Let A = {z, b, c, d, e} and Ry = {(z, z), (6,5), (z,b), (6,2), (2,c), (d, d), (e, e)} a relation on A. a) Find a symmetric relation R, on A which contains all pairs of R, and such that RX + A A b) Find an equivalence relation Rg on A which contains all pairs of R, and such that Rg

The cost of a pair is D) $15 for shorts.

To solve this problem, we need to set up a system of equations based on the information given for both Stephanie and Ashley's purchases. Let T be the cost of a t-shirt and S be the cost of a pair of shorts.

For Stephanie's purchases, we have:

\(2T + 3S = 105\)

For Ashley's purchases, we have:

\(3T + 2S = 95\)

Using matrices, we can solve this system of equations by setting up the augmented matrix and using row operations:

[2 3 | 105]

[3 2 | 95]

After row operations, we get:

[1 0 | 15]

[0 1 | 25]

Therefore, the cost of a pair of shorts is $15.

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Answer:

c.) 27 x - 4

Step-by-step explanation:

We have the expression:

8 - 3(4 - 9x)

We open the brackets

8 - 12 + 27x

= -4 + 27x

This can also be written as:

= 27x - 4

Option C is the correct Option

Answer:

Number of 50sen coins  =  13

Step-by-step explanation:

Let the number of 50sen coins be = x

Let the number of 20sen coins be  = y

Total coins  = 20

x + y = 20 ----------------------(i)

Value of 50sen coins = 0.50*x = 0.50x

Value of 20sen coins = 0.20 *y = 0.20y

Total value = RM 6.10

0.5x + 0.2y = 6.10 -------------------(ii)

Multiply (i) by (-0.5) and then add the equations. So, x will be eliminated and we can find the value of y

(i) * (-0.5)      -0.5x - 0.5y = -10

(ii)                  0.5x  + 0.2y = 6.10 { add and now x will be eliminated}

                              - 0.3y = -3.90

Divide both sides by (-0.3)

y = -3.90/-0.3

y = 13

Plug in the value of y in equation (i)

x + 13 = 20

Subtract 13 from both sides

x = 20 -13

x = 7

Number of 50sen coins  =  13

Answer:

the number of 50sen coins:

x = 7

Step-by-step explanation:

Taking the number of 50sen coins as x

50(x)

∴ the number of 20sen coins is 20-x (as total no. of coins are 20)

20(20-x)

total amount = 6.10RM = 610sen

equating:

50x + 20(20-x) = 610

50x + 400-20x = 610

50x - 20x = 610-400

30x = 210

x = 210/30 = 7

Therefore, the number of 50sen coins is 7

20sen coins is 20-7= 13.

verification=

50*7 + 20*13 = 610

310 + 260 = 610

610sen = 610sen

6.10RM = 6.10RM

L.H.S = R.H.S

hence, verified.

We have the following response after answering the given question: As a equation result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.

In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.

Which nation experienced the hottest summer?

We may examine the average temperature for each nation throughout the observed weekends to determine which nation experienced the hottest summer.

Country A: (21.4°C) (18+20+22+23+24)/5

(24+26+28+29+27)/5 = 26.8°C for Country B.

The summer was therefore hotter in Country B, with an average temperature of 26.8°C.

b) Over the summer, which nation saw more erratic weather?

We may examine the temperature ranges recorded for each nation to determine which experienced more erratic weather during the summer.

24°C - 18°C equals 6°C in Country A.

29°C - 24°C equals 5°C in country B.

As a result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.

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Answer: can you put it in diffrent form beucase the way you have it is really confusing me thanks

Step-by-step explanation:

The matrix of the relation r={(1,2),(2,3),(3,4),(4,5)} on the set x={1, 2, 3, 4, 5}; ordering of x:1,2,3,4,5 is as follows.

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

A relation is a set of ordered pairs.

The matrix of a relation is constructed by using its ordered pairs with their respective values as its entries, and its rows and columns by its domain and range, respectively.

So, the relation r is given as{(1,2),(2,3),(3,4),(4,5)}

The elements in the rows of the matrix correspond to the elements of x, while the elements in the columns of the matrix correspond to the elements of x as well, in that order.

So, the matrix of r on x can be written as:

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

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Given the diagram below

Introducing 'a', as shown above, it can be observed that

It can also be observed that

It can also be observed that

Substitute for y to get z

Hence, the value of y is 34°, while z is 119°.

Y = (1/6)*e^5t  is  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.  

                                     Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

y′′−9y′+26y=e^(5t)

The characteristice equation of the differential equation is : r^2 -9r +26 =0

On solving we get the values of r=4.5 + 2.34i (z1) ,  4.5 - 2.4i(z2)--- (complex roots)

homogeneous solution is: yh = c1e^z1t + c2e^z2t

Plug  Y = Ae^5t in the ODE:

=   25Ae^5t -9*5Ae^5t +26Ae^5t =e^(5t)

25A -45A +26A =1 ;  6A = 1; A =1/6

Y = c1e^z1t + c2e^z2t  is a general solution but we wnata particular solution

So, simply Y = (1/6)*e^5t

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The 30-60-90 triangle is a special type of right triangle, where the three angles measure 30°, 60°, and 90°.

The hypotenuse of the triangle is always twice the length of the shortest side, or the side opposite the 30° angle. The longest side of the triangle, or the side opposite the 90° angle, is always equal to the sum of the other two sides.

The angle opposite of the hypotenuse is the 90° angle. To calculate this we can use the Pythagorean Theorem and the ratios of sides in a 30-60-90 triangle to solve for the length of the side opposite the 90° angle.

The Pythagorean Theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, for a 30-60-90 triangle, we have the equation: a2 + b2 = c2

Since the hypotenuse is c, the side opposite the 90° angle is a, and the side opposite the 30° angle is b, we can rearrange the equation to solve for a:

a = √(c2 - b2)

Since the hypotenuse is twice the length

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The slash indicates a fraction.

=============================================

Proof:

We'll need to consider 4 different cases.

-----------------------

Case (1): j > 0 and k > 0

If j > 0, then 3j > 0 and 3/j > 0

If k > 0, then 3k > 0 and 3/k > 0

The two points (3j, 3k) and (3/j, 3/k) are both in quadrant 1.

-----------------------

Case (2): j > 0 and k < 0

If j > 0, then 3j > 0 and 3/j > 0

If k < 0, then 3k < 0 and 3/k < 0

Points (3j, 3k) and (3/j, 3/k) are both in quadrant 4.

------------------------

Case (3): j < 0 and k > 0

If j < 0, then 3j < 0 and 3/j < 0

If k > 0, then 3k > 0 and 3/k > 0

Points (3j, 3k) and (3/j, 3/k) are in quadrant 3.

------------------------

Case (4): j < 0 and k < 0

If j < 0, then 3j < 0 and 3/j < 0

If k < 0, then 3k < 0 and 3/k < 0

Points (3j, 3k) and (3/j, 3/k) are in quadrant 4.

------------------------

For nonzero integers j and k, we've shown that Points (3j, 3k) and (3/j, 3/k) are in the same quadrant. This concludes the proof.

Answer:

D

Step-by-step explanation:

Answer:

make me brainliest plsssssssss

Step-by-step explanation:

A

Answer: 31.4 mins (2dp).

Step-by-step explanation: To find the volume of the tank.

πr² × h

π2² × 3

= 37.7m³

To find how long it will take to fill the tank:

37.7 ÷ 1.2 = 31.4 minutes (2dp)

The s-orbital is spherical in shape, while the p-orbitals are composed of two lobes that are directed at an angle of 120 degrees apart.

It is composed of three atomic orbitals: one s-orbital and two p-orbitals. The s-orbital is spherical in shape, while the p-orbitals are composed of two lobes that are directed at an angle of 120 degrees apart. The combination of these three orbitals forms a hybrid orbital that is shaped like a flat trigonal planar, with a bond angle of 120 degrees. This hybrid orbital is known as the sp2 hybrid orbital.

The "s" in sp2 stands for the s-orbital, which is a single, spherical orbital. The "p" represents the two p-orbitals, which have two lobes and form an angle of 120 degrees with each other. The "2" in sp2 indicates that two p-orbitals are involved in the hybridization process. The hybridization of the s and two p-orbitals creates the sp2 hybrid orbital, which is trigonal planar in shape.

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The given formula, aₙ = -3aₙ₋₁, where a₁ = -2, is a recursive formula. The first five terms of the sequence are -2, 6, -18, 54, and -162.

In a recursive formula, each term of the sequence is defined in terms of previous terms. In this case, the value of each term aₙ is determined by multiplying the previous term aₙ₋₁ by -3.

To find the first five terms of the sequence, we can use the recursive formula:

a₁ = -2

a₂ = -3a₁ = -3(-2) = 6

a₃ = -3a₂ = -3(6) = -18

a₄ = -3a₃ = -3(-18) = 54

a₅ = -3a₄ = -3(54) = -162

Therefore, the first five terms of the sequence are -2, 6, -18, 54, and -162.

The recursive formula allows us to generate subsequent terms of the sequence by applying the given rule to the previous term. It provides a relationship between terms in a sequential manner.

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Step-by-step explanation:

g(2)=((2)²-2-12)/((2)²-4(2)+4)

=4-2-12/4-8+4

=-10/0=undefined

Answer:

x = 4, 10a

Step-by-step explanation:

3(x-2) + 2(2x+5) = 32

3x - 6 + 4x + 10 = 32

3x + 4x + 10 - 6 = 32

7x + 4 = 32

7x = 32 - 4

7x = 28

Divide both side by 7

x = 4

a + 2a + 7a

They are common because the have the same variables.

'a' is with a coefficient of 1

You add the coefficient and attach the variable to it

Therefore,

a + 2a + 7a = 10a

Answer:

the answer to this question is $32.96

Answer:

equal

Step-by-step explanation:

congruent by SAS side angle side

Answer:

Those are quadrilaterals

Answer: Square Rhombus

Step-by-step explanation:

Answer:y ≥ 15 − 5x

Step-by-step explanation:

Answer:

21 divded by 28= decimal form

Step-by-step explanation:

Your welcome :)

Answer:

x can equal either 0 or 1

Step-by-step explanation:

If we look at the chart, we see that the values of 3^x = 2x+1

when x is 0 and when x is 1

so f(x) = g(x) when x = 0 or 1

sin O = 1/2 = p/h

p=1, h = 2.

by pythagoras tgeorem,

b =

\( \sqrt{3} \)

tan0= p/b

\(1 \div \sqrt{3} \)

Answer:

A. Major Axis

Step-by-step explanation:

Red line shows the Major axis of the ellipse drawn.

A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane.

An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

An ellipse uses two axis, major and minor.

Major axis is the larger one and minor axis is smaller.

The minor axis of an ellipse is the line that contains the shorter of the two line segments about which the ellipse is symmetrical

Now we come to the question.

Here extreme points of the red line are on the ellipse are more distant than the extreme points of the axis perpendicular to the red line.

Therefore, red line shows the Major axis of the ellipse drawn.

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The average rate of change of the function f(x)=x^3 - 9x + 8 over the interval from -6 to -4 is (a) -8. The average rate of change from -1 to 5 is (b) -2. The average rate of change from 5 to 7 is (c) 34.

To find the average rate of change, we need to calculate the difference in the function values at the endpoints of each interval and divide it by the difference in the x-values.

(a) From -6 to -4:

\(f(-6) = (-6)^3 - 9(-6) + 8 = -144 + 54 + 8 = -82 \\f(-4) = (-4)^3 - 9(-4) + 8 = -64 + 36 + 8 = -20\)

The average rate of change is (-20 - (-82))/(-4 - (-6)) = -8.

(b) From -1 to 5:

\(f(-1) = (-1)^3 - 9(-1) + 8 = -1 + 9 + 8 = 16\\f(5) = (5)^3 - 9(5) + 8 = 125 - 45 + 8 = 88\)

The average rate of change is (88 - 16)/(5 - (-1)) = -2.

(c) From 5 to 7:

\(f(5) = (5)^3 - 9(5) + 8 = 125 - 45 + 8 = 88\\f(7) = (7)^3 - 9(7) + 8 = 343 - 63 + 8 = 288\)

The average rate of change is (288 - 88)/(7 - 5) = 34.

Therefore, the average rate of change from -6 to -4 is -8, from -1 to 5 is -2, and from 5 to 7 is 34.

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Answer:

A

Step-by-step explanation:

I just used Pythagorean Theorem for this one

I hope this helps!!

Answer:

your face

Step-by-step explanation:

:)

Let's let A, B, C represent the sides of the triangle from shortest to longest, then:

A = ?

B = A + 2

C = A + 3

To find the perimeter we add all the sides p = A + B + C, and based on the problem

p = A + B + C

26  = A + (A + 2) + (A+3)

26 = 3A + 5

21 = 3A

7 = A

Now we can use the fact that A = 7 in, which is the shortest side, to find all three sides:

A = 7

B = 7 + 2 = 9

C = 7 + 3 = 10

The lengths  of the sides are 7 in, 9 in, and 10 in.

May I get brainliest please? :)

This is the required probability density function for Z.

Since the task is complete only when the computation at both worker nodes is complete, the total time for completion of the task is the maximum of X and Y.

Therefore, we have:

Z = max(X,Y)

The CDF of Z can be written as:

\(F_Z(z)\) = P(Z <= z) = P(max(X,Y) <= z)

Since X and Y are independent, we have:

P(max(X,Y) <= z) = P(X <= z, Y <= z)

Using the properties of exponential distribution, we have:

P(X <= z, Y <= z) = P(X <= z) * P(Y <= z)

\(= (1 - e^{-l1 * z}) * (1 - e^{-l2 * z})\)

Therefore, the CDF of Z is:

\(F_Z(z) = (1 - e^(-l1 * z)) * (1 - e^(-l2 * z))\)

To find the PDF of Z, we differentiate the CDF with respect to z:

\(f_Z(z) = d/dz F_Z(z)\)

\(= l1 * e^{-l1 * z} * (1 - e^{-l2 * z}) + l2 * e^{-l2 * z} * (1 - e^{-l1 * z}) \\\)

Therefore, the PDF of Z is:

\(f_Z(z) = l1 * e^{-l1 * z} * (1 - e^{-l2 * z}) + l2 * e^{-l2 * z} * (1 - e^{-l1 * z})\)

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The three alternative work arrangements - telecommuting, job sharing, and flextime - offer employees and employers different ways to structure work schedules and responsibilities.

Let's discuss each arrangement along with examples:

Telecommuting:

Telecommuting, also known as remote work or working from home, allows employees to perform their job duties outside of the traditional office setting. They utilize technology to communicate and collaborate with their team and complete their tasks remotely.

Example:

An employee in a software development company works from home three days a week. They have access to all the necessary tools and resources, such as a company laptop and secure VPN, to carry out their programming tasks. They communicate with their team through video conferencing, instant messaging, and email.

Job Sharing:

Job sharing involves two or more employees dividing the responsibilities and hours of a single full-time position. Each employee works part-time, sharing the workload and maintaining continuity in job functions.

Example:

In a customer service department, two employees share a full-time customer support role. They coordinate their schedules to ensure coverage throughout the workweek. For instance, one employee works Mondays, Wednesdays, and Fridays, while the other works Tuesdays and Thursdays. They communicate regularly to hand off tasks and ensure a seamless customer service experience.

Flextime:

Flextime allows employees to have control over their work schedules by providing flexibility in determining their start and end times within certain parameters. This arrangement recognizes that employees have different productivity peaks and personal commitments.

Example:

In a marketing agency, employees have flexible work hours between 7:00 am and 7:00 pm. Each employee can choose their preferred start time, such as starting work at 7:00 am and finishing at 3:00 pm or starting at 10:00 am and finishing at 6:00 pm. As long as they meet their required hours and deliverables, they have the freedom to adjust their schedules based on personal preferences or commitments.

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