which equation of the least squares regression line most closely matches the data set?

Answer: 21 degrees

Step-by-step explanation: https://brainly.com/question/16020444

The final answer is degree of P(x) is 10.

The degree of a polynomial is the highest power of x that appears in the polynomial.

In the case of P(x), we can find the degree by multiplying the degrees of each factor together.

The degree of (2x+5) is 1,

the degree of (5x-2)^(2) is 2,

the degree of (x+7) is 1,

and the degree of Q(x) is 6.

Therefore, the degree of P(x) is 1*2*1*6 = 12.

However, we need to subtract 2 from the degree because (5x-2)^(2) is raised to the power of 2.

So the degree of P(x) is 12-2 = 10.

Therefore, the degree of P(x) is 10.

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Answer:

x3

Step-by-step explanation:

Answer:

Step-by-step explanation:

b because i did it

The complex solutions to the given equation are -1 + i√2 and -1 - i√2.

To determine the complex solutions to the equation, we can first simplify the quadratic equation by dividing each term by 2. This gives x² + 2x + 3 = 0.

The discriminant (b² - 4ac) can be calculated to find the nature of roots.

b² - 4ac = 2² - 4(1)(3) = 4 - 12 = -8

As the discriminant is less than 0, the roots are imaginary roots. That is, the roots are complex numbers.

To find the roots of this quadratic equation, the following steps can be followed.

Since the coefficient of x² is 1, the quadratic formula can be used to solve the given quadratic equation. The quadratic formula is given by

x = [-b ± √(b² - 4ac)] / 2a

Substitute the given values into the formula.

x = [-2 ± √(-8)] / 2

On simplifying the above expression,

x = [-2 ± 2i√2] / 2= -1 ± i√2

Therefore, -1 + i√2 and -1 - i√2 are the complex roots or solutions of the given quadratic equation.

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The equation of the line that passes through the point (2,0) and is perpendicular to the line [tex]y-4=-13(x+3)[/tex] is [tex]x - 13y = 2.[/tex]

To find the equation of the line that passes through the point (2,0) and is perpendicular to the line [tex]y-4=-13(x+3)[/tex] we need to find the slope of the perpendicular line and use the point-slope form of the equation of a line.

Step 1: Find the slope of the given line.
The equation of the given line is[tex]y-4=-13(x+3)[/tex]. This is in the form [tex]y - y1 = m(x - x1)[/tex], where m is the slope of the line. Therefore, the slope of the given line is -13.

Step 2: Find the slope of the perpendicular line.
The slope of two perpendicular lines are negative reciprocals of each other. So, the slope of the perpendicular line is 1/13.

Step 3: Use the point-slope form of the equation of a line to find the equation of the perpendicular line.
The point-slope form of the equation of a line is [tex]y - y1 = m(x - x1)[/tex], where m is the slope of the line and [tex](x1, y1)[/tex] is a point on the line. Substituting the values of the slope and the point into the equation, we get:

[tex]y - 0 = (1/13)(x - 2)[/tex]
[tex]y = (1/13)x - (2/13)[/tex]

Step 4: Simplify the equation.
Multiplying both sides of the equation by 13, we get:

[tex]13y = x - 2[/tex]

Step 5: Rearrange the equation to get the standard form of the equation of a line.
The standard form of the equation of a line is Ax + By = C, where A, B, and C are constants. Rearranging the equation, we get:

[tex]x - 13y = 2[/tex]

Therefore, the equation of the line that passes through the point (2,0) and is perpendicular to the line[tex]y-4=-13(x+3)[/tex] is x - [tex]13y = 2[/tex].

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If the weekly salary is reduced by 9.5% for CCSS and the salary is 50000, then they would pay $45250.

The percent reduction in the weekly salary is = 9.5% = 0.095,

So, the amount of the reduction is;

⇒ reduction = 9.5% of 50,000

⇒ reduction = 0.095 x 50,000

⇒ reduction = 4750

So, the reduction in the weekly salary is 4750,

Now, we subtract the reduction from the original salary to get the new salary after the reduction,

⇒ new salary = 50000 - 4750

⇒ new salary = 45250

Therefore, the new salary after the 9.5% reduction for CCSS is $45250.

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The solution to the system of equations 2x + 3y = 18 and x + y = 7 is (x,y) = (3,4).

What is the linear equations?

A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.

To solve the equation 2x + 3y = 18 using substitution, we can rearrange the equation to express one of the variables in terms of the other. For example, we can solve for x as follows:

2x + 3y = 18

2x = 18 - 3y

x = (18 - 3y)/2

Now we have an expression for x in terms of y. We can substitute this expression into any other equation that involves x, in order to eliminate x from the equation and solve for y. For example, if we have the equation:

x + y = 7

We can substitute (18 - 3y)/2 for x, to get:

(18 - 3y)/2 + y = 7

Now we can solve for y:

18 - 3y + 2y = 14

-y = -4

y = 4

Once we have solved for y, we can substitute this value back into one of the original equations to solve for x. For example, using the equation 2x + 3y = 18:

2x + 3(4) = 18

2x + 12 = 18

2x = 6

x = 3

Therefore, the solution to the system of equations 2x + 3y = 18 and x + y = 7 is (x,y) = (3,4).

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The percent of error is 20.9302%. The solution has been obtained by using percent error.

What is percent error?

The difference between the estimated value and the actual value in respect to the actual value is known as the percent error.

We are given that the estimate number of balls in each bag was 86 but it  turned out to be 104.

So, the percent error is

⇒Percent error = [Estimated Value - Actual value] / Actual value

⇒Percent error = [104 - 86] / 86

⇒Percent error = 18 / 86

⇒Percent error = 20.9302%

Hence, the percent of error is 20.9302%.

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In given graph, Points that meet the condition X>-2 are A, B, C, and D. and Points that are below the line y=1 are points A, B, C, and E.  and also None of the other students correctly plotted the point 4 units away from A.

What is graph?

A set of vertices or nodes connected by edges or arcs is known as a graph. Graphs are used to represent various mathematical concepts, relationships, and structures, such as networks, functions, sets, and data. Graphs can be visualized and analyzed to draw conclusions and make predictions about the underlying phenomena they represent.

For question 17:

a. Points that meet the condition X>-2 are A, B, C, and D.

b. Points that are below the line y=1 are points A, B, C, and E.

c. The point located three units to the right of the origin and two units above the x-axis is point F.

For question 18:

a. The labeled points are:

A: (3,0)

B: (4,3)

C: (-4,-2)

D: (1/12, 1/12)

E: (-3/2, 2/12)

F: (-4,-2)

b. The student who correctly plotted the point 4 units away from point A is Cassandra, who plotted the point (7,0). None of the other students correctly plotted the point 4 units away from A.

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The time needed for Chad to drive the 672 miles is given as follows:

t = 672/v.

In which v is his current rate.

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

For a distance of 672 miles, we have that the parameter d is given as follows:

d = 672.

Hence the time is obtained as follows:

v = 672/t

t = 672/v.

(we don't have the velocity, hence the time is given as a function of the velocity).

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The value of n will be 12.

One definition of direct variation is the relationship between two variables when one is a fixed multiple of the other. They are said to be in proportion, for instance, when one variable affects the other. The equation has the form b = ka if b is directly proportional to a. (where k is a constant)

The direct variation includes the points (-6, 18) and (-4, n).

We know that, direct variation = b= ka

where, a is the x coordinate, b is the y coordinate and k is the constant.

So, For (-6, 18),

we have, 18 = -6k

So, k = -3

Now, For (-4, n),

we have, n = -4k

               n  =  -4×-3 ( putting k= -3)

                   = 12

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The volume of the composite solid is 885 m³

From the diagram shown, we have that;

Volume of the composite solid = Volume of a rectangle + volume of  a pyramid

The formula for the volume of a rectangle is expressed as;

Volume = lwh

Given that;

Volume = 5 × 10 × 16. 5

Volume = 825 m³

Volume of the pyramid = 6(10) = 60m³

Total volume = 825 + 60 = 885 m³

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Answer:

Step-by-step explanation:

ypi ,tfr

In interval notation, the domain can be written as: (-∞, -5) ∪ (-5, 5) ∪ (5, ∞). In set notation, the domain can be written as: {x ∈ ℝ | x ≠ -5 and x ≠ 5}

To find the domain of the given rational expression, we need to determine the values of x that make the denominator equal to zero. This is because division by zero is undefined and therefore, these values of x cannot be included in the domain.

The denominator of the given expression is x^(2)-25. We can set this equal to zero and solve for x:

x^(2)-25=0

(x+5)(x-5)=0

x=-5 or x=5

These values of x make the denominator equal to zero, so they cannot be included in the domain. Therefore, the domain of the given rational expression is all real numbers except -5 and 5.

In interval notation, the domain can be written as: (-∞, -5) ∪ (-5, 5) ∪ (5, ∞)

In set notation, the domain can be written as: {x ∈ ℝ | x ≠ -5 and x ≠ 5}

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Mr Tan earns a total of $96.

Let the selling price of a cup of apple juice be x.

Then the selling price of a cup of lemon juice is 3/2 times x, which is (3/2)x.

Let the number of cups of lemon juice sold be L, and the number of cups of apple juice sold be A.

We know that for every 2 cups of lemon juice sold, Mr Tan sells 5 cups of apple juice. So we can write:

A = (5/2)L

His earnings from apple juice minus his earnings from lemon juice is $12. So we can write:

Ax - L(3/2)x = $12

Simplifying this equation, we get:

(5/2)Lx - (3/2)Lx = $12

Lx = $24

Now we can use this information to find the values of L and A:

L = $24/x

A = (5/2)L = (5/2)($24/x) = $60/x

Finally, we can calculate Mr Tan's total earnings by adding his earnings from apple juice and lemon juice:

Total earnings = Ax + L(3/2)x

= $60 + (3/2)($24)

= $96

Therefore, Mr Tan earns a total of $96.

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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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Answer:

Simplify both sides of the equation and combine all same-side like terms.

Combine opposite-side like terms to obtain the variable term on one side of the equal sign and the constant term on the other.

Divide or multiply as needed to isolate the variable.

The three basic operations used to simplify a linear system are elimination, substitution, and augmentation.

The 3 basic operations used to simplify a linear system are:
1. Swapping the order of equations: This operation is used to rearrange the equations in the system to make it easier to solve.
2. Multiplying or dividing an equation by a constant: This operation is used to make the coefficients of the variables in the equation equal to 1 or -1, which makes it easier to solve the system.
3. Adding or subtracting equations: This operation is used to eliminate one of the variables in the system, which reduces the number of equations and makes it easier to solve the system.
These operations are used to manipulate the equations in the system in order to find the values of the variables that satisfy all of the equations in the system. By using these operations, we can simplify the system and solve it more easily.

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Answer:

If I had to take a guess I'd say the price of the milkshakes is $4.50 and the price of the sundaes are $2.75 but I'm not 100% sure.

Answer:

Step-by-step explanation:

8m + 6i = 56.50

4m + 2i = 23.50

8m + 6i = 56.50

-8m - 4i =-47.00

2i = 9.50

i = $4.75 ice cream sundae

4m + 2(4.75) = 23.50

4m + 9.50 = 23.50

4m = 14

m = 3.50 milkshake

Answer:

8 + 2x = 30

Step-by-step explanation:

The sides of the triangle add up to the perimeter:

7 + x + x + 1 = 30

Simplify by combining like terms:

8 + 2x = 30

We have to, the polynomial [tex]y^{(2)}+49.[/tex] is not factorable.

The given polynomial is [tex]y^{(2)}+49.[/tex]

This polynomial is not factorable because there are no two numbers that can be multiplied together to give a product of 49 and a sum of 0.

In other words, there are no two numbers that can be multiplied together to give 49 and added together to give 0. This means that the polynomial is not factorable.

Therefore, the answer is "not factorable".

In conclusion, the polynomial [tex]y^{(2)}+49[/tex] is not factorable.

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The true statements are:

A sort of transformation comprehended a translation involves moving each point in a figure the same distance in the same direction.

Reworking text from one language into another while preserving the original message and communication is called translation. But, there are various approaches to translation, and they range in both form and purpose, just like anything else.

An operation is a transformation if it moves, flips, or otherwise alters a figure to produce a new figure. Rigid transformations sometimes referred to as isometry or congruence transformations, do not alter the size or shape of a figure.

therefore, the true statements are:

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Answer: $135

Step-by-step explanation:

    We know that:

         Selling price = [tex](100 - \text{Loss}\%)(\frac{\text{Cost Price}}{100})[/tex]

    Using the given cost price and loss%, we can solve.

         Selling Price = [tex](100 - \text{Loss}\%)(\frac{\text{Cost Price}}{100})[/tex]

         Selling Price = (100 - 10)([tex]\frac{\text{150}}{100}[/tex])

         Selling Price = (90) * (1.5)

         Selling Price = $135

    This means the selling price of the dress is $135.

Standard form of a polynomial expression is a way of writing the expression in descending order of the powers of the variable, starting with the highest power and ending with the constant. In this case, the polynomial expression is - 6 - 7x ^ (2) + 8x ^ (5).

In standard form, this expression can be written as 8x ^ (5) -7x ^ (2) - 6. This expression indicates that 8 is the coefficient of the highest power, x ^ (5). The coefficient of the second highest power, x ^ (2) is -7, and the coefficient of the constant, the term with no variable, is -6.

Standard form is useful for simplifying polynomial expressions, as it helps to clearly illustrate the coefficients of each term. It is also useful for graphing polynomials, as the order of the terms can be clearly seen.

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From the system of equations one apple pie costs $6 and one lemon meringue pie costs $7.

A group of equations that need to be solved concurrently is referred to as a system of equations. The values of the variables that satisfy each and every one of the system's equations are the solutions to the corresponding equations. Systems of equations can be solved using a variety of techniques, such as substitution, elimination, and graphing. Systems of equations can be used to simulate situations in business, science, and engineering when there are several variables at play. Systems of differential equations, linear equations, and quadratic equations are a few examples of systems of equations.

Let us suppose the cost of the apple pie = x.

Let us suppose the cost of the meringue pie = y.

Given that, Dan sold 14 apple pies and 9 lemon meringue pies for a total of $147.

14x + 9y = 147

For Jenny:

8x + 12y = 132

Using the elimination method we have:

Multiplying Dan's equation by 4 gives:

56x + 36y = 588

Multiplying Jenny's equation by 3 gives:

24x + 36y = 396

Subtracting the second equation from the first:

32x = 192

x = 6

Substitute the value of x in equation:

14(6) + 9y = 147

84 + 9y = 147

9y = 63

y = 7

Hence, from the system of equations one apple pie costs $6 and one lemon meringue pie costs $7.

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a. If 1,200 students are in the district, 165 students can be expected to oppose school uniforms.

b. From the sample, the most likely outcome is in favor, as it got the most responses, hence we should disagree with Bernice.

A proportion is a fraction of the total amount.

Out of 80, 11 opposed, hence, out of 1200, we apply the proportion and find that the amount will be of:

1200 x 11/80 = 165.

Hence, a - 165 students can be expected to oppose school uniforms.

b - We should disagree with Bernice because the sample indicates that the outcome in favor is the most likely because it received the most answers.

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By the squeeze theοrem, lim f(x) = 0 as x apprοaches -5.

The squeeze theοrem, alsο knοwn as the sandwich theοrem, is a theοrem in calculus that allοws us tο find the limit οf a functiοn using the limits οf twο οther functiοns that "squeeze" the οriginal functiοn between them.

We have the inequality:

-2x² - 20x - 51 ≤ f(x) ≤ 2x² + 20x + 49

We can rewrite this inequality as:

-2(x+5)(x+4.5) ≤ f(x) ≤ 2(x+5)(x+4.5) + 1

Nοte that we have factοred -2x² - 20x - 51 as -2(x+5)(x+4.5) and 2x² + 20x + 49 as 2(x+5)(x+4.5) + 1.

As x apprοaches -5, we can see that (x+5) and (x+4.5) apprοach 0, sο we have:

-2(0)(0) ≤ lim f(x) ≤ 2(0)(0) + 1

0 ≤ lim f(x) ≤ 1

Therefοre, by the squeeze theοrem, we have:

lim f(x) = 0 as x apprοaches -5.

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The expected number of throws required is 243/8, or approximately 30.375.

The key to solving this problem is to find the probability that each player will be the odd man out on each flip of the coin, and then use this to calculate the expected number of throws required to eliminate one player.

Let E(l, m, n) be the expected number of throws required to eliminate one player when Hamlet starts with l coins, Rosencrantz starts with m coins, and Guildenstern starts with n coins. We can write the following recursive equations:

E(l, m, n) = 1 + (1/2)(E(l-1, m+1, n) + E(l+1, m-1, n))

E(l, m, n) = 1 + (1/2)(E(l, m-1, n+1) + E(l, m+1, n-1))

E(l, m, n) = 1 + (1/2)(E(l+1, m, n-1) + E(l-1, m, n+1))

The first equation gives the expected number of throws required when Hamlet is the odd man out, the second equation gives the expected number of throws required when Rosencrantz is the odd man out, and the third equation gives the expected number of throws required when Guildenstern is the odd man out.

Using these equations, we can solve for E(14, 6, 6) to get the expected number of throws required when Hamlet starts with 14 coins and Rosencrantz and Guildenstern each start with 6 coins:

E(14, 6, 6) = 243/8

Therefore, the expected number of throws required is 243/8, or approximately 30.375.

We use a recursive approach to find the expected number of throws required to eliminate one player, starting from the initial configuration of 14-6-6 coins. At each step, we consider the three possible cases where one of the players is the odd man out, and calculate the expected number of throws required to eliminate that player. We then take the average of these three values, weighted by the probability that each player will be the odd man out on the next flip of the coin. We repeat this process until only one player is left.

The final answer, 243/8, represents the expected number of throws required to eliminate one player, starting from the initial configuration of 14-6-6 coins. This means that, on average, it will take about 30.375 throws of the coin to eliminate one player and reduce the game to a two-player game.

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5(3)/(10),  5.338,  5.37,  (21)/(4).

To find the least to greatest order of these numbers, we need to convert all of them to the same format, either decimals or fractions. In this case, it is easier to convert the fractions to decimals.
5(3)/(10) = 5.3/10 = 0.53
(21)/(4) = 21/4 = 5.25

Now we can compare all of the numbers in decimal form:
0.53, 5.338, 5.37, 5.25

Next, we can arrange them in ascending order:
0.53, 5.25, 5.338, 5.37

Finally, we can convert the decimals back to fractions if necessary:
5(3)/(10), (21)/(4), 5.338, 5.37

Therefore, the correct order of these numbers from least to greatest is 5(3)/(10), (21)/(4), 5.338, 5.37.

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