Which models represent 56 as a sum of fractions with a common denominator of 6?

The volume of the given solid, with the boundaries, is given as follows:

661.5 cubic units.

The volume of the solid is obtained using a double integral.

The equation for the solid is given as follows:

7x + 9y + z = 63.

z = 63 - 7x - 9y.

The coordinate planes bound the plane, hence:

Hence the double integral that is used to obtain the volume of the solid is given as follows:

[tex]V = \int_{0}^{9}\int_{0}^{7 - \frac{7x}{9}} 63 - 7x - 9y dydx[/tex]

The inner integral is given as follows:

[tex]I = \int_{0}^{7 - \frac{7x}{9}} 63 - 7x - 9y dy[/tex]

Which, applying the Fundamental Theorem of Calculus, has the result given as follows:

[tex]I = -98x + \frac{49x^2}{9} - \frac{(7x + 63)^2}{18} + 441[/tex]

Then the volume of the solid is given by the outer integral as follows:

[tex]V = \int_{0}^{9} \left(-98x + \frac{49x^2}{9} - \frac{(7x + 63)^2}{18} + 441\right) dx[/tex]

Which has a numeric value of:

661.5 cubic units.

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Power Query solve the problem b) Cleaning messy data

Power Query is a Microsoft Excel feature that is designed to help users extract, transform, and load data from a variety of sources. It is particularly useful for solving the problem of cleaning messy data.

Cleaning messy data is a common challenge that many people face when working with large or complex datasets. Data can be messy for a variety of reasons, such as being in an inconsistent format, having errors or typos, or containing duplicates or missing values. Cleaning up this data can be time-consuming and error-prone, especially if it is done manually.

Power Query provides a set of tools and features that make it easier to clean and transform data in Excel. It allows users to easily extract data from various sources, remove unwanted columns or rows, split or merge columns, apply filters and transformations, and more. This helps users save time and effort when working with large or complex datasets, and ensures that their data is clean and ready for analysis.

In summary, Power Query helps users solve the problem of cleaning messy data by providing a set of tools and features that make it easier to extract, transform, and load data in Excel.

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The function of the area of the square is A(t) = 49t².

A function is a relation between the input abd output values.

The length of a square's side starts from 0 cm and increases at a constant rate of 7 cm per second.

Let us assume that the function 'f' determines the area of the square (in cm²)

Also Lets  the length of side of square is x

rate of change of length with respect to time can be denoted as (dx/dt) = 7 cm/sec

⇒ x = 7*t

Area of square = ( length of side )²

{as the length of side is 7t} {varies by time}

Area of square A(t) = ( 7*t )²

Therefore, The function of the area of the square is A(t) = 49t².

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A bar graph is the most popular visual representation of quantitative data.

Another name for them is bar charts. One tool used in statistics for data processing is the bar graph. Using a bar diagram, it is simple and quick to compare sets of data among several groupings. On one axis of the graph are discrete numbers, while on the other are categories. The purpose is to illustrate how the two axes are related. Bar charts can also show significant alterations in data over time.

Given,

A bar graph is the most popular visual representation of quantitative data.

b) Bar graph

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The distance time Graph of Amelia as she gets back home is attached below

What is a distance-time graph?

How far an item has come in a certain amount of time is displayed on a distance-time graph. The graph that shows the result of the distance vs time analysis is a straight-line graph.

The Y-axis represents the distance.

The X-axis is used to plot time.

On a graph of distance vs time, curved lines denote a changing speed.

When analyzing the motion of bodies, we work with the distance-time graph. A distance-time graph related to a body's motion may be created if we measure a body's motion's distance and time and display the resulting data on a rectangle graph.

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Answer:

A' (3,-1)

B' (-2,-5)

C' (5, -2)

Step-by-step explanation:

Notice how the x values stay the same and the y values become the opposite of the original points.

Answer:

9 small boxes and 15 large boxes

Step-by-step explanation:

x = small box

y = large box

x + y = 24

9x + 24y = 441

-9x - 9y = -216

15y = 225

y = 15

x + 15 = 24

x = 9

The value of R is 7 , we can find answer using concept of greatest integer and square root .

What is square root of a number ?

Square root , in mathematics , a factor of a number that , when multiplied by itself , returns the original number.

e.g. Square root of 9 are both 3 and -3.

Symbol = " √ "

In given que, we need to find greatest integer smaller than √51.

Root of 51 will not give exact integer value.

As we know root of 49 is 7 and root of 64 is 8.

And 51 lie between 49 and 64,

So, Square root of 51 will also lie between 7 and 8.

So, the greatest integer smaller than √51 will be 7.

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Answer: Yes

Step-by-step explanation:

Most of the time, if a graph passes through the origin it is a proportional relationship!

The probability that both switches are defective is 1%.

What is a probability answer?

Mathematics' branch of probability, where probability is the likelihood that any event will occur, deals with the occurrence of random events.                      

                            Probability values range from 0 to 1, with 1 being the most likely value.

Given that a shipment contains 10,000 switches, and of these, 1000 are bad, and an inspector draws 2 switches at random, one after the other, to find the probability that both switches are defective the following calculation must be performed:

1000/10000 = 1/10

1/10 x 1/10 = X

0.1 x 0.1 = X

0.01 = X

0.01 x 100 = 1

Therefore, the probability that both switches are defective is 1%.

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The complete question is -

Inspecting switches A shipment contains 10,000 switches. Of these, 1000 are bad. An inspector draws 2 switches at random, one after the other.A) Draw a tree diagram that shows the sample space of this chance process.B) Find the probability that both switches are defective.

The advantage of using the work sampling approach during a training needs assessment is that the assessor : sees the work actually being done , the correct option is (d) .

In the question ,

it is asked about the advantage of using the work sampling approach during the training .

we know that Assessing need special skills and experience to be competent.

Generally,  evaluators or assessors need to  have interpersonal skills and  communicates effectively with students.

So , During the training if the work sampling approach is used then assessor will see the work actually being done before hand .

Therefore , the advantage is that the will see the work actually being done .

The given question is incomplete , the complete question is

The advantage of using the work sampling approach during a training needs assessment is that the assessor:

(a) sees the results of each person doing the work

(b) does not get heavily involved with any job

(c) actually does each job

(d) sees the work actually being done

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On solving the provided question, we can say that the root of the equation [tex](x^2 - 10x+21)(x+7)=0[/tex]are x= -7,+7,3

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

A quadratic equation is a second-order polynomial equation in one variable that goes like this: x ax2 + bx + c=0, where a 0. Given that it is a second-order polynomial equation, the algebraic basic theorem ensures that it has at least one solution. Real or complicated solutions are both possible.

Set the denominator to 0

[tex](x^2 - 10x+21)(x+7)=0\\(x^2-7x-3x+21)(x+7)=0\\(x(x-7)-3(x-7))(x+7)=0\\(x-7)(x+7)(x-3)=0\\ (x-3)(x^2 - 7^2)=0\\x= -7,+7,3[/tex]

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The no. of groups of five can be chosen that contain at most three women is 60.

The method we use to solve this is combination method.

Mathematical combinatorics is a division that deals with counting.

Combinatorics can assist us in counting the possible sequences in which something can occur.

Numerous applications of combinatorics can be found in other branches of mathematics, such as graph theory, coding and cryptography, and probability.

In mathematics, you can also have combinations, such as linear combinations or combinations of functions.

To solve this we use combination method of mathematics

The no. of groups of five can be chosen is

⁵C₃ * ⁴C₂

⇒ (5 * 4 * 3! / 3! * 2!) * (4 * 3 * 2! / 2! * 2!)

⇒ (5 * 4 / 2 * 1) * (4 * 3 / 2 * 1)

⇒ 5 * 2 * 2 * 3

⇒ 60

The no. of groups of five can be chosen that contain at most three women is 60.

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Shawn can type [tex]1\frac{6}{21}[/tex] pages in an one hour.

What is typing speed?

How many words a person can correctly type in one minute. He types at a 60 wpm rate.

Given:

Shawn is typing a paper for class. He can type 1 2/7 pages in 1/3 of an hour.

We have to find how many paged he can type in one hour.

First to convert improper fraction 1 2/7 into a fraction.

⇒ [tex]1\frac{2}{7} = \frac{7*1+2}{7} = \frac{9}{7}[/tex]

So, Shawn can type 9/7 pages in 1/3 of an hours.

i hour = 3/3

So, Shawn can type

9/7 x 3/3 = 27/21 =  [tex]1\frac{6}{21}[/tex] pages in one hour.

Hence, Shawn can type [tex]1\frac{6}{21}[/tex] pages in an one hour.

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The congruency of a triangle is not determined by SSA. As a result, choice C is the right response.

What is a triangle and the response?

Triangles are a particular kind of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here.

                    Three-sided polygons include triangles. Three triangle angles added together equal 180 degrees.

The sides (S) and angles (A) of two triangles are said to be congruent if they are equal.

The triangle must meet the SAS, ASA, SSS, and RHS criteria in order to be congruent.

The congruency of a triangle is not determined by SSA. As a result, choice C is the right response.

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Answer: I believe f(-1) will be -1

Step-by-step explanation:

You'll notice that f(x) is increasing by 7, so instead of adding 7 subtract 7.

Extend the table to the left having the (x) go down

The possible temperatures for the north will be 4 degrees and 6 degrees. The correct option is D and E.

Mathematical statements with at least two terms connected by an operator and containing either numbers, variables, or both are referred to as expressions.

The direction that heat energy will spontaneously flow depends on temperature. Temperature is the degree to which a body is hot or cold. because it was mentioned that the north can occasionally experience temperatures below 3 degrees. D and E are the appropriate choices

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​Yes, the figure indicates that two corresponding angles and their included side are all congruent. Option A

We know that the term congruency can be used to refer to the triangles that are equivalent. For the triangles that are equivalent, we can see that there are some kind of relationship that binds the triangles together.

The kinds of congruency of the triangles that we may have are the following;

Angle Angle side

Side angle side

Side side side

Angle Side angle

If we look at the triangles that we have in the two images that have been conspicuously attached to the question that we are trying to attend to, it is clear that two triangles have similar sides and a similar included angle hence they are congruent by the theorem of SAS.

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Answer:

x+5=12

or,x=12-5

or,x=7

Step-by-step explanation:

x =ky

x=12,y=20

12 =20k

divide both sides by 20

k=12/20

= 6/5

X=6/5y

By using some exponent properties, we will find the equivalent expression:

(m⁻²*n⁻³)⁻⁴ = m⁸*n¹²

Here are some exponent properties that we need to use:

(aⁿ)ˣ = aⁿ*ˣ

(a⁻ⁿ) = (1/a)ⁿ

Here we have the expression:

(m⁻²*n⁻³)⁻⁴

The exponents can be distributed under multiplication, then:

(m⁻²)⁻⁴*(n⁻³)⁻⁴

Now we can use the first property so we get:

(m⁻²)⁻⁴*(n⁻³)⁻⁴ = m⁽⁻²*⁻⁴⁾*n⁽⁻³*⁻⁴⁾

m⁽⁻²*⁻⁴⁾*n⁽⁻³*⁻⁴⁾ = m⁸*n¹²

That is the equivalent expression.

(m⁻²*n⁻³)⁻⁴ = m⁸*n¹²

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No, The side lengths does not make a right triangle.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The sides of the triangle are;

⇒ 20, 20 and √800

Now,

Since, The sides of the triangle are;

⇒ 20, 20 and √800

Hence, We can apply the Pythagoras theorem as;

⇒ (√800) ² = √ 20² + 20²

⇒ 800 ≠ √800

Thus, The side lengths does not make a right triangle.

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Answer:

A linear function is a function whose graph is a straight line. An exponential function is a function in which the variable appears in an exponent. A linear function has a constant rate of change, meaning that the rate of change between two points on the line is the same. An exponential function has a variable rate of change, meaning that the rate of change between two points on the line is not constant.

Explanation: A linear function, has y-values with equal differences. An exponential function has y-values with equal ratios.

The missing measures of the named angles are:

w = 62°

z = 57°

y = 57°

x = 61°

b = 24°

a = 132°

c = 156°

d = 156°

e = 132°

f = 24°

g = 24°

h = 156°

i = 156°

To find the measures of each of the named angles in the figure above, note the following:

Therefore:

w = 62° [alternate interior angles are congruent]

z = 180 - 123 = 57° [angles on a straight line]

y = 180 - 62 = 57° [angles on a straight line]

x = 180 - 62 - 57 = 61° [triangle sum theorem]

b = 24° [base angles of isosceles triangle]

a = 180 - 2(24) = 132°

c = 180 - 24 = 156°

d = 180 - 24 = 156°

e = a = 132°

f = g = 1/2(180 - e)

Plug in the value of e:

f = g = 1/2(180 - 132)

f = g = 24°

h = i = 180 - 24 = 156°

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If they were to add more staff to assist with the check-in process, then the average time parents wait decreases, the maximum time the parents wait decreases and average number of parents waiting to check in their child decreases. So, the correct answer is (i), (ii), (iii).

Parents and students standing in line for check-in and actually checking in. Parents and children are the customers here, and the staff who support parents and students are the servers. A limited number of servers and many clients will increase the queue length. In other words, as more parents enter the queue, the wait time for each parent increases, increasing the average wait time. Additionally, the longer the queue, the longer the maximum wait time.

Therefore, adding check-in staff will increase the number of customers to serve the same number of patients. Queues are split across multiple servers, so you get all three benefits.

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Answer:

Hope this Helps!!!

The remainder will be 33, 9, 7, and 14 for options a, b, c, and d respectively.

The Remainder is the extra part of a number that restricts the number to be divided completely.

a)

(19² mod 41) mod 9

Let us determine 361 mod 41

a=361 = 328+33= 8*41+33 =8d+33

The remainder is the constant in the final expression: 361 mod 41=33

33 mod 9 = 6 (since a=33= 27+6=3*9+6=3d+6)

b)

(32³ mod 13)² mod 11

Let us determine 32 mod 13

a=32=26+6=2*13+6+2d+6

The remainder is the constant in the final expression: 32 mod 13=6

[tex](6^{3} mod13)^{2} mod 11\\(216mod13)^{2} mod 11[/tex]

Let us determine 216 mod 13

a= 216= 208+8=16*13+8 = 16d+8

The remainder is the constant in the final expression: 216 mod 13=8

[tex]8^{2} mod 11\\64 mod 11[/tex] = 9 (since, 64= 55+9= 11*5+6= 11d+6)

c)

(7³ mod 23)² mod 31

[tex](343mod23)^{2} mod 31\\[/tex]

Let us determine 343 mod 23

a=343=322+21=14*23+21=14d+21

The remainder is the constant in the final expression: 343 mod 23= 21

[tex]21^{2} mod 31 = 441 mod 31=7[/tex] (since a = 441=434+7=14*31+7=14d+7)

d)

(21² mod 15)³ mod 22

[tex](441mod15)^{3} mod 22[/tex]

Let us determine 441 mod 15

a=441 = 435+6= 29*15+6= 29d+6

The remainder is the constant in the final expression: 441 mod 15= 6

[tex]6^{2} mod 22=36mod22= 14[/tex] (since a = 36= 22+14= 1*22+14= d+14)

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Answer:

one solution

Step-by-step explanation:

because it has diffrent slopes

The trigonometric equation be tan(-x)cos(-x) then we get -sin (x).

A function of an angle is a trigonometric function. They are utilized to connect the triangle's angles and sides' lengths.

Trigonometry is the study of angles and the angular connections between figures in two and three dimensions. The trigonometric functions that make up trigonometry are cosecant, cosine, cotangent, secant, sine, and tangent. These are also known as the circle functions.

Trigonometry is used to define directions such as the north, south, east, and west. It also tells you the direction to point the compass in order to travel straight forward. It helps to locate a certain location during navigation. The shore's separation from a certain place in the sea can likewise be determined using this method.

Let the given function be tan (-x) cos (-x)

Use the negative angle identity: tan (-x) = -tan (x)

= cos (x) (-tan (x))

Remove parentheses: (-a)= -a

= -cos (x) tan (x)

Express with sin, cos

= -sin (x)

Therefore, simplifying the equation, tan(-x)cos(-x) we get -sin (x).

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tan(-x).cos(-x) = -sin(x)

What are trigonometric ratios?

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.are therefore assessed in relation to sides and angles.

We know that, tan(x) = sin(x)/cos(x)

Now, calculating tan(-x).cos(-x)

⇒ [tex]\frac{sin (-x).cos (-x)}{cos (-x)}[/tex]

⇒ sin(-x)

Since, sin function is an odd function, it can be expressed as below.

sin(-x) = -sin(x)

Thus, tan(-x).cos(-x) = -sin(x)

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Answer:

On attached woksheet

Step-by-step explanation:

The graph has units of time (sec) on the x axis and distance (meters) on the y.  The lines in the graph represent a change in distance from the origin as a function of time.  The slopes of these lines represent the speed, in m/sec., for that line.  Since they are straight lines, the speed is not changing for that time period.  A flat, horizonal, line represent a stationary object.  Distance does not change with time.  Steeper lines represnt faster speeds - the distance changes more quickly for the same time period.

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