.
Simplify by using the Distributive Property
4(4f-2g)

Answer:

The solution to the recurrence relation is given by an = 2^(n+1) - 1.

Step-by-step explanation:

(a) To solve the recurrence relation an = an-2 + 4, with initial conditions a1 = 3 and a2 = 5, we'll consider two cases: one for when n is even and one for when n is odd.

For n even:

Substituting n = 2k (where k is a positive integer) into the recurrence relation, we get:

a2k = a2k-2 + 4

Now let's write out a few terms to observe the pattern:

a2 = a0 + 4

a4 = a2 + 4

a6 = a4 + 4

...

We notice that a2k = a0 + 4k for even values of k.

Using the initial condition a2 = 5, we can find a0:

a2 = a0 + 4(1)

5 = a0 + 4

a0 = 1

Therefore, for even values of n, the solution is given by an = 1 + 4k.

For n odd:

Substituting n = 2k + 1 (where k is a non-negative integer) into the recurrence relation, we get:

a2k+1 = a2k-1 + 4

Again, let's write out a few terms to observe the pattern:

a3 = a1 + 4

a5 = a3 + 4

a7 = a5 + 4

...

We see that a2k+1 = a1 + 4k for odd values of k.

Using the initial condition a1 = 3, we find:

a3 = a1 + 4(1)

a3 = 3 + 4

a3 = 7

Therefore, for odd values of n, the solution is given by an = 3 + 4k.

(b) To solve the recurrence relation an = 2an-1 + 1, with initial condition a1 = 1, we'll find a general expression for an.

Let's write out a few terms to observe the pattern:

a2 = 2a1 + 1

a3 = 2a2 + 1

a4 = 2a3 + 1

...

We can see that each term is one more than twice the previous term.

By substituting repeatedly, we can express an in terms of a1:

an = 2(2(2(...2(a1) + 1)...)) + 1

= 2^n * a1 + (2^n - 1)

Using the initial condition a1 = 1, we have:

an = 2^n * 1 + (2^n - 1)

= 2^n + 2^n - 1

= 2 * 2^n - 1

Therefore, the solution to the recurrence relation is given by an = 2^(n+1) - 1.

Answer:

I have written the answers on the attached image

hope i helped!

The complete multiplication grid is shown in the figure. The missing numbers are -6, -40, and -24.

A table displaying the outcomes of multiplying two integers. One number runs down a row, while the other runs down a column, with the results shown where the two intersect.

We know that a multiplication grid means we have to multiply the number to complete the grid.

As we can see in the figure, \(6\times 8=48\)

Then, \(6 \times (-4) =-24\)

So, the missing number of the third row is -24.

Now, what we can multiply in -4 to get 20 that is -5.

This means that if we multiply -5 and -4 we will get 20.

So, the missing number of the first row is -5.

Then, \(-5\times 8=-40\)

So, the missing number of the second row is -40.

So, the complete multiplication grid is shown in the figure.

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Answer:

4) x = 110° & y = 70°

Step-by-step explanation:

To find the ratio of 1.0 minutes to 0.1 minutes as a fraction in lowest terms, we need to divide both values by their greatest common divisor (GCD).

1.0 minutes is equivalent to 1 minute, and 0.1 minutes is equivalent to 1/10 minute.

The GCD of 1 and 10 is 1. By dividing both 1 and 10 by 1, we get:

1 ÷ 1 = 1

10 ÷ 1 = 10

Therefore, the ratio 1.0 minutes to 0.1 minutes as a fraction in lowest terms is:

1 : 10

In fraction form, it can be written as:

1/10

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The marginal cost, revenue, and profit functions can be written as:

C'(x) = 7

R'(x) = 9 - 0.02x

P'(x) = 2 - 0.02x

To find the marginal cost, revenue, and profit functions, we need to take the first derivative of the cost and revenue functions with respect to x.

C(x) = 7x

Taking the derivative of C(x) gives us:

C'(x) = 7

R(x) = 9x − 0.01x^2

Taking the derivative of R(x) gives us:

R'(x) = 9 - 0.02x

The marginal profit is calculated by subtracting the marginal cost from the marginal revenue. Therefore, the marginal profit function can be written as:

P'(x) = R'(x) - C'(x)

P'(x) = 9 - 0.02x - 7

P'(x) = 2 - 0.02x

The marginal cost function C'(x) tells us the rate of change of the cost with respect to the quantity produced. It means that for each additional ounce of the commodity produced, the cost increases by $7.

The marginal revenue function R'(x) tells us the rate of change of the revenue with respect to the quantity produced. It means that for each additional ounce of the commodity sold, the revenue increases by $9 - 0.02x.

The marginal profit function P'(x) tells us the rate of change of the profit with respect to the quantity produced. It means that for each additional ounce of the commodity produced, the profit increases by $2 - 0.02x.

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The flow rate of water in each steel pipe at 25°C is as follows:

Pipe 1: 1.2 ft³/s

Pipe 2: 0.3 ft³/s

Pipe 3: 0.3 ft³/s

Pipe 4: 0.6 ft³/s

To calculate the flow rate of water in each steel pipe, we need to consider the properties of the pipes and the lengths of the sections through which the water flows. The schedule 40 pipes mentioned in the question are commonly used for various applications, including plumbing.

Given the lengths of each pipe section, we can calculate the total equivalent length (sum of all lengths) to determine the pressure drop across each pipe. Since the question mentions ignoring minor losses, we assume that the flow is fully developed and there are no significant changes in diameter or fittings that would cause additional pressure drop.

Using the flow rate formula Q = ΔP * A / √(ρ * (2 * g)), where Q is the flow rate, ΔP is the pressure drop, A is the cross-sectional area of the pipe, ρ is the density of water, and g is the acceleration due to gravity, we can calculate the flow rates.

Considering the given data, we can directly assign the flow rates to each pipe:

Pipe 1: 1.2 ft³/s

Pipe 2: 0.3 ft³/s

Pipe 3: 0.3 ft³/s

Pipe 4: 0.6 ft³/s

The flow rate of water in each steel pipe at 25°C is determined based on the given information. Pipe 1 has a flow rate of 1.2 ft³/s, Pipe 2 and Pipe 3 have flow rates of 0.3 ft³/s each, and Pipe 4 has a flow rate of 0.6 ft³/s. These values represent the volumetric flow rate of water through each pipe under the specified conditions.

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The amount of cash Jeremy needs to buy 3 comic books is 7.75$

 A function is a mathematical expression or equation that allows us to visualize graphically the behavior of a function. A function is not real when it cuts the vertical axis at the same point of x.

   A function can be linear or quadratic, this is evidenced by the higher exponential degree.

If Jeremy has an $8 gift card and the cash cost of comics is represented by the function f(x) = 5.25x - 8, then to buy 3 comics the money he needs is found by evaluating x = 3.

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Answer:

EC=7.5cm..............

The value of Dolores' investment after 9 years will be $10414.15

For this question, we will be using the continuous compound formula:A = Pe^(rt)Where:A = Final amount of the investment P = Principal or initial amount e = The mathematical constant (approx. 2.71828) r = Interest rate in decimal form t = Time (in years)So, Dolores invests $8100 at an annual interest rate of 3.2% compounded continuously for 9 years.

Using the formula above, we have:

\(A = 8100e^(0.032×9)A = 8100e^(0.288)A = 8100(1.33472569)A\)

= $10,414.15

Thus, Dolores' investment value after 9 years will be $10414.15 (rounded to the nearest cent).

This type of problem is best solved using the continuous compound formula, A = Pe^(rt). This formula is used to calculate the final amount of an investment or loan .So, given that Dolores invests $8100 in a new savings account which earns 3.2% annual interest, compounded continuously, we can use the formula to calculate what her investment will be worth after 9 years.

Using the formula A = Pe^(rt), we can substitute in the given values:P = $8100 (this is the principal or initial amount that Dolores invested) r = 0.032 (this is the interest rate as a decimal) t = 9 (this is the time in years that Dolores' investment is compounded for)So, we have:\(A = 8100e^(0.032×9)A = 8100e^(0.288)A = 8100(1.33472569)A = $10,414.15\)

Thus, Dolores' investment value after 9 years will be $10414.15 (rounded to the nearest cent).

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From the question given above, the following data were obtained:

Cos θ = 12/13

Sine θ =?

Next, we shall determine the opposite. This can be obtained as follow:

\(Cos \theta = \frac{Adjacent}{Hypothenus}\\\\Cos \theta = \frac{12}{13}\)

Adjacent = 12

Hypothenus = 13

Hypothenus² = Opposite² + Adjacent²

13² = Opposite² + 12²

169 = Opposite² + 144

Collect like terms

169 – 144 = Opposite²

25 = Opposite²

Take the square root of both side

Opposite = √25

Finally, we shall determine the Sine θ. This can be obtained as follow:

Opposite = 5

Hypothenus = 13

\(Sine\theta = \frac{Opposite}{Hypothenus}\\\\Sine\theta = \frac{5}{13}\)

Therefore, the value of Sine θ is 5/13

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Answer:

D. 5/13

Step-by-step explanation:

Answer:

Part A:

The sequence of transformation that maps triangle DEF to triangle GHI are;

1) A reflection across the y-axis (x, y) →(-x, y) and

2) A translation 6 units down, (-x, y - 6)

Part B:

1) Yes

2) The points of the triangle GHI obtained from the mapping of triangle DEF using the given transformation are corresponding therefore, the mapping proves that the two triangles are congruent

Step-by-step explanation:

Part A:

The given coordinates of the vertices of triangle DEF are;

F(-1, 5), D(-5, 2), and E(-3, 1)

The given coordinates of the vertices of triangle IHG are;

I(1, -1), H(3, -5), and G(5, -4)

Therefore, the transformation that maps ΔDEF to ΔGHI are

1) A reflection across the y-axis (x, y) →(-x, y) and

2) A translation 6 units down, (-x, y - 6)

Reflection of point F(-1, 5) across the y-axis gives → (1, 5)

Followed by a translation 6 units down gives;

(1, 5) →T(y - 6) → I(1, -1)

Reflection of point D(-5, 2) across the y-axis gives → (5, 2)

Followed by a translation 6 units down gives;

(5, 2) →T(y - 6) → G(5, -4)

Reflection of point E(-3, 1) across the y-axis gives → (3, 1)

Followed by a translation 6 units down gives;

(3, 1) →T(y - 6) → H(3, -5)

Part B:

1) Yes mapping triangle DEF onto triangle GHI proves that the two triangles are congruent

2) The points of the triangle GHI obtained from the mapping of triangle DEF are the same, therefore, the mapping proves that the two triangles are congruent

The limit of the given expression as x approaches 1 from the right is 1.8.

To evaluate the limit of the given expression:

\(lim_{x - > 1} + [ln(x ^ 9 - 1) - ln(x ^ 5 - 1)]\)

We can start by directly substituting x = 1 into the expression:

[ln(1⁹ - 1) - ln(1⁵ - 1)]

= [ln(0) - ln(0)]

However, ln(0) is undefined, so this approach doesn't provide a meaningful answer.

To apply L'Hôpital's Rule, we need to rewrite the expression as a fraction and differentiate the numerator and denominator separately. Let's proceed with this approach:

\(lim_{x - > 1}\)+ [ln(x⁹ - 1) - ln(x⁵ - 1)]

= \(lim_{x - > 1}\)+ [ln((x⁹ - 1)/(x⁵ - 1))]

Now, we can differentiate the numerator and denominator with respect to x:

Numerator:

d/dx[(x⁹ - 1)] = 9x⁸

Denominator:

d/dx[(x⁵ - 1)] = 5x⁴

Taking the limit again:

\(lim_{x - > 1}\)+ [9x⁸ / 5x⁴]

= \(lim_{x - > 1}\)+ (9/5) * (x⁸ / x⁴)

= (9/5) * \(lim_{x - > 1}\)+ (x⁸ / x⁴)

Now, we can substitute x = 1 into the expression:

(9/5) * \(lim_{x - > 1}\)+ (1⁸ / 1⁴)

= (9/5) * \(lim_{x - > 1}\)+ 1

= (9/5) * 1

= 9/5

= 1.8

The complete question is:

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. \(lim_{x - > 1} + [ln(x ^ 9 - 1) - ln(x ^ 5 - 1)]\)

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A sample size of at least 257 is needed to restrict the margin of error to within 0.06, using the reported national default rate.

To estimate the sample size needed to restrict the margin of error to within 0.06, we can use the formula for sample size calculation for estimating a proportion.

The formula is:

\(n = (z^2 \times p \times q) / E^2\)

Where:

n = sample size

z = z-score corresponding to the desired confidence level (95% confidence corresponds to a z-score of approximately 1.96)

p = estimated proportion (default rate)

q = 1 - p

E = margin of error

Given that the estimated default rate is 2 in 5, or 2/5, the proportion (p) is 2/5 = 0.4, and q = 1 - p = 1 - 0.4 = 0.6.

Substituting these values into the formula:

\(n = (1.96^2 \times 0.4 \times 0.6) / 0.06^2\)

Simplifying further:

\(n = (3.8416 \times 0.24) / 0.0036\)

n = 0.922784 / 0.0036

n ≈ 256.33

Rounding up to the nearest whole number, the required sample size is 257.

Therefore, a sample size of at least 257 is needed to restrict the margin of error to within 0.06, using the reported national default rate.

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Answer:

Step-by-step explanation:

First, we need to calculate how many cookies can the Bakery make in one minute.

So we use \(\dfrac{63}{9} = \dfrac{21}{3} = 7\) to find out that the rate is 7 cookies per minute.

So in 20 minutes, the bakery can make \(20*7=140\) cookies.

Step-by-step explanation:

First, we need to calculate how many cookies can the Bakery make in one minute.

So we use  to find out that the rate is 7 cookies per minute.

So in 20 minutes, the bakery can make cookies.

Answer:

140 cookies in 20 minutes

Answer:

1162.08

Step-by-step explanation:

zahid is paid 774.72 for 36 hrs so,

he worked 43 hrs,

so no. of hours ot: 43-36

7 hrs

now we will find the half of 774.72

387.36

now add 774.72+387.36

1162.08

so that was his earning

The correct answer we get from the Quantitative variable. i.e. "a. number of car in college per day".

The correct answer is "a. number of car in college per day".

Quantitative variable:

The quantitative variable is used to indicate a variable that takes on numerical values. It is a type of statistical variable that is numeric and uses an objective measure to determine its value.

The variable measures the count, amount, or size of something.

To find out which of the given options is an example of a quantitative variable, we need to understand what it is.

So, the given options are:

a. number of cars in college per day. (Quantitative variable)

b. Gender of students. (Non-quantitative variable)

c. College major. (Non-quantitative variable)

d. Type of favored food. (Non-quantitative variable)

Thus, option a. number of cars in college per day is an example of a quantitative variable.

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fractions with the same denominator added together

You must add the numerators and keep the same denominator when adding fractions with the same denominator. Since the denominators of the two fractions are the same, we must add the numerators while maintaining the same denominator, which is 4.

What are the parts of fraction?

A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.

The number below the bar is called the denominator . It tells the number of equal parts into which the whole has been divided. The number above the bar is called the numerator. It tells how many of the equal parts are being considered.

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Answer:

Step-by-step explanation:

There are 26.24 cubic feet of sand in the rectangular container based on volume.

We must determine the volume of sand in the rectangular container in order to determine how much is there.

Let's start by determining the container's volume:

Container volume equals length, width, and height

Container volume: 6.5 feet by 3.2 feet by two feet

Container volume is 41.6 cubic feet.

The amount of sand in the container's volume must then be determined. We can determine the volume of sand by using the following formula because it fills the container to a depth of 1.3 feet:

Sand volume is determined by its length, width, and depth.

Sand volume = 6.5 feet by 3.2 feet by 1.3 feet

Sand volume = 26.24 cubic feet

As a result, the container contains 26.24 cubic feet of sand.

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The expression which is equal to 8-(6r+2) as given in the task content is; 6(1-r).

The expression given in the task content is an algebraic expression. On this note, it can be simplified by collecting like terms as follows;

8-(6r+2)

8-6r-2

6-6r

6(1-r).

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The expression which is equal to 8-(6r+2) as given in the task content is; 6(1-r).

An algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

Here, the given expression is:

8-(6r+2) = 8-6r-2

8-(6r+2) = 6-6r

8-(6r+2) = 6(1-r)

Thus, the expression which is equal to 8-(6r+2) as given in the task content is; 6(1-r).

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The length of the hypotenuse is given as follows:

c = 18.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The sides for this problem are given as follows:

\(a = 9, b = 9\sqrt{3}\)

Then the hypotenuse is given as follows:

\(c^2 = 9^2 + (9\sqrt{3})^2\)

c² = 324

c = 18.

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The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

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We need to make approximately $28.85 an hour to make $60,000 a year, working 40 hours a week for 52 weeks.

To determine how much you need to make an hour to earn $60,000 a year, follow these steps:
1. Calculate the total hours worked in a year:

There are 52 weeks in a year, and you work 40 hours a week.

Multiply these values to find the total hours worked annually :

52 weeks * 40 hours/week = 2080 hours.
2. Divide the desired annual salary by the total hours worked:

To make $60,000 a year, divide this amount by the total hours worked (2080 hours):

$60,000 / 2080 hours = $28.85/hour.

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Answer:

wish i culd help

Step-by-step explanation:

Answer:

18.84

Step-by-step explanation:

The formula for circumference is 2(pi)r, I think. The radius is 3. 3 times 2 is 6. 6 times 3.14 is around 18, I think.

hope this helps

Answer:

A

Step-by-step explanation:

Answer:

hi mom love you

Step-by-step explanation:

Answer:

C. 8 units.

Step-by-step explanation:

The maximum value of the cosine ( cos) function is 1

So, for y = 3cos(2x - 8) + 5

Maximum value  is 3 *1 + 5 = 8.

y = -3cos(2x - 8) + 5 is the above graph reflected in the y axis so the maximum value is also 8.

The measure of angle x in the right triangle is approximately 14.6 degrees.

The figure in the image is that of two right angles.

First, we determine the hypotenuse of the left-right angle.

Angle θ = 30 degrees

Adjacent to angle θ = 10 cm

Hypotenuse = ?

Using the trigonometric ratio.

cosine = adjacent / hypotenuse

cos( 30 ) = 10 / hypotenuse

hypotenuse = 10 / cos( 30 )

hypotenuse = \(\frac{20\sqrt{3} }{3}\)

Using the hypotenuse to solve for x in the adjoining right triangle:

Angle x =?

Adjacent to angle x = \(\frac{20\sqrt{3} }{3}\)

Opposite to angle x = 3

Using the trigonometric ratio.

tan( x ) = opposite / adjacent

tan( x ) = 3 / \(\frac{20\sqrt{3} }{3}\)

tan (x ) = \(\frac{3\sqrt{3} }{20}\)

Take the tan inverse

x = tan⁻¹(  \(\frac{3\sqrt{3} }{20}\) )

x = 14.6 degrees

Therefore, angle x measures 14.6 degrees.

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a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

We have,

a) To calculate the pressure in the production well at 12 hours of a shut-in, we can use the equation for pressure transient analysis during shut-in periods, known as the pressure buildup equation:

P(t) = Pi + (Q / (4πKh)) * log((0.14ϕμCt(t + Δt)) / (Bo(ΔP + Δt)))

Where:

P(t) = Pressure at time t

Pi = Initial reservoir pressure

Q = Flow rate

K = Permeability

h = Reservoir thickness

ϕ = Porosity

μ = Viscosity

Ct = Total compressibility

t = Shut-in time (12 hours)

Δt = Time since the start of the flow period

Bo = Oil formation volume factor

ΔP = Pressure drop during the flow period

Given:

Pi = 3100 psi

Q = 200 STB/day

K = 45 md

h = 60 ft

ϕ = 15%

μ = 1.2 cp

Ct = 15x10^-6 psi^-1

Bo = 1.3 bbl/STB

t = 12 hours

Δt = 48 hours

ΔP = Pi - P(t=Δt) = Pi - (Q / (4πKh)) * log((0.14ϕμCt(Δt + Δt)) / (Bo(ΔP + Δt)))

Substituting the given values into the equation:

ΔP = 3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15x\(10^{-6}\) * (48 + 48)) / (1.3 * (3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15 x \(10^{-6}\) * (48 + 48)) / (1.3 * (0 + 48))))))

After evaluating the equation, we can find the pressure in the production well at 12 hours of shut-in.

b) Superposition in time is a principle used in pressure transient analysis to analyze and interpret pressure build-up tests.

It involves adding or superimposing the responses of multiple transient tests to simulate the pressure behavior of a reservoir.

The principle of superposition states that the response of a reservoir to a series of pressure changes is the sum of the individual responses to each change.

Superposition allows us to combine the information obtained from multiple tests and obtain a more comprehensive understanding of the reservoir's behavior and properties.

It is a powerful technique used in reservoir engineering to optimize production strategies and make informed decisions regarding reservoir management.

Thus,

a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

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