I need to find the slope of each line and show my work for it

The first 4 terms of the sequence by the given recursive formula is found as: 6 , 13, 20, 27.

For the stated question:

f(n) :

f(1) = 6

f(n) = f(n - 1) + 7, if n > 1.

Thus,

First term, n = 1: f(1) = 6

Second term, n = 2:  

f(2) = f(2 - 1) + 7

f(2) = f(1) + 7

f(2) = 6 + 7

f(2) = 13

Third term: n = 3.

f(3) = f(3 - 1) + 7

f(3) = f(2) + 7

f(3) = 13 + 7

f(3) = 20

Fourth term: n = 4.

f(4) = f(4 - 1) + 7

f(4) = f(3) + 7

f(4) = 20 + 7

f(4) = 27

Thus, the first 4 terms of the sequence by the given recursive formula is found as: 6 , 13, 20, 27.

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The world population in 2030 will be of 9.0062 billion.

The exponential formula for population growth is given below:

P(t) = P (0)e^rt

Here, P(t) is the population in t years from now P (0) is the population in the current year and r(decimal) is the growth rate, e=2.7 is the Eular number.

If the world population is 7.0 billion in 2012.

2012 is the initial year, P (0) =7

P(t) will be measured in billions of people.

The growth rate is constant at 1 .4%.

So that, r = 0.014

Now, the population in 2030 will be :

2030-2012=18 years after 2012, so this is P(18).

P(t)= 7e^rt

P(18) = 7e^0.0014*18

       = 9.0062

So, the world population in 2030 will be of 9.0062 billion.

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The world population will be 9.0062 billion in 2030.

The population growth exponential formula is as follows:

P(0)ert = P(t)

P(t) denotes the population in t years. P (0) is the current year's population, r(decimal) is the growth rate, and e=2.7 is the Euler number.

If the world population in 2012 is 7.0 billion.

The first year is 2012, and P (0) = 7.

The magnitude of P(t) will be measured in billions of people.

The rate of growth remains constant at 1.4%.

As a result, r = 0.014.

Now, in 2030, the population will be:

2030-2012 = 18 years after 2012, so P (18).

P(t)= 7e^rt

P(18) = 7e^0.0014*18

= 9.0062

As a result, the world population in 2030 will be 9.0062 billion people.

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The z-score for an observation of 200 is approximately -2.000.

Here are the steps to calculate the z-score for an observation of 200 based on a normal distribution with a mean of 500 and a standard deviation of 150:

        x - μ = 200 - 500 = -300

        -300 / 150 = -2

        -2 ≈ -2.000

So, the z-score for an observation of 200 is approximately -2.000.

A z-score is a measure of how many standard deviations a given value is from the mean of a dataset. It is calculated by subtracting the mean of the dataset from a given value and dividing the result by the standard deviation of the dataset.

In the case of a normal distribution with a mean of 500 and a standard deviation of 150, a z-score of -2 would indicate that an observation of 200 is 2 standard deviations below the mean. This information can be used to determine the proportion of data within the dataset that is above or below a certain value, or to make comparisons between different datasets.

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Since not all of the leading coefficients are ones and not all of the rows are in descending order, the above linear equation is not in echelon form.

No, an echelon form does not exist for the given linear system. All leading coefficients must be 1 for the structure to be in echelon form, and all rows must be arranged in decreasing order. The second and third rows in this equation are not in decreasing order, and the leading coefficient in the first row is 2, not 1.

An echelon form cannot be described by the given linear system. All of the leading coefficients in the equations must be 1, and all of the rows must be arranged in descending order for the equation to be in echelon form. The leading coefficient of the first row in the preceding equation is 2, not 1, and the second and third rows are not arranged in descending order. The equation is therefore not in echelon form.

Each row should have one more leading coefficient than the row above it in echelon form, and any row with all zeroes should be at the bottom of the equation. Additionally, all leading coefficients must equal 1. The given equation is not valid since it does not match these requirements.

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The value of x and y for which the graph has undefined slope is y = 0 or x = 2

Given y²(2 - x) = x³

We are asked to determine the point on the curve which has an undefined slope.

Undefined slope means dy/dx = ∞

                                   Now, y²(2 - x) = x³

                               Differentiating both sides

                                   2y dy/dx (2-x) - y² = 3x²

                                                       dy/dx = (3x² + y²)/2y(2-x)

So, (3x² + y²)/2y(2-x) = ∞

For this 2y(2-x) = 0

We can see that the possible cases  y = 0 or x = 2

Hence for y = 0 or x = 2, the slope of the graph is undefined.

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y(t) = 2e^(sin(t) + t) is the antiderivative of the function dy/dt = y cos(t) + y, and satisfies the initial condition y(0) = 2.

This is a first-order linear differential equation, which can be solved by the separation of variables. To do so, we can start by writing:

dy/dt = y cos(t) + y

We can divide both sides by y:

dy/dt / y = cos(t) + 1

Now, we can integrate both sides with respect to t, using the property that d(ln y)/dt = 1/y:

∫(dy/dt / y) dt = ∫(cos(t) + 1) dt

ln|y| = sin(t) + t + C

Where C is the constant of integration. To find its value, we can use the initial condition y(0) = 2:

ln|2| = sin(0) + 0 + C

C = ln|2|

Therefore, the solution of the initial value problem is:

y(t) = 2e^(sin(t) + t)

This is the antiderivative of the function dy/dt = y cos(t) + y and satisfies the initial condition y(0) = 2.

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Answer:

[tex]( - \frac{1}{2 \:} \: - \frac{5}{4} )[/tex]

[tex]( - 0.5 \: \: - 1.25)[/tex]

The pedestrian crossing sign is a parallelogram because both pairs of opposite sides are parallel. The Second option is Correct.

A parallelogram is a quadrilateral that has two pairs of parallel sides, meaning that both sets of opposite sides are parallel. This is opposed to a trapezoid, which has only one pair of parallel sides. The pedestrian crossing sign is typically in the shape of a parallelogram, with the top and bottom sides being parallel, and the sides slanting towards each other to form a point at the top.

This design helps the sign to be easily visible from a distance and clearly recognizable as a pedestrian crossing sign. The parallel sides of the sign are an important characteristic that helps drivers and pedestrians to identify and understand the meaning of the sign.

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Answer:

Step-by-step explanation:

I dont understand the question?

The percentage decrease from first to third year is; 47.725%

To find the percentage decrease, work out the difference (decrease) between the two numbers you are comparing. Thereafter, divide the decrease by the original number and then multiply the answer by 100.

Amount of car in 2010 = £18500

It depreciated by 15% in the first year. Thus;

Amount after first year = (100% - 15%) * 18500

= £15725

It depreciated by 18% in the second year. Thus;

Amount after second year = (100% - 18%) * 15725

= £12,894.5

It depreciated by 25% in the third year. Thus;

Amount after third year = (100% - 25%) * 12,894.5

= £9,670.875

Thus;

Decrease from first to third year = (18500 - 9670.875)/18500 * 100%

= 47.725%

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Answer:

Welcome to Brainly! I saw that this was your very first question. I will gladly assist you with your problem. (see explanation).

Step-by-step explanation:

The calculation of the estimated damaged items in the situation where 23,025 capacitors were produced is displayed below:

(5 times 23,025 capacitors) / (1,535 capacitors)

= 75

Therefore, when 23,025 capacitors are produced, 75 damaged products are expected.

Hope this helped!)

Therefore , the solution of the given problem of angle bisector  comes out to be each measurement will be equivalent to 30 degrees,

A bisector exists for each angle. Additionally, it is the symmetry line that connects an angle's two arms, triangle  whose construction facilitates the creation of smaller angles.

Here,

A 30° angle, for example, might be called for. A 60° angle can be made, and it can then be divided, to accomplish this.

The concept of an angle bisector is used to construct angles such as 90 degrees, 45 degrees, 15 degrees, and others.

Examples :

What is each angle's measurement if an angle bisector divides an angle of 80 degrees?

The answer is that 80 degrees is the measure of an angle.

It is common knowledge that the angle is divided into two equal pieces by the angle bisector.

Consequently, 80 degrees is divided into two equal portions, let's call x.

Hence,

x + x = 80°

2x = 80°

x = 80°/2

x = 40°.

The second option is ineffective since it would result in A' being positioned at (-5, 2) after translation A 3 up and 1 left (5, -2).

The third option: spinning A in a clockwise direction 90 degrees places it at (-1, 4), then reflecting it across the y-axis places it at (1, 4).

In the fourth option, A is rotated 90 degrees counterclockwise, putting it at (1, -4), and it is reflected across the x-axis, putting it at (1, 4).

The fifth option is to rotate A 180 degrees, which positions it at (-3, -4), after translating 3 down & 1 right (3, 4). B(-5, -5) (-5, -5)  Translated results in (-4, -8), and rotated results in (4, 8). Translation of C(-3, -4) results in (-2, -7), and rotation results in (2, 7).

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The absolute minimum value of y =-cos(x) - sin(x) on the closed interval [0, π/2] is  [tex]-\sqrt{2}[/tex]

Consider equation,

y = -cos(x) - sin(x)

Let y = f(x)

Differentiate the function f(x) = -cos(x) - sin(x) with respect to x.

f'(x) = -(-sin(x)) - cos(x)

f'(x) = sin(x) - cos(x)

For f'(x) = 0,

sin(x) - cos(x) = 0

sin(x) = cos(x)

sin(x)/cos(x) = 1

tan(x) = 1                     ..............(tan(θ) = sin(θ)/cos(θ))

x = π/4

For above value of x, the value of function would be,

f(π/4) = -cos(π/4) - sin(π/4)

f(π/4) = [tex]-\frac{1}{\sqrt{2} } -\frac{1}{\sqrt{2} }[/tex]

f(π/4) = [tex]-\sqrt{2}[/tex]

f(0) =  -cos(0) - sin(0)

f(0) = -1

And f(π/2) = -cos(π/2) - sin(π/2)

       f(π/2) = -1

So, the minimum value of f(x) is  [tex]-\sqrt{2}[/tex],  shown in the following graph.

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You can arrange 10 people in a circle in 362880 different ways if two arrangements are considered the same

In mathematics, a combination or combinations are all the possible groupings that can be made of a given number of elements, without repeating them and regardless of the order in which they are found.

Information about the problem:

As the table is round, the first person can take any seat, then the seat on the right can be taken by 1 of 9 people, then the next seat by 1 of 8 and so on until the 10th person has no choice of seats.

This is expressed by:

9*8*7*6*5*4*3*2

9!

362,880

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The angle included by these two sides is (c^2 - 74) / (-70).

What is triangle ?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.

The area of a triangle can be found using the formula:

Area = (1/2) * b * h,

where b is the length of the base and h is the height of the triangle.

Since two of the sides have lengths 5 in and 7 in, we can assume that they are the base and the height of the triangle, respectively. Setting b = 5 in and h = 7 in, we can find the area:

Area = (1/2) * 5 in * 7 in = (1/2) * 35 in^2 = 16 in^2.

This means that the height of the triangle is 7 in and the base is 5 in. To find the angle included by these two sides, we can use the Law of Cosines:

c^2 = a^2 + b^2 - 2ab * cos(C),

where a and b are the lengths of the sides and C is the angle included by these two sides.

Since a = 5 in and b = 7 in, we can find the angle C:

c^2 = a^2 + b^2 - 2ab * cos(C)

c^2 = 5^2 + 7^2 - 2 * 5 * 7 * cos(C)

c^2 = 25 + 49 - 70 * cos(C)

c^2 = 74 - 70 * cos(C)

So , The angle included by these two sides is (c^2 - 74) / (-70).

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The solution for the given equation is y=(93-qa)/(q-67).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is q⋅(a+y)=67y+93

Here, qa+qy=67y+93

qy-67y=93-qa

y(q-67)=93-qa

y=(93-qa)/(q-67)

Therefore, the solution for the given equation is y=(93-qa)/(q-67).

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Answer:

Dont see anything

Step-by-step explanation:

Pls put a picture, no picture = can't help

Answer:

What is "this"? You didn't even post a problem.

Step-by-step explanation:

the general lighting VA requirement be for the building service calculation will be 13500VA.

General lighting, also known as ambient lighting, provides an area with overall, non-specific illumination. Radiating a comfortable level of brightness, General lighting enables one to use and see a space according to its function.

given, you have a 4500 square foot club.

Since,  in the National Electrical Code considers a residence a listed occupancy at 3 VA per square foot; therefore, the general lighting load is determined by multiplying the square footage.

Thus,

General lighting required = 4500*3 VA

General lighting required = 13500VA

therefore,  the general lighting VA requirement be for the building service calculation will be 13500VA.

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Answer:

[tex] \frac{1}{3 {x}^{2} + 4x - 4 } [/tex]

Answer:

y=20*3^x

Step-by-step explanation:

y=20*3^x

a. The amount of rainfall received and level of water in the lake have casual and correlation relation.

b. The number of lights left on each day and the amount of the electric bill have casual and correlation relation.

c.  The increase of warm, sunny days and the number of ice cream vendors visible have not casual but correlation relationship.

d. The number of hours worked and how much money is made, have casual and correlation relation.

We have to shows a relationship that is correlated but not causal, a, b, c, or d.

a. The amount of rainfall received and level of water in the lake.

There have two events:

Event 1: The amount of rainfall

Event 2: The level of water

The both event are related to each other because when the rainfall heavily then the level of water increase

So the relation in the statement is casual and correlation.

b. The number of lights left on each day and the amount of the electric bill.

Event 1: The number of lights left on each day

Event 2: The amount of the electric bill

The both event are related because when the light left then the bill of electricity increases.

So the relation in the statement is casual and correlation.

c. The increase of warm, sunny days and the number of ice cream vendors visible.

Event 1: The increase of warm, sunny days.

Event 2: The number of ice cream vendors visible.

The both events are related to each other because it is possible that in one place have many vendors in other hand some place have no vendors.

So this statement is not casual but there have correlation between them.

d. The number of hours worked and how much money is made.

Event 1: The number of hours worked.

Event 2: How much money is made.

Both event are related to each other because if a person worked extra hours he/she will be paid according to this.

So the relation in the statement is casual and correlation.

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Answer:

50/11

Step-by-step explanation:

because 50/11=4.54

               [tex]\sqrt[3]{100} =4.64[/tex]

              so 4.54<4.64

Answer:

hyy can you my friend,,,,

A life table provides data on the number of living individuals in a particular age class. Age classes are often represented by a time period of 12 month(s).

A life table delivers data on the number of living individuals in a particular age class. Age classes are often represented by a time period of 1 year.

This means that the data in the life table will reflect the number of individuals who are alive in a specific age group, such as 0-1 year, 1-2 years, 2-3 years, and so on. The data in a life table is used to study mortality patterns, life expectancy, and other demographic measures.

By grouping the data into age classes of 1 year, the life table provides a snapshot of the population at different stages of life, making it easier to analyze trends and patterns in the data.

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--The given question is incomplete; the complete question is

"A life table provides data on the number of living individuals in a particular age class. Age classes are often represented by a time period of ______ month(s)."--

The slope of the curve at P is -60, and The equation for the tangent line at P is 60x + y = 245.

a) To find the slope of the curve, the derivative of a function f(x) at the given point is a slope of the curve

Slope of the given curve y = -5 - 2x² at the point P(5, -55) is the derivative f'(x) at P(5, -55)

m = f'(x) = dy/dx

= 0 - 2(2x)

Since the derivative of a constant is zero and the derivative of x² is 2x

f'(x) at P(5, -55) is 0 - 6(2 × 5)

= 0 + (- 6 × 10) = -60

b) To find an equation of the tangent line at P(5, -55) for the curve y = -5 - 2x²

The equation of tangent line in for the function f(x) at P (x1, y1) is (y - y1) = m (x - x1)

x1 = 5 and y1 = -55, f(x) = -5 - 2x² and slope of tangent m = -60

The equation of the tangent line is (y + 55) = - 60(x - 5)

⇒ y + 55 = -60x + 300

⇒ 60x + y = 300 - 55

The equation of tangent is 60x + y = 245.

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The approximate energy requirement for the car when driven at 95 km/h is 789.47 kcal/km.

We have,

If a car averages 38 km/gal when driven at 95 km/h, we can calculate the fuel consumption in gallons per kilometer (gal/km).

Fuel consumption (gal/km) = 1 / (average fuel efficiency in km/gal)

Fuel consumption (gal/km) = 1 / 38

Now, to determine the energy requirement in kcal per kilometer (kcal/km), we multiply the fuel consumption by the energy released per gallon of gasoline:

Energy requirement (kcal/km) = Fuel consumption (gal/km) * Energy released per gallon (kcal/gal)

Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)

Now,

Fuel consumption (gal/km) = 1 / 38

Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)

Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)

≈ 789.47 kcal/km

Therefore,

The approximate energy requirement for the car when driven at 95 km/h is 789.47 kcal/km.

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The complete question:

"Burning gasoline in a car releases approximately 3 x 10^4 kcal/gal. If a car averages 38 km/gal when driven at 95 km/h, what is the energy requirement in kcal per kilometer (kcal/km) for the car?"

Alicia will have £2,238.93 in her account after 10 years if she invests £2130 in a 0.5% account.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.

Here,

principal=£2,130.00

rate=0.5%
time=10 years

Compound interest earned=£108.93

Total amount=£2,238.93

Alicia will have £2,238.93 in the account after 10 years when she invests £2130 into an account that pays 0.5%.

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Complete question:

Alicia invests £2815 into an account that pays 1% compound interest per year. Work out how much Alicia will have in the account after 10 years.

Answer:

Step-by-step explanation:

[tex] {4}^{2} + (10 \times 2) \\ 16 + (10 \times 2) \\ 16 + 20 \: \: \: \: \: \: \: \: \: \: \: \\ 36 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]4^2+(10\times2)[/tex]

[tex]4^2+20[/tex]

[tex]16+20[/tex]

[tex]=\boxed{36}[/tex]

Existence and uniqueness of solutions are guaranteed for all of the given initial value problems.

1. dy/dx = 2x^2y^2: y(1) = -1

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (1, -1), the function f(x, y) = 2x^2y^2 is continuous and the partial derivative ∂f/∂y is also continuous.

2. dy/dx = x ln y: y(1) = 1

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (1, 1), the function f(x, y) = x ln y is continuous and the partial derivative ∂f/∂y is also continuous.

3. dy/dx = cubicroot y: y(0) = 1

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 1), the function f(x, y) = cubicroot y is continuous and the partial derivative ∂f/∂y is also continuous.

4. dy/dx = cubicroot y: y(0) = 0

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 0), the function f(x, y) = cubicroot y is continuous and the partial derivative ∂f/∂y is also continuous.

5. dy/dx = Squareroot x- y: y(1) = 2

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (1, 2), the function f(x, y) = Squareroot x - y is continuous and the partial derivative ∂f/∂y is also continuous.

6. dy/dx = Squareroot x - y: y(2) = 2

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (2, 2), the function f(x, y) = Squarroot x - y is continuous and the partial derivative ∂f/∂y is also continuous.

7. dy/dx = Squareroot x - y: y(2) = 1

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (2, 1), the function f(x, y) = Squareroot x - y is continuous and the partial derivative ∂f/∂y is also continuous.

8. y dy/dx = x - 1: y(0) = 1

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 1), the function f(x, y) = x - 1 is continuous and the partial derivative ∂f/∂y is also continuous.

9. y dy/dx = x - 1: y(1) = 0

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (1, 0), the function f(x, y) = x - 1 is continuous and the partial derivative ∂f/∂y is also continuous.

10. dy/dx = ln(1 + y^2): y(0) = 0

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 0), the function f(x, y) = ln(1 + y^2) is continuous and the partial derivative ∂f/∂y is also continuous.

11. dy/dx = x^2 - y^2: y(0) = 1

Existence and uniqueness of a solution is guaranteed by Theorem I. At the point (x, y) = (0, 1), the function f(x, y) = x^2 - y^2 is continuous and the partial derivative ∂f/∂y is also continuous.

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Answer:(-4,0)

Step-by-step explanation:

Assuming that the standard deviation remains 0.12 ounces, so 16.251 ounces mean weight should Buckley Farms use.

The total weight of each bag follows an approximately normal distribution with a mean of 16.15 ounces and a standard deviation of 0.12 ounces.

Mean (μ) = 16.15

Standard deviation, (σ) = 0.12

n = 6

Buckley Farms decides to increase the mean weight of each bag of chips so that only 5%(0.05) of the bags have weights that are less than 16 ounces. So

P(X > x) = 0.05

P[(X - μ)/(σ/√n) > (x - μ)/(σ/√n)] = 0.05

1 - P(Z ≤ z) = 0.05

Subtract 1 on both side , we get

P(Z ≤ z) = 0.95

z = 1.96

(x' - μ)/(σ/√n) = 1.645

Now putting the value

(x' - 16.15)/(0.15/√6) = 1.645

(x' - 16.15)/(0.15/2.45) = 1.645

(x' - 16.15)/(0.0612) = 1.645

Multiply by 0.0612 on both side, we get

x' - 16.15 = 0.100674

Add 16.15 on both side, we get

x' = 16.251

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The complete question is:

Buckley Farms produces homemade potato chips that it sells in bags labeled 16 ounces. The total weight of each bag follows an approximately normal distribution with a mean of 16.15 ounces and a standard deviation of 0.12 ounces. Buckley Farms ships its chips in boxes that contain 6 bags. Buckley Farms decides to increase the mean weight of each bag of chips so that only 5% of the bags have weights that are less than 16 ounces. Assuming that the standard deviation remains 0.12 ounces what mean weight should Buckley Farms use?