Expand each expression and simplify your answers as far as possible
1. 8x - 2(3 - 2x)
2. 4x + 5-3(2x - 4)

28 degrees is the measure of the angle m<C

The given diagram is a circle geometry. Using the theorem below:

The angle at the vertex is half the difference of angles at the intercepted arc.

Mathematically;

<C = 1/2(arcAE - arcBD)

<C = 1/2(92 - 36)

<C = 1/2(56)

<C = 28 degrees

Hence the measure of the angle m<C from the given diagram is 28 degrees

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Answer:

Step-by-step explanation:

natural numbers start from one but it says greater than 70 so it will start from 71 but to any number as long as it is greater than 70

✨Answer:✨

9 3/4 (simplest form)

✨Step-by-step explanation:✨

1. Convert decimal into fraction:

9.75 = 975/100

2. Simplify:

975/100 = 39/4 = 9 3/4

A. Reduce fraction to lowest terms (25 is the greatest common divisor of 975 and 100. Reduce by dividing both numerator and denominator by 25):

975/100 = 975 ÷ 25   = 39/4

                 100 ÷ 25

B. Convert improper fraction to mixed number:

39/4 = 9 3/4

(39 ÷ 4 = 9 remainder 3)

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \bold{ \sf{x = 2}}}}}}\)

Step-by-step explanation:

\( \sf{2x + 14 = - 6 + 12x}\)

Move 12x to left hand side and change it's sign

⇒\( \sf{2x - 12x + 14 = - 6}\)

Move 14 to left hand side and change it's sign

⇒\( \sf{2x - 12x = - 6 - 14}\)

Collect like terms

⇒\( \sf{ - 10x = - 6 - 14}\)

Calculate

⇒\( \sf{ - 10x = - 20}\)

Divide both sides of the equation by -10

⇒\( \sf{ \frac{ - 10x}{ - 10} = \frac{ - 20}{ - 10} }\)

Calculate

⇒\( \sf{x = 2}\)

Hope I helped!

Best regards!!

The correct statements regarding the pth percentile of a continuous random variable are: the area under the curve to the left of the pth percentile is equal to p, and the area under the curve to the right of the pth percentile is equal to (1-p).

In general, when considering the pth percentile of a continuous random variable, the following statements are always true:

1. The area under the curve to the left of the pth percentile is equal to p: This statement is correct. The pth percentile is the value below which p percent of the data falls. Therefore, the area under the curve to the left of the pth percentile represents p percent of the total area.

2. The area under the curve to the right of the pth percentile is equal to (1-p): This statement is also correct. Since the total area under the curve is equal to 1, the remaining area to the right of the pth percentile is (1 - p).

3. The pth percentile is positive: This statement is not necessarily true. The pth percentile can be positive, zero, or negative depending on the distribution of the random variable. It is possible for a significant portion of the data to fall below zero, resulting in a negative pth percentile.

Therefore, the correct statements are:

- The area under the curve to the left of the pth percentile is equal to p.

- The area under the curve to the right of the pth percentile is equal to (1-p).

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Answer:

the area of the outer part of the rug is 44x + 484 square inches, where x is the side length of the inner square in inches

Step-by-step explanation:

The area of a square can be calculated by squaring its side length.

The area of the inner square in the center of the rug is x^2 square inches.

The side length of the outer region of the rug is equal to the sum of the side length of the inner square and twice the width of the outer region. This can be expressed as:

x + 2(11) = x + 22

Therefore, the side length of the outer region of the rug is x + 22 inches.

The area of the outer region of the rug can be calculated by subtracting the area of the inner square from the area of the larger square:

Area of outer region = (x + 22)^2 - x^2

Expanding the expression, we get:

Area of outer region = x^2 + 44x + 484 - x^2

Simplifying, we get:

Area of outer region = 44x + 484 square inches

Answer:

7x ≥ x + 6

A number signifies x.

Replace "a number" with x and then write out the inequality.

Answer:

B

Step-by-step explanation:

The equation ( ∂P/∂E )T = -P( ∂P/∂V )T - T( ∂T/∂V )P represents a relationship involving partial derivatives of pressure (P), energy (E), and volume (V) with respect to temperature (T).

In the given equation, the left-hand side represents the partial derivative of pressure with respect to energy at constant temperature ( ∂P/∂E )T . On the right-hand side, the equation involves two terms. The first term, -P( ∂P/∂V )T , represents the negative product of pressure (P) and the partial derivative of pressure with respect to volume at constant temperature ( ∂P/∂V )T . The second term, -T( ∂T/∂V )P , represents the negative product of temperature (T) and the partial derivative of temperature with respect to volume at constant pressure ( ∂T/∂V )P .

This equation suggests a relationship between the changes in pressure, energy, and volume, with temperature held constant. It states that the rate of change of pressure with respect to energy is determined by the combined effects of the partial derivatives of pressure with respect to volume and temperature. By understanding this equation and its implications, one can analyze and interpret the behavior of the variables involved in the thermodynamic system.

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Answer: Im pretty sure you do

Step-by-step explanation: your welcome

18 + 108 + 1008 =1,134

Given that v: R² → R is a harmonic-function, the task is to show that the function w: R² → R defined by w(x, y) = v (y² — x², 2xy) is also a harmonic function using Laplace's equation.

:Harmonic functions can be expressed as a solution of Laplace's equation, given as follows:

∇²v(x, y) = 0, where

∇² is the Laplacian operator.

Now, let's differentiate the function w(x, y) twice to get the Laplacian of w.

The first derivative of w is given as follows:

w_x = ∂w/∂x

       = ∂v/∂x(y² − x², 2xy)

       = -2x * ∂v/∂z + 2y * ∂v/∂w

(where z = y² − x², w = 2xy)

The second derivative of w with respect to x is given as:

w_xx = ∂²w/∂x²

         = -2 * ∂(2y * ∂v/∂w)/∂x + 2 * ∂(-2x * ∂v/∂z)/∂x

         = -4y * ∂²v/∂z∂w - 4x * ∂²v/∂w²

The first derivative of w with respect to y is given as:

w_y = ∂w/∂y

       = ∂v/∂y(y² − x², 2xy)

       = 2y * ∂v/∂z + 2x * ∂v/∂w

The second derivative of w with respect to y is given as:

w_yy = ∂²w/∂y²

         = 2 * ∂(2y * ∂v/∂z)/∂y + 2 * ∂(2x * ∂v/∂w)/∂y

          = 4y * ∂²v/∂z² + 4x * ∂²v/∂z∂w

Now, adding both second derivatives:

w_xx + w_yy = -4y * ∂²v/∂z∂w - 4x * ∂²v/∂w² + 4y * ∂²v/∂z² + 4x * ∂²v/∂z∂w

                     = 4(x² + y²) * ∂²v/∂z²

Since the partial derivative of v(x, y) with respect to x² + y² is 0 as it is a harmonic function, we have:

∂²v/∂z² + ∂²v/∂w² = 0

Therefore,we get w_xx + w_yy = 0,

which is Laplace's equation for a harmonic function.

Hence, the function w(x, y) = v (y² — x², 2xy) is also a harmonic function.

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The volume of the cylinder with a radius of 6 cm and a height of 18 cm is calculated, to the nearest hundreth, as: 2035.75 cm³.

Volume of a cylinder = πr²h

Given the parameters of the cylinder:

Volume of the cylinder = πr²h = π(6²)(18)

Volume of the cylinder = 2035.75 cm³

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The long-run cost function is C(q) = 2w(sqrt[rw(q^3)]). The profit-maximizing output can be found by minimizing this cost function with respect to q.

Part a: Deriving the long-run cost function C(q):

To derive the long-run cost function, we need to find the minimum cost of producing a given output level q using the given production function.

Given the production function q = F(L, K) = (KL)^(1/3), we can rewrite it as K = (q^3)/L.

Now, let's express the cost function C(q) in terms of q. We have the cost function as C(q) = wL + rK, where w is the wage rate and r is the rental rate.

Substituting the expression for K in terms of q, we get C(q) = wL + r[(q^3)/L].

To minimize the cost function, we can take the derivative of C(q) with respect to L and set it equal to zero:

dC(q)/dL = w - r[(q^3)/(L^2)] = 0.

Simplifying the equation, we have w = r[(q^3)/(L^2)].

Solving for L, we get L^2 = r(q^3)/w.

Taking the square root, we have L = sqrt[(r(q^3))/w].

Substituting this value of L back into the cost function equation, we get:

C(q) = w(sqrt[(r(q^3))/w]) + r[(q^3)/sqrt[(r(q^3))/w]].

Simplifying further, we have:

C(q) = 2w(sqrt[rw(q^3)]).

So, the long-run cost function C(q) is given by C(q) = 2w(sqrt[rw(q^3)]).

Part b: Solving the long-run profit maximization problem directly:

To solve the profit maximization problem directly, we need to maximize the expression:

max K, L [F(L, K) - wL - rK].

Taking the derivative of the expression with respect to L and K, and setting them equal to zero, we can solve for the optimal values of L and K.

The first-order conditions are:

dF(L, K)/dL - w = 0, and

dF(L, K)/dK - r = 0.

Differentiating the production function F(L, K) = (KL)^(1/3) with respect to L and K, we get:

(1/3)(KL)^(-2/3)K - w = 0, and

(1/3)(KL)^(-2/3)L - r = 0.

Simplifying the equations, we have:

K^(-2/3)L^(1/3) - (3/2)w = 0, and

K^(1/3)L^(-2/3) - (3/2)r = 0.

Solving these two equations simultaneously will give us the optimal values of L and K.

Part c: Using the derived long-run cost function:

In Part a, we derived the long-run cost function as C(q) = 2w(sqrt[rw(q^3)]).

To find the profit-maximizing output, we can minimize the long-run cost function C(q) with respect to q.

Taking the derivative of C(q) with respect to q and setting it equal to zero, we can solve for the optimal value of q.

dC(q)/dq = w(sqrt[rw(q^3)]) + (3/2)w(q^2)/(sqrt[rw(q^3)]) = 0.

Simplifying the equation, we have:

(sqrt[rw(q^3)])^2 + (3/2)(q^2) =

0.

Solving this equation will give us the profit-maximizing output q.

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Answer:

  47

Step-by-step explanation:

You want a two-digit number such that three times the tens digit is 2 less than twice the units digit, and twice the number is 20 greater than the number obtained by reversing the digits.

Let x and y represent the tens digit and ones digit, respectively. The given relations can be written as equations as follows:

  3x = 2y -2 . . . . 3 times tens digit is 2 less than 2 times ones digit

  2(10x+y) = (10y +x) +20 . . . . 2 times the number is 20 more than reversed

Simplifying the equations and expressing them in standard form, we have ...

  3x -2y = -2

  20x +2y = x +10y +20   ⇒   19x -8y = 20

Subtracting 4 times the first equation from the second, we have ...

  (19x -8y) -4(3x -2y) = (20) -4(-2)

  7x = 28 . . . . . . . simplify

  x = 4

Substituting into the first equation, we have ...

  3(4) -2y = -2

  12 +2 = 2y . . . . . add 2y+2

  7 = y . . . . . . . . divide by 2

The two-digit number is 47.

The upper limit of the confidence interval for the proportion of millennials that care about immigration is 0.20.

In order to find the upper limit of the confidence interval for the proportion of millennials that care about immigration,

we first need to calculate the confidence interval using the margin of error (MOE) and sample proportion.

The formula to find the confidence interval is given by:

Confidence Interval = Sample Proportion ± Margin of Error (MOE)

Where Sample Proportion = Poll Result / 100

Let's first find the Sample Proportion of millennials that care about immigration.

Sample Proportion = Poll Result / 100= 17 / 100= 0.17

Now let's calculate the confidence interval using the MOE.

Confidence Interval = Sample Proportion ± Margin of Error (MOE)

Upper Limit of Confidence Interval = Sample Proportion + MOE= 0.17 + 0.03= 0.20

Therefore, the upper limit of the confidence interval for the proportion of millennials that care about immigration is

0.20.

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The positive root of the equation \(4cos(x) - x^4\) using Newton's method is 0.866966.

We begin with an initial guess \(x_{0}=1\), and we can iteratively define the calculation using the formula:

\(x_{i+1}= x_{i} - \frac{ f(x_{i})}{f'(x_{i})}\)

where \(f(x)=4cos(x) - x^4\)and f'(x) is the derivative of f(x).

So, \(f'(x) = -4sin(x) - 4x^3.\)

We repeat this process, using the previous approximation to find the next one, until we reach the desired accuracy.

In each iteration, we substitute the current approximation into the formula to refine our estimate.

Iteration 1: \(x_{1}= x_{0}- f(x_{0})/f'(x_{0})= 1 - \frac{ (4cos(1) - 1^4)}{(-4sin(1) - 4(1)^3)}= 1.576\)

Iteration 2: \(x_{2}= x_{1} - f(x_{1})/f'(x_{1}) = 1.1576 - \frac{(4cos(1.1576) - 1.1576^4)}{(-4sin(1.1576) - 4(1.1576)^3)} = 1.2055\)

Iteration 3: \(x_{3}= x_{2} - f(x_{2})/f'(x_{2}) = 1.2055 - \frac{4cos(1.2055-(1.2055)^4)) }{(-4sin(1.2055) - 4(1.2055)^3)} = 1.2080\)

After several iterations, we get that the positive root of the equation \(4cos(x) - x^4\) is approximate x ≈ 0.866966, accurate to six decimal places.

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Answer:

Sin 21 = p/b

0.358 = 5.5 / x

x = 5.5 / 0.358

therefore , x = 6.97

Step-by-step explanation:

Use sin formula

which is perpendicular/ base

just put the value

Answer:

yes same

Step-by-step explanation:

Answer:

Step-by-step explanation:

23). By applying triangle sum theorem in the given triangle,

    (x + 83)° + (x + 48)° + 65° = 180°

    2x + 196 = 180

    2x = -16

    x = -8

    Measure of angle A = x + 48

                                      = -8 + 48

                                      = 40°

     Therefore, Option A is the answer.

24). By triangle sum theorem,

     (3x + 14)° + 90° + (4 + 3x)° = 180°

     6x + 108 = 180

     6x = 72

     x = 12

     Measure of angle A = (4 + 3x)

                                       = 4 + 3(12)

                                       = 40°

     Therefore, Option A is the answer.

Answer:

It's true - all whole numbers that are odd are going to add up to an even integer. An odd integer can be looked at as an even number plus one. For example, 21 would be 20 (the even number) plus one. So the addition of two odd integers is like saying two even numbers were added to each other (in that example, 20 + 20), and then adding the 1+1 that made them odd (which adds up to 2, an even number). So it would be [20 + 20 + (1 + 1)]

Answer:-72

Step-by-step explanation:

Multiply 6 and negative 12 and your answer is -72

Answer:

It's -72

Step-by-step explanation:

Just confirmed it and got it right.

On an annual basis, the first set of expenses (lottery tickets) is 52% of the second set of expenses (gasoline).

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To compute the annual cost of each expense, we can use the following formulas:

Annual cost of $18 a week on lottery tickets = $18 x 52 weeks = $936

Annual cost of $150 per month on gasoline = $150 x 12 months = $1800

To find the percentage of the first set of expenses (lottery tickets) relative to the second set of expenses (gasoline), we can divide the annual cost of the lottery tickets by the annual cost of gasoline and multiply by 100:

Percentage of lottery ticket expenses relative to gasoline expenses = ($936 / $1800) x 100% = 52%

Therefore, we can complete the sentence as follows: On an annual basis, the first set of expenses (lottery tickets) is 52% of the second set of expenses (gasoline).

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The value of the x is 8.33 under the given condition that  RZ is given as 2x + 5 and TW is given as 5x - 20.

From the given question and illustrative diagram we can clearly see that
RZ = 2x + 5
TW = 5x - 20
Now, we have to find the value of 'x' if RZ = 2x + 5 and TW = 5x - 20.
Then, from the given rectangle figure, we can say  that RZ is equal to TW.
Hence equating both the equation we can  evaluate that the value of x  and the equation can be expressed in the forms of
RZ = TW
2x + 5 = 5x - 20
20 + 5 = 5x - 2x
25 = 3x
x = 25/3
x = 8.33
Then, the value of the x is 8.33.
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a) The recurrence T(n) = T(n/2) + 1 has an asymptotic complexity of O(log(n)).   b) The recurrence T(n) = 2T(n/2) + n has an asymptotic complexity of Ω(nlog(n)).



a) To analyze the recurrence T(n) = T(n/2) + 1, we make a guess that T(n) = O(log(n)). Assuming this guess is correct, we substitute T(n/2) with O(log(n/2)) = O(log(n)) in the recurrence relation. We get T(n) = O(log(n)) + 1. Since O(log(n)) + 1 is dominated by O(log(n)), our guess holds true, and we conclude that T(n) = O(log(n)).

b) For the recurrence T(n) = 2T(n/2) + n, we make a guess that T(n) = Ω(nlog(n)). Assuming this guess is correct, we substitute T(n/2) with Ω((n/2)log(n/2)) = Ω(nlog(n) - nlog(2)) in the recurrence relation. We get T(n) = Ω(nlog(n) - nlog(2)) + n. Simplifying, we have T(n) = Ω(nlog(n) + n - nlog(2)). Since nlog(n) dominates nlog(2), T(n) is Ω(nlog(n)), confirming our guess.

In both cases, the substitution validates our initial guesses for the asymptotic complexity of the recurrences.Therefore, The recurrence T(n) = T(n/2) + 1 has an asymptotic complexity of O(log(n)).   The recurrence T(n) = 2T(n/2) + n has an asymptotic complexity of Ω(nlog(n)).

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For an interest rate of 8%, we divide 72 by 8: 72 / 8 = 9. Thus, it would take around 9 years for the savings to double at an interest rate of 8%.

The "Rule of 72" is a quick estimation method to determine the time it takes for an investment or savings to double in value. By dividing 72 by the interest rate, you can obtain an approximation of the doubling time. For an interest rate of 3%, it would take approximately 24 years for the savings to double. For an interest rate of 8%, it would take around 9 years for the savings to double.

To calculate the doubling time using the Rule of 72, divide 72 by the interest rate. This provides an approximation of the number of years it takes for an investment or savings to double in value.

For an interest rate of 3%, we divide 72 by 3: 72 / 3 = 24. Therefore, it would take approximately 24 years for the savings to double.

For an interest rate of 8%, we divide 72 by 8: 72 / 8 = 9. Thus, it would take around 9 years for the savings to double at an interest rate of 8%.

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The missing proof in the given congruence of triangle is;

∠FAB = ∠FBA.

For the given question;

The given data in the triangle FAB is;

In the step two,

FA = FB (Property of isosceles triangle)

Then, step 4 will be ∠FAB = ∠FBA.

Thus, the missing proof will be ∠FAB = ∠FBA.

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To derive the demand function from the given utility function and endowment, we need to determine the optimal allocation of goods that maximizes utility. The utility function is U(x, y) = -e^(-x) - e^(-y), and the initial endowment is (1, 0).

To derive the demand function, we need to find the optimal allocation of goods x and y that maximizes the given utility function while satisfying the endowment constraint. We can start by setting up the consumer's problem as a utility maximization subject to the budget constraint. In this case, since there is no price information provided, we assume the goods are not priced and the consumer can freely allocate them.

The consumer's problem can be stated as follows:

Maximize U(x, y) = -e^(-x) - e^(-y) subject to x + y = 1.

To solve this problem, we can use the Lagrangian method. We construct the Lagrangian function L(x, y, λ) = -e^(-x) - e^(-y) + λ(1 - x - y), where λ is the Lagrange multiplier.

Taking partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we can find the values of x, y, and λ that satisfy the optimality conditions. Solving the equations, we find that x = 1/2, y = 1/2, and λ = 1. These values represent the optimal allocation of goods that maximizes utility given the endowment.

Therefore, the demand function derived from the utility function and endowment is x = 1/2 and y = 1/2. This indicates that the consumer will allocate half of the endowment to each good, resulting in an equal distribution.

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