find the distance between and midpoint of the line segment defined by the two points (-4,2) and (-1,3)

Call the first number "x" and the second number "y". So the first number is 3.

From the problem statement, we know:

x = y + 4 (the first number is four more than the second number)

2x = 4y + 10 (two times the first number is 10 more than four times the second number)

Now we can solve for one of the variables in terms of the other, and then substitute that expression into the other equation to solve for the other variable. Let's use the first equation to solve for x:

x = y + 4

Substitute this expression for x into the second equation:

2x = 4y + 10

2(y + 4) = 4y + 10

Distribute the 2:

2y + 8 = 4y + 10

Subtract 2y from both sides:

8 = 2y + 10

Subtract 10 from both sides:

-2 = 2y

Divide both sides by 2:

-1 = y

Now we know that the second number is -1. We can use the first equation to find the first number:

x = y + 4

x = -1 + 4

x = 3

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A) The correct features is,

⇒ a = 9000

⇒ r = 15%

B) The equation correctly models the context of the problem is,

⇒ y = 9000 (0.85)ˣ

We have to given that;

Tiffany’s mother bought a car for $9000 five years ago.

And, She wants to sell it to Tiffany based on a 15% annual rate of depreciation.

Now, We have;

the exponential growth formula is,

⇒ y = a(1 − r)ˣ

Here, We have;

⇒ a = 9000

⇒ r = 15%

Thus, We get;

The equation correctly models the context of the problem is,

⇒ y = a(1 − r)ˣ

⇒ y = 9000 (1 - 0.15)ˣ

⇒ y = 9000 (0.85)ˣ

Therefore, We get;

A) The correct features is,

⇒ a = 9000

⇒ r = 15%

B) The equation correctly models the context of the problem is,

⇒ y = 9000 (0.85)ˣ

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Complete question is,

Tiffany’s mother bought a car for $9000 five years ago. She wants to sell it to Tiffany based on a 15% annual rate of depreciation.

Part A. Identify each feature of the problem as it relates to the context and the exponential growth formula: y=a(1−r)t

a=

r=

Part B. Which equation correctly models the context of the problem?

Choose : A. y=9000(0.15)t

or B. y=9000(0.85)t

Answer : The equation is

Part C.

Tiffany wants to buy the car from her mother now. (t = 5)

A fair price for the car will be about $

in 5 years.

Answer: 1

Step-by-step explanation:

From mass unit conversion where using a numeric constant ( 0.001), the total weight of vegitables ( carrots and beans) in a bag is equals to the 3.420 kilograms.

A unit conversion is used to expresses the same property as a different unit of measurement. Unit conversion is a process with serval steps that involves multiplication or division by a numerical factor called conversion factor. So, there are different unit conversions charts like mass unit conversation, length unit conversion etc. Now, we have, a bag contains carrots and beans.

Weight of carrots in bag = 3 kg

weight of beans in bag = 420 grams

We have to determine total weight that bag contains. As we see both weights are present in different units ( i.e, kg and grams). Using unit conversion, 1 kilogram = 1000 grams

=>[tex] 1 gram= \frac{1}{1000}=0.001 kg[/tex]

So, 420 grams = 420× 0.001 = 0.420 kg

Total weight of vegitables in bag = weight of carrots + weight of beans

= 3 kg + 0.420 kg

= 3.420 kg

Hence, required value is 3.420 kilograms.

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An expression that represents the length of one side of the square is √(12x/35).

In Mathematics and Geometry, the area of a square can be calculated by using this mathematical equation (formula);

A = x²

Where:

By substituting the given parameters into the formula for the area of a square, we have the following;

-12x + 36x² = x²

36x² - x² = 12x

35x² = 12x

x = √(12x/35)

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Answer:

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If x=2 and x=3 are roots of the equation 3x

2

−2kx+2m=0 then (k,m)=

Medium

Solution

verified

Verified by Toppr

Correct option is A)

Since x=2 and x=3 are roots of the equation 3x

2

−2kx+2m=0

⇒12−4k+2m=0⇒2k−m=6 ...(i)

and ⇒27−6k+2m=0⇒6k−2m=27 ...(ii)

On multiplying (i) by 3 and subtracting (ii) from it, we get

6k−3m=18

−

6

k

+

−

2m=

−

2

7

−m=−9

∴m=9

On putting m=9 in (i), we get

2k=15⇒k=

2

15

∴(k,m)=(

2

15

,9)

Hence, Option A is correct.

Answer:

A. 2x+3 and B. 3y² - 2y + 4 and E. x²/2 - 3x + 7 are polynomial expressions.

The standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.

To find the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students, we need to use the binomial distribution.

Given that 71.6% of all first-time, full-time freshmen believe that same-sex couples should have the right to legal marital status, the probability (p) that a randomly selected student from this population believes this is:

p = 0.716

Since we are interested in the number of students in a sample of nine who believe this, we can model this using the binomial distribution with parameters n = 9 and p = 0.716.

The formula for the standard deviation of a binomial distribution is:

σ = sqrt(n * p * (1 - p))

Substituting in the values of n and p, we get:

σ = sqrt(9 * 0.716 * (1 - 0.716))

σ = 1.168

Therefore, the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.

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1. For the Midwest region, the average number of sales orders per representative for the group that had training is 0.76 more than the average number of sales per representative for the group that had no training.

2. For the Northeast region, the average number of sales orders per representative for the group that had training is 1.48 more than the average number of sales per representative for the group that had no training.

3. The data from the sales director’s study indicates that the one-month training program  Increases sales.

To calculate the average number of sales orders per representative in the Midwest region, we say

234/50  - 196/50

= 4.68 - 3.92

= 0.76

The questions asked are based on the situation below;

For three months after the training program, the sales director collected the sales data for 200 representative from the Midwest and Northeast region. The director then broke down the number of sales orders for the representative according to whether they received training or not. This data is shown in the table

                             Three months sales orders

                                          Training                    No training

Midwest                                   234                              196

Northeast                                252                               178

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The spares should be kept to maintain a 90% or more probability of system success is 35

Let λ be the normal number of component disappointments per year, at that point the disappointment rate (or rate parameter) is given by λ/52 since there are 52 weeks in a year. Let's signify this by μ = λ/52.

The framework victory likelihood can be modeled utilizing the Poisson dissemination since the disappointments happen haphazardly and freely over time. Let X be the number of component disappointments in a year, at that point X takes after a Poisson conveyance with cruel λ.

To preserve a 90% or more likelihood of system victory, we got to guarantee that the number of saves is adequate to cover at the slightest 90% of the potential disappointments. This implies that the likelihood of having more than k disappointments in a year ought to be less than or break even with 0.1, where k is the number of saves.

Let Y be the number of component disappointments amid the two-week conveyance time. At that point, Y too takes after a Poisson conveyance with cruel μ/26, since there are 26 weeks in a half-year (i.e., two quarters). The likelihood of having more than k disappointments amid the conveyance time is given by:

P(Y > k) = 1 - P(Y ≤ k) = 1 - ∑_[tex]{i=0}^k (e^(-μ/26) (μ/26)^i[/tex]/ i!)

where e is the base of the common logarithm.

To preserve a 90% or more likelihood of system victory, we ought to select k such that P(Y > k) ≤ 0.1. Able to solve for k numerically, employing a spreadsheet or a computer program.

For example, utilizing Microsoft Exceed expectations or Go-ogle Sheets, ready to utilize the taking after an equation to compute P(Y > k) for distinctive values of k:

=1-POISSON(k,μ/26,TRUE)

where POISSON is the Poisson total conveyance work, with the moment contention being the cruel and the third contention being Genuine to indicate an aggregate conveyance.

Beginning with k = 26 (i.e., one save per week), able to increment k until we discover the littlest esteem that fulfills P(Y > k) ≤ 0.1. In this case, we discover that k = 35 saves are required to preserve a 90% or more likelihood of framework victory. 

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Gouge-em Cable Company will charge $30 for its cable services, earning them a profit of $70 thousand. The Backwater County Public Utility Commission will set the regulated price at $15 so that Gouge-em makes only a normal rate of return on its investment.

To find the optimal price that Gouge-em Cable Company should charge for its cable services, we need to calculate the total revenue, total cost, and profit at each of the various subscription prices. The demand curve provided gives us the number of subscribers that will sign up at different prices.

Price Quantity Demanded Total Revenue Total Cost Profit

$10 100 $1,000 $640,200 -$639,200

$20 80 $1,600 $640,160 $959,840

$30 60 $1,800 $640,120 $1,159,880

$40 40 $1,600 $640,080 $959,920

$50 20 $1,000 $640,040 $359,960

To maximize profit, Gouge-em Cable Company should charge the price where marginal revenue equals marginal cost. Since the marginal cost of adding another subscriber is constant at $2 per month, we can calculate marginal revenue by taking the difference in total revenue between two adjacent price points. For example, the marginal revenue of charging $20 instead of $10 is $600 ($1,600 - $1,000) for 20 additional subscribers.

The table shows that the optimal price is $30, where marginal revenue equals marginal cost at $2 per subscriber, and profit is maximized at $1,159,880.

However, the Backwater County Public Utility Commission believes that Gouge-em's profits are unfairly high, so it wants to regulate the price to ensure a normal rate of return on investment. A normal rate of return is typically around 10% of total investment. Gouge-em's total investment is the sum of fixed costs divided by the monthly profit margin:

Total investment = Fixed costs / Monthly profit margin

= $640,000 / ($1,159,880 / 5)

= $27,627,724.51

A 10% return on investment is $2,762,772.45 per year, or $230,231.04 per month. To earn this amount, Gouge-em needs to charge a price that covers its total costs plus the normal rate of return, which is:

Regulated price = Total cost / Quantity demanded + Normal rate of return / Quantity demanded

= $640,000 / 60 + $230,231.04 / 60

= $10.17

Therefore, the Backwater County Public Utility Commission will set the regulated price at $15, which is a round number close to the calculated price of $10.17. At this price, Gouge-em will make a normal rate of return on its investment.

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Answer:

No, it is not. See justification in the diagram.

Step-by-step explanation:

You have to do polynomial long division. My math is shown in the picture below and if you have any questions, please let me know.

At the end, (x+7) does not go into 468.

For a piece of string art created by 16 evenly spaced nails around the circumference of a circle. The measure of angle BXC is equals to the 90°.

We have a piece of string art is made by placing 16 evenly spaced nails around the circumference of a circle. See the above figure. We have to determine the measure of angle BXC. Now, using the inscribed angle theorem , the measure of angle BXC, [tex] m\angle BXC = \frac{ 1}{2} ( m \hat {AD} + m \hat {BC}) [/tex]

Measure of AD = [tex] 2(\frac{ 1}{16})360°[/tex] = 45°

The measure of BC = [tex] 6(\frac{ 1}{16} )360°[/tex]

= 135°

Now, Using the above formula the measure of angle BXC [tex] = \frac{ 1}{2} ( m \hat {AD} + m \hat {BC})[/tex]

[tex]= \frac{ 1}{2} ( 45° + 135°)[/tex]

= 90°

Hence, required value is 90°.

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Complete question:

The above figure complete the question.

28. A piece of string art is made by placing 16 evenly spaced nails around the circumference

of a circle. A piece of string is wound from A to B to C to D. What is measure of angle BXC.

Answer:

10: Rectangular Prism

11: Pyramid

12: Triangular prism

Step-by-step explanation:

Answer:

Solving for y

exact form for y = 4/3

Demical form for y = 1/3

Mixed number for y = 1 1/3

( BTW all of these answers all right it juts depends on what exactly there asking for, for example if there asking for the exact form for y it would be 4/3 )

Answer:

If not choose all that apply, technological process will shift the PPC right (outwards)

Step-by-step explanation:

The production possibilities curve represents the maximum amount of goods and services that a country can produce with its limited resources. It is a graphical representation of the trade-offs a country must make between producing one good or service over another. Any factor that can increase production will shift the curve outward, indicating an increase in the maximum amount of goods and services that can be produced.

An increase in the production of investment goods will shift the curve outward because it will increase the amount of capital goods that can be used to produce other goods and services. Investment goods are items like machinery, equipment, and infrastructure that are used to produce other goods and services. By increasing the production of investment goods, a country can increase its productive capacity, allowing it to produce more goods and services in the future.

An increase in the production of consumer goods will not shift the curve outward because it does not increase the country's productive capacity. Consumer goods are items that are consumed immediately, like food, clothing, and electronics. While an increase in the production of consumer goods can lead to short-term economic growth, it will not increase the country's long-term productive capacity.

Technological progress, on the other hand, will shift the production possibilities curve outward. Technological progress refers to advancements in technology that increase productivity, reduce costs, and improve efficiency. By adopting new technologies, a country can produce more goods and services with its existing resources, allowing it to shift its production possibilities curve outward.

In conclusion, an increase in the production of investment goods and technological progress will shift the production possibilities curve outward, while an increase in the production of consumer goods will not.

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To calculate the covariance between X and Y, we can use the formula:
Cov(X,Y) = E[XY] - E[X]E[Y]
where E[XY] is the expected value of the product of X and Y, and E[X] and E[Y] are the expected values of X and Y, respectively.

Using the given probability distributions, we can calculate the expected values as follows:
E[X] = ∑x∑y xP(X=x, Y=y)
    = (0)(0.26) + (1)(0.74)
    = 0.74
E[Y] = ∑x∑y yP(X=x, Y=y)
    = (0)(0.26) + (1)(0.36) + (2)(0.38)
    = 1.12
E[XY] = ∑x∑y xyP(X=x, Y=y)
     = (0)(0)(0.26) + (0)(1)(0.36) + (1)(0)(0.02) + (1)(1)(0.34) + (1)(2)(0.38)
     = 1.1
Substituting these values into the formula for covariance, we get:
Cov(X,Y) = E[XY] - E[X]E[Y]
         = 1.1 - (0.74)(1.12)
         = 0.0048
Therefore, the covariance between X and Y is 0.0048.

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Answer:

The slope is 5.

Step-by-step explanation:

We are given the points (-2, -5) and (0,5).

We want to find the slope between these 2 points.

The slope (m) is written with the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points.

Let's label the values of the points to avoid any confusion and mistakes when calculating.

[tex]x_1=-2\\y_1=-5\\x_2=0\\y_2=5[/tex]

Now, substitute into the formula.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \frac{5--5}{0--2}[/tex]

This can be simplified to:

[tex]m = \frac{5+5}{0+2}[/tex]

Add the values together.

[tex]m = \frac{10}{2}[/tex]

m = 5

The slope is 5.

The answer is (b) x+y=C.

The given equation is [tex]xdy + ydx = 0.[/tex]

We can rewrite this equation as:

dy/dx = -y/x

This is a first-order linear differential equation that can be solved using separation of variables.

We can write it as:

dy/y = -dx/x

Integrating both sides, we get:

ln|y| = -ln|x| + ln|C|

where C is the constant of integration.

Simplifying this expression, we get:

ln|y| = ln|C/x|

Taking the exponential of both sides, we get:

|y| = |C/x|

Since |C| is a constant, we can replace it with another constant, say k, giving:

|y| = k/|x|

where k is a non-zero constant.

Now, we can rewrite this expression as:

y = ± k/x

where the ± sign depends on the sign of y.

Therefore, the solution to the differential equation xdy + ydx = 0 is y = ± k/x.

We can rewrite this solution in different forms:

a) y = Cx, where C = ± k

b) x + y = C, where C = k/2

c) xy = C, where C = ± k^2

d) x = Cy, where C = ± k

Therefore, the answer is (b) x+y=C.

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The value of x is 11.6 ( option C).

Similar triangles are triangles that have the same shape, but their sizes may vary. The angles of similar triangles are congruent.

Also the ratio corresponding sides of similar triangles are equal. This means for two triangles to be similar , the corresponding angles must be equal and the ratio of corresponding sides are equal.

Therefore,

29/50 = x/20

29×20 = 50x

580 = 50x

divide both sides by 50

580/50 = x

x = 580/50

x = 58/5

x = 11.6

therefore the value of x 11.6

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Vinny's new grade in math, if the playing time reduces to 6 hours per week, would be 85.33.

If we wish to illustrate how Vinny's Math Models grade relates to the amount of time she spends playing computer games, we may employ the formula that defines an inverse proportion:

k = G x T

k = 64 x 8 = 512

For 6 hours playing:

512 = G x 6

G = 512 / 6

= 85. 33

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The the approximate value of √8  is option B: between 2.8 and 2.9

An approximate number is a value derived close to the exact figure, yet a slight variance remains present. It is used to show that exact figures are precise and require no estimation.

However, these numbers are seen as estimates since their exact representation cannot be achieved through a finite number of digits. A close but lower value than a number is known as its approximate value by defect, with a desired level of accuracy.

Therefore, the radical expression for the square root of 8 is √8, but it can also be written as 2√2. Additionally, it can be expressed as a fraction, which is approximately equal to 2.828. Hence option B is correct.

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9 5/2 in radical form is equal to 4√2 + √7.

We are able to rewrite 9 5/2 in radical form through first changing it to an improper fraction.

9 5/2 = (9 x 2 + 5) / 2 = 23/2

Now, we can express 23/2 as a mixed radical by using locating the largest perfect square that may be a aspect of 23. the largest perfect square which is much less than 23 is 16 (that's 4^2).

So, we are able to write:

23/2 = 16/2 + 7/2 = 8 + 7/2

Now, we will express 8 + 7/2 in radical form as:

8 + 7/2 = 4 x 2 + 7/2 = 4√2 + √7

Consequently, 9 5/2 in radical form is equal to 4√2 + √7.

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a) The total number of capsules needed for 4 weeks is C, 112 capsules.

b) The total milliliters needed for the month of October is C, 465 ml.

a) To determine the number of Rimactane 150mg capsules needed for a 10-year-old boy weighing 30 kg, who has been prescribed a dose of 10 mg/kg twice daily for 4 weeks, follow these steps:

1. Calculate the total daily dose: 30 kg * 10 mg/kg = 300 mg/day
2. Determine the number of daily doses: 300 mg/day / 150 mg/capsule = 2 capsules/day
3. Calculate the total number of capsules needed for 4 weeks: 2 capsules/day * 7 days/week * 4 weeks = 112 capsules

The answer is C, 112 capsules.

b) To calculate the number of milliliters of Epanutin suspension (phenytoin 30 mg/5 ml) that a 5-year-old boy weighing 18 kg with epilepsy will take at a dose of 5 mg/kg twice daily during the month of October, follow these steps:

1. Calculate the total daily dose: 18 kg * 5 mg/kg = 90 mg/day
2. Determine the number of milliliters needed for each daily dose: 90 mg/day * (5 ml/30 mg) = 15 ml/day
3. Calculate the total milliliters needed for the month of October: 15 ml/day * 31 days = 465 ml

The answer is C, 465 ml.

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The percentage of budget that is allotted to variable expenses is 46.03%

We first have to determine the solution for what the va,riable expenses is supposed to be

$2,003 (total budget) - $1,081 (fixed expenses)

= $922

Next we will have to solve for the percentage that is the budget which is allocated to the variable expenses

This is simply written as

variable expenses / total budget * 100

($922 (variable expenses) ÷ $2,003 (total budget)) × 100 = 46.03%

Hence the percentage of budget that is allotted to variable expenses is 46.03%

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Answer:

46.03%

Step-by-step explanation:

922 ÷ 2003 x 100 which gives you 46.03

As the cost of producing smartphones has fallen over the past decade, several implications and effects on the market for smartphones can be observed:

1. Lower prices: Falling production costs have led to lower prices for consumers, making smartphones more affordable and accessible to a broader population.

2. Increased demand: Lower prices have also resulted in increased demand for smartphones, as more people can now afford them. This has led to a higher sales volume in the market.

3. Market expansion: The accessibility and affordability of smartphones have led to market expansion, as smartphones become more prevalent in both developed and developing countries.

4. Greater competition: The lower production costs have enabled more companies to enter the smartphone market, increasing competition and leading to more product variety for consumers.

5. Innovation and improvement: Due to the increased competition, companies are constantly seeking ways to differentiate their products through innovative features, improved design, and better performance.

Overall, the falling production costs of smartphones have positively impacted the market by lowering prices, increasing demand, and driving innovation and competition.

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The domain and range for the relation are

for the graph: domain is [-3 3] and range is [-1 3]

domain is [-2 4] and range is [-3 0]

The mathematics domain and range refer, respectively, to a function's input values as well as its output.

The set of possible input values that can be used for the function is called the domain or independant variable(s), while also comprising all necessary values for the calculation of appropriate results.

Conversely, the range or dependent variable(s) represents every conceivable result obtainable from specific sets of inputs within the domain. It essentially displays the function's abilities to produce an output value based on any given input it receives.

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To find the coordinate vector of v relative to the basis S = (v1, v2, v3) for R^3 with v = (40, 36, 24), v1 = (2, 0, 0), v2 = (3, 3, 0), and v3 = (8, 8, 8), follow these steps:

1. Write v as a linear combination of the basis vectors v1, v2, and v3: v = a * v1 + b * v2 + c * v3
2. Substitute the given vectors: (40, 36, 24) = a * (2, 0, 0) + b * (3, 3, 0) + c * (8, 8, 8)
3. This results in a system of linear equations:
  2a + 3b + 8c = 40
  3b + 8c = 36
  8c = 24
4. Solve the system of linear equations:
  From the third equation, we can find c: c = 24 / 8 => c = 3
  Substitute c into the second equation: 3b + 8 * 3 = 36 => 3b + 24 = 36 => 3b = 12 => b = 4
  Substitute b and c into the first equation: 2a + 3 * 4 + 8 * 3 = 40 => 2a + 12 + 24 = 40 => 2a = 4 => a = 2

So, the coordinate vector of v relative to the basis S is (a, b, c) = (2, 4, 3). Therefore, (v)s = (2, 4, 3).

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First, let me explain some key terms related to the question.

- Discrete: This refers to mathematics that deals with countable or finite sets of numbers, rather than continuous sets. In other words, we're dealing with specific, separate values rather than a continuous range.
- Recurrence: This refers to a mathematical sequence where each term depends on one or more previous terms. In other words, we can use a formula to generate the next term based on previous terms.
- Relation: This refers to a mathematical expression that relates one or more variables. In this case, our recurrence relation relates the sequence An to its previous terms.

With that in mind, let's tackle the question!

We're given a recurrence relation: An = 6An-1 – 9An-2. This means that each term in the sequence An depends on the two previous terms, An-1 and An-2.

We're also given initial conditions: a0 = 2 and a1 = 3. This gives us a starting point for the sequence.

To solve the recurrence relation and find the values of An, we'll use a technique called iteration. Essentially, we'll use the recurrence relation to generate the next term in the sequence, then use that term to generate the next one, and so on.

Here's how it works:

- First, we use the initial conditions to find the first two terms of the sequence: a0 = 2 and a1 = 3.
- Next, we use the recurrence relation to generate the third term: a2 = 6a1 - 9a0 = 6(3) - 9(2) = 0.
- We continue this process, using the recurrence relation to generate each subsequent term. For example, to find a3, we use the formula An = 6An-1 – 9An-2 with n = 3: a3 = 6a2 - 9a1 = 6(0) - 9(3) = -27.
- We can keep going like this to find as many terms as we need.

Here's what the first few terms of the sequence look like:

a0 = 2
a1 = 3
a2 = 0
a3 = -27
a4 = -54
a5 = -162
a6 = -270
...
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If the drain for a 90 percent efficient furnace and the drain for the air conditioning coil are run with a common drain, the drain should be sized large enough to accommodate the combined condensate flow from both systems.

To determine the appropriate size, you should:
1. Check the manufacturer's recommendations for both the furnace and the coil.
2. Calculate the maximum condensate flow from each system.
3. Add the two values together to find the total condensate flow.
4. Select a drain size that can handle the combined flow rate.

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The ordered pairs (6, 3), (5, 6), (-1, 1), (6,9), (8,8) does not represent a function

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

(6, 3), (5, 6), (-1, 1), (6,9), (8,8)

The general rule is that

A set of points or ordered pairs that represent a function must have unique x and y values

i.e. the x values must not point to different values

In the ordered pairs (6, 3), (5, 6), (-1, 1), (6,9), (8,8), we can see that the x value 6 points to the y values 3 and 9

This means that the the ordered pairs does not represent a function

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