answer attached
7. The infinite series Στη η 42) 20 n(n+1)(n+2) converges. n= Find an expression for Sm, the mth partial sum of the series. Then find the overall sum S. 10 7. Sm = 5 10 m+2' S5 m+1

The roots of the characteristic polynomial are the values that satisfy the polynomial.

What is a characteristic polynomial ?

In linear algebra, a polynomial that has the eigenvalues as roots and is invariant under matrix similarity is referred to as a characteristic polynomial of a square matrix. The equation created by equating the characteristic polynomial to zero is known as the characteristic equation.

Now the root of the characteristic polynomial are the values which satisfy the polynomial. it means that when this values are substituted in the equation we get the answer as 0.

Hence, The roots of the characteristic polynomial are the values that satisfy the polynomial.

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Answer:

skewed right, mean > median

Step-by-step explanation:

just did it

Answer:

skewed right, mean>median

Step-by-step explanation:

edge 2023

Answer:

if ur going left to right it would be d

Step-by-step explanation:

Answer: 3 1/4 + 2 1/3 = 67/

12

= 5 7/

12

≅ 5.5833333

Step-by-step explanation:

Evaluate:

\( \: \: \: \: \: \: \displaystyle\int\rm {y}^{2} \sqrt[3]{y} \: dy\)

\( {\large\underline{\sf{Solution-}}}\)

\( \: \: \: \: \: \: \displaystyle\int\rm {y}^{2} \sqrt[3]{y} \: dy\)

can be rewritten as

\(\rm \:  =  \: \displaystyle\int\rm {y}^{2} \times {\bigg(y\bigg) }^{\dfrac{1}{3} } \: dy\)

\(\rm \:  =  \: \displaystyle\int\rm {\bigg(y\bigg) }^{2 + \dfrac{1}{3} } \: dy\)

\(\rm \:  =  \: \displaystyle\int\rm {\bigg(y\bigg) }^{\dfrac{6 + 1}{3} } \: dy\)

\(\rm \:  =  \: \displaystyle\int\rm {\bigg(y\bigg) }^{\dfrac{7}{3} } \: dy\)

\(\rm \:  =  \: \dfrac{ {\bigg(y\bigg) }^{\dfrac{7}{3} + 1} }{\dfrac{7}{3} + 1 } + c\)

\(\rm \:  =  \: \dfrac{ {\bigg(y\bigg) }^{\dfrac{7 + 3}{3}} }{\dfrac{7 + 3}{3}} + c\)

\(\rm \:  =  \: \dfrac{ {\bigg(y\bigg) }^{\dfrac{10}{3}} }{\dfrac{10}{3}} + c\)

\(\rm \:  =  \:\dfrac{3}{10} {\bigg(y\bigg) }^{\dfrac{10}{3}} + c\)

Answer:

P(x) = (x-20)(x+3)

Step-by-step explanation:

Answer:

A point. (3,5) represents a point that is 3 units to the right of the Y-axis (x = 3) and 5 units above the X-axis (y = 5).

Step-by-step explanation:

To plot a point, you start at origin and move however many units are specified. To do this, you can either;

 A.) Start at origin. Move along the X-axis to 3, and then go straight up five units on the Y-axis. This will plot the point.

 B.) You can also do this with your other value. Starting at origin, move along the Y-axis to 5. Go right on the X-axis three units, and you will be at the same point.

Answer:

the slope is 2 and a=8 b=6

Step-by-step explanation:

Answer:

A number c increased by 2 is less than or equal to 26 . Translate the sentence into an inequality.

Answer: 10%

Step-by-step explanation:

As per given ,

Initial number of people went to pool = 1060

After 4 weeks periods, number of people went to pool = 1060 - 100 +140 -146  ['+' for addition . '-' for decrease]

= 954

The percent decrease in the number of people who went to the pool over these four​ weeks = \(\dfrac{1060-954}{1060}\times 100\)

\(=\dfrac{106}{1060}\times100\\\\=10\%\)

Hence, the percent decrease in the number of people who went to the pool over these four​ weeks = 10%

Answer:9

Step-by-step explanation:

Step-by-step explanation:

prime numbers from 1 to 20 are those that can be divided by 1 and itself, so

1

2

3

5

7

11

13

17

19

the average is the sum of all of them, divided by how many they are (there are 9 of them)

avg = (1+2+3+5+7+11+13+17+19)/9

avg = 8.67

note: some consider that 1 is not a prime number because in this case the definition "that can be divided by 1 and itself" is redundant. if that's what you learned in class, then you need to remove it from the formula and divide by 8

To find the magnitude and direction of a vector using trigonometry, you can follow these steps:

1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).

2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
  magnitude(A) = √(Ax^2 + Ay^2)

3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
  a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
     angle = arctan(Ay / Ax)
  b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).

4. Convert the direction to degrees or radians, depending on the required format.

Let's consider an example to illustrate these steps:

Suppose we have a vector A with components Ax = 3 and Ay = 4.

1. Identify the components: A = (3, 4).

2. Calculate the magnitude:
  magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

3. Find the direction:
  angle = arctan(4 / 3) ≈ 53.13 degrees.

4. Convert the direction:
  angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.

So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.

Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.

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Answer:

A ∆ with an exterior angle :116° & two interior angles 7x+6 & 4x

The value of angle 7x+6

we know that ,

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non adjacent interior angles of the triangle.

so,

\(7x + 6 + 4x= 116 \\ 11x + 6 = 116 \\ 11x = 116 - 6 \\ 11x = 110 \\ x = 110 \div 11 \\ x = 10\)

so ,the measure of green angle would be

\(7x + 6 \\ placing \: the \: value \: of \: x \: as \: 10 \\ 7 \times 10 + 6 \\ = 70 + 6 \\ = 76\)

To verify our answer ,the sum of the resultant value of green angle and 4x should be 116°(the exterior opposite angle)

so,

\(7x + 6 + 4x = 116 \\ 7 \times 10 + 6 + 4 \times 10 = 116 \\ 70 + 6 + 40 = 116 \\ 76 + 40= 116 \\ 116 = 116 \\ \\ hence,\: verified\)

Solution:

Note that:

Simplify the equation to find x.

Substitute the value of x into the measure of the green angle.

The measure of the green angle is 76°.

Answer:

k = -11

Step-by-step explanation:

The Factor Theorem states that if (x - c) is a factor of the polynomial f(x), then f(c) = 0.

In this case, we know that (x - 3) is a factor of the polynomial f(x) = x³ + 4x² + kx - 30. Therefore, we can use the Factor Theorem to solve for k by equating f(3) to zero.

\(\begin{aligned}f(3)&=0\\\implies 3^3 + 4(3^2) + 3k - 30 &= 0\\ 27 + 4(9) + 3k +33 &= 0\\27+36+3k-30&=0\\3k+33&=0\\ 3k+33-33&=-33\\3k&=-33\\3k \div 3&=-33 \div 3\\k&=-11\end{aligned}\)

Therefore, the value of k is -11.

Answer:

the answer is 6 hours and 30 minutes

Remember that a population parameter is a number that describes something about an entire group or population.

The only study that states a conclusion about an entire group or population is the one in the first option.

Answer: Option 1

Answer:

2200

Step-by-step explanation:

-8*-10/-8*-10

= 80/80

=1

So, 1 is the correct answer. (:

The two triangles are congruent, as the Pythagorean Theorem ensures that the hypotenuse of the two triangles will be equal.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

If two triangles have congruent side lengths, the hypotenuse for the two triangles will also be the same, hence the Pythagorean Theorem ensures the congruence of the two triangles.

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The given statement "Every division algebra A has no idempotents other than 0 and 1A; deduce that if A has dimension > I then A cannot be isomorphic to the path algebra of a quiver and this applies to the R-algebra H of quaternions." is true. Because A has no other idempotent other tahn 1A and 0.

Suppose that there exists an idempotent element e in a division algebra A that is not equal to 0 or 1A. Then, we have:

e^2 = e

Multiplying both sides by e^-1 (which exists since A is a division algebra), we obtain:

e = 1A

which is a contradiction. Therefore, A has no idempotent elements other than 0 and 1A.

Now, suppose that A has dimension greater than 1 and is isomorphic to the path algebra of quiver Q. Let {e_i} be a basis of A as a vector space over the base field, indexed by the vertices of Q. Since A is a division algebra, each e_i is nonzero. Moreover, since A has no nonzero idempotent elements other than 1A, we have:

e_ie_j = 0 for i ≠ j

But this means that the multiplication in A does not satisfy the relations of the quiver Q, and therefore A cannot be isomorphic to the path algebra of Q. Hence, we have shown that if A has dimension greater than 1, it cannot be isomorphic to the path algebra of any quiver.

In particular, this applies to the R-algebra H of quaternions, since H has dimension 4 and is a division algebra. Therefore, H cannot be isomorphic to the path algebra of any quiver.

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When finding local maxima and minima from the graph of a derivative, we need to identify the points where the derivative changes sign. These points represent the locations of local maxima and minima on the original function.

When finding local maxima and minima from the graph of a derivative, we need to understand the relationship between the original function and its derivative. The derivative of a function represents the rate of change of the function at any given point. Local maxima and minima occur where the derivative changes sign from positive to negative or from negative to positive. At these points, the slope of the original function changes from increasing to decreasing or from decreasing to increasing.

By following these steps, we can identify the local maxima and minima from the graph of a derivative.

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Identify the critical points, Determine the intervals, Analyze the sign changes and Check the endpoints

To find the local maximum and minimum points from the graph of a derivative, you can follow these steps:

Identify the critical points: These are the points where the derivative is either zero or undefined. Find the values of x where f'(x) = 0 or f'(x) is undefined.

Determine the intervals: Divide the x-axis into intervals based on the critical points and any other points of interest. Each interval represents a section of the graph where the derivative is either positive or negative.

Analyze the sign changes: Within each interval, observe the sign of the derivative. If the derivative changes sign from positive to negative, there is a local maximum at that point. If the derivative changes sign from negative to positive, there is a local minimum at that point.

Check the endpoints: Also, check the derivative's sign at the endpoints of the graph. If the derivative is positive at the leftmost endpoint and negative at the rightmost endpoint, there is a local maximum at the left endpoint. Conversely, if the derivative is negative at the leftmost endpoint and positive at the rightmost endpoint, there is a local minimum at the left endpoint.

By following these steps and analyzing the sign changes of the derivative within intervals, as well as checking the endpoints, you can identify the local maximum and minimum points from the graph of the derivative.

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Answer:

3

Step-by-step explanation:

The slope is rise/run and for this case, it is 3/1 which equals 3!!!

By using the unit conversion method, 2 million seconds converted to days are equal to 23 days.

A unit conversion expresses the same aspect as another unit of measurement. For example, time can be expressed in minutes rather than hours, and distance can be represented from miles to kilometers, feet, or any other unit of measurement.

In this situation, you need to convert between seconds and days:

A day consists of 24 hours. Therefore, the fraction 24 hours/day is equal to 1. There is no value change when multiplying a number by 1. The same holds true for the conversion factors 1 hour/60 minutes and 1 minute/60 seconds.

If you multiply 2,000,000 seconds (2 million seconds) by these conversion factors, you will change the seconds to days:

2,000,000 sec. x (1 min/60 sec.) x (1 hour/60 min) x (1 day / 24 hours)

Therefore, all that is required is to divide 2,000,000 by the product of 60, 60, and 24.

(2,000,000) / (60*60*24) = 2,000,000 / 86,400 = 23.148 days ≈ 23 days

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Answer:

First, put a multiplications sign in between the brackets:

(5x - 2) * (3x + 4)

Then using distributive property:

5x(3x + 4) - 2(3x + 4)

Then using distributive proper once again:

15x^2 + 20x - 6x - 8

Finally, calculate:

15x^2 + 14x - 8

The answer is. \(15x^2-6x+12\)

The question is of the type in algebraic equations.

Here the first step is multiplying the two algebraic expressions.

5x is multiplied with 3x and 4

-2 should be multiplied by 3x and 4.

we will get. \(5x(3x+4)-2(3x+4)\)

Next, we get. \(15x^2+20-6x-8\) (calculating constants and variables)

Therefore, the final answer = \(15x^2-6x+12\).

This type of equation is called as quadratic equation with one variable as the degree of the equation is 2.

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A confidence interval for the difference between the population proportions = ( .2597 , .3403 )

Confidence interval mean

Estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.

In statistics, a claim to 95% confidence simply means that the researcher has seen one possible interval from a large number of possible ones, from which 19 out of 20 intervals contain the true value of the parameter.

If repeat the test, can expect your estimate to fall between these numbers with a reasonable degree of certainty.

In statistics, confidence is another probability word.

β₁ = x₁/n₁  = 582/600 = 0.97

β₂ = x₂/n₂ = 268/400 = 0.67

( β₁ - β₂) ± z √β₁( 1 -β₁ )/n₁ + β₂(1 - β₂)/n₂

          = (.97 - .67 ) ± 1.645 √.97( 1 - .97)/600 + .97( 1 - .67)/400

          = .30 ± 0.4336

         = ( .2597 , .3403 )

A confidence interval for the difference between the population proportions = ( .2597 , .3403 )

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\(2x*(5x^{2} +17+10)\) is the answer I think

To find the 75th term of the sequence consisting of positive integers that can be expressed as a sum of distinct powers of 3. Thus, the 75th term of the sequence is $111$.

To find the 75th term of the sequence consisting of positive integers that can be expressed as a sum of distinct powers of 3, we can use the base-3 (ternary) numeral system. The 75th term can be represented as the 74th number in base-3 without a digit 2 (as it will require subtraction to form distinct powers of 3).

The 74th number in base-10 is represented as $74_{10}$, which when converted to base-3 is $2202_3$. Since we need to avoid the digit 2, we can carry out the operation similar to addition with carry-over: $2202_3 + 1111_3 = 10310_3$.

Now, we can convert $10310_3$ back to base-10: $(1 \times 3^4) + (0 \times 3^3) + (3 \times 3^2) + (1 \times 3^1) + (0 \times 3^0) = 81 + 0 + 27 + 3 + 0 = 111$.

Thus, the 75th term of the sequence is $111$.

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Answer:

Pi—which is written as the Greek letter for p, or π—is the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi(3.1415).

There are two radii in one diameter. The formula for circumference is pi*d when using diameter which explains the two in front of the formula given by your teacher.

Step-by-step explanation:

Age Frequency

41-45 5

46-50 9

51-55 3

56-60 10

61-65 10

66-70 6

1) Since the frequency represents how many times a given data point occurs within a Data Set. We can fill it in by counting.

2) So let's write them out (Note that in this case the least value is included as well as the greater one):

Age Frequency

41-45 5

46-50 9

51-55 3

56-60 10

61-65 10

66-70 6

And that is the answer