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Does this graph represent a function?

To determine the minimum thickness of the iron, we need to calculate the diffusion flux of hydrogen through the iron and equate it to the maximum allowed hydrogen loss.

The diffusion flux (J) of hydrogen through a material can be calculated using Fick's first law of diffusion:

J = -D * (∆C/∆x)

Where:

J is the diffusion flux

D is the diffusion coefficient of hydrogen in iron

∆C is the difference in hydrogen concentration across the thickness (∆C = C1 - C2)

∆x is the thickness of the iron

We are given:

Maximum allowed hydrogen loss = 50 g/cm²/year

Temperature (T) = 400 °C (673 K)

Hydrogen concentration at surface 1 (C1) = 0.05 H atom per unit cell

Hydrogen concentration at surface 2 (C2) = 0.001 H atom per unit cell

First, we need to convert the hydrogen concentrations into a common unit. The atomic mass of hydrogen (H) is approximately 1 g/mol. The number of atoms in a unit cell for BCC iron is 2.

Concentration in g/cm³:

C1 = (0.05 H atom/unit cell) * (1 g/mol) / (2 atoms/unit cell) ≈ 0.025 g/cm³

C2 = (0.001 H atom/unit cell) * (1 g/mol) / (2 atoms/unit cell) ≈ 0.0005 g/cm³

Now, we can calculate the difference in hydrogen concentration across the thickness:

∆C = C1 - C2 = 0.025 g/cm³ - 0.0005 g/cm³ = 0.0245 g/cm³

Next, we need to determine the diffusion coefficient of hydrogen in iron at 400 °C. The diffusion coefficient can be estimated using the following equation:

D = D0 * exp(-Q/RT)

Where:

D0 is the pre-exponential factor

Q is the activation energy for diffusion

R is the gas constant (8.314 J/(mol·K))

T is the temperature in Kelvin

For hydrogen diffusion in iron, typical values are:

D0 = 5 x 10^-7 cm²/s

Q = 40,000 J/mol

Plugging in the values:

D = (5 x 10^-7 cm²/s) * exp(-40000 J/mol / (8.314 J/(mol·K) * 673 K))

D ≈ 2.70 x 10^-12 cm²/s

Now, we can substitute the values into Fick's first law of diffusion and solve for the thickness (∆x):

J = -D * (∆C/∆x)

Rearranging the equation:

∆x = -D * (∆C/J)

Substituting the given values:

∆x = -(2.70 x 10^-12 cm²/s) * (0.0245 g/cm³ / (50 g/cm²/year))

Converting the year unit to seconds:

∆x = -(2.70 x 10^-12 cm²/s) * (0.0245 g/cm³ / (50 g/cm²/year)) * (1 year / 3.1536 x 10^7 s)

Calculating:

∆x ≈ -0.000347 cm ≈ 3.47 μm

The negative sign indicates that the thickness (∆x) is measured in the opposite direction of the hydrogen diffusion. Thus, the minimum thickness of the iron required to limit the hydrogen loss to no more than 50 g per year through each square cent.

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Answer:

74 degrees and obtuse

Step-by-step explanation:

Answer:

Acute and 74 degrees

Step-by-step explanation:

thats entire side is 12

Step-by-step explanation:

you have to multiply i think im not good at it sorry

Answer:

0,-9,-8,3

Step-by-step explanation:

Domain

0

-9

-8

3

The answer is Regressive

Because is a tax applied uniformly

The correct statement regarding the triangles is given as follows:

Triangle ABC is similar to triangle A prime B prime C prime. because triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 4. and then rotating it about the origin by 180 degrees.

Similar triangles are triangles that share these two features presented as follows:

For this problem, we have that the transformations are given as follows:

The angle measures weren't changed, meaning that they are congruent, and thus the triangles are similar.

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Answer:

3

Step-by-step explanation:

Always include the steps and/or background required to get to the final answer. Let’s help other people understand and solve future problems on their own.

The probability of not getting a diamond card is \(\frac{3}{4}\) .

What is probability ?

 The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

The total number of outcomes of a deck of 52 cards are 52.

Since, there are 13 cards of diamond in a deck of 52 cards, therefore, the total number of favourable outcome that it is not a diamond is ,

=> 52-13= 39.

Therefore, probability P of not getting a diamond card is:

P= \(\frac{39}{52}\) = \(\frac{3}{4}\)

Hence, the probability of not getting a diamond card is \(\frac{3}{4}\) .

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The general Reynolds Transport Theorem (RTT) for conservation of momentum is expressed as:

dB = ΣF = dpdv + √p(v•n) dA (4.1) dt

The general Reynolds Transport Theorem (RTT) is a mathematical expression used in fluid mechanics to describe the conservation of momentum in a system. In this equation, dB represents the change in the extensive property Bsys, which is related to the momentum of a rigid body. ΣF represents the sum of forces acting on the system.

The right-hand side of the equation consists of two terms. The first term, dpdv, represents the rate of change of momentum within the control volume. It accounts for the change in momentum due to the net inflow or outflow of mass through the control surface.

The second term, √p(v•n) dA, represents the surface forces acting on the control volume. Here, p is the pressure, v is the velocity vector, n is the outward normal vector to the control surface, and dA is an elemental area on the control surface. This term captures the momentum flux across the control surface due to pressure forces.

The equation is valid for both steady and unsteady flows and provides a comprehensive representation of momentum conservation within a system.

The general Reynolds Transport Theorem (RTT) expressed by equation (4.1) represents the conservation of momentum in a system. It considers the change in momentum within the control volume and the surface forces acting on the control surface. Understanding and applying this theorem is essential in analyzing and predicting fluid flow behavior and its impact on momentum within a given system.

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The value of 5 ◊ 4 is 23.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

a ◊ b = 3a + 2b

So, a= 5 and b= 4

then, 5 ◊ 4

= 3(5)+ 2(4)

= 15 + 8

= 23

Hence, the value of 5 ◊ 4 is 23.

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Answer:

About .9332

Step-by-step

This tells us that the probability that a z value is less than or equal to 1.5 is about .9332. Thus, the shaded region is about 93.32% of the entire curve. Let's try another example.

Answer:

5

Step-by-step explanation:

Let the number of the kitchen clock sold =a

Let the number of the cuckoo clock sold =b

Let the number of the two-foot high grandfather clocks sold =c

The new saleswoman sold at least two of each of the three models.

Therefore:

\(a\geq 2\\b \geq 2\\c \geq 2\)

In all, she collected $300 from selling these models alone

17a+31b+61c=300

17(2)+31(2)+61(2)=218

300-218=82

Next, we try to express the remainder (82) in terms of 17, 31 and 61

82=17(3)+31

Therefore, she sold:

She sold 5 $17 clocks.

CHECK:

17(5)+31(3)+2(61)=$300

The amount you could save per month would be 25% of your discretionary money.

Discretionary income is the money you have left over after paying taxes and necessary cost-of-living expenses.

The formula for discretionary money is: Discretionary money = Realized income - Fixed expenses. Inputting data, we have: Discretionary money = $3,543.22 - Fixed expenses

Amount to be saved = 25% of discretionary money

Amount to be saved = 0.25 * (Realized income - Fixed expenses)

Therefore, the amount savable is calculated as 0.25 times the difference between your realized income and fixed expenses.

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The probability of winning at least once when playing the instant lottery twice is 0.19, or 19%.

To find the probability of winning at least once in the instant lottery when playing twice, we can use the complement rule.

The complement rule states that the probability of an event occurring (in this case, winning at least once) is equal to 1 minus the probability of the event not occurring (in this case, not winning both times).
Determine the probability of not winning in a single game, which is 1 - 0.1 = 0.9.
Calculate the probability of not winning both times, since outcomes are independent, by multiplying the probabilities of not winning each time: 0.9 * 0.9 = 0.81.
Finally, find the probability of winning at least once by subtracting the probability of not winning both times from 1: 1 - 0.81 = 0.19.

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Answer:

slope m = - 8

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y + 3 = - 8(x - 4) ← is in point- slope form

with slope m = - 8

The slope is :

Solution:

Given: \(\bf{y+3=-8(x-4)}\)

To determine the slope, it's important to know the form of the equation first.

There are 3 forms that you should be familiar with.

The three forms of equations of a straight line are:

This equation matches point slope perfectly.

The question becomes, how do you work with point slope to find slope?

In point slope, m is the slope and (x₁, y₁) is a point on the line.

Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.

The medical devices company must find data for at least 543 MRI machines.

To calculate the number of MRI machines needed for a 98% confidence interval with a margin of error of 0.20 hour, we need to use the formula:

n = [(z*σ)/E]²

where:

Substituting the values:

n = [(2.33*4)/0.20]²

n = 542.89

Rounding up to the nearest whole number, the medical devices company must find data for at least 543 MRI machines to have a margin of error of at most 0.20 hour when calculating a 98% confidence interval.

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The probability of getting the same number of heads on the first two tosses as on the second two tosses is 1/4.

The probability of getting the same number of heads on the first two tosses as on the second two tosses is 1/4. This is because there are only four possible outcomes of tossing a fair coin four times: HHHT, HTHH, THHH, and TTHT. Of these four outcomes, only one has the same number of heads on the first two tosses as on the second two tosses (HTHH). Therefore, the probability of this outcome occurring is 1/4. This can also be determined by considering the possible combinations of heads and tails. There are 16 possible combinations of heads and tails when tossing a coin four times, and four of those combinations are HTHH. This means that, out of the 16 possible combinations, 4 of them will have the same number of heads on the first two tosses as on the second two tosses, making the probability of this outcome 1/4.

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Answer:

-191

Step-by-step explanation:

Replace variables with corresponding value.

3(3) + (-5)^2 - ((3)(-5))^2

Solve exponent.

3(3) + 25 - 225

Multiply.

9 + 25 - 225

Combine like terms.

-191

The chi-square test for independence in a 2x2 contingency table is equivalent to comparing two proportions to determine if they are significantly different.

For a 2x2 contingency table, testing for independence with the chi-square test is the same as conducting a test comparing two proportions, specifically the two proportions of one variable (column) against the proportions of another variable (row).

1. Start with a 2x2 contingency table, which is a table that displays the counts or frequencies of two categorical variables. The table has two rows and two columns.

2. Calculate the marginal totals, which are the row and column totals. These represent the totals for each category of the variables.

3. Compute the expected frequencies under the assumption of independence. To do this, multiply the row total for each cell by the column total for the same cell, and divide by the total sample size.

4. Use the chi-square test statistic formula to calculate the chi-square value. This formula involves subtracting the expected frequency from the observed frequency for each cell, squaring the difference, dividing by the expected frequency, and summing up these values for all cells.

5. Determine the degrees of freedom for the chi-square test. In this case, it is (number of rows - 1) multiplied by (number of columns - 1), which is (2-1) x (2-1) = 1.

6. Compare the calculated chi-square value to the critical chi-square value from the chi-square distribution table at the desired significance level (e.g., 0.05).

7. If the calculated chi-square value is greater than the critical chi-square value, then the proportions of the two variables are significantly different, indicating dependence. If the calculated chi-square value is not greater, then the proportions are not significantly different, suggesting independence.

In summary, testing for independence with the chi-square test for a 2x2 contingency table is equivalent to conducting a test comparing two proportions, where the proportions represent the distribution of one variable against another.

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The magnitude, or absolute value, of a vector is a scalar quantity that represents the length of the vector. The magnitude of vector a is 3.

In this case, we are given vector a = <-2, 1, 2>. To find the magnitude of vector a, we can use the formula:

|a| = √(a₁² + a₂² + a₃²)

where a₁, a₂, and a₃ are the components of vector a. Plugging in the values from vector a, we have:

|a| = √((-2)² + 1² + 2²)

    = √(4 + 1 + 4)

    = √9

    = 3

Therefore, the magnitude of vector a is 3.

In the given vector a = <-2, 1, 2>, the components represent the distances in the x, y, and z directions respectively. To find the magnitude, we calculate the square root of the sum of the squares of these distances. In this case, it is √((-2)² + 1² + 2²) = √(4 + 1 + 4) = √9 = 3. The magnitude of vector a is 3, indicating that its length in three-dimensional space is 3 units. Magnitude is a scalar quantity and is always positive or zero. It provides information about the vector's magnitude without considering its direction.

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The volume of a pyramid with a square base is given as:

Volume = 1/3 x base area x height

The volume of the square base pyramid is 4000 cm³.

A pyramid is a structure where outer surfaces are triangular and converge to a point at the top.

The volume of a pyramid with a square base is given as:

Volume = 1/3 x base area x height

We have,

Pyramid:

Base square side = 20 cm

Height = 30 cm

The volume of the pyramid with a square base.

Volume = 1/3 x base area x height

Base area = side² = 20² = 400 cm²

Volume = 1/3 x 400 x 30 = 400 x 10 = 4000 cm³

Thus,

The volume of the square base pyramid is 4000 cm³.

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Answer:

1.25y=x

Step-by-step explanation:

If A (or y)=5 and B (or x)=4 then I think the equation will be 1.25y=x

I am sorry if I am wrong :(

But Hope this Helps ;)

Answer:

\(\huge \orange {\boxed {y = - \frac{5}{4}x + 5}} \)

Step-by-step explanation:

Line is intersecting x and y axes at the points (4, 0) & (0, 5)

So, y- intercept (b) = 5

\( Slope\: (m) = \frac {(5-0)}{(0-4)} = - \frac {5}{4} \)

Equation of line in slope intercept form is given as:

\( y = mx + b\)

Plugging the values of m and b in the above equation, we find:

\(\huge \purple {\boxed {y = - \frac{5}{4}x + 5}} \)

Answer:

\(area = \pi {r}^{2} \\ = 3.14 \times {(6)}^{2} \\ = 113.04 \: {miles}^{2} \)

Answer:

6^6 = 36

36 x 3.14 = 113.04 miles is your area.

Answer:

Step-by-step explanation:

I think y ≤ 3 - 3x

The critical value t for the given parameters is approximately 1.753.

To determine the critical value t for a 85% confidence interval with degrees of freedom (df) equal to 15, we can use a t-distribution table or a statistical software.

The critical value t depends on the desired confidence level and the degrees of freedom. In this case, with a confidence level of 85% and 15 degrees of freedom, we need to find the value from the t-distribution table.

Consulting a t-distribution table or using statistical software, the critical value t for a 85% confidence interval with 15 degrees of freedom is approximately 1.753 (rounded to three decimal places).

Therefore, the critical value t for the given parameters is approximately 1.753.

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Determine the critical value t for a 85% confidence interval with df=15.

The critical value t is: _____

(Provide your answer with 3 decimal places)

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

<95141404393>

a) The relationship between b and c is that c cannot be zero.

b) b can be any nonzero constant and c is equal to 2.5 in this case.

In two dimensions, the compatibility equations for strain are,0

∂εx/∂y + ∂γxy/∂x = 0

∂εy/∂x + ∂γxy/∂y = 0

where εx and εy are the normal strains in the x and y directions, respectively, and γxy is the shear strain.

Using the given strain field, we can calculate the strains,

εx = -4.5cx² + 10.5cy

εy = 1.5cx² - 7.5cy²

γxy = 1.5bxy

Taking partial derivatives and plugging them into the compatibility equations, we get,

⇒ -9cx + 0 = 0

⇒ 0 + (-15cy) = 0

These equations must be satisfied for the strain field to be compatible. From the first equation,

We get cx = 0, which means c cannot be zero.

From the second equation, we get cy = 0,

Which means b can be any nonzero constant.

For part b:

We are asked to find the displacements u and v corresponding to the given strain field at points (3, 7), assuming they are zero at point (0, 0) and using c = 2.5.

To find the displacement components,

We need to integrate the strains with respect to x and y. We get,

u = ∫∫εx dx dy = ∫(10.5cy) dy = 5.25cy²

v = ∫∫εy dx dy = ∫(1.5cx² ) dx - ∫(7.5cy²) dy = 0.5cx³ - 2.5cy³

Plugging in the values of c and b, we get,

u = 5.25(2.5)(7)²  = 767.62

v = 0.5(2.5)(3)³ - 2.5(7)³ = -8583.75

Therefore,

The displacements at points (3, 7) are u = 767.62 and v = -8583.75.

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On solving the provided question, by properties of parallel lines we got to know that -  1 - A  2 - C  3 - B  4 - D

When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.

Matches are -

1 - A

2 - C

3 - B

4 - D

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To calculate the probability of a woman who owns 19 houses having fire damage in 1 of them in a year, we need to use the binomial distribution formula.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials. In this case, the number of successes is the number of houses that will be damaged by fire, and the trials are the 19 houses that the woman owns.

The formula for the binomial distribution is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where X is the number of successes, n is the number of trials, p is the probability of success, and k is the number of successes we want to find. In this case, n=19, p=0.01 (since 10 houses out of 1000 are expected to be damaged by fire in a year), and we want to find the probability of k=1 success. Plugging in these values, we get P(X=1) = (19 choose 1) * 0.01^1 * 0.99^18 ≈ 0.17959. Therefore, the probability that a woman who owns 19 houses will have fire damage in 1 of them in a year is approximately 0.17959, rounded to five decimal places.

In summary, we used the binomial distribution formula to calculate the probability of a woman who owns 19 houses having fire damage in 1 of them in a year, given that records indicate that 10 houses out of 1000 are expected to be damaged by fire in any year. The result was approximately 0.17959, which is the probability that we were looking for.

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