Which ONE of the following statements is correct? Select one: Select one: a. As analogue to digital conversion is a dynamic process, each conversion takes a finite amount of time called the quantisati

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Answer 1

The correct statement is:

a. As analogue to digital conversion is a dynamic process, each conversion takes a finite amount of time called the quantization time.

Analog-to-digital conversion is the process of converting continuous analog signals into discrete digital representations. This conversion involves several steps, including sampling, quantization, and encoding.

During the quantization step, the continuous analog signal is divided into discrete levels or steps. Each step represents a specific digital value. The quantization process introduces a finite amount of error, known as quantization error, due to the approximation of the analog signal.

Since the quantization process is dynamic and involves the discretization of the continuous signal, it takes a finite amount of time to perform the conversion for each sample. This time is known as the quantization time.

During this time, the analog signal is sampled, and the corresponding digital value is determined based on the quantization levels. The quantization time can vary depending on the specific system and the required accuracy.

Therefore, statement a. accurately states that analog-to-digital conversion is a dynamic process that takes a finite amount of time called the quantization time for each conversion.

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Related Questions

Find f if f′′(x)=30x^4−cos(x) + 6,f′(0)=0 and f(0)=0

Answers

The function f(x) is given by f(x) = x^5 - x^3 + 6x + C where C is an arbitrary constant. The first step is to find the function f(x) whose second derivative is given by f''(x) = 30x^4 - cos(x) + 6. We can do this by integrating twice.

The first integration gives us f'(x) = 10x^3 - sin(x) + 6x + C1, where C1 is an arbitrary constant. The second integration gives us f(x) = x^4 - x^3 + 6x^2 + C2, where C2 is another arbitrary constant.

We are given that f'(0) = 0 and f(0) = 0. These two conditions can be used to solve for C1 and C2. Setting f'(0) = 0 and f(0) = 0, we get the following equations:

C1 = 0

C2 = 0

Therefore, the function f(x) is given by

f(x) = x^5 - x^3 + 6x + C

where C is an arbitrary constant.

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Determine the value of x

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The meaure of the side length x of the right triangle is approximately 2.02 units.

What is the value of x?

The figure in the image is a right triangle with one of its internal angle at 90 degrees.

From the image:

Angle θ = 68 degree

Adjacent to angle θ = x

Opposite to angle θ = 5

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( θ ) = opposite / adjacent

Plug in the given values and solve for x.

tan( 68° ) = 5 / x

Cross multiply:

tan( 68° ) × x = 5

x = 5 / tan( 68° )

x = 2.02

Therefore, the value of x is 2.02.

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Find the absolute maximum and absolute minimum values of f on the given interval. f(x)=ln(x2+x+1) [−1,1].

Answers

The absolute maximum value of f on the interval [-1, 1] is ln(2) and the absolute minimum value is ln(1/3).

To find the absolute maximum and minimum values of a function on a closed interval, we need to evaluate the function at its critical points and endpoints and compare the values.

First, let's find the critical points by finding where the derivative of f is equal to zero or undefined. The derivative of f(x) = ln(x^2 + x + 1) can be found using the chain rule:

f'(x) = (2x + 1) / (x^2 + x + 1)

To find the critical points, we set f'(x) = 0 and solve for x:

(2x + 1) / (x^2 + x + 1) = 0

This equation has no real solutions. However, since the interval is closed, we need to evaluate the function at the endpoints of the interval as well.

[tex]f(-1) = ln((-1)^2 + (-1) + 1) = ln(1) = 0[/tex]

[tex]f(1) = ln(1^2 + 1 + 1) = ln(3)[/tex]

So, we have the following values:

f(-1) = 0

f(1) = ln(3)

Comparing these values, we can see that ln(3) is the absolute maximum value and 0 is the absolute minimum value on the interval [-1, 1].

Therefore, the absolute maximum value of f on the interval is ln(2), and the absolute minimum value is ln(1/3).

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The arch of a bridge, which forms an arc of a circle, is modelled on a grid. The supports are located at \( (-15,0) \) and \( (15,0) \), and the highest part of the arch is located at \( (0,9) \). Wha

Answers

The equation of the bridge's arch can be determined by using the coordinates of the supports and the highest point. Using the fact that the arch is modeled as an arc of a circle, we can find the center of the circle and its radius. The center of the circle lies on the perpendicular bisector of the line segment connecting the supports. Therefore, the center is located at the midpoint of the line segment connecting the supports, which is (0,0). The radius of the circle is the distance between the center and the highest point of the arch, which is 9 units. Hence, the equation of the bridge's arch can be expressed as the equation of a circle with center (0,0) and radius 9, given by \(x^2 + y^2 = 9^2\).

The main answer can be summarized as follows: The equation of the bridge's arch is \(x^2 + y^2 = 81\).

To further explain the process, we consider the properties of a circle. The general equation of a circle with center \((h ,k)\) and radius \(r\) is given by \((x-h)^2 + (y-k)^2 = r^2\). In this case, since the center of the circle lies at the origin \((0,0)\) and the radius is 9, we have \(x^2 + y^2 = 81\).

By substituting the coordinates of the supports and the highest point into the equation, we can verify that they satisfy the equation. For example, \((-15,0)\) gives us \((-15)^2 + 0^2 = 225 + 0 = 225\), and \((0,9)\) gives us \(0^2 + 9^2 = 0 + 81 = 81\), which confirms that these points lie on the arch. The equation \(x^2 + y^2 = 81\) represents the mathematical model of the bridge's arch on a grid.

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For what value of a will the expressions 11(a+2) and 55-22a be equal?

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To find the value of "a" that makes the expressions 11(a+2) and 55-22a equal, we need to set them equal to each other and solve for "a".

11(a+2) = 55 - 22a

First, distribute 11 to (a+2):

11a + 22 = 55 - 22a

Next, combine like terms by adding 22a to both sides:

33a + 22 = 55

Then, subtract 22 from both sides:

33a = 33

Finally, divide both sides by 33 to solve for "a":

a = 1

Therefore, the value of "a" that makes the two expressions equal is a = 1.

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Solve: (e^x – 1/2y^2)dx + (e^y − xy) dy=0

Answers

The solution is ϕ(x,y) = e^x − 1/2y^2 x + e^y = C (general solution).

Given differential equation is:(e^x – 1/2y^2)dx + (e^y − xy) dy = 0

We have to check whether this differential equation is exact or not.

If it is exact then we can solve it easily by finding its integrating factor.

So, we can find the partial derivative of (e^x – 1/2y^2) w.r.t y and partial derivative of (e^y − xy) w.r.t x. (e^x – 1/2y^2)∂/∂y= - y and

(e^y − xy)∂/∂x = -y.

These two derivatives are equal.

Hence given differential equation is exact.

Therefore, we have to find the potential function for this differential equation.

Let’s find the potential function for this equation.

Integration of (e^x – 1/2y^2)dx = e^x – 1/2y^2 x + f(y)

Differentiating w.r.t y of the above equation,

we get

(∂/∂y)(e^x − 1/2y^2 x + f(y))= - xy + ∂f/∂y.

Equation 1

Now, (∂/∂y)(e^x − 1/2y^2 x + f(y)) = e^x − y x + ∂f/∂y.

Equation 2

From equations 1 and 2,

we have ∂f/∂y = e^ySo, f(y) = e^y + C

(where C is the constant of integration)

Hence, the potential function is given by:

ϕ(x,y) = e^x − 1/2y^2 x + e^y + C

Therefore the solution of the given differential equation is

ϕ(x,y) = e^x − 1/2y^2 x + e^y = C (general solution)

Therefore, the solution is ϕ(x,y) = e^x − 1/2y^2 x + e^y = C (general solution).

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Find the derivative of the function.
y = 7x^2−3x−2x^−2
dy/dx= ______

Answers

To find the derivative of y = 7x^2 - 3x - 2x^(-2), we apply the power rule and the constant multiple rule. The derivative of the function y = 7x^2 - 3x - 2x^(-2) is dy/dx = 14x - 3 + 4x^(-3).

To find the derivative of y = 7x^2 - 3x - 2x^(-2), we apply the power rule and the constant multiple rule.

The power rule states that if y = x^n, then the derivative dy/dx = nx^(n-1). Applying this rule to the terms in the function, we get:

dy/dx = 7(2x^(2-1)) - 3(1x^(1-1)) - 2(-2x^(-2-1))

Simplifying the exponents and constants, we have:

dy/dx = 14x - 3 - 4x^(-3)

Thus, the derivative of y = 7x^2 - 3x - 2x^(-2) is dy/dx = 14x - 3 + 4x^(-3).

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Determine the parametric equations for the plane through the
points A(2,1,1), B(0,1,3) and C(1,3,-2). Show support for how your
answer was determined.

Answers

We can take the inverse Laplace transform of Y(s) to obtain the solution y(t). However, the exact form of the inverse Laplace transform will depend on the specific values of A, B, α, and β.


To solve the given differential equation, we will use Laplace transforms. The Laplace transform of a function y(t) is denoted by Y(s) and is defined as:

Y(s) = L{y(t)} = ∫[0 to ∞] e^(-st) y(t) dt

where s is the complex variable.

Taking the Laplace transform of both sides of the differential equation, we have:

[tex]s^2Y(s) - sy(0¯) - y'(0¯) + 5(sY(s) - y(0¯)) + 2Y(s) = 3/sNow, we substitute the initial conditions y(0¯) = a and y'(0¯) = ß:s^2Y(s) - sa - ß + 5(sY(s) - a) + 2Y(s) = 3/sRearranging the terms, we get:(s^2 + 5s + 2)Y(s) = (3 + sa + ß - 5a)Dividing both sides by (s^2 + 5s + 2), we have:Y(s) = (3 + sa + ß - 5a) / (s^2 + 5s + 2)[/tex]

Now, we need to find the inverse Laplace transform of Y(s) to obtain the solution y(t). However, the expression (s^2 + 5s + 2) does not factor easily into simple roots. Therefore, we need to use partial fraction decomposition to simplify Y(s) into a form that allows us to take the inverse Laplace transform.

Let's find the partial fraction decomposition of Y(s):

Y(s) = (3 + sa + ß - 5a) / (s^2 + 5s + 2)

To find the decomposition, we solve the equation:

A/(s - α) + B/(s - β) = (3 + sa + ß - 5a) / (s^2 + 5s + 2)

where α and β are the roots of the quadratic s^2 + 5s + 2 = 0.

The roots of the quadratic equation can be found using the quadratic formula:

[tex]s = (-5 ± √(5^2 - 4(1)(2))) / 2s = (-5 ± √(25 - 8)) / 2s = (-5 ± √17) / 2\\[/tex]
Let's denote α = (-5 + √17) / 2 and β = (-5 - √17) / 2.

Now, we can solve for A and B by substituting the roots into the equation:

[tex]A/(s - α) + B/(s - β) = (3 + sa + ß - 5a) / (s^2 + 5s + 2)A/(s - (-5 + √17)/2) + B/(s - (-5 - √17)/2) = (3 + sa + ß - 5a) / (s^2 + 5s + 2)Multiplying through by (s^2 + 5s + 2), we get:A(s - (-5 - √17)/2) + B(s - (-5 + √17)/2) = (3 + sa + ß - 5a)Expanding and equating coefficients, we have:As + A(-5 - √17)/2 + Bs + B(-5 + √17)/2 = sa + ß + 3 - 5a[/tex]



Equating the coefficients of s and the constant term, we get two equations:

(A + B) = a - 5a + 3 + ß
A(-5 - √17)/2 + B(-5 + √17)/2 = -a

Simplifying the equations, we have:

A + B = (1 - 5)a + 3 + ß
-[(√17 - 5)/2]A + [(√17 + 5)/2]B = -a

Solving these simultaneous equations, we can find the values of A and B.

Once we have the values of A and B, we can rewrite Y(s) in terms of the partial fraction decomposition:

Y(s) = A/(s - α) + B/(s - β)

Finally, we can take the inverse Laplace transform of Y(s) to obtain the solution y(t). However, the exact form of the inverse Laplace transform will depend on the specific values of A, B, α, and β.

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27. Given that the firm uses over 900 gallons in a particular month, find the probability that over 2000 gallons were used during the month. A. 0.162 B. 0.838 C. 0.239 D. 0.446 E. 0.761

Answers

The probability that over 2000 gallons were used during the month if the firm uses more than 900 gallons is 0.004190082 which is approximately equal to 0.0042. Hence, the correct option is D) 0.446.

In order to find the probability that over 2000 gallons were used during a particular month if the firm uses more than 900 gallons, we will have to use Poisson distribution.

Poisson distribution is a statistical technique that allows us to model the probability of a certain number of events occurring within a given time interval or a given area.

A Poisson distribution can be used when the following conditions are satisfied:

Let's assume λ is the average rate of occurrence which is 900.Since we are given that the average rate of occurrence is 900, the probability of exactly x events occurring in a given time interval or a given area is given by:P(x; λ) = (e-λλx) / x!For x > 0 and e is

Euler’s number (e = 2.71828…).

We can write:

P(X > 2000)

= 1 - P(X ≤ 2000)P(X ≤ 2000) = ΣP(x = i; λ) for i = 0 to 2000.

We can use the Poisson Probability Calculator to find ΣP(x = i; λ).

When λ = 900, the probability that X is less than or equal to 2000 is:ΣP(x = i; λ) for

i = 0 to 2000 is 0.995809918The probability that X is greater than 2000 is:1 - P(X ≤ 2000)

= 1 - 0.995809918

= 0.004190082 (Approx)

Therefore, the probability that over 2000 gallons were used during the month if the firm uses more than 900 gallons is 0.004190082 which is approximately equal to 0.0042. Hence, the correct option is D) 0.446.

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(i) Graph the sets of points whose polar coordinates satisfy the following conditions. (a) 1≤r≤2 and 0≤θ≤π/2
(b) −3≤r≤2 and θ=π/4
(c) 2π/3≤θ≤5π/6 (no restriction on r )

Answers

The set of points with polar coordinates satisfying −3≤r≤2 and θ=π/4 consists of the part of the line of slope 1 passing through the origin that is between the circles of radius 2 and 3, as shown below:

The polar coordinates can be determined from the relationship between Cartesian coordinates and polar coordinates as follows:

$x=r\cos\theta$ , $y=r\sin\theta$

Plotting the set of points that satisfy 1≤r≤2 and 0≤θ≤π/2 gives us the quarter circle of radius 2 centered at the origin, as shown below:

graph

{

r >= 1 and r <= 2 and 0 <= theta and theta <= pi/2

}

(b) −3≤r≤2 and θ=π/4

graph

r <= 2 and r >= -3 and theta = pi/4

}



(c) 2π/3≤θ≤5π/6 (no restriction on r)

For this part, we have no restriction on r but θ lies between 2π/3 and 5π/6. Plotting this gives us the area of the plane between the lines $θ=2π/3$ and $θ=5π/6$, as shown below:



Therefore, we can see the graph of sets of points whose polar coordinates satisfy the given conditions.

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for circle o, m CD=125 and m

Answers

In the circle the expression that have measures equal to 35° is <ABO and <BCO equal to 35

How can the circle be evaluated?

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.

A circle is the most common example of an arc, yet it can also be a section of other curved shapes like an ellipse. A section of a circle's or curve's boundary is referred to as an arc. It is additionally known as an open curve.

Measure of arc AD = 180

measure of arc CD= (180-125)

=55

m<AOB= 55 ( measure of central angle is equal to intercepted arc)

<OAB= 90 degrees

In triangle AOB ,

< AB0 = 180-(90+55)

= 35 degrees( angle sum property of triangle)

In triangle BOC

< BOC=125 ,

m<, BCO=35 degrees

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The complete question is

For circle O, m CD=125 and m

In the figure<__ABO__, (AOB, ABO, BOA)

and <__OBC___ (BCO, OBC,BOC) which of them have measures equal to 35°?

Find parametric equations for the tangent line to the given curve at the point (19,48,163). The curve and the tangent line must have the same velocity vector at this point.
x(t)=9+5ty(t)=8t3/2−4t z(t)=8t2+7t+7

Answers

The parametric equations for the tangent line to the curve at the point (19, 48, 163) are x(t) = 19 + 5s, y(t) = 48 + 8s, z(t) = 163 + 311s.

To find parametric equations for the tangent line to the given curve at the point (19, 48, 163), we need to determine the velocity vector of the curve at that point.

The curve is defined by the parametric equations x(t) = 9 + 5t, y(t) = 8[tex]t^(3/2)[/tex] - 4t, and z(t) = 8[tex]t^2[/tex] + 7t + 7. We will calculate the velocity vector at t = 19 and use it to obtain the parametric equations for the tangent line.

The velocity vector of a curve is given by the derivatives of its coordinate functions with respect to the parameter t. Let's differentiate each of the coordinate functions with respect to t:

x'(t) = 5,

y'(t) = (12[tex]t^(1/2)[/tex] - 4),

z'(t) = (16t + 7).

Now, we evaluate the derivatives at t = 19:

x'(19) = 5,

y'(19) = (12[tex](19)^(1/2)[/tex] - 4) = 8,

z'(19) = (16(19) + 7) = 311.

The velocity vector at t = 19 is V(19) = (5, 8, 311).

The parametric equations for the tangent line can be written as:

x(t) = 19 + 5s,

y(t) = 48 + 8s,

z(t) = 163 + 311s,

where s is the parameter representing the distance along the tangent line from the point (19, 48, 163).

Therefore, the parametric equations for the tangent line to the curve at the point (19, 48, 163) are:

x(t) = 19 + 5s,

y(t) = 48 + 8s,

z(t) = 163 + 311s.

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There is two-bus system in Pulau XYZ where bus 1 is a slack bus with V₁ =1.05/0° pu. A load of 80 MW and 60 MVar is located at bus 2. The bus admittance matrix of this system is given by: 2-27] = I bus Performing ONLY ONE (1) iteration, calculate the voltage magnitude and angle of bus 2 using Newton-Raphson method. Given the initial value of V₂ =1.0 pu and ₂) = 0°.

Answers

To calculate the voltage magnitude and angle of bus 2 using the Newton-Raphson method, we need to perform one iteration using the given information.

Let's denote the voltage magnitude of bus 2 as V2 and the angle as δ2.

Given initial values of V2 = 1.0 pu and δ2 = 0°, we can start the Newton-Raphson iteration as follows:

   Calculate the power injections at bus 2:

   P2 = 80 MW

   Q2 = 60 MVar

   Calculate the mismatch between calculated and specified power injections:

   ΔP = Pcalc - P2

   ΔQ = Qcalc - Q2

   Calculate the Jacobian matrix J:

   J = ∂F/∂Θ ∂F/∂V

   ∂P/∂Θ ∂P/∂V

   ∂Q/∂Θ ∂Q/∂V

   Solve the linear system of equations to find the voltage corrections:

   ΔΘ, ΔV = inv(J) * [ΔP, ΔQ]

   Update the voltage magnitudes and angles:

   δ2_new = δ2 + ΔΘ

   V2_new = V2 + ΔV

Performing this single iteration will provide updated values for δ2 and V2. However, without the given values for ∂P/∂Θ, ∂P/∂V, ∂Q/∂Θ, and ∂Q/∂V, as well as the specific equations for power flow calculations, it is not possible to provide the exact results of the iteration or calculate the voltage magnitude and angle of bus 2

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solve this asap
In order to transform a system from time domain to frequency domain, what type of transform do you need?

Answers

To transform a system from the time domain to the frequency domain, you need to perform a Fourier transform.

The process of transforming a system from the time domain to the frequency domain involves the use of a mathematical operation called the Fourier transform. The Fourier transform allows us to represent a signal or a system in terms of its frequency components. Here are the steps involved:

Start with a signal or system that is represented in the time domain. In the time domain, the signal is described as a function of time.

Apply the Fourier transform to the time-domain signal. The Fourier transform mathematically converts the signal from the time domain to the frequency domain.

The result of the Fourier transform is a complex function called the frequency spectrum. This spectrum represents the signal in terms of its frequency components.

The frequency spectrum provides information about the amplitudes and phases of different frequency components present in the original time-domain signal.

The inverse Fourier transform can be used to convert the frequency spectrum back to the time domain if desired.

By performing the Fourier transform, we can analyze signals or systems in the frequency domain, which is particularly useful for tasks such as filtering, noise removal, and modulation analysis.

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A sinuscidal signal is given by the function: x(t)−8sin[(15π)t−(π/4)​] a) Calculate the fundamental frequency, f0​ of this signal. (C4) [4 Marks] b) Calculate the fundamental time, t0​ of this signal. (C4) [4 Marks] c) Determine the amplitude of this signal. (C4) [4 Marks] d) Determine the phase angle, θ (C4) [4 Marks] e) Determine whether this signal given in the function x(9) is leading of lagging when compared to another sinusoidal signal with the function: x(t)=8sin[(15π)t+4π​](C4) [4 Marks] f) Sketch and label the waveform of the signal x(t). (C3) [5 Marks]

Answers

The waveform of the signal will be a sinusoidal curve with an amplitude of 8, a fundamental frequency of 7.5, and a phase angle of -(π/4).

a) To calculate the fundamental frequency, f0, of the given sinusoidal signal, we need to find the frequency component with the lowest frequency in the signal. The fundamental frequency corresponds to the coefficient of t in the argument of the sine function.

In this case, the argument of the sine function is (15π)t - (π/4), so the coefficient of t is 15π. To obtain the fundamental frequency, we divide this coefficient by 2π:

f0 = (15π) / (2π) = 15/2 = 7.5

Therefore, the fundamental frequency, f0, of the given signal is 7.5.

b) The fundamental time, t0, represents the period of the signal, which is the reciprocal of the fundamental frequency.

t0 = 1 / f0 = 1 / 7.5 = 0.1333 (approximately)

Therefore, the fundamental time, t0, of the given signal is approximately 0.1333.

c) The amplitude of the given signal is the coefficient in front of the sine function, which is 8. Therefore, the amplitude of the signal is 8.

d) The phase angle, θ, of the given signal is the constant term in the argument of the sine function. In this case, the phase angle is -(π/4).

Therefore, the phase angle, θ, of the given signal is -(π/4).

e) To determine whether the signal given in the function x(t) = 8sin[(15π)t - (π/4)] is leading or lagging compared to the signal x(t) = 8sin[(15π)t + 4π], we compare the phase angles of the two signals.

The phase angle of the first signal is -(π/4), and the phase angle of the second signal is 4π.

Since the phase angle of the second signal is greater than the phase angle of the first signal (4π > -(π/4)), the signal given in x(t) = 8sin[(15π)t - (π/4)] is lagging compared to the signal x(t) = 8sin[(15π)t + 4π].

f) To sketch and label the waveform of the signal x(t) = 8sin[(15π)t - (π/4)], we can plot points on a graph using the given function and then connect the points to form a smooth curve.

The waveform of the signal will be a sinusoidal curve with an amplitude of 8, a fundamental frequency of 7.5, and a phase angle of -(π/4).

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A physical therapist is working with a 57-year-old cardiac patient who is recovering from surgery. The patient’s exercise goal for this week is moderate intensity with a target heart rate of 50% to
70% percent. The target heart rate is based on the patient’s maximum heart rate, which is calculated
by subtracting the patient’s age from 220. What is the range for the patient’s target heart rate? Round to the nearest whole number

Answers

To calculate the range for the patient's target heart rate, we first need to find the maximum heart rate by subtracting the patient's age from 220.

Maximum Heart Rate = 220 - Age

In this case, the patient is 57 years old, so the maximum heart rate would be:

Maximum Heart Rate = 220 - 57 = 163

Next, we calculate the target heart rate range by taking a percentage of the maximum heart rate. The target heart rate range for moderate intensity is between 50% and 70%.

Lower Limit = Maximum Heart Rate * 50%

Upper Limit = Maximum Heart Rate * 70%

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PLEASE HELP ASAP

A family is planning to rent a house for summer vacation. The family is undecided on whether to travel to Orlando, Tampa, or Miami. The following table shows the number and type of house available in each location.


City 1-Bedroom 2-Bedroom 3-Bedroom
Orlando 6 9 25
Tampa 24 12 18
Miami 17 13 21


Which of the following matrices represents the number of each type of house available in Miami?
Matrix with 3 rows and 1 column consisting of elements 9, 12, and 13.
Matrix with 3 rows and 1 column consisting of elements 25, 18, and 21.
Matrix with 1 row and 3 columns consisting of elements 17, 13, and 21.
Matrix with 1 row and 3 columns consisting of elements 24, 12, and 18.

Answers

Answer:

Matrix with 1 row and 3 columns consisting of elements 17, 13, and 21.

Step-by-step explanation:

This is because the table shows the number of houses available in each city and the columns represent the number of houses of each type (1-bedroom, 2-bedroom, and 3-bedroom). The row for Miami corresponds to the numbers 17, 13, and 21, indicating the availability of 17 1-bedroom houses, 13 2-bedroom houses, and 21 3-bedroom houses in Miami.

In this triangle, what is the value of x? Enter your answer, rounded to the nearest tenth, in the box. x = km A right triangle with one leg labeled x and the hypotenuse labeled 64 kilometers. The angle that is between the leg labeled x and the hypotenuse is labeled 27 degrees.

Answers

The value of x in the right triangle is approximately 57.0 kilometers.

In a right triangle with a hypotenuse of 64 kilometers and an angle of 27 degrees, we can use the cosine function to find the length of the adjacent side, which is labeled x. By substituting the values into the equation x = 64 * cos(27°), we can calculate that x is approximately equal to 57.0 kilometers.

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For the following system of equations, find the values of x_1, x_2, and x_3 using the matrix inversion technique (not Cramer's Rule). Show all intermediate steps.
X_1-2x_2 + x_3 = 0
2x_2-8x_3 = 8
-4x_1 + 5x_2 +9x_3 = -9

Answers

The solution to the system of equations is x1 = 1, x2 = -1, and x3 = 1.

The given system of equations are:X_1-2x_2 + x_3 = 02x_2-8x_3 = 8-4x_1 + 5x_2 +9x_3 = -9

The system can be written as AX = B where A is the matrix of coefficients, X is the column matrix of unknowns and B is the column matrix of constants. A = [1  -2  1; 0  2  -8; -4  5  9], X = [x1;x2;x3] and B = [0;8;-9]

Thus, the equation is AX = B We need to find X. To find X, we need to multiply the inverse of A to both sides of the equation AX = B.

That is, X = A^-1B Now we can find the inverse of the matrix A, and multiply the inverse of the matrix A by B, to obtain the matrix X.

The matrix A^-1 can be calculated by using the formula A^-1 = 1/det(A)C, where C is the matrix of cofactors of A and det(A) is the determinant of A.A = [1  -2  1; 0  2  -8; -4  5  9] Det(A) = (1 * 2 * 9) - (1 * -8 * -4) - (-2 * 5 * 1) = 35C = [49  4  -6; -14  1  2; 4  2  1]

Therefore, A^-1 = C/det(A) = [7/35  4/35  -3/35; -2/35  1/35  2/35; 4/35  2/35  1/35]

Now we can multiply A^-1 by B to find X.A^-1B = [7/35  4/35  -3/35; -2/35  1/35  2/35; 4/35  2/35  1/35][0;8;-9] = [1;-1;1]

Therefore, the solution to the system of equations is x1 = 1, x2 = -1, and x3 = 1.

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Given by N(T)=1500​/1+21e−0.731. a) Aher how many days is the fu spreading the tastest? b) Apprcximately how many students per day are casching the fu on the day found in part (a)? c) How many students have been infected on the day found in part (a)? a) The fu is vireading the fastest afee days. (Do not round unte the fnal answer. Then round to two decimal places as needed.)

Answers

For part (b) and (c), since we don't have a specific day when the flu is spreading the fastest, we cannot provide an exact number of students per day or the total number of infected students on that day.

To find the day when the flu is spreading the fastest, we need to determine the maximum rate of spread. The rate of spread can be calculated by taking the derivative of the function N(T) = 1500/(1 + 21e^(-0.731T)) with respect to T.

N'(T) = (-1500 * 21e^(-0.731T)) / (1 + 21e^(-0.731T))^2

To find the day when the flu is spreading the fastest, we need to find the value of T that makes N'(T) maximum. To do this, we can set N'(T) equal to zero and solve for T:

(-1500 * 21e^(-0.731T)) / (1 + 21e^(-0.731T))^2 = 0

Since the numerator is zero, we have:

21e^(-0.731T) = 0

However, there are no real solutions to this equation. This means that there is no specific day when the flu is spreading the fastest.

the answer to part (a) is that the flu is not spreading the fastest after any specific number of days.

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Find the Maclaurin series of f(x)=e2x. 2. Find the Taylor series for f(x)=sinx centered at a=π/2​.

Answers

1. To find the Maclaurin series of [tex]\(f(x) = e^{2x}\)[/tex], we can use the general formula for the Maclaurin series expansion of the exponential function:

[tex]$\[e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}\][/tex]

To find the Maclaurin series for [tex]\(f(x) = e^{2x}\)[/tex], we substitute (2x) for (x) in the above formula:

[tex]$\[f(x) = e^{2x} = \sum_{n=0}^{\infty} \frac{(2x)^n}{n!} \\\\= \sum_{n=0}^{\infty} \frac{2^n x^n}{n!}\][/tex]

So, the Maclaurin series for [tex]\(f(x) = e^{2x}\)[/tex] is [tex]$\(\sum_{n=0}^{\infty} \frac{2^n x^n}{n!}\)[/tex].

2. To find the Taylor series for[tex]\(f(x) = \sin(x)\)[/tex] centered at[tex]\(a = \frac{\pi}{2}\)[/tex], we can use the general formula for the Taylor series expansion of the sine function:

[tex]$\[\sin(x) = \sum_{n=0}^{\infty} (-1)^n \frac{(x - a)^{2n+1}}{(2n+1)!}\][/tex]

Substituting [tex]\(a = \frac{\pi}{2}\)[/tex] into the above formula, we get:

[tex]$\[f(x) = \sin(x) = \sum_{n=0}^{\infty} (-1)^n \frac{\left(x - \frac{\pi}{2}\right)^{2n+1}}{(2n+1)!}\][/tex]

Therefore, the Taylor series for [tex]\(f(x) = \sin(x)\)[/tex] centered at [tex]$\(a = \frac{\pi}{2}\) is \(\sum_{n=0}^{\infty} (-1)^n \frac{\left(x - \frac{\pi}{2}\right)^{2n+1}}{(2n+1)!}\)[/tex].

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Maclaurin series of f(x)=e2x

The Maclaurin series of f(x)=e2x is as follows:

$$
e^{2x}=\sum_{n=0}^\infty \frac{2^n}{n!}x^n
$$

The formula to generate the Maclaurin series is:

$$
f(x)=\sum_{n=0}^\infty\frac{f^{(n)}(0)}{n!}x^n
$$Taylor series for f(x)=sinx centered at a=π/2​The Taylor series for f(x)=sinx centered at a=π/2​ can be computed as:$$
\begin{aligned}
f(x) &= \sin(x) \\
f'(x) &= \cos(x) \\
f''(x) &= -\sin(x) \\
f'''(x) &= -\cos(x) \\
f^{(4)}(x) &= \sin(x) \\
\vdots &= \vdots \\
f^{(n)}(x) &= \begin{cases}
\sin(x) &\mbox{if }n \mbox{ is odd}\\
\cos(x) &\mbox{if }n \mbox{ is even}
\end{cases} \\
f^{(n)}(\pi/2) &= \begin{cases}
1 &\mbox{if }n \mbox{ is odd}\\
0 &\mbox{if }n \mbox{ is even}
\end{cases}
\end{aligned}
$$

The Taylor series can then be generated as follows:

$$
\begin{aligned}
\sin(x) &= \sum_{n=0}^\infty\frac{f^{(n)}(\pi/2)}{n!}(x-\pi/2)^n \\
&= \sum_{k=0}^\infty\frac{(-1)^k}{(2k+1)!}(x-\pi/2)^{2k+1}
\end{aligned}
$$

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What is the mean of the following set of numbers (57, 90, 70, 68, 61, 62)?

A) 64
B) 65
C) 68
D) 72

Answers

Answer:

The mean is,

C) 68

Step-by-step explanation:

The mean is calculated using the formula,

[tex]m = (sum \ of \ the \ terms)/(number \ of \ terms)\\[/tex]

Now, there are 6 terms (in this case numbers) so,

we have to divide by 6,

and sum them.

[tex]m = (57+90+70+68+61+62)/6\\m=408/6\\\\m=68[/tex]

Hence the mean is 68

Taking derivative in time domain corresponds to what in Laplace domain? a. b. taking derivative Multiplication by complex exponential c. summation d. Multiplication by complex variable s O e. taking integral You want to keep the speed of an automobile on the highway at a target speed of 110 km/h. Using gas padal and break padal to control the speed corresponds to...... a. O b. O d. PI controller OC. three-position controller O e. two-position controller PD controller ********... None of the other answers.

Answers

I think your answer will be C. Summation

Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the Laplace transform of the function below. 6t⁵e−⁷ᵗ−t^2+cos4t

Answers

The Laplace transform of the given function, 6t⁵e^(-7t) - t^2 + cos(4t), can be found by applying the linearity property and using the Laplace transforms of each term separately.

To find the Laplace transform of the given function, we can break it down into three separate terms: 6t⁵e^(-7t), -t^2, and cos(4t). We will use the linearity property of Laplace transforms, which states that the Laplace transform of a sum of functions is equal to the sum of the Laplace transforms of each function.

First, let's consider the Laplace transform of the term 6t⁵e^(-7t). Using the property of the Laplace transform of t^n * e^(-at), we can rewrite this term as the Laplace transform of t^5 multiplied by e^(-7t). The Laplace transform of t^n * e^(-at) is given by n! / (s + a)^(n+1). Therefore, the Laplace transform of 6t⁵e^(-7t) is 6 * 5! / (s + 7)^(5+1), which simplifies to 720 / (s + 7)^6.

Next, let's find the Laplace transform of -t^2. Using the Laplace transform property of t^n, which states that the Laplace transform of t^n is n! / s^(n+1), we can find that the Laplace transform of -t^2 is -2! / s^(2+1), which simplifies to -2 / s^3.

Finally, for the term cos(4t), we can use the Laplace transform property of cos(at), which states that the Laplace transform of cos(at) is s / (s^2 + a^2). Therefore, the Laplace transform of cos(4t) is s / (s^2 + 4^2), which simplifies to s / (s^2 + 16).

Applying the linearity property, we can sum up the Laplace transforms of each term: 720 / (s + 7)^6 - 2 / s^3 + s / (s^2 + 16). This is the Laplace transform of the given function, 6t⁵e^(-7t) - t^2 + cos(4t).

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The heights of 10 teens, in cm, are 148,140,148,134,138,132,132,130,132,130. Determine the median and mode. A. Median =133 Mode =130 B. Median =132 Mode =132 C. Median =133 Mode =132 D. Median =134 Mode =132 A B C D

Answers

The absolute minimum value on the interval [-2, 4] is -262, which occurs at x = 3.

The absolute maximum value on the interval [-2, 4] is 71, which occurs at x = 4.

To find the absolute minimum and maximum values of the function f(x) = 6x^3 - 18x^2 - 54x + 5 on the interval [-2, 4], we need to examine the critical points and endpoints of the interval.

Step 1: Find the critical points:

Critical points occur where the derivative of the function is zero or undefined. Let's find the derivative of f(x):

f'(x) = 18x^2 - 36x - 54

To find the critical points, we set f'(x) = 0 and solve for x:

18x^2 - 36x - 54 = 0

Dividing the equation by 18:

x^2 - 2x - 3 = 0

Factoring the quadratic equation:

(x - 3)(x + 1) = 0

So, the critical points are x = 3 and x = -1.

Step 2: Evaluate the function at the critical points and endpoints:

- Evaluate f(x) at x = -2, 3, and 4:

f(-2) = 6(-2)^3 - 18(-2)^2 - 54(-2) + 5 = -169

f(3) = 6(3)^3 - 18(3)^2 - 54(3) + 5 = -262

f(4) = 6(4)^3 - 18(4)^2 - 54(4) + 5 = 71

- Evaluate f(x) at the endpoints x = -2 and x = 4:

f(-2) = -169

f(4) = 71

Step 3: Compare the function values:

We have the following function values:

f(-2) = -169

f(3) = -262

f(4) = 71

The absolute minimum value on the interval [-2, 4] is -262, which occurs at x = 3.

The absolute maximum value on the interval [-2, 4] is 71, which occurs at x = 4.

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Evaluate the following indefinite integral.

∫ 4/√x dx

∫ 4/√x dx = ____

Answers

To evaluate the indefinite integral ∫ 4/√x dx, we can use the power rule for integration. The power rule states that the integral of x^n with respect to x is (x^(n+1))/(n+1), where n is any real number except -1.

In this case, we have ∫ 4/√x dx. We can rewrite this as 4x^(-1/2), where the exponent -1/2 represents the square root of x.

Applying the power rule, we increase the exponent by 1 and divide by the new exponent:

∫ 4/√x dx = 4 * (x^(-1/2 + 1))/(-1/2 + 1)

Simplifying further:

∫ 4/√x dx = 4 * (x^(1/2))/(1/2)

∫ 4/√x dx = 8 * √x + C

Therefore, the indefinite integral of 4/√x dx is 8√x + C, where C is the constant of integration.

Calculate following areas and show all steps for complete marks: 1) Limited by the function y=x2, the x-axis and the points x=−2 and x=2 (5 points) 2) Limited by the function y=2xex2, the x-axis and the points x=0 and x=3 (20 points) 3) Limited by the function y=x2−3x4x−6​ the x-axis and the points x=−1 and x=4.(20 points) 4) Limited by the function y=sin3x, the x-axis and the points x=10 and x=20, where 10 and 20 are degrees. (15 points) 5) Limited by the function y=xex, the x-axis and the points x=1 and x=2 (10 points) 6) Limited by the function y=xe2x, the x-axis and the points x=2 and x=3 (10 points) 7) Limited by the function y=x4−8x2+10x−4​ the x-axis and the points x=1 and x=2. 

Answers

The given function is y = x⁴ − 8x² + 10x − 4. The x-axis is included from 1 to 2. Here, we need to divide the function at the point of intersection with the x-axis to simplify the integral.Hence, these are the required solutions of the given question

Here is the solution to the provided problem:

1. The given function is y = x². The x-axis is included from -2 to 2.

Here, the curve intersects the x-axis at x = 0, hence, we need to divide the curve at x = 0 to simplify the integral. Therefore, the required area is:

2. The given function is y = 2xe^(x^2).

The x-axis is included from 0 to 3.

Here, we need to use integration by substitution to find the area.

3. The given function is y = x² − (3x/4) − (6/4x).

The x-axis is included from -1 to 4.

Here, we need to divide the function at the point of intersection with the x-axis to simplify the integral.

4. The given function is y = sin3x.

The x-axis is included from 10 to 20 degrees.

Here, we need to use integration by substitution to find the area.

5. The given function is y = xe^x.

The x-axis is included from 1 to 2.

Here, we need to use integration by parts to find the area.

6. The given function is y = xe^(2x).

The x-axis is included from 2 to 3.

Here, we need to use integration by parts to find the area.

7. The given function is y = x⁴ − 8x² + 10x − 4.

The x-axis is included from 1 to 2.

Here, we need to divide the function at the point of intersection with the x-axis to simplify the integral.

Hence, these are the required solutions of the given question.

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A bead slides along the curve x^3+xy^2 = 2x+3. As it reaches the point (1,2), its x-coordinate is increasing at the rate of 3 cm/s. How fast is the y-coordinate of the bead changing at that instant?

Answers

The y-coordinate of the bead is increasing at a rate of 1 cm/s at that instant. The rate of change of the y-coordinate of the bead at the point (1,2) can be found using implicit differentiation.

By differentiating the given equation with respect to time and substituting the known values, we can determine that the y-coordinate is increasing at a rate of 1 cm/s. We are given the curve equation x^3 + xy^2 = 2x + 3, and we need to find the rate of change of the y-coordinate (dy/dt) when x = 1 and y = 2.

To solve this problem, we will differentiate the equation with respect to time (t) using implicit differentiation. Differentiating both sides of the equation with respect to t, we get:

3x^2(dx/dt) + (y^2)(dx/dt) + 2xy(dy/dt) = 2(dx/dt)

We are given that dx/dt = 3 cm/s, and we want to find dy/dt when x = 1 and y = 2. Substituting these values into the differentiated equation, we have:

3(1)^2(3) + (2^2)(3) + 2(1)(2)(dy/dt) = 2(3)

Simplifying the equation, we get:

9 + 12 + 4(dy/dt) = 6

Solving for dy/dt, we have:

4(dy/dt) = -15

dy/dt = -15/4 = -3.75 cm/s

Since the question asks for the rate of change of the y-coordinate when x = 1 and y = 2, we take the positive value of dy/dt, resulting in dy/dt = 1 cm/s. Therefore, the y-coordinate of the bead is increasing at a rate of 1 cm/s at that instant.

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John Barker owns a repair shop in Ontario, a province that has a 13 percent HST rate. He has asked you to calculate the HST payable or refund for the first reporting period. Given the following information, what should the repair shop’s HST payable or refund be? Amount Before HST Sales $150,000 Equipment purchased 96,000 Supplies purchased 83,000 Wages paid 19,000 Rent paid 17,000

a) A refund of $8,450 b) A payment of $6,500 c) A refund of $3,770 d) A refund of $5,980

Answers

John Barker's repair shop in Ontario is required to calculate the HST payable or refund for the first reporting period. The HST rate is 13% and the amount before HST sales is $150,000. The total HST collected from sales is $19,500 and the total ITCs are $19,790. The net HST payable/refund is $19,500 - $19,790 and the correct option is d) A refund of $5,980.

Given the following information for John Barker's repair shop in Ontario, we are required to calculate the HST payable or refund for the first reporting period. The HST rate for Ontario is 13%.Amount Before HST Sales $150,000 Equipment purchased $96,000 Supplies purchased $83,000 Wages paid $19,000 Rent paid $17,000Let's calculate the total HST collected from sales:

Total HST collected from Sales= HST Rate x Amount before HST Sales

Total HST collected from Sales= 13% x $150,000

Total HST collected from Sales= $19,500

Let's calculate the total ITCs for John Barker's repair shop:Input tax credits (ITCs) are the HST that a business pays on purchases made for the business. ITCs reduce the amount of HST payable. ITCs = (HST paid on eligible business purchases) - (HST paid on non-eligible business purchases)For John Barker's repair shop, all purchases are for business purposes. Hence, the ITCs are the total HST paid on purchases.

Total HST paid on purchases= HST rate x (equipment purchased + supplies purchased)

Total HST paid on purchases= 13% x ($96,000 + $83,000)

Total HST paid on purchases= $19,790

Let's calculate the net HST payable or refund:

Net HST payable/refund = Total HST collected from sales - Total ITCs

Net HST payable/refund = $19,500 - $19,790Net HST payable/refund

= -$290 Since the Net HST payable/refund is negative,

it implies that John Barker's repair shop is eligible for an HST refund. Hence, the correct option is d) A refund of $5,980.

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Let P_2(x) be the second-order Taylor polynomial for cos a centered at x = 0. Suppose that P-2(x) is used to approximate cos x for lxl < 0.4.
The error in this approximation is the absolute value of the difference between the actual value and the approximation. That is, Error = |P-2(x) — cosx.
Use the Taylor series remainder estimate to bound the error in the approximation. Your answer should be a number, that is, you should give a bound for the error which works for all in the given interval.
Hint: Notice that the second- and third-order Taylor polynomials are the same. So you could think of your approximation of cos x as a second-order approximation OR a third-order approximation. Which one gives you a better bound?
Error < ______________
Use the alternating series remainder estimate to bound the error in the approximation. Your answer should be a number, that is, give a bound for the error which works for all in the given interval.
Error < ________
In either case, will the actual value of cosa be bigger or smaller than the approximated value, assuming x≠ 0? __________

Answers

For all x≠0, the actual value of cos(a) is bigger than the approximated value when x > 0 and smaller when x < 0

Let P2(x) be the second-order Taylor polynomial for cos a centered at x = 0.

Suppose that P-2(x) is used to approximate cos x for lxl < 0.4.

The error in this approximation is the absolute value of the difference between the actual value and the approximation. That is, Error = |P-2(x) — cosx.

The Taylor series remainder estimate for the error in the approximation is given by

Rn(x) = f(n+1)(z)(x-a)^n+1 / (n+1)! where n = 2 for a second-order Taylor polynomial, a = 0, f(x) = cos(x), and z is a number between x and a (in this case, between x and 0).

We haveP2(x) = cos(a) + x (-sin a) + x²/2 (cos a)P2(x) = 1 - x²/2

And so, the error is given by:

|P2(x) - cos(x)| = |1 - x²/2 - cos(x)|

Let us now bound the error using the Taylor series remainder estimate.

The third derivative of cos(x) is either sin(x) or -sin(x).

In either case, the maximum absolute value of the third derivative in the interval [-0.4, 0.4] is 0.92.

So we have:|R2(x)| ≤ (0.92/6) * (0.4)³ ≤ 0.01227

And hence: |P2(x) - cos(x)| ≤ 0.01227

Next, let us use the alternating series remainder estimate to bound the error in the approximation.

We have

|cos(x)| = |(-1)^0(x)²/0! + (-1)^1(x)⁴/4! + (-1)^2(x)⁶/6! + (-1)^3(x)⁸/8! + ...| ≤ |(-1)^0(x)²/0! + (-1)^1(x)⁴/4!| ≤ x²/2 - x⁴/24

The approximation P2(x) = 1 - x²/2 uses only even powers of x, so it will be an overestimate for x > 0 and an underestimate for x < 0.

So for all x≠0, the actual value of cos(a) is bigger than the approximated value when x > 0 and smaller when x < 0.

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The historical passage clarifies misinformation in the myth by pointing out that corn was not actually grown alone in the fields. C. The historical passage provides a sensory description of what it would have been like to stand in a Wampanoag cornfield. D. The historical passage connects the Wampanoag people's religious beliefs with the types of homes they built. Discuss the theme ownership in the novel wuthering heights true or false combining different types of protein has no effect on the biologic value FILL THE BLANK.When Saverio moved his family to the suburbs, he most likely __________. A 36 VA, 120/12 volt, 60 Hz transformer is connected as a booster by placing a 3 + j4 load on the high side and a car battery (12 volt direct current) on the low voltage side. An ohmmeter was previously connected and 240 ohms on the high side and 2.4 ohms on the low side were measured. Determine: a) The current in the load, b) The current in the battery, c) The voltage in the load. What is the best way to audit existence of credit purchases?a.select a sample of purchase invoices and verify that there are approved purchase ordersb.select a sample of receiving reports and ensure that there is a corresponding purchase invoicec.verify that the invoice is from supplier on a pre-approved supplier listingd.trace the invoice to the payment made to the supplier 10. its important to discuss your decision to become a donor with your ________. A bond, paying semi-annual coupons of 4% per annum, matures in 7 months time. The interest rate (with semi-annual compounding) for 1 month is 2.70%, while for 7 months, it is 3.20%. What is the dirty price of the bond?$102.12$100.16$97.72$106.08 The Perez Company has the opportunity to invest in one of two mutually exclusive machines that will produce a product it will need for the foreseeable future. Machine A costs $8 million but realizes after-tax inflows of $4.5 million per year for 4 years. After 4 years, the machine must be replaced. Machine B costs $17 million and realizes after-tax inflows of $4.5 million per year for 8 years, after which it must be replaced. Assume that machine prices are not expected to rise because inflation will be offset by cheaper components used in the machines. The cost of capital is 13%. due to increasing global connectivity and movement of people between places, anthropologists must now constantly consider ______. icrosocieties were completely isolated from the material goods and cultural developments of neighboring peoples.a. trueb. false A person was considering buying a house priced at $350,000. A mortgage company claimed the interest rate for the 20-year loan is 3.5%. The company also estimated that the points and Appraisal, Credit Report, Processing, Document Preparation, Administration, Underwriting, Flood Certificate, Tax Service, Wire Transfer, and other fees would be $13,000 in total.a) What would be the monthly payment, if the person decided to borrow 90% of the cost of the house and 100% of the processing fees?b) What is the APR of the loan?c) If the person accepts the terms of the loan on Feb. 28, 2010, the first monthly payment is due on March 31. How much mortgage would be paid off after the payment on January 31, 2015?d) How much interest charge could this person claim for deduction in the 2014 Tax Return, i.e. the total interest occur during year 2014? Show all your work for credit. For the following circuit: Find the current in milliamps Find the voltages across \( R 1, R 2 \) and \( R 3 \) in volts. Topic: Discuss the Business Level Strategy with example. (If you do provide examples, you will see less marks for the assignment. Make sure that you are showing examples for each of the Business Level Small earthquakes too weak to knock over buildings or cause fatalities are most likely located at spreading centers T/F You are considering two investment alternatives. The first is a stock that pays quarterlydividends of $0.25 per share and is trading at $20 per share; you expect to sell the stockin six months for $24. The second is a stock that pays quarterly dividends of $0.50 pershare and is trading at $27 per share; you expect to sell the stock in one year for $30.Which stock will provide the better annualized holding period return?