HW: using trigonometric identities, show that the solution of the damped forced oscilla from can be written as: (24) Xlt)=12 Fo/m Sin (wo-w)t sin (wotw)t 7 Wo² - w² 2 2 Hint: ure the identifies for addition and Substraction of angles.

Answer:

polynomial means more than 3 equation and trinomial means 3 equation

Leila served 30 orders, Keith served 36 orders, and Michael served 21 orders.

Let's assume the number of orders served by Michael is M. According to the given information, Keith served 3 times as many orders as Michael, so Keith served 3M orders. Leila served 7 more orders than Michael, which means Leila served M + 7 orders.

The total number of orders served by all three individuals is 87. We can set up the equation: M + 3M + (M + 7) = 87.

Combining like terms, we simplify the equation to 5M + 7 = 87.

Subtracting 7 from both sides, we get 5M = 80.

Dividing both sides by 5, we find M = 16.

Therefore, Michael served 16 orders. Keith served 3 times as many, which is 3 * 16 = 48 orders. Leila served 16 + 7 = 23 orders.

In conclusion, Michael served 16 orders, Keith served 48 orders, and Leila served 23 orders.

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Answer: Infinite solutions

Step-by-step explanation:

Because if you do 2(x+1) you get the same as the other equations:

2x+2=2x+2

Answer:

1232 is the volume because 16×7×11

Answer:

The volume is 1,232 ft³

Step-by-step explanation:

Volume = lwh = Length × Width × Height =

[given that the length is 16, width is 7, and height is 11]

16 × 7 × 11

4 × 4 × 7 × 11

2 × 2 × 2 × 2 × 7 × 11

2 × 2 × 2 × 2 × 77

2 × 2 × 2 × 154

2 × 2 × 308

2 × 616

1232

________

The volume is the measurable capacity of an object or the metrical space that something holds or takes up.

Just like you multiply the net length and width to find the area of a 2 dimensional object, you can extend that 2d object so that is has height by multiplying by the given height.

In this scenario, we are considering an investment that will pay $3,000 in 34 years. We are given an appropriate discount rate of 8 percent. To determine the present value of this investment, we can use the present value formula. Additionally, we are provided with the information that the investment is being sold for $773, and we need to calculate the rate of return investors will earn on this investment.

a. Present value of the investment:

To calculate the present value of the investment, we use the present value formula:

Present Value = Future Value / (1 + Discount Rate)^n,

where Future Value is $3,000, the Discount Rate is 8 percent (0.08), and n is the number of years, which is 34 in this case.

Present Value = $3,000 / (1 + 0.08)^34 = $219.13

Therefore, the present value of the investment, considering an 8 percent discount rate, is $219.13.

b. Rate of return on the investment:

The rate of return on an investment is calculated using the formula:

Rate of Return = (Future Value - Purchase Price) / Purchase Price * 100,

where Future Value is $3,000 and the Purchase Price is $773.

Rate of Return = ($3,000 - $773) / $773 * 100 ≈ 288.46%

Therefore, the rate of return investors can earn on this investment, if they buy it for $773, is approximately 288.46%.

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The area inside the loop of the limacon given by the polar equation r = 7 - 14sin(θ) is 294π square units.

To find the area inside the loop of the limacon given by the polar equation r = 7 - 14sin(θ), we need to evaluate the integral for half of the area and then double the result.

The curve of the limacon has a loop when 0 ≤ θ ≤ π, so we integrate from 0 to π. The area can be calculated as follows:

A = 2 ∫₀^π 1/2 r² dθ

Using the equation for r given, we can substitute and simplify:

A = 2 ∫₀^π 1/2 (7 - 14sin(θ))² dθ

A = 2 ∫₀^π 1/2 (49 - 196sin(θ) + 196sin²(θ)) dθ

A = ∫₀^π (98 - 392sin(θ) + 392sin²(θ)) dθ

Using the trigonometric identity 1 - cos(2θ) = 2sin²(θ), we can simplify further:

A = ∫₀^π (98 - 392sin(θ) + 196 - 196cos(2θ)) dθ

A = ∫₀^π (294 - 392sin(θ) - 196cos(2θ)) dθ

Integrating with respect to θ:

A = [294θ + 392cos(θ)sin(θ) + 98sin(θ)]₀^π

Evaluating at the limits of integration, we get:

A = [294π + 0 + 0] - [0 + 392cos(0)sin(0) + 98sin(0)]

A = 294π - 0 - 0 = 294π

Therefore, the area inside the loop of the limacon r = 7 - 14sin(θ) is 294π square units.

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Answer:

circle and two lines that don't touch and are the same length are parrarell

Answer:

1. No x-intercept/Zero

2. x = 3/4

Step-by-step explanation:

The forward Fourier Transform formula for a signal is X(jω) = F{x(t)}. The inverse Fourier Transform formula is x(t) = F^(-1){X(jω)}. The two formulas are related by the Fourier Transform property called duality or symmetry.

1. The forward Fourier Transform formula is given by:

  X(jω) = ∫[x(t) * e^(-jωt)] dt

  This formula calculates the complex spectrum X(jω) of a signal x(t) by integrating the product of the signal and a complex exponential function.

2. The inverse Fourier Transform formula is given by:

  x(t) = (1/2π) ∫[X(jω) * e^(jωt)] dω

  This formula reconstructs the original signal x(t) from its complex spectrum X(jω) by integrating the product of the spectrum and a complex exponential function.

  The similarity between these two formulas is known as the Fourier Transform property of duality or symmetry. It states that the Fourier Transform pair (X(jω), x(t)) has a symmetric relationship in the frequency and time domains. The forward transform calculates the spectrum, while the inverse transform recovers the original signal. The duality property indicates that if the spectrum is known, the inverse transform can reconstruct the original signal, and vice versa.

3. To determine the Fourier Transform of the given signal x(t) = [-1, 1, 0, -1], we apply the defining integral:

  X(jω) = ∫[-1 * e^(-jωt1) + 1 * e^(-jωt2) + 0 * e^(-jωt3) - 1 * e^(-jωt4)] dt

  Here, t1, t2, t3, t4 represent the respective time instants for each element of the signal.

  Substituting the time values and performing the integration, we can obtain the Fourier Transform of x(t).

Note: Please note that without specific values for t1, t2, t3, and t4, we cannot provide the numerical result of the Fourier Transform for the given signal. The final answer will depend on these time instants.

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To find the slope intercept form, solve the equation for y.

Solve the equation for x:

The product ((4√3) - 4i)((√2) + √2i) in polar form is 8√3 * cis(-π/4).

To find the product of ((4√3) - 4i)((√2) + √2i) in polar form, we can first multiply the two complex numbers using the distributive property: ((4√3) - 4i)((√2) + √2i) = (4√3)(√2) + (4√3)(√2i) - (4i)(√2) - (4i)(√2i)

Simplifying each term, we get:

(4√3)(√2) = 8√6

(4√3)(√2i) = 8√6i

(4i)(√2) = 4√2i

(4i)(√2i) = -4√2

Combining the terms, we have: 8√6 + 8√6i - 4√2i - 4√2

To express the result in polar form, we convert the complex number to its magnitude and argument form. The magnitude (r) can be calculated as the square root of the sum of the squares of the real and imaginary parts: r = √((8√6)^2 + (8√6)^2) = √(384 + 384) = √768 = 8√3

The argument (θ) can be determined as the arctan of the imaginary part divided by the real part: θ = arctan((-4√2 - 4√6) / (8√6 + 8√6)) = arctan(-√2/√3) = -π/4

Therefore, the product ((4√3) - 4i)((√2) + √2i) in polar form is 8√3 * cis(-π/4). The argument -π/4 corresponds to the fourth quadrant of the complex plane, as it is negative and lies between -π/2 and -π.

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Answer:

The bottom left one

Step-by-step explanation:

They are the only graph that has one output for each x value

The height of the curve for a given value of x is closely related to the probability of an observation falling in an interval around x.

The height of the curve, also known as the probability density function (PDF), represents the relative likelihood of different values occurring in a distribution. In probability theory, the area under the curve within a specific interval represents the probability of an observation falling within that interval.

Therefore, the height of the curve at a particular value of x reflects the probability of an observation being close to that value.

The concept of the PDF and its relationship to probability is fundamental in statistical analysis. By examining the height of the curve at different points, we can assess the likelihood of observing specific values or ranges of values.

This information is crucial for making inferences, estimating probabilities, and conducting hypothesis testing in various fields such as finance, biology, and social sciences.

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If the balance will be $1370.55 after 6 years, then The balance will be $1711.03 after approximately 14.3 years.

The formula for calculating the balance in a continuously compounded account is:

\(A = Pe^{rt}\)

Where:

A = final balance

P = principal (initial deposit)

e = Euler's number (approximately 2.71828)

r = annual interest rate

t = time in years

We know that the initial deposit is $1000 and the balance after 6 years is $1370.55, so we can use these values to solve for the annual interest rate:

\(1370.55 = 1000*e^{6r}\)

⇒ \(ln(\frac{1370.55}{1000}) = 6r\)

⇒ \(r = \frac{ln(\frac{1370.55}{1000})}{6}\)

⇒ \(r = 0.0345\)

Now we can use the same formula to find out when the balance will be $1711.03:

\(1711.03 = 1000*e^{(0.0345*t)}\)

⇒ \(ln(\frac{1711.03}{1000}) = 0.0345*t\)

⇒ \(t = \frac{ln(\frac{1711.03}{1000})}{0.0345}\)

⇒ t = 14.3 years.

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Answer:

A

Step-by-step explanation:

If I'm completely honest I'm not really sure of this cause I hv another way of doing this...

   ,

In order to determine the critical values for an independent-samples T-test, the following information needs to be known:

The critical values for an independent-samples t test are used to determine if the differences between two samples are statistically significant. In order to calculate the critical values, the size of the sample (n), the significance level (alpha), the degrees of freedom (df), and the type of t-test (one-tailed or two-tailed) must be known. The degrees of freedom are equal to the number of observations in the sample minus

The size of the sample is the total number of observations in the two samples. The significance level is the probability of making a type-I error (rejecting the null hypothesis when it is true). Finally, the type of t-test is used to determine if the test is one-tailed (testing for a difference in one direction) or two-tailed (testing for a difference in both directions). Once all of this information is known, the critical values can be calculated to determine if the differences between the two samples are statistically significant.

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Normal probability distribution is applied to a continuous random variable. The correct option is D.

The normal probability distribution, also known as the Gaussian distribution, is a probability distribution that is commonly used in statistics and probability theory. It is a continuous probability distribution that is often used to model the behavior of a wide range of variables, such as physical measurements like height, weight, and temperature.

The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). It is a bell-shaped curve that is symmetrical around the mean, with the highest point of the curve being located at the mean. The standard deviation determines the width of the curve, and 68% of the data falls within one standard deviation of the mean, while 95% falls within two standard deviations.

The normal distribution is widely used in statistical inference and hypothesis testing, as many test statistics are approximately normally distributed under certain conditions. It is also used in modeling various phenomena, including financial markets, population growth, and natural phenomena like earthquakes and weather patterns.

Overall, the normal probability distribution is a powerful tool for modeling and analyzing a wide range of continuous random variables in a variety of fields.

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Answer:

5(−2)−3 y = 5 (- 2) - 3

Step-by-step explanation:

y = 5x − 3 y = 5 x - 3 Substitute −2 - 2 for x x and find the result for y y. y = 5(−2)−3 y = 5 (- 2) - 3

The ordered pairs of the inequality expression is (0, 4)

From the question, we have the following parameters that can be used in our computation:

The inequality expression  y>1/2x+3

To determine the ordered pairs of the inequality expression, we set x - 0 and then calculate the value of y

Using the above as a guide, we have the following:

y > 1/2 * 0 + 3

Evauate

y > 3

This means that the value of y is greater than 3 say y = 4

So, we have (0, 4)

Hence, the ordered pairs of the inequality expression is (0, 4)

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The cost of 5 pairs of shoes is 108.78 dollars.

The cost of 3 pairs of shoes is $65.27. At this price, the cost of 5 pairs of shoes can be calculated as follows:

Let's find the cost of each pair of shoes before we can get the cost of 5 pairs of shoes.

Therefore,

3 pairs of shoe = 65.27 dollars

1 pair of shoes = ?

cross multiply

cost of each pair = 65.27 / 3

cost of each pair = 21.76 dollars

Therefore, the cost of 5 pairs of shoes can be found as follows:

cost of 5 pairs of shoes = 21.76 × 5

cost of 5 pairs of shoes = 108.783333333

Therefore,

cost of 5 pairs of shoes = 108.78 dollars

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Answer: x - 15

Step-by-step explanation:

The answer is x - 15

Answer:

x-15

Step-by-step explanation:

Answer:

i think the answer is C. 1.5w^2 + 7.5w + 9

Answer:

In the standard form of a quadratic equation, y = ax^2 + bx + c, changing the value of the h variable inside the parentheses of the x term, y = a(x - h)^2 + k, will shift the vertex of the parabola horizontally by h units.

If h is positive, the vertex will shift to the right, and if h is negative, the vertex will shift to the left. The amount of the shift is determined by the absolute value of h. For example, if h = 2, the vertex will shift to the right by 2 units.

Note that changing the value of h does not affect the shape of the parabola or its orientation. It only changes the position of the vertex.

Therefore , the solution to the given problem of trigonometry comes out to be  angle of elevation : 62.3°.

The area of mathematics called trigonometry examines the correlation between triangle length l. The field first came into existence in the Classical world, presumably in the third-century BC, as a result of the integration of geometry with astronomy studies. Precise approaches mathematics deals with certain trigonometric equations and possible uses of them in calculations. There are six common trigonometric functions in trigonometry. They are known by their respective names and abbreviations sine, trigonometry, tangent, secant, etc. cosecant (csc). The studies of triangle aspects, particularly those right triangles, is known as trigonometry. However, studying geometry entails learning about all polygons' characteristics.

Here,

given  :

An aircraft is being followed by two radar stations, which are 4.3 miles apart.

Station A is 9.6 miles away from the plane in a straight line.

Thus,

To find the angle of elevation  from station A to plane :

Using Trigonometric ratios:

=> Sin A  = 8.5 / 9.6

=> Sin A = 85/96

=> A =  \(Sin^{-1}\)(85/96 )

=> A = 62.302840124651483 °

=> A = 62.3°

Therefore , the solution to the given problem of trigonometry comes out to be  angle of elevation : 62.3°.

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a. The probability that you win on none of your 5 plays is approximately 0.6634. b. The probability that you win 3 or more of your 5 plays of this game is approximately 0.004497.

To solve these problems, we'll use the binomial probability formula.

a. The probability of winning in any one play is 0.08, so the probability of losing in any one play is 1 - 0.08 = 0.92.

The probability of winning on none of your 5 plays can be calculated as the probability of losing on each play, which is 0.92, raised to the power of the number of plays.

P(losing all 5 plays) = (0.92)^5 = 0.6634 (rounded to four decimal places)

Therefore, the probability that you win on none of your 5 plays is approximately 0.6634.

b. To find the probability of winning 3 or more of your 5 plays, we need to calculate the probability of winning 3, 4, or 5 plays and sum them up.

P(winning 3 or more plays) = P(winning 3 plays) + P(winning 4 plays) + P(winning all 5 plays)

P(winning 3 plays) = C(5, 3) *\((0.08)^3 * (0.92)^2\)

                  = 10 * 0.000512 * 0.8464

                  ≈ 0.00434 (rounded to five decimal places)

P(winning 4 plays) = \(C(5, 4) * (0.08)^4 * (0.92)^1\)

                  = 5 * 0.000032768 * 0.92

                  ≈ 0.000151 (rounded to six decimal places)

P(winning all 5 plays) = \((0.08)^5\)

                     ≈ 0.000006 (rounded to six decimal places)

Now we can sum up these probabilities:

P(winning 3 or more plays) ≈ 0.00434 + 0.000151 + 0.000006

                          ≈ 0.004497 (rounded to six decimal places)

Therefore, the probability that you win 3 or more of your 5 plays of this game is approximately 0.004497.

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Answer:

baaababababbabababab

Answer:

b.

Step-by-step explanation:

z = (74 - 58) / 7

Simplifying this expression, we get:

z = 2.286

Rounding this z-score to two decimal places, we get:

z = 2.29

Option (b) is correct.

The z-score for the value 74 when the mean is 58 and the standard deviation is 7 is z = 2.29.How to find the z-score?

The formula for calculating a z-score for a value is:z = (x - μ) / σ wherez is the z-score x is the value μ is the mean of the population σ is the standard deviation of the population Given,

the value x = 74, μ = 58, and σ = 7 To find z,z = (74 - 58) / 7z = 2.29 Therefore, the z-score for the value 74 when the mean is 58 and the standard deviation is 7 is z = 2.29. Thus, option (b) is correct.

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Answer:

m∠DAB+m∠ADC=180

115+ 29 + m∠ADB=180

m∠ADB=180 - 115 -29

= 36°