Math question
finding the slope

The mean of the squared deviations

What is Squared deviations?

The sum of all scores' squared deviations from the mean is lower than the sum of all scores' squared deviations from any other number. The least squares concept governs this.

What is Mean ?

The average of a group of values is referred to as the mean. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

The term "mean square" refers to the sample variance in the analysis of variance (ANOVA) table, which calculates the mean squared deviation.

The average of the deviations' squared

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The zeros of the expression 3x² + 5x - 2 are 1/3 and -2

A quadratic equation can simply be defined as an algebraic equation having the second degree of x.

From the information given, we have that;

3x² + 5x - 2

Equate the expression to zero

3x² + 5x - 2 = 0

Find the pair factors of -6 that sum up to + 5, we get;

+ 6 and -1

Substitute the values into the equation;

3x² + 6x - x - 2 = 0

Enclose in brackets

(3x² + 6x) - ( x - 2) = 0

Factor the common terms

3x( x + 2) - 1( x + 2)

Then,

3x - 1 = 0

x = 1/3

x +2 = 0

x = -2

Hence, the values are 1/3 and -2

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The timeline that represents when the constitution of unites states was written and ratified is 1787 and 1788

What is a timeline?

A timeline is a visual representation of a sequence of events in time. It usually takes the form of a graphic with a long bar with dates paralleling it, usually indicating current occurrences.

We are given a timeline and we have to represent the tine when united states constitution was written and ratified

Now the constitution of united states was written in 1787.

And was ratified in 1788

Now we have to represent this point on the timeline

To do that we use graph

we get,

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Answer:

Step-by-step explanation:3

For the given function the zeroes will be 0,-11/2, and 11 while the degree of the function is 5.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

T(h)=h(2h+1)²(h-11)²

The function is simplified as,

T(h)=h((2h)²+1²+2(2h)(1))(h²+121-22h)

T(h)=h[4h²+1+4h](h²+121-22h)

T(h)=(h³+121h-22h²)(h²+121-22h)

From the above function, it is observed that the degree of the given function is 5.

The zeroes of the given function are obtained as,

T(h)=h(2h+1)²(h-11)²

T(h)=0

h = 0

(2h+1)²=0

2h+1=0

h= -1/2

(h-11)²=0

h=11

Thus, for the given function the zeroes will be 0,-11/2, and 11 while the degree of the function is 5.

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The value of the product of the numbers 10 and 2/3 is less than 10. Then the correct option is C.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The numbers are given below.

10 and 2/3

The product of the numbers 10 and 2/3 will be given as,

⇒ 10 x 2 / 3

⇒ 20 / 3

⇒ 6.67

The value of the product of the numbers 10 and 2/3 is less than 10. Then the correct option is C.

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Polar form of complex numbers is z=a+bi is

z = r(cosθ + i sinθ) . So, first find the absolute value of r and then argument θ. Polar form of given expression are

a) 7(√3/2 + i/2 )

b) 7(√3/2 - i/2)

c) 14(√3/2 + i/2)

d) 14(√3/2 - i/2)

The polar form of complex numbers is a different way of representing complex numbers than the orthogonal form. Complex numbers are usually represented in the form z = x+iy. where "i" is an imaginary number. But in polar form, complex numbers are represented as a combination of modulus and argument.

Problems Algebra Convert to polar form

a) 7(cos(30°) + i sin(30°))

we simplify each term.

The exact value of cos(30°) = √3/2

=> 7((√3/2) + i sin(30°))

The exact value of sin(30°) = 1/2

=> 7(√3/2 + i/2 )

Combine all values we get, 7(√3/2 + i/2 )

7(cos(330°) + i sin(330°))

Using quadrant system

b) cos(330°) = cos(360°- 30°) = cos 30° = √3/2

sin(330°) = sin(360°- 30°) = - sin 30° = -1/2

so, 7 ((√3/2) + i(-1/2))

= 7√3/2 - 7i/2 = 7(√3/2 - i/2)

c) 14(cos(30°) + i sin(30°))

= 14 ((√3/2) + i (1/2)) = 14√3/2 + 14i/2=14(√3/2 - i/2)

d) 14(cos(330°) + i sin(330°))

= 14 (√3/2) + 14i(-1/2) = 14√3/2 - 14i/2

= 14(√3/2 - i/2)

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Answer:

14(cos(330o) + i sin(330o))

Step-by-step explanation:

Cost of another 3 panes of class is 7.95

Given, Number of panes of glass bought = 8

Cost of 8 panes of glass = $21.20

Number of broken panes of glass = 3

We must determine the price of three glass panes.

By unitary method, If 8 panes of glass costs $21.20 , then the cost of one pane of glass will be as follows,

Cost of one pane of glass = 21.20/8

                                            = $2.65

Therefore,  cost of  3 panes of glass it would be $2.65×3 = 7.95

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.

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Answer:

x³ -6x² +11x-6

Step-by-step explanation:

as there are three zeros visible, we assume the function is cubic. It can be written in the form ax³ +bx²+cx +d. Another form of writing a function is by making the brackets (x-x0), where x0 is the zero of the function (the value of the function for x0 is equal zero):  a(x-1)(x-2)(x-3) (I assumed a is 1). By multiplying the brackets, you got the answer.

Answer:

3 years

Step-by-step explanation:

we can use the equation 14+3x=8+5x to determine when they will be they same height. X I'd

∫[tex]r(t)dt=[/tex][tex](0,t,\frac{t^2}{2} )+c[/tex] is accurate in its statement.

A definite integral whose limits are functions of the differential variable can be differentiated using Newton Leibniz Theorem's formula. Differentiation under the integral sign is another name for this. When limits are functions of the differential variable, the Newton Leibniz Theorem makes it simple to handle problems involving the differentiation of a definite integral.

Suppose that F(x) is a function whose derivative is f(x). Consequently, abf(x) dx = F(b) - F (a).

The Newton Leibniz Theorem can be used to determine the derivative of a definite integral when the limits of a definite integral are functions of t and the integrands are functions of x or vice versa.

As a result, statement C is the appropriate response.

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Answer:

Therefore, the equation of the line that is parallel to the given line and passes through the point ( − 6 , 9 ) (−6,9) is y = 4x + 33.

Step-by-step explanation:

To find the equation of a line that is parallel to a given line and passes through a given point, you can use the point-slope form of a linear equation. The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

Where (x1, y1) is the point through which the line passes, and m is the slope of the line.

The slope of a line is given by the difference in the y-coordinates of two points on the line, divided by the difference in the x-coordinates of those points. The slope of a line is also the coefficient of the x-term in the standard form of a linear equation (y = mx + b).

In this case, the given line is x − 6y = −60 − 9x. To find the slope of this line, you can rearrange the equation to standard form:

x − 6y = −60 − 9x

−9x + x − 6y = −60

−8x − 6y = −60

y = 4x + 15

The slope of this line is m = 4.

To find the equation of a line parallel to this line that passes through the point ( − 6 , 9 ) (−6,9), you can use the point-slope form of a linear equation with (x1, y1) = ( − 6 , 9 ) (−6,9) and m = 4:

y - 9 = 4(x - (-6))

y - 9 = 4(x + 6)

y - 9 = 4x + 24

y = 4x + 33

Answer: -4/3x—2

Step-by-step explanation:

Answer: An ISOSCELES triangle.

Step-by-step explanation:

It has two sides of equal length.

The angles opposite to the equal sides are also equal in measure.

The function lim x-->a [sin(x) + a₀ + a₁x + ...+ aₙxⁿ ] has lim x-->a [sin(a) + a₀ + a₁a + ...+ aₙaⁿ] as the limit of the function as x approaches a.

Generally, To evaluate the limit of a function as x approaches a certain value, we need to substitute the value of x with the limit value and see what the function evaluates to.

In this case, we have:

lim x-->a [sin(x) + a₀ + a₁x + ...+ aₙxⁿ]

Substituting x with a, we get:

lim x-->a [sin(a) + a₀ + a₁a + ...+ aₙaⁿ]

This is the limit of the function as x approaches a.

Note that the terms a₀, a₁x, etc. are constants and will not affect the limit of the function. Therefore, the limit of the function as x approaches a is simply sin(a).

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Answer:

y = 51.2

Step-by-step explanation:

y/32=16/10

First, we time 32 on both sides to get y alone

y = 32(16/10)

y = 32(1.6)

y = 51.2

Let's check:

51.2/32 =  16/10

1.6 = 1.6

The answer y = 51.2 is correct!

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Therefore,  the solution to  this question of equation is the correct answer is option A.

Either identity equations or conditional equations classify an equation. Every value of the variables has a corresponding identity. Only particular values of the variables are valid for a conditional equation. The equals symbol ("="), which divides two expressions, denotes an equation.

Here,

Given :

Equation : 70%(p + 3.6) = 70%p + 2.52

This equation matches the option A)

The amount the school district gets in federal aid for 70% of p students for 2.52 months.

Therefore correct option for the equation 70%(p + 3.6) = 70%p + 2.52 is option A)

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Answer:

(b)

Step-by-step explanation:

According to the triangle inequality, the sum of any 2 sides of a triangle must be greater than the third side. The only case that satisfies this is option (b)

Tests are frequently used to initially determine and assess potential worker safety and health issues.

The following factors are essential to a good workplace safety and health program: Leadership and management commitment. Accountability. Concern for safety.

An idea or rule that directs behaviors, processes, or tools with the goal of reducing the possibility or incidence of harm to people, property, or the environment.

In order to protect people's bodily, mental, and material health as well as the community's overall wellbeing, safety is the condition in which risks and circumstances that could cause harm are under control. It is a necessity for daily existence and is required by both individuals and communities in order to realize their objectives.

Workplace safety procedures are established practices that describe how to carry out duties with the least amount of danger to people, property, and working conditions. The processes cover work-related duties that deal with safety issues, safety gear, and work-area safety precautions.

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By using the given information we can prove that  m ∠ABC = m ∠EDC.

What are similar angles?

Polygons' corresponding sides and corresponding angles are compared as part of the geometric tests for congruence and similarity. With care taken to maintain the order of adjacency, each side and each angle in one polygon is paired with a side or angle in the other polygon in these tests.

Given:

m ∠1 = m ∠2

m ∠2 = m ∠4

We have to prove that m ∠ABC = m ∠EDC

Let, ∠ABC = ∠1 + ∠2

and  ∠EDC = ∠3 + ∠4

So, m ∠ABC = m ∠1 + m ∠2

and  m ∠EDC = m ∠3 + m ∠4

From the given information,

m ∠1 + m ∠2 = m ∠3 + m ∠4        (Since m ∠1 = m ∠3,  m ∠2 = m ∠4)

⇒ m ∠ABC = m ∠EDC

Hence, by using the given information we can prove that  

m ∠ABC = m ∠EDC.

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The scatter chart indicates that there is a positive relationship between profits and market capitalization. This means that as profits increase, market capitalization also tends to increase.

The covariance between two variables is a measure of how much the variables tend to change together. A positive covariance indicates that the variables are positively related, which means that as one variable increases, the other tends to increase as well. In this case, a positive covariance between profits and market capitalization indicates that the two variables are positively related.

The correlation coefficient is a measure of the strength of the relationship between two variables. A correlation coefficient of 1 indicates a perfect positive relationship, while a coefficient of -1 indicates a perfect negative relationship. A coefficient of 0 indicates that there is no relationship between the variables. In this case, the correlation coefficient of 0.8229 indicates that there is a strong positive linear relationship between profits and market capitalization.

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The probability that thickness of coin A will exceed thickness of coin B is 0.3905

Here, we are given that the distribution of x1 is n(1, 0.0004) and the distribution of x2 is n(1.01, 0.0009), that is-

X1 ~ N (1,0.0004) and X1 ~ N(1.01,0.0009)

Now, if a coin battery is selected at random,

The probability that the thickness of coin battery a will exceed the thickness of coin battery b = P(X1 > X2 )

It can be rewritten as follows,

P(X1-X2 > 0)

Let Y = X1-X2

The Y ~ N (1-1.01, 0.0004 + 0.0009)

i.e Y ~ N (-0.01, 0.0013)

= P(Z > 0.278)

= 0.3905

Thus, the probability that thickness of coin A will exceed thickness of coin B is 0.3905

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The solution to each of the system of equations is given as follows:

11. (1,-1).

13. (-6,-5).

15. (-4,3).

For item 11, the system is given as follows:

The variable x can be isolated as follows:

Then the solution for y is given as follows:

y + 6  = 3 - 2y

3y = -3

y = -1.

Then the solution for x is of:

5x = -1 + 6

5x = 5

x = 1.

Following the same procedure, in item 13, we have that:

Hence the solution for x is of:

6x + 21 = 4x + 9

2x = -12

x = -6.

The solution for y is of:

3y = 4(-6) + 9

3y = -15

y = -5.

For item 15, we have that:

Hence the solution for y is of:

5 - 3y = -6y + 14

3y = 9

y = 3.

Then the solution for x is of:

x = 5 - 3(3)

x = 5 - 9

x = -4.

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The simplified form of the expression is  5x^3y^3(3x − 9y)

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operators.

between 15 and 45  the common factor is 5

between x^3 and x^4 common factor is x^3

between y^3 and y^4 common factor is y^3

Multiplying the common factors together e have 5x^3y^3

so that the expression becomes  5x^3y^3(3x - 9y)

In conclusion the 5x^3y^3(3x - 9y) is the other form of the expression with their common factors.

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Answer:

The simplified form of the expression is  5x^3y^3(3x − 9y)

Step-by-step explanation:

Answer: 3ft to 1cm

Step-by-step explanation:

After subtracting 2/5 from 5/7, the resultant fraction is 11/35.

A fraction, which also symbolizes a piece of a whole, is a mathematical symbol for any number of equal parts.

When expressed in common English, a fraction, such as one-half, eight-fifths, or three-quarters, specifies the number of components of a specific size. In a simple fraction, both are integers.

In a complex fraction, a fraction can be found in either the numerator or the denominator.

A suitable fraction has a numerator that is less than its denominator.

So, we have:

5/7 and 2/5

Now, perform subtraction as follows:

5/7 - 2/5

5*5 - 7*2/35

25 - 14/35

11/35

Therefore, after subtracting 2/5 from 5/7, the resultant fraction is 11/35.

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Correct question:

Subtract. 5/7−2/5 enter your answer as a fraction in simplest form by filling in the boxes.

Answer:

A) 2

Step-by-step explanation:

5x - 12 = -2  Add 12 to both sides

5x - 12 + 12 = -2 + 12

5x = 10  Divide both sides by 5

[tex]\frac{5x}{5}[/tex] = [tex]\frac{10}{5}[/tex]

x = 2

Answer:

[tex] \sf \: (a) \: 2[/tex]

Step-by-step explanation:

Given equation,

→ 5x - 12 = -2

Now the value of x will be,

→ 5x - 12 = -2

→ 5x = -2 + 12

→ 5x = 10

→ x = 10/5

→ [ x = 2 ]

Hence, the value of x is 2.