Let R Be A Relation On A Set A. Prove The Following: A) If R Is Reflexive, Then R-1 Is Reflexive. B) If R Is Symmetric, Then R-1 Is Symmetric. C) If R Is Transitive, Then R-1 Is Transitive. 3. Let R Be A

The alternative hypotheses that make a hypothesis test one-tailed are 1. Parameter is less than a value and 2. Parameter is greater than a value.

An explanation for a phenomena or a forecast of the results of an experiment are both examples of hypotheses. It is a speculative claim about how two or more variables are related, and it can be verified via more investigation, testing, and data gathering. Usually based on existing information and observations, hypotheses can be confirmed or refuted via scientific investigation.

A hypothesis is created by making an educated guess or prediction about how an experiment will turn out based on prior knowledge and observations. This hypothesis provides the basis for further research, and it may be improved upon and put to the test by gathering more information.

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By using t test, it can be concluded that

The value of t at level of significance = 0.10 with 5 degree of freedom is greater than the value of t at level of significance = 0.10 with 10 degree of freedom

What is t test?

If the observations are from a normal population and the population standard deviation is not known, the distance between the sample mean and the population mean can be calculated by using t test

By using t- table

The value of t at level of significance = 0.10 with 5 degree of freedom = 2.015

The value of t at level of significance = 0.10 with 10 degree of freedom = 1.812

Since 2.015 > 1.812,

The value of t at level of significance = 0.10 with 5 degree of freedom is greater than the value of t at level of significance = 0.10 with 10 degree of freedom

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The teacher has offered his students a(n): algorithm

What is algorithm?

A method which solve a puzzle or carry out a calculation is known as an algorithm. Algorithms are precise lists of instructions that, in either software or hardware-based routines, carry out predetermined operations step by step. In many facets of IT, algorithms are commonly utilized. An algorithm is typically a short process that resolves a recurring issue in mathematics and computer science. Automated systems heavily rely on algorithms, which are also utilised as guidelines for carrying out data processing. Pseudocode, flowcharts, control tables, and plain languages are all ways to express algorithms. Since they are more ambiguous, natural language expressions are uncommon. Algorithms that a computer executes are typically expressed in programming languages.

A high school physics teacher reassures his class that no matter how confusing this week's word problems appear,

And they all may be solved quite handily through the use of the formula F = MA.

Hence this is the prime example of the algorithm.

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To simplify complex fractions with LCD multiply each term in the numerator and denominator by the LCD

Given,

LCD;- Least Common Denominator

When two or more fractions are supplied, the least common denominator is the smallest number among all the common multiples of the denominators.

We have to find the method of simplification of complex fractions with LCD;

Here,

Multiply each term in the numerator and denominator by the LCD to simplify this complicated fraction. It doesn't matter how complicated these fractions are; all you need to do is discover the LCD to convert the complicated fraction into a simpler one. The technique is done more frequently the more fractions there are in an issue

That is,

To simplify complex fractions with LCD multiply each term in the numerator and denominator by the LCD

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Volume of the cone as a polynomial function., Radius of cone = x + 4 units.

According to our question-

Radius of cone = x + 4 units,

Height of cone = 5 units less than radius,

Volume formula.

Solution

We are given the volume formula:

V = (1/3)πr²h

Find the height:

h = r - 5

h = x + 4 - 5 = x - 1

Substitute all into formula:

V(x) = (1/3)π(x + 4)²(x - 1)

You may keep it as is or simplify:

V(x) =

(1/3)π(x² + 8x + 16)(x - 1) =

(1/3)π(x³ + 8x² + 16x - x² - 8x - 16) =

(1/3)π(x³ + 7x² + 8x - 16)

Hence, Volume of the cone as a polynomial function., Radius of cone = x + 4 units.

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The point estimate of the population standard deviation is   2.82

Since the  given  simple random sample is   6 8 10 8 10 6. considering  the data of the sample be denoted by X.  the mean of the sample  is

X'=1/n ∑X, where n is the number of data points

 =6+ 8 +10+ 8+ 10+ 6/ 6   =  6

Since  the  formula for The point estimate of the population standard deviation is:

s= [tex]\sqrt{}[/tex](1/(n-1)* ∑(X−X')^2,  where  X' is the sample  mean and n is the

s=[tex]\sqrt{}[/tex]( 1/(6-1)*{(6-6)^2+(8-6)^2+(10-6)^2+(8-6)^2+(10-6)^2)

= [tex]\sqrt{}[/tex](1/5 *(4+16+4+16)

= [tex]\sqrt{}[/tex](1/5 *(40))

=[tex]\sqrt{}[/tex](8)

=1.41*2

=2.82

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Answer:

Well, since your answer is 4.8n-5, It could be 2+2.4+4n.3+2

Step-by-step explanation:

it's probably wrong but I'm only doing this for points so get rekt

Step-by-step explanation:

just for points

The two expressions can be -5 + 4.8 n and 4.8n + (-5).

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

4.8n-5.

We can write the expression as

-5 + 4.8 n

or, using the integers

4.8n + (-5)

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The domain of the given function is {0, 1, 2 3.... 10}.

The range of the function is: {0, 2.69, 3.17, 3.65, 4.13, 4.61, 5.09, 5.57, 6.03, 6.49, 6.95}

A function has a set of input values (x-values) that are corresponding to a set of output values (y-values).

The set of these input values (x-values) is what is referred to as the range of a function, while the set of the corresponding output values (y-values) is the domain of the function.

Given the graph above, all the set of weight are input values which make up the domain of the function, while the set of corresponding prices is the range of the function.

The domain is therefore: {0, 1, 2 3.... 10}.

The range is therefore: {0, 2.69, 3.17, 3.65, 4.13, 4.61, 5.09, 5.57, 6.03, 6.49, 6.95}

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The stream velocity has no influence on the amount of dissolved load it contains. The amount of dissolved material depends on erosion and deposition carried out in the watercourse. These are affected by factors such as the slope of the land, the resistance of the material to erosion, the size of the sediments transported, etc.

Stream velocity plays an important role in the transport of sediments and dissolved loads in a watercourse. It affects the erosion and deposition processes that occur in the watercourse, which in turn affect the amount of sediment and dissolved load that is carried by the stream. For example, faster stream velocities can cause more erosion of the stream bed, leading to more material being carried in the water.

Sediment is any particulate matter that is transported by a fluid, and it can come in many different forms. The three main types of sediment are:

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Answer:

The double of 8 is 16. Answer is 16.

The total VA( volt-ampere ) that must be used in a service calculation for 50' show window is 125000VA.

A volt-ampere (SI symbol: VA or V A, abbreviated as VA) is the unit of perceived power in an electrical circuit. The apparent power is equal to the product of the root mean square voltage (in volts) and the root mean square current (in amperes). Volt-amperes are commonly used to analyze alternating current (AC) circuits. In direct current (DC) circuits, this product equals the real power in watts. The volt-ampere is dimensionally identical to the watt: 1 VA = 1 W in SI units).

The total VA that must be used in a service calculation for 50' show window is, Therefore, by using VA linear foot method,

200 VA per linear foot×50'=10000VA10000VA×1.25

=125000VA

Hence, the total VA that must be used in a service calculation for 50' shadow is 125000VA.

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The algebric expression represents the cost of a four-line ad that runs for a year will be $(192/5)f.

An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.

Expression is very useful to determine the end or root value of constraint.

The constraint of expression is represented as = or <, >.

As per the given,

A local Pennysaver paper charges f dollars weekly for a five-line classified ad.

Cost of five-line ad = $ f / week

Cost of one line ad = $ f/5 / week

Cost of four line ad = $ (4/5) f / week

It is known that,

1 year = 12 x 4 = 48 weeks

Cost of four line ad for one year = $ (4/5)48 f

⇒ $(192/5)f

Hence "The algebric expression represents the cost of a four-line ad that runs for a year will be $(192/5)f".

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The integers are  3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,

An integer is the number zero (0), a positive natural number (1, 2, 3, etc.) or a negative integer with a minus sign.

A rational number is any number that can be written as a fraction, where both the numerator or demoninator that is the top and the bottom number  are integers, and the denominator is cannot be zero

An irrational number is a type of real number which cannot be represented as a simple fraction.

A integer can always be a rational number but vice versa is not true.

Integer = 3√25 = 3x5 = 15

-185/5 = -37

rational = -1/4, 0.75, 3√25, -185/5, 4√8

irrational = √13,

Therefore, the integers are  3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,

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The  common ratio is 4.

The next 3 terms are 192,768, 3072

What is common ratio?

In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.

Here, 48/12 = 12/3 = 4  ( it is a constant ratio )

Hence it is a geometric sequence and common ratio is 4.

Next 3 terms can be found by multiplying the common ratio with the previous term.

48*4=192

192*4=768

768*4=3072

So, the next 3 terms are 192,768, 3072

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Number of ways to form four letters strings formed using a, b, c, d, e with the given conditions is equal to 150ways.

As given in the question,

Given letters are a, b, c, d, e has

Number of vowel = 2

Number of consonant= 3

Number of letter strings to be formed = 4

Condition:

First letter must be vowel

Last letter must be consonant

First place filled in 2 ways

Second and Third place filled in 5ways

Last place filled in 3 ways

Total number of ways to form four letters strings

= 2 × 5 × 5 × 3

= 150

Therefore, number of ways to form four letter string is 150 ways.

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The rate of change of capital in terms of units of labor is -2.0 As more labor is used, available capital decreases As more capital is used, available labor decreases.

[tex]100x^{0.75} y^{0.25} = 135540[/tex]

x = 1500 units and y = 1000 units

A) [tex]\frac{d}{dx}(100x^{0.75}y^{0.25} = \frac{d}{dx}(135540)[/tex]

[tex]100[{\frac{d}{dx}(x^{0.75})y^{0.25} + x^{0.75}\frac{d}{dx}(y^{0.25})] = 0[/tex]

[tex]0.75 x^{-0.25} y^{0.25} + x^{0.75} (0.25y^{-0.75\frac{dy}{dx} }) = 0[/tex]   ______(1)

X & Y values in equation 1

[tex]0.75(1500^{-0.25}(1000)^{0.25}+(1500)^{0.75}(0.25)(1000)^{-0.75}\frac{dy}{dx} = 0[/tex]

(0.75) (0.16) (5.62) + (0.41) (0.25) (0.0056) [tex]\frac{dy}{dx}[/tex] = 0

0.6744 + 0.3374 [tex]\frac{dy}{dx}[/tex] = 0

0.3374 [tex]\frac{dy}{dx}[/tex] = -0.6744

[tex]\frac{dy}{dx}[/tex] = -1.9988

[tex]\frac{dy}{dx}[/tex] ≈ -2.0

B) If the labor x is increased then the capital invested in manufacturing process decreased

C) As more capital is used then the available labor is reduced

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Mr. Arnett will have to pay $15.75 for the trail mix if it cost $4.50 per pound.

According to the question,

We have the following information:

Amount of trail mix: 15 oz, 14 oz, 10 oz and 17 oz

Cost of 1 pound of trail mix = $4.50

Total amount of trail mix in oz:

15+14+10+17

56 oz

We know that 1 ounce = 0.0625 pounds

So, we have the following expression:

56 oz = 56*0.0625 pounds

56 oz = 3.5 pounds

Now, the cost of trail mix:

3.5*4.50

$15.75

Hence, Mr. Arnett will have to pay $15.75 for the trail mix if it cost $4.50 per pound.

The complete question is here:

At the grocery store, Mr. Arnett allowed each of his children to fill their own bag with trail mix for their hike. The table shows the amount of trail mix for each child.

Child-amount of trail mix in oz

Ava-15

Grayson-14

Mason-10

Tyler-17

The trail mix costs $4.50 per pound. How much will Mr. Arnett pay for all the trail mix?

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The value of x in the similar triangles is 11.4.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

Therefore,

ΔACB ~ ΔEFD

Hence,

AC / EF = CB / FD = AB / ED

Therefore, let's find x

x = AB

ED = 3.8

BC = 15

FD = 5

x / 3.8 = 15 / 5

cross multiply

5x = 15 × 3.8

5x = 57

divide both sides of the equation by 5

x = 57 / 5

x = 11.4

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Using Hypothesis testing,

a) Two samples are independent.

b)H₀: an expectant mother's cigarette smoking has any not effect on the bone mineral content of her otherwise healthy child.

Hₐ : an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

c) Null hypothesis is accepted.

so, an expectant mother's cigarette smoking has no effect on the bone mineral.

We have given that,

A study which is conducted for check an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

For new-born whose mother's cigarette smoking

sample size , n₁= 77

X-bar, x₁-bar = 0.098 g/cm

standard deviations, s₁ = 0.026 g/cm

For new-born whose mother did not cigarette smoking

sample size , n₂ = 161

standard deviations, s₂ = 0.025 g/cm.

mean (X-bar) , x₂-bar = 0.095 g/cm

a) the two samples are independent since they are different types of mothers, smoking mothers and non smoking mothers

b)H₀: an expectant mother's cigarette smoking has any not effect on the bone mineral content of her otherwise healthy child.

Hₐ: an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

c) Test statistic:

t = (x₁-bar - x₂-bar )/S (√1/n₁+1/n₂)

where , S = √(s₁²(n₁ - 1) + s₂²(n₂ -1))/n₁+n₂ - 2

S = √((0.026)²(76) +(0.025 )²(160))/236

= 0.0253

then, t = (0.098 - 0.095 )/0.0253(√1/77 +1/161 )

=> t = 0.859

Using the critacal table critical t is

Critical t = ±1.970065

Degrees of freedom =236.0000

P-Value=0.3935 which is greater than α(0.05),

So , we accept H₀

Thus, an expectant mother's cigarette smoking has not effect on the bone mineral content of her otherwise healthy child.

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Half life of the radioactive substance is 3.6  days

The half life of the element is calculated from the formula

N(t) = N'(1/2)^(t/t')

N(t) = quantity of the substance remaining

N' = initial quantity of the substance

t = time elapsed

t' = half life of the substance

0.4 = 4.8 (0.5)^13/t'

0.4 / 4.8 =  (0.5)^13/t'

take natural logarithm of both sides

㏑(0.4/4.8) = 13/t' ㏑(0.5)

divide through by natural log of 0.5

-2.4849 / ㏑(0.5) = 13/t'

13/t' = 3.58496

t' = 13 / 3.58496

t' = 3.626 days

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The length of the major arc is (203/18)π.

What is a length of an arc?

The distance along the curved line that makes up the arc is measured using the arc length formula (a segment of a circle). The arc length is, to put it simply, the distance that passes through the curved line of the circle that forms the arc.

Here, we have

The circle with center K has an arc with a radius of 7 inches and an angle subtended at the center which measures 70 degrees.

The major arc LNM would have its central angle measured as:

Angle ∅ = 360 - 70 (Sum of angles on a point equals 360)

Angle ∅ = 290

The calculation for the length of an arc is given as;

Length of arc = (∅/360) x 2πr

Where ∅ = 290, and r = 7, the length of the major arc becomes;

Length of arc = (290/360) x 2 x π x 7

Length of arc = (29/36) x 14π

Length of arc = (29 x π x 14)/36

Length of arc = 203π/18

Hence, the length of the major arc is (203/18)π.

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Answer:

y=2x-5

Step-by-step explanation:

1 u must calculate the slop then the amount of b

by -3=1×2-b

-5=b

so after we find the number if y we will make an equation y=2x-5

The four types of agile are:
Scrum, Kanban,
Extreme Programming (XP),
Lean Development, and Cryst.

What is the Agile cycle?

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The systematic succession of phases that a product goes through as it develops from start to finish is known as the agile software development life cycle. Concept, conception, iteration, release, maintenance, and retirement are its six phases.

The project management approach a team decides on will have a small impact on the Agile life cycle. For instance, Scrum teams work in sprints, which are brief timeframes akin to iterations. They also have responsibilities that are precisely defined, like Scrum master. Kanban teams, on the other hand, operate more continuously and don't have set roles. Another illustration is Extreme Programming, where teams frequently work in shorter iterations and give engineering practices more attention.

Hence,

The four types of agile are:

Scrum, Kanban,

Extreme Programming (XP),

Lean Development, and Cryst.

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The average time a customer spend on department store is 1.33 hours.

Average:

In math, mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set is referred as average.

Given,

If there are on average 80 customers at any particular time and 60 customers go through the checkouts every hour

Here we need to find the average time spend by a customer.

Let us consider x be the time spend by the customer on department store.

While we looking into the given question we know that,

Number of customer = 80

Check out per hour = 60.

So, the average time is 1.33 hours.

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The rate of change of the area of the right triangle at that instant is -1.5 sq km/h.

Let ABC be a right triangle, right-angled at B.

the side decreasing be, BC = x

and the increasing side be, AB = y

then, AC = z = √(x² + y²) (using Pythagoras theorem)

It is given that, dx/dt = - 5km/h and dy/dt = 14 km/h

x = 3, y= 9 at certain instant

now, the area of the triangle = 1/2 xy

A = 1/2 xy

dA/dt = 1/2 (y).dx/dt + x/2.dy/dt

at x = 3, y = 9, substituting the values,

(dA/dt) = 1/2 (9)(-5) + 3/2 (14)

= -1.5

therefore, the rate of change of the area of the right triangle at the instant when x=3 and y= 9 is -1.5 sq km/h.

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Answer: If it is one of your choices it should be angle angle side(aas)

The average value of the function f(t) is [tex]4.433*10^{10}[/tex] .

Given,

[tex]f(t)=te^{3t^2}[/tex] over interval [1,3]

To find average value of the function use formula,

[tex]f(x)_{avg} =\frac{1}{b-a}\int\limits^a_b {f(x)} \, dx[/tex] over the interval {a,b}

[tex]f(x)_{avg} =\frac{1}{3-1}\int\limits^3_1 {te^{3t^2}} \, dt\\\\\\f(x)_{avg} =\frac{1}{2}\int\limits^3_1 {te^{3t^2}} \, dt\\[/tex]

let

[tex]u=3t^2\\\\du=6tdt \\\\tdt=\frac{du}{6}[/tex]

replacing u and du ,

[tex]f(x)_{avg} =\frac{1}{2*6}\int\limits^3_1 {e^{u}} \, du\\\\f(x)_{avg} =\frac{1}{12}\ e^u\|\limits^3_1\\ \\f(x)_{avg} =\frac{1}{12}\ e^{3x^2}\|\limits^3_1\\\\f(x)_{avg} =\frac{1}{12}\ [e^{3(3)^2}-e^{3(1)^2}]\\\\f(x)_{avg} =\frac{1}{12}\ [e^{27}-e^{3}]\\\\f(x)_{avg}=4.433*10^{10}[/tex]

Thus, the average value of the function f(t) is [tex]4.433*10^{10}[/tex] .

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The probability the couple will have at least two boys is 0.26.

This type of probability is independent probability. Independent probability can only occur if the events are independent or not dependent on previous event and also this event doesn't affect the next event.

For probability the couple will have at least two boys is equal to probability they have two boys plus probability they have three boys. Mathematically is,

P(x≥2) = P(x=2) + P(x=3)

P(x≥2) = 0.127 + 0.133

P(x≥2) = 0.26 or 26%

Thus, the couple will have at least two boys has a probability of 0.26 or 26%

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Answer: experiment

Step-by-step explanation:

A course of perception that has an unsure result is alluded to as an experiment.

The study of mathematical objects by computing in order to discover their properties and patterns is known as experimental mathematics. It has been described as "that mathematical theory that concerns itself ultimately with both the convention and transmission of insights within the mathematical neighborhood through the use of experimental investigation of conjectures and also more irregular beliefs and just a careful analysis of the information acquired in this endeavor (in either the Galilean, Baconian, Aristotelian or Kantian sense).

The nineteenth century saw the reemergence of experimental mathematical concepts as a distinct field of study as the range of calculations that could be performed was greatly expanded by the development of the electronic computer, which could perform calculations at speeds and with levels of precision that were unimaginable to earlier generations of mathematicians.

A course of perception that has an unsure result is alluded to as an experiment.

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