Let R be an equivalence relation on a set A. Prove the following statement directly from the definitions of equivalence relation and equivalence class. For every a and b in A, if [a] = [b] then a Rb. Some of the sentences in the following scrambled list can be used to prove the statement. By definition of equivalence class, a E[b]. Let b E[a]. Then by definition of equivalence class, b Ra. Since R is symmetric, if b R a then a R b. | Thus, a Ra, and so, by definition of equivalence class, a E [a]. Since [a] = [b] and a E [a], then a E [b] by definition of set equality. | Hence, by definition of equivalence class, a Rb. By definition of equivalence relation, R is reflexive. Proof: Construct a proof by selecting appropriate sentences from the list and putting them in the correct order. 1. Suppose R is an equivalence relation on a set A, a and b are in A, and [a] = [b]. 2. ---Select--- 3. ----Select--- 4. ---Select--- 5. ---Select---

The required balance at the beginning of the incomplete register is $38.25.

Given that,
To determine the beginning balance in the incomplete register.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
In the table, in the register, the balance starts with an entry of $38.25 paycheck. So, the 1 st entry of the register shows the balance in the beginning.

Thus, the required balance at the beginning of the incomplete register is $38.25.

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The number of total different outcomes are, 7,776.

What is rolling dice?

Every face of a cube known as a dice has a unique number.

By throwing a dice into the air, players can advance in any game by getting a certain number. Typically, this dice or dice has numbers from 1 to 6 written on each face or side of the cube-like shape.

Given:

Discrete 5 dice of different colors are rolled, and the number coming up on each dice is recorded.

Since all the dice are of different colors.

So any combination of the numbers on the dice is unique.

Dice has numbers 1 to 6.

So, for each dice there are 6 possibilities.

Since number coming on a dice is independent to the number coming on the another dice.

So, total different outcomes are = 6 x 6 x 6 x 6 x 6 = 6^5 = 7776.

Hence, the number of total different outcomes are, 7,776.

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Answer:

They took 3 vans and 3 buses.

Step-by-step explanation:

Given:

To find:

The number of vans and the number of buses they took.

Explanation:

Let the number of vans = v

Let the number of buses = b

The total number of vans and buses is 6:

[tex]v+b=6[/tex]

⇒[tex]v=6-b....[/tex]Equation(1)

Each van holds 6 students and each bus hold 50 students.

The number of students on the trip is 168.

[tex]6v+50b=168[/tex]....Equation(2)

Substitute equation (1) into equation (2):

[tex]6v+50b=168[/tex]

[tex]6(6-b)+50b=168[/tex]

Then solve the equation for b:

[tex]36-6b+50b=168[/tex]

[tex]44b=168-36[/tex]

[tex]44b=132[/tex]

[tex]\frac{44b}{44}=\frac{132}{44}[/tex]

[tex]b=3[/tex]

Then, solve for v:

[tex]v=6-b=6-3=3[/tex]

Answer:

They took 3 vans and 3 buses.

Answer: y= -4x -24

Step-by-step explanation:

The equation is y=mx + b

We know the b is -24 because it already tells us the coordinate of the y-intercept is (0, -24), so we only need to find x by looking at the rise over run.

The rise is -24, and the run is 6, so -24/6 = -4

So the equation is y= -4x -24

If you can please give me a Brainliest, I only need 3 more to become an Ace, thank you!

Answer: x=4

Step-by-step explanation:

6x + 10 = 5x + 14

x + 10 = 14

x = 4

The arrangements are there with no pair of consecutive letters the same is ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k).

The past step makes six void spots in which three Is might be sorted out, however just three spots should be picked. Request doesn't make any difference, as every one of the three Is are something similar. Along these lines, there are (63) approaches to picking those spots.

Given 2n letters, two of every one of n types. What number of courses of action of these letters are there without any sets of sequential letters something similar? Kindly look at my answer and let me know where my mix-up is!

So such plans where the sets of indistinguishable letters are discernable. Then, at that point, ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k) gives the quantity of such plans by incorporation avoidance (there are (2n−k)! ways for k given matches to be together (by combining the those sets into single components) and the rest randomly requested, 2k ways of requesting inside those given matches, and C(n,k) ways of picking those k pairs).So we can acquire the recipe

∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k)

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when we pay n pesos, then recurrence relation for all the number are in a ways to pay a bill is in this order:[tex]a_{n} =a_{n-1}+a_{n-2}+2a_{n-5}+2a_{n-10}+ a_{n-20}+a_{n-50}+a_{n-100}[/tex]

A recurrence relation is an equation which represents a chain primarily based totally on a few rule. It enables in locating the following time period (subsequent time period) established upon the previous time period (preceding time period). If we recognise the preceding time period in a given series, then we will without difficulty decide the following time period.

Recurrence family members are used to lessen complex issues to an iterative procedure primarily based totally on less difficult variations of the trouble. An instance trouble wherein this technique may be used is the Tower of Hanoi puzzle. Recurrent is some thing that happens frequently or repeatedly. However, in case you are speakme approximately a recurrence relation, then you definitely have a mathematical shape which you are handling and it's miles really specific than a recursive formula. Recursion is the repeated use of a process or action.

pay 1 pesos coin , then n-1 pesos

pay 2 pesos coin , then n-2 pesos if n ≥ 2

pay 5 pesos coin , then n-5 pesos if n ≥ 5

pay 10 pesos coin , then n-10 pesos if n ≥ 10

pay 5 pesos bill , then n-5 pesos if n ≥ 5

pay 10 pesos bill , then n-10 pesos if n ≥ 10

pay 20 pesos bill , then n-20 pesos if n ≥ 20

pay 50 pesos bill , then n-50 pesos if n ≥ 50

pay 100 pesos bill , then n-100 pesos if n ≥ 100

a0=1

so i have recurrence relation as follows:

[tex]a_{n} =a_{n-1}+a_{n-2}+2a_{n-5}+2a_{n-10}+ a_{n-20}+a_{n-50}+a_{n-100}[/tex]

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a) Probability model

P(40) = 1/6

P(0) = 5/36

P(-10) = 25/36

b)  E(X) = -5/18

standard deviation  = 18.331

c) standard deviation  = 91.65

d) Probability = 0.560

From the question, we have

a) X = -10, 0 or 40 for your winnings (or losses). The corresponding probabilities are:

P(40) = 1/6

P(0) = (5/6)(1/6) = 5/36

P(-10) = 1 - 1/6 - 5/36 = 25/36

b) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18

E(X^2) = (100)(25/36) + 1600(1/6) = 3025 / 9

Var(X) = E(X^2) - [E(X)]^2 = 3025 / 9 - (-5/18)^2 = 108875 / 324

standard deviation = sqrt [Var X] = 119043 / 6494 =18.331

c) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18

5 * E(X)  =  - 25/18

standard deviation = 5 * 18.331 = 91.65

d) Probability :

P(X < 0) = P{ z < [0 - (-5/18)] / [(119043 / 6494) / sqrt 100] } = P(z < 0.1515) = 0.560

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

Complete question:

From the Data at Hand to the World at Large 4. New game You pay $10 and roll a die. If you get a 6, you win $50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What's the probability the person running the game makes a profit?

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The odds against selecting a history are 31/16.

Probability is the concept that describes the likelihood of an event occurring. In many situations, it is necessary to foresee how something will turn out in the actual world. We may be aware of the result of an event or not. When this occurs, we state that there is a possibility that the event will occur.

Probability is the ratio of the most likely outcomes to all other possible outcomes of an event. The number of successful outcomes for an experiment with 'n' outcomes may be expressed using the symbol x. The following formula can be used to determine the likelihood of an event.

Probability(Event) = favorable outcome/Total outcome = x/n

Number of playwrights = 47

Number of tragedies = 16

Therefore, the odds against selecting tragedies are

(47 - 16) / 16

= 31/16

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The complete question is:

Of the 47 plays attributed to a​ playwright, 11 are​ comedies, 16 are​ tragedies, 20 are histories. If one play is selected at​ random, find the odds against selecting a tragedy.

The value of x in the given function, f(x) = 3/2x - 4 when f(x) = 5, is x = 6

From the question, we are to determine the value of x in the given function for the given value of f(x).

The given function is

f(x) = 3/2x - 4

and

f(x) = 5

Now, to determine the value of x, put f(x) = 5 in the given function

f(x) = 3/2x - 4

5 = 3/2x - 4

Add 4 to both sides of the equation

5 + 4 = 3/2x - 4 + 4

9 = 3/2x

Multiply both sides by 2

2 × 9 = 2 × 3/2x

18 = 3x

Divide both sides by 3

18/3 = 3x/3

6 = x

Therefore,

x = 6

Hence, the value of x is 6

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At 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.

What is the quadratic equation?

Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

Let x (ft) be the distance from the base of the left pole to the anchor point. Since 2 poles has a distance of 45 ft, the distance from the anchor point to the right pole is 45 - x

The wire length from the top of the left pole to the anchor point is

[tex]L^{2} _l = 30^{2} + x^{2}[/tex]

= x² + 900

Similarly for the 2nd part of the wire

[tex]L^{2} _r = 15^{2} + (45-x)^{2}[/tex]

= 256 + 2025 - 45x + x²

= x² + 2281 - 45x

We want to minimize the length of the wires, or [tex]L_l + L_r[/tex]

√x² + 900 + √ x² + 2281 - 45x

we can take the first derivative of this and set it to 0

[tex]\frac{x}{\sqrt{ x^2 + 900} } + \frac{45 - x}{\sqrt{x^2 + 2281 - 45x} } = 0[/tex]

x = 30

Hence, at 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.

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Answer:

  remaining zeros: {-1/2, √3}

Step-by-step explanation:

Given the polynomial function f(x) = 2x³ +x² -6x -3 has one zero at x = -√3, you want the remaining zeros.

A polynomial with rational real coefficients and zeros that are roots or complex numbers will have all such roots in conjugate pairs.

The root that is the conjugate of -√3 is +√3.

The product of the roots of an odd-degree polynomial will be the opposite of the ratio of the constant to the leading coefficient. Here, that means the product of roots is ...

  -(-3/2) = 3/2

We already know that two of the three roots are ±√3, so their product is -3. The remaining root will be ...

  (3/2)/(-3) = -1/2

The remaining zeros of f(x) are √3 and -1/2.

__

Additional comment

When the degree of the polynomial is even, the constant term will be the product of the roots. This odd/negative, even/positive behavior comes from the fact that each zero (q) corresponds to a factor (x -q).

The product of these binomial factor constants is the constant in the standard-form polynomial. It will have a negative sign if there are an odd number of factors.

The time taken for Bob take to run one lap of the track is 69 seconds

Akira is running around a circular track. Akira runs counterclockwise.

It takes him 95 seconds to run one complete lap

Bob starts running at the same time as Akira

Bob and Akira pass each other for the first time after 26 seconds

It takes him 95 seconds to run one complete lap

In 26 seconds he covers 26/95 laps

In this time Bob must have covered 69/95 laps

An inverse relationship

c/95 = 69/95

c = (69/95) x 95

c = 69

Therefore, time taken for Bob take to run one lap of the track is 69 seconds.

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Answer:

6

Explanation:

x = 3 /cos(60) = 6

Answer:

You could divide 5 in half and then add that to the five to find the amount of flour to use in a triple recipe. Hope this helps.

Step-by-step explanation:

The given statement that a trinomial is always a higher degree than a monomial is false because greater number of terms does not means higher degree.

A monomial is an algebraic expression with only one term. Or we can say that the representation of a single concept is a monomial.

An example of an unary expression is: 12

A trinomial is an algebraic expression containing three terms. An example of a ternary is: x + y + 7

A trinomial is always of higher degree than a monomial is false statement .

A counterexample can be used to explain why this is wrong. Suppose we have a monomial, 8⁵ and then a trinomial x² + 2x + 3 . This is just a random example. This monomial has a higher degree because 5 is greater than 2. So basically it doesn't matter what the monomial is, if the degree is higher it is just a term than the maximum degree of the trinomial. Just because this has three terms does not mean that the highest degree term is greater than his one term in the monomial.

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29.78% of customers will most likely probability be waiting between 4 and 9 minutes.

The formula for the z score is-

z = (x - μ)/σ

In which,

μ =  mean of 10. 3 minutes

σ = standard deviation of 2. 7 minutes.

z score for the x = 4 minutes.

z = (4 - 10.3)/2.7

z = -2.33

z score for the x = 9 minutes.

z = (9 - 10.3)/2.7

z = -0.48

Thus,

Probability that the customer will have to wait between 4 and 9 minutes.

P(4 < x < 9) = P(-0.48 < z <  -2.33)

Use z score table-

P(4 < x < 9) =  0.3085 - 0.0107

P(4 < x < 9) = 0.2978

P(4 < x < 9) = 29.78%

Thus, 29.78% of customers will most likely be waiting between 4 and 9 minutes.

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Answer: At a small savings and loan company, you have to deal with your customers being victims of identity theft. This happens unpredictably to one of your customers once every 9 weeks; and no incident seems to have any connection to any other incident.

Step-by-step explanation:

The vertex and range of the function y = |x - 5| + 5 is (5, 4) and  [4, ∞) respectively

The vertex of the function is located at (h,k) of its vertex form, and will be located at the peak or trough of the parabola on a graph. This is the highest or lowest point of the function, depending on its direction.

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

In the given function;

y = |x - 5| + 4

Using a graph, the lowest point of the function is at x = 5 and y = 4 is the vertex of this function.

vertex = (5, 4)

Range = [4, ∞)

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Answer and explanation in one:

(4+9)/(-2-1) = 13/-3 = -13/3

y=-13x/3 + b

4=26/3 + b

b = 4-26/3 = (12-26)/3 = -14/3

y=-13x/3 -14/3 is the line through the two given points

find the line perpendicular and through (14,-6)

y=3x/13 + b, plug in the point to find b

-6 = 3(14)/13 + b

b = -6 -42/13 = -78/13 - 42/13 = -120/3

y= 3x/13 - 120/13

find the intersection point of the two lines, set them equal

3x/13 -120/13 = -13x/3 - 14/3

multiply by 39

9x - 360 = -169x - 182

178x = 360-182 = 178

x = 1

y= -27/3=-9

the point is (1,-9)

calculate the distance from (1,-9) to (14,-6)

d^2 = 9+169 = 178

d = sqr178 = about 13.34

The total number of pizzas were made in 4 hour in pizza shop is 24.

For the stated question-

For one pizza-

Ounce of cheese required = 5.

Ounces of sauce required = 3.

Total requirement = 8 ounces.

After 4 hours,

Total ounces combined of sauce and cheese used = 192.

Thus,

Number of pizza = 192 / 8

Number of pizza = 24

Thus, the total number of pizzas were made in 4 hour in pizza shop is 24.

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a) Considering the scale factor, the height that she should build the model is of: 22.1 inches.

b) Essence has enough information to build the accurate scale model, as she needs only the scale and either the actual or the drawn model.

An scale is defined as the relation between the actual length of a segment and the length of drawn segment, as follows:

Scale = Actual length/drawn length

The scale for this problem is given as follows:

Scale factor = 300 ft/1 in.

Which means that each inch on the drawing represents an actual height of 300 ft.

The height of the Clingman Dome is given as follows:

6,643 feet.

Considering the scale factor of 300 ft/1 in, the height of the drawing is obtained as follows:

6643/300 = 22.1 inches.

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Six candies would cost $1.44.

Answer:

$1.44

Step-by-step explanation:

We need to figure out how much one piece of candy costs. So you do .96/4, which is going to equal 0.24.

1 piece of candy = $0.24

So we do 0.24*6= 1.44

I hope this helps!!!

Please mark brainliest :)

Answer:

x = - 25

Step-by-step explanation:

the absolute value function always gives a positive value , however , the expression inside the bars can be positive or negative, that is

| - a | = | a | =a

given

| x + 10 | = 15 , then

x + 10 = 15 ( subtract 10 from both sides )

x = 5

OR

-(x + 10) = 15

- x - 10 = 15 ( add 10 to both sides )

- x = 25 ( multiply both sides by - 1 )

x = - 25

solutions are x = 5 , x = - 25

Answer: -25

Step-by-step explanation:

The expression in terms of x that represents the total amount that Zoe paid is 1.2075x.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information, Zoe goes to a restaurant and the subtotal on the bill was x dollars. A tax of 5% is applied to the bill and Zoe decides to leave a tip of 15% on the entire bill.

The expression will be:

= x + (5% × x) + (15% × 1.05x)

= x + 0.05x + 0.1575x

= 1.2075x

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The amount of sales Terry must make is $1667

From the question, we have the following parameters that can be used in our computation:

Commission = 18% of sales

Commission = $300

These parameters mean that

Commission = 18% of sales

Substitute the known values in the above equation, so, we have the following representation

18% of sales = 300

Divide both sides by 18%

Sales = 1667

Hence, the amount is $1667

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{(- 8, 6), (- 4, 3), (0, 0), (4, - 3)}set of ordered pairs (x, y) could represent a linear function

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Linear function is a function whose graph is a straight line

Slope of a line tells us how steep the line is . Slope of a line is same at all the points.

For option A:

m=1+2/3-1=3/2

m=3/2

m=7-4/8-5=3/3=1

Slopes are not same

For option B:

m=3-6/-3+6=-3/3=-1

m=0-3/0+3=-1

m=-4/3

Slopes are not same

For option C:

m=6-8/-1+2=-2

m=4-6/1=-2

m=-3/2

Slopes are not same

For option D:

m=3-6/-4+8=-3/4

m=-3/4

m=-3/4

Slopes are same at every point, so this set of ordered pairs could represent a  linear function

Hence, {(- 8, 6), (- 4, 3), (0, 0), (4, - 3)}set of ordered pairs (x, y) could represent a linear function

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