4. The rate of assessment in Foster, Rhode Island, is 50 percent. The tax rate is $40.20 per $1,000 of assessed value. What is the real estate tax on a piece of property that has a market value of $236,000?
​

In order to use term-by-term differentiation or integration to find a power series centered at x=0 for the given function f(x)=tan−1(x8), we need to first express the function as a power series by using the formula of the power series expansion as follows:$$f\((x)=tan^{-1}(x^8)=\sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{16n+8}$$\)

Now, to find the derivative of this function, we apply the differentiation property of power series. That is, we differentiate each term of the function using the derivative of xⁿ which is nxⁿ⁻¹. Hence, we obtain the derivative of f(x) as follows:$$f'(x)=\frac

{

1

}

{

1+x^8

}

=\sum_{n=0}^\infty (-1)^n x^

{

8n

}

$$

Hence, the power series expansion of f(x) in terms of x is$$f(x)=\tan^{-1}(x^8)=\sum_{n=0}^\infty \frac\({(-1)^n}{2n+1} x^{16n+8}$$$$f'(x)=\frac{1}{1+x^8}=\sum_{n=0}^\infty (-1)^n x^{8n}$$\)

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The probability of selecting a multiple of 10 is 2/11 or 0.182, which can also be expressed as 18.2%.

Given that numbers 20 through 30 were written on individual cards and placed in a bag

If you take one card from the bag, we have to find the probability that it will be a multiple of 10

There are two multiples of 10 between 20 and 30, which are 20 and 30.

The total number of cards in the bag is 11 (20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30).

Therefore, the probability of selecting a multiple of 10 is 2/11 or 0.182, which can also be expressed as 18.2%.

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Answer:

The choice B. 5°

Step-by-step explanation:

The angle in the figure is 90°

\(36 + (11x - 1) = 90 \\ 36 + 11x - 1 = 90 \\ 11x + 35 = 90 \\ 11x = 90 - 35 \\ 11x = 55 \\ \\ x = \frac{55}{11} \\ \\ x = 5\)

Answer:

Rounding to the nearest hundredth of a percent, the APY is 6.8%.

Step-by-step explanation:

A = P * (1 + r/n)^(n*t)

Where:

A = the value of the account after t years

P = the principal amount invested (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years the money is invested

For this problem, we have P = $440, r = 0.066 (6.6% APR), n = 4 (compounded quarterly), and we want to find A after t years. Therefore, the function for the value of the account after t years is:

A(t) = 440 * (1 + 0.066/4)^(4t)

= 440 * (1.0165)^(4t)

= 440 * (1.0165^(4t))

Rounding to four decimal places, the function is:

A(t) = 440 * 1.0165^(4t)

To find the annual percentage yield (APY), we use the formula:

APY = (1 + r/n)^n - 1

Where:

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

For this problem, we have r = 0.066 (6.6% APR) and n = 4 (compounded quarterly). Therefore, the APY is:

APY = (1 + 0.066/4)^4 - 1

= 0.068

= 6.8%

Rounding to the nearest hundredth of a percent, the APY is 6.8%.

Answer:

\(→ {x}^{3} + 2 {x}^{2} - 9x - 18 \\ = {x}^{2} (x + 2) - 9(x + 2) \\ = (x + 2)( {x}^{2} - 9) \\ = \boxed{(x + 2)(x + 3)(x - 3)}\)

(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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To express the polar coordinates in terms of Cartesian coordinates we use the following trigonometric expressions.

That isx=rcosθandy=rsinθTherefore, to find the derivative of the function in terms of t, we use the following formula(dy)/(dx)=(dy)/(dθ) * (dθ)/(dx)Now, r=3, therefore, x = 3 cosθ and y = 3 sinθ. We can rewrite these in terms of t:dx/dt = -3 sin t dy/dt = 3 cos tNow we will find the derivative of y with respect to x and simplify the resulting expression.dy/dx= (dy/dt)/(dx/dt) = 3 cos(t) / (-3 sin(t)) = -cot(t)Therefore, the derivative of y with respect to x is -cot(t).

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Answer:

x=10

Step-by-step explanation:

5x-10 and 3x+10

+10 +10

5x and 3x+20

-3x -3x

2x and 20

divide by 2 on both sides

x=10

Answer:

60% increase

Step-by-step explanation:

Answer:

60%.............................................

Answer:

24

Step-by-step explanation:

253727737273762663552636626636277463726373782883847772

An angle between 0 and 2π that is coterminal with a given angle can be found by adding or subtracting multiples of 2π until the angle falls within the specified range.

To find a coterminal angle, we can add or subtract 2π (which is equivalent to one full revolution) to the given angle. By doing this, we maintain the same initial position but change the number of complete revolutions made. If the resulting angle is still outside the range of 0 to 2π, we can continue adding or subtracting 2π until we obtain an angle within the desired interval.

For example, let's say we have an angle of 3π/4. To find a coterminal angle within the range of 0 to 2π, we subtract 2π from 3π/4:

3π/4 - 2π = -5π/4

The resulting angle is outside the desired range, so we add 2π instead:

-5π/4 + 2π = 3π/4

Now we have an angle of 3π/4, which is coterminal with the original angle and falls within the specified interval.

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Find an angle between 0 and 2π that is coterminal with 5π/4?

Answer:

Since 4 bags cost $8, divide $8 by 4 bags and you get $2 for 1 bag.

Answer:

A

C

D

Step-by-step explanation:

Select three ratios that are equivalent to 4:3.

Choose 3 answers:

(Choice A)

8:6

(Choice B)

9:12

(Choice C)

20:15

(Choice D)

32:24

(Choice E)

36:28

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

To determine which fractions are equivalent to 4:3 express the options in their lowest terms

option 1 - 8 : 6

To transform to the simplest form. divide the numbers by 2

4 : 3 this is equivalent

option 2 : 9 : 12

To transform to the simplest form. divide the numbers by 3

= 3 : 4 this is not equivalent

option 3 : 20:15

To transform to the simplest form. divide the numbers by 5

4 : 3 this is equivalent

option 4 : 32:24

To transform to the simplest form. divide the numbers by 8

4 : 3 this is equivalent

option 5 : 36:28

To transform to the simplest form. divide the numbers by 4

9 : 7 this is not equivalent

Note that the proof required is given based on the AA Similarity Postulate.

Similar triangles: If two triangles are similar then their corresponding angles are equal.

By the transitive property of equality if a = b, and b= c then a = c.

AA postulate of similarity states that when two corresponding angles of two triangles are equal then they are called similar to each other.

Given ΔABC ~ ΔRST; and

ΔDEF ~ ΔRST

To Prove: ΔABC ~ DEF Note that:

ΔABC ~ ΔRST - Given

ΔDEF ~ ΔRST
- Given

∠A  = ∠R, ∠D = ∠R - Definition of Similar Triangles

∠C = ∠T, ∠F = ∠T

∠A= ∠C, ∠D = ∠F  - Transitive property of Equality; Thus,

ΔABC ~ Δ DEF (AA Similarity Postulate)

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The two numbers 7 and 7 have a product of 49 which has the least sum.

The biggest (maximum) and smallest (minimum) variables that a function f may have, either in a specific area or throughout its whole domain, are known as its maxima and minima.

Let f and f′ vary in terms of their derivatives. If f ′ (a) = 0 and f ′′ (a) > 0, and is the comparative minimum of f in that case.

S (x, y) = x + y is the sum of the two values in our function to minimize.

S may be rewritten as s in one variable by using the constraint xy = 49:

xy = 49

y = 49 ÷ x

S(x,y) = x+y

s(x) = x + (49 ÷ x)

s'(x) = 1 + (49 ÷ x²)

x² = 49

x = ±√49

x = ±7

Considering that we are discussing positive numbers:

x = 7

The second derivative test allows us to confirm that it is at least:

s'(x) = 1 + (49 ÷ x²)

s''(x) = 98 ÷ \(x^3\)

s''(x) = 98 ÷ \(x^3\) > 0

The second number is obtained by using the requirement that the combination of the two numbers must equal 49:

x = 7

xy = 49

7y = 49

y = 7

The two numbers 7 and 7 have a product of 49 which has the smallest sum.

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Our assumption that the triangle is equilateral must be false. Therefore, there is no unique solution to this problem.

Let's first find the circumcenter of the equilateral triangle.

An equilateral triangle has all three sides equal and all three angles equal to 60 degrees. The circumcenter is the point where the perpendicular bisectors of the sides meet.

Let's draw the triangle and label the vertices A, B, and C. Let O be the circumcenter. We can draw the perpendicular bisectors of AB and BC and label the intersection points with O as D and E, respectively.

Now, since the triangle is equilateral, AD and BE are also medians of the triangle. Therefore, AD and BE intersect at the centroid of the triangle, which we can label as G.

Since AD and BE are perpendicular bisectors of the sides, we have AO = BO and CO = BO. Thus, the triangle AOB is an isosceles triangle, and we can find the length of OD by using the Pythagorean theorem.

Let x be the length of OD. Then,

OD^2 = AD^2 - AO^2 = (7^2 + x^2) - (7/2)^2

Similarly, we can find the length of OE:

OE^2 = BE^2 - BO^2 = (7^2 + x^2) - (7/2)^2

Since the triangle is equilateral, we know that the distance between any vertex and the circumcenter is the same. Therefore,

OA = OB = OC = sqrt(OD^2 + AO^2) = sqrt(OE^2 + BO^2)

Substituting the expressions for OD and OE, we get:

sqrt(7^2 + x^2) = sqrt(7^2 + x^2) - (7/2)

Simplifying, we get:

7/2 = 0

This is a contradiction, which means that our initial assumption that the triangle is equilateral must be false. Therefore, there is no unique solution to this problem.

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Answer:

system is:

y = 1/2x

y = 1/2x - 2

No Solution to this system

Step-by-step explanation:

The Probability of that more than 7 of them germinate is 0.2948.

We are to determine the probability that more than 7 of 10 seeds (i.e. 8, 0r 9 0r 10) germinate.

The probability that all 10 seeds germinate is equal 0.80¹⁰= 0.1073 = 10.73%.

The probability that only the first (only the second, etc ) seed does not germinate is equal 0.20 X 0.80⁹= 0.0268 = 2.68%.

The probability that 6 seeds germinate is the sum of the probabilities that only the first seed does not germinate, only the second one does not germinate, etc, and equals to 10 X 0.0268  = 0.268 = 26.8%.

The total probability that more than 7 of 10 seeds germinate is the sum of the probabilities that 10 seeds germinate and that 7 seeds germinate, i.e. 2.68 % + 26.8 % = 29.48 %.

Thus, The Probability of that more than 7 of them germinate is 0.2948.

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Answer:

51 adults and 193 children

Step-by-step explanation:

Number of children = c

Cost for c children = c*4 = 4c

Number of adults = a

Cost for a adults = 6a

Total people = 244

a + c = 244  ---------------(I)

   a = 244 - c ----------(II)

Cost for 244 people =  $ 1078

6a + 4c = 1078 -------------(III)

Substitute a = 244 - c in equation (III)

6*(244 - c) + 4c = 1078

1464 - 6c + 4c = 1078

1464 - 2c = 1078

         -2c = 1078 - 1464

        -2c = -386

           c =  -386/-2

c = 193

a = 244 - 193

a = 51

The equation that describes the function is determined as y = x + 3.

The slope of a line is defined as rise over run, or the change in the y values to change in x values.

The slope of the line is calculated as follows;

slope, m = Δy / Δx = ( y₂ - y₁ ) / ( x₂ - x₁)

From the points on the graph, we have;

(x₁, y₁ ) = (-1, 2)

(x₂, y₂) = (1, 4)

m = ( 4 - 2) / ( 1 + 1 )

m = 2/2

m = 1

The y intercept of the line is 3

The general equation of a line is given as;

y = mx + c

where;

y = x +  3

Thus, the equation that describes the function is determined as y = x + 3.

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We know that taking out too many lines of credit can actually harm your credit score, so it's important to be cautious with how many accounts you open.

A way to build good credit is by paying bills when they are due. Additionally, using only secured loans can also help build good credit, as these loans require collateral and can be easier to qualify for.

Using only credit cards can also be a way to build good credit, as long as the cards are used responsibly and payments are made on time.

However, taking out too many lines of credit can actually harm your credit score, so it's important to be cautious with how many accounts you open.

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The measure of angle ∠S in triangle RST is approximately 103.1 degrees.

To find the measure of angle ∠S in triangle RST, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and opposite angles A, B, and C respectively, the following equation holds true:

\(c^2 = a^2 + b^2 - 2abcos(C)\)

In our case, we know the side lengths r = 23 cm, s = 99 cm, and t = 94 cm. We want to find the measure of angle ∠S. Let's substitute the known values into the Law of Cosines equation:

s^2 = r^2 + t^2 - 2rtcos(S)

99^2 = 23^2 + 94^2 - 2(23)(94)cos(S)

9801 = 529 + 8836 - 4348cos(S)

9801 = 9365 - 4348cos(S)

4348cos(S) = 9365 - 9801

4348cos(S) = -436cos(S) = -436 / 4348

cos(S) ≈ -0.1

To find the measure of angle S, we can take the inverse cosine (cos^-1) of -0.1:

S ≈ cos^-1(-0.1)

Using a calculator, we find that S ≈ 103.13 degrees (rounded to the nearest 10th of a degree). Therefore, the measure of angle ∠S in triangle RST is approximately 103.1 degrees.

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The range of the function for this situation is the interval [398.25, 400] gallons.

To determine the range of the function f(x) = 400 - 0.35x for the given situation, we need to find the possible values of the amount of water remaining in the pool.

The function f(x) represents the amount of water remaining (in gallons) after x minutes, where x ranges from 0 to 5.

To find the range of the function, we evaluate f(x) for the extreme values of x in the given range (0 to 5).

For x = 0, the initial amount of water remaining:

f(0) = 400 - 0.35(0) = 400 gallons

For x = 5, the amount of water remaining after 5 minutes:

f(5) = 400 - 0.35(5) = 400 - 1.75 = 398.25 gallons

Therefore, the range of the function for this situation is the interval [398.25, 400] gallons.

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There are 48 ways to choose two different cards from a standard 52-card deck such that (a) The first card is an Ace and the second card is not a Queen.

Explanation: We are given that a standard deck of 52 cards. (a) The first card is an Ace and (b) the second card is not a Queen. In a standard deck of 52 cards, there are four aces. If the first card drawn is an ace, then there are 51 cards left in the deck and 12 cards that are queens. Hence, there are 51 − 12 = 39 cards that are not queens. So, we can say that, There are 4 aces × 39 cards that are not queens = 156 ways to choose two different cards from a standard 52-card deck such that the first card is an Ace and the second card is not a Queen.

However, we have to remove the case where both cards are aces and the second card is a queen. So, we subtract 1 from the previous answer to get, 156 − 1 = 155 ways to choose two different cards from a standard 52-card deck such that (a) The first card is an Ace and the second card is not a Queen.

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Answer:

its 1%

Step-by-step explanation:

At the head of the Sparta government were Two kings and five ephors.

Who were Sparta's two kings?

Kassandra approached Archidamos and Pausanias, the Two Kings of Sparta, to restore the citizenship and their residence.

What kind of political system did the Spartans have?

At the head of the Sparta government were Two kings and five ephors.

Sparta – never ones to do anything by half – had two kings at all . The agenda for the apella was set by the gerousia and the ephors.

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Positive correlation means that both variables tend to increase (or decrease) together. Thus, Option A is the answer.

Positive correlation refers to a relationship between two variables in which an increase in one variable is associated with an increase in the other variable. Negative correlation, on the other hand, refers to a relationship in which an increase in one variable is associated with a decrease in the other variable. No correlation means that there is no relationship between the two variables.

To determine the strength of a correlation, we can use a statistical measure called the correlation coefficient, which ranges from -1 to 1. A correlation coefficient of 1 indicates a perfect positive correlation, a correlation coefficient of -1 indicates a perfect negative correlation, and a correlation coefficient of 0 indicates no correlation.

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Answer:

The coordinates of the vertex will be (-4,-1)

Step-by-step explanation:

Let's recall that the vertex is in the middle point of the roots of a quadratic function.

The root are (-3,0) and (-5,0) so the x-value of the vertex will be:

\(x_{vertex}=\frac{-5-(-3)}{2}-3\)

\(x_{vertex}=-1-3=-4\)

The y-value of the vertex is given by the minimum value, that is -1

Therefore, the coordinates of the vertex will be (-4,-1)      

I hope it hleps you!