Angles jhi and gjh are inscribed angles. we have that m∠jhi = one-half b and m∠gjh = one-halfa by the . angle jhi is an exterior angle of triangle . because the measure of an exterior angle is equal to the sum of the measures of the remote interior angles, m∠jhi = m∠jgi m∠gjh. by the , one-halfb = m∠jgi one-halfa. using the subtraction property, m∠jgi = one-halfb " one-halfa. therefore, m∠jgi = one-half(b " a) by the distributive property.

(a) A recursive backtracking algorithm (O(3^k * p(n))) is proposed for the Triangle Vertex Deletion problem, aiming to find a set of at most k vertices that can remove all triangles in a graph G. (b) An improved algorithm (O(2.562^n * p(n))) selects vertices belonging to multiple triangles, enhancing the efficiency of the Triangle Vertex Deletion problem.

(a) A simple recursive backtracking algorithm for the Triangle Vertex Deletion problem can be formulated as follows:

1. Start with an empty set S of deleted vertices.

2. If all triangles are deleted (i.e., no triangle exists in G), return true.

3. If k = 0, return false since no more vertices can be deleted.

4. Select a vertex v from V.

5. Remove v from V and add it to S.

6. Recursively check if deleting v results in deleting all triangles. If so, return true.

7. Restore v in V and remove it from S.

8. Recursively check if not deleting v results in deleting all triangles. If so, return true.

9. If neither step 6 nor step 8 returned true, move to the next vertex in V and repeat steps 4-9.

10. If no vertex leads to the deletion of all triangles, return false.

The time complexity of this algorithm is O(3^k * p(n)), where p(n) is the time needed to determine if a vertex belongs to a triangle.

(b) To improve the algorithm, we can exploit the idea of selecting a vertex that belongs to two different triangles. The improved algorithm can be defined as follows:

1. Start with an empty set S of deleted vertices.

2. If all triangles are deleted (i.e., no triangle exists in G), return true.

3. If k = 0, return false since no more vertices can be deleted.

4. Select a vertex v that belongs to at least two different triangles.

5. Remove v from V and add it to S.

6. Recursively check if deleting v results in deleting all triangles. If so, return true.

7. Restore v in V and remove it from S.

8. Recursively check if not deleting v results in deleting all triangles. If so, return true.

9. If neither step 6 nor step 8 returned true, move to the next vertex in V and repeat steps 4-9.

10. If no vertex leads to the deletion of all triangles, return false.

The time complexity of this improved algorithm is O(2.562^n * p(n)), where 2.562 is the positive root of the equation x^2 = x + 4.

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The U.S. Census Bureau takes a census every 10 years, which means that they attempt to count every person living in the United States and collect data on various demographic and social characteristics.

A sample is a subset of a larger population, selected in a way that it represents the characteristics of the population from which it is drawn. The purpose of sampling is to estimate or infer something about the population based on the characteristics of the sample.

On the other hand, a census is a survey or count that attempts to measure every member of a population.

In a census, data is collected on every individual or item in a population, rather than just a representative sample.

If you wanted to estimate the average income of households in a city, you could select a sample of households and estimate the average income based on the incomes of the sampled households.

This would be an example of sampling.

Alternatively, you could conduct a census of every household in the city, collecting income data from every household, and calculate the exact average income of all households in the city.

The purpose of the census is to provide a complete and accurate count of the population, which can then be used to allocate political representation and government funding, as well as to provide data for research and planning purposes.

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Explanation

To solve the question, we will be aware that

There are 3 hours between 6PM and 9PM ,

The main pump's emptying rate is 1/4 tanker per hour. It will be open

the entire 3 hours, so it will empty 3/4 of the tank.

this means that the auxiliary pump must empty the remaining 1/4

Thus

Thus, we will have

Therefore

The auxiliary pump should start by 6pm + 45 minutes = 6:45pm

When testing partial correlation, the impact of a third variable is removed.

Partial correlation is a statistical technique used to assess the relationship between two variables while controlling for the influence of one or more additional variables, known as the third variable(s) or covariate(s). The aim of partial correlation is to determine the strength and direction of the association between two variables after accounting for the potential confounding effect of other variables.

By controlling for the influence of third variable(s), partial correlation allows researchers to isolate the unique relationship between the two variables of interest, while holding constant the effects of other variables that may be correlated with both the variables being studied. This helps to assess the direct association between the two variables of interest, beyond the potential influence of other variables.

Partial correlation is commonly used in research and statistics when the relationship between two variables of interest may be confounded by the presence of other variables that could affect the results. It is a valuable tool for examining the specific association between two variables while accounting for the potential influence of other factors, thereby providing a more accurate and nuanced understanding of the relationship between those variables.

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Answer:

The selling price of the bag is $22.5

Step-by-step explanation:

Buying Price = $25,

Selling Price = ?

Since they sold it at a loss of 10%,

So, they sold it for a price 10% less than the buying price,

or at 90% or 0.9 of the buying price,

so,

Selling Price = (0.9)(25) = $22.5

Answer:

no

Step-by-step explanation:

Answer:

x = -5

y = -4

Step-by-step explanation:

Answer:

1) 2v-10

2) 3u-6

3) 21 + 7v

Step-by-step explanation:

Using the distibutive property all you have to do is have the number on the of the parenthesis multiply itself to each component in your parenthesis.

when developing the formula for s(M1-M2), we consider the amount of error for each sample mean, the estimated standard error of M as a statistic, and use an average estimate when dealing with different sample sizes. This helps us determine the total amount of error when using two sample means to approximate two population means.

The independent-measures t statistic is used to determine the total amount of error when using two sample means to approximate two population means. To develop the formula for s(M1-M2), we consider the following points:

1. Each of the two sample means represents its own population mean, but there is some error involved in each case. This error is referred to as the "amount of error."

2. The "amount of error" associated with each sample mean is measured by the estimated standard error of M (sM). This statistic helps us understand how much the sample means may deviate from their respective population means.

3. To find the total amount of error involved in using two sample means to approximate two population means, we consider the size of each sample. If the samples are the same size, we can find the error from each sample separately and add the two errors together.

4. When the samples are of different sizes, a "pooled" or "average estimate" is used to account for the different sample sizes. This approach allows the larger sample to carry more weight in determining the final value of the t statistic.

In summary, when developing the formula for s(M1-M2), we consider the amount of error for each sample mean, the estimated standard error of M as a statistic, and use an average estimate when dealing with different sample sizes. This helps us determine the total amount of error when using two sample means to approximate two population means.

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The simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is 729x^6 - V^2.

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

To simplify the expression using the given values, we substitute \(U = 3x^3\)and V = y + 1 into the original expression:

\(81x^6 - (y + 1)^2\)

Replacing U and V:

\(81(3x^3)^2 - (V)^2\)

Simplifying:

\(81 \times 9x^6 - V^2\)

\(729x^6 - V^2\)

Therefore, the simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is\(729x^6 - V^2.\)

In this way, we can represent the original expression in a simplified form using the assigned values for U and V.

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Consider the expression: \(81x^6 - (y + 1)^2\)

If\(U = 3x^3\) and V = y + 1, what is the simplified form of the expression in terms of U and V?

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

Answer:

y is 12 degrees

x is 30 degrees

Step-by-step explanation:

If angle ABC is equal to angle MNC, that means 5y equals to 60 degrees. 60 divided by 5 equals 12. So, y equals 12 degrees

2x and 4x equals 180 degrees. So, 180 divided by 6 equals to 30. So x equals 30 degrees

Answer:

x = 30, y = 12

Step-by-step explanation:

2 similar equilateral triangles, each corner is 60 degrees.

2x = 60 degrees

divide by 2

x = 30 degrees

5y = 60 degrees

divide by 5

y = 12 degrees

This can be verified by checking 4x + 2x which gives you 180 degrees forming that straight line angle.

Answer:

The null hypothesis: \(\mathbf{H_o: p=0.27}\)

The alternative hypothesis: \(\mathbf{H_1: p \neq 0.27}\)

Test statistics : z = −2.30

P-value:  = 0.02144

Decision Rule: Since the p-value is lesser than the level of significance; then we reject the null hypothesis.

Conclusion: We accept the alternative hypothesis and  conclude that under the same​ circumstances the proportion of offspring peas will be yellow is not equal to 0.27

Step-by-step explanation:

From the given information:

Let's state the null and the alternative hypothesis;

Since The claim is that 27%  of the offspring peas will be yellow.

The null hypothesis state that the proportion of offspring peas will be yellow is equal to 0.27.

i.e

\(\mathbf{H_o: p=0.27}\)

The alternative hypothesis  state that the proportion of offspring peas will be yellow is not equal to 0.27

\(\mathbf{H_1: p \neq 0.27}\)

The test statistics:

we are given 437 green peas and 129 yellow apples;

Hence;

\(\hat p = \dfrac{x}{n}\)

where ;

\(\hat p\) = sample proportion

x = number of success

n = total number of the sample size

\(\hat p = \dfrac{129}{437+129}\)

\(\hat p = \dfrac{129}{566}\)

\(\mathbf{\hat p = 0.2279}\)

Now; the test statistics can be computed as :

\(z = \dfrac { \hat p -p }{\sqrt {\dfrac{p(1-p)}{n} } }\)

\(z = \dfrac {0.2279 -0.27 }{\sqrt {\dfrac{0.27(1-0.27)}{566} } }\)

\(z = \dfrac {-0.043 }{\sqrt {\dfrac{0.27(0.73)}{566} } }\)

\(z = \dfrac {-0.043 }{\sqrt {\dfrac{0.1971}{566} } }\)

\(z = \dfrac {-0.043 }{\sqrt {3.48233216*10^{-4} } }\)

\(z = \dfrac {-0.043 }{0.01866} }\)

z = −2.30

C. P-value

P-value = P(Z < z)

P-value = P(Z< -2.30)

By using the ​ P-value method and the normal distribution as an approximation to the binomial distribution.

from the table of standard normal distribution

move left until the first column is reached. Note the value as –2.0

move upward until the top row is reached. Note the value as 0.30

find the probability value as 0.010724 by the intersection of the row and column values gives the area to the left of

z = -2.30

P- value = 2P(z ≤ -2.30)

P-value = 2 × 0.01072

P - value = 0.02144

Decision Rule: Since the p-value is lesser than the level of significance; then we reject the null hypothesis.

Conclusion: We accept the alternative hypothesis and  conclude that under the same​ circumstances the proportion of offspring peas will be yellow is not equal to 0.27

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\( f(x) = \sqrt{2x - 10} \)

\(Domain \: \: : \: 2x - 10 \geqslant 0\)

Add sides 10

\(Domain \: \: : \: \: 2x - 10 + 10 \geqslant 10 \\ \)

\(Domain \: \: : \: \: 2x \geqslant 10\)

Divided sides by 2

\(Domain \: \: : \: \: \frac{2}{2}x \geqslant \frac{10}{2} \\ \)

\(Domain \: \: : \: \: x \geqslant 5\)

Done...

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Answer:

A. 136 sq. cm.

Step-by-step explanation:

First find the area of the rectangle:

16 times 7 is 112

13-7 is 6

16-8 is 8

The formula for the area of a triangle is ab/2

thus:

6 times 8 is 48/2

Which is 24

Add 112 with 24

Which is 136

Thus the answer is A. 136 sq. cm.

Hope this helps!

Using the probability concept, it is found that 60% of the swim team are sophomores.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The sum of the probabilities of all outcomes of an event is of 1, hence:

P(freshman) + P(sophomore) = 1.

The probability that a sophomore is elected is $3/2$ times the probability that a freshman is elected, hence:

x + 3/2x = 1.

5/2x = 1

5x = 2

x = 0.4.

Thus:

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The polynomial with degree 3, real coefficients, zeros at x = -6 and 3+i, and a y-intercept of (0,30) is given by f(x) = (x + 6)(x - 3 - i)(x - 3 + i).

To find the polynomial with the given conditions, we start by using the zero-product property. Since the zeros are x = -6, 3+i, and 3-i, the corresponding factors of the polynomial are (x + 6), (x - 3 - i), and (x - 3 + i).

Now, to obtain the expanded form of the polynomial, we multiply these factors together:

f(x) = (x + 6)(x - 3 - i)(x - 3 + i)

Expanding this expression, we get:

f(x) = (x + 6)(x^2 - 3x + ix - 3x + 9 - 3i - ix + 3i - i^2)

Simplifying further, we have:

f(x) = (x + 6)(x^2 - 6x + 9 + 1)

f(x) = (x + 6)(x^2 - 6x + 10)

Multiplying the binomials, we obtain:

f(x) = x^3 - 6x^2 + 10x + 6x^2 - 36x + 60

Combining like terms, the expanded form of the polynomial is:

f(x) = x^3 - 26x + 60

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Answer:

m=2/3, b=4

Step-by-step explanation:

Using the rise over run method, you can count from two points. Also since this line is positive. The b is found by seeing where the line crosses the y axis. It crosses at 4.

Step-by-step explanation:

so, we just enter the given data into the given formula. and then calculate. it does not get easier than that.

d = 8km/h × 2h = 16km

Serena ran 16km in these 2 hours.

Answer:

the correct answer is 16km

Step-by-step explanation:

pl.z dont delete this

Answer:

6250

Step-by-step explanation:

Hope the answer is correct.

The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.

Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.

In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.

This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.

However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.

As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.

As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.

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Using the formula n(n+1), the sum of the terms from 501 to 10,000 is calculated to be 49,502,501.Subtracting the sum from 1 to 500 yields the desired result.

To find the sum of the terms from 501 to 10,000 using the formula n(n+1), we first need to determine the values of n. In this case, the first term, 501, corresponds to n = 500 (since n is obtained by subtracting 1 from the given term). The last term, 10,000, corresponds to n = 9,999.

Now we can apply the formula: n(n+1)/2. Plugging in the values, we get (500)(500+1)/2 for the sum from 501 to 500, which equals 250,500. Similarly, for the sum from 501 to 10,000, we calculate (9,999)(9,999+1)/2, resulting in 49,950,000.

However, since we want the sum starting from 501, we need to subtract the sum from 1 to 500. Using the same formula, (500)(500+1)/2, we obtain 125,250 for the sum from 1 to 500. Subtracting this value from the sum from 501 to 10,000, we get 49,950,000 - 125,250 = 49,824,750.

Therefore, the sum of the terms from 501 to 10,000 using the formula n(n+1) is 49,824,750.

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Answer:

-3 I think...

Step-by-step explanation:

y=mx+b. where m is the slope, since -3 is the value for m, it is the slope

Answer:

314.16 mi

Step-by-step explanation:

Answer:

The answer is 314.16

Step-by-step explanation:

We can write a proportion to solve

82 guests 91 guests

------------------- = -------------

656 dollars x dollars

Using cross products

82x = 91 * 656

82x =59696

Divide each side by 82

82x/82 = 59696/82

x =728

The party with 91 guests will cost 728 dollars

To use Euler integration to determine the next values of x and y, given the current values x=2, y=8, and y'=9, with a step size of delta_X=5, we can use the following formula:

x_new = x_current + delta_X

y_new = y_current + delta_X * y'

Using the given values, we have:

x_new = 2 + 5 = 7

y_new = 8 + 5 * 9 = 53

Therefore, the next values of x and y using Euler integration with a step size of delta_X=5 are x=7 and y=53.

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Answer:

Don't know u is correct. Also I'm not a h0* how rude  >:(

Answer:

None of the above because I love you

Step-by-step explanation:

I don't hate you and if some people do they must have there reasons which I don't know, but some people just hate for no reason and if they can hate for no reason some people can love for no reason.

You may be a complete stranger to me but I love you

The months in which the depths decreased are:

Between April and May

Between June and July

The change in depth between April and May is calculated as:

Change in depth = -0.28 - (-0.15) = -0.13 m

Thus, there was a decrease in depth between april and may

The change in depth between May and June is calculated as:

Change in depth = -0.08 - (-0.28) = 0.20 m

Thus, there was an increase in depth between May and June

The change in depth between June and July is calculated as:

Change in depth = -0.01 - (-0.05) = 0.07 m

Thus, there was a decrease in depth between June and July.

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The complete question is:

A scientist measures the depth of the water in a pond each month. The pond is considered full at 0 m. She compares her measures to the height of the water when the pond is considered full and records the change in depth in a table

Between which months did the depth of water decrease?

Answer:

(3,1)

Step-by-step explanation: