A manufacturer knows that their items have a normally distributed length, with a mean of 11.2 inches, and standard deviation of 1.4 inches. If 2 items are chosen at random, what is the probability that their mean length is less than 9 inches

Answer:

62.4

Step-by-step explanation:

Sam's score= x

John's score= 2/3x-4

john's score + sam's score=100

x+2/3x-4=100

5/3x-4=100

5/3x=104

5x=312

x=62.4

Sam's score is 62.4

John's score is 37.6

Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.

By multiplying the value about one unit by the quantity of units required, one can apply the unit technique to solve a problem. The unit procedure is used to separate a single entity integer from a given many, to put it simply. One pen, or 400 rupees, would be needed to purchase 40 needle. There might be a common way to verify this. only one nation. Anything has a unique feature. Algebra, grid logic, and its laminates and reverse are all identical terms used to describe mathematical analysis.

Here,

Given : Ria purchases 19 books for £6.82 apiece.

Thus,

Total cost of book = 19 * 6.82

=> 129.58

Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.

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\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

The value of the greater integer as described in the task content is; -8.

It follows from the task content that the sum of an integer and 2 times the next consecutive integer is -25.

Hence, we have;

x + 2(x+1) = -25

3x +2 = -25

3x = -27

x = -9.

Therefore, the next consecutive integer is; (x+1) = -9 + 1 = -8.

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The value of x in the trapezium is 60 degrees.

A trapezium is a quadrilateral . The sum of angles in the trapezium is 360 degrees. The legs of the trapezium ABCD are congruent.

The length AB and CD are parallel to each other.

Let's find the angle x as follows:

Therefore, using trigonometric ratios,

cos x = adjacent / hypotenuse

Where

adjacent side = 3 m

hypotenuse side = 6 m

Hence,

cos x = 3 / 6

cos x = 1 / 2

x = cos ⁻¹ 0.5

x = 60 degrees

Therefore,

x = 60 degrees.

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Answer:

hello help

Step-by-step explanation:

Answer:

A = 1,133.5 m³

Step-by-step explanation:

Surface area of a sphere, A = 4πr²

π = 3.14

Radius, r = diameter / 2

= 19 m / 2

= 9.5 m

Surface area of a sphere, A = 4πr²

A = 4 * 3.14 * (9.5)²

= 4 * 3.14 * 90.25

= 1,133.54

A = 1,133.54 m³

To the nearest tenth

A = 1,133.5 m³

Answer:

3x+y=7

8x+12y=-9

Step-by-step explanation:

Answer:

Hector makes a tent shaped like a rectangular pyramid the volume is 56 cubic feet and the area is 24 square feet how tall is the tent

Step-by-step explanation:

The population density of Philadelphia is approximately 11,761.76 people per square mile, while the population density of Pottstown is approximately 4,672.16 people per square mile.

To compare the densities of Philadelphia and Pottstown, we need to calculate the population density for each city. Population density is typically measured as the number of individuals per unit area.

For Philadelphia:

Population = 1,579,000

Land area = 134.28 sq miles

Population density = Population / Land area

Population density = 1,579,000 / 134.28

Population density \(^\sim_\sim\) 11,761.76 people per square mile

For Pottstown:

Population = 22,670

Land area = 4.85 sq miles

Population density = Population / Land area

Population density = 22,670 / 4.85

Population density \(^\sim_\sim\) 4,672.16 people per square mile

Therefore, the population density of Philadelphia is approximately 11,761.76 people per square mile, while the population density of Pottstown is approximately 4,672.16 people per square mile.

Comparing the two, we can see that Philadelphia has a higher population density compared to Pottstown.

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Answer:

800 ÷ 30 = 26.66666666666667 or 26.

Step-by-step explanation:

The determinant of the upper triangular matrix R is equal to the determinant of the square matrix A.

Hence prove det ( det(A) det(D) . D

QR decomposition QR decomposition is a technique of expressing a matrix as a product of an orthogonal matrix and an upper triangular matrix.

Here, any real square matrix can be decomposed as A QR where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning Tq = QQ" =I) and R is an upper triangular matrix.

The factorization is unique if A is invertible. In that case, the determinant of A can be written as a product of the determinants of Q and R.

For a triangular matrix, the determinant is the product of the diagonal elements.

That is, if A is an n × n matrix, then A = QR

where Q is an orthogonal matrix of size n × n and R is an upper triangular matrix of size n × n.

The determinant of A can be written as the product of the determinants of Q and R.

That is, |A| = |Q| |R|

Since Q is orthogonal, |Q| = ±1

Also, since R is upper triangular, |R| = Product of diagonal elements of R

Now, for an invertible matrix A|A| ≠ 0So,|Q| |R| ≠ 0|Q| ≠ 0 and |R| ≠ 0So,|A| ≠ 0

Therefore, det(A) det(D) .

D200 can be written as |A| = |Q| |R| |D|200

Now, |R| is the product of diagonal elements of R.

Therefore, |D|200 = 1.So, |A| = |Q| |R|

Now, the determinant of Q is ±1.

Therefore, |A| = ± |R|

Therefore, |R| = |A|

This completes the proof.

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The permeability of the cylindrical core sample is approximately 0.205 Darcy.

To derive the formula for calculating permeability, we start with Darcy's equation, which relates the flow of fluid through a porous medium to the pressure gradient in the direction of the flow. Darcy's equation is expressed as:

Q = (k * A * ∆P) / μL

Where:

Q is the flow rate of the fluid,

k is the permeability of the porous medium,

A is the cross-sectional area of flow,

∆P is the pressure differential,

μ is the fluid viscosity, and

L is the length of the flow path.

To calculate the permeability, we can use Darcy's equation: k = (Q * μ * L) / (A * ΔP), where k is the permeability, Q is the flow rate, μ is the fluid viscosity, L is the length of the sample, A is the cross-sectional area, and ΔP is the pressure differential.

The laboratory linear flow test parameters:

Q = fluid velocity = 0.032 cm/s,

μ = fluid viscosity = 3.5 cP,

L = length of the sample = 20 cm,

ΔP = pressure differential = 4.4 atm.

Let's assume the cross-sectional area A as 1 cm² for simplicity.

Plugging in these values into the equation, we have:

k = (0.032 * 3.5 * 20) / (1 * 4.4) ≈ 0.205 Darcy.

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Answer:

You are left with $1.44

Step-by-step explanation:

Subtract the amount of money you payed to how much the cost actually was to get your answer.

Answer:

20

Step-by-step explanation:

62.8 cm²

Step-by-step explanation:

Circumference of a circle: 2 x pie x radius

Since the entire perimeter of the square is 80 cm². And a square has 4 sides, you divide it.

80÷4= 20 cm² each side

So if the circle fits perfectly in the square that means it has the same width as the square...which would be 20 cm²...which means 20 cm² diameter.

20 cm² diameter in radius 10 cm² [half of it]

so now you just put it in the formula..

2 x pie x 10= 62.8 cm²

The possible functions are f(x) = -x^2 and g(x) = √x

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

(fog)(x) = -√x

One possible solution is:

f(x) = -x^2

g(x) = √x

so that:

(fog)(x) = f(g(x)) = f(√x) = -(√x)^2 = -x

and neither function is identical to (fog)(x) or x.

Another possible solution is

f(x) = -x

g(x) = x^2

so that:

(fog)(x) = f(g(x)) = f(x^2) = -x^2 = -√x

and neither function is identical to (fog)(x) or x.

It's important to note that there are multiple ways to achieve this, these are just two examples.

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Answer: 197.

Step-by-step explanation:

The correct answer is option  C. The first example represents reflected-appraisal; the second example represents social comparison.

Given that: When Abe was young, he learned that he could lighten the mood with humor. Others laughed at his jokes, and he began to see himself as the 'life of the party'.
In the first example, Abe's sense of humor is positively reinforced by others laughing at his jokes, leading to an enhanced self-image. This is an example of reflected appraisal, where one's self-concept is shaped by the feedback received from others.

Also given that:Abe sometimes wishes he could be more studious and serious like his peers.
In the second example, Abe is comparing himself to his peers and wishing to be more like them. This is an example of social comparison, where individuals evaluate their own abilities and attributes by comparing themselves to others.
C. The first example represents reflected appraisal; the second example represents social comparison.

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The correct answer to the given question about colored congruent squares is option A) 0.4 < 0.6

This is because Raul shaded 40/100 of the squares yellow, which can also be written as 0.4 as a decimal. He shaded the other 60/100 of the squares green, which can also be written as 0.6 as a decimal. Therefore, we can compare the two decimals and say that 0.4 is less than 0.6. To show how we find the answer 0.4 < 0.6, we can follow these steps:

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Complete Question

Raul has a figure made up of 100 congruent squares. He shaded 40/ 100 of the squares yellow and the other 60/100 of the squares green. Select the decimal expression from the following

0.4 <0.6

0.04 < 0.06

0.4 = 0.6

0.04 = 0.06

0.4 > 0.6

0.04 > 0.06

1. Indian

2.South

3.Africa

4.stormyy

To maximize the area, the fence should be laid out in a square shape, where both sides measure 15 feet. To maximize the area of a rectangular vegetable garden with a given fence length.

it's important to understand that a rectangle with equal side lengths will yield the maximum area.

Let's denote the length of one side of the rectangle as x and the other side as y. According to the problem, the perimeter of the rectangle is given as 60 feet, so we have the equation:

2x + 2y = 60

Simplifying this equation, we get:

x + y = 30

To maximize the area, we need to maximize the product of x and y. Since x + y = 30, we can rewrite the equation as:

y = 30 - x

Substituting this into the area equation A = x * y, we get:

A = x * (30 - x)

To find the maximum area, we can take the derivative of A with respect to x and set it equal to zero:

dA/dx = 30 - 2x = 0

Solving this equation, we find x = 15. Substituting this back into y = 30 - x, we get y = 15 as well.

Therefore, to maximize the area, the fence should be laid out in a square shape, where both sides measure 15 feet.

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Answer: b

Step-by-step explanation:

Answer: 2,754 students

Step-by-step explanation:

18 / 270= 1/15

(1/15)(41,310) = 2,754 students

Answer:

x=9

Step-by-step explanation:

2(x-3)=12

First you use the distributive property

so you do 2 times x then 2 times -3

rewrite it as 2x-6=12

add 6 on both sides

2x=18

divide 2 from both sides and you get x=9

Answer:

X=3

Step-by-step explanation:

FOIL

2X-6=12

    -6=-6

2X=6

_=_

2   2

The Implied Equity Risk Premium (ERP) is generally considered a better predictor of future equity risk premium

Implied Equity Risk Premium is derived from the current market prices of stocks and other securities. It represents the difference between the expected rate of return on equities and the risk-free rate of return. Investors' expectations about future returns are embedded in market prices, so the implied ERP reflects the collective wisdom and expectations of market participants. It takes into account current market conditions, investor sentiment, and other relevant factors, making it a forward-looking indicator.

On the other hand, historical geometric average and historical arithmetic average equity risk premium are calculated based on past performance data. While historical averages provide valuable insights into the past behavior of equity risk premium, they may not fully capture the changing dynamics of the market or reflect future expectations.

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Answer:

(2,-5)

Step-by-step explanation:

Reflecting (2,5) across x-axis will invert it's y-coordinate and will make it negative.

Answer:

(2,-5).

Step-by-step explanation:

You see, when you reflect over something, one variable has to change. Our line of reflection is the x-axis, or y=0.

Here is a rule to help with these kinds of problems.

If you reflect over the x-axis, the x value is still the same, but the y value changes to be the inverse or opposite value. The opposite of positive is negative, so it will be -5.

For reflected over the y-axis, the y value stays the same, but the x value changes to be the inverse of the original y value.