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The ordered pairs that represent the linear function is Option A, B and C.

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. If the function has more variables, they should all be constants or known variables in order for the function to continue to function as a linear function.

To determine which ordered pairs represent a linear function we use the equation of slope.

The slope is given as:

m = (y2 - y1) / (x2 - x1)

Option A:

m = (5 - 8) / (-4 + 8) = -3 / 4

m = (2 - 5) / (0 + 4) = -3/ 4

The slopes between the consecutive points are same hence option A represents a linear equation.

Similarly, for option B:

m = (1 + 2) / (2 + 1) = 1

m = (4 - 1) / (5 - 2) = 1

Option B is correct.

Option C:

m = (5 - 8) / (1 + 2) = -3 / 3 = -1

m = (2 - 5)/ (4 - 1) = -1

Option C is correct.

Option D:

m = (1- 0)/ (1 + 1) = 1/2

m = (5 - 1) / (7 - 1) = 4 / 6 = 2/3

Option D is incorrect.

Hence, the ordered pairs that represent the linear function is Option A, B and C.

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The number of sheets that can be cut from 22 1/8 inches would be 4 25/38

To solve this, I would first have to convert the values to decimals

4 3/4in = 4.75 inches

22 1/8 = 22.125

To get the full length that can be cut from the 22.125, we would have to divide. That is;

22.125 / 4.75

= 4.657

4 25/38

The number of full sheet that can be cut from this would be 4 25/38

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The graph of f(x) = x^(-1/3) underwent three transformation to give  0.2^3√(x +3) + 4 which are horizontal shift, vertical scaling and vertical shift

The graph of f(x) = x^(-1/3) has undergone the following transformations to give 0.2^3√(x +3) + 4:

Horizontal Shift: The graph has been shifted to the right by 3 units. This is because x has been replaced with x + 3 in the equation.

Vertical Scaling: The graph has been scaled by 0.2^3 in the vertical direction. This is because f(x) has been multiplied by 0.2^3.

Vertical Shift: The graph has been shifted upward by 4 units. This is because f(x) has been added by 4 in the equation.

In summary, the transformations performed on the graph of f(x) = x^(-1/3) to give 0.2^3√(x +3) + 4 are a horizontal shift of 3 units to the right, a vertical scaling by 0.2^3, and a vertical shift of 4 units upward.

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Step-by-step explanation:

The z-score for the price of the family's home can be calculated as follows:

z = (350,000 - 375,000) / 7,500 = -3.333

A negative z-score indicates that the value is below the mean. Therefore, the price the family paid for their home is lower than the average price of homes in their neighborhood, so it can be considered unusual.

So, the answer is: The z-score is -3.333 and it is unusual.

The statement that proves that there is a unique element x such that P(x) is true is: c) 3x(P(x) & Ay(P(y) --> x = y)).

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms.

Here,

In this statement, the quantifier "3x" says that for every element x, and the condition "P(x)" says that x satisfies a certain property. The statement "Ay(P(y) --> x = y)" says that for every other element y, if y also satisfies the property, then it must be equal to x. Hence, if there is a unique element x such that P(x) is true, then this statement is true.

Option (a) says that for every element y, P(y) is equivalent to y = x, but this statement alone does not imply that there is only one element that satisfies P(x).

Option (b) says that for every element x, if P(x) is true, then there is no other element y that also satisfies P(y) and is not equal to x. However, this statement alone does not imply that there exists an element x that satisfies P(x).

The following assertion establishes that there is a unique element x such that P(x) is true: c) 3x(P(x) & Ay(P(y) --> x = y)).

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Answer:

y=-2/6+5

Step-by-step explanation:

The required answer of other parts are 4)  1230, 5) Students = 1230 + 53t, 6)  2025 students.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

As you have calculated average students in a year is 53.So, we can say students are increasing by 53 each year.

4) in 2003, number of students are 1389 and in three year students increase by 53* 3 = 159

in 2000,

Students = 1389 - 159

= 1230

5) We have 1230 students in 2000, and students will increase by 53 each year.

So, for t years equation will be

Students = 1230 + 53t

6) There is 15 years to come 2015, using our equation;

Students = 1230 + 53t

Students = 1230 + 53(15)

Students = 1230 + 795

= 2025 students.

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The limit when we approach x = 3 from the right side is:

[tex]\lim_{x \to 3^+} f(x) = 4[/tex]

Here we have the graph of a function f(x), and we want to find the value of the limit:

[tex]\lim_{x \to 3^+} f(x)[/tex]

That would be the value of f(x) as it approaches x from the right side, in this case, will be the value on the graph when we go from right to left.

We can see an open circle at y = 4

Then we can conclude that the value of the limit when we approach x  = 3 from the positive side is:

[tex]\lim_{x \to 3^+} f(x) = 4[/tex]

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Answer:

Option B. 9 inches

Step-by-step explanation:

Given

Rectangle MNOP and Rectangle WYXZ are similar

Scale factor of the two Rectangles = 2:3 or 2/3

MN=6 in

So

MN/WY = 2/3

6/WY = 2/3

WY = 6×3/2

WY = 18/2

WY=9

Therefore length of side WY is 9 inches

Possible echelon forms for matrix are:

 [tex]\left[\begin{array}{ccc}Y&&\\0&Y&\\0&0&Y\\0&0&0\end{array}\right][/tex]

A collection of integers organised in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics. Matrices have also found usage in computer graphics, where they have been utilised to represent picture rotations and other transformations.

If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “m × n.” For example,  

                                                             [tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\end{array}\right][/tex]  its a 2×3 matrix.

The proof of the theorem proves that the columns, say, A and B must be independent.

In the matrix, there is linearity and the trivial solution would be [ 0, 0 , 0 , 0] for the matrix to exist. In other words, all the unknowns must be zero.

This establishes the fact that the matrix T needs to be independent for the matrix function, say T (x) to be one-to-one.

By definition, one-to-one is ker (T) = {0}

Thus, the null space is occupied only by the zero vector.

Note: if there was no linear independence in the vectors, the solution would not be zero in the vector.

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Answer:

57 ft

Step-by-step explanation:

Solution Given:

BC =40ft it also known as a.

<C=55°

<B=90°

<C=180-90-55=35°

height of the building =? also known as c

we have

law of sines
[tex]\frac{Sin A}{a} =\frac{Sin B}{b}=\frac{Sin C}{c}[/tex]

By inserting value[tex]\frac{Sin 35}{40} =\frac{Sin 55}{c}[/tex]

you can take any two what you want
doing criss cross multiplication

Sin 35*c=Sin55*40

we get
c=sin55 * 40 /Sin35

c=AB=57.12 ft in nearest 10 it is 57 ft

The way the outlier affects the mean, median, and mode is:

The outlier will increase the mean, as it will significantly increase the sum of the values. The presence of an outlier will not affect the median, as it only changes the position of the middle value.

The mode is the value that occurs most frequently in a data set. In this case, the mode will not be affected because the outlier is not the most frequent in the data set and only appears once.

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Answer:

f

Step-by-step explanation:

hvggggggggghgvggjjjj

The inverse operations are (b) and (c)

From the question, we have the following parameters that can be used in our computation:

m/4-18= -10

Operation 1: Option (B)

Add 18 to both sides of the equation, and then multiply through by 4

Using the above as a guide, we have the following:

m/4 = 8

m = 32

Operation 2: Option (C)

Multiply each side by 4 and then add 72

Using the above as a guide, we have the following:

m - 72 = -40

m = 32

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Answer:

Parag will have Rs. 44,68,802 in his account if he retires 26 years from today. This can be calculated by using the formula A = P (1+r)n, where A is the future value of the investment, P is the present value, r is the interest rate, and n is the number of years until retirement. In this case, P = 10,50,000, r = 12%, and n = 26, so A = 10,50,000 (1+0.12)26 = Rs. 44,68,802.

The Euclidean distance between (1.0, 6.1) and (3.3, 8.7) is 3.48, rounded to 1 decimal place.

The Euclidean distance formula  is used to calculate the distance between two points in a two-dimensional plane. The formula for Euclidean distance between two points (x1, y1) and (x2, y2) is given by:

[tex]d = √(x2-x1)2 + (y2-y1)2[/tex]

For our two points, (1.0, 6.1) and (3.3, 8.7), the Euclidean distance is:

[tex]d = √(3.3-1.0)2 + (8.7-6.1)2 \\ = √(2.3)2 + (2.6)2 \\ = √5.29 + 6.76 \\ = √12.05 \\ = 3.48[/tex]

Therefore, the Euclidean distance between (1.0, 6.1) and (3.3, 8.7) is 3.48, rounded to 1 decimal place.

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Answer:

72 inches

Step-by-step explanation:

What we know:

1 yard = 3 feet

3 feet = 36 inches

If 1 yard equals 3 feet, which equals 36 inches, then we can multiply 1 yard, 3 feet, and 36 inches by 2.

1 yard * 2 = 2 yards

3 feet * 2 = 6 feet

36 inches * 2 = 72 inches.

So, the answer is 72 inches.

Check the picture below.

[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&16~\frac{ft}{s}\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&192~ft\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+16t+192\hspace{5em}f(x)=-16x^2+16x+192[/tex]

now, keeping in mind that x-axis is the seconds, however a parabola could go into the 2nd, 3rd and 4th Quadrants, but for this case, we only need it in the 1st Quadrant, because the seconds are positive, it begins at 0 seconds and goes up, then down and hits the ground later on when f(x) = 0, hmmm when is that?

[tex]\stackrel{f(x)}{0}=\stackrel{ \textit{hits the ground} }{-16x^2+16x+192}\implies 0=-16() \\\\\\ 0=x^2-x-12\implies 0=(x+3)(x-4)\implies x= \begin{cases} -3 ~~ \bigotimes\\\\ ~~ 4 ~~ \checkmark \end{cases}[/tex]

now, both values are valid for "x", however for this specific case, we can't have negative seconds, so the negative value won't work.  So the appropriate domain or values for "x" are from 0 to 4, the object went up and down in 4 seconds flat.

The future value of the loan is $1,333.86

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

Values are,

P = 1250, r = 3.31 and t = 2 years

Now, We know that;

⇒ Amount = P (1 + r)ⁿ

Substitute all the values we get;

⇒ Future value = 1250 (1 + 3.31/100)²

⇒ Future value = 1250 (1 + 0.033)²

⇒ Future value = 1250 (1.033)²

⇒ Future value = 1250 × 1.067

⇒ Future value = $1,333.86

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The probability of getting at least one defective disk in a lot of 50 is 0.2217.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

Given that,

P (defective disc) = 0.005

P (non-defective) = 1 - 0.005 = 0.995

Now,

P(Getting one defective) = 1 - P(getting 50 non -defective)

= 1 - (0.995)^(50)

= 1- 0.7783

= 0.2217

Hence, the probability of getting at least one defective disk in a lot of 50 is 0.2217.

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The time it took Aniya to do cartwheels, which can travel at 0.5 mph for a total distance of 0.1 miles, is 12 minutes.

The distance, time, and average speed formulas are based on distance equals to time multiplied by the average speed.

Conversely, the total time taken to cover a certain distance is equal to distance divided by the average speed.

Total distance traveled doing cartwheels = 0.1 miles

Average speed = 0.5 mph

Time = Distance/Average speed

= 0.1/0.5

= 0.2 hours

1 hour = 60 minutes

= 12 minutes (0.2 x 60)

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The value of x is 0.645 and x= 4.645.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x² + 4x-3=0

Now, using Completing the Square method we have to half the coefficient of x and add and subtract the square.

then, x² + 4x-3=0

x² + 4x-3 + 2² - 2² =0

x² + 4x + 2² -3  - 2² =0

(x+ 2)² - 7 = 0

(x+ 2)² = 7

x+ 2= ±2.645

x= 0.645 and x= 4.645

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Answer: 15a

Step-by-step explanation: 6 + 9 = 15, 6a + 9 = 15a

The height of the building is 92.52 ft

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

Using law of sines:

first angle A:

sum of all angles in a triangle = 180 degree

A+B+C = 180

A+90+55 = 180

=> A+145 =180

=> A= 180 - 145 = 35 degrees

Use:

AB= c, BC=a

(sin A)/a = (sin C)/c

=> (sin 35)/40= (sin 55)/c

=> -0.4281/40= -0.99/c

=> 0.0107 = 0.99/c

=> c= 0.99/0.0107 = 92.52 ft

The height of the building is 92.52 ft

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Answer:

2/8 because if their is 6/8, it's denominator is 8 meaning out of 8 so 8/8 - 6/8 = 2/8 of Mario's Rope.

The number of years its to make 3,480 is approximately 23 years.

If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.

Given that, the population of a colony started with 1,120 grows at an annual rate of 4.98%.

Here, A =3480

Now, 3480=1,120(1+4.98/100)ⁿ

(1+4.98/100)ⁿ=3480/1,120

(1.0498)ⁿ=3.107

Take the logarithm of both sides of the equation to remove the variable from the exponent.

Exact Form:

n=ln(3.107)/ln(1.0498)

Decimal Form:

n=23.32644715

Therefore, the number of years its to make 3,480 is approximately 23 years.

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Answer:

yes it will fit;  there would be 35.2 sf remaining

Step-by-step explanation:

Find the dimensions of the table in inches:

2.5/5 = x/6

x = 3 in

2.5/5 = x/8

x = 4 in

Scaled table area = (3 in)(4 in) = 12 in²

Scaled room area = (4 in)(5.2 in) = 20.8 in²

12 < 20.8, Therefore, the table would fit.

How much room is left over:

Find the room dimensions in feet.

2.5/5 = 4/x

x = 8 ft

2.5/5 = 5.2/x

x = 10.4 ft

Room area = (8)(10.4) = 83.2 sf

Table area = (8)(6) = 48 sf

83.2 - 48 = 35.2 sf space would remain