[tex](7^{4} ) ^{4}[/tex]

The closest answer choice to this value is option 1, 33. Therefore, the best estimate for the unicity distance for an affine cipher is 33.

To find the best estimate for the unicity distance for an affine cipher, we can use the following formula:

Unicity Distance  (U) = (keyspace / entropy) × log2(1 / redundancy).

Given the answer choices:
1. 33
2. 35
3. 33
4. 26
5. 17.5

For an affine cipher, the keyspace is 26^2 (since there are 26 possibilities for both 'a' and 'b' in the equation

y = (ax + b) mod 26).

The entropy of English text is roughly 1.5 bits/character, and the redundancy is approximately 0.7.

Using the formula, we have:

U = (26^2 / 1.5) × log2(1 / 0.7)

U ≈ 33.49

Therefore, the best estimate for the unicity distance for an affine cipher is 33.

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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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The calculated measure of the arc PM is 19 degrees

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

The circle

The angles created by secants and tangents that intersect outside a circle, which states that

The size of the angle formed by these two lines is equivalent to half the numerical difference between the measures of the arcs that they cut out from the circle.

So, we have

PM = 1/2 * (59 - 21)

Evaluate

PM = 19

Hence, the measure of the arc is 19 degrees

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Answer:

(6, 8)

Step-by-step explanation:

A dilation scales an object on the coordinate plane using the scale factor, causing it to get bigger or smaller.

We are given that the point (3, 4) is dilated by 2; since 2 is greater than 1, this is an enlargement (in which the figure gets bigger).

So, all we need to do is multiply each of the coordinates by 2, like so:

[tex]3*2=6\\4*2=8[/tex]

Thus, the image of the point (3, 4), after being dilated by 2, is (6, 8).

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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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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Nurse Susan Jones would walk a total of 16,000 feet or approximately 3.03 miles during her shift.
Without knowing the travel times of the two nurses, it is not possible to determine the differences in their travel times for a random day.

Assuming that each trip from the nursing pod to a room and back is approximately 50 feet and each trip to the central medical supply, break room, and linen supply is approximately 100 feet, nurse Susan Jones would walk a total of:
- 7 trips to each of the 12 rooms = 7 x 12 x 2 x 50 feet = 8,400 feet
- 20 trips to the central medical supply = 20 x 2 x 100 feet = 4,000 feet
- 6 trips to the break room = 6 x 2 x 100 feet = 1,200 feet
- 12 trips to the pod linen supply = 12 x 2 x 100 feet = 2,400 feet
Therefore, nurse Susan Jones would walk a total of 16,000 feet or approximately 3.03 miles during her shift.

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Nurse Susan Jones would walk nearly 34.4 miles during her shift.

Assuming that Nurse Susan Jones walks an average of 0.2 miles per round trip, she would walk approximately 34.4 miles during her shift (7 trips x 12 rooms x 2 round trips x 0.2 miles per round trip + 20 trips x 2 round trips x 0.2 miles per round trip + 6 trips x 2 round trips x 0.2 miles per round trip + 12 trips x 2 round trips x 0.2 miles per round trip).

Unfortunately, there is not enough information provided to calculate the differences in travel times between two nurses on a random day. It would depend on factors such as the number and location of rooms each nurse is responsible for, the location of the medical supply and break room, and any additional tasks or responsibilities each nurse has during their shift.

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Answer: a and d

Step-by-step explanation:

1 pear = 3 slices

5 pears = 15 slices

5x3=15

OR

5/1/3=15

Equation A and Equation D are the two equations that Kylie can use to solve the problem.

This is a simple mathematics problem.

Kylie has five pears. She cuts each of her pears into thirds, i.e., three slices of each pear.

So, now Kylie will do the same for each pear she has:

Total Slices with Kylie = 5 x 3

Total Slices with Kylie = 15

Equation D can also be used to define the situation of Kylie. Total pears with her are five and each pear is divided into thirds, i.e., 1/3

Total Slices with Kylie = 5 ÷ 1/3

Total Slices with Kylie = 15

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The p-value is 0.0001, indicating strong evidence that college students study more than 20 hours per week based on the sample data.

To test the hypothesis that the average number of hours that college students study per week is greater than 20, we can use a one-sample t-test.

The null hypothesis is that the population mean is equal to 20 hours per week, while the alternative hypothesis is that the population mean is greater than 20 hours per week.

Let's calculate the t-value:

t = (sample mean - hypothesized population mean) / (sample standard deviation / √(sample size))

t = (22.2 - 20) / (3.9 / √(33))

t = 4.49

The degrees of freedom for the t-test is 33 - 1 = 32.

Using a t-table or calculator, we can find the p-value associated with a t-value of 4.49 and 32 degrees of freedom. The p-value is less than 0.0001 (it is actually very close to 0), which means that there is very strong evidence to reject the null hypothesis and conclude that college students study more than 20 hours per week.

Therefore, the p-value is 0.0001 (rounded to 4 decimal places).

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Answer: 0.75 euros = 1 dollar

Step-by-step explanation:

Unit rate

450 euros ----> 600 dollars

450/600 = 0.75

0.75 euros = 1 dollar

Uni rate for the exchange of dollars to euros is 0.75 euros/dollars.

[tex]\implies[/tex] To find the unit rate of exchange from dollars to euros, divide the amount of euros Monica received by the amount of dollars she paid:

[tex]\largearrow{\sf{\boxd{\boxed{Unit \ change = \dfrac{Number \ of \ euros \ you \got}{Number \ of \ dollars \ you \ have} }}}}[/tex]

[tex]\implies{\sf{Unit \ change = \dfrac{\cancel{450}}{\cancel{600}} }}[/tex]

[tex]\implies{\sf{Unit \ change = 0.75 }}[/tex]

As a result, the unit rate for the exchange of dollars to euros is 0.75 euros/dollar.

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 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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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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The cost per customer becomes $( 10+ x) and the average number of customers can be represented as (16 - 2x). Also the inequality equation is 160 - 4x -2[tex]x^{2}[/tex]  [tex]\geq[/tex] 130 to maintain minimum revenue of $130 after rising price by x number of times by $1 as 2 customers leave on average per hour.

Let x represents the number of $1 increases in the cost of the buffet.

Noah manages a buffet at a local restaurant and charges  $10 for the buffet.

On average, 16 customers choose the buffet as their meal every hour.

That is, the average revenue from 16 customers is = $(10*16)= $160

After surveying Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour.

That is, as cost of buffet for every hour rises by $x from $10 we get, $ (10+x) , and the average number of customers who select the buffet will decrease by 2 per hour.

The new average number of customers per hour after rise in cost of buffet by $x is (16 -2x).

This implies, the revenue earned now is = $(16- 2x)(10 + x) = $(160 + 16x - 20x -2[tex]x^{2}[/tex] ) = $ (160 - 4x -2[tex]x^{2}[/tex] )

The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.

Thus, after the increase in price by $x per hour , the inequality equation that helps Noah to pick best pricing decisions will be ,

160 - 4x -2[tex]x^{2}[/tex]  [tex]\geq[/tex] 130

Here, cost per customer becomes $( 10+ x) and the average number of customers can be represented as (16 - 2x).

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a) Required function is [tex]A(t) = 13,000 \times (1.013)^{2t}[/tex]

b) The balance after 4 years is $15,182.51.

c)The balance after 7.5 years is $16,802.59

a. What is the function represent the balance A in the account after t years?

The function to represent the balance A in the account after t years can be given by:

[tex]A(t) = P \times (1 + \frac{r}{n})^{(nt)}[/tex]

where P is the principal amount (initial deposit), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = $13,000, r = 2.6%, n = 2 (interest is compounded every 6 months), and t is the time in years.

Substituting these values into the formula,

[tex]A(t) = 13,000 \times (1 + \frac{ 0.026}{2})^{(2t)}[/tex]

Simplifying the expression,

[tex]A(t) = 13,000 \times (1.013)^{2t}[/tex]

b. To find the balance after 4 years, we can substitute t = 4 into the formula we derived above:

[tex]A(4) = 13,000 \times (1.013)^{(2 \times 4)} \\ = 13,000 \times (1.013)^8 \\ = 15,182.51[/tex]

Therefore, the balance after 4 years is $15,182.51.

c. To find the balance after 7.5 years, we can substitute t = 7.5 into the formula we derived above:

A(t) = 13,000 × (1.013)¹⁵ = 16,802.59

Therefore, the balance after 7.5 years is $16,802.59.

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Answer:

Step-by-step explanation:

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

The range of heights between 66 inches and 76 inches indicates the center 95% of males' heights from this school.

All the numbers between two specific integers are referred to as an interval.

All actual values between those two are included in this range.

The class interval is calculated by deducting the upper limit from the class' lower limit.

The following is the formula for the class interval: Upper limit - Lower limit equals the class interval.

Let x represent the heights of the male students at this institution.

The Empirical Rule states that given the mean and standard deviation:

1) Approximately 68% of the x values fall within the range of the mean plus or minus one standard deviation.

2) Nearly 95% of the x values fall within the range of the mean plus or minus two standard deviations.

3) Nearly 99.7% of the x values fall within a range of 3 standard deviations either above or below the mean.

Considering the data provided:

mean = 71 inches

Standard deviation = 2.5 inches

We want to know where 95% of the x values fall. The variation from the mean is 2 standard deviations. Therefore,

2 standard deviations = 2 × 2.5 = 5 inches

Heights:

71 - 5 = 66 inches and

71 + 5 = 76 inches

Therefore, the range of heights between 66 inches and 76 inches indicates the center 95% of males' heights from this school.

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Complete question:

In an all-boys school, the heights of the student body are normally distributed with a mean of 71 inches and a standard deviation of 2.5 inches. Using the empirical rule, determine the interval of heights that represents the middle 95% of male heights from this school.

The length of the other leg is 8 cm, and the measures of the two acute angles are approximately 36.87° and 53.13°.

To solve the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we have:

[tex]10^2 = 6^2 + x^2 \\x = sqrt(10^2 - 6^2) = 8 cm[/tex]

So the length of the other leg is 8 cm.

Let θ be one of the acute angles:

sin(θ) = opposite/hypotenuse = 6/10 = 0.6

cos(θ) = adjacent/hypotenuse = x/10 = 8/10 = 0.8

θ ≈ 36.87°.

Since the other acute angle is complementary to θ, its measure is 90° - 36.87° = 53.13°.

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--The complete Question is,  A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Solve the right triangle, finding the length of the other leg and the measures of the two acute angles. --

Answer:

0.1296

Step-by-step explanation:

0.6*0.6=0.36

0.6*0.36=0.216

0.6*0.216=0.1296

The correct answer is: Super Fast Food, because it has a smaller median.

What is the median?

The median is a measure of central tendency that represents the middle value in a set of data when the data is arranged in ascending or descending order.

Based on the given information, Super Fast Food typically has less wait time compared to Fast Chicken.

The median is the middle value in a set of data, and it is often used as a measure of central tendency in box plots. In this case, the median for Super Fast Food is 12, while the median for Fast Chicken is 12.5. Since the median for Super Fast Food is smaller than the median for Fast Chicken, it suggests that the wait times at Super Fast Food are generally lower than those at Fast Chicken.

Hence, the correct answer is: Super Fast Food, because it has a smaller median.

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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 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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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:

Step-by-step explanation:

the inword

The correct option is: "Univariate analysis involves the analysis of a single variable."

The following statement is true with regards to statistical analysis:

Univariate analysis involves the analysis of a single variable.

The other statements are not entirely accurate:

Bivariate analysis is a form of multivariate analysis that examines the relationship between two variables, but multivariate analysis can involve more than two variables.

Regression analysis is a multivariate analysis technique that examines the relationship between one dependent variable and one or more independent variables.

Multivariate analysis involves the examination of the relationship between two or more variables, not necessarily one, two, or more.

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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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It will take 7 years for Janelle's savings account balance to reach $510.50 at an annual interest rate of 0.3%.

The interest rate on a loan or investment is calculated using the original principal amount. It does not take into account the effects of compounding, hence the interest charge or payment does not alter over time. Simple interest can be applied to several sorts of loans or savings accounts. It is computed only on the basis of the principal.

We can use the formula for simple interest to solve this problem:

Simple Interest = Principal * Rate * Time

where Principal is the initial amount in the account, Rate is the annual interest rate, and Time is the number of years.

Let's use the given information to find the time it takes to reach a balance of $510.50:

Simple Interest = $510.50 - $500 = $10.50

Principal = $500

Rate = 0.3% = 0.003 (since the rate is given as a percentage, we need to divide by 100 to get the decimal equivalent)

Substituting these values into the formula, we get:

$10.50 = $500 * 0.003 * Time

Simplifying this equation, we get:

Time = $10.50 / ($500 * 0.003) = 7 years

Therefore, it will take 7 years for Janelle's savings account balance to reach $510.50 at an annual interest rate of 0.3%.

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The probability that the sample mean would be less than 100.9 months is approximately 0.9600.

We can use the central limit theorem to approximate the sampling distribution of the sample mean as a normal distribution with a mean of 97 months (the population mean) and a standard deviation of σ/√n, where σ is the population standard deviation and n is the sample size.

The standard deviation of the sampling distribution can be calculated as follows

σ/√n = √(169)/√59 = 2.065

Therefore, the z-score corresponding to a sample mean of 100.9 months is

z = (100.9 - 97) / 2.065 = 1.75

Using a standard normal distribution table or calculator, we can find that the probability of obtaining a z-score less than 1.75 is approximately 0.9599.

Therefore, the probability that the sample mean would be less than 100.9 months is approximately 0.9599.

Rounding this to four decimal places, we get

P(x < 100.9) ≈ 0.9600

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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 domain of the following graph is equal to [-11. -3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-11, -3].

Range = [-5, 0].

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