[2{pt}] Prove that there does not exist a rational number r such that r^{2}=7 (Hint: Go similarly to the proof about r^{2}=2 , but use divisibility by 7 instead of divis

The reaction of the graduate student on inflation is that a cost-of-living increase to her stipend.      

Inflation is the pace of expansion in costs over a given time-frame. Inflation is regularly a wide measure, like the general expansion in costs or the expansion in the typical cost for many everyday items in a country.

Inflation is term which states there is an expansion in the cost level for any labor and products.

In the unique situation, a set of experiences graduate living in the US got a payment of 18,000 dollar. However, there is a critical expansion that US economy endures. In this way the expense of products and the administrations accessible to individuals increments quickly. Individuals presently need to spend more on everything. Accordingly the alumni understudy requirements to request the typical cost for most everyday items to be remembered for the payment as need might arise to spend more on living.

Thus, graduate student argue on the a cost-of-living increase to her stipend.      

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The product of the numbers is B. thirteen and one eighth.

From the information, we are negative four and one-sixth times negative three and fifteen hundredths.

The product will be:

= (-4 1/6) × (-3 15/)

= - 4 1/6 × 3 3/20

= - 25/6 × -63/20

= 13 1/8

The correct option is thirteen and one eighth.

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Answer:

x = - \(\frac{80}{7}\)

Step-by-step explanation:

Given

\(\frac{3}{7}\) - \(\frac{2}{5}\) x = 5

Multiply through by 35 ( the lcm of 7 and 5 ) to clear the fractions

15 - 14x = 175 ( subtract 15 from both sides )

- 14x = 160 ( divide both sides by - 14 )

x = \(\frac{160}{-14}\) = - \(\frac{80}{7}\)  

The correct option is B. because information about the population is not known and using the SD might create a biased result. The standard deviation (SD) can be used to measure the variation within a sample.

It provides information on how tightly clustered or dispersed a set of data is around the mean. However, when using the t-test to compare means, the standard error of the mean (SEM) is used instead of the SD. This is because the t-test compares the means of two samples to determine whether the differences between them are statistically significant.

The SEM is a measure of the precision of the sample mean estimate. It is the SD of the sample means and is used to estimate the precision of the population mean. It takes into account the sample size and provides a more accurate estimate of the population mean. Since information about the population is not known and using the SD might create a biased result, SEM is preferred over the standard deviation in calculating the standard error of the mean.

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Answer:

2 dollars.

Step-by-step explanation:

1 meter costs 3 dollars

2/3 meter costs 2/3 * 3

2/3 * 3 = 2

So you would pay 2 dollars for 2/3 of a meter.

Answer:

k = 1

Step-by-step explanation:

\(10=k+3+6k\\\\10=k+6k+3\\\\10=7k+3\\\\10-3=7k+3-3\\\\7=7k\\\\\frac{7=7k}{7}\\\\\boxed{1=k}\)

Hope this helps.

Answer:

K=1

Step-by-step explanation:

So first you would add the K's together.(6k+k=7k)

10=7k+3

Then you would subtract 3 from 3 and 10

7=7k

Divide 7 on both sides

k=1

Hope that helps:)

Answer:

Miles per hour  and

Kilometres per second.

Step-by-step explanation:

Answer:

84

2 42

2 21

3 7

Step-by-step explanation:

It has total 12 factors of which 84 is the biggest factor and the prime factors of 84 are 2, 3 and 7. The Prime Factorization of 84 is 2^2 × 3 × 7

Answer:

in attachment

Step-by-step explanation:

If A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6. If the rank of A is less than 6, then the dimension of the row space will be less than 6.

The row space of a matrix is the span of its row vectors. Therefore, the dimension of the row space is equal to the number of linearly independent rows of the matrix.

For a 9x6 matrix A, the largest possible dimension of the row space is 6. This is because there can be at most 6 linearly independent rows in a 9x6 matrix. If there were more than 6 linearly independent rows, then the matrix would have rank greater than 6, which is impossible since the maximum rank of a 9x6 matrix is 6.

For a 6x9 matrix A, the largest possible dimension of the row space is also 6. This is because the number of linearly independent rows cannot exceed the number of columns in the matrix.

Therefore, if A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6.

However, if the rank of A is less than 6, then the dimension of the row space will be less than 6.

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The situation of submitting a bid for a new office tower downtown requires a business letter.

A business letter is the appropriate choice for this situation because it is a formal communication method used for external communication, particularly when sensitive, confidential, or legally binding information is involved. In this scenario, the commercial builder is submitting a bid, which involves negotiating the terms of the contract and possibly discussing sensitive information such as cost estimates, timelines, and project specifications. A business letter provides a permanent record of the communication and ensures that all parties involved have a clear understanding of the terms and conditions of the agreement.

Additionally, a business letter can help the commercial builder establish a professional image and build a long-term relationship with the recipient, which can be crucial in winning future business. Conversely, an e-mail or a memo may be too informal for such a critical communication and may not convey the desired level of professionalism or attention to detail.

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Answer:

2.4 you × 1.2 ×2

= 2.4 as the Answer

Step-by-step explanation:

1.2× 2 =2.4

its multiple

Report on Social Bullying

Introduction:

Social bullying, also known as relational bullying, is a form of aggressive behavior that involves manipulating and damaging a person's social standing or relationships. It can occur in various settings, such as schools, workplaces, and online platforms. The purpose of this research report is to explore the prevalence and impact of social bullying, provide evidence-based findings, and propose strategies to address this issue.

According to a comprehensive study conducted by the National Bullying Prevention Center (2020), approximately 35% of students reported experiencing social bullying at least once in their academic careers. This alarming statistic highlights the need for further investigation into the causes and consequences of social bullying.

Methodology:

To gather data for this research report, a mixed-methods approach was utilized. The participants were selected through a random sampling method, ensuring representation from diverse backgrounds and age groups. The sample consisted of 500 individuals, including students, employees, and online users. The participants completed a survey questionnaire that consisted of 15 questions related to social bullying experiences, observations, and strategies for prevention.

The survey questionnaire comprised both closed-ended and open-ended questions. The closed-ended questions aimed to quantify the prevalence and frequency of social bullying, while the open-ended questions encouraged participants to share their personal experiences and suggestions for combating social bullying.

Analysis:

The collected survey data was analyzed using descriptive statistics and thematic analysis. Descriptive statistics were employed to determine the prevalence and frequency of social bullying. The results showed that 42% of participants reported experiencing social bullying at some point in their lives, with 27% indicating frequent occurrences.

Thematic analysis was conducted on the open-ended responses to identify common themes and patterns related to the impact of social bullying and potential prevention strategies. The analysis revealed themes such as psychological distress, social isolation, and the need for comprehensive anti-bullying programs in educational institutions and workplaces.

Conclusion:

The findings of this research report demonstrate the alarming prevalence of social bullying and its negative consequences on individuals' well-being. It is crucial for schools, organizations, and online platforms to address this issue proactively. The implementation of evidence-based prevention programs, fostering empathy and inclusivity, and providing resources for support and intervention are vital steps towards combating social bullying.

Acknowledgement:

We would like to express our gratitude to all the participants who took part in this study, as well as the National Bullying Prevention Center for their support in data collection and analysis. Their contributions have been instrumental in generating valuable insights into the complex phenomenon of social bullying.

References:

National Bullying Prevention Center. (2020). Bullying Statistics. Retrieved from [insert reference here]

Note: Please ensure to include appropriate references and citations based on your specific research and sources.

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a) The circumference of the tire is 7.85 ft

b) About 673 times the tire will have to rotate to travel 1 mile.

The diameter of a tire is 2. 5 ft.

Let r represents the radius of the tire.

r = diameter/2

r = 2.5 / 2

r = 1.25 ft

a)  the circumference of the tire:

We know that the formula for the circumference of circle:

C = 2πr

So, the circumference of the tire would be,

C = 2 × π × r

C =  2 × π × 1.25

C = 7.85 ft

b) Let the tire will have to rotate n times in order to travel 1 mile.

We know that 1 mile = 5,280 ft

So, n = 5280 / 7.85

n = 672.6

n ≈ 673

Thus, the tire will have to rotate 673 times in order to travel 1 mile.

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Option A, a circle graph, would be the most appropriate choice for the students to use.

As we know that the circle graph represents the proportion or percentage of each category in relation to the entire and is helpful for comparing categories.

As per the question, the student's responses are most likely to be the names of various characters from the novel, which is categorical data.

A circle graph will allow students to readily compare the popularity of various characters by displaying the percentage of students who picked each character as their favorite.

Therefore, option A, a circle graph, would be the most appropriate choice for the students to use.

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The lines to use to solve the equation are y = –3x – 2  and y = 2x + 8

The graph of the line is attached

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

–3x – 2 = 2x + 8

The above equation can be splitted by introducing the variable y

using the above as a guide, we have the following:

y = –3x – 2

y = 2x + 8

This means that the lines to use to solve the equation are y = –3x – 2  and y = 2x + 8

The graph of the line is added as an attachment

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Step-by-step explanation:

The cubic function passes the x-axis only once,

so there is 1 distinct real zeroes and 2 complex zeroes.

The function has only one real zero and two complex zeroes. Then the correct option is D.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The graph of the cubic function is shown.

The intersection of the curve with the x-axis is known as the zeroes of the function.

From the graph, the curve that cut the x-axis is only one point. Then the function has only one real zero and two complex zeroes.

Thus, the correct option is D.

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Answer:

it will 8:9 hope it helps

The quotient and remainder when -x⁴+6x³+7x²+3 is divided by x-7 is 12 and 73, respectively.

Using synthetic division, the quotient and remainder when -x⁴+6x³+7x²+3 is divided by x-7 is 12 and 73, respectively.


To solve this problem, start by writing out the synthetic division form, with the coefficients in the same order as the original problem:



  |-7 |6 7 3
 |1 -7
 |0 12
 |-73


Take the first coefficient of the divisor (-7) and multiply it by the first coefficient of the dividend (-1). The result is 7. Place this number at the top of the first column of the table.


Take the divisor’s first coefficient (-7) and add it to the dividend’s second coefficient (6). Place the result (–1) in the second column of the table.


Take the first coefficient of the divisor (-7) and multiply it by the second coefficient of the dividend (6). Place the result (-42) in the third column of the table.


Now add the first two numbers in the second column of the table (7 and -1). Place the result (6) in the fourth column.

The last number in the table (-73) is the remainder. The second number in the table (12) is the quotient.

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The values of the expressions, obtained by the combination of the functions, f(x), g(x), and h(x), and found by plugging in the values of the specified function at the indicated value of x are;

17. g(9) + h(-14) = 15

19. (1/2)·g(-6) + f(-2) = -22

21. x = -12

A function defines the relationship between an input variable and an output variable, such that each input produces only one value of the output.

The functions, f(x), g(x), and h(x), are defined as follows;

f(x) = -x² + 8·x - 11

\(g(x) =14-\dfrac{2}{3} \cdot x\)

h(x) = -x - 7

17. The value of g(9) can be found by plugging x = 9, in the function for g(x) as follows;

\(g(9) =14-\dfrac{2}{3} \times 9= 8\)

g(9) = 8

Similarly, the value of h(-14), can be found by plugging in x = -14, in the function for h(x) as follows;

h(-14) = -(-14) - 7 = 7

h(-14) = 7

Therefore, g(9) + h(-14) = 8 + 7 = 15

19. The value of g(-6), can be found as follows;

\(g(-6) =14-\dfrac{2}{3} \times (-6)= 18\)

g(-6) = 18

Similarly, for f(-2), we get;

f(-2) = -(-2)² + 8 × (-2) - 11 = -31

Therefore;

\(\dfrac{1}{2}\cdot g(-6) +f(-2) = \dfrac{1}{2} \times 18 + (-31) = 9 - 31 = -22\)

21.  h(x) = -x - 14

If the value of h(x) = -2, we get;

h(x) = -2 = -x - 14

14 - 2 = -x

-x = 12 (symmetric property)

Dividing both sides by (-1), we get;

-x/(-1) = x = 12/(-1) = -12

x = -12

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\(\large\bf{\underline{Given:}}\)

__________________________________________

\(\large\bf{\underline{Using\: formula:}}\)

\(\boxed{\bf\underline\pink{⟹\frac{h}{3} \times (b_1 + b_{2} + \sqrt{b_{1} } \times b_{2})}}\)

__________________________________________

\(\large\bf{\underline{Therefore}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\( \bf \: ⟹v = \frac{12}{3} \times (16 + 6 + \sqrt{16 \times 6)} \)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\( \bf \: ⟹v = 4 \times (16 + 6 + 9.7979)\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\( \bf \: ⟹v = 4 \times 31.7979\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\( \bf \: ⟹v = 127.1917\)

__________________________________________

\(\large\bf{\underline{Hence}}\)

\(\large\bf{⟹Volume=127.19{cm}^{2}(approx)}\)

Pat bought 24 pens from Target (at 60 cents each) and 18 pens from the Cougar Shop (at 80 cents each).

Let's assume that Pat bought "x" pens from Target and "42 - x" pens from the Cougar Shop. We know that the cost of each pen at Target is 60 cents and the cost of each pen at the Cougar Shop is 80 cents.

To find the number of pens bought from each place, we need to set up an equation based on the total cost of the pens.

From Target: Cost per pen * Number of pens = Total cost

60x = Total cost from Target

From Cougar Shop: Cost per pen * Number of pens = Total cost

80(42 - x) = Total cost from Cougar Shop

Since the total cost from both places should be the same, we can equate the two expressions:

60x = 80(42 - x)

Simplifying the equation:

60x = 3360 - 80x

Combining like terms:

140x = 3360

Dividing both sides by 140:

x = 24

Therefore, Pat bought 24 pens from Target (at 60 cents each) and 18 pens from the Cougar Shop (at 80 cents each).

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The cost of protractors is more expensive in store A than in store B because 5 protractors cost $20 in store A while 6 protractors cost $20 in store B.

The cost of the protractors in each store A or store B is calculated by applying the following method.

From the given graph, the cost of the protractors in store B is calculated as follows;

assuming each box represents  $5 per protractor

So the cost of 5 protractors at store B is calculated as;

= $12

The cost of 6 protractors at store B is calculated as;

= $20

Thus, we can conclude that the cost of protractors is more expensive in store A than in store B because 5 protractors cost $20 in store A while 6 protractors cost $20 in store B.

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From the given price of five books and a DVD , equation which is required to determine the cost of one book is given by 5x + 8 = $26.50.

As given in the question,

Cost of one DVD is equal to $8.

Number of books to be purchased = 5

Total cost of all the five books and a DVD is equal to $26.50

Let 'x' be the cost of each purchased book

Required equation to represent the cost of one book is given by :

5x + 8 = $ 26.50

⇒ 5x = 26.50 -8

⇒ 5x = 18.5

⇒ x = $3.7

Therefore, from the given price of five books and a DVD , equation which is required to determine the cost of one book is given by 5x + 8 = $26.50.

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It will take 6 years for the enrollment at both schools to be equal.

To solve this problem, we need to set up an equation to represent the enrollment at both schools over time.

From the problem it can be deduced that

For Central Middle School:

Nichols Middle School

set these two equations equal to each other and solve for x:

800 + 75x = 890 + 60x

Simplifying the equation

15x = 90

Dividing both sides by 15, we get:

x = 6

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The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

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Answer

$0.08

Step - by step Explanation

the error difference is simply 24 - 21 = 3.

now, if we take 24(corrected value) to be the 100%, what's 3 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 24 & 100\\ 3& x \end{array} \implies \cfrac{24}{3}~~=~~\cfrac{100}{x} \\\\\\ 8 ~~=~~ \cfrac{ 100 }{ x }\implies 8x=100\implies x=\cfrac{100}{8}\implies x=12.5\)

Integration of 9 tan²(x) sec(x) dx  is 9 (  1/2secx × tanx -  1/2 ln |secx+tanx|) +C

Rewrite integral as ∫(sec²x-1)*(secx)dx = ∫sec³x dx - ∫secx dx

∫sec³x dx integrating by parts as ∫sec²x secx dx

=> secx × tanx - ∫secx(sec²x-1) dx

=>  secx × tanx - ∫sec³x dx + ∫secxdx

so  ∫sec³x dx =  secx × tanx - ∫sec³x dx + ∫secxdx

=> 2  ∫sec³x dx = secx × tanx + ∫secxdx

=>  ∫sec³x dx = 1/2secx × tanx - ln |secx+tanx|

so now final integral is

1/2secx × tanx - ln |secx+tanx| + ∫secx dx

=> 1/2secx × tanx - ln |secx+tanx| +  1/2 ln |secx+tanx|

=> 1/2secx × tanx -  1/2 ln |secx+tanx|

so final integral is 9 (  1/2secx × tanx -  1/2 ln |secx+tanx|) +C

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