Determine whether each function is linear or nonlinear

1. 2x(5+x)=y
2. Y=7x+15
3. X/y=8

Table A represents a function, but Table B does not represent a function.

Table must meet the following requirements in order to qualify as a function (see the.jpeg picture attached with this response):

The tables below show the values of y corresponding to different values of x: Table A x 3 2 1 y 1 0 0 Table B x 3 5 4 y − 2 1 1

1. Requirement: Each element in the first circle must be linked to at least one element in the second circle.

2. Requirement: There CANNOT be more than one relationship between items in the first circle and those in the second circle.

Table A is in fact a function because it meets BOTH of these requirements.

Table B is not a function since it meets the FIRST criteria but not the SECOND condition.

so

Table A represents a function, but Table B does not represent a function.

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Answer:

The average rate of change of f(x) over the interval from x = 4 to x = 8 can be calculated as follows:

\frac{f(8)-f(4)}{8-4} = \frac{11-(-4)}{8-4} = \frac{15}{4} = 3 \frac{3}{4}

Therefore, the average rate of change of f(x) over the interval from x = 4 to x = 8 is 3 \frac{3}{4}.

The average rate of change of f(x) over the interval from x = 4 to x = 8 is 3.75.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

we have the table,

x     4 5  6  7  8  9  10

f(x) -4 -2 8 10 11 14 18​

So, the value of f(4)= -4 and f(8) = 11

Now, average rate of change

= f(8)- f(4) / (8-4)

= 11 - (-4) / 4

= 15 / 4

= 3.75

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The data set 0, 1, 3, 3, 3, 5, 6 will have the standard deviation.

We are asked to select the sets with the lowest standard deviation. The given sets are

0, 1, 3, 3, 3, 5, 6

0, 25, 50, 100, 125, 150, 1000

0, 1, 2, 3, 4, 5, 6

0, 0, 0, 100, 200, 200, 200

The standard deviation is used to calculate the variability of the data set. It tells us how to spread the data points from the mean value. The standard deviation is the measure of dispersion that tells us about the spread of the data points from the mean value.

In all the options given only in the data given in 0, 1, 3, 3, 3, 5, 6 have all the values near to each other, this data set has less variation between each other. Hence, data set 0, 1, 3, 3, 3, 5, 6 will have the lowest standard deviation.

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(a) All the values in the last column of the truth table are T, the statement [p ^ (p V q)] → q is a tautology.

(b) All the values in the last column of the truth table are T, the statement [(p → q) ^ (q + r)] → (p + r) is a tautology.

(c) All the values in the last column of the truth table are T, the statement [p ^ (p → q)] → q is a tautology.

Here is the truth table for each of the conditional statements

a) [p ^ (p V q)] → q

p p V q p ^ (p V q) q [p ^ (p V q)] → q

T T T T T

T T T F F

T F F T T

F T F T T

F F F T T

F F F F T

Since all the values in the last column of the truth table are T, the statement [p ^ (p V q)] → q is a tautology.

b) [(p → q) ^ (q + r)] → (p + r)

p q r p → q q + r (p → q) ^ (q + r) p + r [(p → q) ^ (q + r)] → (p + r)

T T T T T T T T

T T F T T T T T

T F T F T F T T

T F F F F F T T

F T T T T T T T

F T F T T T F T

F F T T T T F T

F F F T F F F T

Since all the values in the last column of the truth table are T, the statement [(p → q) ^ (q + r)] → (p + r) is a tautology.

c) [p ^ (p → q)] → q

p p → q p ^ (p → q) q [p ^ (p → q)] → q

T T T T T

T F F T T

F T F T T

F T F T T

Since all the values in the last column of the truth table are T, the statement [p ^ (p → q)] → q is a tautology

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Answer:

number of commercials: 6

Number of movies: 4

Step-by-step explanation:

Let x = the number of commercials

Let y = the number of movies

30x + 110 y = 620

x + y = 10     This can be written y = 10 - x (substitute 10 - x for y)

30x + 110y = 620

30x + 110(10 - x) = 620   Distribute the 110

30x + 1100 - 110x = 620    Combine like terms

-80x + 1100 = 620   Subtract 1100 from both sides

-80x = -480   Divide both sides by -80

x = 6

There are 6 commercials.

Substitute 6 for x

x + y = 10

6 + y = 10   Subtract 6 from both sides

y = 4

There are 4 movies.

Check:

x + y = 10

6 + 4 = 10

10 = 10  checks

30x + 110y = 620

30(6) + 110(4) = 620

180 + 440 = 620

620 = 620 checks

If we assumes that the taxpayer has $100,000 as his income on the completed Form 1040, the total tax that the employee is responsible for paying will be $17,836.

A tax bracket is a range of incomes that are taxed at a specific rate. Tax brackets are part of a progressive tax system, which means that tax rates increase progressively as an individual's income increases. Low-income taxpayers pay relatively low tax rates, while higher-income taxpayers pay higher rates.

In 2022, for example, a single filer with taxable income of $100,000 will pay $17,836 in taxes, representing an average tax rate of 18%. However, your marginal tax rate or tax bracket is 24%. As a result, the total tax that the employee is responsible for is $17,836.

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Answer: Convert the mixed numbers to improper fractions, then find the LCD and combine them.

Exact Form:

188

5

Decimal Form:

37.6

Mixed Number Form:

37

3

5

hope this helped have a nice day! :)

Answer:

Step-by-step explanation:

(124+64) /5

= 188/5

Answer is = 37.5

Answer:

The point (4,0) lies on the line.

All the other answers are not applicable for this situatino.

Step-by-step explanation:

A conversion of the decimals to percentages are as follows;

a) 0.543 = 54.3%.

b) 0.0098 =  0.98%

c) 1.67 = 167%.

A conversion of the percentages to decimals are as follows;

a) 10% = 0.1

b) 0.010% = 0.0001

A conversion of the mixed numbers to fractions and decimals are as follows;

a) 2 1/3 = 7/3 = 2.33

c) 5 3/5 = 28/5 = 5.6

A conversion of the fraction to mixed numbers are as follows;

a) 11/4 = 2 3/4

b) 16/7 = 2 2/7

In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to convert decimal numbers to percentages, we would have to multiply the number by 100 as follows;

Decimal number = 0.543 × 100 = 54.3%.

Decimal number = 0.0098 × 100 = 0.98%.

Decimal number = 1.67 × 100 = 167%.

In order to convert percentages to decimal numbers, we would have to divide the number by 100 as follows;

Percentage = 10/100 = 0.1.

Percentage = 0.010/100 = 0.0001

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Answer:

below

Step-by-step explanation:

sin x  is to 13    as  sin 28 is to 21

sinx /13 = sin(28)/21

sinx = 13 * sin (28) /21

sin x = .2906

x = arcsin (.2906) = 16.9°

Answer:

  B = 80°

  b = 11.343

  c = 11.518

Step-by-step explanation:

Given side a=2 and angle A=10° in a right triangle with the right angle at C, you want to know the measures of B, b, and c.

The sum of angles in a triangle is 180°, so we have ...

  10° +B +90° = 180°

  B = 180° -100°

  B = 80°

This mnemonic is intended to remind you ...

  Sin = Opposite/Hypotenuse

  sin(10°) = 2/c

  c = 2/sin(10°) ≈ 11.343

and

  Tan = Opposite/Adjacent

  tan(10°) = 2/b

  b = 2/tan(10°) ≈ 11.518

The calculations are shown in the attachment.

When revolved over the {x} axis will occupy more volume as compared to when revolved over the {y} axis.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the volume occupied between the lines -

x = 4, y = x and x - axis.

Refer to the image attached. The reflection over the {x} axis will occupy more volume as compared to the reflection over the {y} axis. The figure generated in both the cases would be a cuboidal prism structure.

Therefore, when revolved over the {x} axis will occupy more volume as compared to when revolved over the {y} axis.

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An ordered set has the least upper bound property if and only if it has the greatest lower bound property.

Every nonempty subset A0 of an ordered set A is said to have the least upper bound property and has the lowest upper bound that is constrained above. A fulfills this requirement. Assume B0 is a set of any size with a lower bound. We must demonstrate that it has the largest lower bound. Assume LA is the collection of all the set B0's lower bounds.

∃b0∈B0,∀x∈L,x≤b0.

L is therefore bound above. So it has the lowest upper bound. Let b represent the lower limit of L.

∀x∈L,x≤b.

If  ∃b′∈B0,b′≤b, which defies the assertion that b is the lowest upper bound of L. As a result,

b≤y,∀y∈B0.

So, b is the lower bound.

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The intervals of the function's behavior are given as follows:

The intervals are composed by the values of x that respect each condition, as follows:

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The value of the 5 number summery are minimum 1 , Q1 is 4, median is 4.5, Q2 is 5.5 and Maximum is 6.5

A box plot is a visual representation of the localization, dispersion, and skewness of a collection of numerical data through its quartiles.

The center "box" denotes the group's middle 50% of points. The inter-quartile range is the range of scores from the lower to higher quartile. The interquartile range encompasses the middle 50% of the scores. 75 percent of the scores are lower than the highest quartile.

When doing descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.

The data set (20 datas)

1, 1.5, 2.5, 3, 4, 4, 4.5, 4.5, 4.5, 4.5, 4.5, 5, 5, 5.5, 5.5, 5.5, 6, 6, 6.5, 6.5

The Minimum is 1

The maximum is 6.5

The value of Q1 of first 10 datas = (4 + 4 )/2 = 4

The median of the data set (20 datas) = (4.5+ 4.5)/2 = 4.5

The value of Q2 of second 10 datas = (5.5+ 5.5)/2 = 5.5

The value of the 5 number summery are minimum 1 , Q1 is 4, median is 4.5, Q2 is 5.5 and Maximum is 6.5

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To find the probability as per the given question and the information provided, we can compute it as:

a) By using the Bayes formula, we get:

[tex]P[T0|R1] = \frac{P[R1|T0]P[T0]}{P[R1|T0]P[T0] + P[R1|T1]P[T1] }

\\

= \frac{(1 − 0.99) × 0.75}{(1 − 0.99) × 0.75 + 0.98 × 0.25} \\

= \frac{3}{101} ∼= 0.030.[/tex]

b) An error is bound to happen if T0 ∩ R1 or T1 ∩ R0 occur, that is

[tex]P[error] = P[T0 ∩ R1] + P[T1 ∩ R0] \\ = P[R1|T0] × P[T0] + P[R0|T1] × P[T1] \\ = (1 − P[R0|T0]) × P[T0]

+ (1 − P[R1|T1]) × (1 − P[T0]) \\ = 0.01 × 0.75 + 0.02 × 0.25

\\ =

1

80

∼= 0.013[/tex]

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

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[tex]\textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) ~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] ~\dotfill\\\\ (1+a^3)\div (1+a)\implies \cfrac{1+a^3}{1+a}\implies \cfrac{1^3+a^3}{1+a} \\\\\\ \cfrac{~~\begin{matrix} (1+a) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(1^2 - (a)(1)+a^2)}{~~\begin{matrix} 1+a \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 1^2 - (a)(1)+a^2\implies \boxed{a^2-a+1}[/tex]

When the b-component of the equation is 2, the y-intercept for y = 6x + 2 is (0,2).

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

y = 6x + 2

y-intercept=(0,2)

The y-intercept for y = 6x + 2 is (0,2) when the b-component of equation is 2.

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Answer:

In 2020, the baseball card will be worth $1,072.50.

I hope this helps!

Step-by-step explanation:

Currently taking discrete math so this one hits close to home haha :)

Provided that we are given the first term [tex]a_0=8[/tex], the equation is found by subtracting the previous term from the current term. The recursive equation is then used to find the following terms in the sequence.

Notice that each term decreases by three as we move along the sequence, this can be written in the form of the recursive equation:

[tex]a_n = a_n_-_1-3[/tex]

Answer: 60

Step-by-step explanation:

1. You can multiply 2*30 to get 60 and with 4 you can do 4*20 would equal 60

2. 120/60 would equal 2 so it would not have any decimals so this shows it is 60.

Answer:

Yes

Step-by-step explanation:

Since they want 10% off EVERY item, this makes it easier.

Instead of having to do them one of a time, we can add all these prices together, find 10%, and see if it's less than $60.

Let's start off with adding all the items

1.25+2.50+1.50+2.00+5.00+12.50+4.50+1.00 = 30.25

Multiplying by 2 because he wants two of everything

$60.50

Now we take 10% of that $60.50

10% in decimal form is 0.10, so we multiply

(60.50)(.10) = $6.05

Lastly, we subtract that $60.50 and $6.05

$60.50 - $6.05 = $54.45

Sales Tax is 9%

So again, we will multiply then add that sales tax

.09 is 9%

(54.45)(.09) = 4.9

Adding that together

54.45 + 4.9 = $59.35

So yes, he would have enough

Answer:

971.92 square inches of wrapping paper.

Step-by-step explanation:

Please find the attachment for detail

Answer:

34 R 12

Step-by-step explanation:

I will add an explanation later, because I do not have time, I have to go somewhere.

It'll be added in at least 1 day AT MOST.

The tip amount is closest to 18% is,  $15, So Option A is correct

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

Given that,

3 Coffee 5.85

1 Diet Bev. – lg. 3.38

1 Sparkling Water 2.50

3 Ranch Chicken Sandwich 44.97

1 Classic Burger 12.95

1 Thai Stir-fry Special 11.50

2 Club Sandwich 22.98

Subtotal 104.13

Tax (13%) 13.54

Total 117.67

Tip amount 18%  =  117.67x18/100

                            =  14.11

Hence, It is closest to $15

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On solving the provided question, we can say that by unitary method 6 plate cost = $22.69 and 4 more cost = 32.49; total = 32.49+22.69 = $55.18 and cost of each plate = $5.518

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here, by unitary method

6 plate cost = $22.69

and 4 more cost = 32.49

total = 32.49+22.69 = $55.18

cost of each plate = $5.518

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The correct question is -

Pamela found a style of plate that she loves, but her local home goods store is out of stock. She decides to find the same style online. She has 6 plates in her cart right now and her total cost, including a fixed shipping cost is $22.69 . Later she decides to add 4 more plates to her cart. Her total is now $32.49 ,What is the cost of each plate?

The slope of _-1/20__ means the car uses 1 gallon of gas for every 20 miles driven.

The y-intercept of 20___ means there are originally___20 gallons of gas in the tank.

According to the question,

A linear equation is an algebraic equation in the form y=mx+b.

We know,

y = -1/20 x + 20

Linear equations are equations whose power of the variables is 1. The graph of a linear equation is a straight line.

We start with 20 gallons of gas and are decreasing the amount of gas by 1/20 gallon every mile drove.

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The complete question is:

Given this description of a real-life situation and its linear equation, interpret the y-intercept and the slope.

The amount of gasoline y (in gallons) left in your tank after you travel x miles is y=−1/20x+20.

The slope of ___

means the car uses 1 gallon of gas for every ___

miles driven.

The y-intercept of ___

means there is original___

gallons of gas in the tank.