Consider a market in which two firms are engage in quantity competition a la Cournot, but with differentiated products. As in the standard model each firm = 1,2 has a cost function TC(q) F+cq;. However, now each firm may recieve a different price for it's output.
In particular, firm 1 recieves the price Pa-bq-d q₂ and firm 2 recieves the price
dP (a) Use the fact that MR1 P+ to find an expression for MR in terms of a, b, d, qi and 42.
(b) Use your answer from part (a) to find firm 1's reaction function.
(c) Find a simplified expression for each firm's equilibrium output, q
(d) Find each firm's equilibrium price, P. Use your expression for P to find a simplified expression for Pc, the firms markup over marginal cost.

The torque required to cause a shearing stress of 40 MPa in the thin-walled tube is approximately 25.13 Nm. To calculate the torque, we need to consider the shearing stress acting on the wall of the semi-circular tube.

The shearing stress can be calculated using the formula:

τ = (T * r) / (J * t)

Where:

τ = Shearing stress

T = Torque

r = Mean radius of the tube (half the diameter)

J = Polar moment of inertia of the tube cross-section

t = Wall thickness

Since the stress concentration at the corners is neglected, we can consider the tube as a thin-walled circular tube. The polar moment of inertia for a thin-walled circular tube is given by:

J = (π * (D^4 - d^4)) / 32

Where:

D = Outer diameter of the tube

d = Inner diameter of the tube

Given:

Mean diameter (D) = 50 mm

Wall thickness (t) = 6 mm

Shearing stress (τ) = 40 MPa

calculating  the inner diameter:

d = D - 2t = 50 mm - 2 * 6 mm = 38 mm

Next, we can calculate the mean radius:

r = D / 2 = 50 mm / 2 = 25 mm

the polar moment of inertia:

J = (π * (D^4 - d^4)) / 32 = (π * ((50 mm)^4 - (38 mm)^4)) / 32 ≈ 2.43e7 mm^4

Finally, rearranging the shearing stress formula to solve for torque: T = (τ * J * t) / r = (40 MPa * 2.43e7 mm^4 * 6 mm) / 25 mm ≈ 25.13 Nm . The torque required to cause a shearing stress of 40 MPa in the thin-walled tube is approximately 25.13 Nm.

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The measure of the missing side length of the right triangle is approximately 32.1.

The figure in the image is a right triangle.

From the image:

Angle θ = 0.646 rad

Opposite to angle θ = 19.3

Hypotenuse =?

To solve for the missing side length, we use the trigonometric ratio.

Note that: sine = opposite / hypotensue

Plug the given values into the above formula and solve for the hypotenuse.

sin( θ ) = opposite / hypotenuse

sin( 0.646 rad  ) = 19.3 / hypotenuse

Hypotenuse = 19.3 / sin( 0.646 rad  )

Hypotenuse = 32.1

Therefore, the hypotenuse measures 32.1 units.

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The maximum Total Vertical Uncertainty allowed for an IHO Special Order Multibeam Echo Sounder (MBES) survey in 15m of water is 0.08 + 0.015h, where h is the depth of the water in meters.

The International Hydrographic Organization (IHO) sets standards for hydrographic surveys. The total vertical uncertainty (TVU) is one of these requirements. It determines the maximum acceptable margin of error for the depth measurements, which are a crucial component of hydrographic surveying.

The maximum total vertical uncertainty allowed for an IHO Special Order Multibeam Echo Sounder (MBES) survey in 15m of water is 0.08 + 0.015h, where h is the depth of the water in meters. The formula for total vertical uncertainty is expressed as:

TVU = 0.08 + 0.015h

Where:

TVU = Total Vertical Uncertainty

h = Depth of the water in meters

The maximum TVU allowed varies based on the depth of the water. The formula indicates that the TVU rises as the water depth increases.

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Answer:

[tex]x = 5\sqrt3[/tex]

Step-by-step explanation:

We can solve for x in this right triangle by using the ratio of the sides in a 30-60-90 triangle:

We can identify the longest side, or hypotenuse (which corresponds to 2 in the ratio), as 10. We can also see that the second largest side (√3 in the ratio) is x.

Therefore, to solve for x, we can multiply 10 by [tex]\dfrac{\sqrt3}{2}[/tex] because that is the number which gets 2 to [tex]\sqrt3[/tex]:

[tex]\not2 \cdot \dfrac{\sqrt3}{\not2} = \sqrt3[/tex]

[tex]x = 10 \cdot \dfrac{\sqrt3}{2}[/tex]

[tex]\boxed{x = 5\sqrt3}[/tex]

The fraction of an inch that would equal this is 1/3 inches.

Building codes usually specify that deflection (bending downward at the center) in a floor joist for residential buildings should not exceed 1/360 of the span under normal loads.

What fraction of an inch would this equal for a span of 10'-0"?

The maximum allowable deflection for a floor joist is defined in the building codes as 1/360 of the span under normal loads.

A 10'-0" span is given in the problem.

1/360 of a 10'-0" span will be calculated below.

We know that 1/360 = x/120.

The cross-multiply method will be used to solve the equation.

360x = 120x 1 = 3x x = 1/3 inches is the answer.

Therefore, the fraction of an inch that would equal this is 1/3 inches.

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Using standard heats of formation,the standard enthalpy change for the given reaction is -124.5 kJ/mol.

The standard enthalpy change for the reaction NH4NO3(aq) → N2O(g) + 2H2O(l) can be calculated using the standard heats of formation.

First, we need to identify the standard heats of formation for each compound involved in the reaction. The standard heat of formation (ΔHf°) is the enthalpy change that occurs when one mole of a compound is formed from its elements in their standard states at a given temperature and pressure.

The standard heats of formation for NH4NO3(aq), N2O(g), and H2O(l) are as follows:
- NH4NO3(aq): -365.5 kJ/mol
- N2O(g): 81.6 kJ/mol
- H2O(l): -285.8 kJ/mol

Next, we need to determine the stoichiometric coefficients of the compounds in the balanced equation. From the equation, we can see that 1 mole of NH4NO3(aq) produces 1 mole of N2O(g) and 2 moles of H2O(l).

Now, we can calculate the standard enthalpy change using the formula:
ΔH = Σ(nΔHf° products) - Σ(mΔHf° reactants)

Plugging in the values, we have:
ΔH = (1 mol × 81.6 kJ/mol) + (2 mol × -285.8 kJ/mol) - (1 mol × -365.5 kJ/mol)
   = 81.6 kJ/mol - 571.6 kJ/mol + 365.5 kJ/mol
   = -124.5 kJ/mol

Therefore, the standard enthalpy change for the given reaction is -124.5 kJ/mol.

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The commons in the tragedy of the commons situation described is the ground outside the university classroom building where smokers throw their cigarette butts instead of using proper receptacles.

This leads to the need for maintenance staff to clean up the area. The insufficient funds then prevent the classrooms in the building from being equipped with whiteboard markers and erasers. Therefore, option A, the ground outside the building, represents the commons in this scenario.

In the case of the woodlot shared by four families, the sustainable production is 300 mature mushrooms per month, each valued at $2. However, if more mushrooms are harvested, only immature mushrooms are available, and their value is determined by the formula $21,300 divided by the total number of mushrooms harvested. One family has been secretly taking 85 mushrooms per month for several months. To determine the value of their harvest, we need to calculate the total number of mushrooms they took and then substitute it into the value formula. Assuming they took 85 mushrooms per month for a certain number of months, we can multiply 85 by the number of months to obtain the total number of mushrooms taken. Let's say they took 85 mushrooms for 5 months, then the total number of mushrooms taken would be 85 × 5 = 425. Substituting this value into the formula, we get $21,300/425 = $50. Therefore, the value of their harvest would be $50.

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The triangle is an equilateral triangle and it is an acute triangle

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

The triangle

From the figure, we can see that

The three lengths of triangle are congruent

This means that the triangle is an equilateral triangle

Also, we can see that

All angles in the triangle are less than 90

This means that the triangle is an acute triangle

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(a) The average cost of producing 1,000 smart phones is $1,606.
(b) Rounded to two decimal places, the average value of the cost function C(x) over the interval from 0 to 1,000 is $435,333.33.

The cost function for producing x smart phones is given by C(x) = x^2 + 600x + 6000.

(a) To find the average cost of producing 1,000 smart phones, we need to divide the total cost by the number of smart phones produced.

Plugging in x = 1,000 into the cost function C(x), we get C(1,000) = 1,000^2 + 600(1,000) + 6,000.

Evaluating this expression, we find that C(1,000) = 1,000,000 + 600,000 + 6,000 = 1,606,000.

To find the average cost, we divide this total cost by the number of smart phones produced:

Average cost = Total cost / Number of smart phones

                       = 1,606,000 / 1,000

                       = $1,606.

Therefore, the average cost of producing 1,000 smart phones is $1,606.

(b) To find the average value of the cost function C(x) over the interval from 0 to 1,000, we need to find the average cost per smart phone produced in this interval.

We can use the formula for average value, which is the integral of the function divided by the length of the interval:

Average value = (1 / length of interval) * ∫(0 to 1,000) C(x) dx.

The length of the interval is 1,000 - 0 = 1,000.

Now, let's find the integral of C(x) from 0 to 1,000:

∫(0 to 1,000) C(x) dx = ∫(0 to 1,000) (x^2 + 600x + 6,000) dx.

Evaluating this integral, we get:

= [tex][(1/3)x^3 + 300x^2 + 6,000x][/tex] evaluated from 0 to 1,000.

= [tex][(1/3)(1,000)^3 + 300(1,000)^2 + 6,000(1,000)] - [(1/3)(0)^3 + 300(0)^2 + 6,000(0)].[/tex]

Simplifying further, we find:

= (1/3)(1,000,000,000 + 300,000,000 + 6,000,000) - 0.

= (1/3)(1,306,000,000)

= 435,333,333.33.

Now, we can find the average value of the cost function:

Average value = (1 / length of interval) * ∫(0 to 1,000) C(x) dx = (1 / 1,000) * 435,333,333.33.

= 435,333.33.

Rounded to two decimal places, the average value of the cost function C(x) over the interval from 0 to 1,000 is $435,333.33.

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Answer:15%

Step-by-step explanation:

i used my brain

Answer: death if you get covid 19 in cotabato you will have ti see a doctor and the ramifications are sneesing coughing and throwing up and loss of sleep

Step-by-step explanation:

Answer:(2x+3)(2x+3)

Step-by-step explanation:

Question will be like this Factorize the following polynomial.

4x[tex]{2}[/tex] +12x +9

4x[tex]2[/tex] +6x+6x+9

⇒2x(2x+3)+3(2x+3)

⇒(2x+3)(2x+3)

The molarity after dilution is approximately 0.02016 M

To find the resulting molarity (M) after dilution, we can use the equation:

M₁V₁ = M₂V₂

Where:

M₁ = initial molarity

V₁ = initial volume

M₂ = resulting molarity

V₂ = resulting volume

In this case:

M₁ = 0.224 M

V₁ = 0.90 mL = 0.90 cm³

M₂ = ?

V₂ = 10.00 mL = 10.00 cm³

Plugging in the values into the equation, we get:

(0.224 M)(0.90 cm³) = (M₂)(10.00 cm³)

Rearranging the equation to solve for M₂:

M₂ = (0.224 M)(0.90 cm³) / (10.00 cm³)

Calculating the value, we find:

M₂ = 0.02016 M

Therefore, the resulting molarity after dilution is approximately 0.02016 M.

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The molarity of the solution containing 2.746 g of KBr dissolved in enough water to make 561 mL is 4.11 x 10^-2 mol/L.Hence, option (c) is correct.

Molarity is defined as the amount of solute dissolved in 1 liter of the solution. It is denoted as M and measured in mol/L. Given data: Mass of KBr = 2.746 g

Volume of water = Enough to make 561 mL or 0.561 LK

Br: MW = 119.002 g/mol The molarity of the solution can be calculated using the formula:

M = \frac{n}{V}

where n = number of moles of KBr,

V = volume of the solution in liters.

Substitute the given data in the formula: Molarity, M = number of moles of KBr/Volume of the solution Molar mass of KBr (MW) = 119.002 g/mol Number of moles of KB

r = Mass of KBr/M

W= 2.746 g/119.002 g/mol

= 0.02306 mol

Volume of the solution = 0.561 L Substitute the above values in the formula:

Molarity, M = 0.02306 mol/0.561

L= 0.0411 mol/L

Therefore, the molarity of the solution is 4.11 x 10^-2 mol/L.

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1. To determine the optimal number of boxes to make using the Single Period Inventory Excel template in MindTap, we need to consider the costs and revenues associated with producing and selling the boxes.

- The cost per box, including material and labor, is $13.
- The selling price per box before Valentine's Day is $28.
- After Valentine's Day, the price is reduced to $12.
- Suzie has historically sold between 55 and 100 boxes.

To find the optimal number of boxes to make, we can use the Single Period Inventory Excel template in MindTap. This template takes into account the costs and revenues and helps us determine the quantity that maximizes profit.

2. If Suzie can only sell all remaining boxes at a price of $4, her decision would change because the selling price is significantly lower. This means that the revenue generated from selling the remaining boxes would be lower, affecting the overall profit.

In this case, Suzie would need to consider whether it is still profitable to produce the same number of boxes or if she should produce a smaller quantity. By using the Single Period Inventory Excel template in MindTap with the new selling price of $4, she can calculate the optimal number of boxes to make.

It's important to note that the optimal number of boxes may change based on the selling price, as it directly affects the revenue generated. Suzie should carefully evaluate the costs and revenues associated with different scenarios to make an informed decision.

Overall, the Single Period Inventory Excel template in MindTap is a useful tool for determining the optimal number of boxes to make, taking into account the costs, revenues, and various scenarios.

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Ionization energy refers to the amount of energy required to remove an electron from a neutral atom, creating a positively charged ion.

The ionization energy increases from left to right and from the bottom to the top of the periodic table.

The ionization energy is the amount of energy required to remove the most loosely held electron from a neutral gaseous atom, to form a positively charged ion. The amount of energy required is measured in kJ/mol.

The more energy required, the more difficult it is to remove the electron, thus the higher the ionization energy value.The first ionization energy increases as we move from left to right across a period because the number of protons increases and so does the atomic number of the elements.

This means that the effective nuclear charge increases as well, thus it becomes more difficult to remove electrons. Therefore, it takes more energy to remove the electron. Consequently, the ionization energy increases.The ionization energy also increases as we move from bottom to top in a group. This is because the valence electrons are closer to the nucleus as we move up the group. This makes it more difficult to remove the valence electrons, thus the ionization energy increases.

The statement is False. The ionization energy refers to the amount of energy required to remove an electron from a neutral atom, creating a positively charged ion.

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a. To find the present value at t=10, we need to calculate the value of f(t) at t=10. Using the given function f(t) = 500e^(0.04t), we substitute t=10 into the equation:

[tex]\displaystyle \text{Present value} = f(10) = 500e^{0.04(10)}[/tex]

Simplifying the exponent:

[tex]\displaystyle \text{Present value} = 500e^{0.4}[/tex]

Evaluating the exponent:

[tex]\displaystyle \text{Present value} = 500(2.71828^{0.4})[/tex]

Calculating the value inside the parentheses:

[tex]\displaystyle \text{Present value} = 500(1.49182)[/tex]

Calculating the product:

[tex]\displaystyle \text{Present value} \approx 745.91[/tex]

Therefore, the present value at t=10 is approximately $745.91.

b. To find the accumulated money flow at t=10, we need to calculate the integral of f(t) from 0 to 10. Using the given function f(t) = 500e^(0.04t), we integrate the function with respect to t:

[tex]\displaystyle \text{Accumulated money flow} = \int_{0}^{10} 500e^{0.04t} dt[/tex]

Integrating:

[tex]\displaystyle \text{Accumulated money flow} = 500 \int_{0}^{10} e^{0.04t} dt[/tex]

Using the properties of exponential functions, we can evaluate the integral:

[tex]\displaystyle \text{Accumulated money flow} = 500 \left[ \frac{{e^{0.04t}}}{{0.04}} \right]_{0}^{10}[/tex]

Simplifying:

[tex]\displaystyle \text{Accumulated money flow} = 500 \left( \frac{{e^{0.4}}}{{0.04}} - \frac{{e^{0}}}{{0.04}} \right)[/tex]

Calculating the exponential terms:

[tex]\displaystyle \text{Accumulated money flow} = 500 \left( \frac{{e^{0.4}}}{{0.04}} - \frac{1}{{0.04}} \right)[/tex]

Evaluating the exponential term:

[tex]\displaystyle \text{Accumulated money flow} = 500 \left( \frac{{1.49182}}{{0.04}} - \frac{1}{{0.04}} \right)[/tex]

Calculating the subtraction:

[tex]\displaystyle \text{Accumulated money flow} = 500 \left( \frac{{1.49182 - 1}}{{0.04}} \right)[/tex]

Calculating the division:

[tex]\displaystyle \text{Accumulated money flow} = 500 \times 12.2955[/tex]

Calculating the product:

[tex]\displaystyle \text{Accumulated money flow} \approx 6147.75[/tex]

Therefore, the accumulated money flow at t=10 is approximately $6147.75.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

The concentration of the product when the degree of conversion is 0.8 depends on the specific rate constant and the stoichiometry of the reaction.

In a first-order reversible reaction, the rate of reaction is proportional to the concentration of the reactant raised to the power of its order. In this case, the reaction is first order with respect to both A and B. The rate law for the forward reaction can be expressed as:

Rate = k1 * [A] * [B]

Since the reaction is reversible, there is also a reverse reaction with its own rate constant, k2. The rate law for the reverse reaction can be expressed as:

Rate_reverse = k2 * [product]

The degree of conversion, ξ, is defined as the fraction of A that has reacted. In this case, the initial moles of A and B are both 200, so the total initial moles is 400. If the degree of conversion is 0.8, it means that 80% of A has reacted, leaving 20% unreacted.

To determine the concentration of the product when ξ = 0.8, we need to consider the stoichiometry of the reaction. From the balanced equation, we can see that for every two moles of A that react, one mole of product is formed. Therefore, if 80% of A has reacted, the concentration of the product would be 40% of the initial concentration of A and B.

In summary, when the degree of conversion is 0.8, the concentration of the product would be 40% of the initial concentration of A and B. This is based on the stoichiometry of the reaction and the assumption that the reaction follows first-order kinetics with respect to both A and B.

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In managing the global supply chains, a company shall focus on all areas. In other words, the material flow, information flow, and cash flow are important aspects that need attention in managing the global supply chains.

Supply chain management refers to the management of the flow of goods and services as well as the activities that are involved in transforming the raw materials into finished products and delivering them to customers. The process involves the integration of different parties, activities, and resources that are necessary in fulfilling the customers’ needs.

Aspects to focus on in managing the global supply chains:

Material flow: This aspect of supply chain management deals with the movement of raw materials or products from suppliers to manufacturers and finally to consumers.

In managing the global supply chains, it is important to focus on the material flow to ensure that goods are delivered to customers as required.

Information flow: The information flow aspect of supply chain management involves the transfer of information from one party to another regarding the status of the products. In managing the global supply chains, the company should focus on ensuring that the information is accurate and timely.

Cash flow: Cash flow refers to the movement of money between the parties involved in the supply chain process. In managing the global supply chains, companies should focus on ensuring that payments are made on time to avoid delays or other issues that may arise.  

Therefore in managing the global supply chains, all areas should be included.

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The empirical formula of the compound is CCl3.

To determine the empirical formula of the compound based on the given percentages, we need to convert the percentages to moles and find the simplest whole number ratio between the elements.

Assume we have a 100g sample of the compound. This means we have 7.808g of carbon and 92.19g of chlorine.

Convert the masses to moles using the molar masses of carbon (C) and chlorine (Cl).

Moles of C = 7.808g C / molar mass of C

Moles of Cl = 92.19g Cl / molar mass of Cl

Divide the number of moles by the smallest number of moles to obtain the mole ratio.

Mole ratio of C : Cl = Moles of C / Smallest number of moles

Mole ratio of C : Cl = Moles of Cl / Smallest number of moles

Find the simplest whole number ratio by multiplying the mole ratio by the appropriate factor to obtain whole numbers.

The resulting whole number ratio represents the empirical formula of the compound.

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Answer:

2/3

Step-by-step explanation:

To find the value of k, we can use the given information that y is 6 when x is 72. Plugging these values into the equation, we have:

6 = k * 72

To solve for k, we divide both sides of the equation by 72:

k = 6/72 = 1/12

Now that we know the value of k, we can use it to find the value of y when x is 8. Plugging x = 8 into the equation y = kx, we have:

y = (1/12) * 8 = 8/12 = 2/3

Therefore, when x is 8, y is 2/3.

When nitrous acid (HNO2) is hydrolyzed by water (H2O), the resulting products are the nitrite anion (NO2−) and hydronium ion (H3O+).

The hydrolysis reaction of nitrous acid (HNO2) is given by the following equation:HNO2(aq) + H2O(l) ⇌ NO2−(aq) + H3O+(aq). Thus, nitrous acid reacts with water to form nitrite ion and hydronium ion, represented by the following formulas:

.

Thus, nitrous acid reacts with water to form nitrite ion and hydronium ion, represented by the following formulas: Reactants: HNO2(aq) + H2O(l)Products: NO2−(aq) + H3O+(aq)

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The alkali silicate reaction, also known as the alkali-silica reaction (ASR), is a chemical reaction that occurs between alkalis (such as sodium or potassium) present in cement or concrete and reactive forms of silica (such as certain types of aggregates).

This reaction results in the formation of a gel-like substance, which can cause expansion, cracking, and deterioration of the concrete structure over time.

There are no specific calculations involved in the alkali silicate reaction. However, the severity of the reaction can be B by measuring the expansion of the concrete or observing the formation of cracks and other signs of deterioration.

The alkali silicate reaction is a significant concern in the construction industry as it can lead to the degradation of concrete structures. Preventive measures such as using low-alkali cement, incorporating supplementary cementitious materials, and selecting non-reactive aggregates can help mitigate the risk of ASR. Regular monitoring, testing, and maintenance of concrete structures are essential to detect and address any signs of alkali silicate reaction at an early stage. By understanding and managing this reaction, engineers and construction professionals can ensure the durability and longevity of concrete structures.

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Answer:

B

Step-by-step explanation:

hope this helps :)

The diffusive flux of methylene chloride through the glove is [tex]-0.22 g/cm^2-s.[/tex]. This indicates that some methylene chloride can pass through the glove and should be handled with caution.

The diffusive flux of methylene chloride through the glove can be determined by using Fick's first law of diffusion, which relates the diffusive flux of a species through a medium to its concentration gradient and diffusivity. The equation for Fick's law is given by J = -D(dc/dx), where J is the diffusive flux, D is the diffusion coefficient, and dc/dx is the concentration gradient.

For this problem, the diffusive flux of methylene chloride through the butyl rubber glove can be calculated as follows:

J = -D(dc/dx)

=[tex]-110 x 10^-8 cm^2/s x (0.44 - 0.02) g/cm^3 / (0.08 cm)[/tex]

= -0[tex].22 g/cm^2-s[/tex]

Therefore, the diffusive flux of methylene chloride through the glove is[tex]-0.22 g/cm^2-s.[/tex]

This indicates that some methylene chloride can pass through the glove and should be handled with caution.

:Therefore, the diffusive flux of methylene chloride through the glove is [tex]-0.22 g/cm^2-s.[/tex]. This indicates that some methylene chloride can pass through the glove and should be handled with caution.

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The two equations for the number of hours of daylight over time in months are:

1) y = 2sin[(π/6)t] + 12

2) y = -2sin[(π/6)t] + 12

The given problem states that the number of hours of daylight varies sinusoidally over a period of one year. This indicates that the function that models the number of hours of daylight should be a sinusoidal function.

To find the equation for the number of hours of daylight, we need to consider the key parameters: the amplitude, period, and phase shift of the sinusoidal function.

In the first equation, y = 2sin[(π/6)t] + 12, the amplitude is 2, which represents the maximum deviation from the average of 12 hours of daylight. The period is determined by the coefficient of t, which is π/6. Since the period of one year corresponds to 12 months, the coefficient is chosen to divide the period equally among the 12 months.

The phase shift, or horizontal shift, is not explicitly mentioned in the problem, so it is assumed to be zero. Adding 12 to the equation ensures that the average daylight hours are accounted for.

In the second equation, y = -2sin[(π/6)t] + 12, the only difference is the negative amplitude (-2). This equation represents the situation where the number of daylight hours is below the average.

By using these equations, one can calculate the number of daylight hours for each month of the year based on the given sinusoidal variation.

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Answer:

Rule is [tex]n^2+8[/tex]

20th term is 408

Step-by-step explanation:

Notice that [tex]n^2=1,4,9,16,25,...[/tex] so if we add 8 to each term, we get [tex]n^2+8=9,12,17,24,33[/tex]. Therefore, the 20th term would be [tex]20^2+8=400+8=408[/tex]

Based on the information provided, the correct p-value is approximately 0.001 (rounded to the nearest thousandth). It appears there may have been an error in your calculation or in using the formulas in Desmos.

Note: The Desmos notation for this calculation would be:
p = 2*(1-tCDF(-3.873, 14))

To find the p-value for this hypothesis test, we need to calculate the test statistic and compare it to the appropriate distribution. The test statistic for this hypothesis test is the t-score, which is calculated using the formula:

t = (x-bar - μ) / (s / √n)

Where:
- x-bar is the sample mean (48 in this case)
- μ is the hypothesized population mean (50 in this case)
- s is the sample standard deviation (2 in this case)
- n is the sample size (15 in this case)

Substituting the given values into the formula, we get:

t = (48 - 50) / (2 / √15)
  = -2 / (2 / √15)
  = -2 / (2 / 3.873)
  = -3.873

Note: In the formula, √ represents square root.

Next, we need to determine the degrees of freedom for this test. Since we are using a t-distribution and have a sample size of 15, the degrees of freedom is given by n - 1, which is 15 - 1 = 14.

Using the t-distribution table or a statistical calculator, we can find the p-value associated with the test statistic of -3.873 and 14 degrees of freedom.

The p-value represents the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. A small p-value suggests that the observed data is unlikely to have occurred by chance alone, and provides evidence against the null hypothesis.

Based on the information provided, the correct p-value is approximately 0.001 (rounded to the nearest thousandth). It appears there may have been an error in your calculation or in using the formulas in Desmos.

Note: The Desmos notation for this calculation would be:
p = 2*(1-tCDF(-3.873, 14))

I hope this helps clarify the process of finding the p-value for a hypothesis test. If you have any further questions, feel free to ask!

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