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The IQR measures the spread of the middle 50% of the data.

Without knowing the actual values of the fuel economy ratings or the summary statistics, we cannot provide an exact answer. However, we can make some general observations about the effects of removing an extreme outlier on the standard deviation and the interquartile range (IQR).

First, the standard deviation measures the spread of the data around the mean. Removing an extreme outlier that is far from the mean could potentially decrease the standard deviation, as the remaining values may be more tightly clustered around the mean. However, the effect on the standard deviation will depend on the exact values of the data points and how much they vary from the mean.

Second, the IQR measures the spread of the middle 50% of the data. Removing an extreme outlier that is far from the bulk of the data may not have a significant effect on the IQR, as the remaining.

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Answer:

The volume is 1386 cm³ and curved surface area is 396 cm².

Step-by-step explanation:

Given that,

The diameter of a cylinder is 14 cm

Height of the cylinder is 9 cm

We need to find the volume and curved surface area​ .

If r is the radius, r = 14/2 = 7 cm

Volume of a cylinder is given by :

\(V=\pi r^2 h\\\\V=\dfrac{22}{7}\times (7)^2 \times 9\\\\V=1386\ \text{cm}^3\)

The curved surface area of the cylinder is given by :

\(A=2\pi r h\\\\A=2\times \dfrac{22}{7}\times 7\times 9\\\\A=396\ \text{cm}^2\)

So, the volume is 1386 cm³ and curved surface area is 396 cm².

Dependent Events where what happens depends on what happened before, such as taking cards from a deck makes less cards each time.

Independent Events which we learn about here.

Bill flipping a coin and rolling a dice are independent events. Flipping a coin doesn't depend on rolling a die.

Independent

Answer:

arc TBU = 268°

Step-by-step explanation:

the measure of the tangent- chord angle TUV is half the measure of its intercepted arc UT , then

UT = 2 × 46° = 92°

the sum of the arcs in a circle = 360° , that is

TBU + UT = 360°

TBU + 92° = 360° ( subtract 92° from both sides )

TBU = 268°

If two methods agree perfectly in a method comparison study, the slope equals 1.0 and the y-intercept equals 0.0. Therefore, option (b) is the correct answer.

In a method comparison study, the goal is to compare the agreement between two different measurement methods or instruments. The relationship between the measurements obtained from the two methods can be described by a linear equation of the form y = mx + b, where y represents the measurements from one method, x represents the measurements from the other method, m represents the slope, and b represents the y-intercept.

When the two methods agree perfectly, it means that there is a one-to-one relationship between the measurements obtained from each method. In other words, for every x value, the corresponding y value is the same. This indicates that the slope of the line connecting the measurements is 1.0, reflecting a direct proportional relationship.

Additionally, when the two methods agree perfectly, there is no systematic difference or offset between the measurements. This means that the line connecting the measurements intersects the y-axis at 0.0, indicating that the y-intercept is 0.0.

Therefore, in a perfect agreement scenario, the slope equals 1.0 and the y-intercept equals 0.0, which corresponds to option (b).

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The given problem involves integrating a complex function counterclockwise along a specific curve in the complex plane. The curve is defined by the equation |z-1| = 6.

To solve the problem, we need to integrate the function 2+6dz counterclockwise along the curve C defined by |z-1| = 6. Let's break down the solution into two parts: first, we determine the parametric representation of the curve C, and then we perform the integration.

The equation |z-1| = 6 represents a circle centered at z = 1 with a radius of 6. By applying the parametrization z = 1 + 6\(e^{(it)}\), where t is the parameter ranging from 0 to 2π, we can represent the curve C in a parametric form.

Next, we substitute this parametric form into the integral and rewrite the differential dz using the chain rule. The given integral becomes ∫(2+6(1 + 6\(e^{(it)}\)))i(6\(e^{(it)}\))dt.

Expanding and simplifying, we have ∫(2 + 6i + 36i\(e^{(it)}\) - 36\(e^{(it)}\))dt.

Integrating term by term, we get the result as 2t + 6it - 36\(e^{(it)}\). Evaluating the integral from 0 to 2π, we substitute these values into the result expression.

Finally, simplifying the expression, the integrated value for the given problem is 4π - 12i.

In conclusion, integrating counterclockwise 2+6dz = Joz-2 2+6 Joz-2 dz along the curve C, where |z-1| = 6, results in a value of 4π - 12i.

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Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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Step-by-step explanation:

Given

g(x) = x² + 4x - 7

g(-6)= ( - 6)² + 4 * ( -6) - 7

= 36 - 24 - 7

= 5

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In triangle ABC, a perpendicular bisector AD is drawn on BC. We can see that triangle ABD and triangle ACD are right-angled triangles. The missing side x is 9√3/4.

A triangle is a three-sided polygon with three angles. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified in several ways based on their sides and angles.

There are also several important properties of triangles, such as the Pythagorean theorem which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse). Triangles also have several geometric formulas associated with them, such as the area formula (1/2 * base * height) and the perimeter formula (sum of all sides). Triangles are an important concept in geometry and have many practical applications in fields such as engineering and physics.

In triangle ABC, a perpendicular bisector AD is drawn on BC. We can see that triangle ABD and triangle ACD are right-angled triangles.

Using trigonometry, we can write the following equations:

sin(60) = BD/AB (Using triangle ABD)

cos(60) = CD/AC (Using triangle ACD)

We know that AB = x and CD = 3. We need to find x.

Rearranging the first equation, we get:

BD = AB * sin(60)

Substituting the value of BD in the second equation, we get:

cos(60) = CD/AC

cos(60) = 3/2BD

cos(60) = 3/2(AB * sin(60))

cos(60) = 3/2(x * √3/2)

cos(60) = 3√3/4x

Multiplying both sides by 4x/3√3, we get:

4x/3√3 * cos(60) = 3

Simplifying, we get:

x = 9√3/4

Therefore, the missing side x is 9√3/4.

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Answer:

a = 49

b = - 20√2

Step-by-step explanation:

5 - 2√6 / 5 + 2√6

We can rationalise the denominator as follow:

5 - 2√6 / 5 + 2√6

Multiply the numerator and the denominator by the conjugate of

5 + 2√6. The conjugate of 5 + 2√6 is

5 - 2√6

(5 - 2√6 / 5 + 2√6) x (5 - 2√6 / 5 - 2√6)

(5 - 2√6) (5 - 2√6) /(5 + 2√6) (5 - 2√6)

Expand

(25 - 10√6 - 10√6 + 4×6) / (25 - 10√6 + 10√6 + 4×6)

25 - 20√6 + 24 / 25 - 24

25 + 24 - 20√6 / 1

49 - 20√6

Equating 49 - 20√6 with a + b√3, we can obtain the value of a and b as follow:

49 - 20√6 = a + b√3

From the above

a = 49

b√3 = - 20√6

Divide both side by √3

b = - 20√6/√3

Rationalise

b = - 20√6/√3 x √3/√3

b = - 20√(6×3)/ √3×√3

b = - 20√18 / 3

b = - 20√(9×2) / 3

b = - 20 × 3√2 / 3

b = - 20√2

Given info:- Rationalise the denominator and find out the value of "a" and "b"

Given expression: {(5-2√6)/(5+2√6)} = a+b√3

Explanation:-

{(5-2√6)/(5+2√6)} = a+b√3

We know that Rationalising factor of a+b√c is a-b√c.

Therefore, the rationalising factor of 5+2√6 is 5-2√6.

⇛{(5-2√6)/(5+2√6)} × {(5-2√6)/(5-2√6)} = a+b√3

⇛{(5-2√6)(5-2√6)}/{(5+2√6)/(5-2√6)} = a+b√3

⇛{(5-2√6)²}/{5+2√6)(5-2√6)} = a+b√3 [∵(a-b)(a-b)=(a-b)²]

⇛{(5-2√6)²}/{(5)²-(2√6)²} = a+b√3 [∵(a+b)(a-b)=a²-b²]

⇛{(5-2√6)²}/({5*5)-(2*2√6*6)} = a+b√3

⇛{(5-2√6)²}/(25 - 4√6) = a+b√3

⇛{(5-2√6)²}/(25-24) = a+b√3

⇛{(5-2√6)²}/1 = a+b√3

⇛(5-2√6)² = a+b√3

⇛(5)²-(2√6)²+2(5)(2√6) = a+b√3

⇛(5*5) - (2*2√6*6) - 10 - 2√6 = a+b√3

⇛25 - 10 - 4√6 - 2√6 = a+b√3

⇛15 - 4√6 - 2√6 = a+b√3

⇛15 + 6√6 = a+b√3

∴ 15 + 6√6 = a+b√3

On, comparing with both RHS we notice that:

The value of a = 15 and b = 6.

Hope this helps!!

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Answer:

Plan A

The formula is

A=p (1+r)^t

A=2,000×(1+0.06)^(4)

A=2,524.95 ( future value )

Interest earned=A-p

Interest earned=2524.95-2000

Interest earned=524.95

Plan B

Use the simple interest formula

I=prt

I interest earned?

P principle 2000

R interest rate 0.13

T time 4years

I=2,000×0.13×4

I=1,040

The Answer is

Plan B; $1,040

Step-by-step explanation:

Content area the calculation for annual depreciation using the units-of-output method is yearly output.

What are the output method's units?

What is the annual depreciation formula?

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When procedures are mandated by third party payers, the modifier -32 (mandated services) is used. This modifier is used to indicate that a service or procedure is mandated by a third party payer, such as Medicare or Medicaid.

It is used to ensure that the service or procedure is reimbursed appropriately and to avoid denials. The use of the -32 modifier is important to accurately reflect the requirements of the payer and to avoid any potential billing or coding errors. It is important to check with the specific payer to determine if the use of this modifier is required for a particular service or procedure.

When procedures are "mandated" by third-party payers, you would use the modifier -32. This modifier indicates that a service or procedure is being performed due to specific requirements from a third-party payer. It helps to provide the necessary information for reimbursement and ensures that the claim is processed correctly by the payer. Remember to attach the modifier -32 to the appropriate procedure code on the claim form when submitting it to the third-party payer. This will help avoid any potential delays or denials in payment due to insufficient documentation.

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The probability that the other child is also a girl, given that one of them is a girl, is 2/3 or approximately 0.6667.

To determine the probability that the other child is also a girl given that one of them is a girl, we need to consider the possibilities of the gender combinations for Alice's two children.

Let's denote the gender of the first child as G (girl) and B (boy), and the gender of the second child as G' and B'.

There are four possible combinations for the gender of the two children: GG, GB, BG, and BB.

However, we are given that one of the children is a girl. This eliminates the BB combination since we know both children cannot be boys.

Thus, we are left with three possible combinations: GG, GB, and BG.

Out of these three combinations, two of them involve at least one girl: GG and GB. This means there is a 2 out of 3 chance that the other child is a girl.

Therefore, the probability that the other child is also a girl, given that one of them is a girl, is 2/3 or approximately 0.6667.

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Answer:

a = d/4 - b/c

Step-by-step explanation:

Subtract b/c from both sides. We can subtract a fraction

so

a = d/4 - b/c

A period is the difference in x over which a sine function returns to its equivalent state and the amplitude is A/5.

Amplitude:

The amplitude of a periodic variable is a measure of its change over a period of time, such as a temporal or spatial period. The amplitude of an aperiodic signal is its magnitude compared to a reference value. There are various definitions (see below) of amplitude, which is any function of the magnitude of the difference between the extreme values ​​of a variable. In the previous text, the phase of a periodic function is called the amplitude.

                       X = A sin (ω[ t - K]) + b

A is the amplitude (or peak amplitude),

x is the oscillating variable,

ω  is angular frequency,

t is time,

K and b are arbitrary constants representing time and displacement respectively.

According to the Question:

An equation does not have an amplitude. This "equation" represents the formula of a vibration, and was better written as:

X= A/5* sin(1000.t + 120)

These oscillations have a certain amplitude. X values ​​can vary from minimum to maximum. Normally, the stop position of the oscillation is X=0. In this case, we can see that the maximum occurs when the sine is +1 and the minimum occurs when the sine is -1.

For theses cases X= A/5 respectively -A/5.

Therefore,

The amplitude is A/5.

For formulas of this type, the term in front of the sinus (or cosine) is equal to the amplitude.

Complete question:

Can I find the amplitude of this equation? A/5 *