making an argument a linear system in three variables has no solution. your friend concludes that it is not possible for two of the three equations to have any points in common. is your friend correct? explain your reasoning.

The critical value of t for a 90% confidence interval with "df" degrees of freedom is:

1.81 (approximately).

To find the critical value of t for a 90% confidence interval with degrees of freedom (df), follow these steps:

Identify the degrees of freedom (df). In this case, you mentioned "df."

Determine the desired confidence level. Here, it's a 90% confidence interval.

Calculate the tail probabilities. Since it's a two-tailed test, you'll need to find the probability for each tail. A 90% confidence interval leaves 10% in the tails, so each tail has 5% or 0.05.

Use a t-distribution table or calculator to find the critical value corresponding to the given degrees of freedom (df) and tail probability (0.05).

For example, if the degrees of freedom (df) is 10, you would find the critical value of t by looking up the value in a t-distribution table or using a calculator. The critical value for a 90% confidence interval with 10 degrees of freedom is approximately 1.81.

So, the critical value of t for a 90% confidence interval with df degrees of freedom is approximately 1.81 (rounded to two decimal places).

The correct question should be :

Find the critical value of t for a 90% confidence interval with degrees of freedom (df).

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9,820 people in the town spend more than 2 hours a day on their smartphones.

To estimate the number of people in the town of 17,247 who spend more than 2 hours a day on their smartphones based on this survey, we can use the following formula:

estimated proportion ± margin of error = confidence interval

where the estimated proportion is the sample proportion (57%), the margin of error is given (2.2%), and the confidence interval is the range within which the true population proportion is likely to fall.

Using this formula, we can find the confidence interval:

= 57% ± 2.2%

= 0.57 ± 0.022

= (0.548, 0.592)

This means that we are 95% confident that the true population proportion of people in the town who spend more than 2 hours a day on their smartphones falls within the range of 0.548 to 0.592.

To estimate the number of people in the town who spend more than 2 hours a day on their smartphones, we can multiply this proportion by the total population of the town:

estimated number = estimated proportion x population

estimated number = 0.57 * 17,247 = 9,820.79

So, we can estimate that approximately 9,820 people in the town spend more than 2 hours a day on their smartphones.

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Jane is 33 years old and her daughter is 11 years old now.

Let's say Jane's age is "J" and her daughter's age is "D".

According to the problem, we know that J = 3D since Jane is three times as old as her daughter.

We also know that in 12 years, Jane's age will be one year less than twice her daughter's age. This can be represented as:

J + 12 = 2(D + 12) - 1

Now we can substitute J = 3D into this equation:

3D + 12 = 2(D + 12) - 1

Simplifying this equation, we get:

D = 11

So the daughter is 11 years old now. Using J = 3D, we can find that Jane is:

J = 3(11) = 33

Therefore, Jane is 33 years old and her daughter is 11 years old now.

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The area inside the curve r = 3 + sin(θ) is 4.5π square units.

To find the area inside the curve r = 3 + sin(θ), we can use double integrals in polar coordinates. The general formula for finding the area inside a polar curve is given by:

A = (1/2) ∫(θ2-θ1) ∫(r1^2)^(r2^2) r dr dθ

where θ1 and θ2 are the limits of integration for the angle θ, and r1 and r2 are the limits of integration for the radius r. In this case, since we want to find the area inside the curve r = 3 + sin(θ), we have r1 = 0 and r2 = 3 + sin(θ), and θ1 = 0 and θ2 = 2π (since we want to cover the full circle). Therefore, the double integral becomes:

A = (1/2) ∫(0)^(2π) ∫(0)^^(3+sinθ) r dr dθ

Evaluating the inner integral, we get:

∫(0)^^(3+sinθ) r dr = [1/2 r^2]_(0)^(3+sinθ) = 1/2 (9 + 6sinθ)

Substituting this into the double integral and evaluating the outer integral, we get:

A = (1/2) ∫(0)^(2π) 1/2 (9 + 6sinθ) dθ

= (1/4) (9(2π) + 6(∫(0)^(2π) sinθ dθ))

= (1/4) (18π) = 4.5π

Therefore, the area inside the curve r = 3 + sin(θ) is 4.5π square units.
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y-1=3/2(x+3) is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (-3, 1)

We have to find the slope of the line in the given graph

(2, 2) and (-2, -4) are the points

Slope = -4-2/-2-2

=-6/-4

=3/2

We know that the slope is same in parallel lines

Let us find the equation of the line passing through the point (-3, 1) in point slope form

y-1=3/2(x+3)

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Answer:

a)    1/11

b)    25/66

c)     41/66

Step-by-step explanation:

The following is the number of each type of can
Cola (C) = 6

Soda (S) =  5

Fizz  (F) = 1

Total number of cans = 12

Since the sampling is done without replacement, the probability will be different for different draws

Let P(C₁) = Probability of drawing a cola on first draw
P(C₁) = 6/12

P(C₂|C₁) = Probability of cola on second draw given that the first draw was a cola = 5/11  (11 total cans left for second draw and only 5 cans of cola)

The probabilities for the other two types of cans can be calculated in the same way
P(S₁) = 5/12
P(S₂|S₁) = 4/11

P(F₁) = 1/12
P(F₂|F₁) = 0/11 = 0  (since there is only one can of Fizz the probability of drawing a second can of Fizz is 0

a)

In two draws what is the probability that one can is C and other is F

There are two ways in which this can occur - C₁ F₂ and F₁C₂

So the combined probability = sum of these probabilities for both possibilities

P(one C and one F) = P(C₁F₂) + P(F₁ C₂)
P(C₁F₂) = P(C₁) · P(F₂|C₁) = 6/12 · 1/11 = 1/2  ·  1/11 = 1/22  

P(F₁C₂) = P(F₁) · P(C₂|F₁) = 1/12 · 6/11 = 1/12 · 6/11 = 1/22

So P(C₁F₂ or F₁C₂) = 1/22 + 1/22 = 2/22 = 1/11

b)
P(both cans having same contents).
This can be represented as

P(C₁C₂ or S₁S₂ or F₁F₂)
= P(C₁C₂) + P(S₁S₂) + P(F₁F₂)
= P(C₁) x P(C₂|C₁) + P(S₁) x P(S₂|S₁) + P(F₁) x P(F₂|F1)

= 6/12 x 5/11 + 5/12 x 4/11 + 1/12 x 0

= 50/132

= 25/66

c)

Probability that the two cans will differ is the complement of the event the the two cans have the same contents

P(complement of event E) = 1 - P(event E)

P(can contents differ) = 1 - P(can contents are the same)

= 1 - 25/66

= 41/66

I hope I got it right, please let me know .Thanks

The coordinates of the vertices of polygon L'M'N'P'Q'R' after dilation are (0, 0), (1.693, 2.257), (3.77, 2.257), (5.385, 0), (9.231, 0), and (21, 7).

To find the coordinates of the vertices of polygon LMNPQR after dilation, we need to know the scale factor of dilation. The scale factor is the ratio of the corresponding side lengths of the dilated and original polygons. Since we know the location of vertex Q', we can use the distance formula to find the length of Q'Q and then find the scale factor using the fact that LMNPQR and L'M'N'P'Q'R' are similar.

Let's call the center of dilation O. Since O is the origin, we can use the distance formula to find the length of Q'Q:

Q'Q = sqrt((21-12)^2 + (7-4)^2) = sqrt(109)

We know that LMNPQR and L'M'N'P'Q'R' are similar, so the scale factor is equal to the ratio of corresponding side lengths. Let the scale factor be k, then:

k = Q'Q/QP = sqrt(109)/10

Now we can use the scale factor to find the coordinates of the other vertices:

L' = (0, 0)

M' = (k(3), k(4))

N' = (k(7), k(4))

P' = (k(10), k(0))

R' = (k(15), k(0))

So the coordinates of the vertices of polygon L'M'N'P'Q'R' after dilation are (0, 0), (1.693, 2.257), (3.77, 2.257), (5.385, 0), (9.231, 0), and (21, 7).

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Then, the approximate sum S is:
S = round(SN, p)
Note that the rounding function rounds up if the next digit is 5 or greater and rounds down if it is 4 or less. Since the exact value of p is not provided, it's impossible to provide a specific numerical answer.

The given series is:
∑n=1∞ (−1)n * 7n / n * (10−4)
To determine the least number N such that |RN| is less than the given level of accuracy, we need to use the alternating series test. According to this test, the remainder RN of an alternating series is less than or equal to the absolute value of the first neglected term.
In this case, the first neglected term is:
a(N+1) = (−1)N+1 * 7N+1 / (N+1) * (10−4)
So, we need to find the value of N that satisfies the inequality:
|RN| ≤ a(N+1)
|RN| ≤ (−1)N+1 * 7N+1 / (N+1) * (10−4)
Let's assume that the desired level of accuracy is ε, then we have:
(−1)N+1 * 7N+1 / (N+1) * (10−4) ≤ ε
Simplifying this inequality, we get:
7N+1 / (N+1) ≤ ε * (10^4)
7N+1 ≤ ε * (N+1) * (10^4)
N ≥ (7/ε) * (10^4) - 1
Therefore, the least number N such that |RN| is less than the given level of accuracy is:
N = ceil((7/ε) * (10^4) - 1)
To approximate the sum S accurate to p decimal places, we need to evaluate the partial sum SN up to N terms and then round it to p decimal places. The partial sum SN is:
SN = ∑n=1N (−1)n * 7n / n * (10−4)
Then, the approximate sum S is:
S = round(SN, p)
Note that the rounding function rounds up if the next digit is 5 or greater and rounds down if it is 4 or less.
Since the exact value of p is not provided, it's impossible to provide a specific numerical answer. However, the above method can be followed to find the least value of N and approximate the sum S once the desired level of accuracy is given.

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The particular solution to the system of differential equations X’ = [ 2 3 ][ 2 1 ] which satisfies the initial conditions : Xp = [3e^(4t) - e^(-t); 2e^(4t) + e^(-t)]

To obtain the particular solution using the eigenvalue method, we first need to get the eigenvalues and eigenvectors of the coefficient matrix [2 3; 2 1].The characteristic equation is given by:

det([2 3; 2 1] - λ[I]) = 0

where λ is the eigenvalue and I is the identity matrix.Solving for λ, we get:

(2-λ)(1-λ) - 6 = 0

λ^2 - 3λ - 4 = 0

(λ-4)(λ+1) = 0

So, the eigenvalues are λ1 = 4 and λ2 = -1. To get the eigenvector corresponding to λ1, we need to solve the equation:

([2 3; 2 1] - 4[I])v1 = 0

where v1 is the eigenvector.Substituting the values, we get:

[-2 3; 2 -3][x1; x2] = [0; 0]

Solving the system of equations, we get:

-2x1 + 3x2 = 0

2x1 - 3x2 = 0

x1 = 3x2/2

So, the eigenvector corresponding to λ1 = 4 is [3/2; 1]. Similarly, to get the eigenvector corresponding to λ2, we need to solve the equation:

([2 3; 2 1] + 1[I])v2 = 0

where v2 is the eigenvector.Substituting the values, we get:

[3 3; 2 2][x1; x2] = [0; 0]

Solving the system of equations, we get:

3x1 + 3x2 = 0

2x1 + 2x2 = 0

x1 = -x2

So, the eigenvector corresponding to λ2 = -1 is [1; -1]. Now, we can write the general solution to the differential equation as:

X(t) = c1e^(4t)[3/2; 1] + c2e^(-t)[1; -1]

To get the particular solution that satisfies the initial conditions x(0) = [1; 2], we can substitute the values of t = 0 and x(0) into the general solution and solve for the constants c1 and c2.x(0) = c1*[3/2; 1] + c2*[1; -1]

[1; 2] = [3c1/2 + c2; c1 - c2]

Solving the system of equations, we get:

c1 = 2

c2 = -1/2

So, the particular solution is:

Xp = 2e^(4t)[3/2; 1] - (1/2)e^(-t)[1; -1]

Therefore, Xp = [3e^(4t) - e^(-t); 2e^(4t) + e^(-t)]

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The calculated value of the total population of the country is 8530000

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

3582600 is 42%. of the total population of the country

This means that

42%. of the total population of the country = 3582600

Express as product

So, we have

42% * the total population of the country = 3582600

Divide both sides by 42%

the total population of the country = 3582600 /42%

Evaluate

the total population of the country = 8530000

Hence, the total population of the country is 8530000

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There are 25 possible outcomes where we either get a blue die 3 or an even sum or both.

To solve this problem, we need to use the concept of probability. Probability is the likelihood of an event occurring, expressed as a number between 0 and 1. In this case, we want to find the probability of rolling either a blue die 3 or an even sum or both.

First, let's count the number of outcomes where the blue die is 3. There is only one way to get a 3 on the blue die, and the red die can be any number from 1 to 6. Therefore, there are 6 possible outcomes where the blue die is 3.

Next, let's count the number of outcomes where we get an even sum. There are three ways to get an even sum: (1,1), (2,2), and (3,3). For each of these outcomes, the blue die can be any number from 1 to 6. Therefore, there are 18 possible outcomes where we get an even sum.

Finally, let's count the number of outcomes where we get both a blue die 3 and an even sum. There is only one way to get a blue die 3 and an even sum: (3,3). Therefore, there is only one possible outcome where we get both a blue die 3 and an even sum.

To find the total number of outcomes that have either a blue die 3 or an even sum or both, we need to add the number of outcomes where the blue die is 3, the number of outcomes where we get an even sum, and the number of outcomes where we get both. This gives us:

6 + 18 + 1 = 25

Therefore, there are 25 possible outcomes where we either get a blue die 3 or an even sum or both.

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Step-by-step explanation:

64 = 2⁶

so,

log2(64) = 6

therefore,

4x = 6

x = 6/4 = 3/2 = 1.5

The expressions that represent the derivative of the function y = f(x) are:

- dy/dx

- f'(x)

- lim(h→0) [f(x+h) - f(x)]/h

- lim(h→0) [f(x) - f(x-h)]/h

So, the correct options are:

- dy/dx

- f'(x)

- lim(h→0) [f(x+h) - f(x)]/h

- lim(h→0) [f(x) - f(x-h)]/h

Option (C) and option (D) are the same expressions, just with a different notation.

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Therefore, according tot the given information:(a) sin(26°), (b) cos(70°), (c) cos(16θ).

(a) Using the Double-Angle Formula for sine, we get sin(26°)/2. Using the Double-Angle Formula for cosine, we get cos(26°)/2. Multiplying these together gives the simplified expression of cos(26°)sin(26°)/4.
(b) Using the Double-Angle Formula for cosine, we get cos(70°). Using the Double-Angle Formula for sine, we get sin(70°). Subtracting the squares of these gives the simplified expression of cos(140°).
(c) Using the Half-Angle Formula for cosine, we get cos(4°). Using the Half-Angle Formula for sine, we get sin(4°)/2. Subtracting the squares of these gives the simplified expression of cos(8°)/2.
(a) cos(26°)sin(26°)/4, (b) cos(140°), (c) cos(8°)/2.
(a) 2 sin(13°) cos(13°)
Using the Double-Angle Formula for sine: sin(2θ) = 2sin(θ)cos(θ), where θ = 13°.
So, sin(2 × 13°) = sin(26°).
(b) cos²(35°) - sin²(35°)
Using the Double-Angle Formula for cosine: cos(2θ) = cos²(θ) - sin²(θ), where θ = 35°.
So, cos(2 × 35°) = cos(70°).
(c) cos²(8?) - sin²(8?)
Assuming you meant to type "cos²(8θ) - sin²(8θ)", where θ represents an angle.
Using the Double-Angle Formula for cosine: cos(2θ) = cos²(θ) - sin²(θ).
So, cos(16θ) = cos²(8θ) - sin²(8θ)

Therefore, according tot the given information:(a) sin(26°), (b) cos(70°), (c) cos(16θ).

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Answer: The index of refraction for the unknown wavelength is approximately 1.355.

Step-by-step explanation:

We can use Snell's law to relate the incident angle and refracted angle to the indices of refraction:

n1 sinθ1 = n2 sinθ2

where n1 and θ1 are the index of refraction and incident angle of the light in air, and n2 and θ2 are the index of refraction and refracted angle of the light in glass. Since the incident angle is 45.00 degrees, we have:

sinθ1 = sin(45.00) = √2/2

Since we know the index of refraction for the 450.0 nm light is 1.482, we can solve for the refracted angle θ2:

1.000 * √2/2 = 1.482 * sinθ2

sinθ2 = 1.000 * √2/2 / 1.482 = 0.4951

θ2 = sin^(-1)(0.4951) = 29.07 degrees

Now, we can use Snell's law again to relate the index of refraction to the refracted angle for the unknown wavelength:

n1 sinθ1 = n3 sinθ3

where n3 is the index of refraction for the unknown wavelength, and θ3 is the refracted angle for the unknown wavelength. We know that θ3 is 0.8000 degrees greater than θ2:

θ3 = θ2 + 0.8000 = 29.87 degrees

Substituting all the known values into Snell's law, we get:

1.000 * √2/2 = n3 * sin(29.87)

n3 = 1.000 * √2/2 / sin(29.87) = 1.355

Therefore, the index of refraction for the unknown wavelength is approximately 1.355.

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There are probability of total of 5 x 6 = 30 ways to roll 4 dice with the same number and 1 die with a different number in this case.

To calculate the number of ways to roll 4 dice with the same number and 1 die with a different number, we need to consider two cases: the die with the different number can either be the first die or one of the other four.

If the die with the different number is the first die, then there are 6 choices for its value. The remaining 4 dice must all have the same value, which means there is only 1 choice for their value. Therefore, there is a total of 6 ways to roll 4 dice with the same number and 1 die with a different number in this case.

If one of the other four dice has a different number, then there are 5 choices for which die will have the different number. There are also 6 choices for the value of that die.  

The remaining 3 dice must all have the same value, which means there is only 1 choice for their value. Therefore, there are a total of 5 x 6 = 30 ways to roll 4 dice with the same number and 1 die with a different number in this case.

Adding up the two cases, we get a total of 6 + 30 = 36 ways to roll 5 dice with 4 dice having the same number and 1 die having a different number.

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The most accurate statement about the mean absolute deviation (MAD) is:

The MAD is a measure of the variability or spread of a set of data that is calculated by finding the average of the absolute deviations from the mean of the data.

Explanation:

The mean absolute deviation is a statistical measure that is used to calculate the average distance between each data point and the mean of the data set. It provides a measure of the variability or spread of the data set and is often used to compare the dispersion of different data sets.

To calculate the MAD, we first find the mean of the data set. Then, we find the absolute deviation of each data point from the mean, which is the distance between the data point and the mean, ignoring the sign. Finally, we calculate the average of the absolute deviations to get the MAD.

The MAD is a useful measure of variability because it is not affected by extreme values or outliers in the data set, unlike other measures of dispersion such as the variance or standard deviation.

Therefore, the most accurate statement about the MAD is that it is a measure of the variability or spread of a set of data that is calculated by finding the average of the absolute deviations from the mean of the data.

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The area and the circumference are explained below.

Given that are objects having shape of a circle we need to find area and the circumference of these objects,

So,

Circumference = π × diameter

Area = π × radius²

So,

1) The circumference of the dime =

= π × 2×8.95

= 3.14 × 17.9

= 56.21 mm

2) Area of the circle =

3.14 × 8 × 8 = 200.96 cm²

3) Area of the circle =

3.14 × 32 × 32 = 3215.36 mm²

4) The area of a semicircle is half of the area of the circle,

So, area of the desktop = 3.14 × 14 × 14 / 2 = 307.72 in²

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The probability of Ariana rolling a number between 1 and 6 (inclusive) with a standard six-sided die can be described as "certain" or "100%." This means that she is guaranteed to roll a number within the specified range.

When using a standard six-sided die, each face is numbered with a distinct integer from 1 to 6. The probability of rolling any specific number on a fair die is 1 out of 6, as there are six equally likely outcomes. Since Ariana is rolling a die with numbers between 1 and 6 (inclusive), she is guaranteed to obtain a number within that range. In other words, every possible outcome falls within the desired range. Therefore, the probability can be described as "certain" or "100%."

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Debido a que los amortiguadores, por ellos mismos, no son suficientes para absorber completamente los golpes provocados por las irregularidades del terreno, las suspensiones incorporan muelles interpuestos entre el eje y el chasis.

Los amortiguadores son elementos clave en los sistemas de suspensión de los vehículos, ya que absorben la energía generada por las irregularidades del terreno y evitan que las vibraciones lleguen al chasis y a la carrocería del vehículo. Sin embargo, los amortiguadores por sí solos no son suficientes para proporcionar una conducción suave y cómoda. Por esta razón, se incorporan muelles entre el eje y el chasis para ayudar a absorber los golpes y las vibraciones adicionales. Los muelles están diseñados para comprimirse y expandirse de manera controlada, lo que reduce la transferencia de energía al chasis del vehículo y mejora la estabilidad y el confort de la conducción.

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The equation of the variable y in terms of x is y = -2x + 16

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

(2, 12) and (6, 4)

A linear equation is represented as

y = mx + c

Substitute the given points in the above equation, so, we have the following representation

2m + c = 12

6m + c = 4

When the equations are subtracted, we have

-4m = 8

So, we have

m = -2

Next, we have

2(-2) + c = 12

Evaluate

c = 16

Recall that

y = mx + c

So, we have

y = -2x + 16

Hence, the variable y in terms of x is y = -2x + 16

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The statement "the algebraic and spreadsheet formulations of a linear programming model both have advantages" is true. (Option 3)

Both algebraic and spreadsheet formulations have their own advantages and disadvantages. Algebraic models allow for a more formal mathematical representation of the problem, making it easier to see relationships between variables and constraints. They also allow for the use of powerful optimization solvers to quickly find optimal solutions.

On the other hand, spreadsheet models allow for more intuitive modeling and visualization of the problem. They also allow for quick and easy scenario analysis and sensitivity testing. Furthermore, they are more accessible to a wider range of users who may not have the technical background to create and solve complex algebraic models.

Therefore, the choice between the two formulations depends on the specific problem and the preferences and expertise of the modeler.

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Complete Question:

which of the following statements about linear programming models is true? multiple choice question.

Answer:

BF = √(12^2 - 8^2) = √(144 - 64) = √80

= 4√5 = about 8.9 cm

A radical equation is an equation that contains a variable within a radical expression.

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The center of mass (x¯,y¯,z¯) of the homogeneous solid block is located at the geometric center of the block, which is (L/2, W/2, H/2).

To determine the center of mass (x¯,y¯,z¯) of a homogeneous solid block, we need to use the formula:

x¯ = (1/M) ∫∫∫ xρ(x,y,z) dV
y¯ = (1/M) ∫∫∫ yρ(x,y,z) dV
z¯ = (1/M) ∫∫∫ zρ(x,y,z) dV

where M is the mass of the block, ρ(x,y,z) is the density of the block at point (x,y,z), and dV is the volume element at point (x,y,z).

Since the solid block is homogeneous, the density is constant throughout the block, and we can simplify the above formula as:

x¯ = (1/M) ∫∫∫ x dV
y¯ = (1/M) ∫∫∫ y dV
z¯ = (1/M) ∫∫∫ z dV

We can further simplify this formula by using the fact that the solid block is a rectangular parallelepiped, and its volume is given by:

V = L x W x H

where L is the length, W is the width, and H is the height of the block.

Therefore, the mass of the block is given by:

M = ρ V = ρ LWH

Using these values, we can calculate the center of mass as:

x¯ = (1/M) ∫∫∫ x dV = (1/ρLWH) ∫∫∫ x dV = L/2
y¯ = (1/M) ∫∫∫ y dV = (1/ρLWH) ∫∫∫ y dV = W/2
z¯ = (1/M) ∫∫∫ z dV = (1/ρLWH) ∫∫∫ z dV = H/2

Therefore, the center of mass (x¯,y¯,z¯) of the homogeneous solid block is located at the geometric center of the block, which is (L/2, W/2, H/2).

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To be more precise, we can say that there exists an integer k (which is xy) such that cd = abk. This means that ab divides cd without leaving a remainder.

If a, b, c, and d are integers, where a ≠ 0, such that a ∣ c and b ∣ d, then ab ∣ cd.


To prove that ab ∣ cd, we need to show that there exists an integer k such that cd = abk.

Since a ∣ c, there exists an integer x such that c = ax.

Similarly, since b ∣ d, there exists an integer y such that d = by.

Substituting these values in cd = abk, we get axby = abk.

Dividing both sides by ab, we get xy = k.

Since xy is an integer, k is also an integer.

Therefore, we have shown that cd = abk, where k is an integer.

Hence, ab ∣ cd.



To understand why ab ∣ cd, we need to understand what it means for a ∣ c and b ∣ d.

When we say that a ∣ c, we mean that there exists an integer x such that c = ax. This essentially means that c is a multiple of a.

Similarly, when we say that b ∣ d, we mean that there exists an integer y such that d = by. This means that d is a multiple of b.

Now, let's consider ab. Since a ∣ c, we know that c = ax for some integer x. Similarly, since b ∣ d, we know that d = by for some integer y.

Multiplying these two equations, we get cd = (ax)(by) = ab(xy).

Now, we can see that ab ∣ cd because cd is a multiple of ab.

To be more precise, we can say that there exists an integer k (which is xy) such that cd = abk. This means that ab divides cd without leaving a remainder.

Therefore, we have proved that if a, b, c, and d are integers, where a ≠ 0, such that a ∣ c and b ∣ d, then ab ∣ cd.

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False. A fixed ratio schedule provides reinforcement for a response after a fixed number of responses, not based on a fixed time period.

A fixed ratio schedule provides reinforcement for a response only after a fixed number of responses have been made, not after a fixed time period has elapsed. In contrast, a fixed interval schedule provides reinforcement for a response after a fixed time period has elapsed.

Planning examples include support after certain responses have been submitted. The term flat rate is calculated using a fixed response. For example, if the rabbit were to get stronger when the force was pulled exactly five times, it would get stronger in time FR 5.

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Answer:

The diagram is omitted--please sketch it to confirm my answer.

Set your calculator to degree mode.

[tex] \tan( \alpha ) = \frac{110}{450} [/tex]

[tex] \alpha = {tan}^{ - 1} \frac{11}{45} = 13.74 \: degrees[/tex]

The angle of elevation is 13.74°.