find the matrix of the relation r={(1,2),(2,3),(3,4),(4,5)} on the set x={1, 2, 3, 4, 5}; ordering of x:1,2,3,4,5

The given radical expression is (√x)^5. To rewrite it in rational exponent form, we need to express the square root (√) as a fractional exponent.

The square root (√) of x can be written as x^(1/2).

To raise x^(1/2) to the power of 5, we can multiply the exponents: (x^(1/2))^5 = x^(5/2).

Therefore, the radical expression (√x)^5 can be rewritten as x^(5/2) in rational exponent form.

In summary, (√x)^5 is equivalent to x^(5/2) in rational exponent form.

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Answer:

9

Step-by-step explanation:

hi I'm pretty sure this is really wrong but just kinda guessing

+2 is just a positive 2 so it's just known as 2

2+1+6 = 9

Answer: 9

Step-by-step explanation:because if its 2+1+6 then u get 2 and 6 add thats 8 then your 1 and its 9.

Answer:

y = 1.8x, where time is the independent variable, x, and distance is the dependent variable.

Step-by-step explanation:

The independent variable is along the x-axis.

The dependent variable is along the y-axis.

Therefore,

Equation of the line

To find the equation of the line, define two points on the line:

Use the slope formula to find the slope (m) of the line:

\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{9-0}{5-0}=1.8\)

From inspection of the graph, the y-intercept is at (0, 0).

Point-slope form of a linear equation:  \(y = mx + b\)

Substitute the found slope and y-intercept into the formula to create the equation of the line:

\(\implies y=1.8x+0\)

\(\implies y=1.8x\)

Conclusion

y = 1.8x, where time is the independent variable, x, and distance is the dependent variable.

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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Answer:

  circumcenter

Step-by-step explanation:

You want to know the name of the point equidistant from the vertices of a triangle.

The circle that passes through the vertices of a triangle is called a "circumcircle". It circumscribes the triangle. Its center is equidistant from all points on the circle, so is equidistant from the triangle's vertices.

The point equidistant from the vertices of a triangle is the circumcenter.

__

Additional comment

The circumcenter is at the intersection of the perpendicular bisectors of the sides of the triangle.

Answer:

D

Step-by-step explanation:

The total number of students is 15+12= 27

The ratio of girls to total students is 12/27 = 4/9

The simplified expression has the result given as follows:

1.25 x 10^-5.

A number in scientific notation is given as follows:

\(a \times 10^b\)

With the base being \(a \in [1, 10)\), meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.

Hence the base of the simplified expression is given as follows:

9.6 x 7.5/2.4² = 12.5 = 1.25 x 10.

The exponent is obtained as follows:

(-6 - 10 - (-10)) = -6.

(multiplication adds the exponent, division subtracts).

Hence the simplified expression is given as follows:

1.25 x 10 x 10^-6 = 1.25 x 10^-5.

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Answer:

375.

Step-by-step explanation:

Significant Figures:

All non-zero numbers ARE significant. ...

Zeros between two non-zero digits ARE significant. ...

Leading zeros are NOT significant. ...

Trailing zeros to the right of the decimal ARE significant. ...

Trailing zeros in a whole number with the decimal shown ARE significant.

For Nora to minimize the probability that they will object to her request, she should write out her request for them to consider.

A formal request letter is an official letter that is written to a superior individual or organization. In this letter, the writer must indicate the genuine reason(s) they are writing such a request.

This type of letter (request letter) is written when you need a:

Nora, as a single Mom needs to write her request out for her parents, thereby stating the genuine reason(s) to minimize the probability that they will object to her request.

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Answer:

50

Step-by-step explanation:

The smallest positive integer n such that the equation 63a5b4 = 3575n³ is satisfied for some integers a and b is n = 3.

To find the smallest positive integer n such that the equation 63a5b4 = 3575n³ is satisfied for some integers a and b, we need to find the prime factorization of both 63 and 3575 and compare the exponents of their prime factors.

Prime factorization of 63:

63 = 3^2 * 7

Prime factorization of 3575:

3575 = 5^2 * 11 * 13

Comparing the exponents of the prime factors, we have:

3^2 * 7 * a^5 * b^4 = 5^2 * 11 * 13 * n^3

From this comparison, we can see that the exponent of the prime factor 3 on the left side is 2, while the exponent of the prime factor 3 on the right side is a multiple of 3 (n^3).

Therefore, to satisfy the equation, the exponent of the prime factor 3 on the left side must also be a multiple of 3.

The smallest positive integer n that satisfies this condition is n = 3.

Therefore, the smallest positive integer n such that the equation 63a5b4 = 3575n³ is satisfied for some integers a and b is n = 3.

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Answer:

1570.796~

Step-by-step explanation:

v= πr² h/3

r is radius

h is height

v is volume

v=π*10² 15/3

v=π*10² *5

v=π*100 *5

v=π*500

v=1570.796~

Answer:

Step-by-step explanation:

\(\sf x^3-1\)

Let's rewrite 1 as 1 ^3.

\(\sf x^3-1^3\)

Now, we can apply the "Difference of Cubes Formula".

\(\boxed{\sf x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)}\)

_____________________

The agent's maximum revenue for the cruise will be $12,950.

To determine the number of people that should go on the cruise to maximize the agent's revenue, we need to analyze the relationship between the number of people and the cost per person.

Let's denote the number of additional people beyond the initial 30 as "x."

Therefore, the total number of people going on the cruise will be 30 + x.

The cost per person is given by the equation:

Cost per person = $420 - $10x

To maximize revenue, we need to consider both the number of people and the cost per person.

Revenue is calculated by multiplying the number of people by the cost per person.

Revenue = (30 + x) * ($420 - $10x)

Now, let's find the number of people that maximizes revenue by differentiating the revenue function with respect to "x" and setting it equal to zero:

d(Revenue)/dx = 0

Using the product rule and simplifying the equation, we have:

30 - 20x - 10(420 - 10x) = 0

Simplifying further:

30 - 20x - 420 + 100x = 0

Combining like terms:

80x - 390 = 0

Solving for x:

80x = 390

x ≈ 4.875

Since we cannot have a fractional number of people, we can round x to the nearest whole number, giving us x = 5

Therefore, to maximize revenue, the travel agent should have an additional 5 people join the initial 30, making a total of 35 people going on the cruise.

To find the cost per person for the cruise, we substitute the value of x into the cost equation:

Cost per person = $420 - $10x

Cost per person = $420 - $10(5)

Cost per person = $420 - $50

Cost per person = $370

So, the cost per person for the cruise will be $370.

To calculate the maximum revenue, we substitute the value of x = 5 into the revenue equation:

Revenue = (30 + x) * ($420 - $10x)

Revenue = (30 + 5) * ($420 - $10(5))

Revenue = 35 * ($420 - $50)

Revenue = 35 * $370

Revenue = $12,950

Therefore, the agent's maximum revenue for the cruise will be $12,950.

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Answer:

85

Step-by-step explanation:

Answer:

brainliest plsss

Step-by-step explanation:

1) 2

2)

3) 3

4)

5)

Answer:

BC = 20

Step-by-step explanation:

Since B is the midpoint of AC , then

AB = BC = \(\frac{1}{2}\) AC = \(\frac{1}{2}\) × 40 = 20

Answer:

Hello, I solved it out for you and I did an example.

Step-by-step explanation:

Answer : The cardinality of is 15.

It is the union of and and its cardinality is the sum of the cardinalities of the two sets. Thus, the cardinality of is 6 + 9 = 15. The cardinality of a set is the number of elements in the set. In other words, it is the count of the members of a set. For example, if you have a set containing the numbers 1, 2, 3, 4, and 5, then the cardinality of that set is 5, since there are five elements in the set.

In the given problem, is a finite set of cardinality 6. This means that has 6 elements. Similarly, has a cardinality of 9, which means that it has 9 elements. Since is the union of and , it will have all the elements of both and , which means it will have 6 + 9 = 15 elements. Therefore, the cardinality of is 15.

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Answer:

x=14

Step-by-step explanation:

Answer:

-3/5

Step-by-step explanation:

rise/run

since its a negative slope, you count down three and to the right 5. -3/5 is the slope

Answer:

-3/5

Step-by-step explanation:

Equation for slope of a line is:

(y₂-y₁)÷(x₂-x₁)

In your example:

-4-(-1)÷4-(-1)

(-4+1)÷(4+1)=

-3/5

The statement that is FALSE is Reducing the variation of a process will increase the width of a given Confidence Interval relative to that process.

As the confidence level increases the width of the confidence interval also increases. A larger confidence level increases the chance that the correct value will be found in the confidence interval, so option A is true

When estimating the standard deviation in calculating confidence intervals, make sure you use the t tables, we need the t table to estimate SD, so option B is true

A larger sample size or lower variability will result in a tighter confidence interval with a smaller margin of error. A smaller sample size or a higher variability will result in a wider confidence interval with a larger margin of error.

So option c is false, the crrect option is C

Therefore, The statement that is FALSE is Reducing the variation of a process will increase the width of a given Confidence Interval relative to that process.

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Answer:

The function is constant from x = -2 to x = 1.

Step-by-step explanation:

To find the range of where the function is constant, just look at the graph where the line is horizontal. It is horizontal from the x-values of x=-2 to x=1, and this is the range of when the function is constant.

Hope this helps! Feel free to give me Brainliest if you feel this helped. Have a good day and good luck on your assignment. :)

Answer: \(61.9miles/hr\)

Step-by-step explanation:

given data:

distance travelled by the car =  195 miles

time taken = 3 hours and 15mins

solution

average speed of the car

\(= \frac{195miles}{3hrs15mins} \\\\= 61.9miles/hr\)

Answer:

The average speed is \(v=60 miles/h\)

Step-by-step explanation:

The equation of the average speed os given by:

\(v=\frac{\Delta x}{\Delta t}\) (1)

here:

Δx is just 195 miles

Δt is the time traveled. 3.25 h ( 3 h + 15 min or 0.25 h)  

So we just need to put this into the equation (1)

\(v=\frac{195}{3.25}\)

Therefore, the average speed is \(v=60 miles/h\)

I hope it helps you!

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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Answer:

It’s A

Step-by-step explanation:

Cuz it’s just the numbers are replaced in different places but when u multiply u get the same ans ig