The sum of three consecutive integers is 108. What are the integers?​

Answer:

True

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Every number has multiple qualities beyond its distance from zero. Some of the qualities of a number include its sign (positive or negative), its magnitude (Absolute Value), its parity (whether it is even or odd), and its relationship to other numbers (greater than, less than, or equal to). Additionally, numbers can have properties such as being prime or composite, rational or irrational, and real or complex. Therefore, a number is characterized by more than just its distance from zero.

Answer:correct answer is 0.57

5.71

Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

3u^2 + 7u - 8 = 0

Now we can factor the quadratic:

(3u - 1)(u + 8) = 0

Therefore, either:

3cos(θ) - 1 = 0

cos(θ) = 1/3

or:

cos(θ) + 8 = 0

cos(θ) = -8 (not possible, since cos(θ) is between -1 and 1)

So, we have cos(θ) = 1/3. Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse cosine function:

θ = arccos(1/3)

Using a calculator, we find:

θ ≈ 1.2309 or θ ≈ 5.1102

Therefore, in radians, the solutions for θ are approximately:

1.2309 (which is less than 2π)

5.1102 (which is greater than 2π)

So the only answer that satisfies 0 ≤ θ < 2π is:

1.2309 (rounded to four decimal places)

Therefore, the answer is:

The data set that best describes the histogram is

(4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)

We have,

The histogram shows that there are different intervals on the x-axis, and for each interval, there is a corresponding frequency on the y-axis.

From the given data, we can see that there are more passengers in the 11 to 20 interval than in the 1 to 10 interval, and so on.

Looking at the answer choices, we need to choose the data set that matches the histogram.

The first step is to check if the data set has the same range as the histogram.

The histogram has intervals from 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 42 to 50.

Now,

The first answer choice has numbers less than 1 and greater than 50, so it cannot be the correct choice.

The second answer choice has a range from 4 to 42, which matches the histogram.

We can check if the frequencies in the data set match the heights of the bars in the histogram.

For example, the histogram has a bar for the 11 to 20 interval that stops at 4, which means there are 4 passengers in that interval.

The second data set has 4 passengers in the 11 to 20 interval, so it matches.

We can do the same for the other intervals and find that the second data set matches the histogram.

Therefore,

The data set that best describes the histogram is

(4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)

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The angle measures for the triangles are given as follows:

Similar triangles are triangles that share these two features listed as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle Z is given as follows:

m < Z + 20 + 105 = 180

m < Z + 125 = 180

m < Z = 55º.

Hence the measures are given as follows:

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The ratio in simplest form is 1:4, the correct option is C.

We are given that;

The options  A. 2/3 B. 3/4 C. 1/4 D. 4/1

Now,

The letters D and O are used 2 times and 4 times respectively in the words “RATIOS AND PROPORTIONS”. So we can write the ratio as 2:4.

The GCF of 2 and 4 is 2, since 2 is the largest number that can divide both 2 and 4 without leaving a remainder.

To simplify the ratio, we divide both terms by 2:

2:4 = (2/2):(4/2) = 1:2

Therefore, by the ratio the answer will be 1/4.

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Based on the information, the incorrect step is C. step 3.

Step 1: 4(3x – 3y = 6) –3(4x – 7y = 2)

Step 2: 12x – 12y = 24 –12x + 21y = –6

Step 3: 9y = 18

Step 4: y equals 1 over 2

Correct calculation:

3x – 3y = 6 (1)

4x – 7y = 2 (2)

make x the subject in ....(1)

3x - 3y = 6

3x = 6 + 3y

x = 6 + 3y/ 3

x = 2 + y

substitute x = 2 + y into (2)

4x – 7y = 2 (2)

4(2 + y) - 7y = 2

8 + 4y - 7y = 2

8 - 3y = 2

8 + 2 = -3y

10 = -3y

y = 10/-3

y = -3 1/3

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Michael solved the system of linear equations and provided the solution. 3x – 3y = 6 4x – 7y = 2 Step 1 4(3x – 3y = 6) –3(4x – 7y = 2) Step 2 12x – 12y = 24 –12x + 21y = –6 Step 3 9y = 18 Step 4 y equals 1 over 2 In which step did Michael show his first error? Step 2 Step 3 Step 4

The x-intercept will be (5/3, 0) and the y-intercept will be (0, -5/2).

The x-intercept of an equation is the point at which the graph of the equation intersects the x-axis, which means that the y-coordinate of that point is 0. To find a x-intercept, we can set y = 0 in equation and solve for x.

Given the equation: 3x - 2y = 5

Setting y = 0, we get;

3x - 2(0) = 5

3x = 5

x = 5/3

So, the x-intercept is (5/3, 0).

The y-intercept of an equation is the point at which the graph of the equation intersects the y-axis, which means that the x-coordinate of that point is 0. To find y-intercept, we can set x = 0 in equation and solve for y.

Setting x = 0, we get;

3(0) - 2y = 5

-2y = 5

y = -5/2

So, the y-intercept is (0, -5/2).

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Reflecting the triangle Q over the line y = 1 would map it onto triangle T

Reflection over line x = 1

This means that we draw a vertical line that passes through x = 1

And then we create a triangle that is a mirror of the triangle P across the reflection line

The reflection of the triangle is attached

Reflection over line y = 2

This means that we draw a vertical line that passes through y = 2

As done in part (a), we then create a triangle that is a mirror of the triangle P across the reflection line

The reflection of the triangle is also attached

Using the same transformation rule above;

A reflection over the line y = 1 would map the triangle Q onto triangle T

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Answer:

To find the area of the rectangle BCDE, we can use the formula:

Area = length x width

First, we need to find the length and width of the rectangle.

The length of the rectangle is the distance between points B and C, which can be calculated using the distance formula:

distance BC = sqrt((x2 - x1)^2 + (y2 - y1)^2)

= sqrt((-6 - (-9))^2 + (-8 - (-4))^2)

= sqrt(3^2 + (-4)^2)

= sqrt(9 + 16)

= sqrt(25)

= 5

The width of the rectangle is the distance between points C and D:

distance CD = sqrt((x2 - x1)^2 + (y2 - y1)^2)

= sqrt((10 - (-6))^2 + (4 - (-8))^2)

= sqrt(16^2 + 12^2)

= sqrt(256 + 144)

= sqrt(400)

= 20

Since BCDE is a rectangle, the length and width are perpendicular. Therefore, the area of the rectangle can be calculated by multiplying the length and width:

Area = length x width = 5 x 20 = 100

Therefore, the area of BCDE is 100 square units.

Step-by-step explanation:

Answer:

The nearest tenth, Container A is about 46.3% full after the pumping is complete.

Step-by-step explanation:

To solve this problem, we need to find the volume of water in Container A and compare it to the volume of Container B.

The volume of water in Container A can be found using the formula for the volume of a cylinder:

V_A = πr^2h = π(6^2)(9) = 324π cubic feet

The volume of Container B can also be found using the same formula:

V_B = πr^2h = π(5^2)(12) = 300π cubic feet

After the water is pumped from Container A to Container B, Container B will be completely full, which means it will contain 300π cubic feet of water. To find the height of the water level in Container A, we need to find the height of the cylinder that would contain 300π cubic feet if it had a radius of 6 feet:

V_A' = πr^2h' = 300π

h' = 300/(36π) = 25/6 feet

So the height of the water level in Container A is 25/6 feet. Since the height of Container A is 9 feet, the percent of Container A that is full is:

(25/6) / 9 * 100% ≈ 46.3%

Therefore, to the nearest tenth, Container A is about 46.3% full after the pumping is complete.

The function that matches the above graph is Option C - F(x) = (1/2)^x - 3

Here are the properties of the function are given as follows

Domain - The domain of  the function is all real numbers, as there are no restrictions on the input value  x .

Range - the range of the function is (-3, infinity), as the output values approach but never reach - 3 as x approaches negative infinity, and the output values can be arbitrarily large as x approaches infinity.

x -intercept - The x-intercept of the function is (log(2, 3), 0), as F(log(2, 3)) = [( 1/2)^  (log(2, 3) ) ] - 3 = 0.

y-intercept - The y-intercept of the function is (0, -2.5), as F(0) = [(1/2)^0] - 3 = -2.5.

Asymptotes - The horizontal asymptote of the function is y = -3, as the output values approach but never reach -3 as x approaches infinity. There are no vertical asymptotes.

Decreasing function -  The function is a decreasing function, as the output values decrease as x increases.

Continuous function - The function is continuous for all real numbers.

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The formula for the nth term of the geometric sequence is given as follows:

[tex]a_n = 7(-3)^{n - 1}[/tex]

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The formula for the nth term of the sequence is given as follows:

[tex]a_n = a_1q^{n-1}[/tex]

The first term of the sequence is given as follows:

[tex]a_1 = 7[/tex]

Each term is the previous term multiplied by -3, hence the common ratio is given as follows:

q = -3.

Thus the formula for the sequence is given as follows:

[tex]a_n = 7(-3)^{n - 1}[/tex]

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The area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.

Given that, the dimensions of rectangular flower bed are length= 6 feet and  width = 4 feet.

Dimensions of large rectangle are Length = 6+2x and width = 4+2x

Now, area of large rectangle = (6+2x)×(4+2x)

= 24+8x+12x+4x²

Area of a rectangular flower bed = 6×4

= 24 square feet

Tulips and Daisy have same area to plant

So, the equation is 24+20x+4x²=24

4x²+20x=0

Therefore, the area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.

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a) Latonya is correct, as the scale factor of the dilation is of 12.8/4.8.

b) The scale factor was obtained dividing the side length on the dilated figure by the equivalent side length of the original figure.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The ratios for the scale factor are given as follows:

12.8/4.8 = 7.2/2.7 = 4.8/1.8 = 4/1.5 = 8/3.

8/3 as 4 x 2 = 8 and 1.5 x 2 = 3.

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Answer:d

Step-by-step explanation:

Answer:

Mean-27

Step-by-step explanation:

Add all of the numbers and it equals 162

Then divide 162 by the amount of numbers presented.

Since there are 6 numbers listed we divide by 6

162/6=27

Answer:

1/2

Step-by-step explanation:

1/12 +5/12=1/2

hope this helps

Determining if the proportion is true. If is not true and correcting the error v/x = x/v+w is: B. false, it should be  w/x = x/v+w.

In order for us to know whether the proportion v/x = x/v+w is true or not we need to cross multiply and simplify both sides:

v(x + v + w) = x^2

Expand the left-hand side:

vx + v^2 + vw = x^2

Subtract vx from both sides:

v^2 + vw = x^2 - vx

Factor out v on the left-hand side and x on the right-hand side:

v(v + w) = x(x - v)

Divide both sides by (v + w)x:

v/(v + w) = x/(x - v)

Therefore the correct option is B.

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f is onto the set of all binary strings:

This statement is false for the same reason as (e). The range of f is limited to a subset of all binary strings.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

a. The cardinality of the set {u | f(u) = u} is 1:

This statement is true because f(u) returns only the first third of the input string u. Therefore, if f(u) = u, then the second and third thirds of the string u must be empty, and hence u must consist entirely of the first third, which means there can be only one such string.

b. f is a total function:

This statement is false because not all binary strings can be decomposed into three parts with the described property. For instance, a binary string of length 5 cannot be decomposed in this way.

c. If |u| = 24, then f(f(u)) is not defined:

This statement is false. If |u| = 24, then u can be decomposed into three parts with 8 bits in each part. Therefore, f(u) will return the first 8 bits of u, which can be decomposed into three parts with 2, 3, and 3 bits, respectively. Therefore, f(f(u)) will return the first 2 bits of the first third of u, which is well-defined.

d. f is an injection:

This statement is false. Since f only returns the first third of its input, there can be multiple inputs that yield the same output.

e. The range of f is the set of all binary strings:

This statement is false. The range of f only consists of binary strings that are the first third of some input string that can be decomposed as described.

f. f is onto the set of all binary strings:

This statement is false for the same reason as (e). The range of f is limited to a subset of all binary strings.

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The frequency table is plotted and the order for the restaurant is given

Given data ,

A restaurant had 160 lunch customers last weekend.

90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both.

There were 45 customers who ordered seltzer and a veggie sandwich.

Eleven more people ordered a veggie sandwich than a tuna sandwich.

On simplifying the equation , we get

A = 90 - 38 - 45 = 7

B = 75 - 38 = 37

E = 160-90 = 70

C = D + 11

D + 11 + D = 70-37

2D = 33-11

D=22/2

D=11

Thus C = 22

F = 45 + C

F = 45 + 22

F = 22

G = A + D = 18

                  Chicken       Veggie             Tuna               Total

Seltzer            38                 45                     7                    90

Iced Tea           B                  22                     11                    70

Total                 75                 67                    18                    160

Hence , the frequency is completed

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The complete question is attached below :

A restaurant had 160 lunch customers last weekend. Of those, 90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both. There were 45 customers who ordered seltzer and a veggie sandwich. Eleven more people ordered a veggie sandwich than a tuna sandwich. Complete the two-way frequency table for the data.

The dimensions of the plot that would enclose the most area are (width, length) = (125/6, 125/3).

We have,

Let's assume that the barn wall is located on the south side of the rectangular plot, and the fencing is required on the remaining three sides (east, north, and west).

Let's denote the width of the plot as x and the length of the plot as y.

Then, the length of fencing required can be expressed as:

L = x + y + x/2

where x/2 is the length of the shared fencing with the neighbor.

The cost of fencing can be expressed as:

C = 24L

Substituting the value of L, we get:

C = 24(x + y + x/2)

Since the farmer is not willing to spend more than $6000, we have:

24(x + y + x/2) ≤ 6000

Simplifying this inequality, we get:

3x + 4y ≤ 500

Now, we need to maximize the area of the rectangular plot, which is given by:

A = xy

Using the inequality constraint, we can express y in terms of x as:

y ≤ (500 - 3x)/4

Substituting this value of y in the expression for A, we get:

A = x((500 - 3x)/4)

Simplifying this expression, we get:

A = (125/4)x - (3/4)x^2

To find the value of x that maximizes A, we can take the derivative of A with respect to x and set it equal to zero:

dA/dx = 125/4 - (3/2)x = 0

Solving for x, we get:

x = 125/6

Substituting this value of x in the expression for y, we get:

y = (500 - 3(125/6))/4 = 125/3

Therefore,

The dimensions of the plot that would enclose the most area are (width, length) = (125/6, 125/3).

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The volume of the composite figure is

The volume is calculated by dividing the figure into simpler shapes. and adding the individual volumes

The simple shapes used here include

Volume of rectangle = length x width x depth

= 30 * 9 * 7

= 1890 cubic yd

Volume of trapezoid = 1/2 (sum of parallel lines) x height x depth

= 1/2 (30 + 19) x 10 x 9

= 2205 cubic  yd

Total volume

= 1890 cubic yd + 2205 cubic yd

=  4095 cubic yd

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Answer: The region of the graph that contains the solution set of the system of linear equalities y ≤ 1/2x+3 y≥ 2x-2 is the area bounded by the two lines and the x-axis.

Step-by-step explanation:

The objective of the above task to to check your ability to compute various parts of a parallelogram given various inputs. See the solution attached.

A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure.

Note that the corners angles (AB,C,D)are derived as follows;

A = C = θ

B = D = Φ

A + B = 180° = π radians

for a parallelogram that is not a rectangle or square,

0 < A< 90° (0 < A < π/2),

90° < B < 180° (π/2 < B < π)

The diagonals are derived as follows:

Diagonals: d, c

d = √( a² + b² - 2ab cos(A) ) = √( a² + b² + 2ab cos(B) )

c = √( a² + b² + 2ab cos(A) ) = √( a² + b² - 2ab cos(B) )

d² + c² = 2(a² + b²)

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The solution is :Total manufacturing cost per Lamp is $15.10 per lamp.

Explanation:

Cost per part of Material handling = $3000/6000 parts

Cost per part of Material handling = $0.50 per part

Assembling per hour = $7200/3000

Assembling per hour = $2.40 per hour

Packaging per lamp = $4000/2000

Packaging per lamp = $2 per lamp

Total manufacturing cost per Lamp = $8 + (9*$0.50) + ($2.40/4) + $2

Total manufacturing cost per Lamp = $8 + $4.5 + $0.6 + $2

Total manufacturing cost per Lamp = $15.10 per lamp

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complete question:

Traditions Home Accessories Company manufactures decorative lamps using an activity-based costing system to allocate all manufacturing conversion costs. The following information is provided for the month of June: Activity Estimated Indirect Activity Costs Allocation Base Estimated Quantity of Allocation Base Materials handling $3,000 Number of parts 6,000 parts Assembling $7,200 Number of hours 3,000 hours Packaging $4,000 Number of lamps 2,000 lamps Four lamps can be assembled in 1 hour. Each lamp consists of 9 parts. The total direct materials cost per lamp is $8.00. What is the total manufacturing cost per lamp

Yes, The given graph is shows a function.

And, Range = {y | y ≥ - 2}

Domain = (- ∞ , ∞)

We have to given that;

the graph is shown in image.

Now, We can check the graph is a function or not by vertical line test.

Hence, By vertical line test it's shows the function as it cut at one point for each value of y.

Thus, The given graph is shows a function.

Since, The set of all inputs of the function is called Domain of set.

Hence, We get;

Domain = (- ∞ , ∞)

And, The set of all outputs of the function is called range of set.

Hence, We get;

Range = {y | y ≥ - 2}

Thus, Yes, The given graph is shows a function.

And, Range = {y | y ≥ - 2}

Domain = (- ∞ , ∞)

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Answer:

A stem-and-leaf plot is a graphical representation of a dataset where the numbers are separated into two parts: the stem (the leftmost digit or digits) and the leaf (the rightmost digit). The stem values are listed vertically and the corresponding leaf values are listed to the right of the stem in a row. This type of plot allows for quick and easy data analysis, as it shows the distribution of the data and provides information about the frequency and range of the values. It is particularly useful for smaller datasets and can be easily constructed by hand or with software.

Answer:

I can explain how the relationship between the amount of money the painter earns and the number of rooms he paints can be represented in a graph.

The amount of money the painter earns depends on the number of rooms he paints. The painter charges $25 for each room he paints, so the amount of money he earns can be calculated by multiplying the number of rooms painted by $25. However, he also has to pay $100 for supplies regardless of the number of rooms painted.

Therefore, the relationship between the amount of money the painter earns and the number of rooms painted is a linear function, where the y-intercept (when no rooms are painted) is -$100 and the slope (how much he earns per room painted) is $25. This relationship can be represented in a graph as a straight line with a positive slope that intersects the y-axis at -$100.

I hope this helps

Option C is the correct graph for the given condition.

Graphs are a not unusual place technique to visually illustrate relationships withinside the statistics. The reason for a graph is to provide statistics that are too severe or complex to be defined appropriately withinside the textual content and in much less space.

Let's assume that the number of rooms painted is represented by the variable "x". The cost of painting x rooms can be calculated using the following equation:

Cost = 100 + 25x

The $100 is a fixed cost for the supplies, and the $25 is the cost per room painted. The variable "x" represents the number of rooms painted, which can vary.

We can draw a graph of this equation by plotting points for different values of "x" and connecting them with a straight line. For example:

We can continue this process to find additional points, and then plot them on a coordinate grid. Here's what the graph might look like:

The line passes through the point (0, 100), which is the y-intercept. As we move to the right along the x-axis (increasing the number of rooms painted), the cost increases at a constant rate of $25 per room. The slope of the line is therefore 25.

The equation for the line is in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. In this case, we have:

Cost = 25x + 100

This equation gives us the cost of painting x rooms, where x can be any non-negative integer.

The correct graph is option C

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Answer: 7

Step-by-step explanation:

The percentage of students who play a sport but do not like physical education = 16%

The correct answer is an option (B)

The complete two way frequency table for given situation would be,

                                                    Play a Sport  Do not Play a Sport    Total

Like Physical Education                    150                 72                          222

Do Not Like Physical Education        28                 164                         192

Total                                                    178                 236                        414

Now we find the percentage of students who play a sport, and  do not like physical education.

The total number of students who play sport.

n = 178

And the number of students who play a sport but do not like physical education are 28.

Using percentage formula, the required percentgae would be,

P = 28/178 × 100

P = 15.73%

P ≈ 16%

Therefore, the correct answer is an option (B)

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