie 3285 is (105.0 + 0) / 45.0 = 2.33.

So, the weighted average rating for movie 3285 is 2.33. It's important to note that this calculation assumes that these are the only two raters who rated the movie, and that their similarity values accurately reflect their taste in movies.

we'll use the following formula: Weighted Average = (Rating1 * Similarity1 + Rating2 * Similarity2) / (Similarity1 + Similarity2), Plugging in the values: Weighted Average = (15 * 7.0 + 30 * 30.0) / (7.0 + 30.0)
Weighted Average = (105 + 900) / 37
Weighted Average = 1005 / 37
Weighted Average ≈ 27.16

So, the weighted average rating for the movie with ID 3285 is approximately 27.16.

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The error sum of squares is 0.32. So the answer is (B) 0.32.

The total sum of squares represents the variation in the dependent variable that can be explained by the independent variable(s) and the error term.

The regression sum of squares represents the variation in the dependent variable that can be explained by the independent variable(s) in the regression model.

The error sum of squares represents the variation in the dependent variable that cannot be explained by the independent variable(s) in the regression model and is often referred to as the residual variation.

The formula we can use is SSE = SST - SSR

Here we have

In a study where the least squares estimates were based on 34 sets of sample observations,

The total sum of squares SST = 4.53

The regression sum of squares SSR = 4.21

To find the error sum of squares, we use the formula:

=> SSE = SST - SSR

Plugging in the given values, we have:

=> SSE = SST - SSR = 4.53 - 4.21 = 0.32

Therefore,

The error sum of squares is 0.32. So the answer is (B) 0.32.

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Complete Question:

In a study where the least squares estimates were based on 34 sets of sample observations, the total sum of squares and regression sum of squares were found to be: SST = 4.53 and SSR = 4.21. What is the error sum of squares?

Multiple Choice

A. 1.07   B. 0.32     C. 0.92   D. 8.74

If g(x) is not equivalent to 0 for every x and f and g are constant functions, then f/g is additionally constant.

To prove that the function f/g is continuous, we need to show that it satisfies the epsilon-delta definition of continuity.

Let x0 be a point in the domain of f/g, and let ε be a positive real number. We must locate a real number that is positive so that

[tex]|(f/g)(x) - (f/g)(x0)| < ε |(f/g)(x) - (f/g)(x0)| < ε[/tex] whenever [tex]|x - x0| < δ[/tex].

[tex](f/g)(x0) = f(x0)/g(x0).[/tex]

f(x) →  f(x0) and g(x) →  g(x0) as x →  x0 are known since f and g were continuous at x0. Therefore, we can assume that f(x) and g(x) are arbitrarily close to f(x0) and g(x0) respectively, provided x is sufficiently close to x0. Specifically, there exists a positive real number δ1 such that

[tex]|f(x) - f(x0)| < ε|g(x0)|/2[/tex]  and [tex]|g(x) - g(x0)| < ε|g(x0)|/2[/tex]  whenever

[tex]|x - x0| < δ1[/tex].

These disparities allow us to estimate|(f/g)(x) - (f/g)(x0)| as follows:

[tex]|(f/g)(x) - (f/g)(x0)| = |(f(x)g(x0) - f(x0)g(x))/[g(x)g(x0)]|[/tex]

[tex]≤ |f(x) - f(x0)|/|g(x)g(x0)| + |g(x) - g(x0)|/|g(x)g(x0)|[/tex]

[tex]< (ε|g(x0)|/2)/|g(x)g(x0)| + (ε|g(x0)|/2)/|g(x)g(x0)|[/tex]

[tex]= ε/2 + ε/2[/tex] equals to ε,

provided we choose We have therefore demonstrated that f/g is constant at [tex]x0[/tex]. Since [tex]x0[/tex] was arbitrary, we conclude that f/g is continuous on its entire domain.

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Bayes' Theorem is a mathematical theorem that enables the revision of prior probabilities based on new information or evidence.

This theorem is widely used in statistics, machine learning, and other fields that deal with uncertainty and probabilistic reasoning. Contrary to the first option mentioned in the question,

Bayes' Theorem can be used when conditional probabilities are known, and it enables the calculation of posterior probabilities, which is the probability of a hypothesis or event given the available evidence.

Therefore, the third option is correct; Bayes' Theorem enables the use of sample information to revise prior probabilities. This theorem is highly valuable because it allows the integration of new data or knowledge into the decision-making process,

which can lead to more accurate predictions and better-informed decisions. In summary, Bayes' Theorem is a powerful tool that requires knowledge of probabilities and enables the calculation of posterior probabilities based on new evidence or information.

By combining prior probabilities with likelihoods (based on new data), we can calculate posterior probabilities, which represent our updated knowledge.

This process is crucial in making informed decisions in various fields, such as data science, finance, and medical diagnosis.

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The statement that best shows active listening is "The listener focuses on the speaker, remains undistracted, and may ask clarifying questions.". So, correct option is A.

Active listening is an important communication skill that involves paying full attention to what the speaker is saying, both verbally and non-verbally. Active listening requires the listener to be fully engaged in the conversation, understand the speaker's perspective, and respond appropriately.

Option A) best shows active listening because it includes key aspects of this skill. Focusing on the speaker and remaining undistracted shows that the listener is fully engaged in the conversation, while asking clarifying questions demonstrates an effort to understand the speaker's message.

On the other hand, Option B) is not an example of active listening as it suggests the listener is not fully engaged in the conversation. Option C) may be helpful for taking notes, but does not necessarily demonstrate active listening, as the listener may miss non-verbal cues or tone of voice.

Option D) can be seen as interrupting the speaker and not allowing them to fully express their thoughts, which can hinder effective communication.

So, correct option is A.

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it is important to keep in mind that the results of a polygraph test should not be taken as absolute proof of deception or truthfulness, and that other factors should also be considered in evaluating a job applicant

While lie-detector tests (also known as polygraph tests) are sometimes used as part of a job application process, their reliability and accuracy are controversial and have been questioned by many experts in the field. The test measures physiological responses such as heart rate, blood pressure, and sweat gland activity in response to questions, and the results are interpreted by a trained examiner to determine whether the person is being truthful or deceptive.

However, there are several factors that can affect the results of a polygraph test, including the person's physiological state (such as anxiety or stress), the wording and interpretation of the questions, and the skills and biases of the examiner. False positives (indicating deception when the person is actually telling the truth) and false negatives (indicating truthfulness when the person is actually lying) are also possible.

In your case, it is possible that the lie-detector test gave a false positive result, indicating deception when you were actually telling the truth. There could be various reasons for this, such as anxiety or stress during the test, a misunderstanding or misinterpretation of the questions, or an error in the administration or interpretation of the test.

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The given statement is True i.e. if a function f is one-to-one correspondence from its domain to its co-domain, then it has an inverse function.

What is co-domain?

In mathematics, the co-domain of a function is the set of all possible values that the function can output. It is a subset of the target space or range of the function.

The given statement is True.

If a function f is one-to-one correspondence (also known as a bijective function) from its domain to its co-domain, then it has an inverse function. The inverse function is a function that maps the co-domain back to the domain, such that if f(x) = y, then [tex]f^{-1}(y) = x.[/tex]

To show that a function f has an inverse, we need to show that f is both injective (one-to-one) and surjective (onto). If f is injective, then every element in the co-domain has a unique preimage in the domain. If f is surjective, then every element in the co-domain is mapped to by at least one element in the domain. If f is both injective and surjective, then it is bijective, and hence has an inverse function.

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The experimental design in this scenario is a randomized block design. The blocks are the male and female groups, and the treatments (different arm strength regimens) are randomly assigned within each block.

This design allows for better control of potential confounding variables, such as gender, and helps to increase the precision of the results.

This experimental design is called a Stratified Randomized Controlled Trial (RCT). In this design, participants are first divided into separate groups based on a specific characteristic, such as gender (males and females in this case). Then, within each group, treatments are randomly assigned to compare arm strength regimens.

This approach helps ensure that each treatment group has a similar proportion of males and females, reducing potential confounding factors and increasing the of the study's results.

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The expected number of people who will drop out due to either relapse or moving away is 10 + 6 = 16. However, taking into account the standard deviations, it is 16 +/- 5.

To find the expected number of people who will drop out due to either relapse or moving away, we need to add the expected number of people who will drop out due to relapse (10) and the expected number of people who will drop out due to moving away (6).

Expected number of people who will drop out due to either relapse or moving away = 10 + 6 = 16.

However, we also need to take into account the standard deviations for each of these groups. To do this, we can use the square root of the sum of the variances (SD squared) for each group, squared.

Variances:
- Relapse: 4 squared = 16
- Moving away: 3 squared = 9

Square root of the sum of the variances:
- sqrt(16 + 9) = 5

Therefore, the expected number of people who will drop out due to either relapse or moving away, taking into account the standard deviations, is 16 +/- 5.

This means that we can expect anywhere between 11 and 21 people to drop out due to either relapse or moving away during the two-year cohort study.

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To prove that for some n > 0, xi > 0 for all i > n, we can use the fact that (xi) is a sequence that converges to x.

This means that given any ε > 0, there exists an N such that |xi - x| < ε for all i > N.  we can use the fact that (xi) is a sequence that converges to x.

Let's choose ε = x/2. Since x > 0, ε > 0 as well. Then there exists an N such that |xi - x| < ε = x/2 for all i > N. Rearranging this inequality, we get:

x - xi < x/2

xi > x/2

Since xi > x/2 and x > 0, we have shown that for some N > 0, xi > 0 for all i > N.

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It depends on which edge and by how much you are raising the weight in the minimum spanning tree.

Consider the following example to gain a better understanding of this idea. Let T be the smallest spanning tree of G and let G be a connected, weighted graph. Consider increasing an edge's weight in T by a tiny positive amount.

T continues to be a spanning tree of G if is small enough because it is still connected and contains all of G's vertices. However, T is no longer a minimum spanning tree of G because its weight has increased by. Consider any alternative spanning tree T' of G to understand why. We know that the weight of T is less than or equal to the weight of T' because T was the lowest spanning tree prior to the weight increase.

T' is now a better minimal spanning tree than T since, after the weight increase, the weight of T is greater than the weight of T' plus. T' must be the new minimal spanning tree of G as a result.

In conclusion, altering the weight of an edge in a minimum spanning tree may result in the inclusion of a different set of edges, which may result in a change in the tree's structure. The new minimal spanning tree might, however, nevertheless have the same edges as the previous minimum spanning tree if the weight gain is negligibly tiny.

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The number of black - footed Mizjigs in Ragon's colony can be found to be A. 185 black - footed Mizjigs

First, find the number of one - headed Red - footed Mizjigs to be :

= 213 - 105

= 108 one - headed Red - footed Mizjigs

This means that the number of two - headed Mizjigs in the colony are:

= 435 - 213

= 222 two - headed Mizjigs

The number of two - headed black - footed Mizjigs are:

= 222 - 142

= 80 two - headed black - footed Mizjigs

The total black - footed Mizjigs are:

= 105 + 80

= 185 black - footed Mizjigs

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In a case whereby angela walked 12 mile. She took a break for water and then walked some more. In all, she walked 1110 miles then the distance that Angela walk after her break is 1098 miles

The distance that she walks initially = 12 mile

The total distance that she wlaked =1110 miles.

Then the distance she walked after the break =1110 miles -  12 mile

=1098 miles

Then we can come into conclusion that she was able to navigate 1098 miles after she rest during the break 1098 miles which implies that the distance she walked after the break was more.

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Hector made 18 posters and Harley made 12 posters.

represent the number of posters Hector made as "x" and the number of posters Harley made as "y."

According to the given information, Hector made 6 less than twice the number of posters Harley made.

In equation form, this can be expressed as:

x = 2y - 6 ... (1).

It is also mentioned that Hector and Harley made a total of 30 posters. So, the sum of their posters should be equal to 30:

x + y = 30 ... (2)

Now, we have a system of two equations (equation 1 and equation 2) that we can solve simultaneously to find the values of x and y.

Substituting equation 1 into equation 2, we have:

(2y - 6) + y = 30

Combining like terms:

3y - 6 = 30

Adding 6 to both sides:

3y = 36

Dividing both sides by 3:

y = 12

Substituting the value of y back into equation 1:

x = 2(12) - 6

x = 24 - 6

x = 18.

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The following triangle is b) right.

To determine whether the triangle is acute, right, or obtuse, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). If this is not true, then the triangle is either acute or obtuse.

In this case, we have:

a = 7 ft

b = 11 ft

c = √170 ft

We can first check whether this is a valid triangle by verifying that the sum of the lengths of any two sides is greater than the length of the third side. In this case, we have:

a + b > c

7 + 11 > √170

18 > √170

This inequality is true, so we know that the given side lengths can form a triangle.

Next, we can use the Pythagorean theorem to check whether the triangle is right. If we square each of the two shorter sides and add the results, we get:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]7^{2}[/tex] + [tex]11^{2}[/tex] = 170

Then, we can compare this to the square of the longest side, which is:

[tex]c^{2}[/tex] = [tex](\sqrt{170} )^{2}[/tex] = 170

Since [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex], we have a right triangle.

Therefore, the answer is (b) right.

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The ratio of the volumes of the similar solids expressed in lowest terms is 64 : 27

From the question, we have the following parameters that can be used in our computation:

Two similar solids have a scale factor of 4:3

This means that

Ratio = 4 : 3

To calculate the ratio of their volumes expressed in lowest terms, we cube both sides of the expression

So, we have

Volume ratio = 64 : 27

Hence, the ratio of their volumes expressed in lowest terms is 64 : 27

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