Find f'(x), f''(x), and f(3)(x) for the following function. f(x) = 4x2 + 7x² + 2x + f'(x) =

The  solution to this system of equations −4x+9y = 9 and x−3y = − 6 is,

(10, 5)

By using the substitution method, the solution to this system of equations −3x + 3y = 4  and −x + y = 3 is, No solution

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Given that,

System of equation,

−4x + 9y =   9

 4x − 4×3y = − 4×6   (multiplying equation by 4)

 0  - 3y   = -15

         y  =  5

−4x + 9×5 = 5

-4x  = -40

  x  =  10  

Second, system of equations

By substitution method,

−3x + 3y = 4

 −x  +  y  =   3      

Both the lines are parallel ,

so they will never intersect each other

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P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are if we are unclear about how an event will turn out. Statistics refers to the study of occurrences subject to probability.

According to the question

a) Assuming that X is the random variable that takes the place of the number of defectives and has a normal distribution with a mean of 10 ounces and a standard deviation (σ) of 0.15.

The random variable's values deviate from the mean by 1, causing them to either exceed or fall short of (10 + 0.15) and (10-0.15)

= 10.15 or 9.85.

The following formula may be used to determine the likelihood that there will be either more or lesser defects than the range of 10.15 to 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P\((\frac{9.85-10}{0.15} < \frac{X - 10}{0.15} < \frac{10.15-10}{0.15} )\)

P( X < 9.85 or X > 10.15 ) = 1 - φ(1) - φ(-1)

Now we calculate the value of z for z = 1 and z = -1; we have: 0.841345 and 0.158655 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.841345 - 0.158655)

P( X < 9.85 or X > 10.15 ) = 0.31713

P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

b) It is possible to lower the process standard deviation to 0.05 by making modifications to the process design.

The following formula may be used to determine the likelihood that the number of defectives is either larger than 10.15 or lesser than 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P\((\frac{9.85-10}{0.15} < \frac{X - 10}{0.15} < \frac{10.15-10}{0.15} )\)

P( X < 9.85 or X > 10.15 ) = 1 - φ(3) - φ(-3)

Now we calculate the value of z for z = 3 and z = -3; we have: 0.99865 and 0.00135 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.99865 - 0.00135)

P( X < 9.85 or X > 10.15 ) = 0.00271

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

(c) What is the benefit of increasing the number of standard deviations from the mean for process control limits by minimizing process variation?

As we can see from the reduction from a to b above, the key benefit of minimizing process variance is that it will decrease the likelihood of receiving a defective item.

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Answer:

12 because it's big and you will find it easily because 3+4=7 and add 5 to reach this number

Clearing the equation with fractions can indeed make solving the equation easier. To do this, you'll need to multiply both sides of the equation by the least common denominator (LCD). Let me give you a couple of examples:

Example 1:
Let's say we have the equation: (2/3)x - 1/4 = 1/2

To clear the fractions, we need to find the LCD, which is 12 in this case (since it's the smallest number that both 3 and 4 divide into evenly).

Now, we multiply both sides of the equation by 12:
12 * (2/3)x - 12 * (1/4) = 12 * (1/2)

This simplifies to:
8x - 3 = 6

From here, we can solve for x by isolating the variable:
8x = 6 + 3
8x = 9
x = 9/8

Example 2:
Let's take another equation: 3/5x + 1/2 = 2/3

The LCD in this case is 30 (smallest number divisible by both 5 and 2).

Multiplying both sides by 30, we get:
30 * (3/5)x + 30 * (1/2) = 30 * (2/3)

Simplifying further:
18x + 15 = 20

To solve for x, we isolate the variable:
18x = 20 - 15
18x = 5
x = 5/18

Remember, clearing the equation with fractions by multiplying both sides by the LCD helps eliminate the fractions and makes solving the equation more straightforward.

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Answer:

Proportional

Step-by-step explanation:

Let's test this out. So for example you have the fractions: 12/30 and 18/?

Let's solve for ?

12 - 18

30 - ?

Solve: 30×18÷12=45

In the problem it also said 45 on the bottom, so yah they are proportional.

The percent of discount, rounded to the nearest tenth, is approximately 30.7%.

To find the percent of discount, we need to calculate the difference between the original price and the selling price, and then divide that by the original price. Finally, we multiply by 100 to express it as a percentage.

Discount = Original Price - Selling Price = $23,505 - $16,295 = $7,210

Percent of Discount = (Discount / Original Price) * 100 = ($7,210 / $23,505) * 100 ≈ 30.7%

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Answer:

156

Step-by-step explanation:

1) The formula for finding the sum of interior angles of an n-gon is 180(n-2)

2) Plug in 15 for n

180(15-2)

3) Solve

180(15-2)

180(13)

2340

4) There are 15 angles in a 15-gon

5) Divide sum of interior angles by number of interior angles

2340/15 = 156

6) So, the answer is 156 degrees

Answer:

A formula can help solve problems as it gives the person a step-by-step mini key or guide when needing to actually answer a mathematical or scientific equation or question.

There are 6 subgroups of order 7 in Z/28Z. To find them, you need to identify which elements of Z/28Z generate a group of order 7.

These elements are 1, 7, 13, 19, 25, and 27. Each element creates a subgroup of order 7. These subgroups are:

1) {1, 7, 13, 19, 25, 27, 28}
2) {1, 7, 13, 19, 25, 27}
3) {1, 7, 13, 19, 25}
4) {1, 7, 13, 19}
5) {1, 7, 13}
6) {1, 7}

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The 95% "confidence-interval" for "mean-weight" of all bags of potatoes is (20.53614, 21.36386) pounds.

To find 95% "confidence-interval" for mean-weight of all bags of potatoes, we use formula : CI = x' ± t × (s/√(n)),

where CI = confidence interval, x' = sample mean, t = critical-value from the t-distribution based on desired confidence-level and degrees of freedom,

s = sample standard-deviation, and n = sample-size,

we substitute the values,

Sample mean (x') = (20.9 + 21.4 + 20.7 + 21.2)/4 = 20.95 pounds

Sample standard deviation (s) = √(((20.9 - 20.95)² + (21.4 - 20.95)² + (20.7 - 20.95)² + (21.2 - 20.95)²) / 3) ≈ 0.26 pounds

Sample size (n) = 4

Degrees-of-freedom (df) = n - 1 = 4 - 1 = 3,

The "critical-value" (t) for 95% "confidence-interval" and df = 3, is approximately 3.182,

CI = 20.95 ± 3.182 × (0.26/√(4))

= 20.95 ± 3.182 × (0.26/2)

= 20.95 ± 3.182 × 0.13

= 20.95 ± 0.41386

= (20.53614, 21.36386)

Therefore, the required confidence-interval is (20.53614, 21.36386).

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The given question is incomplete, the complete question is

The weights of four randomly and independently selected bags of potatoes labeled 20.0 pounds were found to be 20.9, 21.4, 20.7, and 21.2 pounds. Assume normality.

Find the 95% confidence-interval for the mean weight of all bags of potatoes.

Option (B) is the correct answer.

A company plans to spend $8,000 in year 2 and $10,000 in year 4. At an interest rate of 10% per year, compounded semiannually. The equation that represents the equivalent annual worth A in years I through 4 is given by option (B).That is;Option (B) represents the equation that represents the equivalent annual worth A in years I through 4.

The formula for equivalent annual worth is given by;A = PW (A/P, i, n) + F(A/F, i, n)where,PW = Present WorthF = Future WorthA/P = Present Worth FactorA/F = Future Worth Factori = interest raten = number of yearsSo,A = 8000(P/A, 10/2,2) + 10000(F/A, 10/2,4)A = 8000(3.1051) + 10000(0.6848)A = 24,840.80 + 6848A = $31,688.80The equation that represents the equivalent annual worth A in years I through 4 is represented by the option (B);A = 8000(P/A, 10.25/2,2) + 10000(F/A, 10.25/2,4).

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Answer:

Surface area of cube = 6x²

surface area of cube = surface area of sphere

it means that 6x²=4πr²

x²=

\( \frac{4\pi {r}^{2} }{6} = \frac{4 \pi9}{6} = \frac{4\pi3}{2} = 6\pi\)

\(x = \sqrt{6\pi} \)

\( \sqrt{6\pi} = \sqrt{k\pi} \)

\(6\pi = \pi \: k\)

\(k = 6\)

Answer: a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.

Step-by-step explanation:

Answer:

The cube has nine symmetry planes. Three planes lie parallel to the side squares and go through the centre (picture). Six planes go through opposite edges and two body diagonals. They divide the cube into prisms

y = 3x +4

3 is the slope. Rise 3 run 1 or up 3 right 1.

4 is the y-intercept

A pencil consists of a cylindrical body (10 cm long, radius 0.3 cm) with a cone-shaped eraser (1 cm slant height) and a hemisphere-shaped eraser.

A pencil consists of three main parts: a cylindrical body, a cone-shaped eraser, and a hemisphere-shaped eraser. Let's break down the dimensions of each part:

Cylindrical Body:

Length: 10 cm

Radius: 0.3 cm

Cone-shaped Eraser:

Slant height: 1 cm (assumed height of the cone)

Hemisphere-shaped Eraser:

Since the dimensions of the hemisphere-shaped eraser are not specified in detail, we'll assume a few things:

Let's assume that the hemisphere is attached to the cone in such a way that the flat surface of the hemisphere is aligned with the circular base of the cone.

We'll assume that the radius of the hemisphere is the same as the radius of the cylindrical body, which is 0.3 cm.

Please note that the actual dimensions of a pencil can vary, and these assumptions are made for the purpose of explanation.

It's worth mentioning that the cylindrical body of the pencil is the main part used for writing, while the cone-shaped and hemisphere-shaped erasers are located at the opposite end of the pencil, typically used for erasing mistakes.

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The area of the circular railroad crossing sign in square inches is 706.5 square inches.

The area of the circle is given by the formula,

A = πD²/4

R is the diameter,

A is the Area.

It is given that there is a circular railroad crossing sign that has a diameter of 30 inches.

The area of the circular railroad crossing sign can be calculated by using the above mentioned formula.

Putting the value of the diameter in the above formula,

A = π(30)²/4

A = 706.5 square inches.

So, the area of the sign is 706.5 square inches.

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Answer:

12x-18

Step-by-step explanation:

expanded expression 3⋅x⋅2⋅x+3⋅x⋅4+2⋅x+4

expanded and reduced expression 4+14⋅x+6⋅x

Answer:

2 9/14

Step-by-step explanation:

Answer:

im pretty sure the answer is A 6

Step-by-step explanation:

Any graph that has a horizontal line at a period stays constant for a while.

In all cases, the function is moving right. If the function is moving right but the vertical axis remains constant, forming an horizontal line, the function is constant for that period.

Hence the graph in this problem shows that the height stays constant for a while because it has a horizontal line.

(the problem is incomplete as the graph is not given, but the explanation for a constant function is always this).

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the angle between 0 and 2π that is coterminal with 17π/4 is π/4.

To find the angle between 0 and 2π that is coterminal with 17π/4, we need to find an equivalent angle within that range.

Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of 2π.

To determine the coterminal angle with 17π/4, we can subtract or add multiples of 2π until we obtain an angle within the range of 0 to 2π.

Starting with 17π/4, we can subtract 4π to bring it within the range:

17π/4 - 4π = π/4

The angle π/4 is between 0 and 2π and is coterminal with 17π/4.

what is equivalent'?

In mathematics, the term "equivalent" is used to describe two things that have the same value, meaning, or effect. When two mathematical expressions, equations, or statements are equivalent, it means that they are interchangeable and represent the same mathematical concept or relationship.

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Differential equations and boundary value problems are mathematical equations that contain derivatives of unknown functions and their variables.

These equations are used to model a wide range of physical, biological, and chemical processes. The seventh edition of Fundamentals of Differential Equations and Boundary Value Problems by R. Kent Nagle, Edward B. Saff, and Arthur David Snider is a comprehensive textbook that covers the fundamentals of these equations.Differential equations and boundary value problems are mathematical equations that contain derivatives of unknown functions and their variables.  It includes topics such as first order equations, higher order linear equations, systems of equations, Laplace transforms, Fourier series, and numerical methods. It also contains a variety of worked examples, exercises, and applications to help students understand the material. Examples include solving initial value problems, boundary value problems, and inverse problems. The book also provides a step-by-step approach to solving problems, including the use of formulas such as the Euler-Cauchy formula, the Picard-Lindelof formula, the Runge-Kutta formula, the Laplace transform, and the Fourier series.

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Complete question:

Find the solution to the differential equation dy/dx + 4y = 0, given the boundary values y(0) = 2 and y(2) = 0.

Answer:

Step-by-step explanation:

   9² + 10² + 11² + ......... 20² =

= 9² + 10² + 11² + 12² + 13² + 14² + 15² + 16² + 17² + 18² + 19² + 20² =

= 81 +100 +121 +144 +169 +196 +225 +256 +289 +324 +361 +400 =

= 2666

The quadratic equation x² - 3x - 28 = 0 has two real rational solutions. Therefore the correct option is 3. Two real rational solutions

To determine the type of solutions to the quadratic equation x² - 3x - 28 = 0, we can use the discriminant, which is the term b² - 4ac in the quadratic formula.

In this case, the coefficients are:

a = 1 (coefficient of x²)

b = -3 (coefficient of x)

c = -28 (constant term)

The discriminant is calculated as follows:

Discriminant = b² - 4ac

Discriminant = (-3)² - 4(1)(-28)

Discriminant = 9 + 112

Discriminant = 121

Now, let's analyze the value of the discriminant:

1. If the discriminant is positive (greater than zero), there are two real solutions.

2. If the discriminant is zero, there is one repeated real solution.

3. If the discriminant is negative (less than zero), there are two complex solutions.

In this case, the discriminant is 121, which is positive. Therefore, the quadratic equation x² - 3x - 28 = 0 has two real rational solutions.

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False. The frequency polygon and the histogram are two different ways to represent data, and they have distinct characteristics.

A frequency polygon is a line graph that displays the distribution of a quantitative variable. It shows the frequency of each value or class interval on the horizontal axis and the corresponding frequencies on the vertical axis. The points on the graph are connected to form a line, which gives a visual representation of the data distribution.

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we will need about 21 rolls of carpet to cover the 50-foot by 70-foot restaurant dining room.

We know that a roll of carpet covers an area of 12ft by 14ft, then each roll covers an area of:

a = 12ft*14ft = 168ft^2

And we want to cover an area of 50ft by 70ft, that area gives:

A = 50ft*70ft = 3,500ft^2

The number of rolls that we need is given by the quotient between the areas, we will get:

number of rolls = A/a = (3,500ft^2)/(168ft^2) = 20.83

Rounding to the next whole number, we get 21.

So we will need about 21 rolls of carpet to cover the 50-foot by 70-foot restaurant dining room.

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