Comparing Theater Sales
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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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The probability of drawing a red card, placing it back in the deck, and drawing another red card is 1/4.

According to the given question.

Total number of cards in a deck is 52.

As we know that total number of red cards in a well shuffled deck is 26.

Since, Eric first draws a red card, places it back in the deck, shuffles the deck, and then draws another card. Which means there is a replacement of cards.

So, the probability of drawing the first card is red = 26/52 = 1/2

And the probability of drawing the another card is red = 26/52 = 1/2

Therefore,

The probability of drawing a red card, placing it back in the deck, and drawing another red card

= 1/2  × 1/2

= 1/4

Hence, the probability of drawing a red card, placing it back in the deck, and drawing another red card is 1/4.

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Answer:

The drama club can purchase 1429 programs

Step-by-step explanation:

Answer:

it would be only one solution

Step-by-step explanation:

Using the concept of probability, we can infer that 15 students in a class of 25 are expected to be using smartphones to complete hw.

The ratio of favorable outcomes to all possible outcomes of an event is known as the probability. The number of favorable results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.

Probability(E) = Number of favorable outcomes/Total outcomes .

Given that, 4 out of 10 teenagers are not using smartphones for H.W.

To find out the number of students using smartphones in a class of 25 students:

4/10 = n/25

n = (4 × 25)/10

n = 100/10

n = 10

10 students will not be using smartphones.

Number of students who are using smartphone = 25-10

Number of students who are using smartphone = 15

Therefore, 15 students in a class of 25 are expected to be using smartphones to complete hw.

The complete question is "4 out of 10 teenagers surveyed say they are not using smartphones to help them complete hw assignments. assuming this survey is fairly accurate, how many students in a class of 25 would you expect to be using smartphones to complete hw?"

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Answer:

-3 + 8 = 5

Step-by-step explanation:

When we have a "minus a negative", it's a positive. So the - -8 is the same as + 8.

LMK if you have questions.

-3 + -8 = -11

is that a nice one or something

The combined value of the two accounts on January 1st, 2019, is approximately $31,642.05.

To solve this problem, we'll calculate the value of each investment separately and then combine them.

First, let's calculate the value of your great uncle's investment in treasury bills. The nominal rate of 1.95% compounded every 73 days can be converted to an effective rate per year using the formula:

Effective rate = (1 + (nominal rate / m)) ^ m - 1

Where "m" is the number of compounding periods per year. In this case, there are approximately 365 days in a year, so the number of compounding periods is:

m = 365 / 73 = 5

Effective rate = (1 + (0.0195 / 5)) ^ 5 - 1 = 0.0200

Now, let's calculate the value of the treasury bills investment after 2 years (from January 1st, 2017, to January 1st, 2019):

Value of treasury bills = $20,000 * (1 + 0.0200)^(2 * 365/73) = $20,000 * (1.0200)^(10) ≈ $20,825.40

Next, let's calculate the value of your mother's investment, which is compounding continuously at a rate of 4% per year:

Value of mother's investment = $10,000 * e^(0.04 * 2) ≈ $10,816.65

Finally, let's calculate the combined value of these two accounts:

Combined value = Value of treasury bills + Value of mother's investment

= $20,825.40 + $10,816.65 ≈ $31,642.05

Therefore, the combined value of the two accounts on January 1st, 2019, is approximately $31,642.05.

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Answer: 32 every month or day. if its every month the answer is 384, if its every day it would be 11680

Step-by-step explanation:

Given:

Find the amount of interest:

Find the balance after one year:

Answer: 6x + 2y

Step-by-step explanation:

Jamie should accept the second option to buy a new refrigerator for his apartment.

What is the Annual Interest?

The annual interest rate on an amount borrowed or a loan is the increment added to the loan at a particular rate over the desired period of time.

The objective of this question is to weigh the two options and determine the best means by which Jamie could get a new refrigerator for his apartment.

Option 1:

The annual interest rate for the first card = $1300 x 16.5%

The annual interest rate = $214.5

The monthly finance charge on a credit card can be estimated by finding the average daily balance using the Annual interest rate and the days of the billing cycle.

The monthly finance charge

= 1300 x 0.165/12

The monthly finance charge = $17.88

Now, The minimum monthly payment is 100 + 17.88

The minimum monthly payment for the first month = $117.88

In 12 months, Jamie would have paid off the loan with an additional interest of $214.5

Total amount paid = (117.88 x 12) + 247.5

= $1629.06

Option 2.

The appliance store offers an installment loan;

Using;

S.I. = PRT / 100

Since the loan must be paid in 12 equal payments; we can say the loan is paid monthly which is equivalent to 1 year.

i.e., Time(T) = 1 year

S.I. = 1300 x 12.5 x 1 / 100

The down payment = $300

In the total amount of $1300, Jamie has an outstanding amount of $1000 to pay.

Thus, In 12 equal payment times,

Jamie gets to pay = $1000/12

Jamie gets to pay = $ 83.33 each time .

Total amount paid = $162.5 + 1300

Total amount paid = $1462.5

Therefore, we can conclude that Jamie should accept the second option

to buy a new refrigerator for his apartment since the total amount paid in option 2 is lesser than that of option 1.

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2h – 2h = 28-6 —> 0 = 22

It cannot be solved because 2h -2h equals zero, so there is no h .

 The product of the complex numbers in trigonometric form computed as:

\(\(z_1 \cdot z_2 = r_1 r_2 (\cos(\theta_1 + \theta_2) + i \sin(\theta_1 + \theta_2))\)\)

To find the product of two complex numbers in trigonometric form, we can multiply their magnitudes and add their arguments. Let's denote the complex numbers as follows:

Number 1: \(\(z_1 = r_1(\cos \theta_1 + i \sin \theta_1)\)\)

Number 2: \(\(z_2 = r_2(\cos \theta_2 + i \sin \theta_2)\)\)

The product of these complex numbers can be computed as:

\(\(z_1 \cdot z_2 = r_1 r_2 (\cos(\theta_1 + \theta_2) + i \sin(\theta_1 + \theta_2))\)\)

In this form, \(\(r_1\) and \(r_2\)\) represent the magnitudes of the complex numbers, and \(\(\theta_1\) and \(\theta_2\)\) represent their arguments.

Please provide the values of the complex numbers you want to multiply, and I'll calculate their product in trigonometric form for you.

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Answer:

No, the ratios of the corresponding sides are not equal

Step-by-step explanation:

2in to 4in is multiply by 2

6 multiplied by 6 isn't 6

Answer:

100000 = 8 (4) ^t

Step-by-step explanation:

We are multiplying by 4 each time

y = a (4)^t

The initial amount is 8

y = 8 (4)^t

We want to get to 100000

100000 = 8 (4) ^t

Answer:

B

8 ⋅ 4^t  = 100,000

Step-by-step explanation:

Measuring length and width can determine if the center section is within specification. The given statement is insufficient to be determined as true or false as the statement doesn't specify the length and width of what is being measured.

Therefore, we can not provide the required answer without knowing the complete question. Hence, we need further information on the complete statement. In technical terms, specifications are a set of specifications and requirements that a product, materials, service, or system must meet. Specifications are developed to ensure that products, systems, or services are consistent, trustworthy, and meet the needs of the end-user. Therefore, specifications play a crucial role in ensuring the quality and reliability of a particular product or service. It also helps to determine whether a product or service meets the required safety and performance standards or not.

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We can conclude that there is a 90% chance that the true proportion of adult residents who are parents in this county lies within this interval

We are given that out of 600 residents sampled, 222 had kids. We need to estimate what percent of adult residents in a certain county are parents.

Let p be the proportion of adult residents in the county who are parents. We want to estimate this proportion with a 90% confidence interval.

The formula for the confidence interval is given by P ± z_{α/2} * √(P(1 - P)/n), where P is the sample proportion, n is the sample size, and z_{α/2} is the z-score such that P(Z > z_{α/2}) = α/2.

We are given that n = 600 and P = 222/600 = 0.37.

We need to find the value of z_{α/2} such that P(Z > z_{α/2}) = 0.05/2 = 0.025. Using a calculator, we find that z_{0.025} ≈ 1.96.

Substituting the given values into the formula, we get:

P ± z_{α/2} * √(P(1 - P)/n)

0.37 ± 1.96 * √(0.37(1 - 0.37)/600)

0.37 ± 0.0504

0.3166 ≤ p ≤ 0.4234

The 90% confidence interval for the proportion of adult residents who are parents in this county is approximately 0.3166 to 0.4234, rounded to 4 decimal places. Therefore, we can conclude that there is a 90% chance that the true proportion of adult residents who are parents in this county lies within this interval.

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MÎA or AÎM

the point where the angle is has to be in the middle, but for the other two letters, you can choose which one goes where

The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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The calculated number of people that can go kyacking is 6

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

Amount spent = $341

Parking = $30

Paddles = $45.20 per person

Represent the number of people with x

So, we have

Paddles = 45.2x

The above means that

Amount = 30 + 45.2x

So, we have

30 + 45.2x = 341

Subtract 30 from both sides

45.2x = 311

Divide both sides by 45.2

x = 6.88

So, we have

x = 6 (remove decimal)

Hence, the number of people that can go kyacking is 6

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Answer:

Hello! Your answer would be, C)

Step-by-step explanation:

Hope I helped! Ask me anything if you have more questions! Have a nice mourning! Brainiest plz! Hope you make an 100%! -Amelia♥

Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

Answer:

Add an "x" between "ninety" and "eight". Ninety x Eight = 720.

90 x 8 = 720

Answer:

True

Step-by-step explanation:

\( \sqrt{82} = 9.055 \approx9.1\)

[one decimal place]

The range of possible values for the third side of the triangle is d)6 < x < 26.

The third side of an acute triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides. By using the Pythagorean Theorem, we can find the range of possible values for the third side.

The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle equals the square of the hypotenuse. So, for this triangle, we have 10^2 + 16^2 = x^2.

Solve for x: x^2 = 256, so x = √256 = 16.

The third side must be shorter than the sum of the other two sides. So, the maximum value for x is 16 + 10 = 26.

The third side must be longer than the difference of the other two sides. So, the minimum value for x is 16 - 10 = 6.

Therefore, the range of possible values for the third side of the triangle is 6 < x < 26.

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An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.

Which best describes the range of possible values for the third side of the triangle?

x < 12.5, x > 18.9

12.5 < x < 18.9

x < 6, x > 26

6 < x < 26

The range of scores that Marjorie's can receive in the final exam to earn a C in the course is 67 to 82  .

in the question ,

it is given that

the Marjorie's score in the tests are 67 , 78 , 75 , 78 .

let the score in the final exam be "x"

it is given that the final exam score is worth 6 test scores , which means

the score in final exam is = 6x

and the total number of tests = 6+4 = 10

given that to get the grade C minimum average is = 70

that is  (67 + 78 + 75 + 78 + 6x)/10 = 70

67 + 78 + 75 + 78 + 6x = 700

298 + 6x = 700

6x = 700 - 298

6x = 402

x = 402/6

x = 67

given that to get the grade C maximum average is = 79

that is  (67 + 78 + 75 + 78 + 6x)/10 = 79

67 + 78 + 75 + 78 + 6x = 790

298 + 6x = 790

6x = 790 - 298

6x = 492

x = 492/6

x = 82

the range of scores is 67 to 82 .

Therefore , The range of scores that Marjorie's receive in the final exam to earn a C in the course is 67 to 82  .

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Answer:

20 2 3 6 10 998778889899999