why do we use the standard uncertainty in the mean to quantify the uncertainty in the mean of a data set, but we use the standard deviation to quantify the uncertainty in individual measurements?

Therefore , the solution of the given problem of domain comes out to be  

(-∞,6 ) U (6,∞) and (+∞,-6 ) U (-6,-∞) .

The variety of potential arguments that a function can take is referred to as its domain. These numbers represent the cross of an f-like functional (x). A function's domain is the set of possible values that it can be applied to. This set includes the value the method returns following the insertion of the x value. Y = f is the equation for a functions with y and x serving as predictor variables (x). A variable is said to belong to the domain of a function when one specific value of y may be generated from one single value of x.

Here,

Given:

=> y / y-6 + 15/y+6

So,

the domain for first expression is :

=> y-6 = 0

=> y =6

Domain:

=> (-∞,6 ) U (6,∞)

the domain for second expression is :

=> y + 6 = 0

=> y = -6

Domain :

=> (+∞,-6 ) U (-6,-∞)

Therefore , the solution of the given problem of domain comes out to be  

(-∞,6 ) U (6,∞) and (+∞,-6 ) U (-6,-∞) .

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The inverse of the logarithmic function 3 is 1000 for base 10.

The index or power to which the base must be raised in order to reach the given number is represented by the logarithm of any positive number, whose base is a number that is larger than zero but not equal to one.

mathematical form: [tex]log_ab=x[/tex].

Here for inverse of given function is derived by given formula.

[tex]a^x=b[/tex]

There are two types of logarithm function:

Natural Logarithm and common logarithm.

[tex]log_{a}b=x\\log_{10}b=3\\a^x=b\\10^3=b\\b=1000[/tex]

So inverse of logarithmic function 3 is 1000.

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Answer:

0.5

Step-by-step explanation:

The square root of x can be rewritten as [tex]x^{0.5}[/tex].

Therefore f(x) can now be written as

f(x)=4[tex]x^{0.5}[/tex], and so the power of the function is 0.5

The value of K is 3.

Value is the worth of something, whether it be tangible or intangible. It is often measured in terms of money, but it can also take the form of respect, honor, or admiration. Value can also refer to the worth of something in terms of its usefulness, importance, or desirability. Ultimately, value is based on personal opinion, so it is subjective.

The graph of g(x) = (1/3)^x – h + k is obtained by translating f(x) = (1/3)^x horizontally by h units and vertically by k units. The vertical translation of 3 units will shift the graph of f(x) up by 3 units on the y-axis, which leads to a value of 3 for K.

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If you deposit  $7500 in savings account with interest rate of 5.12% and interest is compounded monthly, then the approximate balance of this savings account be after 3 years is  $8742.5    .

the amount deposited in the savings account (p) = $7500 ;

the interest rate (r) = 5.12%  = 0.0512  ;

number of times interest is compounded (n) = 12 ;

time (t) = 3 years ;

the amount after  "t" years can be calculated by the formula , given as :

⇒ Amount = [tex]p\times (1+\frac{r}{n})^{nt}[/tex] ;

substituting the values ,

we get ;

⇒ Amount = [tex]7500\times (1+\frac{0.0512}{12})^{12\times 3}[/tex] ;

⇒ Amount = [tex]7500\times (1.00426)^{36}[/tex] ;

⇒ Amount = 8742.32584 ;

Amount ≈ $8742.5

Therefore , the approximate balance of this savings account be after 3 years is  $8742.5   .

The given question is incomplete , the complete question is

Suppose you deposit $7500 in a savings account that has an interest rate of 5.12%  .  If the interest is compounded monthly, what will the approximate balance of this savings account be after 3 years ?

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The relationship between two equal amounts is described by the characteristics of equality

The relationship between two equal amounts is described by the characteristics of equality. To maintain balance, each mathematical operation that is done to one side of an equation must also be applied to the opposing side.

a = 2b, then a-c = 2b - c

This is Subtraction Property of Equality

According to the Subtraction Property of Equality, if two equal things have an equal value subtracted from them or deleted, the outcome is a new equal quantity. When two equivalent sides of a mathematical statement are separated by an equal sign, an equation is being expressed. The subtraction property has the expression if a = b, then a - c = b - c.

X = X

This represents the Reflexive Property

In algebra, a number is always equal to itself according to the reflexive property of equality.

3(p-7) = 3p - 21

This represent distributive property.

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

-7k = -42 then k= 6

This is Division Property of Equality

According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0. The same formula may be expressed in writing as follows: If real numbers a, b, and c are present, with a = b and c 0, then a c = b c.

m + n = 15 and n = 2, then m + 2 = 15

This represent Substitution Property

x/4 = -5 then x = -20

This is Multiplication Property of Equality

w² = 2x and 2x = y, then w² = y

This is Transitive Property

c-9 = -1, then c = 8

This is Addition Property of Equality

n = -3, then -3 = n

This is Symmetric Property

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The process of plotting the graph for the parent function on the calculator is explained below.

Here we have to define the process of  plotting the graph for the parent function on the calculator .

In order to plot these, we have to know the definition of parent function.

The term parent function is known as the functions may be classified and grouped into families and each of these groups each have one basic equation called a parent function.

And the parent functions have the U-shaped graph called the parabola and they all have a second degree with the highest exponent.

In order to plot the graph on the calculator, then the

First steps is to label the graph and then we have to set the x and y axis limit on the graph.

then the next steps is to input the function on the graph and makes the table for it.

Then label the table values on it.

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The standard form of a line equation is y = mx + b.   Since you need a line that is parallel to y = 5x - 2, the first thing to do is use the same slope (m), which is 5 in this case

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The net income or loss is transferred from the income statement to the trial balance.

Income statement is referred to as the statements of the money one or an organization has earned in a month or more broadly in an year.

It is used in corporate sectors and also in the field of accounting.

Trial balance can be considered as the balance where all the records are maintained for further tally of the balance sheet. When we are preparing financial accounts, the trial balance is used to identify and repair problems in those  accounting records. Generally , the trial balance is prepared at the end of an accounting period, such as a month or a year.

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The wingspan of the airplane in the scale drawing  is equal to 6.67 inches.

The wingspan of an airplane in a scale drawing can be calculated using the scale factor. If the wingspan of the real airplane is 60 feet and 1 inch represents 9 feet, then the wingspan of the airplane in the scale drawing is 60/9 = 6.67 inches. Knowing the dimensions of the real airplane and the scale factor of the drawing, it is possible to accurately calculate the wingspan of the airplane in the scale drawing. This calculation is important for accurately measuring and drawing scale models of aircraft.

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The system if there are fewer equations than variables has infinite solutions.

There are two types of system of equations - consistent and inconsistent.

Inconsistent means that it has no solution , i.e. the solution does not exist.

Consistent system means a solution of the equation exists.

Now, a consistent system may have a unique solution or an infinite number of solutions where we need to assign an arbitrary value to a free variable to find its solutions.

For e.g. let us consider the system -

x + y+ z = 0

2x + 3y + 4z = 1

Since , (0,0,0) is an obvious solution to this system , its a consistent system .

Also, for a system to be consistent , either a unique solution exists or an infinite number of solutions exist. There is no particular number of solutions.

Also, we see that (-1,1,0) is also a solution other than the zero solution.

We can clearly see that the number of unknown variables , x,y,z is 3 and the number of equations is 2.

Thus, The system if there are fewer equations than variables has infinite solutions.

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The dimensions that will minimize the cost of the metal to manufacture the can is r = 5.42 dm and h = 10.84 dm.

To minimize the cost of the metal to manufacture the can, minimize the surface area of the can. The surface area of a cylinder can be found using the formula 2πr(r + h) where r is the radius and h is the height.

The volume of the cylinder is given by the formula πr²h, and it is known that it needs to be equal to 1000 l or 1000 cubic dm.

Set the volume equation equal to 1000 and rearrange it in terms of r.

πr²h = 1000 cubic dm

h = 1000/(πr²)

Substitute this value of h back into the surface area equation and minimize it with respect to r.

2πr(r + h) = 2πr(r + 1000/(πr²))

To minimize the surface area, take the derivative of this expression with respect to r and set it equal to zero, then solve for r.

d(2πr(r + 1000/(πr²)))/dr = 0

d(2πr² + 2000πr/(πr²))/dr = 0

d(2πr² + 2000/r)/dr = 0

4πr - 2000/r² = 0

4πr = 2000/r²

r³ = 2000/4π

r = ∛(500/π)

r = 5.42 dm

Substitute it back into the equation for h and find the corresponding value of h.

h = 1000/(πr²)

h = 1000/(π(∛(500/π))²)

h = 10.84 dm

So, the dimensions that will minimize the cost of the metal to manufacture the can are r = 5.42 dm and h = 10.84 dm.

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On solving the provided question we can say that equation will be as follows  6x + 55y = 13.15 => x = coins = 2 and y = nickels = 12

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

jesse has  = $6.55 worth of quarters and nickels

the number of nickels is five more than two times the number of quarters

so

let coins be x

and nickels be y

now equation will be as follows

6x + 55y = 13.15

x = coins = 2

y = nickels = 12

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There are several strategies for resolving systems of linear equations, including:

(1) Graphing Techniques

(2) The Substitution Method

(3) Using a linear combination

(4) The Matrix Approach

(1) Graphing Techniques: This is helpful if you only require a general answer or are confident that the intersection occurs at integer locations. Simply plot the two lines to determine their intersection.

(2) The Substitution Method: One linear equation for y must first be solved in terms of x. Then, in the other linear equation, replace y with that expression. You'll receive a formula in x. If you can solve this, you'll know the intersection's x-coordinate. Then, to determine the equivalent y-coordinate, insert x into either equation.

(3) Using a linear combination: In order for the x-terms or the y-terms to cancel out, add (or subtract) a multiple of one equation to (or from) the other equation. To obtain the other coordinate, first solve for x (or y, depending on which is remaining) and then substitute.

(4) The Matrix Approach: Actually, this is only a simplified notation of the Linear Combination method.

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Answer:

The domain would be All Real Numbers. And the range is y>0.

Step-by-step explanation:

You would just look at the graph and see that line goes infinitely so the domain(x) would be all real numbers. For range you just look at the y axis and figure out that all numbers are greater than 0.

If you need the answers in a different format, feel free to tell me.

Answer:y=2x+5

Step-by-step explanation:

y intercept of 5

the distance between the points on x axis is 4

the distance between the points on y axis is 8

8/4=2

gradient of 2

Answer:

2x+5 = two will divide five which is 2.5 so y=1/2 +2.5x makes 5

Step-by-step explanation:

Answer =2x+5

The  simplification of the radical expression gives  √(10×√(5))

A radical expression is an algebraic expression that contains a square root, cube root, or higher-order root. It is written with the radical symbol (√) before the number or expression being rooted.

√(5√(20)) can be simplified as follows:

√(5√(20)) = √(5√(4×5))

                 = √(5×√(4) × √(5))

                 = √(5 × 2 × √(5))

                 = √(10×√(5))

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The 7 rules of logarithms are as: 

1. Rule of product.

2. Rule of division.

3. The Power/Exponential Rule.

4. A new fundamental rule.

5. Rule of the base swap.

6. Log derivative.

7. Log integral.

The alternate format for writing exponents is with logarithms. A number appears base-based logarithm is approximately equivalent to another number. A logarithm performs exponentiation's exact opposite function.

1. Rule of product: According to this rule, adding the individual logarithms of two logarithmic values results in the multiplication of those values.

[tex]Log_b (mn)= log_b m + log_b n[/tex]

2. Rule of division: The difference between each logarithm is equivalent to the division of two logarithmic values.

[tex]Log_b \left(\frac{m}{n}\right)= log_b m - log_b n[/tex]

3. The Power/Exponential Rule: According to the exponential rule, the exponent times the logarithm of m's logarithm is equivalent to m's logarithm with a reasonable exponent.

[tex]Log_b (m^n) = n log_b m[/tex]

4. A new fundamental rule:

[tex]Log_b m =\frac{log_a m}{log_a b}[/tex]

5. Rule of the base swap:

[tex]log_b (a) = \frac{1}{log_a (b)}[/tex]

6. Log derivative: If f (x) = [tex]log_b (x)[/tex], then the derivative of f(x) is given by;

[tex]f'(x) = \frac{1}{(x ln(b))}[/tex]

7. Log integral:

[tex]\int{log_b(x)dx} = x\left(log_b(x) - \frac{1}{ln(b)}\right) + C[/tex]

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The solution to the system of linear equation x, y are -6, 6

A system of linear equations is a collection of two or more linear equations that contain the same variables. Linear equations are equations of the form ax + by = c, where a, b, and c are constants and x and y are variables.

There are different methods to solve a system of linear equations, such as substitution, elimination, and graphing. Each method has its own advantages and limitations, and the choice of method depends on the form of the equations and the type of solution.

In this problem, we have two system of equations which are given as;

Combining both equations and solving via substitution method, the values of x and y are -6 and -6

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The slope of a line perpendicular to 3x + 2y = 6 and passes through the (2,3) is 2/3.

The slope-intercept version of the line's equation is what we need. In other words, we want y=mx+b in the form of ax+by=c. M is the slope and b is the y-intercept in the slope-intercept form.

The slope of the line parallel to the provided line is equal to the reciprocal of the supplied slope in the negative direction. Therefore, the slope is m=-1/m. The original equation is solved to produce the following result in general form:

Equation of line intercept form is

y=mx+c

3x+2y=6

2y=6-3x

y = [tex]\frac{6-3x}{2}[/tex]

y = [tex]\frac{3-3x}{2}[/tex]

y = -[tex]\frac{3x}{2}[/tex] + 3

the slope of the line is m = -3/2

Slope of line which is perpendicular to the given line = 2/3

The new line passes by (2,3)

Equation of new line is y = 2/3x + 3.

So, the slope of a line perpendicular to 3x + 2y = 6 and passes through the (2,3) is 2/3.

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The complete question is:

What is the slope of a Line perpendicular to 3x + 2y = 6 and passes through the (2,3)?

The statement angle 8=85, because 180-115=65 , 180-(65+30)=85 is true.

A triangle is a three-sided polygon that consists of three edges and three vertices.

In the given triangle one measure is given which is 30 degrees.

The angle 7 we calculate because the other side angle is 115 degrees.

The sum should be 180 degrees

115+angle 7=180

angle 7=180-115

angle 7=65 degrees

Now we know that the sum of interior angles of a triangle are 180 degrees.

65+30+angle 8=180

95+angle 8=180

Angle 8=85

Hence, the statement angle 8=85, because 180-115=65 , 180-(65+30)=85 is true.

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a. i. The change in the number of years since 2000 is not proportional to the change in the Burger Company's profit. This is because the profit is increasing by a fixed amount of $3,500 per year, not a proportionate amount based on the number of years.

ii. The number of years since 2000 is also not proportional to the Burger Company's profit. This is because the profit is not directly related to the number of years, but rather is increasing by a fixed amount of $3,500 per year.

b. i. The change in the number of miles driven is proportional to the change in the total cost of the rental car because the total cost is directly related to the number of miles driven, with a cost of $0.05 per mile.

ii. The number of miles driven is proportional to the total cost of the rental car because the total cost increases in direct proportion to the number of miles driven, with a cost of $0.05 per mile.

c. i. The change in the number cups of flour is proportional to the change in the number of cups of sugar because for every 3 cups of flour, there is 1 cup of sugar.

ii. The number of cups of flour is proportional to the number of cups of sugar because for every 3 cups of flour, there is 1 cup of sugar.

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The answer is 7 points per plane.

Points in math are a way of representing a position in space. Points are usually labeled using two numbers, usually called coordinates, which indicate the point's position on a two-dimensional plane. Each point can be described using an ordered pair of numbers, usually written as (x, y). Points are often used to graph equations, plot data, and describe lines and shapes.

This is because the first player scored 10 points per tank and 8 points per plane, while the second player scored 8 points per tank and 9 points per plane. Therefore, the difference in points per plane is 1 point (9 - 8 = 1). Since the difference in total points between the two players is 3 points (43 - 40 = 3), the difference in points per plane must also be 3 points (3/3 = 1). Therefore, each plane is worth 7 points (1 x 7 = 7).

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k = 0 or k = 8, however k = 0 is not feasible if it exists. If not, the equation will only have one variable.

The right answer for an infinite solution is k = 8.

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

A two-variable equation with a line-shaped graph is said to be linear. The set of points in the coordinate plane that make up the graph of the linear equation are all the solutions to the problem.

Given equations exists kx + 4y = k - 4 and 16x + ky = k Thus, we have

[tex]$$\begin{aligned}& a_1=k, b_1=4, c_1=-(k-4) \\& a_2=16, b_2=k, c_2=-k\end{aligned}$$[/tex]

Here condition is [tex]$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$[/tex]

substitute the values in the above equation, we get

[tex]$$\begin{aligned}& \Rightarrow \frac{\mathrm{k}}{16}=\frac{4}{\mathrm{k}}=\frac{(\mathrm{k}-4)}{(\mathrm{k})} \\& \Rightarrow \frac{\mathrm{k}}{16}=\frac{4}{\mathrm{k}} \\& \text { Also } \frac{4}{\mathrm{k}}=\frac{\mathrm{k}-4}{\mathrm{k}} \\& \Rightarrow \mathrm{k}^2=64 \\& \Rightarrow 4 \mathrm{k}=\mathrm{k}^2-4 \mathrm{k} \\& \Rightarrow \mathrm{k}=\pm 8 \\& \Rightarrow \mathrm{k}^2-8 \mathrm{k}=0\end{aligned}$$[/tex]

simplifying the equation, we get

[tex]$$\Rightarrow \mathrm{k}(\mathrm{k}-8)=0$$[/tex]

k = 0 or k = 8 but k = 0 exists not possible other wise equation will be one variable.

k = 8 exists correct value for infinite solution.

The complete question is;

Find the value of k for which the system of linear equation [tex]$\mathrm{kx}+4 \mathrm{y}=\mathrm{k}-4$[/tex] and [tex]$16 \mathrm{x}+\mathrm{ky}=\mathrm{k}$[/tex] has infinite solution.

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The total interest that Gina will Earn on her deposit through the end of the fifth year is, $32.4.

The simple interest formula is I = Prt, where P is the principal (original amount of deposit), r is the interest rate, and t is the time in years.

In Gina's case, the principal is $150, the interest rate is 4%, and the time is 5 years.

To find the interest earned in the first year, we can plug the values into the formula:

     I = 150(0.04)(1) = $6

To find the interest earned in the second year, we calculate the interest on the original deposit plus the interest earned in the first year:

     I = (150 + 6)(0.04)(1) = $6.24

To find the interest earned in the third year, we calculate the interest on the original deposit plus the interest earned in the first and second years:

     I = (150 + 6 + 6.24)(0.04)(1) = $6.48

To find the interest earned in the fourth year, we calculate the interest on the original deposit plus the interest earned in the first, second and third years:

    I = (150 + 6 + 6.24 + 6.48)(0.04)(1) = $6.72

To find the interest earned in the fifth year, we calculate the interest on the original deposit plus the interest earned in the first, second, third and fourth years:

    I = (150 + 6 + 6.24 + 6.48 + 6.72)(0.04)(1) = $6.96

To find the total interest earned through the end of the fifth year, we add up the interest earned in each year:

   6 + 6.24 + 6.48 + 6.72 + 6.96 = $32.4

Therefore, Gina will earn a total of $32.4 in interest on her deposit through the end of the fifth year.

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The missing parts of each quadrilateral and their types are:

i. x = 85^o

 Type of quadrilateral; Trapezoid

ii. x = 57^o

  Type of quadrilateral; Trapezoid

A quadrilateral is a given plane shape or figure on a 2 dimensional plane which is bounded by four straight sides. It has a series of types which are; square, rhombus, rectangle, trapezium etc. Each type of quadrilateral has individual differentiating properties.

In the given question, we have;

1. The sum of the internal angles of a quadrilateral is 360^o. So that:

109^o + 96^o + 70^o + x^o = 360^o

275 + x = 360

x = 360 - 275

  = 85

x = 85^o

The missing part is 85^o. And the type of quadrilateral is a trapezoid.

2. The sum of the internal angles of a quadrilateral is 360^o. So that:

94^o + 87^o + x^o + 122^o = 360^o

303 + x = 360

x = 360 - 303

  = 57

x = 57^o

The missing part is 57^o. And the type of quadrilateral is a trapezoid.

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hi there! the slope for those two points is 10/5

The diagonal length of the fence is 89.44 units.

Square is a polygon which has 4 sides. All four sides of the square are equal length and perpendicular to each other, that means the angle between two adjacent side is 90°.

Given:

The area of the square field is 40,000 squared unit.

We want to but a fence diagonally through the field.

To find the diagonal:

The diagonal of square,

d=a√2, where d is the diagonal and a is the side of the square.

d = √(40000)√2

d = √(80000)

d = 89.44.

Therefore, the length of the fence is 89.44 units.

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By evaluating a cost equation, we will see that Sam needs to pay $4.17

We know that one pound of chocolate costs $6.95, then we have the cost equation:

y = $6.95*x

Where y is the cost and x is the number of pounds of chocolate that you want to buy.

So, if you want to buy 0.6 of a pound, then we have x = 0.6

Then we can evaluate the equation to get:

y = $6.95*0.6

y = $4.17

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There are 126 different selections possible if at least 3 balls must be blue.

Total number of red balls: 8

Total number of blue balls: 8

Also, a woman selects 4 balls

And also at least 3 balls off the 4 must be blue

So the first combination is 3 blue and 1 red remember the woman picks up 4 balls.

And the second combination is 4 blue and 0 Red remember at least 3 blue balls

So the equation is as given below:

[tex]^nC_{r} =\frac{n(n-1)(n-2)(n-3)..... r terms.}{1*2*3..... r terms.}[/tex]

Now substitute values in the formula:

(8C3*8C1 + 8C4*8C0)=(56+70)=126 selections.

Hence, There are 126 different selections are possible if at least 3 balls must be blue.

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