why is an understanding of the central limit theorem essential to the concepts of estimation an hypothesis testing?

The Linear equations can have 2 or more answers if the lines overlap each other .

In the question ,

it is asked that can two linear equations have 2 answers or solutions .

We know that ,

(1) two linear equations can have No Solution / Zero Solution if two lines are parallel .

(2) two linear equations can have One Solution/Unique Solution if two line intersect at a point .

(3) two linear equations can have infinitely many solution if lines overlap on each other .

So from (3) , we can conclude that linear equations can have 2 or more solutions when the line are overlapping .

Therefore , Yes, the linear equations can have two answers .

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Answer:

A = 2; B = 3; C = -3

Step-by-step explanation:

The curve goes to negative infinity as x decreases and positive infinity as x increases.

This looks like a 3rd degree polynomial.

f(0) = -3

f(x) = Ax^B + x + C

f(0) = A(0^B) + 0 + C = -3

C = -3

f(x) = Ax^B + x - 3

f(1) = A(1^B) + 1 - 3 = 0

A - 2 = 0

A = 2

f(x) = 2x^B + x - 3

f(1.125) = 2(1.125)^B + 1.125 - 3 = 1

2(1.125)^B + 1.125 - 3 = 1

2(1.125)^B = 2.875

(1.125)^B = 1.4375

log (1.125)^B = log 1.4375

B × log (1.125) = log 1.4375

B = (log 1.4375)/(log 1.125)

B = 3

f(x) = 2x^B + x - 3

Answer: A = 2; B = 3; C = -3

The original size of the bag is given by the equation A = 14 ounces

What is an Equation?

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.

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 data ,

Let the original size of the bag be = A

Now , the equation will be

The increased size of the bag = 16.8 ounces

The percentage increase in the size of the bag = 20 %

So , the equation for the percentage increase in the size of the bag is

Original size of the bag + ( 20/100 ) x percentage increase in the size of the bag = increased size of the bag

Substituting the values in the equation , we get

A + ( 20/100 ) x A = 16.8

( 120 / 100 ) A = 16.8

On simplifying the equation , we get

Multiply by 100 on both sides of the equation , we get

120A = 1680

Divide by 120 on both sides of the equation , we get

A = 14 ounces

Therefore , the value of A is 14 ounces

Hence , The original size of the bag is 14 ounces

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Yes. Parabola is possible to write an equation in the form f(x) = (x-a)(x-b)

Parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.

A parabola can be described in the form of a general equation

[tex]y=ax^{2} +bx+c[/tex], with a, b, c is integers.

The form f(x)=(x-a)(x-b) can be made in other forms :

[tex]y=(x-a)(x-b)[/tex]

[tex]y=x^{2} -bx-ax+ab[/tex]

[tex]y=x^{2} -(b+a)x+ab[/tex]

That form of the equation is the same as : [tex]y=ax^{2} +bx+c[/tex]

With :  

a = 1

b = -(b+a)

c = ac  

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Therefore width = 10cm

                 height = 20cm

                 length = 20cm

given that

volume = 4,000[tex]cm^{3}[/tex]

let height = h

    width = w

    length = l

width and length are equal

height = length = h

volume of box = height × width × height

             4000  = h × w × h

             4000 = [tex]h^{2}[/tex]w

                  w = 4000/[tex]h^{2}[/tex]

surface area(SA) = area of base + sum of area of each side

                           =  [tex]h^{2}[/tex] + hw + hw + hw + hw

                           =  [tex]h^{2}[/tex] + 4hw

substitute y = 4000/[tex]h^{2}[/tex]

SA =  [tex]h^{2}[/tex]  + 4x(4000/ [tex]h^{2}[/tex] )

SA =  [tex]h^{2}[/tex]  + 16000/h

Taking the derivative:

SA' = 2h - 16000/ [tex]h^{2}[/tex]

making SA' = 0:

0 = 2h - 16000/ [tex]h^{2}[/tex]

2h = 16000/ [tex]h^{2}[/tex]

2[tex]h^{3}[/tex] = 16000

[tex]h^{3}[/tex] = 8000

h = 20 cm

w = 4000 /  [tex]h^{2}[/tex]  = 4000 / 20² = 10 cm

Therefore width = 10cm

                 height = 20cm

                 length = 20cm

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Three rules that prove two triangles are similar  AA, SAS, SSS.

When two shapes in geometry have the same shape but different sizes, they are said to be comparable. A square with sides of 21 cm and one with sides of 14 cm would be comparable. A square with sides of 14 cm and an equilateral triangle with sides of 21 cm are not comparable because they are different shapes.

Applying three triangle-specific theorems makes it simple to distinguish between similar triangles.

In geometry, correspondence refers to the exact relationship between a specific part on one polygon and a part that is similarly positioned on another polygon.

These theorems knows as

Angle-Angle (AA) = Two pairs of corresponding angles are equal.

Side-Angle-Side(SAS) = Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.

Side-Side-Side(SSS) = Three pairs of corresponding sides are proportional.

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Using system of linear equations, the number of students in year book is 25 and that of film making are 39

System of linear equations can be defined as the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.

Using variables x and y to represent to unknown values;

x + y = 64 ...eq(i)

x = 14 + y ...eq(ii)

Put eq(iii) into eq(i)

14 + y + y = 64

14 + 2y = 64

2y = 64 - 14

2y = 50

y = 25

Put y = 25 into eq(ii)

x = 14 + 25

x = 39

The number of students in film making is 39 and year book is 25

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Answer:

Therefore, when s is equal to 30, t is equal to 30 / 5 = <<30/5=6>>6.

Step-by-step explanation:

Direct variation means that the ratio between two variables is always constant. In this case, the constant ratio between s and t is equal to 20/4 = 5. This means that when t is equal to 4, s is equal to 20 and the ratio between the two is 5. If s is equal to 30, we can find the corresponding value of t by setting up the following equation:

s / t = 5

We can then solve for t by multiplying both sides of the equation by t to get:

s = 5 * t

If we substitute 30 for s, we get:

30 = 5 * t

We can solve for t by dividing both sides of the equation by 5:

t = 30 / 5

Therefore, when s is equal to 30, t is equal to 30 / 5 = <<30/5=6>>6.

Answer:

x=16

y=10

Step-by-step explanation:

(8x-14) + (5y+16) =180, because together they make a straight line.

(5x+34) = (8x-14), because they are alternate exterior angles.

Solve for x:

48=3x

x=16

Let's plug that into the first equation, then solve for y.

(8(16)-14) + (5y+16) =180

128-14+5y+16=180

130+5y=180

5y=50

y=10

Answer:

After rotating the ordered pairs 90° counterclockwise around the origin, they will become:

(3, -2)

(-7, -4)

(-4, 5)

(-6, 8)

To rotate a point 90° counterclockwise around the origin, you can use the following transformation matrix:

[[0, -1],

[1, 0]]

To rotate a point (x, y) by 90° counterclockwise, you can multiply the transformation matrix by the point, which will give you the new coordinates of the point after the rotation. For example, to rotate the point (2, 3) 90° counterclockwise, you can multiply the transformation matrix by the point:

[[0, -1],

[1, 0]] * [2, 3] = [3, -2]

Similarly, you can rotate the other points 90° counterclockwise using the same transformation matrix.

Answer:

9/20

Step-by-step explanation:

hope it helps!

Could you please give me brainliest for this? Thank you!

Answer:

Hope it helps

Step-by-step explanation:

f(3)-g(5) = 8(.5) - (2(5)+1) = 4 - 11 = -7

If you have a trend then the process is non-stationary, but if you account for the time trend, it's still stationary around the line.

What is Null hypothesis?

The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.

Consider the given process:

      [tex]x_{t} = c+\alpha x_{t-1}+\beta _{t} \\E[\beta _{t}]=0\\[/tex]

Obtain mean,

     [tex]E[x _{t}]=\frac{c}{1-\alpha }[/tex]

This works only when |α|<1. If α=1 this doesn't work, it blows up, because , [tex]E[x _{t}]\neq E[x _{t-1}][/tex] i.e. the process is not stationary.

The constant refers to the term c.

The trend is easy too:

    [tex]x_{t} +c+\alpha t+\alpha x_{t-1} +\beta_{t}[/tex]

In this case,

  [tex]E[x _{t}]=\frac{c+\alpha t}{1-\alpha }[/tex]

So, if you have a trend then the process is non-stationary, but if you account for the time trend, it's still stationary around the line.

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The length of the perimeter of the rectangle = 112 cm or 44 inches

Given in the question,

Area = [tex]105in^{2}[/tex]

= 677.4 [tex]cm^{2}[/tex]

Length of one side of the rectangle = 7 inches

= 17.7 cm

∴ Since the length of one side of the rectangle is given in the question we need to find the width of the rectangle to calculate the total perimeter of the rectangle

⇒ Area = length x width

⇒ 677.4 = 17.7 x width

⇒ Width = [tex]\frac{Area}{Length}[/tex]

⇒ Width = [tex]\frac{677.4}{17.7}[/tex]

⇒ Width = 38.2 cm

As we got both the length and the width of the rectangle, now we can calculate the perimeter,

⇒ Perimeter = [tex]2( length + width)[/tex]

⇒ Perimeter = [tex]2(17.7 + 38.3)[/tex]

⇒ Perimeter = 2 x 56 cm

⇒ Perimeter = 112 cm

⇒ In inches = 44 inches

Therefore, the length of the perimeter is = 112cm or 44 inches

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Answer:

The length of the side of the square should be 10ft

Step-by-step explanation:

Calculation of the length of the side:

Since A square has an area of 40 square feet.

As we know that the square does have 4 sides

So, the length of the side of the square should be

40 divided by 4

= 10ft

The correlation coefficient that represents a perfect linear relationship between x and y is 1 and -1. (Option C and D)

The correlation coefficient refers to a statistical measure of the strength of a linear relationship between two variables and lies with the range from -1 to 1. In other words, a correlation coefficient is a statistical measure of the degree to which changes to the value of one variable predict change to the value of another.

A linear relationship is a statistical term which is used to describe a straight-line relationship between two variables. A perfect linear relationship refers to a relationship in which one of the variables can be perfectly explained by a linear function of the other and can be achieved by the correlation coefficient of 1. A correlation of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation.

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Therefore, 6 minutes and 40 seconds are needed to test possibilities.

Combinations are sometimes known as selections. Combinations are the results of selecting elements from a set assortment. Nothing specific is being organized here. We are choosing them. To denote the number of unique r-selections or combinations among a set of n items, we write n C r. Combinations are distinct from arrangements or permutations.

Here,

The first two numbers in this three-term series are 17 and 24, and the third one remains a mystery.

Given that there are 40 options for the third number and that each try takes 10 seconds, we have 40 x 10 seconds, or 400 seconds, to try every possible combination.

Thus,

=> 400 seconds  is equals to 6 minutes and 40 seconds

Therefore, 6 minutes and 40 seconds are needed to test every scenario.

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Answer: $18.50

Step-by-step explanation:

Take 277.50 divided by 15 = $18.50

The required price of each tube for rent is given as $18.6.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Renting 15 tubes for a float down the Ichetucknee River costs $277.50 for a group.
So,
Let the rent of each tube be x,
According to the question,
15x = 277.50
x = 277.50 / 15
x = 18.6

Thus, the required price of each tube for rent is given as $18.6.

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It is false, that the margin of error of a confidence interval is the error from biased sampling methods.

The margin of error of a confidence interval is the amount of accuracy in a sample with respect to the population. It is calculated by taking the sample standard deviation and dividing it by the square root of the sample size. The margin of error helps to quantify the reliability of estimates and provides a range within which the population parameter is likely to fall. It does not refer to errors in sampling methods, which are typically a result of bias. Bias is a systematic error that arises from the sampling procedure, resulting in estimates that are not an accurate representation of the population.

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Hence, the factors of [tex](10x+1)^2=100x^2+1+20x[/tex].

What are the factorization?

Factorisation or factoring is defined as the breaking or decomposition of an entity into a product of another entity, or factors, which when multiplied together give the original number.

Here given expression is

[tex]100x^2+1[/tex]

[tex](10x)^2+(1)^2[/tex]

[tex](10x+1)^2[/tex]

As we know that,

[tex](a+b)^2=a^2+b^2+2ab[/tex]

Here

[tex]a=10x\\b=1[/tex]

So,

[tex](10x+1)^2=(10x)^2+(1)^2+2(10x(1))\\\\(10x+1)^2=(10x)^2+(1)^2+20x\\\\(10x+1)^2=100x^2+1+20x[/tex]

Hence, the factors of [tex](10x+1)^2=100x^2+1+20x[/tex].

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The factors of the expression 100x² + 1 are (10x+i) (10x-i).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

The given expression is 100x² + 1.

The given expression is a quadratic function.

The standard form of quadratic function:

ax²+bx +c, where a is not equals to zero.

Comparing with the standard form we get,

a = 100, b = 0 and c = 1

Simplifying,

100x² + 1

=  100x² - (-1)

= (10x)² - (-1)

= (10x)² - (i)²   ,{i² = -1}

= (10x+i) (10x-i)

Therefore, (10x+i) (10x-i) are the factors.

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Answer:

Step-by-step explanation:

cdcdfcdfvdsfdf

The value of the obtuse angle by applying sine rule for the attached diagram is equal to x° = 38.2°.

As given in the question,

Diagram of the obtuse angle triangle is attached.

In the given triangle,

Name the vertex of angle x as 'C' and side opposite to angle x as AB.

Draw a perpendicular from point A to BC at point D such that AD = z .

Given m ∠ACB = x°

AB = 2y

AC = y

m ∠ABC = 18°

In ΔADB,

sinB = AD / AB

⇒ sin 18° = z / 2y __(1)

In ΔACD,

sin ACD = AD / AC

⇒ sin ( 180 - x )° = z  / y  __(2)

Divide (1) by (2) we get,

sin18° / sin ( 180 - x )° = ( z / 2y ) / ( z / y )

⇒ sin 18° / sinx° = 1 / 2

⇒ sinx° = 2sin18°

⇒ sinx° = 2 (0.309 )

⇒ x° = sin⁻¹( 0.618)

⇒x° =  38.2°

Therefore, the obtuse angle for the given attached diagram using sine rule is equal to 38.2°.

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This cannot be furtherly simplified because the sum or difference of 2b+8 depends upon the value of b.

An expression is combination of variables, numbers and operators.

The given expression is 2b+8.

In the given expression b is the variable and 2 is the coefficient of the variable b. eight is the constant value and plus is the operator.

As there is a plus sign we need to add the two terms 2b and 8.

We do not know the value of b so we cannot simplify the expression further. The value of 2b plus eight depends upon the value of b, if it is positive then we add two terms and if it is negative we use difference,

Hence, the sum or difference of 2b+8 depends upon the value of b and cannot be furtherly simplified.

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The evergreen tree grew 2.4 feet taller the next year.

Percentage can be derived by dividing the given value by the total value, and then multiplying the result by 100.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

It is given by:

Percentage = (given value / total value) * 100%

From the question, the tree has a base height of 20m, if it grew 20% taller then;

tree height = 12 x (20/100)

tree height = 12 x 0.2

tree height = 2.4

Therefore, the tree grew 2.4 feet taller the next year.

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Answer:

Step-by-step explanation:

1.75+ 14.50+ 3.25= 19.5

8.25% of  19.5= 1.60875

19.5 + 1.60875= 19.7 rounded

19.7+ 17%= 19.87

$19.87 is the total

I rounded so the closest to this might be the answer

Answer:

Step-by Graph the line using the slope and y-intercept, or two points

Slope=3

y-intercept=18-step explanation:

Answer:

Step-by-step explanation:

x=-40