What is the approximate percent decrease from 1,865 to 1,240?

Answers

Answer 1

Answer:

It is approximately 33.5%

Answer 2

Answer:

A

Step-by-step explanation:

33.5%


Related Questions

1. Use the spinner at the​ right, which is divided into equal​ sections, to detemine the following probability. ​P(brown or greater than 9​)
2. Using a green number cube and a blue number​ cube, find the following probability. ​P(green less than 9 and blue greater than 3​)
3. You choose a tile at random from a bag containing 5 ​A's, 2 ​B's, and 3 ​C's. You replace the first tile in the bag and then choose again. Find ​P(C and C​). Question content area bottom Part 1 ​P(C and C​)=enter your response here ​
4. You pick a coin at random from the set shown at the​ right, and then pick a second coin without replacing the first. Find the probability. ​P(penny then nickel​)

1. Use the spinner at the right, which is divided into equal sections, to detemine the following probability.

Answers

Using it's concept, the probability is calculated as follows:

P(brown or greater than 9​) = 3/5.

What is a probability?

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

In the context of this problem, we have that:

The desired outcomes are the five brown regions, plus the green region with the number 10, which is a number greater than 9.The total outcomes are the 10 regions of the spinner.

The desired probability is calculated as follows:

P(brown or greater than 9​) = 6/10 = 3/5.

Both 6 and 10 can be simplified by 5, hence the simplified probability is of 3/5.

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find the value of k.

(x^2+5x+k)/(x+6) has a remainder of 9.

if anyone could help, please do!! this is urgent!

Answers

The value of k in the polynomial is 3

How to solve for k?

The quotient is given as:

(x^2+5x+k)/(x+6)

The remainder is 9

Set the denominator to 0

x + 6 = 0

Solve for x

x = -6

This means that:

f(-6) = 9

So, we have:

(-6)^2 + 5(-6) + k = 9

Evaluate

6+ k = 9

Subtract 6 from both sides

k = 3

hence, the value of k is 3

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Write a story that can be represented using the equation y=x+1/5x

Answers

A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?

How to illustrate the equation?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.

This can be illustrated as:

y = x + 1/5x

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Which numbers are less than –83? Select all that apply.

Answers

Step-by-step explanation:

there aren't any answer choices but on the number line it is anything to the left of -83

Answer:

You didn't provide the answers, but I can still help you :)

Step-by-step explanation:

____________________________________________________________

    anything back here will be correct :)                        -83

It is possible for 2 lines to
intersect in such a way
that 3 of the angles
formed have measures 20,
70, and 20.?

Sometimes true,
Never true,
Always true.

Answers

Answer:

sometimes true

Step-by-step explanation:

Given, two straight lines intersect each other in such a way that one of the angles formed measure 90°.

We know that, lines which intersect to form a right angle are known as perpendicular lines

In the above figure , AB is perpendicular to CD

Considering ∠AOC=90°

Now,

∠AOC+∠AOD=180°     [Linear pair]

90°+∠AOD=180°

∠AOD=90°

Similarly,

∠AOC+∠BOC=180° and ∠BOD+∠AOD=180°   [Both making linear pair]

So, we get ∠BOC=90° and ∠BOD=90°

Hence, ∠AOC=∠AOD=∠BOC=∠BOD=90°

Factor completely. 4x^2-x-5

Answers

The factors of the given equation 4x^2-x-5 are 5/4 and -1.

What is referred as the factors of the polynomial?Factoring polynomials is the inverse procedure of multiplying polynomial factors. Factors of polynomials are zeros of polynomials that take the form of some other linear polynomial. If we divide a given polynomial by any of its factors after factorisation, the remainder would be zero.Factors are integers which are multiplied together to create the original number. The factors in the particular instance of polynomials are the polynomials that are multiplied to generate the original polynomial.

For the given question, the expression is given as;

= 4x^2-x-5

as, 4×5 = 20, break the number such that on subtraction we will get -1.

=  4x^2 - 5x + 4x -5

Taking x common from first two digit.

= x(4x - 5) + (4x - 5)

Taking common again.

= (4x - 5)(x + 1)

Put the equation equal zero to find the factor.

4x - 5 = 0

x = 5/4

and, x + 1 = 0

x = -1

Thus, the factors are found as 5/4 and -1.

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HELP!
Which sentence is correct?
A. -2/5 = 0.4
B. - 2/5 = -0.4
C. -5/2 = 2.5
D. 5/2 = -2.5

Answers

Answer:

B

Step-by-step explanation:

First find out that 2/5=0.4

And if both side don't have/have the negative sign, it's right so the correct answer is B

Answer:

Step-by-step explanation:

B is correct

-2 divided by 5 = - 0.4

Solve this system of equations:
2x + 10y= 24
X = y-6

Answers

Answer:

(-3,3)

Step-by-step explanation:

Substitute x for the first equation

2(y-6) + 10y= 24

2y-12+10y=24

12y=36

y=3

Now solve for x by plugging in 3

x = 3-6

x=-3

Answer:

x = -3

y = 3

Step-by-step explanation:

2x + 10y = 24

x = y - 6

plugin x = y - 6 into the first equation

2(y - 6) + 10y = 24

solve for y

2y - 12 + 10y = 24

12y = 36

y = 3

plug y back into x = y - 6

x = 3 - 6

x = -3

Factor completely 50a2b5 − 35a4b3 + 5a3b4

Answers

The complete factorisation of 50a²b⁵ − 35a⁴b³ + 5a³b⁴ is 5a²b³(10b² - 7a² + ab)

How to factorise?

Factorisation is the process of writing an expression as a product of two or more common factors.

The expression is written as a product of several factor.

Therefore,

50a²b⁵ − 35a⁴b³ + 5a³b⁴

Hence, the complete factorisation is as follows;

5a²b³(10b² - 7a² + ab)

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At a local fitness​ center, members pay a ​$6 membership fee and ​$4 for each aerobics class. Nonmembers pay ​$5 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the​ same?

Answers

For members :

Membership fee = $6.

Cost of each aerobics class = $3.

Slope -intercept form for total cost for members:

y = 3x + 6.

For non-members:

Cost of each aerobics class = $4.

Slope -intercept form for total cost for non-members:

y= 4x.

When cost will be same,

4x = 3x+6.

Solving equation for x now.

Subtracting 3x from right side, we get

4x-3x = 3x-3x+6

x = 6.

Therefore, 6 number of aerobics classes will the cost for members and nonmembers be the same.

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The manager of an office supply store can sell 10 boxes of pencils at a price of $2. 19 per box. If the price is $1. 70, she can sell 24 boxes. The total cost of buying x boxes of pencils is C(x)=0. 55x+20 dollars.


Assuming the demand function is linear, find an equation for D(x). Do not round your answer

Answers

The profit generated from selling x boxes of pencils is a linear function of x, with a slope of $0.80 and a y-intercept of -$12.60

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range) with the property that each input is related to exactly one output.

Let us first define the demand function as D(x), where x is the number of boxes of pencils sold. We know that the manager can sell 10 boxes of pencils at a price of $2.19 per box, which means that the revenue generated from this sale is:

10 * $2.19 = $21.90

Similarly, when the price is $1.70, she can sell 24 boxes of pencils, which gives a revenue of:

24 * $1.70 = $40.80

Now, we can use these two data points to find the equation of the demand function. Since we assume that the demand is linear, we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept. In our case, y represents the revenue generated by selling x boxes of pencils.

To find the slope, we use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the two data points we have.

m = ($40.80 - $21.90) / (24 - 10)

m = $18.90 / 14

m = $1.35

To find the y-intercept, we can use either of the two data points and solve for b:

$21.90 = $1.35 * 10 + b

b = $7.40

Therefore, the demand function for the pencils is:

D(x) = $1.35x + $7.40

This means that for each additional box of pencils sold, the revenue generated increases by $1.35. The y-intercept of $7.40 represents the revenue generated when no pencils are sold, which includes fixed costs such as rent, utilities, and wages.

We also have the cost function C(x) = 0.55x + $20, which represents the total cost of buying x boxes of pencils. The profit function P(x) is defined as the difference between the revenue and the cost:

P(x) = D(x) - C(x)

Substituting the expressions for D(x) and C(x), we get:

P(x) = ($1.35x + $7.40) - (0.55x + $20)

Simplifying this expression, we get:

P(x) = $0.80x - $12.60

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Please help me with this problem trying to help my son to understand.Factor.9x^2−49y^2 Enter your answer in the box.

Please help me with this problem trying to help my son to understand.Factor.9x^249y^2 Enter your answer

Answers

This binomial can be factored as a difference of two squares. Taking the square root of each term, we get:

\(\begin{gathered} a^2=9x^2 \\ a=\sqrt[]{9x^2} \\ a=\sqrt[]{9}\sqrt[]{x^2} \\ a=3x \end{gathered}\)\(\begin{gathered} b^2=49y^2 \\ b=\sqrt[]{49y^2} \\ b=\sqrt[]{49}\sqrt[]{y^2} \\ b=7y \end{gathered}\)

Difference of two squares formula

\(a^2-b^2=(a+b)(a-b)\)

Substituting with the values of a and b found, we get:

\(9x^2-49y^2=(3x+7y)(3x-7y)\)

PLEASE HELP! DUE TONIGHT!!!!
I will make you brainlist please show all steps worth 30% of my class mark

PLEASE HELP! DUE TONIGHT!!!!I will make you brainlist please show all steps worth 30% of my class mark

Answers

Answer:

Step-by-step explanation:

Equation:

y=(x+5)(x-1)

a) zeroes happen when you solve for x when y=0, you can set each parentheses =0

       x+5=0             and             x-1=0

>        x= -5            and               x =  1

b) see image

d) the x coordinate for the vertex in the middle of the 2 zeroes.  The middle of -5 and 1 is -2

> -2

e)  substitute -2 into equation:

y=(x+5)(x-1)

y=((-2)+5) ((-2)-1)

y=(3)(-3)

> y= -9

f) see second image

PLEASE HELP! DUE TONIGHT!!!!I will make you brainlist please show all steps worth 30% of my class mark
PLEASE HELP! DUE TONIGHT!!!!I will make you brainlist please show all steps worth 30% of my class mark

compute the flux of the vector field f = i 4 j − 2 k through the oriented rectangular region s shown in x y z s 1 1 2 lying above the square d = {(x, y) : 0 ≤ x, y ≤ 1 }

Answers

The flux of the vector field f through the oriented rectangular region S is equal to zero.

The rectangular region S is shown in the x-y plane with the square D in it. The orientation of the rectangular region S is determined by the right-hand rule. The direction of the normal to the region S is given by the vector (0,0,-1).By using the divergence theorem, the flux of the vector field f through the oriented rectangular region S can be computed. The divergence theorem states that the flux of the vector field across a closed surface is equal to the volume integral of the divergence of the vector field over the enclosed volume.V = {(x,y,z): 0 ≤ x, y ≤ 1, 0 ≤ z ≤ 2}.Therefore, the flux of the vector field f through the oriented rectangular region S is equal to the volume integral of div f over V. We can express the vector field f in terms of its component functions: f(x, y, z) = (1, 4, -2). Thus, div f = 0. T

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The radius of a cylinder is 4 inches and the height is 5 inches. Which statements are correct? Check all that apply.The area of the two bases is 16π in2.The area of the two bases is 32π in2.The lateral area is 40π in2.The lateral area is 72π in2.The total surface area is 72π in2.The Correct Answer is: 2,3,5

Answers

The radius of a cylinder is 4 inches and the height is 5 inches. The surface area is equal to the sum of the areas of all the faces of a solid.

A cylinder has two circular bases, and each circular base has an area of πr² square units, where r is the radius of the base. The lateral area of a cylinder is the area of the cylinder's curved surface, which is the height of the cylinder multiplied by the cylinder's base perimeter. It is given by the formula: 2πrh. The surface area of the cylinder is obtained by summing the lateral area and two times the area of the base. Hence, we have:

Surface area = 2πrh + 2πr²

Let us calculate the area of the two bases by plugging the given values into the formula.

Area of one base = πr²= π (4)²= 16π square inches

Therefore, the area of the two bases is 2 × 16π = 32π square inches. Thus, statement 2 is correct

Lateral area of a cylinderLateral area = 2πrh= 2 × π × 4 × 5= 40π square inches.

Thus, statement 3 is correct.

The total surface area of the cylinderTotal surface area = Lateral area + 2 × Area of base= 2πrh + 2 × πr²= 2πr(h + r)= 2π × 4(5 + 4)= 72π square inches.

Therefore, statement 5 is correct.

Therefore, the following statements are correct:Statement 2: The area of the two bases is 32π square inches.Statement 3: The lateral area is 40π square inches.Statement 5: The total surface area is 72π square inches are true.Therefore, the correct statements are 2, 3, and 5.

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Determine the product of the binomial -5x-7 and the trinomial
3x2-4x-5. To earn full credit, show your work using a method explained in
the Orientation

Answers

Answer:

\(( - 5x - 7)(3 {x}^{2} - 4x - 5) \\ \\ - 15 {x}^{3} + 20 {x}^{2} + 25x - 21 {x}^{2} + 28x + 35 \\ \\ - 15 {x}^{3} + 20 {x}^{2} - 21 {x}^{2} + 25x + 28x + 35 \\ \\ = - 15 {x}^{3} - {x}^{2} + 53x + 35\)

I hope I helped you^_^

which triangle is congruent to an isosceles triangle that has the two long sides and the bottom line is short

Answers

An isosceles triangle with two long sides and a short bottom side can have infinitely many possible congruent triangles. However, assuming that the two long sides have a fixed length of 1 unit and the length of the short bottom side is less than 1 unit, there are only two possible congruent triangles.

One of the congruent triangles would have angles of approximately 22.62°, 22.62°, and 135.76°, while the other congruent triangle would have angles of approximately 157.38°, 11.25°, and 11.25°. Therefore, the answer to this question depends on the specific length of the short bottom side and the context of the problem.

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7 1
The equation Y-2-3(x-4) is written in point-slope form. What is the y-intercept of the equation?

Answers

9514 1404 393

Answer:

  -10 or (0, -10) as an ordered pair

Step-by-step explanation:

The y-intercept is the value of y when x=0. Using x=0 in the equation gives ...

  y -2 = 3(0 -4)

  y = -12 +2

  y = -10 . . . . . the y-intercept

7 1The equation Y-2-3(x-4) is written in point-slope form. What is the y-intercept of the equation?

what is the equation of the straight line that passes through the points (0,3) and (4,3)

Answers

Answer:

\(y=3\)

Step-by-step explanation:

The slope of a line is given as \(m=\frac{\Delta y}{\Delta x}\), where \(\Delta y\) is change in y-value and \(\Delta x\) is change in x-value for any two points the line passes through.

Using the points (0, 3) and (4, 3) as given in the problem, we have:

\(m=\frac{0}{-4}=0\). Therefore, the slope of this line is 0.

In slope-intercept form, we have \(y=mx+b\). Since we've found out that \(m=0\) the entire term \(mx\) will be equal to 0 and we are left with \(y=b\), where \(b\) is the y-intercept. We can plug in the coordinates of any point the line passes through to find this value:

Using the point (4, 3) as given in the problem:

\(3=0(4)+b,\\3=0+b,\\b=3\)

Thus, the equation of our line is \(y=0x+3,\\\boxed{y=3}\)

Two angles are supplementary. The first angle is 3x degrees. The second angle is (2x + 25) degrees. Determine the measure of each angle.

Answers

Answer: a = 3x

b = 2x+25

180 = a + b

180 = 3x + 2x + 25

180 = 5x + 25

155 = 5x

x = 31

a = 3*31 = 93

b = 2*31 + 25 = 87

Step-by-step explanation: pls mark as branlyest

The table below shows a proportional relationship. True or False?

Answers

According to the image, the table shows a relationship that is not proportional. First of all, you cannot multiply a number by 0 and get something other than 0. Anything multiplied by 0 is always 0.

Second, the rule is different for each row.

2x5=10

4x4=16

6x3.6=22

A proportional relationship must increase by the same amount, and this does not, which means it is not proportional.

The table below shows a proportional relationship. True or False?

Find common ratio

0+4(1)=42+4(2)=104+4(3)=166+4(4)=22

Yes they are proportional

The table below shows a proportional relationship. True or False?

fill in the blank. anthony placed an advertisement for a new assistant on november 1. he hired marquis on december 1. his _______ was 30 days.

Answers

Anthony's "hiring process" or "recruitment period" was 30 days.

The blank can be filled with "hiring process" or "recruitment period" to indicate the duration between placing the advertisement for a new assistant on November 1 and hiring Marquis on December 1. This period represents the time it took Anthony to evaluate applicants, conduct interviews, and make the decision to hire Marquis.

The hiring process typically involves several steps, such as advertising the job opening, reviewing applications, conducting interviews, and finalizing the selection. The duration of this process can vary depending on various factors, including the number of applicants, the complexity of the position, and the efficiency of the hiring process.

In this case, the hiring process took 30 days, indicating the length of time it took for Anthony to complete the necessary steps and choose Marquis as the new assistant. This duration provides insight into the timeframe Anthony needed to assess candidates and make a hiring decision.

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how does attitude, beliefs and knowledge impact how a teacher delivers a lesson

Answers

Attitude, beliefs, and knowledge shape a teacher's delivery: attitude affects engagement, beliefs influence instructional decisions, and knowledge enables effective communication and learning facilitation.

Attitude, beliefs, and knowledge play crucial roles in shaping how a teacher delivers a lesson. Here's a detailed explanation of their impacts:

Attitude:

Attitude refers to a teacher's mindset, emotions, and approach towards teaching. A positive attitude fosters enthusiasm, motivation, and a genuine passion for the subject matter. This translates into an engaging and dynamic teaching style, creating an environment conducive to learning. Conversely, a negative attitude can lead to disinterest, lack of enthusiasm, and a disengaged teaching approach, which can hinder students' engagement and comprehension.

Beliefs:

A teacher's beliefs influence their instructional decisions and pedagogical strategies. Beliefs about students' capabilities, learning styles, and the purpose of education can shape the teacher's approach to delivering a lesson. For example, if a teacher believes that all students have the potential to succeed, they may employ differentiated instruction techniques to cater to diverse learning needs. Conversely, if a teacher holds limiting beliefs about students' abilities, they may adopt a one-size-fits-all approach, which may hinder student progress.

Knowledge:

A teacher's knowledge encompasses both subject matter expertise and pedagogical content knowledge. Profound knowledge of the subject allows a teacher to effectively structure and present the lesson, answer student queries, and provide relevant examples. Pedagogical content knowledge helps in selecting appropriate instructional strategies, adapting to student needs, and assessing learning effectively. Without a strong knowledge base, a teacher may struggle to deliver accurate information, engage students, or address misconceptions.

Collectively, attitude, beliefs, and knowledge significantly impact a teacher's delivery of a lesson. A positive attitude enhances student motivation and engagement. Strong beliefs in students' potential and individualized instruction foster a supportive learning environment. Adequate subject knowledge and pedagogical skills enable effective communication and facilitate meaningful learning experiences. By combining these elements, teachers can create an impactful and effective learning environment that nurtures student growth and achievement.

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Convert rational numbers to their equivalent decimals

Answers

Answer:

 In order to change a rational number to a decimal, we just convert the number into the form of a fraction. We then divide the numerator with the denominator and find out the exact value of the division.

PLS answer asap stuck on this

PLS answer asap stuck on this

Answers

It should be increased by 0.75 amount

a 16 pound bag of kitty kibbles is $24. an 8 pound bag of feline flavors is 11.20. which statement about the unit prices is true

Answers

Feline Flavor is cheaper per pound than Kitty Kibbles (or Kitty Kibbles is more expensive than Feline Flavor per pound).

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

To find the unit price you divide the total cost of the bag by the amount of pounds in the bag.

Thus, the unit price of Kitty Kibbles is 24/16, or 1.5.  This means that each pound of Kitty Kibbles costs $1.50.

Also, the unit price of Feline Flavor is 11.20/8, or 1.4.  This means that each pound of Feline Flavor costs $1.40

Feline Flavor is cheaper per pound than Kitty Kibbles (or Kitty Kibbles is more expensive than Feline Flavor per pound).

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someone pls help me out on one of these!!!!! it’s questions 3-9 I really need help!

someone pls help me out on one of these!!!!! its questions 3-9 I really need help!

Answers

Two other names of line g are WQ and QW.R, Q, and S are collinear.The intersection of two lines is point Q on Plane V.Three segments with endpoint q are WQ, RQ, and SQ.All angles with vertex M are JMK and KML.The pair of adjacent angles is KML and KLM.The pair of supplementary angles are JMK and KML

What are supplementary angles?

When two angles add up to 180 degrees, they are supplementary (a Straight Angle). As long as the sum is 180, they don't have to be close to each other.

Given, a graph in which two lines g and f intersect each other at a point "Q" on a plane "V".

Two rays that have a common endpoint and are referred to as the angle's sides and vertices, respectively, form an angle. Two rays can form angles in the plane where they are positioned.

Angles with a sum of 180 degrees are referred to be complementary angles. Complementary angles are those formed by straight lines.

The 90-degree angles between the two lines are known as supplementary angles.

Therefore, WQ and QW are two other names for line g. R, Q, and S intersect at R. Point Q on Plane V is where two lines meet. WQ, RQ, and SQ are the three segments that have endpoint q. Every angle that has the vertex M is JMK and KML. KML and KLM are the two nearby angles. JMK and KML are the pair of supplementary angles.

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If B is between A and C and AB = 3x + 1, BC = 2x - 7, and AC = 24, then
find the value of x.

Answers

AB + BC = AC

3x+1 +2x -7 = 24

5x -6 = 24

5x = 30

x = 6

The value of x is 6.

It is required to find the scientific notation.

What is line?

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

GIven:

let AC is straight line and B is on line.

B is between A and C

AB = 3x + 1,

BC = 2x - 7,

AC = 24,

We have to find the value of x.

According to given question we have,

AB + BC = AC

3x+1 +2x -7 = 24

5x -6 = 24

5x = 30

x = 6

Therefore, the value of x is 6.

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What is the independent variable in this function?

What is the independent variable in this function?

Answers

Answer:

p.

Step-by-step explanation:

p is the independent variable.

The dependent one is h.

The value of h depends on the value of p.

A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be 0.2 centimeters in diameter. The variance of the bolts should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level? Step 1 of 5: State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary. A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be 0.2 centimeters in diameter. The variance of the bolts should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level? Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is twotailed, separate the values with a comma. Round your answer to three decimal places. A bolt manufacturer is very concerned about the consistency with which his machines produce boits. The bolts should be 0.2 centimeters in diameter. The variance of the boits should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level?

Answers

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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