State where the power series is centered.
Σ (n=0) [infinity] nx ^n

Answer:

30

Step-by-step explanation:

The population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

All these elements are taken into account when formulating the population growth formula.

r = [(b + i) - (d + e)]/1000

Put the values in the formula.

r =  [(2,000 + 100) - (500 + 200)]/1000

r = 2100 - 700/ 1000

r = 1.4

Thus, the population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

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Answer:

26

Step-by-step explanation:

3³ is basically 3×3×3 which equals to 27

1² is 1×1 which obviously is 1 lol

so,

27 - 1

= 26

Answer: 3*3*3 - 1*1    =    26

Step-by-step explanation:

Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

The value of d = 6 and the value of YZ = 42

Since XY=32, YZ=7d, and XZ=74

Based on this question, it should be noted that the addition of XY and YZ will equal to the value of XZ. Therefore,

XY + YZ = XZ

32 + 7d = 74

Collect like terms

7d = 74 - 32

7d = 42

Divide through by 7

7d/7 = 42/7

d = 6

Since d is 6, the value of YZ will be:

= 7d = 7 × 6 = 42

In conclusion, the value of d = 6 and the value of YZ = 42.

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Answer:

45000

Step-by-step explanation:

Jk it's wrong lol

The solution for the value of x by definition of linear pair angle is 21.

Used the concept of linear pair angle that states,

The sum of a linear pair angle in a straight line would be 180 degrees.

Given that the two linear pair angles are,

(3x + 18) and (4x + 15)

Now, the sum of linear pair angles would be 180 degrees.

Hence, it can be written as,

(3x + 18) + (4x + 15) = 180°

Solve for x,

3x + 4x + 18 + 15 = 180°

7x + 33 = 180

Subtract 33 on both sides,

7x = 180 - 33

7x = 147

Divide 7 on both sides,

x = 147/7

Therefore, the value of x is,

x = 21

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the SVDs of the given matrices are:

(a) (ATA)^(-1) = VΣ^(-1)U^T      (b) (ATA)^(-1)AT = VU^T  

(c) A(ATA)^(-1) = UU^T            (d) A(ATA)^(-1)AT = I.

To compute the SVDs of the given matrices, we start with the SVD of the original matrix A = UΣV^T, where U and V are orthogonal matrices, and Σ is a diagonal matrix containing the singular values of A.

(a) To compute the SVD of (ATA)^(-1), we use the SVD of A. We have (ATA)^(-1) = (VΣ^TU^T)(UΣV^T)^(-1) = VΣ^(-1)U^T.

(b) For the SVD of (ATA)^(-1)AT, we use the SVD of A and the fact that (ATA)^(-1) = VΣ^(-1)U^T. We get (ATA)^(-1)AT = VΣ^(-1)U^TAT = VΣ^(-1)ΣU^T = VU^T.

(c) To find the SVD of A(ATA)^(-1), we multiply the SVD of A with (ATA)^(-1). We have A(ATA)^(-1) = UΣV^TVΣ^(-1)U^T = UΣΣ^(-1)U^T = UU^T.

(d) For the SVD of A(ATA)^(-1)AT, we use the results from (c) and (b). We get A(ATA)^(-1)AT = UU^TVU^T = I.

In summary, the SVDs of the given matrices are:

(a) (ATA)^(-1) = VΣ^(-1)U^T

(b) (ATA)^(-1)AT = VU^T

(c) A(ATA)^(-1) = UU^T

(d) A(ATA)^(-1)AT = I.

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Answer:

28.27

Step-by-step explanation:

Area of a circle A≈ πr2

3.14 x 3^2 ≈ 28.27

The expression is a polynomial and and the degree of the polynomial(quadratic equation) is 2.

A polynomial expression is an algebraic expression that takes the form \(\mathbf{ax^{n > 1}+bx+c}\). It consist of variables, arithmetic operator, non-integers and coefficient.

A quadratic equation is a form of polynomial equation due to the fact that it comprises of a power of x for which x is a non-negative integer. However, the degree of a quadratic equation is 2.

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Answer:

3 hours

Step-by-step explanation:

but it can be a cent off, so it might be wrong.

Answer:

Step-by-step explanation:

This is about understanding real and complex numbers.

Complex Numbers; 7 - 5i, √-6, 0 + 9i, , -i² + i³

Real Numbers; i⁶, 2 - 7i², -12, √(-5)²

Let's first define real and complex numbers.

The. expressions we are given are;

i⁶, 2 - 7i², 7 - 5i, √-6, 0 + 9i, -12, √(-5)², -i² + i³

       2 - 7i² = 2 - 7(-1) = 9 which is a real number.

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An equation in mathematics is a statement that two expressions are equal. It consists of two sides, the left-hand side (LHS) and right-hand side (RHS), separated by an equal sign (=). In the context of equations, the standard form typically refers to a specific format for writing linear equations.

To find the value of s in the equation 3r = 10 + 5s when r = 10, we can substitute the value of r into the equation and solve for s.

Let's start by substituting r = 10 into the equation:

3(10) = 10 + 5s

Simplifying the left side of the equation:

30 = 10 + 5s

Next, let's isolate the variable term, 5s, by subtracting 10 from both sides of the equation:

30 - 10 = 10 + 5s - 10

20 = 5s

Finally, let's solve for s by dividing both sides of the equation by 5:

20/5 = 5s/5

4 = s

Therefore, the value of s in the equation 3r = 10 + 5s, when r = 10, is s = 4.

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The value of s in the equation 3r = 10 + 5s when r = 10 is s = 4.

To find the value of s in the equation 3r = 10 + 5s when r = 10, we can substitute the value of r into the equation and solve for s.
Given: 3r = 10 + 5s and r = 10
Substituting r = 10 into the equation, we have:
3(10) = 10 + 5s
Simplifying the left side of the equation:
30 = 10 + 5s

To isolate the variable s, we can subtract 10 from both sides of the equation:
30 - 10 = 10 + 5s - 10
20 = 5s
Now, to solve for s, we can divide both sides of the equation by 5:
20/5 = 5s/5
4 = s

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Answer:

0,-2        0,-5

2,-3          1,-4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

The distance between -4 and zero is 4.

Step-by-step explanation:

If you count from -4 to 0 you will count 4 which is the answer.

Answer: Okay, the answer is x^2/68+(y+3)^2/17=1.

Step-by-step explanation: Step. 1 Complete the square for 4y^2+24y: 4(y+3)^2−36.

Step 2. You’ll need to substitute 4(y+3)^2−36 for 4y^2+24y in the equation x^2+4y^2+24y=32: x^2+4(y+3)^2–36=32.

Step 3. So you’ll need to move –36 to the right side of the equation by adding 36 to the both sides: x^2+4(y+3)^2=32+36.

Step 4 You add 32 and 36: x^2+4(y+3)^2=68.

Step 5. You divide each term by 68 to make the right side equal to one: x^2/68+4(y+3)^2/68=68/68.

And step 6. You’ll need to simplify each term in the equation in order to set the right side equal to 1. The standard form of an ellipse or hyperbola requires the right side of the equation be 1: x^2/68+(y+3)^2/17=1. I hope you download Math-way app to calculate this ellipse in standard form to be extremely helpful, please mark me as brainliest, and have a great weekend! :D

To calculate the present value of a zero-coupon bond, we can use the formula: Present Value = Future Value / (1 + Interest Rate)^n

where Future Value is the par value of the bond, Interest Rate is the annual market interest rate, and n is the number of years. In this case, the Future Value is $2,000, the Interest Rate is 10% (or 0.10), and the number of years is 5. Using Excel, we can calculate the present value as follows:
1. In cell A1, enter the Future Value: 2000
2. In cell A2, enter the Interest Rate: 0.10
3. In cell A3, enter the number of years: 5
4. In cell A4, enter the formula for calculating the present value: =A1 / (1 + A2)^A3
5. Press Enter to get the result.

The present value of the 5-year zero-coupon bond with a $2,000 par value and an annual market interest rate of 10% is $1,620.97.

The formula for present value calculates the current worth of a future amount by discounting it back to the present using the interest rate. In this case, the future value is $2,000, and we divide it by (1 + 0.10)^5 to account for the effect of compounding over 5 years. The result is the present value of $1,620.97, which represents the amount that is considered equivalent to receiving $2,000 in 5 years at a 10% interest rate.

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Proportionately, the average class size at Lexington Middle School a decade ago was 20.

Proportion is the ratio or relative numerical relationship of two or more values equated to one another.

Proportions are fractional values, showing how much of a number is contained in another or the whole.

Proportions are depicted as decimals, fractions, or percentages.

The current average class size at Lexington Middle School = 21 students

The percentage increase in class size = 5%

Let the current average class size = 105% (100 + 5)

The previous decade's average class size = 21/105% = 20

Thus, a decade ago, the average class size was 20, proportionately increasing by 5%.

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The common sum is 18.

What is a common sum?

The following item in an arithmetic sequence is obtained by adding or subtracting a specified amount (the common sum). To find the common sum in an arithmetic sequence, add the first term from the second term.

Here,

We have a number on a vertex.

It will be counted in 3 different faces since any vertex is the intersection of three edges.

Therefore, each number 1, 2, .... 7,8 will be added to the total sum 3 times.  

Our total sum is 3(1+2+....+8) = 108.

since there are 6 faces in a cube, we get

our common sum is :

= 108/6

= 18

Hence, the common sum is 18.

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The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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The projection of the point (4,4) onto the line passing through (3,1) is the point on the line that is closest to (4,4). To find this projection, we need to first find the direction vector of the line, which is (3-1, 1-0) = (2,1).

Next, we need to find the vector from the point (3,1) to the point (4,4), which is (4-3, 4-1) = (1,3).

Then, we can use the formula for projecting a vector onto another vector:

proj_v u = ((u · v) / (v · v)) v

where u is the vector we want to project, v is the vector we want to project onto, and · denotes the dot product.

Applying this formula, we get:

proj_v u = ((1,3) · (2,1)) / ((2,1) · (2,1)) (2,1)

= (5/5) (2,1)

= (2,1)

So the projection of (4,4) onto the line passing through (3,1) is the point (3,1) + (2,1) = (5,2).

To find the projection of vector (4, 4) onto vector (3, 1), you can follow these steps:

Step 1: Calculate the dot product of the two vectors.
Dot product = (4 * 3) + (4 * 1) = 12 + 4 = 16

Step 2: Calculate the magnitude squared of the vector you are projecting onto (3, 1).
Magnitude squared = (3 * 3) + (1 * 1) = 9 + 1 = 10

Step 3: Divide the dot product by the magnitude squared.
Scalar = 16 / 10 = 1.6

Step 4: Multiply the scalar by the vector you are projecting onto (3, 1) to find the projection.
Projection = 1.6 * (3, 1) = (4.8, 1.6)

So, the projection of (4, 4) onto (3, 1) is (4.8, 1.6).

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Answer:

96

Step-by-step explanation:

25% of what is 24?

25% of X is 24

To find X we do 24/25%.

Converting percent to decimal:

25%/100 = 0.25

X = 24/0.25

X = 96

Answer:

x > -9

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

9 - 5x < 54

Step 2: Solve for x

Here we see that any value x greater than -9 would work as a solution to the inequality.

Answer:

27

Step-by-step explanation:

x / 3 = 9

x = 3 * 9

  = 27

Hope I helped!

The given statement "The misuse of statistics is sometimes intentional." is True, because there are instances where people intentionally misuse statistics to manipulate or deceive others.

The misuse of statistics can be an intentional act by individuals or organizations to manipulate or deceive others. This is often done by selectively choosing data or statistics that support a particular argument or position, while ignoring or downplaying information that does not support it.

One way this can be achieved is by distorting graphs or charts. For example, a bar chart can be designed to visually exaggerate the differences between data points, making the differences appear more significant than they actually are. This can be done by adjusting the scale of the chart or by changing the width of the bars.

Another way that statistics can be misused is by making false claims based on the data. For example, someone may use a correlation between two variables to imply a causal relationship, even though there may not be any evidence to support this claim.

Similarly, statistics can be used to mislead people by presenting them in a way that is misleading. For example, a statistic may be presented without any context or compared to an irrelevant baseline, making it appear more significant or less significant than it actually is.

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To prove that in any group, an element and its inverse have the same order, we need to show that if we have an element `a` in a group and `n` is the order of `a`, then the order of `a`'s inverse, denoted as `a⁻¹`, is also `n`.

Let's assume that `a` has order `n`. This means that the smallest positive integer `n` such that `aⁿ = e` (the identity element) is `n`. We want to show that the order of `a⁻¹` is also `n`.

First, let's consider the order of `a⁻¹`. By definition, the order of `a⁻¹` is the smallest positive integer `m` such that `(a⁻¹)ᵐ = e`.

Now, we can use the fact that `aⁿ = e` to rewrite `a⁻¹` raised to the power of `n`:

(a⁻¹)ᵐ = ((aⁿ)⁻¹)ᵐ = (e⁻¹)ᵐ = eᵐ = e.

This shows that `(a⁻¹)ᵐ = e`, which implies that the order of `a⁻¹` is at most `m`.

To prove that the order of `a⁻¹` is exactly `n`, we need to show that `m` cannot be smaller than `n`.

Suppose, for contradiction, that `m < n`. Then we have:

(aⁿ)⁻¹ = (aⁿ)⁻¹ᵐ = aⁿᵐ = e.

This would imply that `aⁿ` has an inverse and `(aⁿ)⁻¹` has order `m`, which contradicts the definition of `n` as the smallest positive integer satisfying `aⁿ = e`.

Therefore, we conclude that the order of `a⁻¹` cannot be smaller than `n`. Since we have shown that it is at most `m` and not smaller than `n`, it follows that the order of `a⁻¹` is exactly `n`.

Hence, in any group, an element and its inverse have the same order.

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To determine the number of gallons of paint needed to cover office 143, we need to know the square footage of the office.

Once we have that information, we can divide the square footage by the coverage rate per gallon to calculate the required amount of paint.

Let's assume the square footage of office 143 is 800 square feet.

Number of gallons needed = Square footage / Coverage rate per gallon

Number of gallons needed = 800 square feet / 50 square feet per gallon

Number of gallons needed = 16 gallons

Therefore, you would need approximately 16 gallons of paint to cover office 143, assuming each gallon covers 50 square feet.

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