Probability and statistics for engineers and scientists 9th

The center of mass of the rod of length L whose mass density changes from one end to the other quadratically is; X_cm =  ³/₄L(ρ₀ + ρ₀)/(2ρ₀ + ρ₁)

The formula for the center of mass of a body is defined as;

X_cm = (1/M) ∫r.dm

Where;

X_cm is the position of the center of mass

M is the total mass of the body

r is the position with respect to an origin

The density of a body is the relationship between two of its magnitudes that change constantly and so we have;

ρ = m/x

Applying small changes and we have;

ρ = dm / dx

dm = ρ*dx

We are given the expression;

ρ₀ = ρ₀ + (ρ₁ -ρ₀) (x/L)²

Thus;

dm = (ρ₀ + (ρ₁ -ρ₀) (x/L)²)dx

Since the whole system is on the x-axis, we integrate from the initial point x = 0 to the upper limit X = L. This gives;

X_cm =  M⁻¹  ∫ x  [ρ₀ + ( ρ₁-ρ₀) (x/L)²] dx

X_cm = M⁻¹  [∫ ρ₀ x dx + I (ρ₁-ρ₀) / L² x³ dx]

X_cm = M⁻¹  [ρ₀ x²/ + (ρ₁ -ρ₀) / L² x⁴/4]

X_cm = M⁻¹ [ρ₀/2 (L2-0) + (ρ₀₁ -ρ₀) /4L² (L⁴-0)

X_cm = M⁻¹ [ρ₀ L²/2 + (ρ₁ -ρ₀)/4  L²]

X_cm = M⁻¹ L² [ρ₀/4 + ρ₁/4]

X_cm = M⁻¹ L²/4 ( ρ₀ +ρ₁)

The only parameter that we don't know explicitly is the total mass, but we can look for their relationship using the concept of density.

M = ∫dm = ∫ρ.dx

M = ∫[ρ₀ + (ρ₁ -ρ₀)/L²x²] dx

We integrate between the limits of integration x = 0 and x = L to get;

M = ρ₀ x + (ρ₁ -ρ₀)/L² *x³/3

M = ρ₀ L + (ρ₁ -ρ₀)/3L²  L³

M = ρ₀ L + (ρ₁-ρ₀)/3  L

M = L(ρ₀ + ρ₁/3   -ρ₀/3)

M = L(2/3 ρ₀ + ρ₁/3)

M = ¹/₃L(2ρ₀ + ρ₁)

We will replace and simplify in the center of mass equation to get;

X_cm = ¹/₄L²[ρ₀ + ρ₁] / [L/3 (2ρ₀ + ρ₀)/L]

X_cm =  ³/₄L(ρ₀ + ρ₀)/(2ρ₀ + ρ₁)

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Answer:

an should be there isn't it

An expression for the Ksp for hydroxyapatite would be written as follows:

                            Ksp =   [tex][(Ca^{++})^5][OH^{-}][(PO_4)^3][/tex]

In Chemistry, the solubility product constant (Ksp)​ can be defined as the equilibrium constant that describes a solid substance (solute) which is being dissolved in an aqueous solution.

This ultimately implies that, Ksp is typically used in chemistry to denote an equilibrium level at which a solute dissolves in an aqueous solution.

Mathematically, an expression to represent the solubility product constant (Ksp)​ for hydroxyapatite is written as follows:

                               Ksp =   [tex][(Ca^{++})^5][OH^{-}][(PO_4)^3][/tex]

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the ans for this is true as it i the only internal struggle

The expression "i did not have strange dreams." validates the statements below "I did not eat spicy foods" and "there is no thunder while I sleep"

In this exercise, the person gave three logical statements which are

Now since the person did not have/ experience strange dream, this proves that the person did not eat spicy food and there was not thunder while the person was asleep.

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Answer:

quizlet/494283439

Explanation:

I used this for my test not sure if im too late or not but here it for future students

Also the quizlet is wrong on a few questions (im not sure if its like this for everyone but it was like this for me):

6. B.292.3 meters

7. B.154 ft

8. D.912 meters

9. A.307 feet

Again these were the correct answers for me not sure if its the same for everyone they might have changed it.

(Also, I'm not sure about 11-15 bc my teacher said i didnt have to do those ones) Hope this helps :))

The mortgage process is known to be a very complicated on but its involves:

When one has submitted papers for a mortgage, The lender will have to review your application and documentation and see if one qualifies.

They often check the property through the act of lender's valuation. and by the reviewing of your application and the result of the valuation, they will make final decision regarding if they will give you or not.

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A statistical inference is a process through which a researcher or analyst makes inferences about a population based on the statistics calculated from the sample.

The purpose of statistical inferences are:

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Geometric Series is known to be the exact sum of the terms of a geometric sequence. Its practice work example is given below:

This is known to be the terms that exist  between two nonconsecutive terms that belongs to a geometric sequence.

The Method to used in the above question is Geometric sequence.

The Rule of geometric sequence is that f (n)arⁿ⁻¹

Where A  =  the first term,

r = the  common ratio

Therefore, r = -6 ÷ -3 = 2n

f (n) = -3. 2ⁿ⁻¹

Then you change the term n with 9

f (9) = 3.2⁹⁻¹

= -768

Therefore, the the stated term is 768.

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It is useful to have a bank account and routing numbers when using tax preparation software so as to indicate where tax refunds should be sent.

A tax preparation software can be defined as a type of computer software that is designed and developed to assist individuals when they are filing their taxes, tax returns and bank account preparations.

Basically, it is very useful and important for individuals to have a bank account and routing numbers when using tax preparation software because it would help them to indicate where tax refunds should be sent.

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The kinetic energy of the two-block system with the given masses before the collision is determined as ³/₂Mvs².

The kinetic energy of the blocks before the collision is calculated as follows;

For a negligible friction effect, the kinetic energy of the two - block system after the collision is equal to the kinetic energy before the collision.

K.E(initial) = K.E(after)

K(after) = ¹/₂(m₁ + m₂)vs²

K(after) = ¹/₂(m + 2m)vs²

K(after) = ¹/₂(3m)vs²

[tex]K.E(after) = \frac{3}{2} Mv_s^2[/tex]

Thus, the kinetic energy of the two-block system with the given masses before the collision is determined as ³/₂Mvs².

The complete question is below:

block x of mass m slides across a horizontal surface where friction is negligible. block x collides with block y of mass 2m that is initially at rest, as shown in figure 1. after the collision, both blocks slide together with a speed vs , as shown in figure 2.

What is the kinetic energy of the two-block system before the collision?

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The forms of each of the matrices depicts how the row and column elements of the matrices are arranged

The matrix A is given as:

[tex]\left[\begin{array}{cccc}4&11&2\\0&-5&8\\0&0&-2\end{array}\right]\left[\begin{array}{c}-6&7&3\end{array}\right][/tex]

The elements on the leading diagonals are: 4, -5 and -2

The elements under the leading diagonals are 0, 0 and 0

When the elements under the leading diagonals are 0, then the augmented matrix is row echelon form

The matrix B is given as:

[tex]\left[\begin{array}{cccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\left[\begin{array}{c}-6&3&3\end{array}\right][/tex]

The elements on the leading diagonals are: 1, 1 and 1

All other elements in the matrix are 0's

When the elements on the leading diagonals are 1's, and other elements are 0's, then the augmented matrix is reduced row echelon form

The matrix C is given as:

[tex]\left[\begin{array}{cccc}1&0&3\\0&6&0\\7&0&1\end{array}\right]\left[\begin{array}{c}-6&8&13\end{array}\right][/tex]

The above matrix is neither in row echelon form nor in reduced row echelon form, because it does not satisfies the condition of both forms of matrices

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Answer:

in picture below that I got from edg 23 precalc

Explanation:

The Gibbs free energy ΔG for the vaporisation of 2-methylbutane, in KJ/mol is 8.24 KJ/mol

The Gibbs free energy for the reaction can be obtained as follow:

ΔG = ΔH – TΔS

ΔG = 25.22 – (201 × 8.448×10¯²)

ΔG = 25.22 – 169.8048

ΔG = 8.24 KJ/mol

Thus, the ΔG for the reaction is 8.24 KJ/mol

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The angular speed simply describes the way that things turn which is described in units such as revolutions per minutes, degree per seconds, etc.

Your information is incomplete as the diagram isn't provided. Therefore, an overview will be given.

It should be noted that angular speed simply means the measure of how fast the central angle of the rotating body changes with respect to time.

The angular speed is simply calculated by multiplying the angle of rotation and the time taken to complete the rotation.

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An example of parallel and perpendicular lines are the steps walk of a straight ladder, the opposite sides of a rectangle.

When there are two non vertical lines that are in found to be in the same plane such as the same slope, then a person can say that the lines are parallel.

But when two non-vertical lines in that are same to be of the same plane intersect at a right angle one can therefore say that they are perpendicular lines.

An example is "write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the given equation". The equation that fits the graph (attached) is y = 2x + 1.

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The probability both balls are black, given that the first one is black, is gotten as;  ⁵/₁₂

By using the probability of an event formula,

There are 5 black balls out of a total of 12 balls, so the probability of obtaining a black on a single draw is ⁵/₁₂, and the probability of obtaining a white is ⁷/₁₂



Since the balls are drawn with replacement, the two draws are independent events.

Use Multiplication and Union Rules to obtain the following probability:

P(F) = P(B, B) + P(B, W)

P(F) = (⁵/₁₂ * ⁵/₁₂) + (⁵/₁₂ * ⁷/₁₂)

P(F) =  ⁵/₁₂

Thus, the probability both balls are black, given that the first one is black, is  ⁵/₁₂

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These are the complete sentences using the preterite tense:

In this exercise, the sentences are conjugated in the preterite tense.

The Spanish preterite tense ("pretérito perfecto simple" in Spanish) is used to talk about actions completed at some point in the past.

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Answer:

Oaxaca

Explanation:

Oaxaca de Juárez is one of the most important destinations in Mexico

My impressions of the characters from the story in his steps are :

Impression connote the views or opinions one has concerning a person.

Based on the text, The impressions of the Rachel character is known to be that she has a strong character. Rachel primary characteristics is that she is in her 20's and a beautiful singer at her Church.

Jasper on the other hand is quite a young writer that was in love with Rachel and He also proposed  marriage to her.

See full question below

What are your impressions of the following character? Is she a strong or weak character? (from the story in his steps)

Rachel

What are her primary characteristics?

What are your impressions of the following character? Is he a strong or weak character?

Jasper

What are his primary characteristics?

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Answer:

-74 is -144

Explanation:

Hope it helps <3

Answer:

-74 is -144

Explanation:

hope it help

Answer:

forces the gun back in the opposite direction

Explanation:

Newton's Third law of Motion describes that when you shoot a gun, the action of the bullet firing out of the gun in one direction forces the gun back in the opposite direction because of the power of the bullet.

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                           hello here is your answer!

juice~

The wavelength of the sound wave if the frequency is increased to the given value is 0.44m.

Wavelength is simply the distance over which the shapes of waves are repeated. It is the spatial period of a periodic wave.

It is expressed as;

[tex]\lambda = \frac{v}{f}[/tex]

Where v is velocity and f is frequency.

Given the data in the question;

Speed of sound wave; [tex]v =\ ?[/tex]

Wavelength of sound wave b; [tex]\lambda _b = ?[/tex]

First, we calculate the velocity of the sound wave in air from sound wave a.

[tex]\lambda = \frac{v}{f}\\ \\1.76m= \frac{v}{196s^{-1}}\\\\v = 1.76m * 196s^{-1}\\\\v = 344.96m/s[/tex]

Now, we determine the wavelength of sound wave b using the velocity of sound wave in air calculated above.

[tex]\lambda = \frac{v}{f}\\ \\\lambda = \frac{344.96m/s}{784s^{-1}}\\\\\lambda = 0.44m[/tex]

Therefore, the wavelength of the sound wave if the frequency is increased to the given value is 0.44m.

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Answer:

It decreases by 1.32 meters.

Explanation:

The other person was wrong.

Answer: If a linear system has no solution, the two lines are parallel. If it has one solution, the lines will intersect at exactly one point because they have different slopes.

The pH of the solution is 10.74. the pH refers to the hydrogen ion concentration. It is a measure of the acidity of the solution.

pH is the degree of acidity or alkalinity of a solution.

The equation of the reaction is;

KOH + HBrO ==> KBrO + H2O

The number if moles of KOH =20.0 ml x 1 L / 1000 ml x 0.150 mol/L = 0.003 moles KOH

The number of moles of HBrO = 20.0 ml x 1 L / 1000 ml x 0.300 mol/L = 0.006 moles HBrO

Since the reaction is 1:2;

[BrO-] = 0.003 mols / 0.04L = 0.075M

Now the pH, is obtained from;

KBrO + H2O ==> KOH + HBrO

BrO- + H2O ==> HBrO + OH-  

Kb of BrO- = 1x10-14 / 2.5x10-9 = 4x10-6

Kb = 4x10-6 = [HBrO][OH-] / [BrO-]

From the ICE table;

4x10^-6 = (x)^2 / 0.075

x = 5.48x10-4 M = [OH-]

pOH = -log 5.48x10-4 M = 3.26

pH = 14 - pOH

pH = 10.74

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Answer:

1. 1906 2. San Francisco

False, frozen water is denser than liquid water and does not allow lake organisms to survive water.

By definition, density is the mass per unit volume of a substance, a property which is characteristic to each substance.

By convention, solid state of a substance are said to be denser than liquid state of the same substance. Hence, it follows that frozen water is denser than liquid water and does not allow lake organisms to survive.

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Answer:

True

Explanation:

I took the quiz

The building of a hacker rank is one that cost a lot of money and as such the minimum cost is  4.

The minimum cost is the lowest cost that is needed to complete a building.  It depends on:

When one is given input such as : [[1,2,3],[1,2,3],[3,3,1]] (the values in column stands for the cost of materials)

The output : 4

So you have to:

Select  material-1 of cost 1 in first house(row)

Select  material-2 of cost 2 in second house(row)

Select   material-3 of cost 1 in third house (row)

total = 1+2+1 -> 4

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Answer:

By multiplying it with each others

Answer:

multiply

Explanation: