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the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).

What is a fraction?

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.

To convert these polar coordinates to Cartesian coordinates (x, y), we use the following formulas:

x = r cos(θ)

y = r sin(θ)

Substituting the given values, we get:

x = 6 cos(-π/3) = 6 × (1/2) = 3

y = 6 sin(-π/3) = 6 × (-√3/2) = -3√3

Therefore, the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).

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Answer:

D. y ≥ x² - 4x - 5

Step-by-step explanation:

We can observe two characteristics of this graphed inequality:

1. its shading is above it, therefore the inequality sign must be greater than

2. its boundary line is continuous, not dotted, so the inequality sign must include or equal to

From these two observations, we can assert that D. x² - 4x - 5 is the correct answer because it is the only one which has a greater than or equal to sign.

____________

Note:

We can also check that the equation for the inequality is correct by converting it to vertex form by completing the square, then graphing it ourselves:

[tex]y \ge (x-2)^2 - 9[/tex]

Answer:

The answer is y≥ x²-4x-5

Step-by-step explanation:

x=a,x=b

where a,b are roots of the equation

a= -1 b=5

x= -1,x=5

x+1=0,x-5=0

(x+1)(x-5)=0

x²-5x+x-5=0

x²-4x-5=0

The x-axis and y-axis are two parallel number lines that meet at (0, 0) to form the shape of the letter t.

Geometric objects and mathematical equations are represented on the coordinate plane, a two-dimensional graph. It is made up of the x-axis and y-axis, two parallel number lines that meet at the starting point (0, 0). The horizontal coordinate is represented by the x-axis, while the vertical coordinate is represented by the y-axis. They combine to create the Cartesian coordinate system.

Positive numbers are labelled to the right of the origin and negative values are labelled to the left of the origin on the x-axis. Positive numbers are written above the origin of the y-axis, and negative numbers are written below it. An ordered pair (x, y), where x denotes the horizontal coordinate and y denotes the vertical coordinate, is used to represent each point on the coordinate plane.

For graphing linear equations, quadratic equations, and other functions, the coordinate plane is a helpful tool. Additionally, it is employed to depict geometric forms like polygons, circles, and lines. The distance between two points, the slope of a line, and other significant features of mathematical objects can be calculated by graphing points on the coordinate plane. With applications in physics, engineering, economics, and computer science, the coordinate plane is a fundamental idea in mathematics.

The graph is shown below when y=1.

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Graph attached below,

The coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is y = [tex]\frac{1}{2}x-4[/tex].

Now put x= 1 then y = [tex]\frac{1}{2}\times1-4 =\frac{1-8}{2}=\frac{-7}{2}=-3.5[/tex]

Now put x=2 then [tex]y=\frac{1}{2}\times2-4=1-4=-3[/tex]

Now put x=4 then [tex]y=\frac{1}{2}\times4-4=2-4=-2[/tex]

Now put x=6 then [tex]y=\frac{1}{2}\times6-4=3-4=-1[/tex]

Then coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

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The graph will have a horizontal line from 4 to 15 hours (since there is no change in snow depth during that time) and two downward sloping lines from 0 to 4 hours and from 15 to 22 hours (representing snowfall and snow melt, respectively)

To make a graph of the inches of snow on the ground over time, we can use the following steps:

We can divide the time into different intervals based on the snowfall, the break in the storm, and the snow melt. We have:

We can then calculate the inches of snow on the ground at the end of each interval, starting with the initial 3 inches of snow. We have:

We can now plot these points on a graph with time (in hours) on the x-axis and inches of snow on the y-axis. The graph will have four points: (0,3), (4,7), (15,17), and (22,3).

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Answer:

13.416407865

Step-by-step explanation:

You wouldn't use soh cah toa

There is no angle given. Instead you should do 6²+12²=180

And then you would square root 180=13.416407865

Therefore the answer is 13.416407865

The rejection of the null hypothesis in a hypothesis test that claims the mean gestation period for a fox is more than 48.9 weeks implies there is sufficient evidence to support the claim, indicating a statistically significant difference between the observed sample mean and the hypothesized mean.

If a hypothesis test is performed that rejects the null hypothesis that the mean gestation period for a fox is 48.9 weeks or less, it means that there is sufficient evidence to support the claim that the mean gestation period for a fox is more than 48.9 weeks.

The rejection of the null hypothesis implies that the observed sample mean is significantly different from the hypothesized mean, and this difference is unlikely to have occurred by chance alone. The statistical test used to evaluate the hypothesis would have produced a p-value less than the significance level, indicating that the evidence against the null hypothesis is strong.

Therefore, the scientist can conclude that there is evidence to support their claim that the mean gestation period for a fox is more than 48.9 weeks, and this finding could have important implications for understanding fox reproductive biology and management.

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Answer: Problems Involving FractionsIn solving word problems, first, identify what is asked. Then, look for the given facts. Establish the number sentence and the operation/s to be used. Make sure that the operation/s used will bring out the correct answer. Check the answer using the number sentence and see if it will satisfy the given condition.

Step-by-step explanation: Learning Task 2:Answers:16 1/4 square meters₱322,362.50Step-by-step explanation:Solutions:1. Given: 6 1/2 square meters - area which Ruben can paint in an hour

Two consecutive integers in algebraic language would be 7 and 8

Let's call the first integer "X" then the next consecutive integer would be "x+1".

so if the sum of the two integers is 15, we can write the following expression.

x + (x+1) = 15

Solving for x  we get  
2x + 1 = 15
2x =14
x = 7

Hence, the two consecutive integers in this case are 7 and 8.

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Translation:

Two consecutive integers in algebraic language

Answer: Let's say we want to find out how many red Skittles we need to add to the bag to have the same ratio of red Skittles as in the original bag.

Suppose the original bag contains x red Skittles. Then, the ratio of red Skittles to the total number of Skittles in the bag is x/100.

Let's say we add y red Skittles to the bag, so the total number of red Skittles in the bag becomes x + y. The total number of Skittles in the bag becomes 100 + y, since we only added red Skittles.

For the ratio of red Skittles to be the same as in the original bag, we need:

(x + y) / (100 + y) = x / 100

Cross-multiplying, we get:

100(x + y) = x(100 + y)

Simplifying and rearranging, we get:

y = 100x / (100 - x)

So, we need to add 100x / (100 - x) red Skittles to the bag to have the same ratio of red Skittles as in the original bag. For example, if the original bag has 20 red Skittles, we need to add:

y = 100(20) / (100 - 20) = 25

So, we need to add 25 red Skittles to the bag to have the same ratio of red Skittles as in the original bag.

Step-by-step explanation:

The ordered pair (z, 11) is not a solution of the inequality.

Explain inequality

An inequality is a statement that compares two values, expressing that one value is greater than or less than the other, or that they are not equal. Inequalities are represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). They are used to describe relationships between numbers, variables, and expressions.

According to the given information

To determine whether the ordered pair (z, 11) is a solution of the inequality 2z < 15, we need to substitute z = 11 into the inequality and see if it is true or false:

2z < 15

2(11) < 15

22 < 15 (this is false)

Since 22 is not less than 15, the ordered pair (z, 11) is not a solution to the inequality.

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For the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.

On a map, scales are frequently present. The scale factor in geography usually applies to how accurately the scale depicted on the map reflects actual distance. Find the corresponding sides upon that two figures before obtaining the scale factor.

Then, divide the new figure's measurement by the old figure's measurement. Your scale factor, i.e., how many times bigger or less than your new image is in comparison to the old, is the consequence.

From the diagram:

coordinate of A = (1,1)

coordinate of A' = (5,5)

Thus, the coordinates of A is multiplied by 5 to get the coordinates of A'

Same applies with the coordinates of B, C and D.

Thus, for the given diagram, the square ABCD is transformed into square A'B'C'D' by the dilation using the scale factor of 5.

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Answer:

negative

y=-x

y=-2x+6

y=(-1/2)x+1

y=-5x+20

undefined

x=4

x=-3

zero slope

y=2

y=-100

The two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.

Coterminal angles are two or more angles that have the same initial and terminal sides, but differ by a multiple of 360 degrees or 2π radians. In other words, coterminal angles are angles that overlap each other when drawn in standard position (with their initial side on the positive x-axis).

To find two coterminal angles with 3/4 radians, we can add or subtract multiples of 2π radians (which is equivalent to a full circle).

One positive coterminal angle is obtained by adding 2π radians to 3/4 radians:

3/4 + 2π = 3/4 + 8π/4 = 3/4 + 2π

Simplifying, we get:

3/4 + 2π = (3π + 4)/4

Therefore, one positive coterminal angle is (3π + 4)/4 radians.

One negative coterminal angle is obtained by subtracting 2π radians from 3/4 radians:

3/4 - 2π = 3/4 - 8π/4 = 3/4 - 2π

Simplifying, we get:

3/4 - 2π = (-5π + 4)/4

Therefore, one negative coterminal angle is (-5π + 4)/4 radians.

Hence, the two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.

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The radius of convergence is 4.

To find the radius of convergence, R, of the collection, we can use the ratio test:

[tex]lim_n→∞ |(a_(n+1)/[/tex][tex]a_n)|[/tex]

[tex]lim_n→∞ |(a_{(n+1})/[/tex]

[tex]= lim_n→∞ |(x+8) / 4| * |ln(n+1) / ln(n)|[/tex]

For the series to converge, this limit need to be less than 1. therefore, we've:

[tex]|(x+8) / 4| * lim_n→∞ |ln(n+1) / ln(n)| < 1[/tex]

For the reason that[tex]lim_n→∞ |ln(n+1) / ln(n)| = 1[/tex], we will simplify this to:

|(x+8) / 4| < 1

Taking the absolute cost under consideration, we have cases:

Case 1: (x+8)/4 < 1

In this case, we have x < -4.

Case 2: (x+8)/4 > -1

In this case, we have x > -12.

Consequently, the radius of convergence is the distance from the center of the collection (x = -8) to the closest endpoint of the c language (-12 on the left and -4 at the right):

R = min{8, 4} = 4

So, 4 is the radius of convergence.

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Answer:

£12063.57

Step-by-step explanation:

The value of Alfred’s car after 12 years can be calculated using the formula for exponential decay: Final Value = Initial Value * (1 - rate of depreciation)^(number of years). Plugging in the values we get: Final Value = 13960 * (1 - 0.0075)^12. Therefore, after 12 years, Alfred’s car will be worth approximately £12063.57.

Answer:

Step-by-step explanation:

the inword

1. The mean number of households that will have one or more cats is 15.

2. This means that getting 10 or fewer households with cats out of 50 is not extremely unusual, as there is a 5.3% chance of it happening by random chance alone.

The mean number of households that will have one or more cats can be calculated as:

Mean = (30/100) x 50 = 15

Therefore, the mean number of households that will have one or more cats is 15.

The standard deviation can be calculated using the formula:

Standard deviation = [tex]\sqrt{(npq)}[/tex]

where n is the sample size (50), p is the probability of success (30/100 = 0.3), and q is the probability of failure (1 - p = 0.7).

Standard deviation = sqrt(50 x 0.3 x 0.7) = 3.08

Rounding to 1 decimal place, the standard deviation is 3.1.

If 10 of the 50 random households had one or more cats, we can calculate the z-score as:

z = (x - μ) / σ

where x is the observed number of households with cats (10), μ is the mean (15), and σ is the standard deviation (3.1).

z = (10 - 15) / 3.1 = -1.61

Looking up the z-score in a standard normal distribution table, we find that the probability of getting a z-score of -1.61 or lower is 0.053.

This means that getting 10 or fewer households with cats out of 50 is not extremely unusual, as there is a 5.3% chance of it happening by random chance alone.

However, it is somewhat lower than the expected value of 15, which suggests that the sample may not be fully representative of the population.

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The balloon payment at the end of 7 years would be $173,819.97, which is option A.

A 7/23 balloon mortgage means that April will make payments on the loan as if it were a 23-year mortgage, but the remaining balance of the loan will be due in full after 7 years.

To find the balloon payment at the end of 7 years, we can first calculate the monthly payment using the loan amount, interest rate, and loan term:

n = 23 * 12 = 276 (total number of payments)

r = 4.15% / 12 = 0.003458 (monthly interest rate)

P = (r * PV) / (1 - (1 + r)^(-n))

where

PV = $197,000

P = (0.003458 * $197,000) / (1 - (1 + 0.003458)^(-276)) = $1,007.14 (monthly payment)

Now we can calculate the remaining balance on the loan after 7 years. Since April is making payments as if it were a 23-year mortgage, she will have made 7 * 12 = 84 payments by the end of the 7th year.

Using the formula for the remaining balance of a loan after t payments:

B = PV * (1 + r)^t - (P / r) * ((1 + r)^t - 1)

Where

t = 84 (number of payments made)

B = $197,000 * (1 + 0.003458)^84 - ($1,007.14 / 0.003458) * ((1 + 0.003458)^84 - 1)

B = $173,819.97

Therefore, the balloon payment at the end of 7 years would be $173,819.97, which is option A.

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The domain of the function is (-∞, ∞) and the range of the function is [2, ∞).

In mathematics, the range of a function refers to the set of all possible output values (dependent variable) that the function can produce for its corresponding input values (independent variable).

The given function is y = 3x² + 2.

The domain of a function is the set of all possible values of the independent variable (x) for which the function is defined. Since the given function is a polynomial function, it is defined for all real numbers.

Therefore, the domain of the function y = 3x² + 2 is (-∞, ∞), which means that the function is defined for all real values of x.

The range of a function is the set of all possible values of the dependent variable (y) that the function can take. In this case, the function is a quadratic function with a leading coefficient of 3, which means that the parabola opens upwards and its vertex is at the point (0,2).

Since the minimum value of the function is 2, the range of the function is [2, ∞).

Therefore, the domain of the function is (-∞, ∞) and the range of the function is [2, ∞).

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Answer:

r = 2

center: ( -7,0 )

Step-by-step explanation:

Amy needs 78 inches of fabric for her pants if she follows the given rule.

Define inches ?

An inch is a unit of length that is equal to exactly 2.54 centimeters. It is commonly used in the United States and other countries that use the Imperial system of measurement.

To determine how much fabric Amy needs for her pants, we can use the rule provided to us. The first step is to measure from the waist to the finished length of the pants, which in this case is 35 inches.

Next, we need to double this measurement, which gives us 2 * 35 = 70 inches. This is because we need to account for the fabric that will make up both the front and back of the pants.

Finally, we need to add 8 inches to the doubled measurement, which gives us 70 + 8 = 78 inches. This additional 8 inches is to account for any seams, hems, or other finishing touches that may be required to complete the pants.

Therefore, Amy needs 78 inches of fabric for her pants.

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The probability that a student selected at random is a girl who chose apple as her favorite fruit is 0.32, or 32% rounded to the nearest hundredth.

To calculate the probability that a student is a girl who chose apple as her favorite fruit, we need to use the information provided in the table. First, we need to find the total number of girls who participated in the survey, which is the sum of the number of girls who chose apples, oranges, and mangoes as their favorite fruit, i.e., 46 + 41 + 55 = 142.

Next, we need to find the number of girls who chose apples as their favorite fruit, which is 46. Therefore, the probability that a student is a girl who chose apple as her favorite fruit is given by:

Probability = Number of girls who chose apples / Total number of girls in the survey

Probability = 46 / 142

Probability = 0.32

This means that out of all the girls who participated in the survey, 32% of them chose apple as their favorite fruit.

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Complete question is:

three hundred students in a school were asked to select their favorite fruit from a choice of apples, oranges, and mangoes. this table lists the results.

               Boys Girls

Apple    66     46

Orange   52     41

Mango    40     55

if a survey is selected at random, what is the probability that the student is a girl who chose apple as her favorite fruit?

The probability of exponential random variables that your job will be ready before 10:01 is approximately 0.0693, or about 6.93%.

We can use the cumulative distribution function (CDF) of the exponential distribution to solve this problem. Let X be the random variable representing the time it takes to print a job. Then, X follows an exponential distribution with parameter λ = 1/12, since the expectation of X is 12 seconds.

The probability that your job will be ready before 10:01 is equal to the probability that the printer finishes the first two jobs in less than 1 minute since your job is third in line.

Let Y be the random variable representing the time it takes to print the first job. Then, Y also follows an exponential distribution with parameter λ = 1/12.

The probability that the first job is finished before 10:01 is given by:

P(Y < 60) = 1 - [tex]$e^{(-\lambda t)}$[/tex] = 1 - [tex]e^{(-(1/12)(60))}[/tex] = 0.3935

Similarly, the probability that the second job is finished before 10:01 is also 0.3935, since it is also an exponential random variable with the same parameter. Therefore, the probability that your job will be ready before 10:01 is:

P(X < 60) = P(Y < 60) × P(Y < 60) × P(X < 60) = 0.3935² × (1 - [tex]$e^{(-\lambda t)}$[/tex]) = 0.0693

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Answer:

5 1/4

Step-by-step explanation:

The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

The equation would be:

C is the total cost and m is the miles driven.

We know that:
Charge of the truck: $35

Charge per mile: $2.50

Then, form the equation as follows:

C = 35 + 2.50m

Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

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The correct expression showing the total area of the five rooms is A. (3 x 14²) + (2 x 17²), which simplifies to 1918 square feet.

An expression is a combination of numbers, symbols, and operators (such as addition, subtraction, multiplication, and division) that represent a mathematical calculation. An expression can be a single number, a variable, or a combination of both, and can be used to represent mathematical formulas, equations, or relationships.

In the given question,

C. (3 × 17²) + (2 × 14²)

To find the total area of the five rooms, we need to add the area of each room. The area of a square is found by squaring the length of one side.

For the three rooms with sides of 14 feet each, the area of each room is:

14^2 = 196 square feet

So the total area of these three rooms is:

3 × 196 = 588 square feet

For the two rooms with sides of 17 feet each, the area of each room is:

17^2 = 289 square feet

So the total area of these two rooms is:

2 × 289 = 578 square feet

Therefore, the total area of all five rooms is:

588 + 578 = 1166 square feet

Option C, (3 × 17²) + (2 × 14²), gives the correct expression for this calculation.

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Step-by-step explanation:

2x+20  and 2x-4  are supplementary angles...they form a straight line and thus = 180 degrees when added together

2x+20      +    2x-4     = 180          simplify

4x + 16 = 180                               subtract 16 from both sides

4x  = 164                                     divide both sides by 4

x = 41 degrees

The total amount of interest paid over the life of the loan is $1863.45.

The present value of the loan.

Since there are 12 months in a year, and the loan has n-years, there are 12n monthly payments.

Let's use the formula for the present value of an annuity due:

[tex]PV = PMT \times ((1 - (1 + r) ^(-n)) / r) \times (1 + r)[/tex]

PV is the present value of the loan, PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.

Substituting the given values, we get:

[tex]PV = \$800 \times ((1 - (1 + 0.12/12) ^(-12n)) / (0.12/12)) \times (1 + 0.12/12)[/tex]

[tex]PV = \$800 \times ((1 - (1.01)^(-12n)) / 0.01) \times 1.01[/tex]

[tex]PV = \$800 \times ((1 - 1.01^(-12n)) / 0.01) \times 1.01[/tex]

[tex]PV = \$800 \times ((1 - 0.887^(-n)) / 0.01) \times 1.01[/tex]

The formula for the interest paid in any given month of an annuity due:

[tex]I = PV \times r \times (1 + r) ^(m - 1)[/tex]

I is the interest paid in the 45th month, PV is the present value of the loan, r is the monthly interest rate, and m is the month.

Substituting the given values for the 45th month, we get:

[tex]\$424.45 = PV \times 0.01 \times (1 + 0.01 )^(45 - 1)[/tex]

[tex]\$424.45 = PV \times 0.01 \times (1.01)^4^4[/tex]

[tex]PV = \$424.45 / (0.01 \times (1.01)^4^4)[/tex]

PV =[tex]\$75799.45[/tex]

Now that we know the present value of the loan, we can calculate the total amount of interest paid over the life of the loan.

Let's use the formula for the total interest paid in an annuity due:

[tex]Total interest = (PMT \times n \times (n + 1) / 2) - PV[/tex]

Substituting the given values, we get:

Total interest = [tex](\$800 \times 12n \times (12n + 1) / 2) - \$75799.45[/tex]

Total interest = [tex]\$9600n^2 + \$4800n - \$75799.45[/tex]

We can solve for n by using the fact that the interest paid in the 45th month is $424.45:

[tex]\$424.45 = \$800 \times (n \times 12 - 44) \times 0.01 \times (1 + 0.01)^(45 - 1)[/tex]

[tex]\$424.45 = \$800 \times (n \times 12 - 44) \times 0.01 \times (1.01)^4^4[/tex]

n = 4.5

Substituting n = 4.5 into the formula for total interest, we get:

Total interest =[tex]\$9600 \times (4.5)^2 + \$4800 \times 4.5 - \$75799.45[/tex]

Total interest = $1863.45

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Without specific data from the survey, I cannot provide the exact average length of time a person lived in the slums. I can be found by collecting data and finding average.

In general, surveys can be used to gather information on a population's characteristics and experiences, including their life expectancy. If the survey conducted in the slums of Nairobi included questions about life expectancy or mortality rates, the average lifespan of the individuals surveyed could be calculated using the data collected. It's important to note that the average lifespan in the slums may differ from that of other areas in Nairobi or other regions of the world.
Based on the information provided, Dr. Salon mentioned a survey conducted in the slums of Nairobi. To determine how long the average person lived in the slums, we would follow these steps:

1. Collect the data: The survey would gather information about the length of time people lived in the slums.
2. Calculate the average: Add up the total number of years all respondents lived in the slums and divide by the total number of respondents.

Without specific data from the survey, can't provide the exact average length of time a person lived in the slums. Please provide more information or refer back to Dr. Salon's lecture for the results of the survey.

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