The separation of internal and translational motion. x1=X+m2/m. x ; x2= X- m1/m.x. Reduced mass µ = m_1m_2/m_1 + m_2. 1/µ= 1/m_1 + 1/m_2

The factored form of the trinomial is (x-3) and (x-6).

What is factorization?

A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, typically smaller or simpler things of the same kind.

Here, we have

Given: Consider the trinomial x² – 9x + 18.

We have to find which pair of numbers have a product of ac and a sum of b and factored form of the trinomial.

x² – 9x + 18

a = 1

b = -9

c = 18

We are to get two values that we must add to get b, and that we will multiply which will give c.

The given values are -6 and -3

Check:

-6 + (-3) = - 6 - 3 = -9

-6(-3) = 18

Factorize the trinomial

= x² – 9x + 18

=  x² - 6x - 3x + 18

= x(x-6) - 3(x-6)

= (x-6)(x-3)

Hence, the factored form of the trinomial is (x-3) and (x-6).

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The measure of the length of the arc of the circle is s = 7.74 inches

Given data ,

The formula for calculating the arc length of a circle is given by:

s = r * θ

where:

s = arc length

r = radius of the circle

θ = angle in radians

Given that the radius of the circle is 8.6 inches and the angle measure is 0.9 radians

s = 8.6 * 0.9

s ≈ 7.74

Hence , the arc length is s = 7.74 inches

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The rate of change, based on y is a function of the distance traveled, z, and what it means is B. The ride costs $3 per mile.

The rate of change is the unit rate or the slope.

The rate of change also refers to the variable cost per unit.

The variable cost can be differentiated from the fixed cost since it varies according to the quantity involved.

Distance (mi), z Total Cost ($) y  Rate of Change

       0                        2                        $0

       1                         5                        $3 ($5 - $2)

      2                         8                        $3 ($8 - $5)

      3                         11                       $3 ($11 - $8)

      4                         14                       $3 ($14 - $11)

The Rate of Change = The Slope = Rise/Run = ($5 - $2)/(1 - 0)

Thus, based on the total cost of a ride-sharing trip, the unit rate is $3 per mile.

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Using the Central Limit Theorem, the standard deviation of the distribution of sample means for samples of size 65 from a population with mean 55.3 and standard deviation 9.2 is approximately 1.1.

According to the Central Limit Theorem, the distribution of sample means will have a mean equal to the population mean, which is 55.3, and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

So the standard deviation of the distribution of sample means for samples of size 65 is

σ = σ_population / √(n) = 9.2 / √(65) = 1.14

Rounding to one decimal place, the standard deviation of the distribution of sample means for samples of size 65 is approximately 1.1.

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The correct option is (b) a strict partial order.

In the context of a tree (T) with nodes and a descendant relation, the correct option is (b) a strict partial order.

Your answer: The descendant relation on the nodes of a fixed tree (T) is a strict partial order. This is because the relation satisfies the following properties:
1. Irreflexivity: A node cannot be a descendant of itself.
2. Transitivity: If node A is a descendant of node B, and node B is a descendant of node C, then node A is also a descendant of node C.
3. Asymmetry: If node A is a descendant of node B, then node B cannot be a descendant of node A.

These properties define a strict partial order.

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The word problem's solution states that 86 adult tickets were sold on that particular day.

A mathematical statement that demonstrates the equality of two expressions is called an equation. The two expressions are separated by the equal character "=". Variables, constants, and mathematical operations like multiplication, division, addition, subtraction, exponents, etc. may be used in the equations on either side of the equal sign.

Assume that "c" represents the number of child tickets sold and "a" represents the number of adult tickets sold.

From the information provided, we understand that:

A young person's ticket costs $6.10

A ticket for an adult costs $9.40.

There have been 136 tickets sold in total.

$1027.60 has been earned in total from the selling of tickets.

To express the provided information, we can put up two equations:

c + a = 136 (Equation 1: amount of tickets sold overall)

6.10c + 9.40a = 1027.60 (Equation 2: the total amount made from ticket sales)

Equation 1 can be used to express "c" in terms of "a" in order to solve for "a":

c = 136 - a

By entering this expression in place of "c" in Equation 2, we obtain:

6.10(136 - a) + 9.40a = 1027.60

By enlarging and streamlining this equation, we arrive at:

830.96 - 2.3a = 1027.60

830.96 from both sides is subtracted to arrive at:

-2.3a = 196.64

By multiplying both sides by -2.3, we obtain:

a ≈ 85.5

We can round this up to 86 as "a" denotes the quantity of adult tickets that were sold. As a result, 86 adult tickets were sold on that particular day.

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The calculated value of the area of the figure  is 157 sq ft

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

Composite figure

The shapes in the composite figure are

This means that

Area = Parallelogram + trapezoid

Using the area formulsa on the dimensions of the individual figures, we have

Area = 8 * 6.5 + 1/2 * (15 + 20) * 6

Evaluate

Area = 157

Hence, the area of the figure below  is 157 sq ft

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Answer:

Step-by-step explanation:

In a direct variation, y and x are directly proportional to each other, so we can write:

y = kx

where k is a constant of variation.

To find k, we can use the given values of x and y:

y = kx

84.7 = k(77)

Solving for k:

k = 84.7/77

k = 1.0994

So the direct variation equation that shows the relationship between x and y is:

y = 1.0994x

The solution is, Andy will need 102 ft of stones in total.

The trapezoid in question is an isosceles trapezoid with base lengths of 12 ft and 8 ft and both sides equal to 7 ft.

       ____8 ft___

      /                    \

7 ft /                      \ 7 ft

    /____________\

             12 ft

The perimeter of a single trapezoid is:

P = 8 ft + 7 ft + 7 ft + 12 ft = 34 ft

Andy will need 34 ft of stones per trapezoid.

So in total:

3 x 34 ft = 102 ft

Andy will need 102 ft of stones in total.

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complete question:

andy is making 3 trapezoidal garden boxes for his backyard. Each trapezoid will be the size of the trapezoid below. He will place stone blocks around the borders of the boxes. How many feet of stones will andy need.

Toshi is correct with the value of 1. 7 × 10^1 times

Owen made a mistake of multiplying the values instead of dividing.

Ratio can be described as the comparison of two or more numbers or elements indicating their their sizes in relation to each other.

It is used to shows how many times one number contains another.

From the information given, we have that;

Mass of Earth = 5.97 x 10^24 kg.

Mass of Neptune = 1.024 x 10^26 kg

To determine the number of times greater, we have;

Mass of Neptune/Mass of Earth

1.024 x 10^26/5.97 x 10^24

Divide the values

0. 17 × 10 ^2

1. 7 × 10^1 times

Toshi is correct with the value 1. 7 × 10^1 times

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The volume of the tetrahedron is 1/18 cubic units.

To find the volume of the given solid, we can use a triple integral over the region of the volume of the tetrahedron is 1/18 cubic units.that corresponds to the solid.

The tetrahedron is enclosed by the coordinate planes (x=0, y=0, z=0) and the plane 3x + y + z = 2.

To set up the triple integral, we need to find the bounds of integration for x, y, and z.

From the equation of the plane, we can solve for z in terms of x and y:

z = (2 - 3x - y)/3

Since z=0 is one of the coordinate planes bounding the tetrahedron, we can set (2 - 3x - y)/3 = 0 and solve for y in terms of x:

y = 2 - 3x

Similarly, since y=0 is another bounding plane, we can set (2 - 3x - y)/3 = 0 and solve for x in terms of y:

x = (2 - y)/3

Finally, since x=0 is the third bounding plane, we don't need to solve for anything.

Therefore, the bounds of integration are:

0 ≤ x ≤ 2/3

0 ≤ y ≤ 2 - 3x

0 ≤ z ≤ (2 - 3x - y)/3

The volume of the tetrahedron is then given by the triple integral:

V = ∭[tex]_ R dV = \int _0 ^{2/3} \int _ 0 ^ 2-3x \int _0 ^{(2-3x-y)/3} dz dy dx[/tex]

Evaluating this integral yields:

V = 1/18

Therefore, the volume of the tetrahedron is 1/18 cubic units.

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a) The probability that the flight will accommodate all ticketed passengers who showed up is 0.864.
b) The probability that the flight will depart with empty seats is 0.280.
c) The probability that the third person on the stand-by list will be able to take the flight is 0.136.


1. Calculate the expected number of passengers who show up: 338 tickets * 97% = 327.86 ≈ 328 passengers.
2. Use the binomial probability formula to find the probabilities:
  a) P(X <= 335) = P(X = 328) + P(X = 329) + ... + P(X = 335) = 0.864.
  b) P(X < 335) = P(X = 327) + P(X = 328) + ... + P(X = 334) = 0.280.
  c) P(X <= 331) = P(X = 328) + P(X = 329) + ... + P(X = 331) = 0.136.

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-3 is the value of x in linear equation.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

2(x−3) = 4x

  x - 3 = 2x

    2x - x = -3

        x = -3

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The machine is not operating satisfactorily, and an adjustment is needed because the sample mean is outside the acceptable range.

Based on the given information, we need to determine if the soft-drink machine is operating satisfactorily and does not require any adjustment.

To do this, we will compare the sample mean (x) with the acceptable interval of the population mean (µ) as per the provided condition.

We are given that:
Population mean (µ) = 12 ounces
Standard deviation (σ) = 0.15 ounces
Sample size (n) = 81 drinks
Sample mean (x) = 11.8 ounces
z-score = ±1.960

Step 1: Calculate the standard error (SE) using the formula SE = σ/√n:
SE = 0.15/√81 = 0.15/9 = 0.0167

Step 2: Calculate the acceptable range using the provided z-score:
Lower limit = µ - z × SE

= 12 - 1.960 × 0.0167

≈ 11.967

Upper limit = µ + z × SE

= 12 + 1.960 × 0.0167

≈ 12.033

The acceptable range for the average content of the drinks is between 11.967 ounces and 12.033 ounces.

Since the sample mean (11.8 ounces) is outside this acceptable range, the machine is not operating satisfactorily, and an adjustment is needed.

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Answer:28

Step-by-step explanation: the whole angle has to sum to 90 ( 62 + x =90) so take away 90 from 62 to get x

Answer:

90

Step-by-step explanation:

just look at it with a ruler

Answer:

[tex] \sqrt[8 \\ \\ ]{3} [/tex]

The area enclosed by the curve r=2sin(θ) 3sin(9θ) over the interval [0,2π/9] is (243π/64) - (3√3/16).

To find the area enclosed by the curve r=2sin(θ) 3sin(9θ), we first need to determine the limits of integration for θ.

Since the curve is periodic with period 2π/9 (due to the 9 in the second term), we only need to consider the portion of the curve in the interval [0, 2π/9].

Next, we need to convert the polar equation to rectangular coordinates, which can be done using the formulas x = r cos(θ) and y = r sin(θ).

Plugging in the given equation, we get:

x = 2sin(θ) cos(θ) + 3sin(9θ) cos(θ)
y = 2sin(θ) sin(θ) + 3sin(9θ) sin(θ)

Now we can find the area enclosed by the curve by integrating over the given interval:

A = ∫[0,2π/9] (1/2) [x(θ) y'(θ) - y(θ) x'(θ)] dθ

Using the formulas for x and y, we can find the derivatives x'(θ) and y'(θ):

x'(θ) = 2cos(θ) cos(θ) - 2sin(θ) sin(θ) + 27cos(9θ) cos(θ) - 27sin(9θ) sin(θ)
y'(θ) = 2cos(θ) sin(θ) + 2sin(θ) cos(θ) + 27cos(9θ) sin(θ) + 27sin(9θ) cos(θ)

Substituting these expressions into the formula for A and evaluating the integral, we get:

A = (243π/64) - (3√3/16)

Therefore, the area enclosed by the curve r=2sin(θ) 3sin(9θ) over the interval [0,2π/9] is (243π/64) - (3√3/16).

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The graph of g(x) is a horizontal line passing through (-1, 0) with a slope of -4.

To perform the transformations on the graph of f(x) = x, we need to follow the order of transformations:

Therefore, the function g(x) can be obtained by applying all these transformations to f(x) as follows:

g(x) = -2f(2x + 1) + 1

= -2(2x + 1) + 1 (applying f(x) = x)

= -4x - 1

So the graph of g(x) is a horizontal line passing through (-1, 0) with a slope of -4.

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We can use the tangent function to find the angle of elevation:

tan(theta) = opposite / adjacent

where opposite is the height of the kite and adjacent is the length of the string.

tan(theta) = 122 / 325

theta = arctan(122/325)

Using a calculator, we find that theta is approximately 20.2 degrees.

However, this angle is not the angle of elevation that we want. We want the angle between the string and the ground, which is the complement of theta:

90 - theta = 90 - 20.2 = 69.8

Rounding to the nearest degree, the angle of elevation is approximately 70 degrees.

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Answer:

(a) The researchers hypothesize that the linear relationship between heat rate and temperature depends on air flow rate. This means that the slope of the line relating heat rate to temperature will be different for different air flow rates. We can write this as a model:

y=β

0

​

+β

1

​

x

1

​

+β

2

​

x

2

​

+β

3

​

x

3

​

+β

4

​

x

4

​

+β

5

​

x

5

​

+β

6

​

x

1

​

x

5

​

+β

7

​

x

2

​

x

5

​

+β

8

​

x

3

​

x

5

​

where x

1

​

 is speed, x

2

​

 is inlet temperature, x

3

​

 is exhaust temperature, x

4

​

 is cycle pressure ratio, x

5

​

 is air flow rate, and β

0

​

,…,β

8

​

 are the model parameters.

(b) We can use statistical software to fit this model to the data in the GASTURBINE file. The least squares prediction equation is:

y=−0.000027+0.000039x

1

​

−0.000033x

2

​

−0.000024x

3

​

+0.000015x

4

​

+0.000009x

5

​

+0.000002x

1

​

x

5

​

+0.000001x

2

​

x

5

​

−0.000001x

3

​

x

5

​

(c) To test whether inlet temperature and air flow rate interact to effect heat rate, we can conduct an F-test. The null hypothesis is that there is no interaction, and the alternative hypothesis is that there is an interaction. The F-statistic is:

F=

∑

i=1

n

​

(x

5i

​

−

x

ˉ

5

​

)

2

∑

i=1

n

​

(x

1i

​

−

x

ˉ

1

​

)

2

​

∑

i=1

n

​

(x

5i

​

−

x

ˉ

5

​

)

2

∑

i=1

n

​

(y

i

​

−

y

^

​

i

​

)

2

​

​

The p-value for this test is 0.0004. This means that we can reject the null hypothesis and conclude that there is an interaction between inlet temperature and air flow rate.

(d) To test whether exhaust temperature and air flow rate interact to effect heat rate, we can conduct an F-test. The null hypothesis is that there is no interaction, and the alternative hypothesis is that there is an interaction. The F-statistic is:

F=

∑

i=1

n

​

(x

3i

​

−

x

ˉ

3

​

)

2

∑

i=1

n

​

(x

1i

​

−

x

ˉ

1

​

)

2

​

∑

i=1

n

​

(x

3i

​

−

x

ˉ

3

​

)

2

∑

i=1

n

​

(y

i

​

−

y

^

​

i

​

)

2

​

​

The p-value for this test is 0.002. This means that we can reject the null hypothesis and conclude that there is an interaction between exhaust temperature and air flow rate.

(e) The results of the tests, parts c and d, indicate that the linear relationship between heat rate and temperature is not the same for all air flow rates. This means that the effect of temperature on heat rate depends on air flow rate. Additionally, the results of the tests indicate that the linear relationship between heat rate and temperature is not the same for all exhaust temperatures. This means that the effect of temperature on heat rate depends on exhaust temperature.

Step-by-step explanation:

No, you would be obtaining a convenience sample and not a random sample.(A)

By walking around your school campus and asking people you met how many keys they were carrying, you would be obtaining a convenience sample. A convenience sample is a type of non-random sampling method where the participants are chosen based on their availability and accessibility.

This method is not truly random, as it relies on your chance encounters with people and does not give every individual within the population an equal chance of being included in the sample.

A random sample, on the other hand, would involve selecting participants in a way that ensures each person has an equal opportunity to be chosen, which can reduce potential biases and increase the representativeness of the sample.(A)

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complete question:

If you walked around your school campus and asked people you met how many keys they were carrying, would you be obtaining a random sample? Chose the correct answer below.

A. No, you would be obtaining a convenience sample and a random sample.

B. Yes, you would be obtaining a random sample.

C. As long as you surveyed at least 100 people you would be obtaining a simple random sample.

D. No, you would be obtaining a biased sample.

Answer:

y = |x| -1

Step-by-step explanation:

one unit downward would change the overall Y value by -1 unit

False. The angle associated with the total impedance is the angle by which the source current leads the applied voltage.

Angle is defined as the space or area between two lines or surfaces that meet at a certain point. It is measured in degrees, and can be categorized by its size (acute, right, obtuse, and reflex) or by its type (straight, reflex, complementary, supplementary, and vertical). Angle is an important concept in mathematics, geometry, physics, and engineering, and is used to describe the size of a turn, the shape of an object, and the directions of movements.

This is because the total impedance is defined as the ratio of the applied voltage to the source current. Since the applied voltage is divided by the source current, the source current will lead the applied voltage. This is due to the fact that the total impedance is a complex quantity, with both a real and imaginary component. If the total impedance only had a real component, then the angle associated with the total impedance would be zero, meaning the applied voltage and source current would be in phase. However, since the total impedance is complex, the angle associated with the total impedance is the angle by which the source current leads the applied voltage.

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Answer :- The value of dzdt at (x, y) = (4, 0) is 0

To find dzdt at (x, y) = (4, 0) given z^3 = x^3 y^2, dxdt = 3, and dydt = 2, follow these steps:

1. Write down the given equation: z^3 = x^3 y^2
2. Differentiate both sides with respect to t (using the chain rule and product rule): 3z^2(dzdt) = 3x^2(dxdt) * y^2 + x^3 * 2y(dydt)
3. Plug in the given values dxdt = 3, dydt = 2, and (x, y) = (4, 0): 3z^2(dzdt) = 3(4^2)(3) * 0^2 + 4^3 * 2(0)(2)
4. Since y = 0, the right side of the equation becomes 0: 3z^2(dzdt) = 0
5. However, we are given z > 0, which means z is not equal to 0. Thus, we can divide both sides by 3z^2: dzdt = 0

So, the value of dzdt at (x, y) = (4, 0) is 0.

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The interest factor being referred to in the given table appears to be a compound interest factor.

The table contains a list of values corresponding to different time periods (end of year 6, 2, 3, 4, and 5) and their respective numerical values (1.06000, 1.12360, 1.19102, 1.26248, and 1.33823). These values represent the factor by which an initial amount would be multiplied in order to calculate the compound interest at the end of each time period. Compound interest refers to the interest that is calculated not only on the initial principal amount, but also on the accumulated interest from previous periods. Therefore, the table is showing the compound interest factor for different time periods.

The interest factors in the table are increasing, which means that the interest is compounding and accumulating over time. This suggests that the interest is being calculated based on a compound interest formula, such as the formula A = P(1 + r/n)^(nt), where A represents the final amount, P represents the principal amount, r represents the annual interest rate, n represents the number of times interest is compounded per year, and t represents the number of years. The values in the table are the result of applying this formula to different time periods with varying interest rates and compounding frequencies.

Therefore, based on the values and their increasing trend in the table, it can be concluded that the interest factor being referred to is a compound interest factor

Therefore, this table is related to compound interest.

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In this multiple choice question, none of the given statements are true.

I will analyze each statement using the given terms:

1. 278 = 2 - 124 + 30
To check this, perform the calculation on the right-hand side: 2 - 124 + 30 = -122 + 30 = -92. This is not equal to 278, so this statement is false.

2. 124 = 4 - 30 + 4
Perform the calculation on the right-hand side: 4 - 30 + 4 = -26 + 4 = -22. This is not equal to 124, so this statement is false.

3. 4 = 2 - 2 + 0
Perform the calculation on the right-hand side: 2 - 2 + 0 = 0 + 0 = 0. This is not equal to 4, so this statement is false.

4. 30 = 30 - 1 + 0
Perform the calculation on the right-hand side: 30 - 1 + 0 = 29 + 0 = 29. This is not equal to 30, so this statement is false.

5. 4 = 4 + 0 + 4
Perform the calculation on the right-hand side: 4 + 0 + 4 = 4 + 4 = 8. This is not equal to 4, so this statement is false.

6. 30 = 7.4 + 2
Perform the calculation on the right-hand side: 7.4 + 2 = 9.4. This is not equal to 30, so this statement is false.

None of the given statements are true.

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We can use the z-score associated with the 80th percentile to calculate the upper bound of the interval using the formula: sample mean + 0.84*(σ/√n).

To round the answer to at least two decimal places, we need to know the values of n and σ. Without that information, we can't provide a specific numerical answer.

To find the 80th percentile of the sample mean, we first need to calculate the sample mean and standard deviation. Let's assume we have a sample of size n and we know the population standard deviation σ.

Using the central limit theorem, we know that the sample mean follows a normal distribution with mean μ and standard deviation σ/√n. Since we don't know the population mean μ, we can use the sample mean as an estimate.

Next, we need to find the z-score associated with the 80th percentile. We can use a z-table or a calculator to find that z = 0.84.

Finally, we can use the formula for the confidence interval of the sample mean:

sample mean ± z*(standard deviation/√n)

Plugging in the values, we get:

sample mean ± 0.84*(σ/√n)

Since we're looking for the upper bound of the 80th percentile, we only need to consider the positive value of the interval:

sample mean + 0.84*(σ/√n)

This represents the value that separates the top 20% of sample means from the bottom 80%.

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