Factor the following quadratic:
y=3x^2-13x-10

The account will have $27,698.10 after 24 months.

(a) Here, the initial balance is 0. The deposit in the second month is $10. The deposit in the third month is $20. The deposit in the nth month is N(n) such that N(n) = 10(n-1). Let B(n) be the balance in the nth period. Using the formula for the sum of the arithmetic series and simplifying, we get B(n) = 5n(n-1).

Therefore, the balance during the nth period is given by N1 B(n) = N*(1+B)N-2-1

=10(1+5n(n-1))n-2-1

=10(1+5n²-5n))n-3

=(10n²+1)n-3

Thus, (8) 1 is verified.

(b) We have N(n) = 10(n-1). Let B(n) be the balance in the nth period. We want to show that B(n) = N(n)(1+B(n-1)).

Using the values of N(n) and B(n-1), we get B(n) = 10(n-1)(1+5(n-1)(n-2)) = 5n(n-1). Therefore, B(n) = N(n)(1+B(n-1)) is verified. Hence (9) 82 holds.

(c)The deposit in the first month is $10. The deposit in the second month is $20. The deposit in the nth month is N(n) such that N(n) = 10(n-1).Let B(n) be the balance in the nth period. The interest rate is 0.5% per month. Therefore, the monthly interest rate is 0.5/100 = 0.005. Using Eq. (9) 82 with N = N(n), n = 24 and B(1) = 10, we get

B(24) = N(24)/(1+0.005)24-1-1

=27698.10

Therefore, the account will have $27,698.10 after 24 months.

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Answer:

Volume = 36 in ³ ( cubed )

SA = 66 in ² ( squared )

Step-by-step explanation:

The volume of a rectangular prism is:

l x w x h,

where in this case:

l = 4 in

w = 3 in

h = 3 in

So, the total volume would be:

4 in x 3 in x 3 in = 36 in ³ ( cubed )

Now the formula for the surface area of a rectangular prism is:

2 ( l x w + l x h + w x h )

So if we plug in the values in the formula, we get:

2 ( 4 in x 3 in + 4 in x 3 in + 3 in x 3 in ) = 66 in ² ( squared )

The color that has the largest range is Blue and this shows that it has a larger variability.

Range is a statistical measure that describes the spread or variability of a set of data. It is calculated as the difference between the largest and smallest values in a set of data.

Therefore, a larger range indicates a larger variability of the data. This means that the data points are spread out over a wider range of values, suggesting that there is greater diversity or variation in the observations. With blue having a larger range, it therefore has more variability.

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Answer: The total surface area of the toy chest is 212.754 square feet (ft²)

Step-by-step explanation:

The total surface area of the rectangular prism can be found using the formula:

SA = 2 ( lw + lh + wh ),

where: l = 8.25 ft, w = 6 ft, h = 3 ft

The width of the prism is found with the diameter of the cylinder, and the height of the prism is equal to the radius, which is half of the diameter of the cylinder.

In this case, the top of the rectangular prism is covered, so we'll just account for one of them, which would look like:

2 ( wh+ lh ) + lw

Now, the surface area of a full cylinder is:

SA = 2 * pi * radius * height

But, in this case, the cylinder is cut in half, so we just divide the total surface area by 2.

SA = pi * radius * height

pi = 3.14159

radius = 3

height = 8.25

All together, the formula for the total surface area would look like:

2 ( wh+ lh ) + lw + (pi * radius * height)

∴ if we plug in the values we get:

2 ( 8.25 * 3 + 6 * 3 ) + 8.25 * 6  + ( 3.14159 *  3 * 8.25 )  =

212.754 feet squared (ft²)

The graphs of f(x) and g(x) are the inverses of each other, reflected in the straight line y = x. 

The graphs f(x) = −log x and g(x) = log x are reflections of each other on the straight line y = x. This is because the function f(x) gives the pH of the solution as a function of the hydrogen ion concentration, and the function g(x) gives the hydrogen ion concentration as a function of pH.

The graph of f(x) is a decreasing function. That is, the value of f(x) decreases as x increases. This makes sense because the higher the concentration of hydrogen ions, the more acidic the solution and the lower the pH.

The graph of g(x) is an increasing function. That is, as x increases, the value of g(x) increases. This also makes sense because as the pH of a solution increases (that is, it becomes less acidic), the concentration of hydrogen ions decreases.

Overall, the graphs of f(x) and g(x) are inverses of each other, reflections of each other across the straight line y = x. 

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Answer:

the answer is 5

Step-by-step explanation:

Answer:

∴Option D: Neither

Step-by-step explanation:

Taking the first ordered pair:

[tex](-3, 3) = (x, y)[/tex]

Substitute [tex]x = -3[/tex] in the provided equation to see what the corresponding value of y comes out to:

[tex]y = 4(-3) + 9[/tex]

[tex]y = -12 + 9[/tex]

[tex]y = -3[/tex] which is ≠ 3

∴[tex](-3, 3)[/tex] is NOT a solution of the equation

Taking the second ordered pair:

[tex](-2, 2) = (x, y)[/tex]

Substitute [tex]x = -2[/tex] in the provided equation to see what the corresponding value of y comes out to:

[tex]y = 4(-2) + 9[/tex]

[tex]y = -8 + 9[/tex]

[tex]y = 1[/tex]  which is ≠ 2

∴[tex](-2, 2)[/tex] is NOT a solution of the equation

∴Option D: Neither

Thus, the total cost paid by Adrian for the 4 notebooks including the sales tax is: $14.91.

The sales tax calculation is a straightforward algebraic problem that requires calculating a percentage to either a decimal and multiplying the result by the item's price to determine the ultimate sales tax amount.

The equation looks as follows as it is written out: Sales tax percent divided by 100 is the sales tax rate.

Given data:

Number of notebooks bought by Adrian = 4.

Cost of each notebook: $3.50

Total cost : 3.50*4 = $14.0.

Sales tax = 6.5%

Sales price = 0.065*14 = $0.91.

Price paid = total cost + sales cost

Price paid = $14.0. + $0.91.

Price paid = $14.91.

Thus, the total cost paid by Adrian for the 4 notebooks including the sales tax is: $14.91.

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We know that the distance between the given numbers using absolute value and the distance by evaluating the absolute value expression.10 and 18 is 11.

Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression.

4 and 15

We know that the distance between p and q is given by

p-q or q-p

So, the distance between 4 and 15 is

4-15 or 15-4

Now, for 4-15

4-15 = -11

4-15 = 11

Now, for 15-4

15-4 = -11

15-4 = 11

On solving both, we get 11

Therefore, the distance between 4 and 15 is 11. We know that the distance between the given numbers using absolute value and the distance by evaluating the absolute value expression 10 and 18 is 11.

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Answer:

x = 8, y = 13

Step-by-step explanation:

Me disculpo de antemano por cualquier error de idioma, ya que estoy usando un traductor.

Como ya tenemos "y" en la primera ecuación, simplemente necesitamos usarlo como sustituto en la segunda ecuación.

x + ( x + 5 ) = 21

2x + 5 (-5) = 21 (-5)

2x = 16

x = 8

Entonces podemos usar el valor de "x" en la primera ecuación para encontrar "y".

y = (8) + 5

y = 13

The probability that a student who does not like bike riding also does not like skating is 50/90 = 5/9, or approximately 0.56.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To create a two-way table, we can use the information given in the problem as follows:

                              Likes Bike Riding     Does Not Like Bike Riding     Total

Likes Skating              20                                      70                                 90

Not Like Skating         60                                      50                                110

Total                            80                                      120                               200

Part A:

From the table, we can see that 20 students like bike riding but not skating, and 80 - 20 = 60 students like both bike riding and skating. Therefore, the percentage of students surveyed who like both bike riding and skating is (60/200) x 100% = 30%.

Part B:

To find the probability that a student who does not like bike riding also does not like skating, we need to look at the table entry for "Does Not Like Bike Riding" and "Does Not Like Skating". From the table, we can see that there are 50 students who do not like skating and do not like bike riding. The total number of students who do not like bike riding is 40 + 50 = 90.

Therefore, the probability that a student who does not like bike riding also does not like skating is 50/90 = 5/9, or approximately 0.56.

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The man should swim the entire distance at 2 miles per hour because the minimum walking speed that would make it quicker to walk the entire distance is infinity, which is not practical.

Let's assume the distance the man needs to travel is d miles. If the man swims at 2 miles per hour, he can swim the distance in d/2 hours. If he walks at a speed of x miles per hour, he can walk the distance in d/x hours. Therefore, the total time T it takes to travel the distance using swimming and walking is:

T = d/2 + d/x = d(1/2 + 1/x)

We want to find the walking speed x that minimizes the total time T. To do this, we can take the derivative of T with respect to x and set it equal to zero:

d(T)/dx = -d/2x^2 + d/x^2 = d/x^2(1/2 - 1) = -d/2x^2

Setting d(T)/dx = 0, we get:

d/2x^2 = 0

Solving for x, we get:

x = infinity

This means that the minimum walking speed for which it is quickest to walk the entire distance is infinity, which is not a practical solution. Therefore, the man should swim the entire distance at 2 miles per hour.

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The  inequality of the given equations can be done by substituting the left side and right side equations.

(1) The inequality is n > 75.

(2) The inequality is e < 3.3.

(3) The inequality is t < -8.

(4) The inequality is h > 127.8.

(5) The inequality value is m < 2.        

(1). n/5 + 4.3 > 19.3

4.3 is subtracted from both sides:

n/5 > 15

n > 75 when both parts are multiplied by 5.

The disparity is n > 75 as a result.

(2). 4e - 7.2 < 6

7.2 added to both sides:

4e < 13.2

e < 3.3 after multiplying both parts by 4.

The disparity is therefore e 3.3.

(3). 44 < -4t + 12

12 is subtracted from both sides:

32 < -4t

Flipping the inequality sign and dividing both parts by -4

t < -8

The disparity is therefore t <-8.

(4). h/3 - 0.3 > 42.3

0.3 more on both sides:

h/3 > 42.6

Adding 3 to both sides:

h > 127.8

h > 127.8 is the disparity as a result.

(5). 9.2m + 12 < 30.4

Subtracting 12 from both sides:

9.2m < 18.

4

Dividing both sides by 9.2:

m < 2

Therefore, the inequality is m < 2.

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Answer:

72 because 8*9

28

27

42

56

Given, A = [6, 1] and B = [5, 10]

(a) A + B: Add the corresponding elements of A and B.

A + B = [6+5, 1+10] = [11, 11]

(b) A - B: Subtract the corresponding elements of B from A.

A - B = [6-5, 1-10] = [1, -9]

(c) 2A: Multiply each element of A by 2.

2A = [2*6, 2*1] = [12, 2]

(d) 2A - B: First find 2A, then subtract the corresponding elements of B.

2A - B = [12-5, 2-10] = [7, -8]

(e) B + A: Add the corresponding elements of B and A (same as A + B).

B + A = [5+6, 10+1] = [11, 11]

In conclusion:

A + B = [11, 11]

A - B = [1, -9]

2A = [12, 2]

2A - B = [7, -8]

B + A = [11, 11]

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Answer:

y = (x - 1)² - 10

Step-by-step explanation:

y = x² - 2x - 9

using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 2x

y = x² + 2(- 1)x + 1 - 1 - 9

y = (x - 1)² - 10 ← in vertex form

Answer:

A.

Step-by-step explanation:

The line with length 2x - 9 is a bisector.

14 = 2(2x-9)

7 = 2x - 9

16 = 2x

x = 8

The correct answer is Option A.

Lengths of the above question, we have BF = 3GM = 36, since GM = 12.

A triangle is a clοsed geοmetric shape that cοnsists οf three line segments that intersect at three endpοints tο fοrm three angles, with the sum οf the angles being 180 degrees. It is οne οf the basic shapes in Euclidean geοmetry.

Let M be the midpοint οf side BC. Since G is the centrοid οf triangle ABC, we knοw that GM is οne-third the length οf median BF, and hence BF = 3GM.

Since G is the centrοid, we knοw that GD is twο-thirds the length οf median CD, and hence GD = 2/3 * CD = 2/3 * 30 = 20.

Let x be the length οf AM. Then AG is alsο a median οf triangle ABC, sο AG = 2/3 * AE. We have:

BM = BC/2 = 18 (since BG = 6)

GM = BM - BG = 12

AM = 2GM = 24

ME = AE - AM = 8 (since AE = 32)

Therefοre, AE = AM + ME = 24 + 8 = 32, and AG = 2/3 * AE = 2/3 * 32 = 64/3.

Finally, we have BF = 3GM = 36, since GM = 12.

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The exact value of this expression is: (a) tan(arctan(6)) is 6 and  (b) sin−1(sin(7π/3)) is π/3

The exact value of each expression can be found by using the inverse trigonometric functions and the properties of the trigonometric functions.
(a) tan(arctan(6))
Using the property of the inverse trigonometric functions, we can simplify this expression:
tan(arctan(6)) = 6

(b) sin−1(sin(7π/3))
Using the property of the inverse trigonometric functions, we can simplify this expression:
sin−1(sin(7π/3)) = 7π/3

However, since the range of the inverse sine function is [-π/2, π/2], we need to find an angle in this range that has the same sine value as 7π/3. We can do this by subtracting 2π from 7π/3 until we get an angle in the desired range:
7π/3 - 2π = π/3

Therefore, the exact value of this expression is:
sin−1(sin(7π/3)) = π/3

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Answer:

Step-by-step explanation:

sinA= 4.8/6, with the help of trignometric ratios.

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement. 

Hence, sinA= 4.8/6, with the help of trignometric ratios.

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The average rate of change for the given function f(x) = +3 from x = 2 to x = 5 is 1/3 (units: 1/x).

The average rate of change for a function f(x) over an interval [a,b] can be found by taking the difference between the function evaluated at the endpoints of the interval, a and b, and dividing it by the difference between the endpoints. This can be expressed mathematically as: Average Rate of Change = (f(b) - f(a))/(b-a).

In this case, the function provided is f(x) = +3, so the average rate of change from x = 2 to x = 5 can be calculated as:

Average Rate of Change = (f(5) - f(2))/(5-2)

= (3 + 3 - (3 + 2))/(5-2)

= (6 - 5)/(3)

= 1/3

The average rate of change from x = 2 to x = 5 is 1/3. (units: 1/x)

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The sοlutiοn set fοr the system οf equatiοns is {(0, 3), (3, 9)}

A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn in οne variable, typically in the fοrm οf ax² + bx + c = 0, where a, b, and c are cοnstants and x is the variable. The sοlutiοns tο the quadratic equatiοn are given by the quadratic fοrmula οr by factοring the equatiοn intο twο linear factοrs.

Tο find the sοlutiοn set fοr the system οf equatiοns shοwn, we need tο sοlve fοr the values οf x and y that satisfy bοth equatiοns simultaneοusly. Here are the steps:

Set the twο equatiοns equal tο each οther:

2x² - 4x + 3 = 2x + 3

Simplify the equatiοn by mοving all the terms tο οne side:

2x² - 4x - 2x = 3 - 3

2x² - 6x = 0

Factοr οut 2x frοm the left-hand side:

2x(x - 3) = 0

Use the zerο prοduct prοperty tο find the values οf x:

2x = 0 οr x - 3 = 0

x = 0 οr x = 3

Substitute each value οf x intο either equatiοn tο find the cοrrespοnding value οf y:

When x = 0: y = 2(0)² - 4(0) + 3 = 3

Sο οne sοlutiοn is (0, 3).

When x = 3: y = 2(3)² - 4(3) + 3 = 9

Sο the οther sοlutiοn is (3, 9).

Therefοre, the sοlutiοn set fοr the system οf equatiοns is {(0, 3), (3, 9)}.

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The C = -1/2 Substituting C in the above equation, we get,y = (½ - x)e^(-2x) + (x² - 1/2) e^(-2x) Thus the required solution of the given first-order linear differential equation is;y = (½ - x)e^(-2x) + (x² - 1/2) e^(-2x)Therefore, the symbolic expression for y(x) is given as;y = (½ - x)e^(-2x) + (x² - 1/2) e^(-2x)

The solution of the given first-order linear differential equation is given by the following steps below. Solve the first-order linear differential equation given below;dy da + 2y -3x2 – 3x + 1 y(0) = 0 y(x) = symbolic expression Solution:Given the first-order linear differential equation,dy da + 2y -3x2 – 3x + 1 y(0) = 0 ------(1)In order to solve this differential equation, we need to find the integrating factor (I.F).

To find I.F we use the following formula;I.F = e^(∫P(x) dx)where P(x) is the coefficient of y in the given differential equation.dy da + 2y -3x2 – 3x + 1------(1)Coefficients of y = 2Hence P(x) = 2∴ I.F = e^(∫2 dx)e^(∫2 dx) = e^(2x)

Multiplying both sides of equation (1) with e^(2x), we get,e^(2x)dy da + 2e^(2x)y - 3x²e^(2x) - 3xe^(2x) + e^(2x) = 0 Now, consider this expression as an exact differential equation, and rearrange as follows;d/dx(y e^(2x) - x²e^(2x)) = - e^(2x) + 3xe^(2x) - e^(2x) + 1d/dx(y e^(2x) - x²e^(2x)) = 2xe^(2x) - e^(2x) + 1 Integrating both sides of the above equation w.r.t x, we get;y e^(2x) - x²e^(2x) = ½ e^(2x) - x e^(2x) + x + C where C is the constant of integration On solving this equation, we get,y = (½ - x)e^(-2x) + (x² + C) e^(-2x)We have to find y(0) = 0,

hence on substituting x = 0 and y = 0 in the above equation, we get;0 = ½ + C therefore, C = -1/2 Substituting C in the above equation, we get,y = (½ - x)e^(-2x) + (x² - 1/2) e^(-2x)Thus the required solution of the given first-order linear differential equation is;y = (½ - x)e^(-2x) + (x² - 1/2) e^(-2x)Therefore, the symbolic expression for y(x) is given as;y = (½ - x)e^(-2x) + (x² - 1/2) e^(-2x)

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The answer is "x = xo + voxt, y = yo + voyt - 1/2gt^2."

The set of equations that describe the x and y positions of a particle as a function of time is:x = xo + voxt, y = yo + voyt - 1/2gt^2.An object of mass m is in free fall. It is necessary to describe the x and y positions of the particle as a function of time. These positions are dependent on the time taken to reach each position during the free fall.Therefore, we can write the positions in terms of the initial position, velocity, acceleration due to gravity, and time. The set of equations that describes the x and y positions of the particle is:x = xo + voxt, y = yo + voyt - 1/2gt^2Where,x = x-coordinate of the particle at time t.xo = initial position of the particle in the x direction.vo = velocity of the particle in the x direction.t = time elapsed since the initial time.y = y-coordinate of the particle at time t.yo = initial position of the particle in the y direction.voy = velocity of the particle in the y direction.g = acceleration due to gravity. (taken as -9.8 m/s²)Therefore, the answer is "x = xo + voxt, y = yo + voyt - 1/2gt^2."

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As per the volume, the distance between the centroid of the semicircular region and the x-axis is 2.

In this case, the region being revolved is the semicircular region bounded by y = √(r²− x²) and the x-axis. Its area can be found using the formula for the area of a circle, divided by two, which is π r²/2.

The distance traveled by the centroid during the revolution is simply the distance between the centroid of the semicircular region and the x-axis, which is equal to the radius r.

So, using the Theorem of Pappus, we have:

Volume of the solid sphere = (Area of semicircular region) x (Distance traveled by centroid)

4/3 π r³ = (π r²/2) x r

Simplifying this equation, we get:

4/3 π r³ = 2/3 π r³

Dividing both sides by π r³/3, we get:

4 = 2/3 d

Where d is the distance between the centroid of the semicircular region and the x-axis. Solving for d, we get:

d = 6/3 = 2

This means that the centroid of the semicircular region is located at a height of 2 units above the x-axis.

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Complete Question:

Use the Theorem of Pappus and the fact that the volume of a sphere of radius r is 4/3 π r³ to find the centroid of the semicircular region bounded by the curve y = √(r²− x²) and the x -axis.

53. tan2x - 1 = 0  

x = 0, 180  

54. tan x + 1 = 0  

x = -1  

55. 2 cos x + V3 = 0  

x = -V3/2  

56. 2 cos x - V3 = 0  

x = V3/2  

57. cot x = 1  

x = 0, 180

58. cot x = -1  

x = 90, 270

59. sin x(1 + 2 cos x) = 0  

x = 0, 180, 360  

60. cos x(1 - 2 sin x) = 0  

x = 0, 90, 270  

61. tan x cos x = tan x  

x = 0, 90, 180, 270  

62. cot2x = 1  

x = 0, 90, 180, 270

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Answer:

x = 9

Step-by-step explanation:

8.88 = 4.44 (x-7)

8.88 = 4.44x - 31.08

39.96 = 4.44x

x = 9

Answer:

x = 9

Step-by-step explanation:

[tex]8.88 = 4.44 (x-7)[/tex]

Divide both sides by 4.44.

[tex]2 = x-7[/tex]

Add 7 to each side and switch sides.

[tex]9 = x\\x = 9[/tex]

Answer:

Null, alternative

Step-by-step explanation:

803.84 [tex]in^{2}[/tex] plastic laminate is needed to cover the top of the table. The solution has been obtained by using area of circle.

What is area of circle?

The area of a circle is the region that its circumference encloses or encompasses. Its unit of measurement is the square.

We are given that a round crafts table has a diameter of 32 inches.

We know that the area of circle is given by the following:

Area = π[tex]r^{2}[/tex]

The radius is half of the diameter which means that

Diameter = 2r

Now, using this we get

⇒Area = π [tex](\frac{32}{2})^{2}[/tex]

⇒Area = π ([tex]16^{2}[/tex])

⇒Area = 256π

⇒Area = 256 * 3.14

⇒Area = 803.84 [tex]in^{2}[/tex]

Hence, 803.84 [tex]in^{2}[/tex] plastic laminate is needed to cover the top of the table.

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The degrees of freedom (df) for the regression sum of squares, the error sum of squares, and the total sum of squares can be calculated using the following formula:

df = n - k - 1

where n is the sample size and k is the number of independent variables in the regression model.

Since the model includes 8 independent variables, k = 8. The sample size is given as n = 166.

Therefore, the degrees of freedom for the regression sum of squares, the error sum of squares, and the total sum of squares are:

df for the regression sum of squares = k = 8

df for the error sum of squares = n - k - 1 = 166 - 8 - 1 = 157

df for the total sum of squares = n - 1 = 166 - 1 = 165

Hence, the degrees of freedom for the regression sum of squares, the error sum of squares, and the total sum of squares are 8, 157, and 165, respectively

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