Reduce each fraction to lowest terms by first factoring the numerator and denominator into product of prime factors and then dividing out any factors they have in common.

Answer:

270725 different ways

Step-by-step explanation:

The problem tells us that the order of the letters does not matter. Therefore, in the combination the order is NOT important and is signed as follows:

C (n, r) = n! / r! (n - r)!

We have to n = 52 and r = 4

C (52, 4) = 52! / 4! * (52-4)! = 52! / (4! * 48!) = 270725

Which means that there are 270725 different ways in total to make that raffle

Answer:

1 : 3

Step-by-step explanation:

The ratio of strawberries : grapes = 6 : 18 ( divide both values by 6 )

ratio = 1 : 3 ← in simplest form

Answer:

1 : 3

Step-by-step explanation:

The ratio of strawberries : grapes = 6 : 18 ( divide both values by 6 )

ratio = 1 : 3 ← in simplest form

Answer:

what is the actual problem?

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I think you missed attaching the picture, so hope my photo fits your questions well!

We must consider the median of the data sets, it may  represent the center of the dispersion measure. Then we see answer C is the most suitable one, this is because it's median is approximately to $60.

Answer:

[tex]D(t)=100(0.4)^t[/tex]

Step-by-step explanation:

The temp is 100 at time t = 0

After 1 sec, the temp difference would be:

[tex]100-(\frac{100-60}{100})[/tex]

After 2 sec, the temp difference would be:

[tex]100-(\frac{100-60}{100})^2[/tex]

Similarly for 3 seconds, 4 seconds etc.

We notice that the parenthesis part is 40% of it, so we can also write:

100(40%)^t,

where

t is the time

40% can be written as 40/100  = 0.4

SO, the function is:

[tex]d(t)=100(0.4)^t[/tex]

Answer:

[tex]D(t)=100*0.4^t[/tex]

Step-by-step explanation:

Initially, the difference between the rod's and the water's temperatures is 100°

i.e D(t)=100 When t=0

After 1 seconds, the temp drops by 60%.

Therefore, the new value of D will be the old value multiplied by (100-60)%.

D(1)=100 X (100%-60%) = 100*0.4

After 2 seconds, the temp difference would be:

D(2)=100*0.4*0.4= [tex]100*0.4^2[/tex]

We notice that for any t, the percentage at which the difference is reduced is raised to the power of t.

Therefore, temperature difference in degrees Celsius, D(t), t seconds after the rod was plunged into the water is given as:

[tex]D(t)=100*0.4^t[/tex]

Answer:

Veggie

Step-by-step explanation:

I corrected your question for a better situation.

At a party there were four large submarine sandwiches all the same size . During the party 2/3 of the chicken sandwich three over 4 of the tuna sandwich 7/12 of the roast beef sandwich and 5/6 of the veggie sandwich were eating which sandwich had the least amount left

Here is my answer:

So the sandwich had the least amount is Veggie

Answer:

The amount Declan saves from the discount is 15% of $35,000

which is $5250

This Amount $5250 is the amount Declan invests in the bank

This is the Amount the bank pays at the end of the time T of saving

Step-by-step explanation:

The simple Interest is calculated by

I = (P x R x T) / 100

where I is the Interest

R  is the rate in percentage

T  is the time the money will be saved

Another Important quantity is the Amount A

A = I + P

Answer:

False

Step-by-step explanation:

We are told that there is a 33% probability that physics students belong to ethnic minorities, therefore if the sample is 10 people, the amount would be given as follows:

10 * 33% = 3.3 people would be from ethnic minorities. What means of those 10 no more than 4 (to round the number) people belong to an ethnic minority.

Therefore, this statement is false, because it does not represent exactly the probability established in the university.

It is possible to clarify that what affirmation is true part because it fulfills what it says, because the probability says that 4 or less, and the affirmation says that 6 or less, however, the affirmation mentions that it corresponds to the probability of 33% and that if it is false, to correspond it should be between 51% and 60%.

Answer:

The answer is: 3

Step-by-step explanation:

1. At the begining of the program we start by declairing the variables:

 double x=1, double y=1 and int i=0.

2. The structure do...while is used to defined the loop. x<2.5 is the finalization condition of the loop. i is the counter of the loop.

y=x/2 is the first calculation

x=x+y is the second one. Here is where the values of the variable x changes.

a) for the first iteration, the values of y and x are shown below:

[tex]\\\\x=1\\y=1\\y=1/2=0.5\\x=1+0.5=1.5\\i=1[/tex]

The variable x is minor to 2.5 so the loop will continue computing.

b)   the second iteration, the values of y and x are shown below::

 [tex]y=0.5\\x=1.5\\y=\frac{1.5}{2}=0.75\\ x=1.5+0.75=2.25\\i=2[/tex]

The variable x is still minor to 2.5 so the loop will continue computing.

c) third iteration:

[tex]y=0.75\\x=2.25\\y=\frac{2.25}{2} =1.1125\\x=2.25+1.125=3.375\\i=3[/tex]

The condition x<2.5 is not true so the loop ends.

3. System.out.print(i + " "); displays the value of the variable i wich value is 3.

Therefore the number 3 is display.

Answer:

Therefore the required polynomial is

M(x)=0.83(x³+4x²+16x+64)

Step-by-step explanation:

Given that M is a polynomial of degree 3.

So, it has three zeros.

Let the polynomial be

M(x) =a(x-p)(x-q)(x-r)

The two zeros of the polynomial are -4 and 4i.

Since 4i is a complex number. Then the conjugate of 4i is also a zero of the polynomial i.e -4i.

Then,

M(x)= a{x-(-4)}(x-4i){x-(-4i)}

      =a(x+4)(x-4i)(x+4i)

      =a(x+4){x²-(4i)²}      [ applying the formula (a+b)(a-b)=a²-b²]

      =a(x+4)(x²-16i²)

      =a(x+4)(x²+16)      [∵i² = -1]

      =a(x³+4x²+16x+64)

Again given that M(0)= 53.12 . Putting x=0 in the polynomial

53.12 =a(0+4.0+16.0+64)

[tex]\Rightarrow a = \frac{53.12}{64}[/tex]

      =0.83

Therefore the required polynomial is

M(x)=0.83(x³+4x²+16x+64)

Answer:

27/2

Step-by-step explanation:

Answer:

[tex]x = 2\,\frac{4}{5}\,ft[/tex]

Step-by-step explanation:

The equation of elevation for the dolphin is:

[tex]-\frac{67}{4} + 5\cdot x = -\frac{21}{4}[/tex]

[tex]5\cdot x = \frac{56}{4}[/tex]

[tex]x = 2\,\frac{4}{5}\,ft[/tex]

Answer:

5x -16 3/4 = -5 1/4

Note: This is based off of Study Island's multiple choice answers

Step-by-step explanation:

We're trying to figure out how far the dolphin travels with each kick. The dolphin starts at an elevation of -16 3/4 feet and ends up at an elevation of -5 1/4 feet. In other words, what can we add to -16 3/4 to get -5 1/4?

The elevation is our variable (x). The dolphin kicks 5 times to get from point a to point b. So we should add 5x to -16 3/4 to get -5 1/4. This equation will solve for the length in feet traveled per kick. Our equation is now:

5x + -16 3/4 = -5 1/4

Adding a negative is the same thing as subtracting a positive, so our final equation is:

5x - 16 3/4 = -5 1/4

If we want to solve this:

5x - 16.75 = -5.25

5x = 11.5

x = 2.3 feet per kick

Answer:

Step-by-step explanation:

The standard form of an exponential function is

[tex]y=a(b)^x[/tex] , where a is the initial value and b is the growth factor.

You will always find your initial value at the y value where x = 0.  From your table where x = 0 and y = 1/2:

[tex]\frac{1}{2}=a(b)^0[/tex]

Any number or variable raised to the power of 0 = 1, therefore

[tex]\frac{1}{2}=a(1)[/tex] which gives us an initial value, a, of 1/2.

Answer:

7) 6 is not a perfect square, sqrt(6) can't be written in a fraction form

8) 2 is not a perfect cube, cuberoot of 2 can't be written in a fraction form

9) 3/2 is already a fraction, so clearly rational

Answer:

W = 15 ft. and L = 30 ft.

Step-by-step explanation:

Perimeter = 90 ft.

Twice as long as it is wide: L=2W

P = 2(L + W) = 2(2W + W) = 6W

90 = 6W

W = 15 ft. and L = 30 ft.

Answer:

The dimensions are: Width= 15ft

Length=30ft

Step-by-step explanation:

Perimeter of fence=90feet

He wants to make a rectangle with dimensions length and with.

The rectangle length is twice as long as the width= L= 2W

Perimeter of a rectangle = 2(L + W)

90= 2(2W +W)

90= 6W

90/6=W=15ft

L=2W= 2× 15=30ft

Answer:

y will increase if x is increased,

y will decrease if x is decreased.

Step-by-step explanation:

1/F=1/X+ 1/Y

1/F-1/X=1/Y

X-F/FX=1/Y

FX/X-F=Y

Rearranging, Y=FX/X-F

So this is the function in terms of X, and F is just a constant

Therefore, the function becomes Y=65X/X-65

Explanation:

y = focusing distance

x = distance from lens

Focusing distance y will increase if the object x moves far away from the lens i.e. x is increased,

Similarly, focusing distance y will decrease if the object x moves closer and closer to the lens i.e. x is decreased.

An asymptote is a function that mimics a curve f(x) as x approaches infinity.

A vertical asymptote, however, cannot be crossed in a function.  Remember that a function cannot have multiple y values for a given x value, hence the vertical line test for a function.  If a function crossed a vertical asymptote and then went back to it, then it would have to go back over itself as it becomes arbitrarily close to the asymptote. Therefore, it is not possible to cross a vertical asymptote.

The focal point, F, the object distance from the lens, X, and the image distance from the the lens, Y, vary according to the lens formula

1. The value of the focusing distance, Y, is negative and increases in

magnitude, when X < 65, and positive and decreasing in magnitude when

X > 65, the line X = 65 is a vertical asymptote.

2. When X > 65, the value of Y is positive and increasing as the object

moves closer to the lens. At X = 65, there is no image when 0 ≤ X < 65, the

value of Y is negative and increasing towards 0.

3. A vertical asymptote is a discontinuity, where the function is not defined

Reasons:

Known;

[tex]\dfrac{1}{F} = \dfrac{1}{X} + \dfrac{1}{Y}[/tex]

Where;

F = The focal length

X = Object distance from lens

Y = Location of film = Image distance from lens

(a) Given that F = 65, we have;

[tex]\dfrac{1}{65} = \dfrac{1}{X} + \dfrac{1}{Y}[/tex]

[tex]\dfrac{1}{65} - \dfrac{1}{X} = \dfrac{1}{Y}[/tex]

[tex]Y = \dfrac{65 \cdot X}{X - 65}[/tex]

Given that 65·X > X - 65 When X > [tex]-\dfrac{65}{64}[/tex], we have;

As X is increased, Y is decreases, with the rate of decrease reducing as the

value of X gets larger.

(b) As the object moves closer to the lens, when X > 65, the value of Y

increases, at X = 65, the value of Y is infinity, which is a vertical asymptote,

as the object moves closer, the value of Y becomes negative, with the

value increasing (becoming less negative) and when X = 0, Y = 0

3. It is not possible to cross the asymptote because the function has a

discontinuity at the asymptote, which represent the point where the image

is at infinity, such that giving that the distance of the image increases as X

approaches the asymptote, crossing the asymptote results in the image

located further than infinity (which is impossible).

Learn more here:

https://brainly.com/question/2098689

Answer:

Step-by-step explanation:

a)

Number of children under 5    Number of household   Relative frequency

      0                                                      17                           17 / 50 = 0.34

       1                                                      14                           14 / 50 = 0.28

       2                                                      14                           14 / 50 = 0.28

       3                                                       3                            3 / 50 = 0.06

       4                                                        2                            2 / 50 = 0.04

                                                                50

Note,

Relative frequency  = Class frequency / Total Frequency

b) Percentage of households has two children under the age of 5 ,

= [tex]\frac{14}{50}[/tex] x 100

= 0.28 x 100

= 28%

Final answer:

To calculate the percentage of households with two children under the age of 5, divide the frequency of 2 by the total number of households and multiply by 100.

Explanation:

To calculate the percentage of households with two children under the age of 5, we need to find the relative frequency of 2 in the given data. The relative frequency is calculated by dividing the frequency of 2 by the total number of households, which is 50 in this case. The frequency of 2 is 0.06, so the relative frequency of 2 is 0.06/50 = 0.0012. To convert it to percentage, we multiply by 100, so the percentage of households with two children under the age of 5 is 0.0012 * 100 = 0.12%.

Answer:

The correct answer to the question is

4. How likely is it that, in a sample of 45, the true mean amount of time needed to find a parking spot is less than 20 minutes?

Step-by-step explanation:

Confidence interval provides a range of likely values for an unknown parameter. The interval is weighted based on probabilities of occurrence, such as 95% or 99% based on the result of a sample of test data.

It gives the probability that a given parameter such as the mean will be of a certain value range based on a given number of times.

As such the confidence level of the given mean amount of time needed to find a parking spot should be known.

Answer:

A and D

Step-by-step explanation:

We are given that

(3/4,2/3),(1/4,1),(1,1/2) and (1/2,1)

[tex]x_1=\frac{3}{4}[/tex]

[tex]y_1=\frac{2}{3}[/tex]

[tex]x_2=\frac{1}{4},y_2=1[/tex]

[tex]x_3=1,y_3=\frac{1}{2}[/tex]

[tex]x_4=\frac{1}{2},y_4=1[/tex]

k=[tex]\frac{1}{2}[/tex]

Direct proportion:

[tex]\frac{x}{y}=k[/tex]

Inverse proportion:[tex]xy=k[/tex]

[tex]\frac{x_1}{y_1}=\frac{3}{4}\times \frac{3}{2}=\frac{9}{8}\neq \frac{1}{2}[/tex]

Therefore, it is not in direct proportion.

[tex]\frac{1}{4\times 2}=\frac{1}{8}\neq\frac{1}{2}[/tex]

[tex]\frac{1}{\frac{1}{2}}=2\neq \frac{1}{2}[/tex]

[tex]x_1y_1=\frac{3}{4}\times \frac{2}{3}=\frac{1}{2}[/tex]

[tex]x_2y_2=\frac{1}{4}\times 2=\frac{1}{2}[/tex]

[tex]x_3y_3=1\times \frac{1}{2}=\frac{1}{2}[/tex]

[tex]x_4y_4=\frac{1}{2}\times 1=\frac{1}{2}[/tex]

Therefore, [tex]xy=k=\frac{1}{2}[/tex]

Hence, the given points form an inverse variation .

[tex]xy=\frac{1}{2}[/tex]

[tex]y=\frac{1}{2x}[/tex]

Option A and D is true.

Answer: A and D

Step-by-step explanation:

Cause edg2020

Answer:

$58,544

Step-by-step explanation:

Given that Baylor charges tuition fees at $41,194, Room at $13038 and Required fees at $4598 p.a. We also know that the scholarship pays $44194 p.a.

#The additional money for the four years is the total  minus the scholarship  multiplied by 4 yrs:

[tex]C_{p.a}=Tution+Room+Required\\\\=41194+13038+4598\\\\=58830\\\\Scholarship=44194\\\\\bigtriangleup p.a=58830-44194\\\\=14636[/tex]

The additional cost to attend the college for the next four years is:

[tex]\bigtriangleup p.a=14636\\\\\sum{\bigtriangleup p.a _i}=4\times 14636\\\\=58544[/tex]

Hence, Amanda needs an additional $58,544 to attend Baylor for the 4 years.

Answer:

The total amount spent during 2003 was $725.78.

Step-by-step explanation:

Given:

During the 2004 season, New York theater goers bought 11.3 million tickets for a total of $749.0 . Theater goers spent a total of 3.2% more than the year before.

Now, to find the total amount that was spent during 2003.

Let the amount spent during 2003 be [tex]x.[/tex]

The amount spent during 2004 = $749.0.

As, given theater goers spent a total of 3.2% more than the year before.

So, we put equation to get the amount spent during 2003:

[tex]x+3.2\%\ of\ x=749[/tex]

[tex]x+\frac{3.2}{100} \times x=749[/tex]

[tex]x+\frac{3.2x}{100}=749[/tex]

[tex]\frac{100x+3.2x}{100} =749[/tex]

[tex]\frac{103.2x}{100} =749[/tex]

Multiplying both sides by 100 we get:

[tex]103.2x=74900[/tex]

Dividing both sides by 103.2 we get:

[tex]x=\$725.78[/tex]

Therefore, the total amount spent during 2003 was $725.78.

Leah asked her dance students to hand out at least 10 flyers for their upcoming dance recital and construct a histogram to display the data.

In this question, Leah asked her dance students to each hand out at least 10 flyers for their upcoming dance recital. Then, she constructed a histogram to display the number of recital flyers handed out by the students.

To solve this, Leah can tally the number of students who handed out a specific number of flyers and create intervals on the x-axis of the histogram to represent the number of flyers. The height of each bar in the histogram will represent the number of students who handed out the corresponding number of flyers. By constructing the histogram, Leah can visualize the distribution of the number of flyers handed out by her dance students.

Final answer:

The question is related to Mathematics, specifically the creation and analysis of histograms, frequency tables, and probability distributions, often used in statistics to visualize and interpret various sets of data.

Explanation:

The student's question falls under the subject of Mathematics, specifically related to statistics and data analysis. In this instance, various exercises are mentioned where the creation and interpretation of histograms are central. These exercises are multifaceted, requiring students to compile data, calculate statistical measures such as means and probabilities, and graphically represent data using histograms and other charts.

For example, when Leah asks her dance students to hand out flyers, she is gathering data that can be represented in a histogram to visualize the distribution of flyers handed out. Similarly, the ballet instructor's data on retention rates can form a probability distribution. When Jill delivers flyers for her yard sale, her travel distances and times could be used to create a time series graph.

Histograms, frequency tables, and probability distributions are tools used in these exercises to better understand the data collected, whether it's related to dance flyer distribution, car sales, or family size among classmates.

Approximately 85.33% of the exam scores are between 68 and 77.99 points.

To find the proportion of exam scores between 68 and 77.99 points in a normally distributed set, we can use the Z-score formula:

[tex]\[ Z = \frac{X - \mu}{\sigma} \][/tex]

where X is the score, [tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation.

Given:

- Mean [tex]\( \mu = 71.33 \)[/tex]

- Standard deviation [tex]\( \sigma = 3 \)[/tex]

- We need to find the proportion of scores between [tex]\( X_1 = 68 \)[/tex] and [tex]\( X_2 = 77.99 \)[/tex].

1. Calculate the Z-scores for [tex]\( X_1 = 68 \)[/tex]:

[tex]\[ Z_1 = \frac{68 - 71.33}{3} = \frac{-3.33}{3} = -1.11 \][/tex]

2. Calculate the Z-scores for [tex]\( X_2 = 77.99 \)[/tex]:

[tex]\[ Z_2 = \frac{77.99 - 71.33}{3} = \frac{6.66}{3} = 2.22 \][/tex]

Next, we look up these Z-scores in the standard normal distribution table or use a calculator to find the corresponding proportions:

- The proportion corresponding to [tex]\( Z_1 = -1.11 \)[/tex] is approximately 0.1335.

- The proportion corresponding to [tex]\( Z_2 = 2.22 \)[/tex] is approximately 0.9868.

The proportion of scores between [tex]\( X_1 = 68 \)[/tex] and [tex]\( X_2 = 77.99 \)[/tex] is the difference between these two proportions:

[tex]\[ P(68 < X < 77.99) = P(Z < 2.22) - P(Z < -1.11) \][/tex]

[tex]\[ P(68 < X < 77.99) = 0.9868 - 0.1335 = 0.8533 \][/tex]

Answer:

D

Step-by-step explanation:

Cause if you se it close you wil get it

Answer:

16 possible ways

Step-by-step explanation:

Using the formular Cp,k= p!/I! (P-k)!

Where k= number of selected committee members

P= available number that can sit in the committee

For doctors,there are 5 doctors

C= 5!/2!(3)!= 120/12 = 10ways

For nurses,there are 4

C= 4!/2!(2)! = 24/4 =6ways

Total possible ways=10 + 6 = 16 ways

Answer:

60

Step-by-step explanation:

(2 out of 5 doctors) * (2 out of 4 nurses)

Answer:

(b) 4 x = 4 5 is the needed expression to solve for the value of x.

Step-by-step explanation:

Here, the given proportion is simplified as:

[tex]\frac{4}{5} = \frac{9}{x}[/tex]

Now, to simplify any proportion of the form [tex]\frac{a}{b} = \frac{c}{d}[/tex]  the simplest way is CROSS MULTIPLICATION.

So, cross multiplying  [tex]\frac{a}{b} = \frac{c}{d} \implies ad = bc[/tex]

Similarly cross multiplying [tex]\frac{4}{5} = \frac{9}{x}[/tex], we get:

4 (x)  = (9) (5)

or, 4 x  = 45

Hence, 4 x = 45 is the needed expression to solve for the value of x.

Answer:

4x=45

Step-by-step explanation:

4/5=9/x, so first you would multiply 5×9 (because cross products are always equal) and you would get 45. Since 4x has to also equal 45, the answer is 4x=45.

Hope this helps (P.S. I got it right on the test)!

Answer:

Step-by-step explanation:

Given that the mean salary for a new teacher in your town is $48,000

You believe it is higher for new teachers in a neighboring town.

So to prove or disprove your claim you have to show statistical evidence.

For that hypothesis testing is necessary.

You must conduct a hypothesis test for comparing the mean of salary of new teacher with neighbouring places

The hypotheses wouldbe

[tex]H_0: \mu = 48000\\H_1: \mu >48000[/tex]

where mu is the average for neighbouring states.

Answer: it would take them 40/13 hours

Step-by-step explanation:

If Naomi were to paint her living room alone, it would take 5 hours. it means that the rate at which she paint her living room alone is 1/5

Her sister Jackie could do the job in 8 hours. it means that the rate at which Jackie paint the living room is 1/8

If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be

1/5 + 1/8 = (8 + 5)/40 = 13/40

Assuming it takes t hours for both of them to clean the room working together, the working rate per hour would be 1/t. Therefore,

13/40 = 1/t

t = 40/13 hours

Answer:

The new mean = 3 × (the old mean) = 150

The new standard deviation is also = 3 × (The old standard deviation) = 15

Step-by-step explanation:

µ = 50 and σ = 5

The mean is the sum of variables divided by the number of variables.

Mean = (Σx)/N = µ = 50

x = each variable

N = number of variables

If each variable changed to 3x

Mean becomes

Mean = (Σ(3x))/N = 3 (Σx)/N = 3 × µ = 3 × 50 = 150.

The standard deviation is the square root of variance. And variance is an average of the squared deviations from the mean.

The standard deviation measures the rate of spread of the data set around the mean.

Standard deviation = σ = √[Σ(x - µ)²/N]

x = each variable

µ = mean

N = number of variables

If each variable changed to 3x

Recall µ changed to 3µ

Standard deviation = σ = √[Σ(3x - 3µ)²/N]

σ = √[Σ 3² (x - µ)²/N] = √[(3²)Σ(x - µ)²/N] = 3×√[Σ(x - µ)²/N] = 3 × σ = 3 × 5 = 15

If every score is multiplied by 3, it is logical to reason that the average of the new set of numbers also is 3× the old average.

And the new set of numbers spread out similarly around this new mean, only that the new space of spread is now 3× the old one.

When every score in a population is multiplied by a constant, both the mean and the standard deviation are multiplied by that constant. So, in the given example, the new mean would be 150 and the new standard deviation would be 15.

In mathematics, when every score in a population is multiplied by a constant, both the mean (µ) and the standard deviation (σ) are also multiplied by that constant.

So, if every score in a population with µ = 50 and σ = 5 is multiplied by 3, the new mean (µ_new) would be 50 * 3 = 150, and the new standard deviation (σ_new) would be 5 * 3 = 15.

https://brainly.com/question/31538429

#SPJ3

Answer:

Option C) Quadratic regression model

Step-by-step explanation:

Quadratic regression model

where x is the independent variable and [tex]\hat{y}[/tex] is the dependent variable.

Thus, the correct answer is

Option C) Quadratic regression model

The (c) quadratic regression model is used to model a nonlinear relationship between the independent and dependent variables by including the independent variable and the square of the independent variable.

The correct answer to this question is C. Quadratic regression model. In statistics, a quadratic regression model is used to model a nonlinear relationship between the independent and the dependent variables. This is achieved by including the independent variable and the square of the independent variable in the model. For example, if 'x' is the independent variable, the model would include both 'x' and 'x²'. The quadratic term allows for the model to fit simple curved relationships between the dependent and independent variable. The other models listed, such as multiple regression model, least squares regression model and a simple regression model, tend to represent linear relationships.

Here is a simple illustrative example: suppose you wanted to model the relation between the amount of fertilizer used (independent variable 'x') and the height of a plant (dependent variable 'y'). If the relation isn't linear (meaning more fertilizer does not always result in more growth, and growth rate declines after a certain point, forming a curved pattern in the data), you could use a quadratic regression model

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