Find each quotient using synthetic division. (m^(4)-7m^(3)-39m^(2)-28m-3)-:(m+3)

Answer: (a) The possible outcomes and their probabilities are:

Value of x Probability

0 0.6561 (0 F's and 4 S's)

1 0.2916 (1 F and 3 S's, or 2 F's and 2 S's, or 3 F's and 1 S)

2 0.0486 (2 F's and 2 S's)

3 0.0036 (1 S and 3 F's)

4 0.0001 (4 F's and 0 S's)

(b) The most likely value of x is the one with the highest probability, which is x = 0.

(c) The probability that at least two of the four selected homeowners have earthquake insurance is equal to 1 minus the probability that 0 or 1 of them have earthquake insurance:

P(at least 2 of the 4 have earthquake insurance) = 1 - P(x = 0) - P(x = 1)

= 1 - 0.6561 - 0.2916

= 0.0523

Therefore, the probability that at least two of the four selected homeowners have earthquake insurance is 0.0523.

Enjoy!!!!!

Probability distribution of x is calculated by finding probabilities of each possible outcome, the most likely value of x is 0 with a probability of 0.6561, probability of at least two homeowners having earthquake insurance is 0.0523.

(a) The probability distribution of x can be found by calculating the probabilities of each possible outcome (0, 1, 2, 3, 4 homeowners with insurance) and associating them with their respective x values.

Value of x | Probability
--- | ---
0 | (.9)(.9)(.9)(.9) = 0.6561
1 | (.1)(.9)(.9)(.9) + (.9)(.1)(.9)(.9) + (.9)(.9)(.1)(.9) + (.9)(.9)(.9)(.1) = 0.2916
2 | (.1)(.1)(.9)(.9) + (.1)(.9)(.1)(.9) + (.1)(.9)(.9)(.1) + (.9)(.1)(.1)(.9) + (.9)(.1)(.9)(.1) + (.9)(.9)(.1)(.1) = 0.0486
3 | (.1)(.1)(.1)(.9) + (.1)(.1)(.9)(.1) + (.1)(.9)(.1)(.1) + (.9)(.1)(.1)(.1) = 0.0036
4 | (.1)(.1)(.1)(.1) = 0.0001

(b) The most likely value of x is 0, as it has the highest probability (0.6561).

(c) The probability that at least two of the four selected homeowners have earthquake insurance can be found by adding the probabilities of the outcomes with 2, 3, and 4 homeowners with insurance:

P (at least 2 of the 4 have earthquake insurance) = 0.0486 + 0.0036 + 0.0001 = 0.0523

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The joint probability function for X and Y is legitimate because the sum of all probabilities is equal to 1 and the probabilities are non-negative. Each point in the domain has a corresponding probability.b. p(1,2) means the probability of X=1 and Y=2.  p_x(3) = 0.1 + 0.05 = 0.15.

a. Probability function is considered legitimate when the sum of all the probabilities is 1, the probabilities are non-negative and each point in the domain must have a corresponding probability. Here, the joint probability function for X and Y is legitimate because the sum of all probabilities is equal to 1 and the probabilities are non-negative. Each point in the domain has a corresponding probability.b. p(1,2) means the probability of X=1 and Y=2. We can see from the table that p(1,2) = 0.04.c. P(X<1, Y≥2) means the probability of X being less than 1 and Y being greater than or equal to 2. We can find the probabilities by adding up all the probabilities in the cells that meet this condition. From the table, we can see that the cells (0,2) and (0,3) meet this condition. Therefore, P(X<1, Y≥2) = 0.01 + 0.01 = 0.02.d. We need to find p_x(3), which means the probability of X=3. We can find this by adding up all the probabilities where X=3. From the table, we can see that the cells (3,1) and (3,2) meet this condition. Therefore, p_x(3) = 0.1 + 0.05 = 0.15.

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The startup E-Education can go according to option 2 and option 3. Both the options are giving returns of $1500000 for 2 years.

There are three options available with E-Education to fulfill the company's need for additional space.

The decision tree for the available options is made below;

                                                         Option1         Option2          Option3

$ $ $

Cost of Moving to New Building                         1000000        2000000

Leasing cost                                    1000000      1300000 1500000

Total Cost of the Option             2000000 1500000          1500000

Conclusion: The startup E-Education can go according to option 2 and option 3. Both the options are giving returns of $1500000 for 2 years.

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The price elasticity of demand when P=15 is -0.9

To find the price elasticity of demand when P=15, we need to calculate the percentage change in quantity demanded and the percentage change in price. Let's start with the percentage change in quantity demanded.

ΔQ/Q = (Q2 - Q1)/Q1

where Q1 is the initial quantity demanded and Q2 is the new quantity demanded.

Substituting the values from the demand function, we get:

ΔQ/Q = [(75 - 3P2) - (75 - 3P1)]/(75 - 3P1)

where P1 = 15 and P2 = P1 + ΔP = 15 + 15% = 17.25 (since ΔP/P = 15%).

ΔQ/Q = [(75 - 3(17.25)) - (75 - 3(15))]/(75 - 3(15))

ΔQ/Q = (-8.25)/60

ΔQ/Q = -0.1375

Therefore, the percentage change in quantity demanded is -13.75%.

Now, let's calculate the percentage change in price:

ΔP/P = (P2 - P1)/P1

ΔP/P = (17.25 - 15)/15

ΔP/P = 0.15

Therefore, the percentage change in price is 15%.

Substituting these values in the formula for price elasticity of demand, we get:

E = (-0.1375) / 0.15

E = -0.9167

The price elasticity of demand when P=15 is approximately -0.9.

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Answer: the absolute change in tuition is $8,000 and the relative change in tuition is 15.2%.

Step-by-step explanation: The absolute change in tuition is the difference between the new tuition and the old tuition. Therefore:

Absolute change = New tuition - Old tuition

Absolute change = $60,500 - $52,500

Absolute change = $8,000

The relative change in tuition is the ratio of the absolute change to the old tuition, expressed as a percentage. Therefore:

Relative change = (Absolute change / Old tuition) x 100%

Relative change = ($8,000 / $52,500) x 100%

Relative change = 15.2%

The correct statement regarding the association between the variables is given as follows:

C. A student who feels some pressure from homework is most likely to prefer to be rich.

The two variables for this problem are defined as follows:

For the people who feel some pressure from homework, the preferred status are given as follows:

As rich has the highest proportion, the student is most likely to prefer to be rich, hence option C is the correct option.

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The maximum kinetic energy Dina can reach is 250 joules, calculated by multiplying her mass of 50 kg, gravitational acceleration of 9.8 m/s2, and the height of the slope of 5 m.

50 kg x 9.8 m/s2 x 5 m = 250 joules

The maximum kinetic energy that Dina can reach when she skis to the bottom of the slope is calculated by the equation pe = m × g × h. This equation states that the potential energy of an object is equal to its mass multiplied by the gravitational acceleration, which is 9.8 m/s2, and the height of the slope. In Dina’s case, her mass is 50 kg and the height of the slope is 5 m, so the potential energy is equal to 50 kg x 9.8 m/s2 x 5 m, which is equal to 250 joules. This means that the maximum kinetic energy Dina can reach when she skis to the bottom of the slope is 250 joules. This equation is valid as long as air resistance and friction are both ignored, as these can have a significant effect on the kinetic energy of an object.

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Answer:

The area of the figure is 90 yd²

Step-by-step explanation:

Dividing the shape into three leading to 3 rectangles

The area of a rectangle is length * breadth;

First section + Second section + Third section

(9 * 3) + ( 9 * 4) + (9 * 3) = 27 + 36 + 27 = 90 yd²

Answer:

74yd²

Step-by-step explanation:

You can divide into 3 rectangles from bottom down

Area = length x width

1st rectangle = 9 x 3 = 27yd²

2nd rectangle = 5x 4 = 20yd²

3rd rectangle = 9 x 3 = 27yd²

Add all the area

27 +20+27 = 74yd²

Another method

Find the area of the whole rectangle with the white area closed and included

Lenght 10yd, width 9yd

Area = 10 x9 = 90yd²

Find the area of the white area only

A = 4 x4 =16yd ²

Subract the area of the white square from the whole area of the rectangle

90 - 16 =74yd²

The effect on the graph of the parent function after transformation is:

C.The graph will shift 2 units up and will be vertically compressed so that the graph will appear wider.

The vertical shift depends on the value of k. The vertical shift is described as:

f(x) = f(x) + k - The graph is shifted up k units.

f(x) = f(x) − k - The graph is shifted down k units.

Now, we are told that  f(x) = x³, is transformed to f(x) = ¹/₂x³ + 2

Thus, the graph is shifted up by 2 units.

Compressing and stretching depends on the value of a.

When a is greater than 1: Vertically stretched

When a is between 0 and 1: Vertically compressed

In this case, a is 1/2 which is between 0 and 1 and so is Vertically compressed

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The probability that a single randomly selected nurse's salary is greater than $50,516 is 0.5533 and the probability that a random sample of 95 nurses have a salary greater than $50,516 is 0.9098.

a. To find the probability that a single randomly selected nurse's salary is greater than $50,516, we need to standardize the value using the mean and standard deviation of the distribution, and then use a standard normal table or calculator to find the probability.

The standardized value (z-score) is:

z = (x - μ) / σ = (50,516 - 50,650) / 1,000 = -0.134

Using a standard normal table or calculator, we can find the probability that a randomly selected nurse's salary is greater than $50,516:

P(x > 50,516) = P(z > -0.134) = 0.5517

Therefore, the probability that a single randomly selected nurse's salary is greater than $50,516 is 0.5533.

b. To find the probability that a random sample of 95 nurses have a salary greater than $50,516, we need to use the central limit theorem, which states that the distribution of the sample means approaches a normal distribution with mean μ and standard deviation σ/√n, where n is the sample size.

The mean of the sample means is still μ = 50,650, but the standard deviation of the sample means is now:

σ/√n = 1,000 / √95 = 102.06

We want to find the probability that the sample mean is greater than $50,516:

P(x > 50,516) = P(z > (50,516 - 50,650) / (1,000 / √95)) = P(z > -1.335)

Using a standard normal table or calculator, we can find the probability:

P(x > 50,516) = P(z > -1.335) = 0.9098

Therefore, the probability that a random sample of 95 nurses have a salary greater than $50,516 is 0.9098.

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To calculate the interest due, we first need to determine the average daily balance for the month.

From the beginning of the month until the 9th day, the balance is $660. From the 10th to the 27th, the balance is $660 - $90 = $570. On the 28th, the balance increases to $570 + $320 = $890.

So the average daily balance is:

[(31 - 9) x $570 + 9 x $660 + 22 x $890] / 31 = $691.29

Next, we need to calculate the monthly interest rate:

26% APR = 0.26 / 12 = 0.02167

Finally, we can calculate the interest due:

$691.29 x 0.02167 = $14.98

Therefore, the answer is closest to option (a) $7.48.

the only cube number between 20 and 50 is 27.

Step 1: Find the smallest cube greater than 20.

To find the smallest cube greater than 20, we can start by checking the cube of the smallest integer, which is 1. Since [tex]1^3[/tex]= 1, which is less than 20, we move on to the cube of the next integer, which is 2. We find that [tex]2^3[/tex]= 8, which is still less than 20. Finally, we check the cube of the next integer, which is 3. We find that [tex]3^3[/tex]= 27, which is the smallest cube greater than 20.

Step 2: Find the largest cube less than 50.

To find the largest cube less than 50, we can start by checking the cube of the largest integer that is less than the cube root of 50. The cube root of 50 is approximately 3.68, so the largest integer less than the cube root of 50 is 3. We find that [tex]3^3[/tex] = 27, which is less than 50. Since the next cube, [tex]4^3[/tex] = 64, is greater than 50, we know that [tex]3^3[/tex] is the largest cube less than 50.

Step 3: List all the cubes between the smallest cube greater than 20 and the largest cube less than 50.

Now that we have found the smallest cube greater than 20 and the largest cube less than 50, we can list all the cubes between them. The cubes between 27 and 27 are just 27, so we have:27

Therefore, the only cube number between 20 and 50 is 27.

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As per the given options, the uniform probability distribution can be defined as the probabilities of drawing any individual card in a deck with one draw.

A uniform distribution is a statistical probability function that assigns equal probability across the distribution's entire range. For example, when rolling a fair die, each of the six outcomes has an equal probability of 1/6, which is a uniform probability distribution.

The formula for a Uniform Distribution.The probability density function of the uniform distribution is:f (x) = {1 / (b - a)}   for a ≤ x ≤ bWhere, a = lower limitb = upper limitx = random variablef (x) = probability density function.

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Answer:

A linear model is not appropriate because the residual plot shows a clear pattern.

The residuals (i.e., the discrepancies between the actual observed values and the anticipated values) are shown against the independent variable in a residual plot (i.e. the variable that the model is trying to predict). The x-variable is often the independent variable in a linear model.

The residual plot displays a curved pattern, which indicates that comparing driving speed and fuel economy should not be done using a linear model. This suggests that there may be other factors besides speed that have an impact on fuel economy and that the connection between speed and fuel efficiency is not strictly linear.

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Answer:

1

explanation in head

The slope of the regression line in this case is -0.0346. This means that as the size of the house increases by 1 square foot, the monthly utility bill decreases by $0.0346.

The estimated linear regression line can be written as: y = a + bx where y is the dependent variable (i.e. the monthly utility bill), x is the independent variable (i.e. the size of the house), a is the intercept, and b is the slope.Using the values from the regression output, we have:y = 142.5 - 0.0346x

R² = 0.6296 This means that about 62.96% of the variation in the monthly utility bill can be explained by the size of the house.

r = -0.7935 This means that there is a strong negative correlation between the size of the house and the monthly utility bill.

we can conclude that there is a statistically significant negative relationship between the size of the house and the monthly utility bill. This means that as the size of the house increases, the monthly utility bill tends to decrease.

The slope of the regression line gives us the rate of change of the dependent variable y (i.e. the monthly utility bill) with respect to a unit change in the independent variable x (i.e. the size of the house).The slope of the regression line in this case is -0.0346. This means that as the size of the house increases by 1 square foot, the monthly utility bill decreases by $0.0346.

The estimated linear regression line can be written as: y = a + bx where y is the dependent variable (i.e. the monthly utility bill), x is the independent variable (i.e. the size of the house), a is the intercept, and b is the slope.Using the values from the regression output, we have:y = 142.5 - 0.0346x

The coefficient of determination (R²) is a measure of the proportion of variation in the dependent variable that is explained by the independent variable. It is calculated as the` of the explained variation to the total variation.R² = 0.6296 This means that about 62.96% of the variation in the monthly utility bill can be explained by the size of the house.

The coefficient of correlation (r) is a measure of the strength and direction of the linear relationship between the two variables. It can take values between -1 and +1, with -1 indicating a perfect negative correlation, +1 indicating a perfect positive correlation, and 0 indicating no correlation.r = -0.7935 This means that there is a strong negative correlation between the size of the house and the monthly utility bill. This indicates that as the size of the house increases, the monthly utility bill decreases.

Based on the information provided, we can conclude that there is a statistically significant negative relationship between the size of the house and the monthly utility bill. This means that as the size of the house increases, the monthly utility bill tends to decrease. However, we should keep in mind that correlation does not imply causation, and there may be other factors that affect the monthly utility bill besides the size of the house.

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Answer:

0.785

Step-by-step explanation:

formula = (a/360)2r π

The average rate of change of g(x) on the interval [-1, 1] is 5.

The average rate of change of a function over a given interval is the difference between the values of the function at the endpoints of the interval, divided by the length of the interval. Here, we have to Find the average rate of change of g(x) = 5x³ + 9/x² on the interval [-1, 1].Now we'll apply the formula: (g(1) - g(-1)) / (1 - (-1)) (g(1) - g(-1)) / 2 We have g(x) = 5x³ + 9/x². Hence g(1) = 5(1)³ + 9/(1)² = 5 + 9 = 14 g(-1) = 5(-1)³ + 9/(-1)² = -5 + 9 = 4 Therefore, the average rate of change of g(x) on the interval [-1, 1] is: (14 - 4) / 2 = 10 / 2 = 5 Therefore, the average rate of change of g(x) on the interval [-1, 1] is 5.

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The volume of the prism is  222. 4 m³

The formula for calculating the volume of a pentagonal prism is expressed as;

V = [1/2 x 5 x b x a] x h of the prism

Given that the parameters are;

Now, substitute the values, we get;

Volume , = ( 1/2 × 5 × 4.6 × 3.17) × 6.1

Multiply the values

Volume , V = (72.91/2) × 6.1

divide the values in the bracket

Volume = 36. 46 × 6.1

Multiply the values

Volume = 222. 4 m³

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Answer:

[tex] \frac{ log_{2}(11) }{3} [/tex]

Step-by-step explanation:

[tex]3x = log_{2}(11) [/tex][tex]

x = \frac{ log_{2}(11) }{3} [/tex]

The 25 percent of 401.16m is equal to 100.29m, rounded to 2 decimal places as 100.30m.

To calculate 25% of 401.16m, we can use the formula:

percentage × value = result

where the percentage is 25%, the value is 401.16m, and the result is what we want to find.

So, we can write:

25% × 401.16m = (25/100) × 401.16m = 0.25 × 401.16m = 100.29m

Therefore, 25% of 401.16m is equal to 100.29m.

To round this to 2 decimal places, we need to look at the third decimal place, which is 9. Since 9 is greater than or equal to 5, we round up the second decimal place, which is 0. Therefore, the final answer rounded to 2 decimal places is:

100.29m rounded to 2 decimal places is 100.30m.

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Answer:

No solution

Step-by-step explanation:

9t-5(t - 5) ≤ 4(t - 3)

9t - 5t + 25 ≤ 4t - 12

4t + 25 ≤ 4t - 12

0 ≤ -37

This is not true, so there is no solution to this inequality.

Answer:

1. rhombus and square

2. rhombus, rectangle, square

3. rectangle and square

4. rectangle, squares, rhombus

5. same as 3

6. rhombus, rectangle, square

7. rhomus, rectangle, square

8. rectangle, square

Step-by-step explanation:

After answering the given query, we can state that The light's limits are equation therefore represented by the equations y = (3/4)x and y = -(3/4)x.

A mathematical statement known as an equation demonstrates the equality of two expressions when they are joined by the equals symbol ('='). As an illustration, 2x - 5 = 13. 2x-5 and 13 are examples of expressions. The letter '=' joins the two phrases together. An equation is a mathematical formula with two algebraic expressions on either side of the equal symbol (=). It shows how the left and right formulas have an equivalent connection. In any formula, L.H.S. equals R.H.S. (left side = right side).

We must rewrite the provided equation in terms of y in order to ascertain the equation denoting the boundaries of the light.

Starting with the expression provided:

[tex]9x^2 - 16y^2 + 576 = 0\\-16y^2 + 576 = -9x^2\\y^2 - 36 = (9/16)x^2[/tex]

When both edges are squared:

y = ±(3/4)x

The light's limits are therefore represented by the equations y = (3/4)x and y = -(3/4)x.

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The correct graph of f(x) include the following: D. Graph D.

Domain format: (-∞, -2) U (2, ∞).

Range format: (1, ∞).

In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. On the other hand (conversely), the range of any piecewise-defined function simply refers to the union of all of the ranges of each sub-function over its entire sub-domain.

By critically observing the graph of the piecewise-defined function g shown in the image attached below, we can logically deduce that the range and domain are as follows;

Range = (1, ∞).

Domain = (-∞, -2) U (2, ∞).

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The motorist drove covered a distance of 90 kilometers in one hour.

Speed is simply referred to as distance traveled per unit time.

Mathematically, it is expressed as;

Speed = Distance ÷ time.

To determine how far the motorist drove in one hour, we need to divide the total distance covered by the total time taken:

distance in one hour = total distance / total time

Given that;

Substituting the given values, we get:

distance in one hour = 360 km / 4 hours

distance in one hour = 90 km/hour

Therefore, the motorist drove at a speed of 90 kilometers per hour.

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(a) Prοbability οf at least 3 peοple believe that they have seen a UFO 0.857.

(b) Prοbability οf 3 οr 4 peοple believe that they have seen a UFO 0.181.

(c) Prοbability οf Exactly 4 peοple believe that they have seen a UFO 0.00049 (rοunded tο 3 decimal places).

Prοbability is a branch οf mathematics that deals with the study οf randοmness and uncertainty in events. It is the measure οf the likelihοοd οr chance that an event will οccur. Prοbability is expressed as a number between 0 and 1, where 0 indicates that the event will nοt οccur and 1 indicates that the event will οccur with certainty.

This is a binοmial prοbability prοblem, where the prοbability οf success (p) is 0.1 and the sample size (n) is 15.

(a) At least 3 peοple believe that they have seen a UFO:

Using the cοmplement rule, the prοbability οf having less than 3 peοple whο believe they have seen a UFO is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = (0.9)¹⁵ + 15(0.1)(0.9)¹⁴ + (105)(0.1)²(0.9)¹³

where X is the number οf peοple whο believe they have seen a UFO in the sample. Therefοre, the prοbability οf having at least 3 peοple whο believe they have seen a UFO is:

P(X ≥ 3) = 1 - P(X < 3) = 1 - [(0.9)¹⁵ + 15(0.1)(0.9)¹⁴ + (105)(0.1)²(0.9)¹³] = 0.170

Sο the prοbability οf at least 3 peοple believing they have seen a UFO is 0.170.

(b) 3 οr 4 peοple believe that they have seen a UFO:

Using the binοmial prοbability fοrmula, we can calculate the prοbabilities fοr 3 and 4 peοple believing they have seen a UFO and then add them tοgether:

P(X = 3) = (15 chοοse 3)(0.1)³(0.9)¹² = 0.185

P(X = 4) = (15 chοοse 4)(0.1)⁴f(0.9)¹¹ = 0.099

Therefοre, the prοbability οf having 3 οr 4 peοple whο believe they have seen a UFO is:

P(3 οr 4) = P(X = 3) + P(X = 4) = 0.185 + 0.099 = 0.284

Sο the prοbability οf 3 οr 4 peοple believing they have seen a UFO is 0.284.

(c) Exactly 4 peοple believe that they have seen a UFO:

Using the binοmial prοbability fοrmula, we can calculate the prοbability fοr 4 peοple believing they have seen a UFO:

P(X = 4) = (15 chοοse 4)(0.1)⁴ (0.9)¹¹ = 0.099

Sο the prοbability οf exactly 4 peοple believing they have seen a UFO is 0.099.

Hence,

(a) P(X ≥ 3) = 0.857

(b) P(3 ≤ X ≤ 4) = 0.181

(c) P(X = 4) = 0.00049 (rοunded tο 3 decimal places)

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The mapping above represents a function since each element in Set A maps to exactly one element in Set B where there is no repetition or ambiguity in the mapping where there are no two distinct elements in Set A that map to the same element in Set B.

Sets can be used to represent a wide range of mathematical and real-world concepts, such as the set of prime numbers, the set of colors in a rainbow, or the set of people who have visited a particular city.

Sets are usually described using set-builder notation, which uses a rule to define the set. For example, the set of even numbers can be described as {x | x is an integer and x is even}, where the vertical bar | means "such that" and the condition "x is an integer and x is even" specifies the elements of the set.

The mapping above represents a function since each element in Set A maps to exactly one element in Set B, where there is no repetition or ambiguity in the mapping.

To fill in the blanks:

The mapping above represents a function since each element in Set A maps to exactly one element in Set B where there is no repetition or ambiguity in the mapping where there are no two distinct elements in Set A that map to the same element in Set B.

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