Round 2798.01 to 2 significant figure

To check if the given differential equation is homogeneous. A first-order differential equation of the form M(x,y)dx + N(x,y) dy = 0 is said to be homogeneous if both M(x,y) and N(x,y) are homogeneous functions of the same degree.

In this case, we have 3x dy - 3y dx = 100 + 10(x^8y''). We can see that 3x and 3y are both homogeneous functions of degree 1, while 100 and 10(x^8y'') are both homogeneous functions of degree 0. So, the given differential equation is not homogeneous.

However, we can make it homogeneous by dividing both sides by x^3. This gives us:

3(dy/dx) - (y/x) = 100/x^3 + 10(x^5)(dy/dx)

Now, we can see that both 3(dy/dx) and (y/x) are homogeneous functions of degree 0, while 100/x^3 and 10(x^5)(dy/dx) are homogeneous functions of degree -3 and 5, respectively.

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Answer:

because it has 7 cm a helper of right angle triangle and me can also use phythogorreas triplet formula

Answer:

-0,8777 the answer is at least it seems

Step-by-step explanation:

0.1144283374 is its answer..

Outer area:

= πr²h

= 3.14 × 5 × 5× 4

= 3.14 × 20 × 5

= 314

Inner area:

= πrh

= 3.14 × 2 × 2× 4

= 3.14 × 8 × 2

= 50.24

Area of tank

= outer area - inner area

= 314 - 50.24

= 263.76 ft²

The equation to determine the number of hours worked by the plumber is 190 = 35 + 50x and the number of hours is 3.1 hours option (A) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Jerald is having drain issues at his home and decides to call a plumber.

The plumber charges $35 to come to his house and $50 for every hour they work.

Let x be the number of hours:

190 = 35 + 50x

50x = 155

x = 3.1 hours

Thus, the equation to determine the number of hours worked by the plumber is 190 = 35 + 50x and the number of hours is 3.1 hours option (A) is correct.

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Answer: 8 hours

Step-by-step explanation:  240 mph ÷ 30 = 8 hours

Answer:

This correlation simply means that, in every twin whether identical or fraternal twins, there is a relation between their IQ scores and when they are raised together.

Regarding to the test carried out, it showed that, when an identical twin is raised together, their IQ score tends to be higher in direct comparison with a fraternal twin that was raised together. That is, if the fraternal twin IQ is 100, then, the identical twin IQ is going to be above 100 (probably around 120)

Step-by-step explanation:

Given:

Given that

Required:

To find the other five trig ratio.

Explanation:

Now the hypotenuse is,

Now,

Final Answer:

The six trig ratio are

Answer:

see explanation

Step-by-step explanation:

CY = CB + BY

     = 6b + 5a - b

     = 5a + 5b

---------------------

CX = CA + AX

     = CA + \(\frac{1}{3}\) AB , find AB

AB = AC + CB

     = - 3a + 6b

     = 6b - 3a

Thus

CX = CA  + \(\frac{1}{3}\) AB

      = 3a + \(\frac{1}{3}\)(6b - 3a)

      = 3a + 2b - a

      = 2a + 2b

---------------------

and

\(\frac{2}{5}\) CY

= \(\frac{2}{5}\) (5a + 5b)

= 2a + 2b = CX

Hence CX = \(\frac{2}{5}\) CY ⇒ Proven

Using complementary angles, the measure of angle 4 is of 39º.

If two angles A and B are complementary, the sum of their measures is of 90º.

In this problem, angles 3 and 4 are complementary, hence:

m<3 + m<4 = 90º.

Angles 1 and 3 are opposite by the same vertex, hence they are congruent and we can find x as follows:

m<1 = m<3

4x - 13 = 2x + 19.

2x = 32

x = 16.

The measure of angle 3 is given by:

m<3 = 2(16) + 19 = 51.

Hence the measure of angle 4 is found as follows:

m<3 + m<4 = 90º.

51 + m<4 = 90º.

m<4 = 39º.

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Answer:

\(\huge\boxed{b=\dfrac{24}{5}\to b=4\dfrac{4}{5}\to b=4.8}\)

Step-by-step explanation:

\(12=\dfrac{5}{2}b\to\dfrac{5}{2}b=12\qquad|\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup\cdot\dfrac{5}{2\!\!\!\!\diagup}b=12\cdot2\\\\5b=24\qquad|\text{divide both sides by 5}\\\\\dfrac{5b}{5}=\dfrac{24}{5}\\\\b=\dfrac{24}{5}\to b=4\dfrac{4}{5}\to b=4.8\)

The pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

What is vertical opposite angle ?

When 2 lines meet one another, then the other angles, shaped thanks to intersection ar known as vertical angles or vertically opposite angles. A try of vertically opposite angles ar continuously adequate to one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to a hundred and eighty degrees.

Main body:

1st pair of line intersect each other , so ∠1 = ∠2 by using vertical opposite angle.

2nd pair of line also intersect each other , so ∠3 ,∠4 are adjacent angles.

Hence ,pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

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Answer:

3

Step-by-step explanation:

5(-3) -4(-3) - 3 + 9

-15+12-3+9 = 3

5c-4c+c-3c = 3

3. The statement is true,  the correlation coefficient is close to -1. 4. temperature for a city with a latitude of 48 is 43. 5. The statement is false. 6. cannot make a reasonable estimate

Equations can be used to model real-world situations and solve problems in many fields, including science, engineering, finance, and more. They are an essential tool in mathematics and are used extensively in algebra, calculus, and other advanced branches of math.

Equations can involve various mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and others.

Question 3:

The statement is true. We can check this by calculating the correlation coefficient between the latitude and temperature data points, which should be close to -1. The calculated line of best fit is also consistent with the given data.

Question 4:

To estimate the temperature for a city with a latitude of 48, we can use the equation of the line of best fit:

y = -1.07x + 92.87

Substituting x = 48, we get:

y = -1.07(48) + 92.87

y = 42.79

Rounding to the nearest whole number, the estimated temperature for a city with a latitude of 48 is 43.

Question 5:

The statement is false. We can check this by calculating the correlation coefficient between the passengers and suitcases data points, which should be close to 1. The given line of best fit has a negative slope, which is inconsistent with the positive correlation between the variables.

Question 6:

To estimate the number of suitcases for a flight carrying 250 people, we can use the equation of the line of best fit:

y = -1.98x + 7.97

Substituting x = 250, we get:

y = -1.98(250) + 7.97

y = -485.03

However, it does not make sense for the number of suitcases to be negative. Therefore, we cannot make a reasonable estimate for the number of suitcases on a flight carrying 250 people using this line of best fit.

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Answer:

Step-by-step explanation:

The calculated t-value for the independent samples t-test (-1.709) is within the range of the critical t-value at α = 0.05 and df = 55. Therefore, we fail to reject the null hypothesis, indicating no significant difference in anxiety levels between bullies and victims.

To determine the exact answer, we can perform a two-sample t-test to compare the means of the bully group and the victim group. The formula for the t-test statistic is:

t = (x₁ - x₂) / √((s₁² / n1) + (s₂² / n₂))

Where

x₁ and x₂ are the sample means of the bully group and victim group, respectively.

s₁ and s₂ are the sample standard deviations of the bully group and victim group, respectively.

n₁ and n₂ are the sample sizes of the bully group and victim group, respectively.

Given the following data:

Bully group: n₁ = 30, x₁ = 21.5, s₁ = 10

Victim group: n₂ = 27, x₂ = 25.8, s2 = 9

Let's calculate the t-test statistic:

t = (21.5 - 25.8) / √((10² / 30) + (9² / 27))

Calculating the values within the square root

t = (21.5 - 25.8) / √((100 / 30) + (81 / 27))

= (21.5 - 25.8) / √(3.333 + 3)

Now, evaluating the square root and simplifying further:

t = (21.5 - 25.8) / √(6.333)

= (21.5 - 25.8) / 2.516

Finally, computing the numerator and denominator:

t = -4.3 / 2.516

≈ -1.709

Therefore, the exact value of the t-test statistic is approximately -1.709.

To compare the calculated t-value (-1.709) with the critical t-value at a significance level of α = 0.05 with a two-tailed test, we need to determine the degrees of freedom (df) first.

The degrees of freedom (df) for the independent samples t-test is given by the formula:

df = n₁ + n₂ - 2

In this case, n₁ = 30 (number of bullies) and n2 = 27 (number of victims). Therefore:

df = 30 + 27 - 2

df = 55

Next, we need to find the critical t-value from the t-distribution table or a statistical software for a two-tailed test at α = 0.05 and df = 55.

For a two-tailed test at α = 0.05 and df = 55, the critical t-value is approximately ±2.004.

Since the calculated t-value (-1.709) is within the range of the critical t-value (-2.004 to 2.004), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that there is a significant difference in anxiety levels between bullies and victims.

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The sequence\(f_n(x) = e^{-nx}\) does not converge uniformly to the limit function\(f(x) = 0\) on the interval \(I = [0, \infty)\).

To examine the uniform convergence of the sequence\(f_n(x) = e^{-nx}\) on the interval\(I = [0, \infty)\), we need to check if the sequence converges uniformly to a limit function on that interval.

For uniform convergence, we need the following condition to hold:

Given any\(\(\epsilon > 0\\)), there exists an \(\(N \in \mathbb{N}\\)) such that for all \(n > N\) and for all \(x \in I\), we have\(\(\left| f_n(x) - f(x) \right| < \epsilon\)\), where \(\(f(x)\)\) is the limit function.

Let's find the limit function\(\(f(x)\\)) of the sequence \(f_n(x) = e^{-nx}\) as \(n\) approaches infinity. Taking the limit as \(\(n\)\)goes to infinity

\(\[f(x) = \lim_{n \to \infty} e^{-nx}\]\)

We can rewrite this limit using the exponential function property:

\(\[f(x) = \exp\left(\lim_{n \to \infty} -nx\right)\]\)

Since the limit inside the exponential is\(\(-\infty\)\) as \(\(n\)\) goes to infinity, we have:

\[f(x) = \exp(-\infty) = 0\]

Therefore, the limit function \(f(x)\) is the constant function\(\(f(x) = 0\\)) on the interval \(I = [0, \infty)\).

To check for uniform convergence, we need to evaluate the difference \(\left| f_n(x) - f(x) \right|\) and see if it is less than any given \(\epsilon > 0\) for all \(n > N\) and for all \(x \in I\).

\(\[\left| e^{-nx} - 0 \right| = e^{-nx}\]\)

To make this expression less than\(\(\epsilon\),\) we need to find an \(N\) such that \(e^{-nx} \(< \epsilon\)\) for all\(n > N\) and for all\(\(x \in I\).\)

However, as \(\(x\)\) approaches infinity, \(e^{-nx}\) approaches 0. But for any finite \\((x\)\) in the interval \([0, \infty)\), \(e^{-nx}\)  will always be positive and never exactly equal to 0. This means we cannot find an\(\(N\)\)that satisfies the condition for uniform convergence.

Therefore, the sequence\(f_n(x) = e^{-nx}\) does not converge uniformly to the limit function \(f(x) = 0\) on the interval \(I = [0, \infty)\).

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Answer:

Height of the parallelogram = 37.5 cm

Step-by-step explanation:

As given,

Base of a parallelogram = 75 cm

Height of a parallelogram = 25 cm

As,

we know that

Area = Base × Height

        = 75 × 25

        = 1875 cm²

As the parallelogram is same

So, Area = Base × Height

⇒1875 = 50 × Height

⇒ Height = \(\frac{1875}{50}\) = 37.5 cm

So, we get

Height of the parallelogram = 37.5 cm

The inverse of the function 6-x/5

Given function,

5x + y = 6

Now,

y = 6-5x

Let y = f(x)

then,

\(x = f^{-1}(y)\)

Now put \(f^{-1} (y)\) in place of x,

y = 6 - 5\(f^{-1} (y)\)

\(f^{-1} (y)\) = 6-y/5

Now interchange the function in variable x,

\(f^{-1} (x) =\) 6 - x /5

Hence the inverse of 5x + y = 6 is 6-x/5 .

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Answer:

-1, -2, -3 Are all consecutive

Step-by-step explanation:

-1 + -2 + -3 = -6

Answer:

0,-2,-4

Step-by-step explanation:

The statistics z is -1.878 and the p value is 0.0302

Given,

Number of random sample selected, n = 6967

Number of surveys returned, x = 1331

Estimated proportion of return rate;

p = 1331/6967 = 0.192

Significance level, ∝ = 0.01

z would represent the statistic

We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:

Null hypothesis, p₀ ≥ 0.2

Alternative hypothesis, p₀ < 0.2

The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)

That is,

z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878

Using the alternative hypothesis and the following probability, we can now get the p value:

p value  = p(z < - 1.878) = 0.0302

We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.

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The number of cans of soup purchased and the number of frozen dinners purchased can be found using the system of equations,

x - 2y = 0 and 7x + 10y = 96.

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations.

Let x and y be the number of cans of soup purchased and the number of frozen dinners purchased respectively.

Amount of sodium in one can of soup = 350 mg

Amount of sodium in x can of soup = 350x

Similarly,

Amount of sodium in one frozen dinner = 500 mg

Amount of sodium in y frozen dinner = 500y

Given that, Julia purchased twice as many cans of soup as frozen dinners.

x = 2y

⇒ x - 2y = 0

They all collectively contain 4800 mg of sodium.

350x + 500y = 4800

⇒ 7x + 10y = 96

Hence the system of equations are x - 2y = 0 and 7x + 10y = 96.

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Answer:

2 rows of 15.

Step-by-step explanation:

2 rows of 15= 30

3 rows of 10= 30

5 rows of 6= 30

Example: 30÷2 = 15

2 rows of 15 is equally 30.

The least positive integer we can get as the product is 2.

Here we have the following set of numbers:

{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}

And we want to take the product between 3 of them and find the least positive integer that we can get as the product.

So it makes sence to choose the smallest absolute value numbers (not zero) such that one is positive and two are negative (we want two negative ones so the signs cancell eachother)

Then we will get:

1*(-1)*(-2) = 2

That is the least positive integer we can get as the product.

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Answer:

4).

Step-by-step explanation:

sin A = cos B

Because sin A = CB/AB and cos B = CB/AB.

The final itinerary will depend on your preferences, the specific national parks you plan to visit, and the distances between them.

Let's clarify the itinerary for the 15-day tour visiting 5 national parks.

You have a 15-day tour, and you plan to visit 5 national parks. Each park will have a stay of two days.

When you multiply the number of parks (5) by the number of days spent in each park (2), you get a total of 10 days allocated for staying in those 5 parks.

However, there seems to be a discrepancy in the calculation because allocating 10 days for park stays leaves only 5 days remaining, not 15.

To resolve this issue and ensure a 15-day tour, we need to reevaluate the itinerary. Let's assume you want to spend two days at each park, which gives you a total of 10 days for park stays.

To fill the remaining 5 days, you have a few options:

1. Travel Days: You can allocate a day for travel between each park, which would require an additional 4 days. This accounts for the transportation time and allows you to enjoy the journey between the parks.

2. Additional Park Visits: If there are other nearby national parks or attractions in the area, you can extend your tour to include visits to these places. This would allow you to explore more diverse locations and make the most of your 15-day tour.

3. Rest and Relaxation: Alternatively, you might choose to use the extra days for relaxation or leisure activities. You can spend some time enjoying the amenities and attractions available near the parks, such as hiking trails, wildlife observation, or local cultural experiences.

Ultimately, the final itinerary will depend on your preferences, the specific national parks you plan to visit, and the distances between them. Make sure to consider travel times, desired activities, and any additional locations you wish to explore when creating your 15-day tour.

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The only kind of data generated by observational research is correlations or patterns in the data that have been observed. By using correlations, one variable's value can be used to predict the value of another.

Explanation:

Accurate predictions using data correlation can be ensured by using a variety of methods. Firstly, it is important to ensure that the data is free from errors and is of high quality. This can be done by cleaning and validating the data to remove any inconsistencies and outliers. Secondly, it is important to analyze the data thoroughly and identify any patterns or trends. Furthermore, it is beneficial to use appropriate statistical tests and algorithms such as linear regression, logistic regression, and decision trees to identify the predictive relationships between the variables. Finally, it is important to evaluate the model’s performance to determine the accuracy of the predictions.

The most effective methods for ensuring accurate predictions using data correlation are:

1. Perform Exploratory Data Analysis: Exploratory data analysis is an essential step in any predictive modeling process. It involves exploring the data to identify patterns, trends, and relationships within the data. This helps to identify any potential issues or biases within the data that could affect the accuracy of predictions.

2. Use Statistical Tests: Statistical tests can be used to measure the strength of the relationship between two variables. These tests can help to identify which variables are most strongly correlated with each other and can help to determine which variables should be used in a predictive model.

3. Use Machine Learning Algorithms: Machine learning algorithms can be used to create predictive models that can identify and learn patterns in the data. These algorithms are particularly effective at identifying complex relationships between variables that may not be identified by statistical tests.

4. Validate Predictions: Predictions should always be validated to ensure that they are accurate and reliable. This can be done by comparing the predictions against known outcomes or by testing the model on a separate data set.

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Answer:

Number A is correct I think, coz if uu take the feet convert them into decimals u'll get accurate answers

Answer:

3 OR 8  hope this helps!

Step-by-step explanation: