Determine the domain of the function F(x) =2-x/12x^2+8x

Considering the definition of an equation, the cost for one admission and r rides is Cost= 10 + 2×r

An equation in mathematics is defined as an equality established between two expressions, in which there may be one or more unknowns that must be solved.

The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.

The solution of a raised equation, means to determine by means of certain procedures the value that satisfies it.

Being "r" the number of rides, and knowing that:

the equation in this case is:

Cost= 10 + 2×r

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Answer: 85% or 17/20

Step-by-step explanation: Ok, so 17 being what percent of 20 is 17/20. Then, simply divide from there to get 0.85, also known as 85%.

Thus, the time taken to drop the caffeine from 80 mg to 60 mg is 2.46 hours.

Calculating the exponential growth as well as decay of a given collection of data is done using an exponential function, which is a mathematical function.

Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread. An exponential function has the following form at its most fundamental level.

f(x) = [tex]a^{x}[/tex]

Exponential equation for the amount of Caffeine

C = 80[tex](2)^{-t/6}[/tex]

Amount of caffeine C = 60 mg.

60 = 80[tex](2)^{-t/6}[/tex]

3/4 = [tex](2)^{-t/6}[/tex]

Taking log on both sise:

[tex]log_{2}(3/4) = -t/6[/tex]

Solve the log function using the log calculator:

-t/6 = (-0.41)

t = 0.41 * 6

t = 2.46 hours

Thus, the time taken to drop the caffeine from 80 mg to 60 mg is 2.46 hours.

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Correct question:

The biological half-life of caffeine is about 6hr. If one cup of coffee has 80 mg of caffeine, then the amount of caffeine C (in mg) remaining after t hours is given by C = 80[tex](2)^{-t/6}[/tex]

How long will it take for the amount of caffeine to drop below 60 mg?

Respuesta (Español/Spanish):

20 lapices

Explicación paso-a-paso (Español/Spanish):

Multiplica 28 por 5/7.

Answer (English/Inglés):

20 pencils

Step-by-step explanation (English/Inglés):

Multiply 28 by 5/7

Answer:

The given statement is False. When the interest is compounded half yearly the number of conversion periods will be two because a year comprises 12 months and has two periods of six months each.

Step-by-step explanation:

if it helped you please mark me a brainliest :))

The HCF is 6x^2yz^3

HCF means Highest Common Factor. HCF of two or more numbers is the greatest factor that divides the numbers. It is also the greatest possible number of all their common factors.

To find the HCF of the following,

24x^3yz^4 , 30x^2y^2z^3, 36x^3y^2z^3

To find the HCF among the first value,

24 , 30 and 36

Factors of 24 are 2, 3, 4, 6, 8, 12, 24

Factors of 30 are 2, 3, 5, 6, 10, 15, 30

Factors of 36 are 2, 3, 4, 6, 9, 12, 18, 36.

The highest common factor that it can be divisible with is 6

Among x^3 , x^2 and x^3

The factors of x^3 are x, x^2, x^3

Factors of x^2 are x, x^2

Factors of x^3 are x, x^2, x^3

The highest common factor is x^2

Among y , y^2 and y^2

Factors of y is y

Factors of y^2 are y, y^2

The highest common factor is y

And among z^4 , z^3 and z^3

Factors of z^4 are z, z^2, z^3, z^4

Factors of z^3 are z, z^2, z^3

The highest common factor here is z^3

Therefore, the highest common factor is 6x^2yz^3

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The five-number summary for data and construct a box plot is: 59, 62, 65, 70, 77
The IQR for the data is 8.

What is median ?

The median is a measure of central tendency in statistics. It is the value separating the higher half from the lower half of a data sample. To find the median of a data set, the data is first arranged in ascending or descending order, and then the middle value is identified. If the data set has an odd number of values, the middle value is the median. If the data set has an even number of values, the median is the average of the two middle values. The median is a useful measure of central tendency when the data contains outliers or extreme values that may affect the mean.

According to the question:
a. The five-number summary consists of the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum. To find these values:

Minimum: 59

Q1: the median of the lower half of the data, which is the median of the first 20 values (when ordered from smallest to largest): (62 + 62) / 2 = 62

Median (Q2): the middle value when the data is ordered from smallest to largest: (65 + 65) / 2 = 65

Q3: the median of the upper half of the data, which is the median of the last 20 values: (70 + 70) / 2 = 70

Maximum: 77

Therefore, the five-number summary is: 59, 62, 65, 70, 77

To construct a box plot, we can draw a number line and mark the five-number summary points. We then draw a box from Q1 to Q3, with a line at the median (Q2) inside the box. Finally, we draw whiskers from the box to the minimum and maximum values, unless there are outliers that are more than 1.5 times the interquartile range (IQR) away from the box.

b. The interquartile range (IQR) is the difference between the upper and lower quartiles, or Q3 - Q1. From part (a), we have Q1 = 62 and Q3 = 70, so:

IQR = Q3 - Q1 = 70 - 62 = 8

Therefore, the IQR for the data is 8.

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Answer:

D equilateral triangle.

Step-by-step explanation:

An equilateral triangle has three sides with equal length and three interior angles with the same measure of 60 degrees. Therefore, an equilateral triangle can also be considered as a regular polygon with three sides.

Plane A 4 hours to travel 2300 miles.

Plane takeoff angle.

Angel

During take off, a plane leaves the ground and travels in a straight line until it reaches a height of 10 km. The distance the plane flies during take off should be in the range 57 km to 62 km. What is the smallest possible angle that the path of the plane could make with the ground? Give your answer in degrees to 1 d. p.

Let's assume that the plane travels a distance of x km during take off and reaches a height of 10 km. Then, using trigonometry, we can find the angle θ between the ground and the path of the plane:

tan(θ) = 10/x

We want to find the smallest possible angle θ, which means we need to maximize x. From the given information, we know that x must be in the range 57 km to 62 km. Therefore, to maximize x, we choose x = 62 km.

Plugging this into the equation above, we get:

tan(θ) = 10/62

θ = arctan(10/62) ≈ 8.8°

Therefore, the smallest possible angle that the path of the plane could make with the ground is approximately 8.8 degrees.

Angel

Xochitl spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7425 feet. Xochitl initially measures an angle of elevation of 19° to the plane at point A. At some later time, she measures an angle of elevation of 37° to the plane at point B.

Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary

Let's assume that the distance from Xochitl to point A is d1 and the distance from Xochitl to point B is d2. We want to find the distance the plane traveled from point A to point B, which is the difference between d1 and d2.

From the given information, we can set up the following two equations:

tan(19°) = 7425/d1

tan(37°) = 7425/d2

Solving for d1 and d2, we get:

d1 = 7425/tan(19°) ≈ 22977.6 feet

d2 = 7425/tan(37°) ≈ 13060.2 feet

Therefore, the distance the plane traveled from point A to point B is:

d1 - d2 ≈ 9917.4 feet ≈ 3021 meters

Rounding to the nearest foot, we get that the distance the plane traveled from point A to point B is approximately 9917 feet.

Angel

Plane B is flying 75mph 75 ⁢ mph faster than Plane A. Find the time it takes for Plane A to travel 2300 2300 miles if it takes Plane B the same amount of time to travel 2600 2600 miles.

Let's start by using the formula for distance, rate, and time:

distance = rate x time

Let's assume that Plane A's speed is r mph. Then we know that Plane B's speed is r + 75 mph.

We also know that Plane A travels 2300 miles and Plane B travels 2600 miles. Since they take the same amount of time to travel their respective distances, we can set up the following equation:

2300/r = 2600/(r + 75)

To solve for r, we can cross-multiply and simplify:

2300(r + 75) = 2600r

2300r + 172500 = 2600r

300r = 172500

r = 575 mph

Now that we know Plane A's speed, we can use the formula for distance, rate, and time to find the time it takes for Plane A to travel 2300 miles:

distance = rate x time

2300 = 575 x time

time = 4 hours

After answering the provided question, we can conclude that  the oil industry and related sectors were the primary direct beneficiaries.

An expression in mathematics is a collection of representations, octal, and huge corporations that resemble a clear association or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include inclusion, subtraction, rapid spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

Option 2 is the correct response. Texas benefited from OPEC's oil production restrictions in 1973 because it resulted in a significant increase in oil prices, which brought wealth to the state. At the time, Texas was the largest oil-producing state in the United States.

Option 1, 3, and 4 are incorrect. While OPEC's restrictions did increase competition from other countries, which could have affected employment in the oil industry, there is no evidence that it resulted in fewer jobs in Texas overall. Finally, while transportation industries may have benefited indirectly from the increase in oil prices, the oil industry and related sectors were the primary direct beneficiaries.

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The sum of the rational expression as required to be determined in the task content is; (7x² + 11) / (x² + 6x + 5).

It follows from the task content that the rational expression whose sum is to be determined is;

x / x+1 + 6x / x+5

Therefore, by using the LCM; (x + 1) (x + 5).

Therefore, the sum is as follows;

{x(x + 5) + 6x (x + 1)} / (x + 1) (x + 5).

= (7x² + 11) / (x² + 6x + 5)

Ultimately, the sum as required is; (7x² + 11) / (x² + 6x + 5).

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Answer:

[tex] \frac{x(7x + 11)}{(x + 1)(x + 5)} [/tex]

Step-by-step explanation:

[tex]1. \: \frac{x(x + 5) +6x(x + 1)}{(x + 1)(x + 5)} \\ 2. \: \frac{x(x + 5 + 6(x + 1))}{(x + 1)(x + 5)} \\ 3. \: \frac{x(x + 5 + 6x + 6)}{(x + 1)(x + 5)} \\ 4. \: \frac{x((x + 6x) + (5 + 6))}{(x + 1)(x + 5)} \\ 5. \: \frac{x(7x + 11)}{(x + 1)(x + 5)} [/tex]

Therefore, nine rabbits will need 7.5 sacks of food for one week.

The unitary method is a mathematical technique that involves finding the value of a single unit to determine the value of a given number of units. It is a method of solving mathematical problems that involve proportional relationships between quantities. The unitary method is commonly used in various areas of mathematics, such as algebra, arithmetic, and geometry. It is also used in everyday life to solve problems related to money, time, distance, and other quantities.

Here,

To solve this problem, we can use proportionality. We know that the number of sacks of food needed is directly proportional to the number of rabbits.

Let x be the number of sacks needed for 9 rabbits. Then, we can set up the following proportion:

6/10 = 9/x

Cross-multiplying, we get:

6x = 90

Dividing both sides by 6, we get:

x = 15/2 or 7.5

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Complete question:

If six rabbits need 10 sacks of food per week, how many sacks will nine rabbits need to eat for one week?

The lost annual income from savings on those refunds would be $43,032,000.

o calculate the lost annual income from savings on those refunds, we need to first calculate the total amount of money refunded, and then calculate the lost income from that amount.

The total amount refunded would be:

421,000 people x $3,400 per person = $1,434,400,000

Next, we can calculate the lost income from that amount at an interest rate of 3 percent. To do this, we can use the simple interest formula:

I = P x R x T

Where:

I = interest

P = principal (the amount refunded)

R = interest rate (as a decimal)

T = time (in years)

Substituting the values we have:

I = $1,434,400,000 x 0.03 x 1

I = $43,032,000

Therefore, the lost annual income from savings on those refunds would be $43,032,000.

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Answer:

one solution (6, 2 )

Step-by-step explanation:

x - y = 4 → (1)

x + y = 8 → (2)

add the 2 equations term by term to eliminate y

(x + x) + (y - y) = 8 + 4

2x + 0 = 12

2x = 12 ( divide both sides by 2 )

x = 6

substitute x = 6 into (2) and solve for y

6 + y = 8 ( subtract 6 from both sides )

y = 2

the system has one solution , that is (6, 2 )

Option b is likely to give the teachers the most accurate data for deciding the end of the year field trip for the 8th graders.

In statistics, a sample is a subset of individuals or observations taken from a larger population. The sample is used to gain insights and make inferences about the population from which it was drawn. Samples are often used when it is not feasible or practical to gather data from every individual in a population, which could be too large or too time-consuming to survey.

Here,

A random sample of 8th graders are directly affected by the decision and are therefore the most appropriate group to survey. Asking a random sample of 6th, 7th, and 8th graders (option a) would include students who are not directly affected by the decision, and may not have the same level of understanding or investment in the trip. Asking the football team (option c) would likely provide biased results, as the football team may have different preferences and priorities than the wider 8th grade class. Asking all the teachers (option d) may also provide biased results, as teachers may have different opinions and preferences than the students. Ultimately, the most accurate data will come from surveying the group of students directly affected by the decision.

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Both angles on the parallel lines are related as ∠1=180°-∠7

Vertical angles, also known as vertically opposed angles, are generated when two lines intersect. Angles that are vertically opposite one another are always equal to one another. Moreover, a vertical angle and the angle to which it is next are supplementary angles, meaning their sum is 180 degrees.

To find: measure ∠1 through ∠7

∠7=∠5 ( vertically opposite angle)

∠5=∠2( co-exterior angle)

∠1+∠2=180°

( A straight line has a maximum angle of 180°.)

∠1=180°-∠2

∠1=180°-∠5

∠1=180°-∠7

Hence, both angles on the parallel lines are related as ∠1=180°-∠7

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Step-by-step explanation:

For RIGHT triangles   sin (angle) = opposite LEG / hypotenuse

 for this triangle sin (10) = 500/x

then   x = 500 / sin (10°) = 2879.4 m     Round as necessary

Answer:

4

Step-by-step explanation:

This is a right triangle, so you can use the Pythagorean Theorem.

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]  C has to be the longest side. In this case, that is 5

[tex]a^{2}[/tex] + [tex]3^{2}[/tex] = [tex]5^{2}[/tex]

[tex]a^{2}[/tex] + 9 = 25  Subtract 9 from both sides

[tex]a^{2}[/tex] + 9 - 9 = 25 - 9

[tex]a^{2}[/tex] = 16   Take the square root of both sides.

[tex]\sqrt{a^{2} }[/tex] = [tex]\sqrt{16}[/tex]

a = 4

Helping in the name of Jesus.

Answer: 0

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

0 divided by 1 is 0 similarly to other numbers.

For example 5/1 = 5

Although, 1/0 is undefined as it isn't legal.

The equation of the line is y=-4x+9. In order to find the equation of the line, we must first calculate the slope (m) of the line.

Slope is a measure of the steepness of a line on a graph. It is calculated by finding the ratio of the vertical change between two points, divided by the horizontal change between the same two points.

The slope is calculated by dividing the change in y-coordinates (rise) by the change in x-coordinates (run).

In this case, the rise is -5 – (-9) = 4, and the run is 1 – 0 = 1. Therefore, the slope of the line is m = 4/1 = 4.

Next, we plug the slope and a point on the line into the point-slope form of a line equation: y - y1 = m(x - x1).

We can choose any point on the line, so let's use (0, -9).

Plugging in the values, we get:

y - (-9) = 4(x - 0)

Simplifying, we get:

y = 4x - 9

Therefore, the equation of the line is y = 4x - 9.

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Answer:

Step-by-step explanation:

You want the different ways sides of similar triangles can be shown as proportional.

From shorter to longer, the corresponding sides in the similar triangles are ...

Smaller ... Larger

  b . . . . . . . e

  a . . . . . . . d

  c . . . . . . . f

The proportions are written by choosing two letters and their corresponding letters. The two chosen can be from different columns (part 1) or from the same column (part 2). The corresponding letters are written in the same place in the proportion fraction

  [tex]\dfrac{a}{d}=\dfrac{b}{\boxed{e}}=\dfrac{\boxed{c}}{f}[/tex]

  [tex]\dfrac{a}{b}=\dfrac{d}{e}\qquad\dfrac{b}{\boxed{c}}=\dfrac{e}{f}\qquad\dfrac{c}{a}=\dfrac{f}{\boxed{d}}[/tex]

__

Additional comment

Any proportion can be written "sideways" or "upside down." Corresponding parts have the same relationship in any case.

  [tex]\dfrac{a}{b}=\dfrac{d}{e}\ \Leftrightarrow\ \dfrac{a}{d}=\dfrac{b}{e}\ \Leftrightarrow\ \dfrac{b}{a}=\dfrac{e}{d}\ \Leftrightarrow\ \dfrac{d}{a}=\dfrac{e}{b}[/tex]

The vοlume οf the cylinder in terms οf straight pi and cubic inches is apprοximately 5235.5 cubic inches.

A cylinder is a three-dimensiοnal geοmetric shape that cοnsists οf twο parallel bases that are cοngruent circles and a curved lateral surface that cοnnects the bases.

1. The circumference οf the cylinder is given as 13 inches. We knοw that the fοrmula fοr the circumference οf a cylinder is 2πr, where r is the radius οf the cylinder. Sο, we have:

2πr = 13

r = 13/(2π)

Nοw, we can use the fοrmula fοr the vοlume οf a cylinder, which is V = πr²h, where h is the height οf the cylinder:

[tex]V = \pi (13/(2\pi ))^2(9) = 119.8 cubic inches[/tex]

Sο, the approximate vοlume of the cylinder is 119.8 cubic inches.

2. The diameter οf the cylinder is given as 63.5 cm, which means the radius is 31.75 cm (since the radius is half οf the diameter). The height is given as 28 inches.

The formula fοr the vοlume of a cylinder is [tex]V = \pi r^2h[/tex], so we can substitute the values we have tο get:

[tex]V = \pi (31.75)^2(28) = 85816.8 ~cm^3[/tex]

Tο cοnvert this tο cubic inches, we need tο knοw that 1 cubic inch is equal tο 16.3871 cubic centimeters, sο we have:

V = 85816.8/16.3871 ≈ 5235.5 cubic inches

Hence, the vοlume οf the cylinder in terms οf straight pi and cubic inches is apprοximately 5235.5 cubic inches.

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Answer:

1:3

Step-by-step explanation:

We Know

Arturo earns 1,800 per month.

He pays 600 a month on rent.

What is the ratio of his rent to his monthly income?

The ratio is

600:1800

Simplify by 600; we get the ratio

1:3

So, the ratio of his rent to his monthly income is 1:3

y=3

Step-by-step explanation:

3×5=15

2×3=6

15-6=9

Thus, the surface area of paper is needed to wrap 6 cylindrical mini muffins is 23 and 4 over 7  in².

In geometry, a cylinder is just a three-dimensional shape. A cylinder is cylindrical in shape and has a circle-shaped top and bottom. The top and bottom are both flat and uniform in size. The shape of a cylinder is best described, in my opinion, by picturing a soup can.

Given data:

surface area of 6 cylindrical mini muffins = 6*(π*r²*h)

= 6* (22/7 * 1² * 1.25)

= 23.55 in²

= 23 ⁴/₇ in²

Thus, the surface area of paper is needed to wrap 6 cylindrical mini muffins is 23 and 4 over 7  in².

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The slope of the line that best suits the data is -0.1463.

slope = [tex]\sum (( x -\bar x )( y - \bar y )) / \sum ( x - \bar x ) ^2[/tex]

where x is the number of ice cream treats sold, y is the number of coffee drinks sold, x bar is the mean of the number of ice cream treats sold, and ȳ is the mean of the number of coffee drinks sold.

Using the given data, we find that:

[tex]\bar x =[/tex] (16 + 19 + 28 + 27 + 28 + 36 + 38 + 41 + 41 + 48) / 10 = 32.2

[tex]\bar y =[/tex] (55 + 43 + 51 + 46 + 32 + 36 + 43 + 25 + 10 + 33) / 10 = 36.4

Next, we calculate the terms needed for the formula:

[tex]\sum (( x - \bar x )( y - \bar y ))[/tex] = (16 - 32.2)(55 - 36.4) + (19 - 32.2)(43 - 36.4) + ... + (48 - 32.2)(33 - 36.4) = -686.6

[tex]\sum ( x - \bar x )^2[/tex] = (16 - 32.2)² + (19 - 32.2)² + ... + (48 - 32.2)² = 4690.6

Plugging these values into the formula, we get:

slope = [tex]\sum (( x - \bar x )( y - \bar y )) / \sum ( x - \bar x )^2[/tex] = -686.6 / 4690.6 = -0.1463

Therefore, the slope of the line that best fits the data is -0.1463.

Interpreting the slope in terms of the situation, we can say that for every additional ice cream treat sold, the number of coffee drinks sold decreases by an average of 0.1463.

To write the equation of the line that best fits the data, we use the slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept. We already know the value of m, so we just need to find b. To do this, we can use the mean values of x and y:

y = mx + b

36.4 = (-0.1463)(32.2) + b

b = 41.9

Therefore, the equation of the line that best fits the data is:

y = -0.1463x + 41.9

To estimate the number of coffee drinks sold on a day that 32 ice cream treats were sold using the equation of the line of best fit, we simply substitute x = 32 into the equation and solve for y:

y = -0.1463(32) + 41.9

y ≈ 36.9

So we can estimate that approximately 36.9 coffee drinks were sold on a day that 32 ice cream treats were sold. This conclusion is justified because we used the equation of the line that best fits the data to make the estimate, which takes into account the overall trend of the data and the relationship between the number of ice cream treats sold and the number of coffee drinks sold. However, it's important to note that this is only an estimate and there may be other factors that could affect the actual number of coffee drinks sold on a particular day.

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Answer: forgot

Step-by-step explanation:

1. Mark is late. Do you think he forgot about the dinner?

0 + (-66) Plus 18 = -48 is indeed the common sum for every one of these pairings. Hence, -48 is the solution.

The total of the first n terms in the arithmetic sequence is equal to the sum (addition) of the n terms in AP. It is equal to n split by 2 times total sum of thrice the first term, "a," and the product of difference between the second and first term, "d," also; known as the common difference, plus (n-1), where n is the number of terms to be added.

The following step is to add -62 to all of the three remaining integers to create three new ones: -62 + (-4) (= -66, -62 Plus (-2) = -64, & -62 plus 80 = 18. From these three numbers, we now need to select two pairs that sum up to the same number.

We are able to observe that -66 plus -64 is -130, therefore the answer is 18. We obtain 148 when we multiply 130 by 18. As a result, the following three sets of numbers add up to a single total:

-80 and -80, -62 and - 4, and -148

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We can use logical reasoning to conclude that the order is "teenager, little boy, tall man, and woman" as per the explanation below, based on the clues.

Logical reasoning is a process of using rational thinking and deduction to arrive at a conclusion based on available information. In the given problem, logical reasoning is used to analyze the provided clues and determine the order of the four people standing in line.

By carefully examining the clues and using a process of elimination, we can deduce the position of each person in the line. We use logical reasoning to eliminate the possibilities that contradict the given information, and to arrive at the correct sequence that fits all of the provided conditions.

First, we know that the tall man is between the woman and the little boy. So, they can appear in either of the following orders:

However, we are told that the little boy is next to a teenager who is not last. So:

Thus, we can conclude that we have correctly answered this question.

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