Which of the following statements regarding the expansion of (x + y)" are
correct?
A. The coefficients of xay and xbya are equal.
B. The coefficients of x-1 and y-1 both equal 1.
C. The coefficients of x" and y both equal 1.
D. For any term xay in the expansion, a - b = n.

The correct values that create ordered pairs that are solutions to the solutions to the equation 3x - 5y = 20 are,

⇒ y₁ = - 1

⇒ x₂  = 10

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The equation is,

⇒ 3x - 5y = 20

Now, If (5, y₁) is the solution of above equation, then it satisfy the equation.

⇒ 3x - 5y = 20

⇒ 3 × 5 - 5y₁ = 20

⇒ 15 - 5y₁ = 20

⇒ 15 - 20 = 5y₁

⇒ - 5 = 5y₁

⇒ y₁ = - 1

And, If (x₂, 2) is the solution of above equation, then it satisfy the equation.

⇒ 3x₂ - 5y = 20

⇒ 3x₂ - 5×2 = 20

⇒ 3x₂ - 10 = 20

⇒ 3x₂ = 20 + 10

⇒ 3x₂ = 30

⇒ x₂  = 10

Thus, The correct values that create ordered pairs that are solutions to the solutions to the equation are,

⇒ y₁ = - 1

⇒ x₂  = 10

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The fractions found in the 2/n table in the Rhind Mathematical Papyrus.

2/7 = (m n 2 ) 1 n (m n 2 )

= (2 7 2 ) 1 7 (2 7 2 )

= (14 2 ) 1 7 (14 2 )

= 7 1 7 + 7 1 14

2/35 = (m n 2 ) 1 n (m n 2 )

= (2 35 2 ) 1 35 (2 35 2 )

= (70 2 ) 1 35 (70 2 )

= 35 1 35 + 35 1 70

2/91 = (m n 2 ) 1 n (m n 2 )

= (2 91 2 ) 1 91 (2 91 2 )

= (182 2 ) 1 91 (182 2 )

= 91 1 91 + 91 1 182

Using the identity (m n 2 ) 1 n (m n 2 ) we can decompose the fractions 2/7, 2/35, and 2/91 into unit fractions. For 2/7, we obtain the decomposition 7 1 7 + 7 1 14, for 2/35 the decomposition 35 1 35 + 35 1 70, and for 2/91 the decomposition 91 1 91 + 91 1 182. This matches the fractions found in the 2/n table in the Rhind Mathematical Papyrus.

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The five vectors in the span {v1, v2} are (0 0 0), (3 1 2), (-4 0 1), (-1 1 3) and (7 1 1)

We are given that two vectors

v1 = ( 3 1 2 ) and v2 = ( −4 0 1 )

We have to list five vectors in the span {v1, v2}

Let us choose five sets of weights as:

w = {0, 0}, {1, 0}, {0, 1}, {1, 1}, {1, -1}

So, the five vectors are:

V1 = 0 (v1) + 0 (v2) = (0 0 0)

V2 = 1 (v1) + 0 (v2) = (3 1 2)

V3 = 0 (v1) + 1 (v2) = (-4 0 1)

V4 = 1 (v1) + 1 (v2) = (3-4 1+0 2+1) = (-1 1 3)

V5 = 1 (v1) - 1 (v2) = (3+4 1-0 2-1) = (7 1 1)

Hence, the five vectors in the span {v1, v2} are (0 0 0), (3 1 2), (-4 0 1), (-1 1 3) and (7 1 1)

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The expressions that equal 36 is:

E) 53 − (2. 5 × 30) − 20

Evaluated the mathematical expressions in each response to see if they equal 36.

A. (14⋅32)2−28 = (448)² - 28 = 14⁴ - 28 = 2016 - 28 = 1988, not equal to 36.

B. 23 + (58−54)2 + 122 = 23 + (4)² + 12 = 23 + 16 + 12 = 51, not equal to 36.

C. 92 − (43 + 32) + 30050 = 9² - (7 + 3) + 30050 = 81 - 10 + 30050 = 30021, not equal to 36.

D. 124 + (82 − 42) − 99 = 124 + (64 - 16) - 99 = 124 + 48 - 99 = 73, not equal to 36.

Thus, only the expressions listed in my previous answer equal 36.

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The probability that a defective component can be detected by only one inspector is 0.2112. the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.

(a) To calculate the probability that a defective component will be detected by only one inspector, we can use the formula for conditional probability: P(detected by first inspector | not detected by second inspector) = P(detected by first inspector and not detected by second inspector) / P(not detected by second inspector).

The probability that a defective component will be detected by the first inspector and not detected by the second inspector can be calculated as follows: P(detected by first inspector and not detected by second inspector) = P(detected by first inspector) * P(not detected by second inspector | detected by first inspector) = 0.88 * (1 - 0.88) = 0.1056.

The probability that a defective component will not be detected by the second inspector is: P(not detected by second inspector) = 1 - P(detected by second inspector) = 1 - 0.88 = 0.12.

The probability that a defective component will be detected by exactly one of the two inspectors can be calculated as follows: P(detected by exactly one inspector) = P(detected by first inspector and not detected by second inspector) + P(detected by second inspector and not detected by first inspector) = 0.1056 + 0.1056 = 0.2112.

(b) To calculate the probability that all three defective components in a batch escape detection by both inspectors, we can use the formula for independent events: P(all three defective components escape detection) = P(first defective component escapes detection) * P(second defective component escapes detection) * P(third defective component escapes detection) = (1 - 0.88)^3 = 0.00178.

So the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.

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Complete question : components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). the first inspector detects 88% of all defectives that are present, and the second inspector does likewise. at least one inspector does not detect a defect on 24% of all defective components. what is the probability that the following occur? (a) A defective component will be detected only by the first inspector? A defective component will be detected by exactly one of the two inspectors? (b) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?

The local extrema is at point (3, -22).

The function is increasing at interval (3, infinity) and decreasing at interval (- infinity, 3).

Now, According to the question:

The  function is :

[tex]f(x)=x^4-4x^3 +5[/tex]

Graphing Functions:

In order to graph a function, we first need to know the characteristics of that given function. On the other hand, we also need to simplify first the given function or rewrite it in general form for easier graphing.

Now, Graphing the function, we have

From the graph, the local extrema is at point (3, -22).

The function is increasing at interval (3, infinity) and decreasing at interval (- infinity, 3).

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If a patient took 400 mg of acetaminophen which has the half life of 4 hour, the amount of acetaminophen that will be in the patient is:

The half-life of acetaminophen is 4 hours, which means that every 4 hours, half of the initial dose of 400 mg will still remain in the patient's body.

At 4 hours after taking the dose, the amount of acetaminophen in the patient's body would be:

400 mg / 2 = 200 mg

At 2 hours after taking the dose, the amount of acetaminophen in the patient's body would be:

400 mg / (2^(4/4)) = 200 mg / 2 = 100 mg

At 1 hour after taking the dose, the amount of acetaminophen in the patient's body would be:

400 mg / (2^(4/4)) = 100 mg / 2 = 50 mg

In conclusion, the amount of acetaminophen in the patient's body decreases by half every 4 hours.

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Answer:3/2

Step-by-step explanation: just did the test

As all sides have grown by 2/3 times, The scale factor is  2/3. Thus, option A is correct.

In its simplest form, a scale factor is the proportion between the model measurement and the actual measurement. The scale factor, as opposed to a scale ratio, does not contrast various measurement units. A model car that is scaled at one-twentieth of its real-world counterpart is said to be that size. The car is also 20 times bigger than the model, according to this statement.

16 feet is the length of a fence. The fence is depicted as being 4 inches tall on a map. Write a ratio comparing the two quantities before attempting to calculate the scale factor of the drawing to the actual fence.

Given triangle side are 6, 6, 8 and scaled triangle is 9,9,12

The corresponding sides are

6/9, 6/9, 8/12

When you simply, we get

2/3, 2/3, 2/3

As all sides have grown by 2/3 times, The scale factor is  2/3. Thus, option A is correct.

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Answer: 45 cents.

Step-by-step explanation: We can find the cost per inch of wire by dividing the total cost by the total length of wire:

75 cents / 15 inches = 5 cents/inch

Now that we know the cost per inch, we can find the cost of 9 inches of wire by multiplying the cost per inch by 9:

5 cents/inch * 9 inches = 45 cents.

Answer:45 cents for 9 inches of wire

Step-by-step explanation:

Per every 5 incheses is 0.25 cents 0.75/15=$0.25 and then taking 0.25/5=$0.05 cents. So 1 inch costs 0.05 cents. So multiply 0.05×9=$0.45 cents. 45 cents

A product-focused process is commonly used to produce: high-volume, low-variety products.

There are other types of processes. This process is completely developed around the product, it is considered a continuous process with high volume of products that have low variety. It presents a high facility utilization (this is considered an advantage), organized by product, which receives a high-fixed price, but the variable cost is low.

Product focused prodction is one that focuses on improving the product by arranging sets of people into production lines to increase efficiency of production.

Equipment and people are grouped based on products being produced. For example in a manufacturing plant assembly lines are formed that focuses on one product.

This tends to be used for products that have low differentiation and are to be produced on high volume.

Example automobile plants, clothing factories, and food factories.

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(OCF): OCF = Net Income + Depreciation & Amortization - Changes in Working Capital, (CapEx): CapEx = Investment in Property, Plant & Equipment + Investment in Intangible Assets. therefore, (FCFF): FCFF = OCF - CapEx

The Free Cash Flow to Firm (FCFF) is a measure of a company’s cash flow available for distribution to shareholders and debt holders. To calculate FCFF, the following three steps are taken:

1. Calculate Operating Cash Flow (OCF): OCF is calculated by taking net income, adding back depreciation and amortization, and subtracting any changes in working capital.

2. Calculate Capital Expenditures (CapEx): CapEx includes investments in property, plant, and equipment, as well as any investments in intangible assets.

3. Calculate Free Cash Flow to Firm (FCFF): FCFF is calculated by subtracting CapEx from OCF. This figure represents the cash flow available for distribution to shareholders and debt holders.

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Answer:

Week 7

Step-by-step explanation:

Connie will have $170 in week 7, because in 3 weeks she will add $30 to her account.

Ling will have $117.5 in week 7, because in 3 weeks he will add $4.50 to his account.

170-117.5=52.5

52.5 is greater than 50, so it satisfies the question.

Answer:

To show that all three medians of a triangle intersect at the same point, we can use the property that the midpoint of each median is the centroid of the triangle.

The centroid of a triangle is a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. This means that the centroid divides each median in a 2:1 ratio, with two thirds of the median length being on one side of the centroid and one third on the other side.

Since the centroid is the same for all three medians, it follows that all three medians must intersect at the same point, which is known as the centroid or the center of gravity of the triangle. This point is denoted by the letter G.

Therefore, we can conclude that all three medians of triangle ABC intersect at point G, which is the centroid of the triangle.

The Coase theorem states that if property rights are well-defined and transaction costs are low, then the allocation of resources will be efficient, regardless of the initial allocation of property rights.

If Winston and Chloe successfully apply the Coase theorem to solve the problem of Winston's loud music externalizing a cost onto Chloe, they may reach a mutually beneficial agreement. This could result in either Winston reducing the volume of his music or compensating Chloe for the cost of the externalization, or a combination of both.

The goal is to reach a solution where the costs and benefits are more efficiently allocated between the two parties.

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Answer:

$1.5 per book

Step-by-step explanation:

Since y=1.5x, the rate of change is 1.5/1. Rate of change: y/x. Hence, the rate of change is 1.5/1 since y=1.5 and x=1.

1.5 / 1 = 1.5

Hence, the rate of change is 1.5.

But what's 1.5 represent?

1.5 is the number of dollars earned per book sold.

Hence, the rate of change is $1.5 per book.

The area covered by the wallpaper will be 164.25 square feet.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know the area of a rectangle is (length×width).

Given, A wallpaper measures 9 feet by 18 1/4 feet.

Therefore, The area of the wallpaper will be,

= (9×73/4) square feet.

= 164.25 square feet.

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The circumference of the circle is given by C = 2 * π * r, where r is the radius. In this case, the circumference of the circle is 2 * π * 14 = 88 cm.

Let's call the linear speed of the object v. Then, in 20 seconds, the object travels a distance of v * 20. This distance is equal to the arc length of the central angle of 1/2 radian:

v * 20 = (1/2) * (C/2π) = (1/2) * (88/2π) = 22/π cm

Solving for v, we get:

v = (22/π) / 20 = 22 / (20π) cm/s

The angular speed ω can be found by dividing the central angle by the time it took to travel that angle:

ω = 1/2 / 20 = 1/40 rad/s

So the linear speed of the object is v = 22 / (20π) cm/s, and the angular speed is ω = 1/40 rad/s.

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The sum of all the elements present in the first six rows of the Pascal's triangle is equal to 63.

Pascal's triangle elements are represented by :

                                                     1

                                             1                1

                                   1                2                 1

                           1              3                 3             1

                      1           4                 6              4             1

               1            5            10               10             5            1

Sum of all the elements of first six rows are:

First row : 1

Second row : 1 + 1 = 2

Third row : 1 + 2 + 1 = 4

Fourth row : 1 + 3 + 3 + 1 = 8

Fifth row : 1 + 4 + 6 + 4 + 1 = 16

Sixth row : 1 + 5 + 10 + 10 + 5 + 1 = 32

Sum of all the six row elements = 1 + 2 + 4 + 8 + 16 + 32

                                                    = 63

Therefore, the sum of all the elements of the first six row of Pascal's triangle is equal to 63.

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On September 1 the debit and cash is as follows

Debit: Cash $32,000

Credit: Owner's Equity $32,000

On September 1, Justin Wallace invested $32,000 cash into the business to start the business. This transaction increases the business's Cash account and increases the Owner's Equity account, which represents the owner's investment in the business.

September 2:

Debit: Accounts Payable $9,800

Credit: Cash $9,800

On September 2, the business purchased computer equipment on account for $9,800. This transaction increases the Accounts Payable account, which represents the business's obligation to pay the supplier, and decreases the Cash account.

September 2:

Debit: Cash $3,900

Credit: Rent Expense $3,900

On September 2, the business paid cash for September's office rent of $3,900. This transaction decreases the Cash account and increases the Rent Expense account, which represents the cost of renting office space.

September 3:

Debit: Service Revenue $6,400

Credit: Accounts Receivable $6,400

On September 3, the business recorded $6,400 revenue for services rendered to clients on account. This transaction increases the Service Revenue account, which represents the business's revenue from providing services, and increases the Accounts Receivable account, which represents the business's right to receive payment from clients for services rendered.

Mensuration is the branch of mathematics that deals with the measurement of geometric shapes and figures, such as length, area, and volume. It typically includes the study of geometric shapes, such as circles, triangles, and polygons, and their properties, such as perimeter, area, and volume. Mensuration is used in many fields, including engineering, physics, and computer graphics.

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Answer:  The length of AC is approximately 5.196 units.

Step-by-step explanation:

To find the length of AC, we can use the fact that DE is parallel to AC and AD is parallel to FE, which forms a pair of corresponding angles. Therefore, we can set up a proportion using the fact that corresponding angles are congruent.

DE/AC = AD/FE

We know that DE = 5 and AD = 6, so we can substitute these values into the proportion:

5/AC = 6/FE

We can cross-multiply and solve for AC:

5 * FE = 6 * AC

Next, using the fact that triangle ABC is a triangle, we can use the Pythagorean theorem to find the value of FE.

AB^2 + BC^2 = AC^2

17^2 + BC^2 = (AC)^2

289 + BC^2 = AC^2

Now, substitute the value of FE into the equation we have,

5 * sqrt(AC^2 - 289) = 6 * AC

multiply the both sides of the equation by the reciprocal of 5,

sqrt(AC^2 - 289) = (6/5) * AC

Square both sides of the equation,

AC^2 - 289 = 36/25 * AC^2

subtract the left side from the right side

-289 = -(36/25) * AC^2

divide both sides by -(36/25)

AC = sqrt(289/(1-(36/25)))

AC = sqrt(289/11/25)

AC = sqrt(289/275)

AC = sqrt(289/11)

AC = sqrt(26)

AC = approx 5.196152422706632

Therefore, the length of AC is approximately 5.196 units.

height = 10.74 inches

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The volume of a cone = (1/3) πr2h cubic units

Therefore, the volume of a cone = 20.93 cubic units

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The real exponential sequence for f[k]=f[kt] is f[k]=b^k.

What is exponential sequence ?

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers.

The real exponential sequence for f[k]=f[kt] can be shown to be f[k]=b^k by using the definition of exponential functions. If f[k]=f[kt], then f[k]=f[k-1]t and f[k-1]=f[k-2]t, and so on. By substitution, we have:

f[k]=f[k-1]t

f[k-1]=f[k-2]t

f[2]=f[1]t

f[1]=f[0]t

So we can write:

f[k]=f[k-1]t=f[k-2]t^2=...=f[1]t^(k-1)=f[0]t^k

Next, we can define b as f[0] and substitute it into the above equation:

f[k]=b^k

Therefore, the real exponential sequence for f[k]=f[kt] is f[k]=b^k.

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Answer:

[tex]18 + \sqrt[12]{2} [/tex]

= 34.97056

Answer:

Step-by-step explanation:

we will maintain an accurate count of all inventories.

so A is correct.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{-12x < 36}[/tex]

[tex]\huge\textbf{DIVIDE \boxed{\rm{\bf -12}} to both sides:}[/tex]

[tex]\mathsf{\dfrac{-12}{-12}x < \dfrac{36}{-12}}[/tex]

[tex]\huge\textbf{SIMPLIFY it:}[/tex]

[tex]\mathsf{x < \dfrac{36}{-12}}[/tex]

[tex]\mathsf{x > -3}[/tex]

[tex]\large\text{It is a(n) \boxed{\rm{o p e n e d}} circle SHADED to the RIGHT of your number line}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x > -3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The required Fourth term of the given geometric sequence is 1.

Similar to how the word arithmetic series denotes that each phrase is the arithmetic mean of its two neighbors, the name geometric series denotes that each term is the geometric mean of its two neighbours.

A geometric sequence always multiplies (or divides) by the same number to move from one term to the next. Therefore, 1, 2, 4, 8, 16,... is geometric since each step is a multiple of two; 81, 27, 9, 3, 1, 31... is geometric since each step is a multiple of three.

Sequesnce; 27 , 9

Common ratio(r) = 9/27 = 1/3

Then, we know that

[tex]a_{n}=ar^{n-1}[/tex]

So,

a₄ = 27(1/3)³

a₄ = 27/27 = 1

a₄ = 1

Thus, fourth term of the sequence is 1.

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Answer:

1

Step-by-step explanation:

1 is the correct one i got it right on test

Answer:

24 vowels

Step-by-step explanation:

A B C D E F G

  two out of 7 are vowels....you would expect to get 2/7 ths of 84 spins to be vowels

2/7 * 84 = 24 vowels

The probability that vertex b will be the bottom vertex will be 1/16

The ant has four equally likely possibilities for his initial step from the top vertex, each heading to one of the four vertices close to the top vertex.

When the ant reaches vertex A, he has four equally likely next steps, each heading to one of the vertices next to vertex A.

Only one of these possibilities, however, will send him to the bottom vertex: the one that brings him straight to the bottom vertex.

As a result, the ant's chance of reaching the bottom vertex after two steps is 1/4 * 1/4 = 1/16.

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