Find two acute angles that satisfy the equation sin(2x + 8) = cos(x + 28). Check that your answers make sense.
The smaller angle is
°.
The larger angle is

The length of DB, AD and AC are 24 m, 32 m, 42 m respectively. The measurement of ∠C = 67.38°.

What is a right angle triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

Given that, in △BCD

BD = 24 m

DC = 10 m

BC = 26 m

△BCD is a right angle triangle.

The trigonometry ratio of sine is ratio of height to hypothenuse.

With respect to C, the height of △BCD is 24m and hypothenuse is 26m.

sin C = height/hypothenuse

sin C = 24/26

C = 67.38°

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1/1/3 i do not know i looked it up

Answer:

1.5 hours

Step-by-step explanation:

Answer:

65,300,000,000 mcg

Step-by-step explanation:

ladder of conversion

hence 65.3 kgs = 65.3 * 1000 = 65,300 grams (g)

and then 65,300 g = 65,300 * 1,000,000 = 65,300,000,000 µg or mcg

Answer:

13,000

_____

4%

I'm sorry if this is incorrect

(a) The monopolist's profit-maximizing quantity is 50 units, and the price is $100 per unit.

(b) To achieve the allocatively efficient quantity, the government should set the price at $60 per unit.

(c) Producing the allocatively efficient quantity may not be economically feasible for the monopolist as the price is lower than the average total cost of production.

(d) To have the monopolist earn zero economic profit, the government should set the price at $80 per unit.

(e) The deadweight loss will decrease compared to that of the unregulated monopolist.

(a) The profit-maximizing quantity is where marginal revenue equals marginal cost, which occurs at 50 units, and the corresponding price is $100 per unit. At this quantity, the monopolist's total revenue is $5000, and its total cost is $2500, resulting in a profit of $2500.

(b) To achieve allocative efficiency, the government should set the price at the point where the demand curve intersects the marginal cost curve, which is at 70 units and a price of $60 per unit. At this quantity, the price is equal to the marginal cost, and society maximizes its total surplus.

(c) Producing the allocatively efficient quantity may not be economically feasible for the monopolist because the price of $60 per unit is lower than the average total cost of production, which is $75 per unit. Thus, the monopolist will incur losses if it produces at this quantity.

(d) To regulate the monopolist to earn zero economic profit, the government should set the price at the point where the demand curve intersects the average total cost curve, which is at 80 units and a price of $80 per unit. At this quantity, the price is equal to the average total cost, and the monopolist earns zero economic profit.

(e) The deadweight loss will decrease compared to that of the unregulated monopolist because the allocatively efficient quantity is being produced. However, there may still be some deadweight loss due to the difference between the price and the average total cost.

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Answer:

325.6g

Step-by-step explanation:

weight of phone + weight of case

= 310 + 15.6

= 325.6g

mark as brainliest pls

Answer: Yes

Step-by-step explanation:

Remember, a fraction with a negative sign anywhere is a negative fraction; in other words, it represents a negative quantity. As long as you write only one negative sign, it doesn't matter whether you put it before the denominator, before the numerator or before the entire fraction

The power series constructed is y(x) = a₀ + (-a₁/3)x + (-a₀/2)x² + (-a₁/3)x³ + (a₀/8)x⁴ + (a₁/15)x⁵ + ...

The Emden Equation and determine the coefficients a₀, a₁, a₂, a₃, a₄, and a₅, substitute a power series into the equation and match the coefficients term by term.

Let's assume the power series solution for y(x) is:

y(x) = a₀ + a₁x + a₂x² + a₃x³ + a₄x⁴ + a₅x⁵ + ...

Substituting this series into the Emden Equation, we have:

x(y'' + 2y' + xy) = 0.

Differentiating y(x) with respect to x, we get:

y' = a₁ + 2a₂x + 3a₃x² + 4a₄x³ + 5a₅x⁴ + ...

Differentiating again, we have:

y'' = = 2a₂ + 6a₃x + 12a₄x² + 20a₅x³ + ...

Now, let's substitute these expressions into the Emden Equation:

x((2a₂ + 6a₃x + 12a₄x² + 20a₅x³ + ...) + 2(a₁ + 2a₂x + 3a₃x² + 4a₄x³ + 5a₅x⁴ + ...) + x(a₀ + a₁x + a₂x² + a₃x³ + a₄x⁴ + a₅x⁵ + ...) )= 0.

Expanding and grouping terms by powers of x, we have:

(2a₂ + a₀) x + (6a₃ + 2a₁) x² + (12a₄ + 3a₂) x³ + (20a₅ + 4a₃) x⁴ + ... = 0.

For this equation to hold for all values of x, each coefficient of xⁿ must be equal to zero.

Therefore, we can determine the coefficients as follows:

Coefficient of x°: 2a₂ + a₀ = 0 => a₀ = -a₀/2.

Coefficient of x¹: 6a₃ + 2a₁ = 0 => a₃ = -a₁/3.

Coefficient of x²: 12a₄ + 3a₂ = 0 => a₄ = -a₂/4 = a₀/(2ₓ4) = a₀/8.

Coefficient of x³: 20a₅ + 4a₃ = 0 => a₅ = -a₃/5 = a₁/(3ₓ5) = a₁/15.

Therefore, the coefficients of the power series solution are:

a₀ = a₀ a₁ = -a₁/3 a₂ = -a₀/2 a₃ = -a₁/3 a₄ = a₀/8 a₅ = a₁/15

The power series

y(x) = a₀ + (-a₁/3)x + (-a₀/2)x² + (-a₁/3)x³ + (a₀/8)x⁴ + (a₁/15)x⁵ + ...

This series is known as the power series solution for the Lane-Emden equation, which is used to describe the structure of self-gravitating, spherically symmetric gas clouds, such as in stellar astrophysics.

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Answer:

a=4

Step-by-step explanation:

2a+3b=12

+

a-3b=0

3a=12

a=4

a) The equation 3u + 40 + 2u = 6u - 30 - u has no solution.

b) The equation 2.2z + 3z = 4.5 - 3.2 has one solution.

c) The equation 2.3y + 3.2 - y = 2.1 + 1.3y + 1.1 has infinitely many solutions.

d) The equation 20 + 4r = 32 - 2r has one solution.

What is an equation with infinitely many solutions ?

The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept.

Let's check which of the given equations have one solution , infinitely many solutions or no solution.

a)

3u + 40 + 2u = 6u - 30 - u

reordering the terms :

5u + 40 = 5u - 30

or subtract 5u from both sides.

5u - 5u + 40 = 5u - 5u - 30

40 = - 30

which is not possible , that meant this equation has no solution.

b)

2.2z + 3z = 4.5 - 3.2

2.2z + 3z = 4.5 - 3.2

5.2z = 1.3

z = 1.3/5.2

or

z = 13/52

This equation has one solution.

c)

2.3y + 3.2 - y = 2.1 + 1.3y + 1.1

Reordering the terms :

1.3y + 3.2 = 1.3y + 3.2

0 = 0

This equation has infinitely many solutions.

d)

20 + 4r = 32 - 2r

Reordering the terms :

6r = 12

r = 2

This equation has one solution.

Therefore , the answers are :

a) The equation 3u + 40 + 2u = 6u - 30 - u has no solution.

b) The equation 2.2z + 3z = 4.5 - 3.2 has one solution.

c) The equation 2.3y + 3.2 - y = 2.1 + 1.3y + 1.1 has infinitely many solutions.

d) The equation 20 + 4r = 32 - 2r has one solution.

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If the semi-annual rate is 0.5%, then the Annual Percentage Rate is 0.0001%.

To find the Annual Percentage Rate (APR), we need to double the semiannual rate since there are two semiannual periods in a year.

So, the APR would be 1% (0.5% * 2).

2. To find the Effective Annual Rate (EAR), we can use the formula:

\(EAR = (1 + r/n)^n - 1\)

where r is the nominal interest rate and n is the number of compounding periods per year.

In this case, the nominal interest rate (r) is 0.5% and the compounding periods per year (n) is 2 (since it's a semiannual rate).

Plugging in these values into the formula:

EAR = (1 + 0.005/2)^2 - 1

EAR = (1.0025)^2 - 1

EAR = 1.005025 - 1

EAR = 0.005025

Therefore, the EAR (rounded to 6 decimal points) is 0.005025.

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Answer:

It's 0.75

Step-by-step explanation:

But if in fraction -3/-4

Answer:

te56

Step-by-step explanation:

y8888888755555555555555578

For the probability density function, \(f(x) = \[ \begin{cases} \frac{10}{x²}& x ≥10 \\ 0 & x< 10\end{cases} \] \),

a) The probability that the device will last more than 20 hours is equals to \(= \frac{1}{2} \).

b) The cumulative distribution function (CDF) of X is \(F(x) = \[ \begin{cases} 1- \frac{10}{x}& x ≥10 \\ 0 & x< 10\end{cases} \]\).

c) The probability that of 6 such type of devices at least 3 will function at least 15 hours is equals to 0.31960.

d) The average lifetime of such type of device is infinity.

e) The expected value and variance is 1.25 and 2.066 respectively.

The probability density function is integrated to compute the cumulative distribution function. We have a probability density function (pdf) of X, for lifetime of a certain type of electronic device, \(f(x) = \[ \begin{cases} \frac{10}{x²}& x ≥10 \\ 0 & x< 10\end{cases} \]\).

We have answer the following questions,

a) The probability that the device will last more than 20 hours, P( X> 20) \(= \int_{20}^{\infty } \frac{ 10}{x²} dx\)

\(= [ \frac{- 10}{x} ]_{20}^{ \infty } \ \)

\(= [\frac{-10}{\infty}-\frac{(-10)}{20}]\)

\(= \frac{1}{2} \)

b) The cumulative distribution function (CDF) of X, is represented as, \(= \int_{10}^{x}\frac{10}{y²}dy\)

\(= - 10 [ \frac{ 1}{y} ]_{10}^{ x } \)

\(= [ \frac{ -10}{x } + \frac{10}{10} ]\)

\(= 1- \frac{ 10}{x } \)

\(F(x) = \[ \begin{cases} 1- \frac{10}{x}& x ≥10 \\ 0 & x< 10\end{cases} \]\).

c) The probability that of 6 such type of devices at least 3 will function at least 15 hours, \(P( X>15) = \int_{15}^{\infty} ( \frac{10}{x²}) dx\)

= \( \frac{2}{3}\)

Now, \(P( X ≥ 3) = P(X= 0) + P( X=1) + P( X = 2) + P( X = 3) \\ \)

\( = ⁶C₀( \frac{2}{3})⁰( \frac{2}{3})⁶+ ⁶C₁( \frac{2}{3})¹ (\frac{1}{3} )⁵ + ⁶C₂(\frac{2}{3})²(\frac{1}{3})⁴ +⁶C_3(\frac{2}{3})³(\frac{1}{3})³ \\ \)

= 0.001371 + 0.01646 + 0.08230 + 0.21947

= 0.31960

So, the probability is 0.31960.

d) the average lifetime of such type of device, \(E(X) = \int_{10}^{\infty} \frac{10}{x} dx\)

\(=10[ln(x) ]_{10}^{\infty}\)

\(=\infty\)

e) Let X be a random variable with pdf, f(x) = \(f(x) = \[ \begin{cases} \frac{ {x}^{2} }{3}& - 1 < x < 2 \\ 0 &otherwise\end{cases} \]\)

The expected value, \(E(X) = \int_{-1}^{2}\frac{x³}{3}dx\)

\(= [\frac{x⁴}{12}]_{-1}^{2} \)

= 1.25

The variance value of g(X) = 3−4X

\( {X^2}= \int\limits_{ - 1}^2 {\dfrac{{{x^4}}}{3}} dx = (\frac{x^5}{15})_{ - 1}^{2} \\ \)

= 2.066

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Complete question :

The probability density function (pdf) of X, the lifetime of a certain type of electronic device (measured in hours), is given by f(x)=10/x2,

x≥10, 0, x <10.

a. Find the probability that the device will last more than 20 hours.

b. What is the cumulative distribution function (CDF) of X?

c. What is the probability that of 6 such type of devices at least 3 will function at least 15 hours?

d. What is the average lifetime of such type of device?

e. Let X be a random variable with pdf

f(x)=x2/3,−1<x<2, 0 otherwise

Find the expected value and variance of g(X)=3−4X

Although there is consensus that employees who work oversees should be trained, less than half of the U.S. companies surveyed recently indicated they had training programs.

The U.S. companies surveyed indicated they had training programs for employees who work overseas.

The survey found that only 44% of the companies had such training programs.

It is despite the fact that there is a growing consensus among business leaders and experts that such training is crucial for the success of international assignments without proper training, employees may struggle to adapt to the local culture, navigate communication barriers or even put themselves in danger due to unfamiliar customs or safety risks. Companies should consider investing in cross-cultural training programs to ensure the success and safety of their employees abroad.

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The double integral for \(3xy^2/x^2+1\) is 8㏑(2).

\(3\int\limits^1_0 \int\limits^2_2 \frac{xy^2}{x^2 + 1} \, dy dx\)  

3* 1/2 (㏑(2) - ㏑(1) ) * 1/3 (8+8)

8㏑(2)

A multiple integral in mathematics is a definite integral of a function with multiple real variables, such as f(x, y), or f(x, y) (x, y, z). In the real-number plane, integrals of functions of two variables over an area are referred to as double integrals, and integrals of functions of three variables over a region in real-number three-dimensional space are referred to as triple integrals.

The Cauchy formula for repeated integration can be used to calculate multiple integrals of a single-variable function.

The double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane that contains its domain, just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis.

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9514 1404 393

Answer:

  74.8 m²

Step-by-step explanation:

The hint is usually a good place to start.

  A = (1/2)(11 m)(15 m)sin(115°) ≈ 74.8 m²

_____

Additional comment

As is often the case with over-specified triangle problems, the answer you get depends on how you work the problem. Here, the hint suggests you use the angle. If you use the three side lengths, you find the angle is 114.7° and the area is about 74.9 m².

The value of x that makes the shape a parallelogram is 2/3

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are kite, square, rectangle, parallelogram and so on.

A parallelogram is a quadrilateral with two pairs of parallel sides. Each parallel sides are equal. Also, the diagonals of a parallelogram bisect each other.

From the diagram, the diagonals bisect each other in other to be a parallelogram, hence:

6x = 3x + 2

3x = 2

x = 2/3

The value of x is 2/3

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Step-by-step explanation:

Let A be the number of adult tickets and

let S be the number of student tickets.

From the question we know that

A + S = 480

The revenue from the adult tickets is

A x $8

and the revenue from the student tickets is

S x $5

So the total revenue is

A x $8 + S x $5 = $3369

We can change the first equation to

S = 480 - A

and then plug this into the second equation to get

A x $8 + (480 - A) x $5 = $3369

Simplify the equation to obtain

A = 323

Plug this value into the first equation to obtain

S = 157

Answer:

False

Step-by-step explanation:

5-2(3-x) =

3(3-x) = (not sure about this step)

9-x, this answer does not equal 4x + 10

The question is: When we're both stock values the same? Then all you have to do is match both equations and solve for x, like this

Factoring the trinomial you get

Which implies that

Therefore, since x corresponds to the number of months, then the values ​​of the two shares were equal at 3 and at 6 months.

The result of multiplying 40 by the distance to the finish line is equal to the total distance covered.

To calculate the product of 40 and the distance to the finish line,

1. Determine the distance to the finish line. This could be measured in any unit of length, such as meters or feet.

2. Take the value of the distance to the finish line and multiply it by 40. This can be done by simply multiplying the two numbers together.

  Result = Distance to finish line * 40

3. Perform the multiplication to find the product. The result will be the total distance covered from the starting point to the finish line.

For example, if the distance to the finish line is 100 meters:

  Result = 100 * 40

         = 4000 meters

  Therefore, the product of 40 and the distance to the finish line is 4000 meters.

Remember to adjust the units of the result based on the units used for the distance to the finish line.

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Answer: 65π

Step-by-step explanation:

you can draw the cone to make it easier for you to understand.

to find the curved surface area of a cone, you multiply the base radius of the cone by pie. Then multiply your answer by the length of the side of the cone.

to do this you need the length of the side and the radius of the cone.

to find radius, divide the diameter by 2.

\(\frac{10}{2}\) = 5

then use the right angle triangle in the cone to find the length of the side

use Pythagoras theorem which  states that a² + b²= c²

a= 5, b= 12, c= x (length of side)

∴\(x^{2} 5^{2} + 12^2 =x^{2} \\25 + 144 = x^{2} \\169= x^{2} \\x=\sqrt{169} \\x= 13\)

no that you have found the length

multiply the base radius by pie

which is:

5 ×π = 5π

then multiply this by the length of the side

5π × 13 = 65π

there you go!

hope it helps!

Answer: The answer for this question is C.

a. C(x+1) - C(x) =  0.6.

b. The cost of generating the 45th unit is 132.

a. To find C(x+1) - C(x), we substitute the expressions for C(x) and C(x+1) into the equation and simplify:

C(x+1) - C(x) = (105 + 0.6(x+1)) - (105 + 0.6x)

             = 105 + 0.6x + 0.6 - 105 - 0.6x

             = 0.6

Therefore, C(x+1) - C(x) is equal to 0.6.

b. To find the cost of producing the 45th unit, we substitute x = 45 into the expression for C(x):

C(45) = 105 + 0.6 * 45

     = 105 + 27

     = 132

Therefore, the cost of producing the 45th unit is 132.

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Answer:

Step-by-step explanation:

you hav to times it

The modeling process begins with the framing of a conceptual model that shows the relationships between the various parts of the problem being modeled. This model helps to identify the mathematical correlations between variables and provides a foundation for developing a more detailed and accurate mathematical model.

The modeling process begins with the framing of a mathematical model that shows the relationships between the various parts of the problem being modeled. This model is often based on data analysis and utilizes statistical techniques to establish correlations between the different variables in the problem. Ultimately, the goal of the modeling process is to create a predictive tool that can be used to make informed decisions about the problem at hand.

Process models involve graphically representing processes or functions that capture, manage, store, and distribute information between the system and its environment and physical objects. One type of process model is the flowchart (DFD). A data flow is a diagram that shows the movement of data between external sources and processes and the data stored in the system. While several different tools have been developed for modeling, we focus only on data streams as they are effective tools for modeling. While not all organizations use all analytical methods, including these methods such as data flow, they have a significant impact on the development process.

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Answer: 186+14-26+5=179 pounds

Step-by-step explanation:

1. Regainged 5 pounds and weighed 179 pounds = So he weiged 179-5=174 pounds."and lost 26 pounds"

2. To weigh 174 pounds,so he used to weigh 174+26=200 pounds, David gained 14 pounds over the winter, so he weighed 200-14=186 pounds.

3. Check 186+14-26+5=179 pounds

If you are doing algebra, then X+14-26+5=179

Solve for X.

HOPE THIS HELPS!! :)) TRIED MY BEST!!