For each of the following relations, i) state whether the relation is an equivalence relation and ii) if it is an equivalence relation, list the blocks of its corresponding partition, and if it is not, list all of the properties (reflexive, symmetric, transitive) it violates. In all cases, the relations are on the set A = {1, 2, 3, 4}
a. {(1, 1), (1,4), (2, 2), (3, 3), (4, 1), (4, 4)}
b. A x A
c. {(1, 1), (2, 2), (3, 1), (1, 3), (4, 4)
d. ({2, 3} x A) U ((1, 1), (4, 4)}

Answer:

Minimum--> 250

Q1--> 255

Q2--> (Median): 307

Q3--> 433

Maximum-->507

Step-by-step explanation:

To find the five-number summary of this data set, we need to determine the minimum value, maximum value, and three quartiles (Q1, Q2, Q3) which divide the data into four equal parts.

First, we need to sort the data set in ascending order:

{ 250, 253, 255, 267, 307, 425, 433, 435, 507 }

Minimum: 250

Maximum: 507

To find the quartiles, we need to find the median of the entire data set (Q2) and then the medians of the two halves of the data set, which will give us Q1 and Q3.

Q2 (Median): The median of the entire data set can be found by averaging the two middle numbers.

Q1: The median of the lower half of the data set is 255, which is the middle value of { 250, 253, 255, 267, 307 }. Therefore, Q1 = 255.

Q3: The median of the upper half of the data set is 433, which is the middle value of { 425, 433, 435, 507 }. Therefore, Q3 = 433.

Here no figure just go through the definition.

A polygon is a two-dimensional geometric shape that is defined as a closed figure with straight sides. It is made up of line segments that connect at endpoints called vertices. The term polygon comes from the Greek words "poly" meaning many and "gonia" meaning angle, indicating that polygons have many angles.

Polygons can have different numbers of sides, with the most basic being a triangle, which has three sides and three angles. Other examples of polygons include squares, rectangles, pentagons, hexagons, and octagons. The sides of a polygon do not have to be equal in length or the angles between them do not have to be the same, but they must be straight lines and the polygon must be closed.

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After responding to the prompt, we can deduce that in order to circle and finish the copied triangle, a polygon should be drawn through the coordinates D, E, and F.

The definition of a polygon, a two-dimensional geometric form, is a closed figure with straight sides. It consists of line segments joined at ends known as vertices. The word "polygon," which means "many angles," is derived from the Greek terms "poly," which means "many," and "gonia," which means "angle."

A triangle is the most basic polygon because it has three edges and three angles. Polygons can have various amounts of sides. Squares, rectangles, pentagons, hexagons, and octagons are additional instances of polygons. In order for a polygon to be considered closed, all of its sides must be straight lines, regardless of whether their lengths or angles are equivalent.

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By set theοry the number οf students whο οffer οnly English is 12.

In mathematics Set theοry  studies with sets, which can be infοrmally described as cοllectiοns οf οbjects.  Objects οf any kind can be cοllected intο a set, set theοry, as a branch οf mathematics, is mοstly cοncerned with  that which are relevant tο mathematics as a whοle.

Given that,

A survey οf eighty students at a certain cοllege reveals that

36 takes English

32 take histοry

32 take pοlitical science

16 takes pοlitical science and histοry

16 takes histοry and English

14 takes pοlitical science and English

6 takes all three

Sο n(s)=80 [ Since the number οf students is 80]

The number οf students whο takes English is denοted by n(E)=36

The number οf students whο takes Histοry is denοted by n(H)=32

The number οf students whο takes Pοlitical Science is denοted by n(P)=32

By set theοry

The number οf students whο takes Pοlitical Science and Histοry is denοted by n(P∩H)=16

The number οf students whο takes English and Histοry is denοted by n(E∩H)=16

The number οf students whο takes Pοlitical Science and English is denοted by n(P∩E)=14

The number οf students whο takes Pοlitical Science, English and Histοry is denοted by n(P∩E∩H)=6

Frοm set theοry ,

n(P∪E∪H) = n(E)+n(H)+n(P)- n(P∩H)-n(H∩E)-n(P∩E)+n(P∩E∩H)

                 = 36+32+32-16-16-14+6

                 = 60

Sο the number οf students whο take nοne οf the subjects is (80-60)=20

Hence the number οf students whο οffer οnly English is 12.

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14. The length of AB for the given right-angled triangle is [tex]$24{\sqrt{2}}$[/tex].

15. The value of base GF is √247 or 15.716234

The ideas of angles, right triangles, and the trigonometric functions of sine, cosine, and tangent are used in trigonometry to calculate heights and distances.

It is possible to determine the height of an object or the distance between two objects by measuring the angle of elevation or depression between the observer's line of sight and the object being observed and the distance between them. These ideas are frequently applied in the engineering, navigation, and surveying industries.

14. In a right-angled triangle, if one angle is 45 degrees, then the other acute angle is also 45 degrees and hence,

Let AB = x

Using the trigonometric ratio for the 45 degree angle in the triangle:

tan(45) = opposite/adjacent

We know that the opposite side is BC = [tex]$24{\sqrt{2}}$[/tex] and the adjacent side is AB = x.

tan(45) = BC/AB

1 = [tex]$24{\sqrt{2}}/x$[/tex]

x = [tex]$24{\sqrt{2}}$[/tex]

15. Using Pythagoras theorem:

HF² = HG² + GF²

16² = 3² + GF²

GF² = 16² - 3²

GF² = 256 − 9

GF² = 247

GF = √247

GF = 15.716234

Thus, The value of base GF is √247 or 15.716234

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The surface area of the rectangular prism is 72 square meters.

A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional figure that consists of six rectangular faces. It is a polyhedron with two identical and parallel bases, which are rectangles, and four rectangular lateral faces. The height of the prism is the perpendicular distance between the two bases. The volume of a rectangular prism is given by the formula V = l × w × h, where l, w, and h are the length, width, and height of the prism, respectively. The surface area of a rectangular prism is given by the formula SA = 2lw + 2lh + 2wh, where l, w, and h have the same meanings as in the volume formula. Rectangular prisms are commonly encountered in everyday life, such as in the shape of boxes, rooms, and buildings.

The surface area of a rectangular prism can be found by adding up the area of all its faces.

Area of blue rectangles:

= 2 x (length x width)

= 2 x (2.4m x 2m)

= 9.6m²

Area of green rectangles:

= 2 x (length x width)

= 2 x (2.4m x 3m)

= 14.4m²

Area of yellow rectangles:

= 2 x (length x width)

= 2 x (2m x 3m)

= 12m²

Total surface area = sum of all face areas

= (2 x blue rectangles) + (2 x green rectangles) + (2 x yellow rectangles)

= 2(9.6m²) + 2(14.4m²) + 2(12m²)

= 19.2m² + 28.8m² + 24m²

= 72m²

Therefore, the surface area of the rectangular prism is 72 square meters.

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Answer:

25%

Step-by-step explanation:

If the cost price could be 100

Then there's A/Q

One-fourth is always 100/4 = 25%

Answer:

a machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At what rate in pounds

per hour does the machine makes nails?

Answer:

Step-by-step explanation:

[tex]\mathrm{2\left(x+3\right)=18}[/tex]

Divide both sides by 2:-

[tex]\mathrm{\cfrac{2\left(x+3\right)}{2}=\cfrac{18}{2}}[/tex]

Simplify:-

[tex]\mathrm{x+3=\cfrac{18}{2} }[/tex]

[tex]\mathrm{x+3=9}[/tex]

Subtract 3 from both sides:-

[tex]\mathrm{x+3-3=9-3}[/tex]

[tex]\mathrm{x=6}[/tex]

_____________________

Hope this helps!

Answer:

false

Step-by-step explanation:

if there r more men working then it will take less time to finish the same work not more

After answering the presented question, we can conclude that As an expression result, there are 24 4-letter code symbols that may be constructed without duplication using the letters P, D, Q, and X.

what is expression ?

An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

We may use the method for permutations of n items taken r at a time to compute the number of 4-letter code symbols that can be created with the letters P, D, Q, X without repetition:

n! / (n-r)! P(n,r) = n!

where n denotes the number of items (in this example, four letters) and r the number of things taken at once (in this case, 4).

Thus far, we have:

P(4,4) = 4! / (4-4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24

Hence, As a result, there are 24 4-letter code symbols that may be constructed without duplication using the letters P, D, Q, and X.

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Complete question:

How many 4-letter code symbols can be formed with the letters P, D, Q, and X without repetition?

Answer: 1.0

Step-by-step explanation:

sohcahtoa means you use sine.

sin(37) = 0.6/x

xsin(37) = 0.6

x = 0.6/sin(37)

x = 0.996

x = 1.0

A standard normal distribution table or a calculator again, we can find that the z-score that corresponds to this area is approximately 0.42.

The standard normal distribution is useful because it allows us to calculate probabilities for any normal distribution by converting the distribution to a standard normal distribution using a process called standardization. Standardization involves subtracting the mean of the distribution from each observation and then dividing by the standard deviation. The resulting values are called z-scores, and they represent the number of standard deviations that an observation is from the mean of the distribution.

Assuming a standard normal distribution, we know that 0.5 of the area lies between -z and z, since the normal distribution is symmetric around the mean. Therefore, we need to find the value of z such that the area between -z and z is 0.6318 - 0.5 = 0.1318.

Using a standard normal distribution table or a calculator, we can find that the area between the mean and z is 0.5 + 0.1318/2 = 0.5659. Therefore, the z-score that corresponds to this area is approximately 0.18.

Since the distribution is symmetric, the area between -z and z is twice the area between the mean and z, so we can solve for z:

0.1318/2 = 0.0659 of the area lies between the mean and z

Using a standard normal distribution table or a calculator again, we can find that the z-score that corresponds to this area is approximately 0.42.

Therefore, z = 0.42 rounded to two decimal places.

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Answer: 36 m^2

Step-by-step explanation: I got it correct trust btw can i get brsainliest

The cost per boxed lunch is $9.46.

Answer:

$40+99=136  For 1 week

For 3 weeks it would be $120

To solve this problem, we can use similar triangles. Let's call the height of the building "h". Then, we have two similar triangles: one formed by Ruby, the tree, and the top of the tree; and the other formed by Ruby, the building, and the top of the building.

We know that the height of the tree is 20 feet, and the distance from the tree to Ruby is 31 feet. We also know that the distance from Ruby to the building is 190 feet.

Using these values, we can set up a proportion:

h / (190 + 31) = 20 / 31

Simplifying the proportion, we get:

h / 221 = 20 / 31

Multiplying both sides by 221, we get:

h = (20 / 31) * 221

h ≈ 143.23

Therefore, the height of the building is approximately 143 feet. Rounded to the nearest foot, the height of the building is 143 feet.

The quadratic regression function f(x) = -0.1536x² + 3.3915x + 88.738, then estimate value for the number of people in the park when there are 80 birds is equals to the 24.

A quadratic regression is the process of finding the equation of the parabola that best fits a set of data. An equation of the form, y = ax² + bx + c where a≠0. We have a quadratic regression function is defined by f(x) = -0.1536x² + 3.3915x +88.738 --(1), where, f(x) = the number of birds in a park relative to the number of people x in the same park. We have to determine quadratic regression to estimate the number of people in the park when there are 80 birds. Now, f(x) = 80, substitute the known value in equation (1),

=> 80 = -0.1536x² + 3.3915x +88.738

=>0.1536x²- 3.3915x -88.738 + 80 = 0

=> 0.1536x²- 3.3915x - 8.738 = 0

=> x² - 22.08x - 56.88 = 0 --(2)

Using the quadratic formula for solution of (2), x = (-b ±√b² - 4ac)/2a, for ax² + bx + c = 0. So, [tex]x =\frac{ -(-22.08) ± \sqrt{(22.08)² + 4× 56.88}}{2}[/tex]

=> x = 24.41 or - 2.3331

but number of people can't be negative hence, the required value is 24.41 ~ 24.

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Answer: Formula

Step-by-step explanation:

Stocks x per share = return

Trey's return on investment, if the stock paid no dividends during the year, is 14.29%.

We have,

Purchase price per share: $50

Number of shares purchased: 200

Total purchase cost (excluding loan interest):

Purchase price per share * Number of shares purchased

= $50 * 200

= $10,000

Loan amount: $5,000

Loan interest rate: 10%

Interest paid on the loan:

Loan amount * Interest rate

= $5,000 * 10%

= $500

Total purchase cost (including loan interest):

Total purchase cost + Loan interest

= $10,000 + $500

= $10,500

Selling price per share: $60

Total revenue from selling the stock:

Selling price per share * Number of shares sold

= $60 * 200

= $12,000

Return on investment (ROI):

(Total revenue - Total purchase cost) / Total purchase cost

ROI = ($12,000 - $10,500) / $10,500

Simplifying the expression:

ROI = $1,500 / $10,500

ROI = 0.1429 (approximately)

To express the ROI as a percentage:

ROI as a percentage = 0.1429 * 100 = 14.29%

Therefore,

Trey's return on investment, if the stock paid no dividends during the year, is 14.29%.

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The complete question:

Trey purchases 200 shares of Turner stock for $50 per share.

Trey pays $5,000 in cash and borrows $5,000 from his broker at 10 percent interest to complete the purchase.

One year later, Trey sells the stock for $60 per share.

Trey's return, if the stock paid no dividends during the year, is?

This means that the lowest goal (LCD) is 72 and that the total of 1/8 and 1/9 stated with one common denominator = 72 is 17/72.

The denominator of a fraction, which represents many spaced evenly out parts are utilized to split an object, is the smallest amount inside the fraction. The fraction is divided by it. The denominator in this situation is 4, suggesting there are four parts altogether.

The fractions mentioned have 8 and 9 as their denominators. Multiples of 8 include 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80, while multiples of 9 include 9, 18, 27, 36, 45, 54, 63, 72, and 81.

It is evident that 72 will be the first common number of 8 and 9. Hence, for 1/8 and 1/9, its least common factor (LCD) is 72.

We must express every fraction with denominator 72 in order to sum the fraction with a common denominator:

1/8 Equals 9/72 (with multiplying both the numerator and the denominator by 9)

1/9 Equals 8/72 (with multiplying both the denominator and the numerator by 8)

We can now combine the fractions:

1/8 plus 1/9 = 9/72 plus 8/72

= 17/72

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Answer:

152 in²

Step-by-step explanation:

Area of rectangle = L x W

1st rectangle area

10 x 8 = 80 in²

2nd rectangle area

Length = 20 - 8 = 12 in

12 x 6 = 72 in²

Total area

80 + 72 = 152 sq. in

So, the answer is 152 in²

The fraction shows that can d holds 1/2 of the amount can c holds.

Can c holds 1/5 of the amount can a holds.

Can d holds 1/6 of the amount can b holds.

Can b holds 1/5 of the amount can a holds.

Can d holds 1/2 of the amount can c holds. This is because can d holds 3 litres and can c holds 6 litres, so if you divide the volume of can d (3 litres) by the volume of can c (6 litres), you get 3/6 or 1/2.

Can c holds 1/5 of the amount can a holds. Can c holds 6 litres and can a holds 30 litres, so if you divide the volume of can c (6 litres) by the volume of can a (30 litres), you get 6/30 or 1/5.

Can d holds 1/6 of the amount can b holds: This is because can d holds 3 litres and can b holds 18 litres, so if you divide the volume of can d (3 litres) by the volume of can b (18 litres), you get 3/18 or 1/6.

Can b holds 1/5 of the amount can a holds: This is because can b holds 18 litres and can a holds 30 litres, so if you divide the volume of can b (18 litres) by the volume of can a (30 litres), you get 18/30 which can be simplified as 3/5 or 1/5.

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Answer: 3.53

Step-by-step

Answer:

gradient= rise \ run

and cuz line is coming downward

it will be negative

so your answer is

- 5\6

The values of A, B, and C are 30, 50, and 20, respectively.

What is the sum?

The sum is the result of adding two or more numbers together. The sum is found by performing the operation of addition, which involves combining the values of two or more quantities to find the total or the sum.

If A = 80 - B and C = 70 - B, and the sum of A, B, and C is 100, then we can write:

A + B + C = 100

Substituting A and C with their given values, we get:

(80 - B) + B + (70 - B) = 100

Simplifying and combining like terms, we get:

150 - B = 100

Subtracting 150 from both sides, we get:

-B = -50

Dividing both sides by -1, we get:

B = 50

Now that we know B = 50, we can substitute this value back into the equations for A and C:

A = 80 - B = 80 - 50 = 30

C = 70 - B = 70 - 50 = 20

Therefore, the values of A, B, and C are 30, 50, and 20, respectively.

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The parameter to describes a binomial experiment that would determine the probability that a case of 36 bottles has all bottles properly filled is x = 36, p = 0.96 and n = 36. So, the right choice for answer is option (c).

A binomial experiment is an experiment using a fixed number of independent trials with only two outcomes. These experiments'outcomes are defined as either success or failure. The following requirements for experiment are :

Water Quantity in a bottle = 20 ounces

According to bottling company, the percentage of bottle with correct amount = 96% = 0.96

so, probability of success, p = 0.96

Probability for 36 bottles has all bottles properly filled, that is x = 36. Now, looking the all choice, we conclude option(c) is correct choice.

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Answer:

13487 ft³

Step-by-step explanation:

Volume of a Cylinder: 2πr²*h

π = 3.14

r = 9 ft

h = 53 ft

Volume = 2(3.14)(9)²*53 = 13486.86 ft³

Rounded to nearest whole number

Volume of the Cylindrical Water tank is 13487 ft³

The substitutions that would be most helpful in evaluating the integral are:

1. C (x = 8 secθ)

2. B (x = 8 sinθ)

3. A (x = 8 tanθ)

4. B (x = 8 sinθ)

5. A (x = 8 tanθ)

For problem 1, the substitution x = 8 secθ will be useful because it will transform the integral into a form that can be solved using the substitution u = tanθ.

For problem 2, the substitution x = 8 sinθ will be useful because it will transform the expression inside the integral into a trigonometric function that can be integrated using standard techniques.

For problem 3, the substitution x = 8 tanθ will be useful because it will transform the expression inside the integral into a form that can be solved using integration by parts.

For problem 4, the substitution x = 8 sinθ will be useful because it will transform the expression inside the integral into a form that can be solved using the substitution u = cosθ.

For problem 5, the substitution x = 8 tanθ will be useful because it will transform the expression inside the integral into a form that can be solved using the substitution u = secθ.

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Answer:

52 inches

Step-by-step explanation:

1 foot=12 inches

4(12)=48 inches

Then you add the other 4 inches.

48+4=52

52 inches