Consider the sets below. U = {x| x is a real number} A = (x x is an odd integer} R = {x | x = 3, 7, 11, 27) IsRC A? • yes, because all the elements gf set A are in set R O yes, because all the elements of set R are in set A • no, because each element in set A is not represented in set R • no, because each element in set R is not represented in set A

Answer:

  (x, y) = (-3, 0)

Step-by-step explanation:

You want a graphical solution to the system of equations ...

A graph of the system is attached. The lines intersect at (-3, 0).

The solution to the equations is (x, y) = (-3, 0).

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The solution to the system of equations is x = -3 and y = 0.

The given system of equations is:

Equation 1: y = -3x - 9

Equation 2: 3x + 4y = -9

To find the solution to this system, we need to find the values of x and y that satisfy both equations simultaneously.

We can start by substituting Equation 1 into Equation 2:

3x + 4(-3x - 9) = -9

Simplifying the equation:

3x - 12x - 36 = -9

Combine like terms:

-9x - 36 = -9

Now, let's isolate the variable x:

-9x = -9 + 36

-9x = 27

Divide both sides of the equation by -9 to solve for x:

x = 27 / -9

x = -3

Now that we have the value of x, we can substitute it back into Equation 1 to find the value of y:

y = -3(-3) - 9

y = 9 - 9

y = 0

Therefore, the solution to the system of equations is x = -3 and y = 0.

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D.It is not a function because there are two different y-values for a single x-value.

A function is a relation where each input(x) has a single output(y).

From the given graph we can see that there are 2 different values of y

i.e. y=-2 and y=4 for single x=4.

Therefore, D is the right answer.

The graph is not a function because it is not a function because there are two different y-values for a single x-value.

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Question

Which explains why the graph is not a function?

A.It is not a function because the points are not connected to each other.

B.It is not a function because the points are not related by a single equation.

C.It is not a function because there are two different x-values for a single y-value.

D.It is not a function because there are two different y-values for a single x-value

The equation that represents an inverse variation is y = 4/x

From the question, we have the following parameters that can be used in our computation:

The list of options

By definition, an inverse equation is represented as

y = k/x

Where

k = constant of variation

From the list of options, we have

y = 4/x

Where

k = constant of variation = 4

Hence, the equation is y = 4/x

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Question

Which equation represents an inverse variation?

y = 2x

y = 4/x

y = 4x

y = –5x

The calculated value of x in the triangle is 23.57 degrees

From the question, we have the following parameters that can be used in our computation:

The right triangle

From the triangle, we have

Angle x

Also, we have the following sides in relation to x

Opposite = 6

Hypotenuse = 15

This means that we make use of the sine ratio

i.e. sin = opposite/hypotenuse

So, we have

sin(x) = 6/15

Evaluate

sin(x) = 0.4

Take the arc sin of both sides

x = 23.57

Hence, the value of x is 23.57 degrees

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The average Height for a two-year-old is 32.67 inches.

A scatter plot is a graph that depicts the connection between two variables. The independent variable is generally plotted on the x-axis, whereas the dependent variable is plotted on the y-axis. The independent variable is used to forecast the dependent variable, and this relationship is reflected in a line on the scatter plot.What is a linear equation?

Linear equations depict straight lines on a graph. They are frequently expressed in the following manner: y = mx + b. The y value is the dependent variable, while the x value is the independent variable. The m value is the slope of the line, or the rate at which the y value changes in relation to the x value. The b value is the y-intercept, or the point where the line intersects the y-axis. Linear equations are frequently used in algebra, geometry, and science to describe the connection between two variables.Let's take a closer look at the given problem and how it can be resolved.The scatter plot demonstrates the average heights of children up to age 5. We must utilize the linear equation y = mx + b to predict the average height for a two-year-old. If we can establish the slope and y-intercept of the line, we can calculate any value on the line.Let's begin with the y-intercept. If we look at the graph, we can see that the line passes through the y-axis at around 28.

Therefore, b = 28.We can now calculate the slope. Let's examine two points on the line to accomplish this. For example, we could utilize the points (2, 33) and (5, 40).m = (y2 - y1) / (x2 - x1)m = (40 - 33) / (5 - 2)m = 7/3Therefore, the equation for the line is:y = (7/3)x + 28Now that we have the equation for the line, we can forecast the average height for a two-year-old.x = 2y = (7/3)(2) + 28y = 32.67

Therefore, we can predict that the average height for a two-year-old is 32.67 inches.

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Answer:

[tex]sin^{-1}[/tex] (0.5) = 30°

Step-by-step explanation:

taking the sine if an angle gives a value

doing the reverse ( the inverse ), that is the inverse sine [tex]sin^{-1}[/tex] of the value obtained by sine gives the angle, that is

sin30° = 0.5 , then

[tex]sin^{-1}[/tex] (0.5) = 30°

Answer:

To calculate the probability of winning the jackpot in this particular lottery, we need to determine the probability of selecting the correct five numbers between 1 and 37 and the correct single number between 1 and 47.

The probability of selecting the correct five numbers between 1 and 37 can be calculated as follows:

P(correct five numbers) = 1 / (total possible combinations of five numbers)

In this case, there are C(37, 5) possible combinations of five numbers, which represents the number of ways to choose five numbers out of 37. The formula for calculating combinations is given by:

C(n, k) = n! / (k! * (n - k)!)

Plugging in the values:

C(37, 5) = 37! / (5! * (37 - 5)!)

The probability of selecting the correct single number between 1 and 47 is:

P(correct single number) = 1 / (total possible numbers between 1 and 47)

Since there are 47 possible numbers to choose from, the probability is:

P(correct single number) = 1 / 47

To calculate the probability of winning the jackpot, we multiply the probability of selecting the correct five numbers by the probability of selecting the correct single number:

P(jackpot) = P(correct five numbers) * P(correct single number)

P(jackpot) = (1 / C(37, 5)) * (1 / 47)

Calculating this expression will give you the probability of winning the jackpot in this particular lottery.

The relationship between  acute and equilateral triangles is equilateral triangle is consistently acute, not every acute triangle is equilateral.

An equilateral triangle is always acute as all of its angles measure less than 90 degrees.

An acute-angled triangle is one where all three angles are less than 90 degrees in measure. Alternatively, an equilateral triangle is a three-sided polygon in which all three sides and angles are congruent, with each angle measuring 60 degrees.

An equilateral triangle is always acute as all of its angles measure less than 90 degrees. As an equilateral triangle comprises three angles of 60 degrees each, all angles in the triangle are acute.

To put it simply, while an equilateral triangle is consistently acute, not every acute triangle is equilateral. Acute-angled triangles exhibit different side measurements and angles, as long as all the angles measure less than 90 degrees.

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Answer:

x < 4

Step-by-step explanation:

The inequality:

[tex]x2.5 < 10[/tex]

Divide each side by 2.5 to isolate x (make x alone):

[tex]\frac{x2.5}{2.5} < \frac{10}{2.5} \\x < 4[/tex]

There is no point that is NOT included in the graph of the step function.

The coat check service charges $2 for the first hour and $1 for each additional hour or fraction of an hour.

To determine the point that is NOT included in the graph of the step function, we need to consider the charging scheme and analyze the pattern of charges.

The step function can be represented as follows:

For the first hour, the charge is a flat rate of $2.

For each additional hour or fraction of an hour, the charge is $1.

Let's analyze the points included in the graph:

(1, 2): This point represents the charge for the first hour, which is $2.

Now, let's consider the additional hours:

2. (2, 3): This point represents the charge for 2 hours, which is $2 for the first hour and $1 for the additional hour.

(3, 4): This point represents the charge for 3 hours, which is $2 for the first hour and $2 for the additional 2 hours.

(4, 5): This point represents the charge for 4 hours, which is $2 for the first hour and $3 for the additional 3 hours.

Based on the charging scheme, we can observe a pattern where the charge increases by $1 for each additional hour or fraction of an hour.

Since the charging scheme allows for any additional hour or fraction of an hour, there is no specific point that is excluded from the graph. Any positive value of x greater than or equal to 1 will have a corresponding point on the graph.

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The next number in the given sequence 6, 12, 15, 60, 65 is 70, assuming that the pattern of alternating multiplication and addition operations continues.

To identify the next number in the given sequence 6, 12, 15, 60, 65, we need to observe the pattern and look for a rule or relationship between the numbers.

Looking closely at the sequence, we can see that the numbers are not following a simple arithmetic or geometric progression. Therefore, we need to explore other possibilities.

One possible pattern in the sequence is that each number is obtained by performing some mathematical operations on the previous number(s). Let's analyze each number to see if we can identify a consistent rule:

6: No obvious pattern.

12: Obtained by multiplying 6 by 2.

15: Obtained by adding 3 to 12.

60: Obtained by multiplying 15 by 4.

65: Obtained by adding 5 to 60.

From this analysis, we can observe that the pattern alternates between multiplication and addition operations. In the first step, we multiply the previous number by a factor of 2, and in the second step, we add a fixed number.

Based on this pattern, we can predict the next number in the sequence by following the alternating pattern. Starting with the last operation of addition, we add 5 to 65. Therefore, the next number in the sequence is 70.

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The factoring of the polynomials gives;

1) Option C

2) Option A

3) Option B

4) Option C

5) Option A

6) Option B

7) Option C

8) Option C

9) Option B

10) Option B

1) 9x - 9

9(x - 1)

2) [tex]3x^2 - 9x[/tex]

3x(x - 3)

3) [tex]36x^2 - 1[/tex]

By the difference of two squares;

(6x + 1) ( 6x - 1)

4) [tex]x^2 - 4[/tex]

By the difference of two squares;

(x + 2) (x - 2)

5)

[tex]x^2 + 12x + 36\\x^2 + 6x + 6x + 36[/tex]

x(x + 6) + 6(x + 6)

(x + 6) (x + 6)

[tex](x + 6)^2[/tex]

6)

[tex]25x^2 - 20x + 4\\5x^2 + 2(5x) -2 + (-2)^2\\(5x - 2)^2[/tex]

7) [tex]x^2 - 3x - 54[/tex]

(x + 6) (x - 9)

8) [tex]2x^2 + 9x + 18 x+ 81\\ 2x^2 + 18 x + 9x + 81[/tex]

2x(x + 9) + 9 (x + 9)

(2x + 9) (x + 9)

9)

[tex]9y^2 + 18y + 8\\9y^2 + 12y + 6y + 8[/tex]

3y(3y + 4) + 2y(3y +4)

(3y + 2) (3y + 4)

10)

[tex]20z^2 - 3z - 9\\20z^2 - 15z + 12z - 9[/tex]

5z(4z - 3) + 3(4z - 3)

(5z - 3) (4z + 3)

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A coordinate plane is a two-dimensional grid that has an x-axis (horizontal) and a y-axis (vertical). A point on the coordinate plane has an x-coordinate (abscissa) and a y-coordinate (ordinate) that show its position on the grid. The distance between two points can be found by using the distance formula, which is derived from the Pythagorean theorem. The distance formula is:

d=(x2​−x1​)2+(y2​−y1​)2​

where d is the distance, (x1​,y1​) and (x2​,y2​) are the coordinates of the two points. In this problem, the coordinates of point A are (6,0) and the coordinates of point B are (0,−8). Plugging these values into the formula, we get:

d=(0−6)2+(−8−0)2​

d=36+64​

d=100​

d=10

Therefore, the distance between A and B is 10 units.

The probability values for the questions posed are :

A.)

Number of students Taking a public speaking class majoring in business administration.

P(PS or BA) = 55/100 = 11/20

Therefore, the probability of PS or BA is 11/20

B.)

For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.

Hence, as inferred from P(A|B) ; probability of A given B.

C.)

P(PS|BA) = n(PSnBA) / n(BA)

n(PS) = 10+20 = 30

n(PSnBA) = 10

P(PS|BA) = 10/30 = 1/3

Therefore , the probability of PS|BA is 1/3.

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Mr. Dieter will need to purchase 528 square tiles that measure 9 inches by 9 inches each to tile the family room in his basement.

As we can see in the image provided, the shape of the floor is a rectangle with dimensions 16 feet by 18 feet. To title the family room using square tiles that measure 9 inches by 9 inches each, we need to convert the dimensions from feet to inches. 1 foot is equal to 12 inches, so we have:

16 feet x 12 inches/foot = 192 inches

18 feet x 12 inches/foot = 216 inches

Now we can divide the length and width of the floor by the length and width of each tile to find out how many tiles are needed. Since each tile measures 9 inches by 9 inches, we have:

192 inches ÷ 9 inches = 21.33 tiles ≈ 22 tiles needed for the length

216 inches ÷ 9 inches = 24 tiles needed for the width

Therefore, we need 22 tiles for the length and 24 tiles for the width, which gives us a total of:

22 tiles x 24 tiles = 528 tiles

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You can find the area by using the formula: S = πr². In this case, r = 4, π = 3.14, so the area equals to 3.14 * 16 = 50.24.

The area is:

50.24 cm²

Work/explanation:

The formula for a circle's area is:

[tex]\boxed{\!\!\boxed{\quad\sf{A=\pi r^2\quad}}\!\!}[/tex]

A = area

π = 3.14

r = radius

Diagram:

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 4\ cm}\end{picture}[/tex]

Now to solve further, plug in the data from the problem:

                            [tex]\Large\begin{gathered}\sf{A=\pi r^2}\\\sf{A=3.14\times4^2}\\\sf{A=3.14\times16}\\\sf{A=50.24\:cm^2}\end{gathered}[/tex]

And we get that A = 50.24 cm².

The graph of the function y = 1/3x - 2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

So, the equation is

y = 1/3x - 2

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking note of the above transformations rules

The graph of the function is added as an attachment

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There will be 5 boxes in the tenth row.

To represent the arithmetic sequence of boxes in each row, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1) * d

Where:

a_n represents the nth term of the sequence,

a_1 represents the first term of the sequence,

n represents the position of the term in the sequence,

d represents the common difference between consecutive terms.

In this case, the first row has 23 boxes, so a_1 = 23. Additionally, each row has 2 fewer boxes than the row below, so the common difference is d = -2.

To find the number of boxes in the tenth row (n = 10), we substitute these values into the formula:

a_10 = 23 + (10 - 1) * (-2)

= 23 + 9 * (-2)

= 23 - 18

= 5

Therefore, the eleventh row will include 5 boxes.

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The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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According to the information we can infer that the Fuel budget percentage: 12.8%, Hotel budget percentage: 17.9%, Restaurant budget percentage: 30.8%, and Attraction budget percentage: 38.5%

To find the percentage of each item in the budget, we divide the individual budget amounts by the grand total amount and multiply by 100. Given:

Fuel budget percentage:

Hotel budget percentage:

Restaurant budget percentage:

Attraction budget percentage:

According to the above, the percentage breakdown of the budget is approximately:

Note: This question is incomplete. Here is the complete information:
Grand total amount: $390

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From the question the correct sequence can be obtained as an = 3(2)^n. Option D

A sequence is a specific type of ordered list where each element is associated with a unique position or index. The elements in a mathematical sequence are typically numbers or mathematical objects that follow a specific pattern or rule. Each element in the sequence is identified by its position, often denoted by a subscript or index.

Testing the sequence;

3(2)^0 = 3

3(2)^1 = 6

3(2)^2 = 12

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The probability that a randomly chosen customer purchased a Toe-tastic shoe and is very pleased is 0.71.

To solve this problem, let's define some events:

A = The event that a customer purchased a Toe-tastic shoe.

B = The event that a customer is very pleased.

We are given the following probabilities:

P(A) = 0.64 (the probability that a customer purchased a Toe-tastic shoe)

P(B) = 0.36 (the probability that a customer is very pleased)

P(A or B) = 0.69 (the probability that a customer purchased a Toe-tastic shoe or is very pleased)

We want to find the probability of both events A and B occurring, which can be represented as P(A and B).

Using the formula for the probability of the union of two events, we have:

P(A or B) = P(A) + P(B) - P(A and B)

Rearranging the formula, we can solve for P(A and B):

P(A and B) = P(A) + P(B) - P(A or B)

Substituting the given probabilities:

P(A and B) = 0.64 + 0.36 - 0.69

P(A and B) = 0.71

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Answer:

[tex]27x^9y^8[/tex]

Step-by-step explanation:

[tex](3x^7y^3)(9x^2y^5)=27x^{7+2}y^{3+5}=27x^9y^8[/tex]

Jolly Goods Limited may not be able to accept the order for 2,000 ornaments due to the limited capacity of the finishing department. While the cutting and assembling departments have the capacity to fulfill the order by working at 100% capacity, the finishing department cannot complete the required work within the given deadline. The company as a whole is operating at 85% of capacity, which suggests that the finishing department is already working close to its maximum capacity.

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Answer:

45

43

Step-by-step explanation:

88-45

43

88-43

45

the measurements of the angels are 43 and 45

The best assessment of the linearity of the relationship between the day of the month and account balance would be "Because the residual plot has no obvious pattern, and the scatterplot appears linear, it is appropriate to use the line of best fit to predict the account balance based on the day of the month."The correct answer is option C.

When assessing linearity, it is important to examine both the scatterplot and the residual plot. The scatterplot is used to visualize the relationship between the variables, while the residual plot helps us assess the appropriateness of a linear model by examining the pattern of the residuals (the differences between observed and predicted values).

If the scatterplot appears reasonably linear, it suggests that there is a linear relationship between the variables. In this case, since the scatterplot appears linear, it supports the use of a linear model to predict the account balance based on the day of the month.

Furthermore, the residual plot is used to check for any patterns or systematic deviations from the line of best fit. If the residual plot exhibits no obvious pattern and the residuals appear randomly distributed around zero, it indicates that the linear model captures the relationship adequately.

Therefore, if the residual plot shows no obvious pattern, it provides further evidence in favor of using the line of best fit to predict the account balance based on the day of the month.

In conclusion, when the scatterplot appears linear and the residual plot shows no obvious pattern, it is appropriate to use the line of best fit to predict the account balance based on the day of the month.

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Answer:

person above

Step-by-step explanation:

the obvious

The binary and quinary numbers of P = (10A010)₂ and Q = (1B3)₅, indicates;

5. (a) A = 1

(b) B = 2

(c) P - Q = 100₂

Binary numbers are numbers represented using only the digits of 0 and 1.

5. The binary number is P = (10A010)₂

The quinary number is Q = (1B3)₅

(a) The value of A if P = 42₍₁₀₎ is therefore;

42/2 = 21 R 0

21/2 = 10 R 1

10/2 = 5 R 0

5/2 = 2 R 1

2/2 = 1 R 0

1/2 = 0 R 1

42₍₁₀₎ = 101010₂ = (10A010)₂

A = 1

(b) P + Q = 80₍₁₀₎

P = 42₍₁₀₎, therefore;

Q = 80₍₁₀₎ - 42₍₁₀₎ = 38₍₁₀₎

Convert 38₍₁₀₎ to base 5, we get;

38/5 = 7 R 3

7/5 = 1 R 2

1/5 = 0 R 1

42₍₁₀₎  = 123₅ = (1B3)₅

B = 2

(c) P - Q = 42₍₁₀₎ - 38₍₁₀₎ = 4₍₁₀₎

The value of the decimal 4₍₁₀₎ to base 2 can be found as follows;

4/2 = 2 R 0

2/2 = 1 R 0

1/2 = 0 R 1

4₍₁₀₎ = 100₂

P - Q = 100₂

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Answer:

x = mp - n

Step-by-step explanation:

m = [tex]\frac{x+n}{p}[/tex] ( multiply both sides by p to clear the fraction )

mp = x + n ( isolate x by subtracting n from both sides )

mp - n = x

Answer:

Step-by-step explanation:

R-2=W

R-2(+2)=W+2

R=W+2

Key concept:

x+(−x)=0

If we have a+x=b, adding the opposite of a to both side we have:

a+x+(−a)=b+(−a)⟺x=b−a

The formula is:

Work/explanation:

Rearrange the formula for R.

All we should do is add 2 to each side :

R - 2 = W

R = W + 2

Hence, this is the right answer.