Why we use mean method?

The set of rational numbers is closed under addition, subtraction, multiplication, and division (division by zero is not defined) because if you complete any of these operations on rational numbers, the solution is always a rational number. -1 and 1.

What is a closed set ?

A Closed Set Math has a way of explaining a lot of things, and one of those explanations is called a closed set.

Closure property holds for addition and multiplication of whole numbers. The sum of any two whole numbers will always be a whole number, i.e. if a and b are any two whole numbers, a + b will be a whole number. The difference between any two whole numbers may or may not be a whole number. Hence, the whole numbers are not closed under subtraction.

According to the given question:

A set is closed under addition if you can add any two numbers in the set and still have a number in the set as a result. A set is closed under (scalar) multiplication if you can multiply any two elements, and the result is still a number in the set.

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Answer:Square Root Formula

The square root formula of a number, x is given as,

√x = x1/2

Suppose, x is any number such that, x = y × y, the formula to calculate the square root of x will be,

√x = √(y × y) = y

where, y is the square root of any number x. This also means that if the value of y is an integer, then x would be a perfect square.

Step-by-step explanation:

The value of x+y is 289

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Given is an expression, x²+74x+2021=y²

On solving, we get

x²+2×37x + 37² = y²-652

(x+37)²= y²-652

(x+37)²- y² = -652

(x+y+37) (x-y+37) = 289 × -2

Thus, x+y+37 = 289......(i)

x-y+37  = -2.......(ii)

Solving the equations, we get

x = 125 & y=164

Therefore,

x+y = 125+164

= 289

Hence, The correct answer is x+y = 125+164 = 289

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∡ABD and ∡BAD = ∡55°

As we can see Δ ABD is isosceles

so,

∡ABD = ∡BAD (let us assume them to be ∡F)

Therefore

∡ABD+∡BAD+∡ADB = 180°

2∡F+∡ADB = 180°

2∡F + 70° = 180°

∡F = 55°

∡ABD = ∡BAD = 55°

Now

∡ABD + ∡CBD = 180° (Supplementary Angles)

55° + ∡CBD = 180°

∡CBD = 125°

As the sum of all the angles in a triangle is 180°

∡BDC +∡DCB +∡CBD = 180°

∡BDC + 29° +125° = 180°

Hence

∡BDC = 26°

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Step-by-step explanation:

angle3 is the supplementary angle to angle2.

that means together they are 180°.

180 = 117 + angle3

angle3 = 180 - 117 = 63°

The size of the angle C is θ = 56°, given that BC and DE are tangents to the circle.

The tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

Considering the Isosceles triangle ∆AOB and its exterior angle ∠BOD;

∠BOD = 180° - 2(48) {exterior angle of a triangle equals 2 opposite interior angles}

∠BOD = 96°

If the line DE is extended to line BC at E' we will have a quadrilateral BODE' and a triangle ∆CE'D, hence;

∠B = ∠D = 90° (angles between radius and lines tangent to the circle)

so;

∠BOD + ∠OBD + ∠ODE' + ∠BE'D = 360° {sum of interior angles of a quadrilateral}

96° + 90° + 90° + ∠BE'D = 360°

276° + ∠BE'D = 360°

∠BE'D = 360° - 276° {subtract 276° from both sides}

∠BE'D = 84°

Considering triangle ∆CE'D;

∠DE'C = 180° - 84° {sum of angles on a straight line}

∠DE'C = 96°

We thus derive θ using the triangle ∆CE'D;

θ = 180° - (28 + 96)° {sum of interior angles of a triangle}

θ = 180° - 124°

θ = 56°

In conclusion, we have derived the size of the angel θ as 56° by proper application of the tangent to a circle theorem.

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2909/2000

Based on the given conditions, formulate: 16 divided by 11

Evaluate the equation/expression: 1.4545

Convert decimal into fraction: 14545/10000

Reduce the fraction: 2909/2000

Answer: 2909/2000

As pert the t-test there is sufficient evidence that the average family size in this school district differ from the national average.

Let us assume null and alternate hypothesis.

H₀ = Average family size is 3.18

Hₐ = Average family size is not 3.18

The value of t = (Sample Mean - 3.18) / s/√n

where,

Sample Mean = 3.83

n = 24

s = 1.43

So, t = (3.83 - 3.18) / (1.43 / √24)

t = 2.2268

Degree of freedom = n - 1 = 23

The p-value = 0.0360

As the p-value <0.05, so the null hypothesis will be rejected.

Therefore, there is enough proof to conclude that this school district's average family size is different from the national average.

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For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.

Given solution to t²y'' - 4ty' + 6y = 0 is

y₁(t) = t²

Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,

y₂ = vt²

y₂' = 2vt + t²v'

y₂'' = 2v + 2tv' + 2tv' + t²v''

y₂'' = 2v + 4tv' + t²v''

Substituting this

t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0

t⁴v'' = 0

v'' = 0

v' = c, c is a constant

v = ct

Therefore, y₂(t) = ct×t²

y₂ (t) = ct³

Therefore general solution will be y(t) = c₁t² + c₂t³

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The given statement "the value in the middle of a confidence interval is always the point estimate for the population parameter" is TRUE.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

The point estimate for the population parameter is always the value at the center of a confidence range.

You have a 5% probability of being incorrect with a 95% confidence interval.

We have a 10% probability of being incorrect with a 90% confidence interval.

A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).

Therefore, the given statement "the value in the middle of a confidence interval is always the point estimate for the population parameter" is TRUE.

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Answer:

(3,1)

Step-by-step explanation:

(x+ 6, y -4)

The x tells us the movements are right or left. Right would be a positive movement and left would be a negative movement.

The y tells us the movements are up or down.  Up would be a positive movement and down would be a negative movement.

D is at the point ( -3,5)  

(x + 6, y -4)  Is telling us that from the point of D, move right 6 spaces and down 4 spaces.  You will know be at the point (3,1).

Answer:

like a ratio

Step-by-step explanation:

A multiplicative comparison involves comparing two quantities such that when one is multiplied by a specified number, the other is produced. For example, Sam has twice as many balloons as Sid. Sid has 3 balloons.

The equation in slope-intercept form of the line that crossed the x-axis at 36 and is perpendicular to the line represented by y = -4/9x + 5​ is y = 9/4 ( x ) + 36

Given :

line equation is y = -4/9 x + 5

We have to find the line equation which is perpendicular to the given line in slope intercept form.

y = mx + c where m is slope and c is intercept.

slope m = -4/9

perpendicular slope = -1/m

= -1 / -4 / 9

= 9 / 4

x - intercept of x - axis = 36

so the equation is y = 9/4 ( x ) + 36 .

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since we have our two medians, we need to add them up 1st then divide the sum by two;

50+60

    2

= 110

    2

= 55

55 is the median

Answer:

  5 units

Step-by-step explanation:

You want to know the side length of the rhombus with vertices (2, 0), (7, 0), (5, 4), and (10, 4).

You can find the length of the horizontal edges by counting the grid squares, or by subtracting the x-coordinates:

  7 -2 = 5

  10 -5 = 5

The slanted sides are each the hypotenuse of a 3-4-5 right triangle, so are also 5 units long. (You expect all of the sides of the rhombus to be the same length.)

Each side is 5 units long.

The answer is 5, 4.47, 5, and 8.94.

                The distance formula is d = √(x2-x1)^2 + (y2-y1)^2

                                    d = √(7-2)^2 + (0-0)^2

                                    d = √(5)^2 + (0)^2                

                                    d = √(25) + (0)

                                    d = 5

                                     d = √(5 - 7)^2 + (4 - 0)^2

                                      d = √(-2)^2 + (4)^2

                                      d = √4 + 16

                                      d = √20

                                      d = 4.47

                                      d = √(10 - 5)^2 + (4 - 4)^2      

                                      d = √25 + 0

                                      d = 5

                                       d = √(2 - 10)^2 + (0- 4)^2

                                       d = √(-8)^2 + (-4)^2

                                       d = √64 + 16

                                       d = √80

                                       d = 8.94

Therefore, each side of the rhombus has a length of 5, 4.47, 5, and 8.94.

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The system of linear equations are said to have no solution if they are parallel to each other or have infinitely many solutions if they are coincident.

Considering two system of equations:

y1 = mx +c and  y2 = px+ q.

The lines are said to be parallel if their slopes m and p are equal but the y intercepts c and q are not equal. Which further concludes that the system of equations has no solution.

The lines are said to be coincident if their slopes m and p are equal along with the y intercepts c and q being equal. And hence we conclude that the system of equations have infinitely many solutions.

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The nature of the roots of the equation x^2 - 5 = 0 is real and unequal.

We know that the general form of a quadratic equation is:

ax^2 + bx + c =0

The equation we have is:

x^2 - 5 = 0

Comparing the given equation with the general form of a quadratic equation, we get that:

a = 1, b= 0, and c = -5

If D = b^2 - 4ac > 0, then we say that the roots of the quadratic equation are real and unequal.

Here, (0)^2 - 4x1x(-5) = 20 >0,

hence we conclude that nature of the roots of the equation x^2 - 5 = 0 is real and unequal.

The question is incomplete, the complete question is:

x^2 - 5 = 0.

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By Dilation, if the scale factor is greater than 1 image gets enlarged.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.

Enlargement is the term used when a dilatation results in a larger image.

Reduction occurs when a dilatation results in a smaller picture.

As the scale factor of given question is greater than 1 it is Enlargement.

By Dilation, if the scale factor is greater than 1 image gets enlarged.

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The linear equation y = 3x + 5 has an infinitely many solutions.

We looked for as many solutions as possible to the given equation.

y = 3x + 5 is a linear equation with two variables as of ax + by + c = 0.

Thus,

A linear equation with two variables hence has an endless number of solutions.

y = 3x + 5 thus has an endless number of solutions.

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The correct question is-

What is the solution of y =  3x + 5?

As per the given ratio, the total number of flowers in shipment is 180.

The term Ratio in math basically compares quantities, which means that it shows the value of one quantity with respect to the other quantity.

Here we have given that the florist ordered a shipment of red, blue, and white carnations to use for table decorations at a banquet.

And we need to find  the total number of carnations in the shipment.

While we looking into the given question, we know that the ratio of red : blue : white carnations in the shipment is 3:1:2.

Here we aloo know that there are 60 white carnations in the shipment

Then let us consider if a and b are two values, their ratio will be a:b,

Then the ratio of flowers is written as

=> red: blue: white = 3:1:2

Where red flowers are 3x, and the blue flowers are x, and the white flower are 2x.

So, the total number of flowers = 3x+x+2x = 6x

When we apply the value of whit\te flowers = 60

Then the value of x is calculated as,

=> 2x = 60

=> x = 30

Therefore, the total number of flowers = 6x = 6×30 = 180

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Answer:

Step-by-step explanation:

Part A: you can just restate parts of the text to make a vaild argument or you can make you own

Part B: he should measure N, O, P and Qas

Triangles MNO and QPO are congruent. To find the width of the creek, Andre should find the measurement of NP

When two triangles are congruent, their corresponding three sides and their three angles match precisely.

Given that

O is the midpoint of NP,

NP is perpendicular to MN, and

NP is perpendicular to PQ.

When two lines intersect at a specific point, the opposite angles formed in this situation are equal.

a) Then ∠MNP =∠QPO=90°

∠MON=∠QOP

Also, NO = OP (by the definition of midpoints)

Therefore, Triangles MNO and QPO are congruent by ASA rule

And,

b) To find the width of the creek, Andre should find the measurement of NP, because according to the figure the width is represented by NP. He should find NO and OP and then add it.

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800 ways meal be ordered.

There are 5 main courses to choose from, so there are 5 ways to choose a main course. There are 4 vegetables to choose from, so there are 4 ways to choose a vegetable. There are 5 beverages to choose from, so there are 5 ways to choose a beverage. And there are 4 desserts to choose from, so there are 4 ways to choose a dessert.

The total number of ways to order a meal is the product of the number of choices for each category.

So there are 5 * 4 * 5 * 4 = 800 ways to order a meal.

Hence, 800 ways meal be ordered.

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The most common occurrence of a number or the one that does so most frequently is known as the mode of the data.

A set of data values' mode is the value that appears the most frequently.

The value of X at which the probability mass function reaches its highest value is known as the mode if X is a discrete random variable.

In other words, it is the value that will be sampled most frequently.

The number that appears the most frequently, or the one that does so most frequently.

Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers  {4, 2, 4, 3, 2, 2}.

Therefore, the most common occurrence of a number or the one that does so most frequently is known as the mode of the data.

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The population of the region is 1300 people.

It should be noted that population simply means the number of people on a particular region or area. Population density is the number of people per unit of area.

Since the population density of a certain region is 50 people per square kilometer and the region covers 26 square kilometer, the population will be:

= Number of square kilometers × Number of region

= 50 × 26

= 1300

The population is 1300 people.

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Answer:

x = (6 i)/5 or x = -(6 i)/5

Step-by-step explanation:

Solve for x:

25 x^2 + 36 = 0

Subtract 36 from both sides:

25 x^2 = -36

Divide both sides by 25:

x^2 = -36/25

Take the square root of both sides:

Answer:  x = (6 i)/5 or x = -(6 i)/5

3 pyramids can fit inside a rectangular prism if both figures have the same measures of bases.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges.

The ratio of volume of pyramid and a prism is 1:3 when they have the same base and height.

A cylinder with the same radius and height is precisely filled with the contents of three conical cups. A prism with the same base and height as three rectangular-base pyramids is exactly filled with their contents.

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Remove the parentheses before performing the reverse operations of addition and subtraction, Remove the parentheses before reversing the process of division and multiplication, Flip The Inequality Sign When Adding, Subtracting, or Multiplying By A Negative Number.

Hence, Remove the parentheses before performing the reverse operations of addition and subtraction, Remove the parentheses before reversing the process of division and multiplication, Flip The Inequality Sign When Adding, Subtracting, or Multiplying By A Negative Number.

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According to the sum of n terms in geometric progression, the total time she took to complete her first five homework assignments is 219 minutes.

The time taken to complete first assignment is 70 minutes.

She takes 0.8 times as long to complete each homework assignment as she took to complete the preceding assignment.

This shows that the given series is in geometric progression, where

a = first term = 70

r = common ratio = 0.8

The sum of first n terms in geometric progression is given by,

Sₙ = a (rⁿ - 1) / r - 1

S₅ = 70 (0.8⁵ - 1) / 0.8 - 1

S₅ = 219

Therefore, the total time she took to complete her first five homework assignments is 219 minutes.

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Answer:

34 m

Step-by-step explanation:

s=side of square

A=Area of square

P = Perimeter of square

s*s = A

s*s = 289

s^2 = 289

s = [tex]\sqrt{289}[/tex]

s = 17 m

P = s + s + s + s

P = 4s

P = 4(17)

P = 68 m

68/2 = 34 m