How does the closure property relate to the addition of polynomials?

Answer:

12

Step-by-step explanation:

Using the properties of a 45-45-90 triangle, [tex]x=\sqrt{2}(6\sqrt{2})=12[/tex].

The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.

We have a rectangular storage container without a lid.

The formula of volume of the box is

V = l × w × h

Where

So, the height is

10 = 2w × w × h

10 = 2w² × h

h = 10/2w²

h = 5/w²

To find the total cost, calculate the area of base and sides of the box!

See the picture in the attachment!

The base area is

A₁ = 2w × w = 2w² m²

The sides area is

A₂ = 2(2wh + wh)

A₂ = 2(3wh)

A₂ = 6wh

A₂ = 6w(5/w²)

A₂ = 30/w m²

The total cost is

C = $15(2w²) + $9(30/w)

C = $30w² + $270/w

The function of the total cost is

C(w) = 30w² + 270/w

Hence, the function of constructing the box is C(w) = 30w² + 270/w.

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The proportion of the laptops is equal to 0.6 with the price range between 624 dollars to 768 dollars for the given mean and standard deviation.

As given in the question,

Given condition:

Price of of given laptops set are normally distributed:

Mean 'μ' is equal to 750 dollars

Standard deviation 'σ' is 60 dollars

let 'X' represents the price of laptops

Range of price is given by:

624 < X < 768

= (624 - μ)/σ < (X - μ)/σ < (768 - μ)/σ

= (624 - 750)/60 < (X - μ)/σ < (768 - 750)/60

= -126 /60 < (X - μ)/σ  <  18 /60

= -2.1 < Z < 0.3

From the table , value of z-score is equal to

z-score for -2.1 = 0.01786

z-score for 0.3 = 0.6179

Required proportion is equal to

0.6179 - 0.01786

= 0.6179 - 0.0179

= 0.6

Therefore, the proportion of laptops with the price between 624 and 768 is equal to 0.6.

The complete question is :

A set of laptop prices are normally distributed with a mean of 750 dollars and a standard deviation of 60dollars.

What proportion of laptop prices are between 624 dollars and 768 dollars?!

You may round your answer to four decimal places.

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Answer: 20/48=0.416 repeat

Step-by-step explanation: All I know for probability is you divide the chances of winning by total number of chances winning. Example if you by one panthers hockey ticket with 100 of other panthers hockey tickets being sold the probability is 1/100. I hope this helps

The system of inequalities that are graphed are:

y < (1/2)x + 4

y > 2x - 1

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Two coordinates from the graph of the green line.

(0, 4) and (2, 5)

The equation of the line.

y = mx + c

m = (5 - 4) / (2 - 0) = 1/2

m= 1/2

(0, 4) = (x, y)

4 = (1/2) x 0 + c

c = 4

y = (1/2)x + 4

Two coordinates from the graph of the Blue line.

(1, 1) and (2, 3).

The equation of the line.

y = mx + c

m = (3 - 1)/(2 - 1) = 2/1 = 2

m = 2

(1, 1) = (x, y)

1 = 2 + c

c = 1 - 2

c = -1

y = 2x - 1

Now,

The system of  linear inequalities that are graphed on the given graph are:

y < (1/2)x + 4

y > 2x - 1

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No, there is not a significant difference between these two values at the 95% confidence level.

The difference between the mean and literature values is 0.011 g/ml, which is less than the standard error of the mean (0.00387 g/ml). Therefore, the difference is not statistically significant. To reach a 95% confidence level, the difference must be greater than two standard errors of the mean. This would mean that the difference must be greater than 0.00773 g/ml, which it is not. Therefore, there is no significant difference between these two values at the 95% confidence level.

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A study that compares two groups of people: people with the disease or condition being studied (cases) and a very similar group of people without the disease or condition.

A cohort study is a type of longitudinal study, an approach that follows study participants over a period of time, often over many years. Specifically, cohort studies recruit and track participants who share common characteristics such as:  Specific Occupational or Demographic Similarities.

Association measures quantify the relationship between exposure and disease between two groups.

A case-control study (also called a case-reference study) is a type of observational study in which two existing groups with different outcomes are identified and compared based on putative causal attributes. A case-control study is a study of a medical condition/disease by comparing patients with the condition/disease (“cases”) to otherwise similar patients (“cases”) who do not have the condition/disease. Commonly used to identify possible contributing factors. It requires fewer resources but provides less evidence for causal conclusions than randomized controlled trials. Case-control studies yield inferior odds ratios as a measure of the strength of association compared to relative risk.

A cohort study is a type of research design that tracks a group of people over time. Researchers use data from cohort studies to understand human health and the environmental and social factors that affect it. The word "cohort" means a group of people. Cohort studies can be prospective or retrospective.

A prospective cohort study is also known as a prospective cohort study. "Prospect" refers to the future.

A retrospective cohort study is also called a retrospective cohort study. "Retrospective" means to look into the past.

To conduct a prospective cohort study, researchers identify the population to study, plan the study in advance, and collect data over time. In retrospective her cohort studies, researchers use data already available in specific groups.

A statistical measure of association, one of several factors or coefficients used to quantify the relationship between two or more variables. Association measures are used in a variety of research fields, but are most widely used in the fields of epidemiology and psychology, where they are often used to quantify the relationship between exposure and disease or behavior.

Measures of association can be determined by one of several different analyses, such as correlation analysis or regression analysis. (The terms correlation and association are often used interchangeably, but in the narrower sense correlation refers to linear correlation and association for any relationship between variables. Used to determine strength of association How it is done depends on the properties of the data in each variable. Data can be measured on an interval/ratio scale, an ordinal/rank scale, or a nominal/category scale. These three characteristics can be displayed as continuous, integer, and qualitative categories respectively.

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Answer: 120 copies

Step-by-step explanation:

Takes 480 divided by 4 = 120 copies per minute

The relationship between lines a and c, where both line a and c are perpendicular to line b is that line a and c are parallel, a ║ c

Please find attached an example drawing of the lines a and c created with MS Excel.

Parallel lines are coplanar lines that have a fixed distance between them and do not meet.

The specified information are;

the lines that are on the same plane = a, b, and c

The relationship between line a and b = a is perpendicular to b (a ⊥ b)

The relationship between line b and c = b is perpendicular to c (b ⊥ c)

The slope of a line perpendicular to another line with slope, m, is the negative inverse of m or -1/m

(The slope of parallel lines are the same)

Let the slope of line a = m, therefore;

The slope of the line b  which is perpendicular to a is -1/m

Therefore, the relationship between the lines b and c which are perpendicular (b ⊥ c) is as follows;

The slope of the line b = -1/m, therefore;

The slope of the line c, perpendicular to b is the negative inverse of the slope  of b

The slope of the line c = -1/(-1/m)) = 1/(1/m) = m

The slope of the line c = m

Therefore, the slope of the line c (m) is the same as the slope of the line a (m), which indicates that the lines a and c are parallel.

a ║ c.

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Answer:

I am so sorry but I dont see attachment

Answer:

No, the solution to the equation 8x = 72 is x = 9. To solve this equation, you can divide both sides by 8 to obtain the value of x. This gives us x = 72/8 = 9.

The equation of the line with slope [tex]1[/tex] and y-intercept is [tex]7[/tex] i.e. [tex]y=x+7[/tex]

The slope-intercept form is

[tex]y=mx+c[/tex]

Here, m is the slope and c is the y-intercept

y=x+7

The equation of the line is [tex]y=x+7\\[/tex]

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Answer:

0.5ft

Step-by-step explanation:

Answer:

12 311 12 13 14142131 32 3341 42 4351 52 5361 62 6371 72 73 7481 82 83 84014 5 6 7 8 9 1015 16 17 18 19 2022 23 2424 25 26 27 28 29 3000 0935 36 37 38 39 4044 45444546 47 48 49 5055 56 57 58 59 6066 67 68 69 7075 76 77 78 79 8085 86 87 88 89 90343454 555464 6501

Step-by-step explanation:

The set of numbers are shaded on the hundred chart are,

⇒ Only the multiple of 33.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The set of numbers are shaded on the hundred chart.

Now, We get;

Shaded numbers are,

⇒ 33, 66, 99, ...

Thus, The set of numbers are shaded on the hundred chart are,

⇒ Only the multiple of 33.

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Answer:

Step-by-step explanation:

-50 since an integer is the opposite of a whole number positive or negative.

Answer: -50

Step-by-step explanation:

Answer: 7/8?

Step-by-step explanation:

There are 13340783196 ways to allocate marks to the questions.

It is given that the exam has 12 problems.

There are 11 questions that need to be assigned at least 5 marks while the last answer needs to be assigned at least 10 marks.

Hence the least marks to be assigned

= 11 X 5  + 10

= 65.

Hence are left with assigning 35 marks.

here,

n = 12

r = 35

In this type of problem, we need to use the formula

C(n + r -1 , r)

= ⁴⁶C₃₅

= 46! / (35! X 11!)

Hence no. of way to assign marks

= 13340783196 ways.

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the answer of the question is -The current temperature and wind speed in Philadelphia

Weather describes the condition of the atmosphere, including how hot or cold, wet or dry, quiet or stormy, clear or cloudy, and so forth. The troposphere, the section of the planet's atmosphere immediately below the stratosphere, is where the majority of weather events on Earth take place.

Contrarily, climate refers to the weather patterns that can be determined by using data collected in a certain area over an extended period of time to produce adequate averages.

There are several weather conditions, such as cloudy, sunny, wet, windy, and snowy. Air masses are among the most important variables that impact the weather.

answer of the question is -The current temperature and wind speed in Philadelphia

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Answer: stars

Step-by-step explanation: if every 5th row has moons, then only the rows that are multiples of 5 have moons such as row 5, row 10, row 15 etc. since every other row has stars and 24 isn’t a multiple of 5, row 24 has stars :)

Answer:

Step-by-step explanation:

First row has moons, every fifth has moons. Therefore, 1, 6, 11, 16, 21, 26.

So the 24th row has stars.

Option-D is correct that is the larger the difference, the larger the value of chi-square, and the greater the probability of rejecting the null hypothesis.

Given that,

We have to find how will the results of a chi-square test be affected if there is a significant discrepancy between the expected and observed frequencies.

We know that,

If the observed values and expected values have a large difference then the chi-square value will be in large quantity that provides evidence against the null hypothesis and explain the huge difference between the sample data and null hypothesis.

The Chi-square statistic is,

X²=Σ i,j=0 to n (O i, j-E i,j)²/E i,j

Where,

O is the observed frequency value.

E is the Expected frequency value.

Therefore, Option-D is correct that is the larger the difference, the larger the value of chi-square, and the greater the probability of rejecting the null hypothesis.

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The student react:  Ask for a cost-of-living increase to her stipend.

"Information available from the question"

In the question:

An economics graduate student in the united states earns an $18,000 stipend per year. the u.s. sees significant inflation.

How might the student react?

Now, According to the question:

Inflation in the economy means that the price level will rise. This would lead to a decline in purchasing power. The real income of the student will decline because of the rise in price. In this situation, the student can ask for a raise in stipend proportionate to increase in the price level to counterbalance the inflationary pressures.

Hence, Ask for a cost-of-living increase to her stipend.

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A. The equations for the amounts of money Lyle and Shaun have in their accounts are represented as:

f(x) = 20x + 100

g(x) = 10x + 500

B. When f(x) = g(x), x = 40.

A linear equation can be written in slope-intercept form y = mx + b. Here, the value of m is the unit rate or slope, while the value of b is its y-intercept or initial value.

Part A:

Equation for Lyle:

y-intercept / initial value (b) = $100

Slope / unit rate (m) = $20

To write the equation, substitute m = 20 and b = 100 into f(x) = mx + b:

f(x) = 20x + 100.

Equation for Lyle:

y-intercept / initial value (b) = $500

Slope / unit rate (m) = $10

To write the equation, substitute m = 10 and b = 500 into g(x) = mx + b:

g(x) = 10x + 500.

Part B: To solve the system, we would do the following:

20x + 100 = 10x + 500

20x - 10x = -100 + 500

10x = 400

x = 400/10

x = 40

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AAA is not a congruence shortcut.

SSS, SAS, ASA, and AAS are the four shortcuts that let students know that two triangles must be congruent.

Two figures are considered to be "congruent" if they can be positioned precisely over one another.

Both of the bread slices are the same size and shape when stacked one on top of the other.

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the shapes, the shape and size should remain the same.

AAA is not a congruence shortcut we can easily proof.

Angle-Angle-Angle if we take 2 triangles all the angles are 60°.

but there may be a chance that both triangles side length are not same

one triangle has bigger length that the other.

AAA is not sufficient for  a congruence shortcut.

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By Polynomial Addition, 1st,2nd equations goes to 3rd box; 3rd,4th equations goes to 2nd box; 5th,6th equations goes to 1st box.

Steps to solve polynomial addition:

1) Take the equation.

2) Arrange the polynomial such that common terms are placed at one place.

3) Group the like terms, Like terms are terms which has equal degree and equal  variables.

4) Simplify by combining like terms.

5) Solve the equation

1st equation:

[tex]x - 3 + 2x + 3 + 2x\\= 5x + 0\\= 5x[/tex]

goes to 3rd box

2nd equation:

[tex]6x - 9 - 5x +4 - x+5x+5\\= 5x +0\\=5x[/tex]

goes to 3rd box

3rd equation:

[tex]3x+5-2x-5x+9+8x\\= 4x + 5+9\\=4x + 14[/tex]

goes to 2nd box

4th equation:

[tex]4x+x-11-5x+25+4x\\=4x + 14\\[/tex]

goes to 2nd box

5th equation:

[tex]x+8+4x-3x-4\\=2x+4[/tex]

goes to 1st box

6th equation:

[tex]5+9x-7-4x-3x+6\\=2x+4\\[/tex]

goes to 1st box

By Polynomial Addition, 1st,2nd equations goes to 3rd box; 3rd,4th equations goes to 2nd box; 5th,6th equations goes to 1st box.

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The word "to" comes before infinitives. Because they are unconstrained by time, like the idea of infinity, these verbs are known as infinitives.

In the given question, we have to explain why an infinitive called an infinitive.

The verb form known as an infinitive can be employed as a noun, adjective, or adverb. When describing acts without actually performing them, they are typically created by adding the term to before the base verb.

The word "to" comes before infinitives. Because they are unconstrained by time, like the idea of infinity, these verbs are known as infinitives. The conjugated forms of the verb, sometimes referred to as the finite forms of the verb, are derived from the infinitive.

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The probability of the given event is 1/9.

The odds against the event are 8 to 1.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

When we roll 2 dice, then

Sample space i. e possible outcomes are

{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

n(S) = 36

Let A be the event of getting a total of 5.

Therefore,

A = {(1, 4), (2, 3), (3, 2), (4, 1)}

⇒ n(A) = 4

⇒ P(A) = Probability of A = n(A) / n(S) = 1 / 36 = 1/9

(a) Probability of given event = 1/9

(b) Odds against the event = 1- P(A) / P(A)

                                             = (1 - 1/9) / (1/9)

                                             = (8/9) / (1/9)

                                             = 8/9 x 9/1

  Odds against the event    = 8/1

The reduced odds against the event are 8 to 1.

Hence, the probability of the given event is 1/9.

The odds against the event are 8 to 1.

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The estimated length of each paper clip is  0.6785 inches.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, it takes exactly 26 paper clips laid end to end to make a length of  [tex]17\frac{7}{8}[/tex]  or (17×8 + 7)/8 = 143/8 inches.

∴ The length of each clip is (143/8)/26 inches.

= 0.6785 inches.

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The probability of getting heads is 3/8.

Probability:

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty. that an event will occur. A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2 (also written as 0.5 or 50%).

Since 3 is a small number, let's list out all possible combinations.

H represents a head while T represents a tail.

3 Heads

HHH

2 Heads

HHT

HTH

THH

1 Head

HTT

THT

TTH

0 Head

TTT

The answer is

3/1+3+3+1=3/8

                                            OR

In general, we will find that the list resembles a particular row of the pascal's triangle.

If you want to know the probability of getting r heads (or tails) from n flips, it is the sum of the rth  elements in the n + 1 line. All elements of the series n+1.

[tex]\left[\begin{array}{ccc}N\\\\R\end{array}\right][/tex]/ 2ⁿ = [tex]\frac{n!}{r! * (n - r)!* 2^{n} }[/tex]

n this case,

N =3andR= 2

   3!/ 2!×1! × 2³

= 6/ 2× 1 × 8

= 3/8

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The equation of a line that is perpendicular to 2y 3x 10 and passes through (- 6 1) is -3y + 2x -1 with slope.

1. Start by finding the slope of the given line by taking the coefficient of x and dividing it by the coefficient of y.

2. To find the slope of the line perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line.

Slope of the perpendicular line: m = -2/3

3. We know that the equation of a line in slope intercept form is: y = mx + b, where m is the slope and b is the y-intercept.

4. So, the equation of the line perpendicular to 2y 3x 10 and passes through (-6 1) is:

y = -2/3x + b

5. To find the y-intercept, substitute the given point (-6 1) in the equation and solve for b.

-1 = -2/3(-6) + b

b = 1

6. Therefore, the equation of a line that is perpendicular to 2y 3x 10 and passes through (- 6 1) is -3y + 2x -1

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