The fill size for a small bag of peanuts distributed by a popular airline is 50 grams. The producer wishes to set up a set of control charts for this process and collects the data shown in the table. What are the upper and lower control limits of their X-bar chart?
A) 53.87, 50.78 B) 54.41, 50.32 C) 53.51, 51.18 D) 54.84, 49.85

The formula for the discriminant is

d = b^2 - 4ac

If d < 0, then there are no real number solutions

If d = 0, then you have exactly one real solution

If d > 0, then you have two different real number solutions

88 cm is the circumference of a circle with a diameter of 28 cm.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The circumference of a circle with a diameter of 28 cm.

Radius = 28/2

Radius is 14 cm.

Circumference=2πr

=2×3.14×14

=87.92=88 cm

Hence, 88 cm is the circumference of a circle with a diameter of 28 cm.

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The matrix P that orthogonally diagonalizes matrix A is : P = [1 1;

To find the matrix P that orthogonally diagonalizes matrix A, we need to find its eigenvalues and eigenvectors.

Given matrix A:

A = [4 1; 1 4]

To find the eigenvalues, we solve the characteristic equation:

|A - λI| = 0

Where λ is the eigenvalue and I is the identity matrix.

Calculating the determinant:

|A - λI| = |4-λ 1| = (4-λ)(4-λ) - 1*1

|1 4-λ|

Expanding and simplifying:

(4-λ)(4-λ) - 1*1 = λ^2 - 8λ + 15 = 0

Factoring the quadratic equation:

(λ - 5)(λ - 3) = 0

So, the eigenvalues are λ1 = 5 and λ2 = 3.

To find the corresponding eigenvectors, we substitute each eigenvalue into the equation (A - λI) * X = 0, and solve for X.

For λ1 = 5:

(A - 5I) * X1 = 0

Substituting the values:

(4-5 1)(x1) = (0)

(1 4-5)(y1) = (0)

Simplifying:

-1x1 + y1 = 0

x1 - 1y1 = 0

This gives us x1 = y1. Let's choose x1 = 1, which leads to y1 = 1.

So, the eigenvector corresponding to λ1 = 5 is X1 = [1; 1].

Similarly, for λ2 = 3:

(A - 3I) * X2 = 0

Substituting the values:

(4-3 1)(x2) = (0)

(1 4-3)(y2) = (0)

Simplifying:

1x2 + y2 = 0

x2 + 1y2 = 0

This gives us x2 = -y2. Let's choose x2 = 1, which leads to y2 = -1.

So, the eigenvector corresponding to λ2 = 3 is X2 = [1; -1].

Now, we can construct the matrix P by using the eigenvectors as columns:

P = [X1 X2] = [1 1; 1 -1]

To find P^(-1), the inverse of P, we can use the formula for the inverse of a 2x2 matrix:

P^(-1) = (1 / (ad - bc)) * [d -b; -c a]

Substituting the values:

P^(-1) = (1 / (1*(-1) - 1*1)) * [-1 -1; -1 1]

= (1 / (-2)) * [-1 -1; -1 1]

= [1/2 1/2; 1/2 -1/2]

Finally, we can determine P^(-1)AP:

P^(-1)AP = [1/2 1/2; 1/2 -1/2] * [4 1; 1 4] * [1/2 1/2; 1/2 -1/2]

Performing the matrix multiplication:

P^(-1)AP = [5 0; 0 3]

Therefore, the matrix P that orthogonally diagonalizes matrix A is:

P = [1 1;

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The elevation gain of Mount Everest is 15,028 feet, a very impressive feat considering it is the highest elevation gain of any mountain in the world.

The difference between the height at the base of Mount Everest, which is 14,000 feet and the summit, which is 29,028 feet is 15,028 feet. This is also known as the elevation gain. It can be calculated using the following formula:

Elevation Gain = Summit Height - Base Height

So in this case, Elevation Gain = 29,028 ft - 14,000 ft

Which gives us: Elevation Gain = 15,028 ft

The elevation gain of Mount Everest is 15,028 feet, a very impressive feat considering it is the highest elevation gain of any mountain in the world. It is also the highest mountain in the world, with the summit standing at an impressive 29,028 feet. This is a testament to the power of nature and the sheer scale of Mount Everest.

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Effective situational leaders demonstrate a high degree of flexibility.

Flexibility is a key quality for situational leaders since they must modify their style of leadership according to the circumstances, the demands of their team, and the objectives to be met. They are able to modify their strategy, communication style, and decision-making process to suit the demands of various situations.

Flexibility stands out as a crucial feature that enables leaders to negotiate a variety of situations and guide their teams to success, even though honesty, extraversion, empathy, and other qualities are also important in leadership.

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Answer:

y = 2x

Step-by-step explanation:

The slope is 2.  Find a point on the line, to go back to the line, go up two and one to the right.  You will be back on the line.  This pattern repeats over and over and again.

A random variable is a variable that takes on values that are uncertain or probabilistic in nature.

Therefore, the correct option is a) A variable that takes on values that are uncertain.

Random variables can be discrete, meaning they can only take on specific values, or continuous, meaning they can take on any value within a certain range.

These variables are commonly used in statistical analyses and probability theory to model various phenomena, such as the outcome of a dice roll or the height of individuals in a population.

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Answer:

This was a nice way to spend my time :) how'd I do?

Step-by-step explanation:

Total: 6

1. +8

After stop 1, total is 14 people

2. +4, -2

After stop 2, total is 16 people

3. +15, -4

After stop 3, the total is 27 people

4. -8

Total # of people on the bus: 19

(A little voice in the back of my mind is telling me that I overthought this entire problem, and that the answer is just 6)

4.) The correct equation that represents Fred's score would be = 2+f = 16. That is option B.

5.) coefficient = 5

variable = x

constant= -8 and 12

Sally game scores= 2 + f

Fred game scores = f

The total scores of Sally = 16 points

Therefore to calculate the score of Fred = 2+f = 16

Make f the subject of formula = f = 16-2 = 14

For the given equation which is 5x - 8 = 12. The parts of the equation include the following;

Coefficient= This is the number that is used to multiple a variable. Example is the 5 attached to X.

Variable: This is part of an equation that is varying or changing which is represented by a letter such as X in the given equation.

Constant: This is a fixed quantity that doesn't vary.

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Answer:

C(0.7) = 26

Step-by-step explanation:

Given:

C(x) = 30x + 5

where,

x = gigabytes of data used over the monthly allowance.

1. Find C(0.7) and explain what it means in this situation

C(0.7) means he used 0.7 gigabytes of data over the monthly allowance

Substitute x = 0.7 into the equation to find the monthly cost of the option

C(x) = 30x + 5

C(0.7) = 30(0.7) + 5

= 21 + 5

= 26

C(0.7) = 26

When x = 0.7, his total cost will be 26

The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

You failed to make the minimum payment by the due date. This is an action that can result in a message that "you've triggered the Penalty APR so that it has now climbed to 28.99%."

A charge APR is a charge that can be applied if you don't pay your bills on time. It may be set up so that future transactions may be subject to a penalty APR that is higher than the card's standard rate.

If the minimum payment was not made by the due date, Penalty APR would be applied.

But if the card also has a penalty APR and you trigger it, you will likely lose that promotional offer. Federal consumer protections that limit penalty APRs don't apply to small-business credit cards. That means issuers can be more punitive, such as applying penalty APRs sooner than 60 days after not making payments.

Therefore,

The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

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The sample size is 68.

Standard deviation is also known as root-mean-square deviation" because it is the square root of the means of the squared deviations from the arithmetic mean.

Given a population is estimated to have a standard deviation of 15. We want to estimate the population mean within 3, with a 90% level of confidence.

We must determine the required sample size.

In this case, the margin of error is E = 3

For 90% CI z value is 1.645 as P(-1.645<z<1.645)

And the standard deviation is σ=15    

So we will find n using the formula of E

E = z x σ/√n

√n = (zx σ)/E

Squaring on both sides

n=(〖zxσ/E)〗^2

= [(1.645 x 15)/3]2

= 67.6506

= 68

Therefore the required sample size is 68

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Answer:

95.0

Step-by-step explanation:

Area of a circle

A = πr2

Radius is half the diameter = 11/2 = 5.5

A = π x 5.5 x 2

= 95.033177...

= 95.0

Answer:11.2

Step-by-step explanation:

    5.6

       2

______

11.2

Answer:

Step-by-step explanation:

Surface Area

(1)

Triangular Prism

Given that:

Find the surface area!

Surface area =

bh + d(b+2y) =

(7 × 6) + (10×(7+(2×9))) =

42 + 250 =

___________________

(2)

Cuboid

Given that:

Find the surface area!

Surface area =

2LW + 2LH + 2WH =

(2×(11×10)) + (2×(11×3)) + (2×(10×3)) =

220 + 66 + 60 =

______________

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- kexcvi -

Answer:

3 times

Step-by-step explanation:

Equation: 810 = 288x

x = 2.8 meaning you need to fill up the tank 3 times

Answer:

125 units^3

Step-by-step explanation:

Volume is l*w*h = V. A cube has all equal sides so wecan divide 1000 by 3 and get our side lengths.

You then divide the sides by 2 because the question says the second cubes sides are half the size

5*5*5 = 125

The volume of the second cube is 125 units³.

In mathematics, ‘Volume’ is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Given that a cube has volume 1000 units³ and another smaller cube has smaller volume has side only half as long.

We need to find the volume of the second cube,

So, let the side of the first cube be x,

We know that the volume of a cube = side³

Therefore,

x³ = 1000

x = ∛1000

x = 10 units

Therefore, the second cube will have a side of 10/2 = 5 units

Volume of second cube = 5³ = 125 units³.

Hence the volume of the second cube is 125 units³.

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Answer:

The common ratio is 15/3=5 or 75/15 =5.

Step-by-step explanation:

The common ratio of the sequence is 5

Common ratio is the ratio between the preceding and the succeeding term of a sequence

Given the sequence 3, 15, 75 ...

T1 = 3

T2 = 15

T3 = 75

common ratio r = T3/T2 = T2/T1

r = 75/15 = 15/3 = 5

Hence the common ratio of the sequence is 5

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Answer:

Step-by-step explanation:

thank you you amazing stranger

Answer:

Step-by-step explanation:

time=distance/speed

=4800/48

100

Answer:

\(\Huge \boxed{\mathrm{100 \ seconds}}\)

Step-by-step explanation:

4.8 kilometers is 4800 meters.

\(\sf \displaystyle time \ (s) = \frac{distance \ (m) }{speed \ (m/s)}\)

\(\sf \displaystyle t = \frac{4800}{48}\)

\(\sf \displaystyle t = 100\)

It will take the object 100 seconds.

Step-by-step explanation: x =9

Answer:

\(AC = 20\)

Step-by-step explanation:

Given

\(AC = 2x + 8\)

\(AB = 4x - 16\)

\(BC = 3x - 6\)

Required

Find AC

First, we need to solve for x

Since B is between A and C, then

\(AC = AB + BC\)

Substitute values for AC, AB and BC

\(2x + 8 = 4x - 16 + 3x - 6\)

Collect Like Terms

\(2x - 4x - 3x = -16 - 6 - 8\)

\(-5x = -30\)

Divide through by -5

\(\frac{-5x}{-5} = \frac{-30}{-5}\)

\(x = \frac{-30}{-5}\)

\(x = 6\)

Substitute 6 for x in \(AC = 2x + 8\)

\(AC= 2 * 6 + 8\)

\(AC= 12 + 8\)

\(AC = 20\)

Answer:

C. 5.3

step by step explanation:

Answer:

C. 5.3

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=47x

Answer:  The correct answer is b=2a

Step-by-step explanation:

Solve for b

A = (a + b)/3

Flip the equation

1/3a + 1/3b = a

Add (-1)/3a to both sides.

1/3a + 1/3b + −1/3a = a + −1/3a

1/3b = 2/3a

Divide both sides by 1/3

(1/3b)/(1/3) = (2/3a)/(1/3)

b=2a

Answer:

\(b = 3A - a\) (if A and a are two different variables).

\(b = 2a\) (If the A and a denote the same variable.

Step-by-step explanation:

\(A = \frac{(a + b)}{3}\)

Isolate the variable, b. Note the equal sign, what you do to the one side, you do to the other.

Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, multiply 3 to both sides of the equation:

\(A (*3) = \frac{(a + b)}{3} (* 3)\\A * 3 = (a + b)\)

Next, subtract a from both sides of the equation:

\(A * 3 = a + b\\3A = a + b\\3A (-a) = a (-a) + b\\b = 3A - a\)

\(b = 3A - a\) is your answer.

IF, however, you meant to put both lower case variable a (or vice versa), then you can further simplify:

\(b = 3a - a\\b = 2a\)

\(b = 2a\) is your answer if the a are supposed to be the same variable.

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Answer:

its 1.4

Step-by-step explanation:

Answer:

1.4

Step-by-step explanation:

Answer:

$22,880.04 Without paying off the debt

$18,880.04 After paying off the debt

Step-by-step explanation: