evaluate sum in closed form
f(x) = sin x + 1/3 sin 2x + 1/5 sin 3x + ....

Answer:

They are 17 units away from each other!

Step-by-step explanation:

Because they have the same y coordinate, this make us not have to do the formula. To find how far they are away, add the absolute value of each x coordinate. The answer is 17 units.

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The preparation of the stockholders' equity statement for the year ended December 31, 2021, is as follows:

Court Casuals

Statement of stockholers' equity

December 31, 2021

Common Stock                        $116,000

Additional Paid-in Capital  $5,326,000

Retained Earnings              $3,677,000

Treasury Stock                         $-2,000

Total stockholders' equity  $9,117,000

The stockholders' equity statement includes the common stock, additional paid-in capital, retained earnings, and the subtraction of the treasury stock.

Court Casuals

Stockholers' equity on January 1, 2021

Common Stock $90,000

Additional Paid-in Capital $4,100,000

Retained Earnings $3,000,000

Net income for the year, 2021, = $900,000

May 18: Cash $1,300,000 Common Stock $26,000 Additional Paid-in Capital $1,274,000 (26,000 x $50 - $26,000)

May 31: Treasury Stock $4,500 Additional Paid-in Capital $175,500 (4,500 x $40 - $4,500) Cash $180,000

Jul 1: Cash Dividend $223,000 (90,000 + 26,000 - 4,500) x $2 Dividends Payable $223,000

July 31: Dividends Payable $223,000 Cash $223,000

August 18: Cash $130,000 Treasury Stock $2,500 Additional Paid-in Capital $127,500 (2,500 x $52 - $2,500)

Statement of Retained Earnings, December 31, 2021:

Beginning balance  $3,000,000

Net income                 $900,000

Dividends                     -223,000

Ending balance        $3,677,000

Beginning balance  $90,000

May 18: Cash              26,000

Ending balance       $116,000

Beginning balance  $4,100,000

May 18: Cash              1,274,000

May 31: Cash                -175,500

August 18: Cash            127,500

Ending balance      $5,326,000

May 31: Cash                 $4,500

August 18: Cash             -2,500

Ending balance            $2,000

Thus, we can summarize from the stockholders' equity that Court Casuals has outstanding shares of 114,000 (116,000 - 2,000) at $1 par, which is the difference between the ending balances of the common stock and the treasury stock accounts, after reflecting the equity transactions for the year.

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The ratio of the surface area to the volume is 14/15 in²/in³.

To find the ratio of surface area to volume for a given object, we divide the surface area by the volume. In this case, we have a ratio of 280 in² to 300 in³.

The surface area represents the total area of all the exposed surfaces of the object, while the volume represents the amount of space occupied by the object.

To calculate the ratio, we divide the surface area by the volume:

Ratio = Surface Area / Volume

Ratio = 280 in² / 300 in³

Simplifying the ratio:

Ratio = (280/300) in²/in³

Ratio = (28/30) in²/in³

Ratio = (14/15) in²/in³

Therefore, the ratio of the surface area to the volume is 14/15 in²/in³.

This ratio represents the relationship between the amount of surface area and the amount of volume for the given object. It indicates that, for every 15 cubic inches of volume, there are 14 square inches of surface area.

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Answer:

4/5

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

0.8

=8/10

=4/5

Answer:

she read 25 pages in 60 minutes

Step-by-step explanation:

Answer:

Step-by-step explanation:

B

x is approximately equal to 6.

The ratios of the sides of a right triangle are called trigonometric ratios.

Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

sin = Perpendicular/ Hypotenuse

Cos = Base / Hypotenuse

tan = Perpendicular/Base

In the figure attached with the answer we can see that in Triangle ABC ,

tan 50.1 = x / 5

5(tan 50.1) = x

Therefore x is approximately equal to 6.

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Answer:

9x10^7 is your scienctific notation, which is also 90000000 in expanded form

The maximum amount of a lien that can be claimed   by a subcontractor in thisscenario would be $16,000.

Since the subcontractor first provided labor and materials on May 1 and continued billing the general contractor until   September 30 at a rate of $4,000 per month,the total unpaid amount would be $16,000.

This unpaid amount   represents the maximum lien claim that the subcontractor can make against the two  family residential property.

A lien is a legal claim or right that allows a creditor tohold property as collateral until a debt   is paid.

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Answer:

1152in²

Step-by-step explanation:

Given the following

Length = 10in

Width = 16in

Height = 16in

surface area of the prism = 2(LW + WH + LH)

surface area of the prism = 2(10*16+ 16*16 + 10*16)

surface area of the prism = 2(160+256+160)

surface area of the prism = 2(576)

surface area of the prism = 1152in²

Step-by-step explanation:

[tex]\pi \times {7}^{2} = 3.14 \times 49 = 153.86 \\ 15 \times 25 = 375 \\ 153.86 + 375 = 523.86 \: {ft}^{2} [/tex]

Given:

The graph of a relations.

To find:

Whether the relation is a function or not.

Solution:

A relation is a function if there exist unique outputs for each input. If a graph passes the vertical line test then is a function.

Vertical line test: Each vertical line intersect the curve at most one.

In the given figure draw a vertical at [tex]x=1[/tex] as shown in the below figure.

From the below graph, it is clear that the vertical line intersects the curve at two points. So, it does not pass the vertical line test.

Therefore, the given relation is not a function.

The cook added 6 ounces more molasses than should have been added since the assumption was wrong.

a) The assumption the cook made that was incorrect was that the volume of molasses is the same as its weight. The cook measured 12 fluid ounces of molasses instead of 12 ounces of molasses by weight. It is assumed that weight and volume are the same, but this is not always the case because the density of different substances varies.

b) The amount of molasses the cook added than should have been added can be calculated by converting 12 fluid ounces of molasses to weight ounces. We can use the density of molasses to calculate the weight. Let's assume the density of molasses is 1.5 ounces per fluid ounce.

Then, the weight of 12 fluid ounces of molasses = 12 fluid ounces × 1.5 ounces/fluid ounce = 18 ounces

The cook added 6 ounces more of molasses than should have been added because:

12 fluid ounces - 12 weight ounces = 6 ounces

Therefore, the cook added 6 ounces more molasses than should have been added.

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Answer:

P x Q

Step-by-step explanation:

The Cartesian product of two sets P and Q can be written as,

P × Q.

Sets are groups of well-defined objects or components in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.

Given:

P and Q are the two sets.

The Cartesian product of two sets P and Q can be written as,

P × Q.

For example,

if A = {1, 2} and B = {3, 4},

then the Cartesian Product of A and B is {(1, 3), (1, 4), (2, 3), (2,4)}.

Therefore, P × Q is the required expression.

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Answer: C) y = 0.25m + 30

Step-by-step explanation:

Since the rental fee (y) of the car is $30 plus $0.25 per mile (m), then the cost will be:

= $30 + $0.25(m)

= 30 + 0.25m

For example, to calculate the cost of someone who rented the car and used 20 miles will be:

= 30 + 0.25m

= 30 + 0.25(20)

= 35

Answer:

b. y=19x

Step-by-step explanation:

Step-by-step explanation:

diameter is 84 thereare 2 time 42 .84.

follow me nice study bye .

Answer:

4/9, 0.5, 0.583, 5/9, 65%, 0.714, 0.75, 0.777, 9/11, 83.3%!

Step-by-step explanation:

Hope this helps

Answer:

pay back is so good!..

Step-by-step explanation:

The resulting sequence will also converge when the corresponding terms of the two sequences are added together, "an + bn," and its limit will be equal to the sum of the limits of the individual sequences, which is "a + b."

Let's say we have two sequences in mathematics: a} and {b}. If the sequence "a" converges to a particular value, let's call it "a," and the sequence "b" converges to a different value, let's call it "b," then the sequence "an + bn" (where an and bn represent the terms of the sequences "a" and "b") will converge to the sum of the two values, which is a + b. Convergence of a sequence means that the values get closer to a In this way, if the two successions {a} and {b} combine, it suggests that their separate terms approach their particular restricts (an and b) as we think about additional terms.

As a result, the final sequence will also converge when we add the terms of the two sequences, "an + bn," and its limit will be equal to the sum of the limits of the individual sequences, which is "a + b."

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Dividing 3x^2 - 11x - 4 by x - 4 results in the quotient of 3x + 1 and a remainder of -23.

To divide 3x^2 - 11x - 4 by x - 4, we can use long division.

First, we divide the highest degree term of the dividend by the divisor. In this case, (3x^2) / (x) gives us 3x as the first term of the quotient.

Next, we multiply the divisor (x - 4) by the first term of the quotient (3x) to obtain (3x)(x - 4) = 3x^2 - 12x.

We subtract this result from the dividend (3x^2 - 11x - 4) to get a new polynomial: (3x^2 - 11x - 4) - (3x^2 - 12x) = x + 8x - 4.

Now, we repeat the process with the new polynomial (x + 8x - 4). We divide the highest degree term (x) by the divisor (x - 4), which gives us the second term of the quotient, 8.

Multiplying the divisor (x - 4) by the second term of the quotient (8) gives us (8)(x - 4) = 8x - 32.

Subtracting this from the new polynomial (x + 8x - 4) - (8x - 32) = 40, we obtain the remainder.

Therefore, the division of 3x^2 - 11x - 4 by x - 4 gives the quotient 3x + 1 and the remainder -23.

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The Laplace transform of the function f(t) = t sin(4t) +1 is

L[f(t)] = (4 / (s^2 + 16) + 1) / s

To find the Laplace transform of the function f(t) = t sin(4t) + 1, we can use the linearity property of the Laplace transform.

The Laplace transform of t sin(4t) can be found using the derivative property and the Laplace transform of sin(4t). The derivative property states that if F(s) is the Laplace transform of f(t), then sF(s) is the Laplace transform of f'(t).

Taking the derivative of t sin(4t) with respect to t, we get:

f'(t) = 1⋅sin(4t) + t⋅(4⋅cos(4t))

Now, we can find the Laplace transform of f'(t) using the derivative property:

L[f'(t)] = sL[f(t)] - f(0)

Since f(0) = 0, the Laplace transform becomes:

L[t sin(4t)] = sL[t sin(4t) + 1]

Next, we need to find the Laplace transform of sin(4t). The Laplace transform of sin(at) is [tex]a / (s^2 + a^2)[/tex]. Therefore, the Laplace transform of sin(4t) is [tex]4 / (s^2 + 16).[/tex]

Now, substituting these values into the equation, we have:

sL[t sin(4t)] - 0 = sL[t sin(4t) + 1]

Simplifying, we get:

sL[t sin(4t)] = sL[t sin(4t) + 1]

Dividing both sides by s, we have:

L[t sin(4t)] = L[t sin(4t) + 1] / s

Now, we can substitute the Laplace transform of sin(4t) and simplify further:

[tex]L[t sin(4t)] = (4 / (s^2 + 16) + 1) / s[/tex]

Therefore, the Laplace transform is: [tex]L[f(t)] = (4 / (s^2 + 16) + 1) / s[/tex]

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Answer:

question 3= c     question 4= a

Step-by-step explanation:

Multiple linear regression model is used to fit the observed data, in order to characterize the relationship between the response variable y and i covariates of interest.

The following regression model is used:

                [tex]y=Xβ+ ε[/tex]

where:y denotes the n × 1 response vector.

[tex]β[/tex]represents the [tex]p × 1[/tex]parameter vector consisting of [tex]p = k + 1[/tex] regression coefficients.

[tex]X[/tex]denotes the n × p model matrix.

[tex]ε[/tex] denotes the [tex]n × 1[/tex] vector of error terms.

The entries of the first column of X are all equal to 1.

The entries of other columns of X correspond to the i covariates of interest.

It is given that the model matrix X is an n × p full-column-rank matrix.

The least squares estimator of [tex]β[/tex] is given by:

                     [tex]β^ = (X'X)^-1X'y[/tex]

The error terms are assumed to be independent and identically distributed normal random variables.

The variance-covariance matrix of the least squares estimator is given by:

                   [tex]Var(β^) = σ^2(X'X)^-1[/tex]

It is given that all covariates have the same variance-covariance structure.

Hence,

           [tex]σ^2 = σ0^2[/tex] for every i.

It is also given that a, σ0 for every i, where a represents a positive constant.

Hence,

       [tex]σ^2 = σ0^2[/tex]

             = [tex]a^2[/tex]

Show that Var and the equality would be attained if

       [tex]X'X = a^2I[/tex],

where [tex]β^[/tex] represents the ith entry of the least square estimator [tex]β[/tex].

From the given data, the variance-covariance matrix of the least squares estimator is given by:

     [tex]Var(β^) = σ^2(X'X)^-1[/tex]

                  [tex]= (a^2/n)(X'X)^-1[/tex]

It is given that all covariates have the same variance-covariance structure.

Hence,

             [tex]σ^2 = σ0^2[/tex] for every i.

It is also given that a, σ0 for every i, where a represents a positive constant.

Hence,

           [tex]σ^2 = σ0^2[/tex]

                    [tex]= a^23[/tex]

Hence,

               [tex]Var(β^) = (a^2/n)(X'X)^-1[/tex]

Now, let the diagonal entries of (X'X) be d1, d2, ..., dp.

Hence,

         (X'X) = [dij]

i=1,2,...,p;

X¹ = [0, 0, ..., 1, ..., 0]'

Let X¹ denote the ith column of X.

Hence, X¹ is given by:

                                 [tex]X¹ = [0, 0, ..., 1, ..., 0]'[/tex]

where 1 is in the ith position.

Hence, the ith diagonal entry of X'X is given by:

              [tex](X'X)ii = Σj(Xj¹)^2[/tex]

where the sum is over all i.

From the given data, the entries of the first column of X are all equal to 1.

Hence, [tex]X1¹ = [1, 1, ..., 1]'.[/tex]

Hence, [tex](X'X)ij = nai[/tex] and

[tex](X'X)ij = nai[/tex] for [tex]i ≠ j.[/tex]

Hence,[tex](X'X) = a^2I + n11'[/tex]

The inverse of (X'X) is given by:

             [tex](X'X)^-1 = (1/n)(I - (1/n)a^-2(1 1'))[/tex]

Hence,

     [tex]Var(β^) = (a^2/n)(X'X)^-1[/tex]

                     =[tex]a^2[(1/n)(I - (1/n)a^-2(1 1'))][/tex]

The variance of the ith entry of the least square estimator is given by:

 [tex]Var(β^i) = ai^2[(1/n)(I - (1/n)a^-2(1 1'))]ii[/tex]

Hence,

           [tex]Var(β^i)[/tex]= [tex]ai^2[(1/n)(1 - (1/n)a^-2)][/tex]

                          = [tex]a^2/n[/tex]

Therefore, the variance of the ith entry of the least square estimator is given by:

        [tex]Var(β^i) = a^2/n[/tex]

The equality would be attained if

          [tex]X'X = a^2I,[/tex]

where β^i represents the ith entry of the least square estimator β^. Therefore, the required result has been obtained.

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Answer:

C.

Step-by-step explanation:

Edge2021

The graph of the answer is plotted and attached.

Inequality is the mathematical statement formed when two expressions are joined by an inequality operator.

The inequality is  –9x² + 4y² – 18x + 16y – 29 ≤ 0,

The inequality represents a hyperbolic inequality.

The graph of inequality is plotted and attached with the answer.

The shaded portion is the representation of inequality.

The shaded portion shows that the graph is a graph of a hyperbola.

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The given binary operations are defined as below:

For the integers x and y, the binary operations are defined as: x + y = max (x, y) and x – y = min (x, y)

a) Commutative Property: The commutative property holds for both binary operations, + and – , because: For any x, y ∈ Z,x + y = y + x and x – y = -(y – x)Therefore, both + and – are commutative.

Associative Property: Associativity can also be shown for both binary operations, + and –, as follows: For any x, y and z ∈ Z,x + (y + z) = max (x, max(y, z)) = max (max(x, y), z) = (x + y) + z(x – y) – z = min (x, min (y, z)) = min (min(x, y), z) = (x – y) – z

Therefore, both + and – are associative.

Distributive Property: The distributive property can be shown for these binary operations, + and –, as follows: For any x, y, and z ∈ Z,x + (y – z) = max (x, min (y, z)) = min (max(x, y), max(x, z)) = (x + y) – (x + z)Therefore, both + and – are distributive.

b) For the given operations, the element that violates the property x + 0 = x is:0If x = 2, then x + 0 = max (2, 0) = 2If x = 0, then x + 0 = max (0, 0) = 0So, the property x + 0 = x holds for all integers except for 0.

For this particular element, the value of x + 0 is always 0.

Therefore, the given property fails to hold.

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Answer:

If you are referring to the y-intercept, then the answer is 5. Otherwise, the answer is probably 6.

Step-by-step explanation:

Answer:

i got 1

Step-by-step explanation:

Answer: I- 81 pints,  II-9 pints

Step-by-step explanation:

Given

The first type of juice has 30% pure Juice

The second type of juice has 80% pure Juice

The final mixture has 95 pints of 35% pure juice

Suppose we take x pints from the first Juice

So, the second Juice contributes 90-x

for 35% content

[tex]\Rightarrow 35=\dfrac{x\times 30+(90-x)80}{90}\\\\\Rightarrow 3150=30x+7200-80x\\\\\Rightarrow 50x=4050\\\Rightarrow x=81\ \text{pints}[/tex]

First contributes 81 pints. second contributes 9 pints

Answer:

(1,1) (2,2) (1,2) (1,5) (4,4) (4,5)

there are a lot more but those are some.

Step-by-step explanation: