Marginal Cost The total weekly cost (in dollars) incurred by Lincoln Records in pressing x compact discs is given by the following function. C(x) = 2000 + 2x − 0.0001x2 (0 ≤ x ≤ 6000)
a. What is the actual cost incurred in producing the 1021st and the 1801 st disc?
b. What is the marginal cost when x = 1020 and 1800?

The probability that a randomly selected member of Congress who favours corporate tax reform is a Democrat is 0.4444, rounded to four decimal places.

To solve this problem, we can use Bayes' theorem. Let D represent the event that the selected member is a Democrat, and R represent the event that the selected member is a Republican, and I represent the event that the selected member is an Independent. Let F represent the event that the selected member favors some type of corporate tax reform. We are given the following probabilities:

P(R) = 0.28, P(D) = 0.50, P(I) = 0.22

P(F|R) = 0.34, P(F|D) = 0.35, P(F|I) = 0.31

We want to find P(D|F), the probability that the selected member is a Democrat given that they favor corporate tax reform. We can use Bayes' theorem:

P(D|F) = P(F|D)P(D) / [P(F|D)P(D) + P(F|R)P(R) + P(F|I)P(I)]

Plugging in the values we know, we get:

P(D|F) = 0.35 * 0.50 / [0.35 * 0.50 + 0.34 * 0.28 + 0.31 * 0.22]

P(D|F) = 0.4444 (rounded to four decimal places)

Therefore, the probability that the selected member is a Democrat given that they favour corporate tax reform is 0.4444.

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The number of significant figures for each given value is as follows: 0.098200 has 5 significant figures, 1.68×10^4 has 3 significant figures, 78,000,120 has 9 significant figures, and 1.008 has 4 significant figures.

Significant figures represent the precision and accuracy of a number. They include all the digits that carry meaning in a measurement or calculation. In the case of 0.098200, all the digits are non-zero and are considered significant. Therefore, it has 5 significant figures.

For 1.68×10^4, the number is written in scientific notation. The digits before the multiplication sign represent the significand, which in this case is 1.68. The exponent of 10 indicates the number of places the decimal point is moved to obtain the actual value. In this case, it is 4, which means the decimal point is moved four places to the right. The significand, 1.68, has three significant figures, and the exponent of 10 does not affect the significant figures. Therefore, the value has 3 significant figures.

In 78,000,120, the zeros are considered significant because they are between nonzero digits. Hence, all the digits contribute to the significant figures, resulting in 9 significant figures.

Lastly, for 1.008, the trailing zero after the decimal point is significant, as it indicates precision. Therefore, it has 4 significant figures.

In summary, the number of significant figures for each given value is 0.098200 with 5 significant figures, 1.68×10^4 with 3 significant figures, 78,000,120 with 9 significant figures, and 1.008 with 4 significant figures.

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Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

La fórmula para calcular la longitud de una circunferencia es:

Longitud = π * Diámetro

En este caso, si el diámetro es de 32 cm, podemos calcular la longitud de la siguiente manera:

Longitud = π * 32 cm

El valor de π (pi) es una constante que representa la relación entre la circunferencia de un círculo y su diámetro. Usualmente, se aproxima a 3.14159.

Por lo tanto, la longitud de la circunferencia sería:

Longitud ≈ 3.14159 * 32 cm

Calculando el resultado:

Longitud ≈ 100.53096 cm

Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

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Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Answer:

y=1/2x+9

Step-by-step explanation:

Answer:

Step-by-step explanation: This relationship can either be within the species or between the two different species. The species with this relationship is termed as symbionts. Mutual relationship is seen in all living organisms including human beings, animals, birds, plants and other microorganisms like bacteria, virus, and fungi. Mutualism is a sort of symbiosis.

Answer:

7/2

Step-by-step explanation:

The solution to the equation x - 5 = 2 is x = 7.

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.

Yes, your steps are correct. Here's the solution to the equation:

x - 5 = 2

To isolate x, we add 5 to both sides of the equation:

x - 5 + 5 = 2 + 5

Simplifying both sides of the equation, we get:

x = 7

Therefore, the solution to the equation x - 5 = 2 is x = 7.

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The complete question is:

Solve the equation to isolate the variable x: x - 5 = 2

Start with her regular taxable income: $145,000

Therefore, Juanita's TMT would be $37,700 if her AMT base is $145,000, all ordinary income.

Start with her regular taxable income: $497,500

Therefore, Juanita's TMT would be $139,400 if her AMT base is $497,500, all ordinary income.

Start with her regular taxable income: $129,000 (subtracting the $16,000 of qualified dividends)

Therefore, Juanita's TMT would be $33,540 if her AMT base is $145,000, which includes $16,000 of qualified dividends.

What is Juanita's AMT liability if base is $497,500?

Start with her regular taxable income: $481,500 (subtracting the $16,000 of qualified dividends)

Therefore, Juanita's TMT would be $134,820 if her AMT base is $497,500, which includes $16,000 of qualified dividends.

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Answer:

πr²= 12.56

r²=12.56/3.14 = 4

r= 2

therefore , diameter = 2r = 2×2= 4 mm

c = 1/2, and the pdf is fx(x) = { 1/2 \((1-x^{2} )^{-1}\), −1 ≤ x ≤ 1or 0 otherwise and cdf of X is: FX(x) = { 0, x ≤ -1 or -1/2 \(tan^{-1}(x/\sqrt{1-x^{2} )}\) + 1/2, -1 < x < 1 or 1 ,x ≥ 1

(a) To find c, we need to integrate the pdf over its support and set the result equal to 1 since the pdf must integrate to 1 over its entire support. Therefore, we have:

1 = ∫c \((1-x^{2} )^{-1}\) dx from -1 to 1

Using the substitution u = 1 - \(x^{2}\), we have:

1 = c∫ \(u^{-1/2}\) dx from 0 to 1

Solving the integral, we get:

1 = 2c

Therefore, c = 1/2, and the pdf is:

fx(x) = {

1/2 \((1-x^{2} )^{-1}\) , −1 ≤ x ≤ 1

0 otherwise

To sketch the pdf, we can notice that it is symmetric about x = 0 and that it approaches infinity as x approaches ±1. Therefore, it will have a peak at x = 0 and decrease as we move away from x = 0 in either direction.

(b) To find the cdf of X, we can integrate the pdf from negative infinity to x for each value of x in the support of the pdf. Therefore, we have:

FX(x) = ∫fX(t) dt from -∞ to x

For x ≤ -1, FX(x) = 0, since the pdf is zero for x ≤ -1. For -1 < x < 1, we have:

FX(x) = ∫1/2 \((1-t^{2} )^{-1}\) dt from -1 to x

Using the substitution u = \(t^{2}\) - 1, we have:

FX(x) = -1/2 ∫\((x^{2} -1)^{-1/2}\) du

Solving the integral, we get:

FX(x) =  -1/2 \(tan^{-1}(x/\sqrt{1-x^{2} )}\)  + 1/2

For x ≥ 1, we have FX(x) = 1, since the pdf is zero for x ≥ 1. Therefore, the cdf of X is:

FX(x) = {

0 x ≤ -1

-1/2 \(tan^{-1}(x/\sqrt{1-x^{2} )}\)  + 1/2 -1 < x < 1

1 x ≥ 1

To sketch the cdf, we can notice that it starts at 0 and increases gradually from x = -1 to x = 1, where it jumps to 1. The cdf is also symmetric about x = 0, similar to the pdf.

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The probability that David will select a blue Skittle from each bag is 17/30

Given that, David has 8 red Skittles, 6 blue Skittles, and 6 green Skittles in one bag and second bag contains 5 red Skittles, 4 blue Skittles, and 6 green Skittles.

He randomly selected 1 Skittle from each bag, we need to find the probability that David will select a blue Skittle from each bag,

So, the total number of skittles in one bag = 20

P(getting blue from one bag) = 6/20

The total number of skittles in 2nd bag = 15

P(getting blue from 2nd bag) = 4/15

P(selecting a blue Skittle from each bag) = 6/20 + 4/15 = 17/30

Hence, the probability that David will select a blue Skittle from each bag is 17/30

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Therefore, our initial assumption that a and n are not relatively prime must be false, and we can conclude that a and n are indeed relatively prime numbers.

To prove that both a and b are relatively prime to n given that ab ≡ 1 (mod n), we will use contradiction. Assume that a and n are not relatively prime, meaning they have a common factor greater than 1. Then, we can write a = kx and n = ky, where k > 1 and x and y are relatively prime.

Substituting a = kx into ab ≡ 1 (mod n), we get kxb ≡ 1 (mod ky). Multiplying both sides by x, we get kxab ≡ x (mod ky). Since k > 1 and x are relatively prime, kx and ky are also relatively prime. Therefore, we can cancel out kx from both sides of the congruence, leaving b ≡ x (mod y). Now, suppose that b and n are not relatively prime, meaning they have a common factor greater than 1. Then, we can write b = jy and n = jm, where j > 1 and y and m are relatively prime.

Substituting b = jy into ab ≡ 1 (mod n), we get ajy ≡ 1 (mod jm). Multiplying both sides by y, we get ajym ≡ y (mod jm). Since j > 1 and y are relatively prime, jy and jm are also relatively prime. Therefore, we can cancel out jy from both sides of the congruence, leaving am ≡ 1 (mod j). But since k and j are both greater than 1, and n = ky = jm, we have k and j as common factors of n, which contradicts the assumption that x, y, and m are relatively prime.

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Answer: x=-5

Step-by-step explanation:

Answer:

njj

Step-by-step explanation:

Answer:

A. 272 cm^2

Step-by-step explanation:

The area of the rectangle is 17cm * 7cm = 119 cm^2

The area of the right triangle is (25-7) * 17cm * 1/2 = 153cm^2

Answer: 119+153 = 272 cm^2

Let x represents the number of months it will take Kelsey to have more money than Kyle.

Given that Kelsey starts with $150 in her account and she adds $25 a month, it means that the amount that he would have saved after x months is

150 + 25 *x

= 150 + 25x

Given that Kyle starts with $200 in his account and adds $20 a month to his account, it means that the amount that he would have saved after x months is

200 + 20 *x

= 200 + 20x

For Kelsey to have more money than Kyle, the inequality would be

150 + 25x > 200 + 20x

25x - 20x > 200 - 150

5x > 50

Answer:

b

Step-by-step explanation:

negative means you have to go down so -4 means go down negative 7 and right 7

Answer: good luck to you!

Step-by-step explanation:

Answer:

tysm for the points <33

Step-by-step explanation:

:)

Answer: 33 groups

Step-by-step explanation:

Number of people that signed for help = 130 people

Number of people that can join a group = 4.

Number of groups that will be formed will be:

= Number of people that signed for help / Number of people that can join a group

= 130/4

= 32.5

= 33 groups

Since there'll be a remainder of 2 people, they will form a new group making 33 groups.

The area of the rectangle is found to be 20 - 2·√(10) sq. units.

Let x be the length of the rectangle.

Let y be the width of rectangle.

Then, length is reduced by 4 and with is increased by 5.

x - 4 = y + 5 , (becomes square) ....eq 1

Area of square = 40 cm²

Then,

(x - 4) × (y + 5) = 40 cm²

From eq 1

(y + 5) × (y + 5) = 40 cm²

y² + 10y + 25 = 40

y² + 10y + 25 - 40 = 0

y² + 10y - 15 = 0

Solving equation by quadratic formula:

y = -5 + 2·√(10)

Then, for x:

x - 4 = 5 + -5 + 2·√(10) = 2·√(10)

x = 4 + 2·√(10)

Now,

Area of the rectangle, A = x × y

Put the values:

A = (-5 + 2·√(10)) × (4 + 2·√(10))

A = 20 - 2·√(10)

Thus, the area of the rectangle is found to be 20 - 2·√(10) sq. units.

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Answer: 360cm^2

Step-by-step explanation: the rectangle is 24 by 15

The initial Jacobian matrix evaluated at the point (x1, x2) = (5, 3) is,\($$J = \begin{bmatrix}1 & -6\\0 & 1\end{bmatrix}$$\).

The Jacobian matrix is a matrix of first-order partial derivatives that describes the rate at which a vector-valued function changes with respect to its input variables. More formally, if f: R^n -> R^m is a differentiable function that maps a vector x in n-dimensional space to a vector y in m-dimensional space, then the Jacobian matrix J of f is an m x n matrix whose entries are given by the partial derivatives of the components of f with respect to the components of x.

The Jacobian matrix of f(x1, x2) is given by:

\(\frac{\partial f_1}{\partial x1} & \frac{\partial f_1}{\partial x2}\\\frac{\partial f_2}{\partial x1} & \frac{\partial f_2}{\partial x2}\end{bmatrix}$$\)

where f1(x1, x2) = x1 - x2^2 and f2(x1, x2) = x2 - 2.

Evaluating the Jacobian at the point (x1, x2) = (5, 3), we have:

\($$J = \begin{bmatrix}\frac{\partial (x1-x2^2)}{\partial x1} & \frac{\partial (x1-x2^2)}{\partial x2}\\\frac{\partial (x2-2)}{\partial x1} & \frac{\partial (x2-2)}{\partial x2}\end{bmatrix}_{(5,3)}\)

\(=\begin{bmatrix}1 & -2x2\\0 & 1\end{bmatrix}_{(5,3)} =\begin{bmatrix}1 & -6\\0 & 1\end{bmatrix}$$\)

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Answer:

a=(z-2)/2

Step-by-step explanation:

You need to isolate your "a" variable so first you want to subtract 2 from both sides, leaving you with:

z-2=2a

then you want to divide by 2 on both sides to isolate your "a" variable which would leave you with

a=\(\frac{(z-2)}{2}\)

Answer: 70 degrees 35 times 2

Answer:

13/18

Step-by-step explanation:

The two negatives cancel out.

1/6 * 4 1/3 is 13/18, first turn 4 1/3 to 13/3.

Hope this helps

Answer:

Step-by-step explanation:

6-3x=12-6x

Only one solution of  x=2

Answer:

x+y

Step-by-step explanation:

#boys+#girls=#children

Answer:

Answer:

Multiply the numerator by the reciprocal of the denominator. Multiply x x by 1 1 . Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=1x f - 1 ( x ) = 1 x is the inverse of f(x)=1x f ( x ) = 1 x .

Step-by-step explanation:

:)