A, B and C are faces of the cuboid below. Calculate the area of each labelled face. Give your answers in m²​

By using the concept of relation, it can be proved that

If R is a Reflexive relation, then [tex]R^{-1}[/tex] is a Reflexive relation

If R is a Symmetric relation, then [tex]R^{-1}[/tex] is a Symmetric relation

If R is a Transitive relation, then [tex]R^{-1}[/tex] is a Transitive relation

What is a relation?

Relation on a set [tex]X_1, X_2,....,X_n[/tex] is the subset of the cartesian product

[tex]X_1 \times X_2 \times..... \times X_n[/tex]

A)

Let R be a reflexive relation .

Let (x, x) ∈ R

Then (x, x) ∈ [tex]R^{-1}[/tex]

So [tex]R^{-1}[/tex] is reflexive

B)

Let R be a symmetric relation such that [tex]xR^{-1}y[/tex] holds
so yRx holds

Since R is symmetric, xRy holds

[tex]yR^{-1}x[/tex] hold

[tex]R^{-1}[/tex] is symmetric

C)

Let R be a transitive relation such that [tex]xR^{-1} y[/tex] and [tex]yR^{-1}z[/tex] holds

Then yRx and zRy holds

Since R is transitive

zRx holds

[tex]xR^{-1}z[/tex] holds

[tex]R^{-1}[/tex] is transitive

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Complete Question

Let R Be A Relation On A Set A. Prove The Following: A) If R Is Reflexive, Then [tex]R^{-1}[/tex] Is Reflexive. B) If R Is Symmetric, Then [tex]R^{-1}[/tex]Is Symmetric. C) If R Is Transitive, Then [tex]R^{-1}[/tex] Is Transitive.

The correct answer is mean.

The characteristic which is being calculated here is the mean or the average of the data set.

(20.73 + 20.76 + 20.68 + 20.75)/4

when we divide it by 4 because there are four data sets

= 82.92 / 4

= 20.73

The complete question is 'Francine makes several measurements of the mass of a metal block and the data set is shown in the table below. The measurement mass of metal blocks(g) are a) 20.73 b) 20.76 c) 20.68 d) 20.75 . After analyzing the given data set, Francine calculates a value of 20.73 g so which of these characteristics has been calculated?'

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Answer: x-2

and 2x+4

Step-by-step explanation:

The correct option C 0.28; for the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed.

This problem involves a binomial probability distribution.

Now that five thumbtacks have been thrown, we want to determine the likelihood that at least two of them will land pointing up. As it is written;

P(X ≥ 2) = P(2) + P(3) + P(4) + P(5)

Based on the histogram

P(5) = 0.02

P(4) = 0.02

P(3) = 0.05

P(2) = 0.19

So,

P(X ≥ 2) = 0.19 + 0.05 + 0.02 + 0.02

P(X ≥ 2) = 0.28

Thus, the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed is 0.28.

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A thumbtack that is tossed can land point up or point down. The probability of a tack landing point up is 0.2. A simulation was conducted in which a trial consisted of tossing 5 thumbtacks and recording the number of thumbtacks that land point up. Many trials of the simulation were conducted and the results are shown in the histogram.

Based on the results of the simulation, which of the following is closest to the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed?

A 0.09

B 0.19

C 0.28

D 0.72

E 0.91

The approach to identify linear functions is whether the change in y will always have the same value for any given change in x.

Possibly the most significant mathematical function is the linear function. One of the simplest functions to comprehend, it frequently appears when you least expect it. We frequently turn more complex functions into linear functions for understanding purposes since it is so convenient to do so. The linear function is incredibly straightforward for one variable. A linear function is one with the formula f(x)=ax, where an is a real number of any value. The parameter an is the slope of the line through the origin that makes up the graph of the function f.

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The answer is all real numbers greater than or equal to -3, as domain and range.

What is the domain and range of function?

A function's domain and range are its components. A function's range is its potential output; its domain is the set of all conceivable input values. Domain, Function, and Range. If a function f: A B exists that maps every element in A to an element in B, then A is the domain and B is the co-domain. The image of an element 'a' under a relation R is provided by 'b,' where (a,b) R. The set of photographs makes up the function's range.

The domain of a relation or a function is the set of all possible values for an input in that relation/function.

The range of a relation or function is the set of all possible values that can be the result of a relation or function.

From the graph, nothing can be seen on the left side of x = - 3 and the graph is continuous and going in the direction of infinity on the right side of the x axis.

Hence all real numbers greater than or equal to -3

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Answer: 3 and 1

Step-by-step explanation: 3 is a prime number, which means its only factors are the number itself and 1. The number 3 is not divisible by anything else. You can only multiply 3 and 1.

The set of side measurements that could be used to form a triangle is 9, 13, 21.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

9, 13, 21 : 9 + 13 > 21 ; 13 + 21 > 9 ; 9 + 21 > 13

8, 9, 18 : 8 + 9 < 18

3, 18, 21 : 3 + 18 = 21

2, 5, 9 : 2 + 5 < 9

Hence, the side measurements 9, 13, 21 is the only set that can be used to form a triangle.

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The four types of function are One One Function , Many to One Function , Onto Function and Into Function .

The four types of functions are :

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Using simple Units Measurement System,

Dressmaker cut total 40 pieces of length 18 inch from 15 of given rolls of ribbon.

We have given that,

total length of roll of ribbon = 6 feet

the length of ribbon cut by dressmaker = 18 inch

As we know , 1 inch = 2.5 cm --(1)

then 1 feet = 30cm --(2)

from (1) and (2) , we get

1 feet = 12 inch

total length of roll ribbon in inch = 6×12

= 72 inches

we have total number of ribbons = 5

so, total number of inches = 5 ×72 = 360 inches

As per question given that dressmaker need to cut 18 inch piece for making dress .

So, total number of 18 inch pieces Dressmaker has is equal to ratio of total length of ribbon / length of ribbon dressmaker needed

= 720/18

= 40

Hence, total 40 pieces of length 18 inch dressmaker have.

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The slope intercept form of the given line equation is y=-5/6 x+1.

The given equation of a line is 5x+6y=6.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Here, the equation can be written in slope intercept form as

5x+6y=6

6y=6-5x

y=-5/6 x+1

Therefore, the slope intercept form of the given line equation is y=-5/6 x+1.

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Answer:

The area of the base of the cylinder (the circle face) is the same as the area of the base of the prism (the triangle face).

Step-by-step explanation:

The volume of a prism is the area of the base of the prism multiplied by its height.

The volume of a cylinder is the area of the base of the cylinder multiplied by its height.

So because the volumes are both equal, and the heights are both equal

Then the area of the bases should also be equal.

Answer:

Step-by-step explanation:

solving by elimination means to get rid of one of the variables,  pick either one,  X or Y  and use the other equation to make it zero.

3x - y = 5

4x + y = 9

+______  add the two equations, column for column,

7x + 0y = 14

now solve for x,  that is, get x by itself

7x / 7 = 14/7

x = 2

Now that you've solved for x,  plug that x into either equation.

3(2) - y = 5

6-y = 5

6-5 = y +5-5

1 = y

Now you have both :)

The component form of the force vector required to move the object of 300 pounds is (272, 127)

Suppose we have a vector v  with angle θ to the positive x-axis, then the horizontal and vertical components of the vector are given as:

vx = v cos θ

vy = v sin θ

In the given problem, the vector is a force vector of 300 pounds.

w = 300

θ = 25⁰

Hence,

horizontal component = wx = w cos 25⁰

                                         = 300 . cos 25⁰ = 272

vertical component = wy = w sin 25⁰

                                         = 300 . sin 25⁰ = 127

Hence, the component form of the given force vector is (272, 127)

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Answer:

Its D on edge

Step-by-step explanation:

By using the principal of mathematical induction, it can be proved that

[tex]a_n = a_{n-1} - 2a_{n-2}+2[/tex] for [tex]a_n = n^2[/tex]

What is Principle of Mathematical Induction?

Suppose a statement P(n) is given. At first P(n) is proved to be true for

n =  1. Then P(n) is assumed to be true for n = m. If it can be proved that P(n) is true for n = m + 1, then by principle of Mathematical Induction, it can be proved that P(n) is true for all natural numbers

Here

[tex]a_n = n^2\\P(n) = 2a_{n-1} - a_{n-2} + 2\\P(0) = 0^2 = 0\\P( 1)= 1^2 = 1\\P(2) = 2a_1-a_0 + 2\\P(2) = 2(1)^2 - 0^2+2 =4[/tex]

Let us assume P(0), P(1),... P(k) is true

[tex]a_{k+1} = 2a_k - a_{k-1} + 2\\a_{k+1} = 2k^2 - (k-1)^2 + 2\\a_{k+1} = 2k^2 - k^2 +2k -1 + 2\\a_{k+1} = k^2+2k + 1\\a_{k+1} = (k+1)^2[/tex]

P(k+1) is true

By Principle of Mathematical Induction,

P(n) is true for all natural numbers

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Answer:

Yes, the measurements 3cm, 4cm and 5cm are possible to create a triangle!

Step-by-step explanation:

Each probability lies between 0 to 1, If a customer purchases 2 stoves, the probability is 0.1379 they will also purchase two refrigerators, the average number of refrigerators purchased is 0.93, and the variance in the number of refrigerators purchased is 0.6051.

A)     0            1            2          stoves

0      0.08       0.14      0.12      0.34

1       0.09       0.17      0.13      0.39

2      0.05       0.18      0.04     0.27

RF    0.22       0.49     0.29     1

B) Each probability lies between 0 to 1

All the probabilities sum up to 1

C) P(2 Ref/ 2 stoves) = P(2 Ref and 2 stoves) / 2 stoves)

= 0.04/0.29 = 4/29 = 0.1379

D) Average number of Ref purchased E(x) = ∑xi pi

X        0          1         2

Prob.  0.34    0.39   0.27

= 0.39 + 0.54

= 0.93

E) Var(x) = ∈(x)² - (∈{x})²

= (0.39 + 1.08) - (0.93 * 0.93)

= 1.47 - 0.8649

= 0.6051

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The school will purchase 80 chairs and 10 tables.

A system having more than two equations is known as a system of equations.

Given that, the school can spend $5200 and the cost of one table is $200 and the cost of one chair is $40.

Let x represents the number of chairs purchased and y represents the number of tables purchased.

The total cost of purchasing x chairs and y tables is:

Total cost = 40x + 200y

Since the budget of the school is $5200 only, substitute "Total cost =5200" into the above equation,

5200 = 40x + 200y

Since each table requires 8 chairs, it follows:

x = 8y

Hence, the system of equations is:

5200 = 40x + 200y      (1)

x = 8y                            (2)

To solve the system of equations, substitute x = 8y into equation (1):

5200 = 40(8y) + 200y

5200 = 320y + 200y

5200 = 520y

y = 10

Substitute y = 10 into equation (2):

x = 8(10)

x = 80

Hence, the school will purchase 80 chairs and 10 tables.

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If we standardize both variables what would the regression equation the mortgage amount will be 220.88 and the interest amount will be 7.768.

[tex]b_1[/tex] = r*[tex]S_{xy}/S_{xx}[/tex]

= -0.84

[tex]b_0 = y - b_1x[/tex]

Regression model is used to identify the relation between two variables.In the relation between two variables.

From the given question the regression model fits best to identify the mortgage amount from interest rates.

The interest rate and mortgage both are quantitative values so the regression model is most suitable for this given condition.

Therefore If we standardize both variables what would the regression equation the mortgage amount will be 220.88 and the interest amount will be 7.768.

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The conclusion of step 4 and step 5 are not valid . Therefore, this is an invalid proof that all isosceles triangles.

Each step is valid, but the conclusion is not. At the end of step 4, there are a series of isometric maps that lead A to D and C to F, as claimed.. After the final rotation in Step 5, the sequence of isometries takes B to E and C to F —but here’s the hitch—there is no reason why it should still take A to D, in fact it can’t take A to D unless the rotation angle is zero.

If the rotation angle in Step 5 is zero, then the isometries take [A,B,C] to [D,E,F] and the two triangles are indeed similar. But this requires the dilation in Step 2 to have made A′B′ congruent to DE , in other words, it requires assuming the triangles are similar before performing any of of the transformations.

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Complete Question:

This is an invalid proof that all isosceles triangles are similar. Explain which step is invalid and why. 1. Draw 2 isosceles triangles ABC and DEF where AC = BC and DF = EF. 2. Dilate triangle ABC to a new triangle A'B'C' using center C and scale factor DF/AC so that A'C= BC - DF = EF. 3. Translate by directed line segment CF to take A'B'C' to a new triangle A" B" F. Since translation preserves distance, A"F = A'C=DF and B" F = BC = EF. 4. Since A"F=DF, we can rotate using center F to take A" to D. 5. Since B" F = EF, we can rotate using center F to take B" to E. 6. We have now established a sequence of dilations, translations, and rotations that takes A to D, B to E, and C to F, so the triangles are similar.

The point-slope form of the line is y - 2 = 1/3(x - 3).

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

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.

The equation of the line into point slope-form is equal to

y - y1 = m(x - x1)

slope(m) = 1/3

(3,2)....x1 = 3 and y1 = 2

now we sub

y - 2 = 1/3(x - 3)

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There are three major forms of linear equations:

Point slope form:

The point-slope form, as its name suggests, identifies a point on a line and its slope. Not frequently is this form provided to assist with line graphing. To get from a verbal or visual representation of a line to its slope-intercept or standard form, however, is where it is more frequently utilized.

Slope intercept form:

A line's slope and y-intercept are communicated using the slope-intercept form. Technically speaking, it is an exception to the point-slope form.

Standard form:

An equation's conventional form is as follows:

Ax+By=C

Where A is not a negative number and B, C, and all three are whole numbers.

Hence we get the required answer.

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y-intercept of the function = 4

What in mathematics is a y-intercept?

A point on the y-axis at which the slope of a line passes is referred to as an intercept in mathematics.

It is a place on the y-axis where a straight line or a curve crosses. This is shown by writing the equation for a line as y = mx+c, where m denotes the slope and c the y-intercept.

Here the given function is

f(x) = 4 – 5x

Which can be rewritten as

f(x) = – 5x + 4

Which is of the form f(x) = mx + c

Where m = - 5 , c = 4

Hence y-intercept of the function = 4

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The complete question is -

What is the y-intercept of the function f(x)=4 – 5x?

–5

–4

4

5

Answer:

There are 6 integers between sqrt7 and sqrt77.

Step-by-step explanation:

Sqrt9, sqrt16, sqrt25, sqrt36, sqrt49, sqrt64 are all between sqrt7 and sqrt77. Since these are all perfect squares, they simplify to integers.

sqrt9 = 3

sqrt16 = 4

sqrt25 = 5

sqrt36 = 6

sqrt49 = 7

sqrt 64 = 8

There are 6 integers between sqrt7 and sqrt77.

The E(T) is 4 when A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on).

Given that,

A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on). The heads and tails are recorded in order. The game is over and the winner is the person who throws the tail if there is a head followed by a tail (HT sub-sequence).

We have to find what is the anticipated game length. Let the game continue for T number of coin tosses. Find E (T).

We know that,

Here,

E(T )=first time sequence HT occurs

E(T) = P(first H)× P(expected number till 1st T |first H)+ P(first T)× P(expected number till 1st HT |first T)

E(T) =0.5×(1+2)+0.5×(1+E(T))

0.5×E(T)=0.5×4

E(T) =4

Therefore, The E(T) is 4 when A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on).

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The given pair of events are independent when your first coin flip results in heads. and your second coin flip results in heads.

Events that occur independently of any other events are referred to as independent events. if we flip a coin in the air and get the head, we will then flip the coin again, but this time we will get the tail. The occurrence of both events is unrelated in either instance. Tossing the coin the first time does not affect the outcome of the second toss.

Note that the events are not mutually exclusive as it is possible that both the first and the second toss are headed.

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Maintenance primarily involves modifying programs to meet new business needs, but also debugging of errors that were not detected when testing the developed code.

Preventive maintenance schedules can be regular or periodic (time-based). When an issue is discovered, corrective maintenance is performed. Maintenance is predetermined and follows a factory schedule. Condition-based maintenance occurs when a situation or condition indicates the need for maintenance.

What is modifying a program?

A program modification is defined as a programmatic change that does not clearly qualify as a new program or a nonsubstantive change, such as a new program composed primarily of course work from a previously approved program; an approved program to be offered at an off-campus location; a change in the.

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Full Question:_____ primarily involves modifying programs to meet new business needs, but also debugging of errors that were not detected when testing the developed code.

The rate at which the volume of the box of height 10 inches is changing when the width is 8 inches and the length is 6 inches is 440 cubic inches per second

The volume of a rectangular box is the product of the length, the width and the height of the box.

The height of the rectangular box, h = 10 inches

The rate of change of the length of the box is; [tex]\frac{dl}{dt}[/tex] = 2 in/sec

The rate at which the width is decreasing is; [tex]\frac{dw}{dt}[/tex] = 4 in/sec

When the length is 8 inches and the width is 6 inches, we get;

[tex]\dfrac{dV}{dt} = \dfrac{d}{dt} \left(l\cdot w \cdot h\right)[/tex]

[tex]\dfrac{dV}{dt} =h\times \left(l\cdot \dfrac{dw}{dt} + w \cdot \dfrac{dl}{dt} \right)[/tex]

When l = 8, and w = 6, we get;

[tex]\dfrac{dV}{dt} =10\times \left(8\times 4 + 6 \times 2 \right)=440[/tex]

The rate at which the volume of the rectangular box is changing in cubic inches per second is therefore;

[tex]\dfrac{dV}{dt} =440 \ in^3/sec[/tex]

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In the given triangle, the length of missing side is 15.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

In the given triangle,

Side BD = 5, CE = 3 and AE = 9

Let the side AD is x,

Since, line BC and DE and parallel to each other,

Therefore, by side splitter theorem,

A line that is parallel to one side of a triangle and crosses the other two sides equally divides the side in proportional ratio.

Implies that,

AD/BD = AE/EC

x/5 = 9/3

x/5 = 3

x = 15

The value of side AD is 15.

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The correct answer is amount of dilute solution is 4 gallons and amount of concentrated solution is 6 gallons.

Let the dilute amount of solution be x and the amount of salt in the solution be 0.13x

Then the concentrated amount be 10-x  and the amount of salt in the solution be 0.33x (x-10).

Solving the equation

⇒ 0.13x + 0 .33 (10 - x ) = 2.5

⇒ 0.13x + 3.3 - 0.33x  = 2.5

⇒ -0.2 x = 2.5 - 3.3

⇒ -0.2x = - 0.8

⇒ x = 4

Hence, the amount of dilute solution is 4 gallons and amount of concentrated solution is 6 gallons.

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