The base of the following pyramid is a square. what is the surface area of the pyramid?

It is true that an interaction term can be used to properly examine the effect of a categorical independent variable in a multiple linear regression model.

In a multiple linear regression model, an interaction term is a product of two or more independent variables. It allows the model to capture the effect of the interaction between the variables on the dependent variable.

For example, suppose you are using a multiple linear regression model to examine the relationship between income, education level, and job satisfaction. You might include an interaction term for education level and income, which would allow the model to capture the effect of the interaction between these two variables on job satisfaction.

Using an interaction term can be especially useful when you want to examine the effect of a categorical independent variable on the dependent variable since it allows you to control for the effects of other variables in the model.

Therefore, it is true

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It is proved that T/F a calculus is used  for computing filippov's differential inclusion with application to the variable structure control of robot manipulators.

In this we also get to know more about the calculus concepts and it also helps in paper to develops a calculus for computing Filippov's differential inclusion which simplifies the analysis of dynamical systems described by differential equations with discontinuous right-hand-side. In particular, when a slightly generalized Lyapunov theory is used, the rigorous stability analysis of variable structure systems is routine. As an example, a variable structure control law for rigid-link robot manipulators is described and its stability is proved.

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The distance between the start of the walkway and the middle person is 52 feet.

It is given that a 100 foot long moving walkway moves at a constant rate 6 feet per second.

AI steps into the start of the walkway and stands this means speed of AI is 6 feet per second.

Bob steps onto the start of  he walkway two second later and stolls forward along walkway 4 feet per second that means 10 feet [per seconds.  

And CY reaches the starts of the walkway and walks briskly forward beside the walkway at a rate of 8 feet per second.

At the time s we gave that,

[tex]\frac{8(s-4)+10(s-2)}{2}[/tex] = 6s

[tex]\frac{8s -32 + 10s - 20}{2}[/tex]  = 6s

      18s - 52 = 12s

              6s  = 52

                s  = [tex]\frac{26}{3}[/tex]

At the time AI has travels,  

6* [tex]\frac{26}{3}[/tex] = 52 feet.

Therefore distance between the start of the walkway and the middle person is 52 feet.

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the predicted interval of time between eruptions would be 53.16 minutes with regression equation.

The equation of the regression line is y = 33.35 + 13.29x.

Plugging in x = 4, we get y = 33.35 + 13.29(4) = 53.16 minutes.

The equation of the regression line is y = 33.35 + 13.29x. This equation is used to predict the interval of time between eruptions based on the duration of the previous eruption. By plugging in the value of x (4) into the equation, the predicted y value is 53.16 minutes. This means that if the previous eruption lasted 4 minutes, the predicted interval of time between eruptions would be 53.16 minutes.

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The value of (p+q+r+s) / (a+b+c) is 3.66 if the basketball player has probability 0.4 to make a perfect shot.

We know that if probability is given for r distribution and if question is asking distribution for n terms, we need to use binomial probability distribution which is given by [tex]^nC_r[/tex][tex]p^r[/tex][tex]q^r[/tex] where p is defined as the success probability and q is called as failure probability.

We have success probability =0.4

Failure probability(q) = 1-p=1-0.4=0.6

From 9 terms, we need to choose single term having success probability =0.4 and failure probability=0.6

So, this can be given by =[tex]^9C_1[/tex] × (0.4)¹ ×(0.6)⁹⁻¹

which is equivalent to =9 × (0.4) × (0.6)⁸

On comparing with the given equation =([tex]p^a[/tex] × [tex]q^b[/tex]×[tex]r^d[/tex]) / [tex]s^c[/tex] ,we get

p=9,a=1,q=0.4,b=1,r=0.6,d=8,s=1,c=1.

So,value of p+q+r+s = 9+0.4+0.6+1=11

and value of a + b + c = 1+1+1=3

So, value of (p + q + r + s) / (a + b + c)= 11 / 3=3.66

Hence, required value is 3.66

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(a) In 70,572,902,400 ways can you select and arrange 10 of the 17 books on the shelf.

(b) In 19,448 ways can you arrange 10 of the 17 books on the shelf if you insist they must be arranged alphabetically by author.

In the given question, in an attempt to clean up your room, you have purchased a new floating shelf to put some of your 17 books you have stacked in a corner. These books are all by different authors. The new book shelf is large enough to hold 10 of the books.

Total number of books = 17

Number of books which self hold = 10

We have to find the following.

(a) We have to find how many ways can you select and arrange 10 of the 17 books on the shelf.

Number of ways to select the 10 books out of 17 books = [tex]^{17}C_{10}[/tex]

Now,

The number of ways of arranging the 10 books = [tex]10![/tex]

Total number of ways of selecting and arranging 10 books out of 17 = [tex]^{17}C_{10}\times10![/tex]

Total number of ways of selecting  and arranging 10 books out of 17 = [tex]\frac{17!}{10!(17-10)!}\times10![/tex]

Total number of ways of selecting  and arranging 10 books out of 17 = [tex]\frac{17!}{10!7!}\times10![/tex]

Total number of ways of selecting  and arranging 10 books out of 17 = [tex]\frac{17\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7!}{7!}[/tex]

Total number of ways of selecting  and arranging 10 books out of 17 = 17×16×15×14×13×12×11×10×9×8

Total number of ways of selecting  and arranging 10 books out of 17 = 70,572,902,400

Hence,

Total number of ways of selecting  and arranging 10 books out of 17

(b) We have to find how many ways can you arrange 10 of the 17 books on the shelf if you insist they must be arranged alphabetically by author.

Number of ways to select the 10 books out of 17 books = [tex]^{17}C_{10}[/tex]

Number of ways of arranging the 10  books alphabetically = 1

Total number of ways of arranging 10 books out of 17 in the shelf = [tex]^{17}C_{10}[/tex]

Total number of ways of arranging 10 books out of 17 in the shelf = [tex]\frac{17\times16\times15\times14\times13\times12\times11\times10!}{10!\times7\times6\times5\times4\times3\times2\times1}[/tex]

Total number of ways of arranging 10 books out of 17 in the shelf = 19,448

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Answer:

A) 2y + x = 5. 5x - y = 3

Step-by-step explanation:

twice a number = 2y (y represents the larger number in this case)

added to a smaller number, so 2y + x (letting x represent the smaller number) equals 5, so 2y + x = 5

Then 5 times the smaller number, x = 5x

the difference of 5x and the larger number (y) = 5x - y = 3

so all together your equation would be 2y + x = 5. and 5x - y = 3.

Answer:

17 $

Step-by-step explanation:

let y  - total cost of a gift

x - price of the gift

the total cost of the gift is its price + 14% delivery, which can be written as:

y = x + 14% * x = x + 0.14x = 1.14 x

by making the substitution with the data from the task

19.38 = 1.14*x

x = 19.38/1.14 = 17

If (x + 8) is a factor of f(x), then the true statement is f(-8) = 0 .

In the question ,

it is given that , x [tex]+[/tex] 8 is factor of f(x) ,

we have to select the correct option about f(x) from the given options .

When solving the polynomials, a factor of the polynomial gives the solution of  the polynomial.

that means , x + 8 = 0

So , x = -8 ,

So , it means that when x = -8 , then the value of the function f(-8) will be zero ,

which means that x = -8 will be a root of the given function f(x) .

Therefore , the true statement is f(-8) = 0 .

The given question is incomplete , the complete question is

If (x + 8) is a factor of f(x), which of the following must be true ?

(a) Both x = –8 and x = 8 are roots of f(x).

(b) Neither x = –8 nor x = 8 is a root of f(x).

(c) f(–8) = 0

(d) f(8) = 0

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It is important to know what qualified ministerial service are because they are activities that are considered to be tax-exempt under Internal Revenue Service (IRS) rules. These activities are typically related to religious or spiritual work, and may include preaching, teaching, and leading worship services. Understanding what qualifies as ministerial service can help individuals and organizations ensure that they are in compliance with tax laws and can claim the appropriate tax exemptions. It can also help individuals understand their tax liability and plan their finances accordingly.

The magnitude and direction form with the magnitude rounded to the nearest tenth and the direction rounded to the nearest degree 5.4<cos335°<, sin335°

What is direction ?

Direction is characterized as the course that anything follows, the route that must be taken to go to a particular location, the direction in which something is beginning to take shape, or the direction you are facing. When you turn right instead of left, that is an illustration of direction.

The basis of the x, y, and z directions of a line or unit vector is identified by the number triplet known as the direction number. They are easily identified as a percentage of a unit vector.

u = 7cos300°i + 7sin300j

v = 4cos70i + 4sin70 j

u = 7*0.5i + 7*(-√3/2)j

  = 3.5i - 6.062j

v = 1.368i + 3.758j

u + v =(3.5+1.368)i +(-6.062+3.758)j

        = 4.868i +(-2.304)j

Magnitude of (u+v) = √(4.868)² +(2.304)²

                               = 5.385 ≈ 5.4

For direction

tanФ = y/x

        = -2.304/4.868

    Ф = -25.327

∴(u+v) is in 4th Quandrant

∴ Ф = 360 - 25.327

     = 334.672

    ≈ 335°

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The test statistic calculated for this scenario is the test of the significance of the mean.

Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

For example, if there are 3 students getting numbers 10, 20, and 30 in math then their mean is 10 + 20 + 30 / 3 = 60 / 3 = 20.

Given:

According to a survey of 1,362 adult college students, n = 1362,

The mean number of alcoholic beverages consumed, μ = 15,

The standard deviation, σ = 3,

As you can see here the sample is greater than 30 i.e. n > 30 and the value of standard deviation is also present then,

The static test, z can be given as shown below,

z = (X  - μ) / σ  / √n

Here, z is the static test and X is the sample mean.

Thus, the test of the significance of the mean can be calculated for this scenario.

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The t-statistic for these two sample is 3.80 with 73 df

T-value is a ratio of the difference between the mean of two samples sets an the variation exist within the sample sets .
The numerator value is difference of mean of two samples.

According to the question,

We have two different sample

Sample 1

n1 = 35 (sample size)

x1 = 13.6 (sample mean)

s1 = 5.8 (standard deviation)

Sample 2

n2 = 40

x2 = 10.1

s2 = 8.5

To calculate the t-value of difference of sample means

[tex]t = \frac{\bar{x_1} - \bar{x_2}}{\sqrt{\frac{s_1^2}{n_1} - \frac{s_2^2}{n_2}}}[/tex]

Substituting all the values

=> [tex]t = \frac{13.6-10.1}{\sqrt{\frac{5.8^2}{35} - \frac{8.5^2}{40}}}[/tex]

Solving ,

=> t = 3.5 / 0.9192

=> t = 3.807

With degree of freedom = n1 + n2 - 2

=> df =73

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The required volume of the 35% acetic acid solution that will combine with the 0.5 gallons of the 10% acetic acid solution to make a solution that is 15% acetic acid solution is 0.125 gallons, which indicates, using the dilution formula, that the correct options for the completed table are;

[tex]{}[/tex]                        Amount of Solution Acid Concentration  Amount of Acid

10% Acid[tex]{}[/tex]        0.5                             0.10                             (0.10)·(0.5)

35% Acid      [tex]{}[/tex]  v                                0.35                            0.35·v

Mixture           v + 0.5             [tex]{}[/tex]          0.15                            0.15·(v + 0.5)

The dilution formula indicates that the product of the concentration and volume of the initial solution is equivalent to the product of the concentration and volume of the intended solution to be made.

The volume of the 10% acetic acid solution in the mixture = 0.5 gallons

The volume of the 35% acetic acid solution = v

The concentration of the acetic acid solution Eli wants to make = 15%

The dilution formula for mixtures is; C₁·V₁ = C₂·V₂

Therefore; 0.1 × 0.5 + 0.35 × v = (v + 0.5) × 0.15

0.35 × v - (v + 0.5) × 0.15 = -0.1 × 0.5 = -0.05

0.2·v - 0.075 = -0.05

v = (0.075 - 0.05)/0.2 = 0.125

The volume of the 35% solution required, v = 0.125 gallons

The completed table is therefore;

    [tex]{}[/tex]                  Amount of Solution    Acid Concentration   Amount of Acid

10% Acid    [tex]{}[/tex]      0.5                               0.10                              (0.10)·(0.5)

35% Acid [tex]{}[/tex]         v                                  0.35                             0.35·v

Mixture           v + 0.5                   [tex]{}[/tex]        0.15                             0.15·(v + 0.5)

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There are 9 CD's can she place on a shelf.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Each shelf is 28 inches long and each CD is 1 3/ inch thick.

Now,

Since, Each shelf is 28 inches long and each CD is 1 3/ inch thick.

Hence, The number of CD's = 28 x 1/3

                                            = 9.33

                                            = 9

Thus, There are 9 CD's can she place on a shelf.

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Answer:

  3.  (a)  x, y ∈ W

  5.  (b)  x, y ∈ W

Step-by-step explanation:

Given two problems in which x and y represent numbers of seats, you want to know what, if any, domain the variables are restricted to.

A number of seats is a counting number, possibly including zero. Generally, it will be a member of the set of whole numbers: {0, 1, 2, 3, ...}. They will not be negative, and will not have a fractional part: x ≠ -1, x ≠ 2.3.

In both your problems, x and y are defined as numbers of seats, so will be from the domain of whole numbers.

  x ∈ W, y ∈ W

__

Additional comment

The various named domains are usually represented by ...

ℝ — real numbers

ℕ — natural numbers {1, 2, 3, ...}

ℚ — rational numbers

ℤ — integers

ℂ — complex numbers

W — whole numbers (Natural numbers and zero)

We're unfamiliar with the use of I, which we presume is intended to represent Integers.

Answer: True

Step-by-step explanation:

They appeal to how humans are empathetic towards others who may not speak their language. Also, they are more inclusive and may talk about things considered "taboo".

Hope this helps! :)

Answer:

False

Step-by-step explanation:

Option A. A special type of relation that pairs each domain value with exactly one range value. This means that for each input value, there is only one corresponding output value.

A function is a special type of relation that takes an input value (domain) and maps it to exactly one output value (range). This means that for each input value, there is only one corresponding output value.

This type of relation is often represented graphically, with the domain values on the x-axis and the range values on the y-axis. Functions are also commonly represented using equations, which allows for more precise calculations. In many cases, the output value of a function is determined by a mathematical operation that is performed on the input value. In this way, functions can be used to model real-world phenomena, such as population growth or the trajectory of a rocket.

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The difference between the two temperatures is 33 degrees.

The city's maximum temperature was 42 degrees and the minimum was 9 degrees.

The difference between the two temperatures can be calculated as follows;

The difference in temperature is the subtraction of the minimum temperature from the maximum temperature.

Therefore,

difference between the temperature = maximum temperature - minimum temperature

maximum temperature = 42 degrees

minimum temperature = 9 degrees

Hence,

difference between the temperature = 42 - 9

difference between the temperature = 33 degrees.

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The p value is greater than α.

Hence we made a conclusion that:

There is a significant difference between treatments.

There is no significant difference between treatments.

Given:

An experiment has been conducted for four treatments with eight blocks.

Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatments 900 Blocks 400 Error Total 1800 Use A = .05 to test for any significant differences.

we are asked to find:

The p-value is = ?

What is your conclusion = ?

P value of treatments = 0.0001

Hence p value is less than α = 0.05

so we reject H₀

P value for blocks = 0.0650

Hence p value is greater than α = 0.05

so we fail to reject H₀

Conclusion:

There is a significant difference between treatments.

There is no significant difference between treatments.

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In the picture the correct option is A when the function shown in graph (A) has a constant additive rate of change is -1/4.

Given that,

We have to find which function has an additive change rate that is -1/4 constant throughout time. a line in the coordinate plane with a downward slope. (negative 2, 2) and the line (2, 1).

We know that,

The line goes through the points:

(-2, 2) and (2, 1)

y - 1 = (1-2)/(2+2)[x -2]

y - 1 = (-1/4)[x -2]

y = -x/4 + 1/2 + 1

y = -x/4 + 3/2

The change at a constant additive rate is -1/4.

Therefore, In the picture the correct option is A when the function shown in graph (A) has a constant additive rate of change is -1/4.

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The full price when the sales price is £32.24 is £96.72

The full price when the sales price is £86.08 is  £258.24

The full price when the sales price is £105.48 is £316.44

The full price when the sales price is £230.62 is £691.86

The sales price is one third of the full price of the items. Thus, in order to determine the full price, multiply the sales price by 3.

Full price = sales price x 3

Full price when the sales price is £32.24 = 3 x £32.24 = £96.72

Full price when the sales price is £86.08 = 3 x £86.08 = £258.24

Full price when the sales price is £105.48 = 3 x £105.48 = £316.44

Full price when the sales price is £230.62 = 3 x £230.62 = £691.86

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Therefore, the solution to the question is T = 2.5 is the test statistic and the manufacturer's claim is supported by the data at the.05 significance level, according to the test's p-value of 0.007 <0.05.

In statistical hypothesis testing, a test statistic is a statistic that is employed. A hypothesis test is often defined in terms of a test statistic, which is a numerical summary of a data set that can be used to execute the test and reduces the data to one value.

Here,

The test's p-value was 0.007 0.05, indicating that the evidence at the.05 level of significance supports the manufacturer's claim.

1000 hours on average. See if there is more.

We examine the null hypothesis, that is, whether the mean is 1000 hours, by asking:

[tex]H_{0}[/tex]: u=1000

If the mean is greater than1000 hours, we test the alternative hypothesis, which is:

[tex]H_{A}[/tex] : u > 1000

Test statistics:

t=  [tex]\frac{X-u}{\frac{S_{d} }{\sqrt{n} } }[/tex]

t=  [tex]\frac{X-u}{\frac{S_{d} }{\sqrt{n} } }[/tex]

t=[tex]\frac{1025-1000}{\frac{310 }{\sqrt{1000} } }[/tex]

t=25/9.80

t≈2.5

The test statistic is t = 2.5

P-value for the test and judgment

The right-tailed test's p-value, which has t = 2.5 and 100 - 1 = 99 degrees of freedom, measures the likelihood that a sample mean will be higher than 1025 hours.

This p-value is 0.007 according to a t-distribution calculator.

The manufacturer's claim is supported by the data at the.05 significance level, according to the test's p-value of 0.007 <0.05.

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No, the expression ( x - 1 ) as required to be checked is not a factor of the given polynomial function g ( x ) = -2x⁴ + 4x³ - x + 9.

It follows from the task content that the expression ( x - 1 ) is required to be checked if it's a factor of the given polynomial function.

Since the given factor can be equated to 0 so that we have; x - 1 = 0; x = 1.

On this when g (1) is evaluated, the result must be zero in order to confirm ( x - 1 ) is a factor of g ( x ) = -2x⁴ + 4x³ - x + 9.

Hence; g ( 1 ) = -2 ( 1 )⁴ + 4 ( 1 )³ - 1 + 9.

g (1) = -2 + 4 - 1 + 9

g (1) = 10

Ultimately, since g (1) ≠ 0; the expression ( x - 1 ) is not a factor of the given expression; g ( x ) = -2x⁴ + 4x³ - x + 9.

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The value of find f(-2)-g(-2), if f(a) = 3a + 5 and g(a) = a² + 4 is -9.

In the case of a function from one set to the other, each element of X receives exactly one element of Y. The function's domain and co-domain are respectively referred to as the sets X and Y as a whole.

Given function:

f(a) = 3a + 5 and g(a) = a² + 4

Calculate the f(-2) - g(-2) by putting value -2 in both function

f(-2) = 3(-2) + 5 = -6 + 5

f(-2) = -1

g(-2) = (-2)² + 4

g(-2) = 4 + 4

g(-2) = 8

Hence,  f(-2) - g(-2) = -1 - 8 = -9

Therefore, the value of find f(-2)-g(-2), if f(a) = 3a + 5 and g(a) = a² + 4 is -9.

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The given statement "A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 5 participants in each treatment condition. This study uses a total of 25 participants." is true.

The term probability refers the occurrence of a random event.

Here we have given the statement "A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 5 participants in each treatment condition. This study uses a total of 25 participants."

And we have to identify whether this one is true or not.

While looking into the given question, we have identified the value like the following,

level in factor A = 2

levels in factor B = 3

Number of participants = 5

Then the total number of participants is calculated as,

=> (3 + 2)  x 5

Now, we have to expand the given equation, then we get,

=> 5 x 5

Then the total number of participants is 25.

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The approximate distance from the playground to the road along the other path is 1.3 miles.

A town park has two paths leading to the playground. One path is 2 miles from the road and the other path makes a right angle with the road. The two paths intersect at an angle of  50 degrees.

The approximate distance from the playground to the road along the other path can be calculated as follows;

using trigonometric ratios,

cos 50° = adjacent / hypotenuse

let

x =  distance from the playground to the road along the other path

Hence,

cos 50 = x / 2

cross multiply

x = 2 cos 50°

x = 2 × 0.64278760968

x = 1.28557521937

x = 1.3 miles.

Therefore,

distance form play ground to the road = 1.3 miles.

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For given data of ten professional athletes:

A) A scatter plot of the data is as shown below.

B) An equation of the line of best fit is:

y = 1.7946x + 2.1956

C) The line of best fit on the scatter plot is as shown below.

D) The y-intercept of the line of best fit is: a = 2.1956

The y-intercept represents, on average players with no endorsements earn million dollars each year.

In this question we have been given a random sample of ten professional athletes. In data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars).

A) A scatter plot of the data is as shown below.

B) For given scatter plot we can obsere that the variables show a linear regression.

And the equation of the line of best fit is:

y = 1.7946x + 2.1956

And the coefficient of regression is: R² = 0.9657

C) The line of best fit on the scatter plot is as shown below.

D) The y-intercept of the line of best fit is:

a = 2.1956

The y-intercept means that on average, players with no endorsements earn million dollars each year.

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The complete question is:

A random sample of ten professional athletes produced the following data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars).

x  y  x  y

0  2  5  11

3  8  4  9

2  6  3  8

1  3  0  3

6  14  5  10

A) Draw a scatter plot of the data.

B) Use regression to find the equation for the line of best fit. (Round your answers to three decimal places.)

ŷ = ____ + ____ x

C) Draw the line of best fit on the scatter plot.

D) What is the y-intercept, a, of the line of best fit? (Round your answer to three decimal places.)

a =

What does it represent? (Round your answer to three decimal places.)

Answer:

Below

Step-by-step explanation:

See image below

Using basic geometric sequence rule with common ratio of 3, The answer is 216.

A sequence is a list of objects that is in order in mathematics (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered elements (potentially infinite).

Each phrase in a geometric sequence is obtained by multiplying the one before it by a constant.

Formula for common ratio is:

[tex]r= \frac {x^{n+1}}{x^{n}}[/tex]

r= 24/8

=3

Next term in sequence = 72 * 3

=216

To learn more about sequences visit:

https://brainly.com/question/21961097

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