A stone is thrown into a pond, creating a circular ripple that spreads over the pond in such a way that the radius is increasing at a rate of 4 flsec. Complete parts a through c. a) Find a function for the radius in terms of t. r(t)= (Use integers or decimals for any numbers in the expression.) b) Find a function A(r) for the area of the ripple in terms of the radius r. A(r)= (Type an exact answer, using π as needed.) c) Find (A∘r)(t). (A∘t)(t)= Complete parts a through c. Choose the correct answer below. A. The function gives the area of the ripple in terms of t. B. The function gives the square of the area of the ripple in terms of L. C. The function has no specific meaning. D. The function gives the perimeter of the ripple in terms of t

Answer: The system of equations is:

3x + y = 18

3x + y = 16

To determine how many solutions this system has, we can subtract the second equation from the first:

(3x + y) - (3x + y) = 18 - 16

0 = 2

This is a contradiction, since 0 can never be equal to 2. Therefore, there are no solutions to this system of equations. Geometrically, these two equations represent two parallel lines in a coordinate plane that never intersect, so there is no point that satisfies both equations at the same time.

Step-by-step explanation:

The polynomial function P(x) with a quadratic function zero of 3-4i and an additional zero is P(x) = (x2 - 6x + 25)(x - additional zero).

A polynomial function, P(x), is a function that can be written in the form P(x) = anxn + an-1xn-1 + ... + a1x + a0, where n is a non-negative integer and an, an-1, ..., a1, a0 are real numbers. A quadratic function is a polynomial function of degree 2, which means it can be written in the form P(x) = ax2 + bx + c.

If a polynomial function has a zero of 3-4i, then it must also have a zero of 3+4i, since complex zeros always come in conjugate pairs. This means that the polynomial function must have factors of (x - (3-4i)) and (x - (3+4i)). Multiplying these two factors together gives us (x - 3 + 4i)(x - 3 - 4i) = x2 - 6x + 25.

If the polynomial function also has an additional zero, then it must have a factor of (x - additional zero). Multiplying this factor with the previous one gives us P(x) = (x2 - 6x + 25)(x - additional zero).

So, the polynomial function P(x) with a quadratic function zero of 3-4i and an additional zero is P(x) = (x2 - 6x + 25)(x - additional zero).

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Step-by-step explanation:

The lines IJ and KL are parallel , so the slopes of the lines are equal and the value of b is -4.75

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be I ( -4 , 17 )

Let the second point be J ( 1 , -3 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = ( 17 - ( -3 ) ) / ( -4 - 1 )

Slope m₁ = -20/5

Slope m₁ = -4

Now , the lines IJ and KL are parallel , so the slopes are equal

Let the third point be K ( b , 3 )

Let the fourth point be L ( -5 , 4 )

Slope m₂ = ( 4 - 3 ) / ( -5 - b )

Slope m ₂ = 1/ ( -5 - b )

where m₁ = m₂

On simplifying , we get

1/ ( -5 - b ) = -4

Multiply by ( -5 - b ) on both sides , we get

1 = 20 + 4b

Subtracting 20 on both sides , we get

4b = -19

Divide by 4 on both sides , we get

b = -4.75

Therefore , the value of b is -4.75

Hence , the slope of the lines is m = -4

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The expressions are equivalent to g + h + (j + k) is g+(h+j)+k and (g+h)+j+k.

What is an associative property?

As some binary operations have the associative property, moving parenthesis around in an expression won't affect the outcome. Associativity is a legitimate rule of replacement for expressions in logical proofs in propositional logic.

Here, we have

Given:  g + h + (j + k)

We have to find the expressions that are equivalent to the given expression.

By applying the associative property of equality: (a + b) + c = a + (b + c)

we can see that the parenthesis does not mean anything when we are only doing addition.

Hence, the expressions are equivalent to g + h + (j + k) is g+(h+j)+k and (g+h)+j+k.

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Applying the angle of intersecting chords theorem, the measure of arc UT is: 180°.

The angle of intersecting chords theorem states that when two chords intersect within a circle, the angle they create measures half the sum of the intercepted arc and its corresponding vertical arc.

Based on the above theorem, we can state that:

m<UST = 1/2(measure of arc AV + measure of arc UT)

Substitute

120 = 1/2(60 + measure of arc UT)

240 = 60 + measure of arc UT

240 - 60 = measure of arc UT

Measure of arc UT = 180°

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To estimate the average height of black spruce trees in a 1,000 ha plot with 99% confidence that the estimate is within 0.5 m, you need a sample size of at least 19. This is based on the standard deviation of tree heights in a nearby location of 1.10 m as determined in a study conducted last year.

To estimate the average height of black spruce trees in a 1,000 ha plot with 99% confidence that the estimate is within 0.5 m, we can use the formula for sample size calculation:

n = (z² × σ²) / E²

Where:

n = sample size

z = z-score for the desired confidence level (99% confidence level corresponds to a z-score of 2.576)

σ = standard deviation (1.10 m)

E = margin of error (0.5 m)

Plugging in the values into the formula, we get:

n = (2.576² × 1.10²) / 0.5²n = 18.15.

Therefore, the sample size must be at least 19 black spruce trees to have 99% confidence that the estimate is within 0.5 m.

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The average rate of change for the week is calculated by subtracting the first day's attendance (1,534) from the last day's attendance (2,394) and then dividing by the number of days (7).

Number is an abstract concept used to describe a quantity or amount of something. It is used to measure, count, and label objects, people, places, and other things. Numbers can be used to describe size, shape, location, and many other concepts. They are also used to represent data, money, and other mathematical operations. Numbers are the cornerstone of mathematics, and they are used in a variety of ways in everyday life.

This yields an average rate of change of +77.71 people per day.

This average rate of change is only a good measure for how the number of people changed throughout the week if the number of people changed in a consistent manner. If the attendance was relatively stable from day to day, then the average rate of change would accurately reflect the number of people who attended. However, if the attendance changed drastically from day to day, the average rate of change would not accurately reflect the attendance for the entire week.


Complete questions as follows-
The table shows the number of people, n, who went to see musical , on the duh day of April. What is the average rate of 'change for the number of people from day to day 7? 1,534 2,324 2,418 b. Is the average rate of change a good measure for how the number of people changed throughout the week? Explain your reasoning; ''. ` 2,281 2,350 2,394 1,720 weight (02) 369 Algebra 1".

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A large p-value indicates that the data is likely to have come from the theoretical distribution.

A. SIMIO is classified as a discrete event simulation language because it uses events to model the behavior of the system being simulated. The SIMIO software is based on the idea of constructing models of systems to support managerial decision-making processes.B. A static simulation is a simulation where nothing changes over time, whereas a dynamic simulation is a simulation where changes occur over time. The outcome of a static simulation cannot change once it has been run. On the other hand, the outcome of a dynamic simulation can change depending on the inputs and parameters used.C. A deterministic simulation is a simulation where all parameters and inputs are known and fixed, whereas a stochastic simulation is a simulation where one or more parameters or inputs are randomly generated. A deterministic simulation will produce the same output every time it is run with the same inputs and parameters, whereas a stochastic simulation may produce different outputs each time it is run with the same inputs and parameters.D. Discrete event simulation of a continuous system is a process where a model of the system is created, which enables the simulation of the system behavior over time using a set of discrete events.E. A variable is a quantity that can change and is usually represented by a symbol, whereas an attribute is a quality that describes a variable. An example of a variable is the temperature, and an example of an attribute is the color of a car.F. An activity is an event that represents an action or process, whereas a delay is an event that represents a waiting time or a period of inactivity. An example of an activity is a customer purchasing a product, and an example of a delay is a customer waiting in line.G. An observed statistic is a statistic that is measured at a particular time and is specific to that time, whereas a statistic that is time persistent is a statistic that is measured over a period of time and is consistent over that period of time.H. A goodness-of-fit test is a statistical test that compares the distribution of a sample of data to a theoretical distribution.I. To use the Kolmogorov-Smirnoff Test, the data must be continuous, and to use the Chi-Squared Test, the data must be categorical.J. In the context of goodness-of-fit tests, a p-value represents the probability of obtaining a sample of data with the same distribution as the theoretical distribution being tested. A small p-value indicates that the data is unlikely to have come from the theoretical distribution, while a large p-value indicates that the data is likely to have come from the theoretical distribution.

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Answer: To calculate the incidence of cervical cancer among women in the United States in 2019, we need to divide the number of new cases (346) by the total population at risk (i.e., the number of women without cervical cancer) and then multiply by 100,000 to express the result per 100,000 women.

Number of women without cervical cancer = Total number of women - Number of women with cervical cancer

Number of women without cervical cancer = 166,238,619 - 295,382

Number of women without cervical cancer = 165,943,237

Incidence of Cervical Cancer = (New cases / Number of women without cervical cancer) x 100,000

Incidence of Cervical Cancer = (346 / 165,943,237) x 100,000

Incidence of Cervical Cancer = 0.21 per 100,000 women

Therefore, the incidence of cervical cancer among women in the United States in 2019 was 0.21 per 100,000 women.

Step-by-step explanation:

The book sold 38,100 copies in its first month of release. then approximately 537,324 copies have been sold to date.

What is the percentage?

A percentage is a ratio, fraction, or portion of a whole which is represented as 100.

Let "x" be the total number of copies sold to date.

According to the problem, 38,100 is 7.1% of x, which can be written as:

38,100 = 0.071x

To find x, we can solve for it by dividing both sides of the equation by 0.071:

x = 38,100 / 0.071

x = 537,323.94 (rounded to the nearest whole number)

Therefore, approximately 537,324 copies have been sold to date.

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Organizing the survey results in a two-way table with the marginal frequencies is as follows:

                                                              Number of        Marginal

                                                           Respondents   Frequencies

Have Played a Musical Instrument            118                56.5%

Have Participated in a Sport                      57                 27.3%

Have not Played or Participated                34                 16.3%

Total                                                          209

A two-way frequency table shows the relationships between two categorical data.

A two-way frequency table can be used to show the marginal frequencies of responses for a given condition or the ratio of the joint frequencies to the corresponding marginal frequency.

The total number of students surveyed = 397

The total number of respondents = 209 (118 + 57 + 34)

The number of students who have played a musical instrument = 118

The number of students who have participated in a sport = 57

The number of students who have not played a musical instrument or participated in a sport = 34

                                                              Number of        Marginal

                                                           Respondents   Frequencies

Have Played a Musical Instrument            118                56.5% (118/209)

Have Participated in a Sport                      57                 27.3% (57/209)

Have not Played or Participated                34                 16.3% (34/209)

Total                                                          209

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The speaker has a volume of about 34.67 cubic inches.

V = (1/3) * 13 * 8

= 104/3

≈ 34.67 cubic inches

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc.

Volume is sometimes referred to as capacity. The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Many forms have various volumes. The several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.

From the question:

The following formula can be used to determine a pyramid's volume:

V = base area * height * (1/3)

Since the speaker in this instance is shaped like a triangular pyramid, we can use the base area of 13 square inches and the height of 8 inches to calculate the volume.

When the values are added to the formula, we obtain:

V = (1/3) * 13 * 8

= 104/3

≈ 34.67 cubic inches

Hence, the speaker's volume is roughly 34.67 cubic inches.

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The solution to the given proportion is 7 / 8. The solution has been obtained by using the cross multiplication method.

The cross multiplication approach involves multiplying the denominator of the first phrase by the numerator of the second fraction, and vice versa.

We are given a proportion as

2 / (3b - 3) = 4 / (1 - 2b)

Now, by using cross multiplication method, we get

⇒2 (1 - 2b) = 4 (3b - 3)

⇒2 - 4b = 12b - 12

⇒-16b = -14

⇒16b = 14

⇒b = 14 / 16

⇒b = 7 / 8

Hence, the solution to the given proportion is 7 / 8.

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The solution to 4 is a>-162. This is because the inequality can be rewritten as -162 > -21, meaning that any number greater than -162 will satisfy the inequality.

Inequality is the unequal distribution of opportunities, resources, or rights among people or groups. It can be found in wealth, income, health, education, access to services and resources, and legal rights. Inequality is a social phenomenon that affects people differently depending on race, gender, age, or background. Inequality can be a result of unequal access to resources, differences in power dynamics, or the unequal distribution of resources among people or groups. It can lead to disparities in health, education, and economic outcomes for those who experience it. Inequality can be addressed through policies that promote equity and inclusion, such as targeted education initiatives and access to employment opportunities.

The reason this is happening is because when solving inequalities, we must isolate the variable on one side of the inequality sign. In this case, we can do this by adding 162 to both sides of the inequality. This will move the -21 to the other side and the result is a>-162.

In order to ensure that the solution is correct, it is important to check the answer by substituting a value larger than -162 into the inequality. If the value satisfies the inequality, then the solution is correct.

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The sοlutiοn tο 4 is a>-162. This is because the inequality can be rewritten as -162 > -21, meaning that any number greater than -162 will satisfy the inequality.

Inequality is the unequal distributiοn οf οppοrtunities, resοurces, οr rights amοng peοple οr grοups. It can be fοund in wealth, incοme, health, educatiοn, access tο services and resοurces, and legal rights. Inequality is a sοcial phenοmenοn that affects peοple differently depending οn race, gender, age, οr backgrοund. Inequality can be a result οf unequal access tο resοurces, differences in pοwer dynamics, οr the unequal distributiοn οf resοurces amοng peοple οr grοups. It can lead tο disparities in health, educatiοn, and ecοnοmic οutcοmes fοr thοse whο experience it. Inequality can be addressed thrοugh pοlicies that prοmοte equity and inclusiοn, such as targeted educatiοn initiatives and access tο emplοyment οppοrtunities.

The reasοn this is happening is because when sοlving inequalities, we must isοlate the variable οn οne side οf the inequality sign. In this case, we can dο this by adding 162 tο bοth sides οf the inequality. This will mοve the -21 tο the οther side and the result is a>-162.

In οrder tο ensure that the sοlutiοn is cοrrect, it is impοrtant tο check the answer by substituting a value larger than -162 intο the inequality. If the value satisfies the inequality, then the sοlutiοn is cοrrect.

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Complete question:

What is the solution to 3/4a>-16?

a>-21 1/3

a<-21 1/3

a>21 1/3

a<21 1/3

The leading coefficient of the given polynomial 4x^(6)+3x^(5)+x^(4)+5 is 4.

A polynomial is an expression of the form anxn + an-1xn-1 + ... + a1x + a0, where an, an-1, ..., a1, and a0 are constants and x is a variable.

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In the given polynomial, the term with the highest degree is 4x^(6), so the leading coefficient is 4.

Therefore, the leading coefficient of the given polynomial 4x^(6)+3x^(5)+x^(4)+5 is 4.

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We know here that the effect that the circled point will have on the y-intercept is B and that the y-intercept will decrease because the point pulls the least-squares regression line toward it.

In statistics, we know that an intercept is the value of the dependent variable when the independent variable or variables is equal to zero and that it is often represented by the symbol "b" in a linear equation.

We can take an example here:

A simple linear equation has the form y = mx + b, where "y" is the dependent variable, "x" is the independent variable, "m" is the slope of the line, and "b" is the y-intercept. The y-intercept is the point where the line crosses the y-axis so, we can see here that the effect that the circled point will have on the y-intercept is B. The y-intercept will decrease because the point pulls the least-squares regression line toward it.

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The average speed of the boat relative to the water is approximately 17.08 mph.

The average speed of the boat relative to the water can be found by using the formula for distance, speed, and time:

distance = speed × time

We can use this formula to set up two equations, one for the downstream trip and one for the upstream trip:

38 = (s + 6) × t₁

38 = (s - 6) × t₂

We can then use the given information about the total time of the trip to find the values of t₁ and t₂:

4.75 = t₁ + t₂

We can rearrange the first two equations to solve for t₁ and t₂ in terms of s:

t1 = 38/(s + 6)

t2 = 38/(s - 6)

Substituting these values into the third equation and simplifying gives us:

4.75 = 38/(s + 6) + 38/(s - 6)

4.75s² - 57s - 114 = 0

Using the quadratic formula, we can solve for s:

s = (57 ± √(57₂ - 4(4.75)(-114)))/(2(4.75))

s ≈ 17.08 or s ≈ -3.01

Since the speed of the boat cannot be negative, t

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Blake needs to now at least 17 lawns in order to earn at least $200 to buy a new stereo system.

To solve this problem, we can set up an inequality that represents the situation. Let's let x be the number of lawns that Blake needs to mow. The inequality will be:
12x >= 200

This inequality states that the amount of money Blake earns from mowing lawns (12x) must be greater than or equal to the amount of money he wants to earn ($200).

To solve for x, we can divide both sides of the inequality by 12:
x >= 200/12

Simplifying the right side of the inequality gives us:
x >= 16.67

Since Blake cannot mow a fraction of a lawn, we need to round up to the next whole number. This means that Blake needs to now at least 17 lawns in order to earn at least $200 to buy a new stereo system.

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Answer:

Albert receives $10,000, Brian receives $20,000, and Charles receives $30,000.

Step-by-step explanation:

1 + 2 + 3 = 6

Next, we can find out what fraction of the estate each person is entitled to:

Albert: 1/6 of the estate

Brian: 2/6 (or 1/3) of the estate

Charles: 3/6 (or 1/2) of the estate

Now, we can calculate the amount each person receives by multiplying their share by the total value of the estate:

Albert: (1/6) x $60,000 = $10,000

Brian: (1/3) x $60,000 = $20,000

Charles: (1/2) x $60,000 = $30,000

Answer:

a = 1

Step-by-step explanation:

6a + 5a + 1 = 12

Subtract one to both side leaving a by itself.

6a + 5a = 12 - 1

Now simply by add or subtracting, multiply or dividing.

11a = 11

Divide 11 to both side leaving a = ?

a = 1

Answer:

a= 1

Step-by-step explanation:

6a + 5a + 1 = 12

(-1) + 6a + 5a +1 = 12 -1

6a + 5a = 11

11a = 11

11a/11 = 11/11

a= 1

Rounding to the nearest whole number, we can estimate that about 566.49 visitors would be expected to buy no costume when there are 1200 visitors to the website.

The first 10 integers are known as the fundamental numbers in mathematics. These fundamental integers are given from 0 to 9. Basic integers in the 0 to 9 range include 0 through 1, 2, 3, 4, 5, 6, 7 and 8.

According to the information given, 93 visitors purchased no costume, 94 visitors purchased one costume, and 10 visitors purchased more than one costume. Let's calculate the total number of costumes purchased:

Total number of costumes purchased = 1(94) + 2(10) = 114

Next, let's calculate the total number of visitors to the website:

Total number of visitors = 93 + 94 + 10 = 197

To estimate the number of visitors who are likely to purchase no costume when there are 1200 visitors to the website, we can use a proportion:

93/197 = x/1200

x = (93/197) * 1200 ≈ 566.49

Rounding to the nearest whole number, we can estimate that about 566.49 visitors would be expected to buy no costume when there are 1200 visitors to the website.

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Answer:

x= 3 or x = -3

Step-by-step explanation:

We can see here that the two values that x can have if 5x² + 41 = 86 is -3 and +3.

To find the values of x that satisfy the equation 5x² + 41 = 86, we can start by isolating the term with the variable on one side of the equation. Here's the step-by-step solution:

Subtract 41 from both sides of the equation:

5x² + 41 - 41 = 86 - 41

5x² = 45

Divide both sides of the equation by 5:

(5x²) / 5 = 45 / 5

x² = 9

Take the square root of both sides of the equation:

√(x²) = √9

x = ±3

Therefore, the equation 5x² + 41 = 86 has two solutions: x = 3 and x = -3.

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The distance between Point A and Point B is 840 meters.

Let's start by using the formula:

distance = speed x time

Since Coco swam at a constant speed of 1.2 m/s, we can find his distance using:

distance(Coco) = speed(Coco) x time

where time is the same for both Coco and Azlinda. Let's call this common time "t".

distance(Coco) =[tex]1.2 m/s \times t[/tex]

Now, let's consider Azlinda's situation. After 5 minutes (or 5/60 = 1/12 hours), she had swum a distance of 420 m and was 37 m away from Coco. Let's call the distance between Point A and Point B "d".

Since Azlinda was swimming towards Point A, she must have covered a distance of (d - 37) m by the time she had swum 420 m. We can use the formula above to find her speed:

speed(Azlinda) = distance(Azlinda) / time

speed(Azlinda) = (d - 37) m / (1/12) h

speed(Azlinda) = 12(d - 37) m/h

Now, we know that Azlinda and Coco were swimming towards each other for a total of 5 minutes (or 1/12 hours), so their total distance apart at that time was:

distance apart = distance(Coco) + distance(Azlinda)

distance apart = [tex]1.2 m/s \times t + 12(d - 37) m/h \times (1/12) h[/tex]

distance apart =[tex]1.2t + d - 37[/tex]

We also know that when they were 37 m apart, Azlinda had swum a distance of 420 m, so we can write:

420 = d - 37 - distance(Coco)

Substituting the expression for distance(Coco) from above, we get:

420 = d - 37 - 1.2t

Now we have two equations with two unknowns (d and t). We can substitute into the other equation and solve for one variable in terms of the other. For example, we can solve the second equation for t:

[tex]1.2t = d - 37 - 420\\1.2t = d - 457\\t = (d - 457) / 1.2[/tex]

When we enter this into the initial equation, we obtain:

distance apart = [tex]1.2t + d - 37[/tex]

distance apart = [tex]1.2((d - 457) / 1.2) + d - 37[/tex]

distance apart = [tex]d - 380.6[/tex]

Now we can substitute this expression for distance apart into the second equation:

[tex]420 = d - 37 - 1.2t\\420 = d - 37 - 1.2(d - 457) / 1.2\\420 = d - 37 - (d - 457)\\420 = -d + 420\\d = 840[/tex]

Therefore, the distance between Point A and Point B is 840 meters.

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The rectangle has a length of y + 2xy + x meters and a width of (y + 7x) / (2y + x) meters.

What is a formula of area of rectangle?

Formula for rectangle's area

When calculating a rectangle's area, we multiply the length by the width of the rectangle.

The area of a rectangle is given by the formula:

A = L × W

where A is the area, L is the length, and W is the width.

In this case, we are given that the area is:

[tex]A = y^2 + 8xy + 7x^2[/tex]

and the length is:

L = y + xy + xy + x = y + 2xy + x

To find the width, we can rearrange the formula for the area:

W = A/L

Substituting the given values, we get:

[tex]W = (y^2 + 8xy + 7x^2)/(y + 2xy + x)[/tex]

Now, we can simplify this expression by factoring the numerator:

W = [(y + 7x)(y + x)] / [(y + x)(2y + x)]

Canceling out the common factor of (y + x), we get:

W = (y + 7x) / (2y + x)

Therefore, the width of the rectangle is:

W = (y + 7x) / (2y + x)

So the rectangle has a length of y + 2xy + x meters and a width of (y + 7x) / (2y + x) meters.

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The correct answer is c. 7.81.

To find the variance for the distribution of ungrouped data, we need to use the formula:

Variance = (Σ(x^2)f - (Σxf)^2 / n) / n

Where x is the data value, f is the frequency of the data value, and n is the total number of data values.

For the first question:

1. The variance for the following distribution of ungrouped data to its right is:

Dato (x) Frecuencia (f) xf x^2f
3.2 3 9.6 30.72
1.3 4 5.2 6.76
2.4 2 4.8 11.52
Total 9 19.6 49

Variance = (49 - (19.6)^2 / 9) / 9
Variance = (49 - 42.46) / 9
Variance = 0.73

Therefore, the correct answer is a. 0.79.

For the second question:

2. The variance for the following distribution of ungrouped data to its right is:

Edad (x) Frecuencia (f) xf x^2f
6 7 42 252
7 12 84 588
8 10 80 640
9 8 72 648
10 5 50 500
Total 42 328 2628

Variance = (2628 - (328)^2 / 42) / 42
Variance = (2628 - 2570.29) / 42
Variance = 1.38

Therefore, the correct answer is c. 7.81.

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Jenny buys 15 pieces of bags every month, which means she buys 180 pieces of bags in a year

This question can be solved by unitary method

To find out how many pieces of bags Jenny buys in a year, we can use the following formula:

Total pieces of bags in a year = Number of pieces of bags bought every month × Number of months in a year

We are given that Jenny buys 15 pieces of bags every month, and there are 12 months in a year. So, we can plug in these values into the formula:

Total pieces of bags in a year = 15 × 12

Total pieces of bags in a year = 180

Therefore, Jenny buys 180 pieces of bags in a year.

Answer: 180.

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The exact form of the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24 are x=-4, x=-3/2, x=2, and x=1.

To find all the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24, we need to find the values of x that make c(x)=0. One way to do this is by using the Rational Root Theorem, which states that if a polynomial has rational zeros, then they must be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The factors of the constant term, 24, are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24. The factors of the leading coefficient, 3, are ±1 and ±3. Therefore, the possible rational zeros are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24.

Using synthetic division, we can test these possible zeros to see if they are actually zeros of the polynomial. After testing, we find that the zeros are -4, -3/2, 2, and 1.

So, the exact form of the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24 are x=-4, x=-3/2, x=2, and x=1.

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The expression when simplified is (d)

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

Using the above as a guide, we have the following:

The given expression is

3 * Black triangle + 2 * White triangle + 2 * Black square + 1 * White square

This gives

-3x + 2x - 2 + 1

Evaluate the like terms

-x - 1

This means

1 Black triangle and 1 Black square

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Therefore, the probability of this event is 3/6 or 1/2.

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. It is used to quantify the uncertainty or risk associated with a particular event or situation.

given by the question.

Event: Rolling a standard die and landing on either 1, 2, or 3.

A standard die has six faces, numbered from 1 to 6. Rolling the die is a random experiment that can result in any of the six possible outcomes with equal probability. The event described in the statement only includes three of the six possible outcomes, namely 1, 2, and 3

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