Use Algorithm, to find the transitive closures of these relations on {1, 2, 3, 4). a) {(1, 2), (2,1), (2,3), (3,4), (4,1)) b) {(2, 1), (2,3), (3,1), (3,4), (4,1), (4,3)} c) {(1, 2), (1,3), (1,4), (2,3), (2,4), (3,4)} d) {(1, 1), (1,4), (2,1),(2,3), (3,1), (3, 2), (3,4), (4,2))

(a) A distance r from the cylinder axis is pr/2∈₀ and (b) expression for E when r > R is πR²lρ/2πϵ₀

(a) Consider a Gaussian surface in the form of a cylinder with radius r and length A, coaxial with the charged cylinder. An “end view” of the Gaussian surface is shown as a dashed circle. The charge enclosed by it is

q = ρV = πr²lp

V = volume of cylinder

If ρ is positive, the electric field lines are radially outward, normal to the Gaussian surface, and distributed uniformly along with it. Thus, the total flux through the Gaussian cylinder is  Φ = E(2πrl). Now, Gauss’ law leads to :

2π∈₀rlE = πr²lp

E = pr/2∈₀

(b) ) Next, we consider a cylindrical Gaussian surface of radius r > R. If the external field [tex]E_{ext}[/tex] then the flux is  Φ=2πϵ₀[tex]E_{ext}[/tex]

​ The charge enclosed is the total charge in a section of the charged cylinder with length A. That is,  q=πR²lρ. In this case, Gauss’ law yields :

2πϵ₀[tex]E_{ext}[/tex] = πR²lρ

[tex]E_{ext}[/tex] = πR²lρ/2πϵ₀

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Using the sketch, the possible range of values of x for which 2x² + 3x - 2≤0 is [-2, 0.5].

The domain of a function is a possible set of values of the independent variable. Based on the domain of a function, the codomain and range are determined.

Take the inequality as 2x²+3x-2≤0.

Solve the inequality.

2x²+3x-2≤0

(2x-1)(x+2)≤0

→ -2≤x≤0.5

The inequality is sketched in the graph and the area is also shaded for which 2x²+3x-2≤0. The range values of x mean the set of all points in the inequality -2≤x≤0.5, that is, [-2, 0.5].

Therefore, the obtained answer is [-2, 0.5].

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Answer:

5

Step-by-step explanation:

6/1.2=5

Answer:

55 L of water

Step-by-step explanation:

11-L of 60% acid contains 0.6 × 11 L = 6.6 L acid

Let x = amount of pure water.

Let y = total amount produced of 90% water solution.

A 90% water solution is a 10% acid solution.

Amounts of solutions:

x + 11 = y

Amounts of acid:

6.6 = 0.1y

y = 66

x + 11 = 66

x = 55

Answer: 55 L of water

55 L water has 0 acid.

11 L 60% acid solution has 6.6 L acid.

66 L of 10% acid solution has 6.6 L acid

Answer: 34

Step-by-step explanation:

The first step is if you multiply 8x4 you get 32

And then if you add 32+2 you get 34

According to PEMDAS

P=Parenthesis

E=Exponents

M=Multiplication

D=Division

A=Addition

S=Subtraction

Thus, you have to multiply, then add. If not you will get a way off answer. Also, because M comes before A.

Answer:

34

Step-by-step explanation:

To evaluate the expression 2 + 8m when m = 4, we can simply substitute 4 for m in the expression and simplify:

2 + 8m = 2 + 8 * 4

= 2 + 32

= 34

So, when m = 4, the value of the expression 2 + 8m is 34.

Answer:

23:15 as a decimal and 23 3/20

Step-by-step explanation:

Just divide by 100 to get decimal. For the fraction divide by 100 and simplify

1) All boys: Probability = 1/16 , 2) All girls: Probability = 1/16, 3) Exactly 3 boys: Probability = 5/16, 4) At least 1 boy: Probability = 15/16, 5) At most 3 girls: Probability = 15/16.

1) All boys: There are 16 possible combinations of 4 children, with each gender combination having an equal probability of 1/16. Therefore, the probability of all boys is 1/16.

2) All girls: Similarly, the probability of all girls is also 1/16.

3) Exactly 3 boys: To find the probability of exactly 3 boys, we need to consider all the cases with 3 boys and 1 girl. There are 4 possible combinations of 3 boys and 1 girl, so the probability of exactly 3 boys is 4/16, or 5/16.

4) At least 1 boy: To find the probability of at least 1 boy, we need to consider all the cases with 1, 2, 3, or 4 boys. There are 15 possible combinations with at least 1 boy (1 boy, 2 boys, 3 boys, and 4 boys), so the probability of at least 1 boy is 15/16.

5) At most 3 girls: To find the probability of at most 3 girls, we need to consider all the cases with 0, 1, 2, or 3 girls. There are 15 possible combinations with at most 3 girls (0 girls, 1 girl, 2 girls, and 3 girls), so the probability of at most 3 girls is 15/16.

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Equating the mathematical expressions, we can determine that the siblings need to sell 12 bags of cookies for them to raise the same amount of money.

Mathematical expressions are the combination of variables, constants, numbers, and values using mathematical operands like addition and subtraction.

Mathematical expressions are also described as algebraic expressions.

The initial amount that you have = $24

Your selling price per bag of cookies, c, = $3

The total amount you will make is given by Expression 1: 24 + 3c

Your sister's selling price per bag of cookies, c, = $5

The total amount your sister will generate is given by Expression 2: 5c

To determine the number of bags of cookies you must sell to raise the same amount of money between the two siblings, we equate the two expressions as follows:

24 + 3c = 5c

24 = 2c

12 = c

Check:

5c = 60 (5 x 12)

24 _ 3c = 60 (24 + 36)

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The length of JL is 9x + 22.

What are properties of rectangle?

A rectangle is a four-right-angle quadrilateral. It can also be classified as an equiangular quadrilateral because all of its angles are equal; or a parallelogram with a right angle. A square is a rectangle with four equal-length sides.

In a rectangle, opposite sides are equal in length. So, JL is equal to KM.

We have the expressions for the lengths of JN and NM. Using this information and the fact that JKLM is a rectangle, we can set up an equation:

JN + NM = JL + KM

Substituting the given expressions, we get:

(13x - 10) + (5x + 54) = JL + KM

Simplifying the left side, we get:

18x + 44 = JL + KM

But we know that JL = KM, so we can replace both JL and KM with JL:

18x + 44 = 2JL

Now we can solve for JL:

2JL = 18x + 44

JL = (18x + 44)/2

JL = 9x + 22

Therefore, The length of JL is 9x + 22.

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The kind of sample described in the given information is a stratified random sample.

What is stratified random sample ?

A stratified random sample is a type of probability sampling method used to obtain a representative sample of a population by dividing the population into smaller, more homogeneous groups called strata, and then selecting a random sample from each stratum.

This method is used when the population has certain characteristics or subgroups that are of interest to the researcher, and the goal is to ensure that the sample accurately represents each subgroup in proportion to its size in the population.

The process of selecting a stratified random sample involves dividing the population into strata based on some relevant characteristic, such as age, gender, education level, income, or geographic location. Then, a random sample is selected from each stratum, using a simple random sampling method. The sample size from each stratum is proportional to the size of that stratum in the population.

The advantage of a stratified random sample is that it can provide a more accurate representation of the population than other types of sampling methods, as it ensures that each subgroup is adequately represented in the sample.

According to given information :

The population of interest is people age 60 or older from the three surrounding counties. To obtain a representative sample of the population, the director of the hospital pharmacy has divided the population into three strata (i.e., the three surrounding counties) and selected a random sample of 100 people age 60 or older from each stratum. This ensures that the sample includes a proportionate number of participants from each county, which should help to reduce the potential for sampling bias that might result from selecting participants from only one county.

Therefore, this is an example of a stratified random sample.

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The probability of Y is greater than or equal to 1 given that X is equal to 2 i.e. P(Y ≥ 1 | X = 2) is 2/3.

To find P(Y ≥ 1 | X = 2), we will calculate the conditional probability of Y being greater than or equal to 1 given that X is equal to 2.

First, let us find the probability of X = 2, which is the number of 2 tickets in the box divided by the total number of tickets as follows -

P(X = 2) = 3/9

Next, let us find the probability of Y ≥ 1 and X = 2, which is the number of tickets with Y greater than or equal to 1 and X equal to 2 divided by the total number of tickets as follows -

P(Y ≥ 1, X = 2) = 2/9

Finally, using the formula for conditional probability to find P(Y ≥ 1 | X = 2) we get -

P(Y ≥ 1 | X = 2) = P(Y ≥ 1, X = 2) / P(X = 2)

P(Y ≥ 1 | X = 2) = (2/9) / (3/9)

P(Y ≥ 1 | X = 2) = 2/3

Therefore, the probability of Y is greater than or equal to 1 given that X is equal to 2 is 2/3.

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The process that will create a congruent figure is a translation of four units up, followed by a rotation (option B).

A figure is said to be congruent with another if they both have the same shape and the dimensions are the same. This means the figures are almost identical, although it is allowed that they are a reflection or that they are placed in the opposite direction.

Based on this, to create a congruent figure you need to translate the original figure and rotate it but not change its size (option B).

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The distribution of the indicator function Z, which denotes the probability of S being greater than T, can be expressed in terms of the marginal density and the cumulative distribution function of the independent random variables S and T.

In probability theory, a random variable is a variable whose value depends on the outcome of a random event. The distribution of a random variable describes the probability of the variable taking on different values.

Now, let's consider the two independent random variables S and T with common continuous density f. We define X as the minimum of S and T, and Y as the maximum of S and T.

The indicator function Z is defined as the probability of the event {S > T}. In other words, Z takes on the value of 1 if S is greater than T, and 0 otherwise.

To find the distribution of Z, we need to consider the joint probability distribution of S and T. Since S and T are independent, their joint distribution is given by the product of their marginal distributions:

f(S,T) = f(S) * f(T)

Now, let's consider the event {S > T}. This event occurs when S is on the right side of the diagonal line T=S in the (S,T) plane. The probability of this event can be obtained by integrating the joint density over this region:

P(S > T) = ∫∫ {S > T} f(S,T) dS dT

We can simplify this integral by changing the order of integration:

P(S > T) = ∫∞-∞ ∫S∞ f(S,T) dT dS

= ∫∞-∞ f(S) ∫S∞ f(T) dT dS

= ∫∞-∞ f(S) (1 - F(S)) dS

where F(S) is the cumulative distribution function of the random variable T, which gives the probability that T is less than or equal to S.

Thus, we have obtained the distribution of Z as a function of the marginal density f and the cumulative distribution function F:

P(Z=1) = ∫∞-∞ f(S) (1 - F(S)) dS

P(Z=0) = ∫∞-∞ f(S) F(S) dS

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Complete Question:

Let X be the minimum and Y the maximum of two independent random variables S and T with common continuous density f, i.e X = min{S,T}, Y = max{S, T}, and let Z =>t denote the indicator function of the event {S > T}.

What is the distribution of Z?

[tex]D(x)=\frac{f(x)}{g(x)}[/tex]

[tex]D'(x)=\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^{2} }[/tex]

Quotient rule in calculus is method finding the derivative of the differentiable functions which are in the division form

There are different methods to prove the quotient rule formula, given as,

Here, we are using implicit differentiation method to solve this quotient rule,

Let us take a differentiable function ,

[tex]D(x)=\frac{f(x)}{g(x)}[/tex]--------(1)

So, [tex]f(x)={D(x)}*{g(x)}[/tex]

Using the product rule we get,

[tex]f'(x)= D'(x).g(x)+g'(x).D(x)[/tex] solving for [tex]D'(x)[/tex] we get,

[tex]\frac{f'(x)-g'(x).D(x)}{g(x)} = D'(x)[/tex]------(2)

substitute for D(x) sub (1) in (2)

[tex]D'(x) =\frac{f'(x)-g'(x).\frac{f(x)}{g(x)} }{g(x)}[/tex]

⇒[tex]D'(x) =\frac{f'(x)g(x)-g'(x){f(x)} }{(g(x))^{2} }[/tex]

Hence,[tex]D'(x)=\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^{2} }[/tex] proved.

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The missing statements and reasons in the two column proof are;

1. AOC and BOD.

2. All radii of a circle are congruent

3. SAS congruency theorem

4. CPCTC

A two-column proof is defined as a geometric proof consists of a list of statements, and the reasons that we know those statements are true.

The two column proof of the angles is;

Statement 1: Central angles ∠AOC and ∠BOD are congruent

Reason 1: Given

Statement 2: The segments AO, CO, BO, and DO are congruent

Reason 2: All radii of a circle are congruent

Statement 3: Triangle AOC is congruent to triangle BOD

Reason 3: SAS congruency theorem

Statement 4: Chord AC is congruent to chord BD

Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

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Answer:

The answer to the expression, (x + 6)^2 is [tex]x^2+12x+36[/tex].

Step-by-step explanation:

We can solve this problem by breaking (x + 6)^2 into (x + 6) (x + 6).  Now, we can use FOIL to figure out the expression that is equivalent to the problem.

(x + 6) (x + 6)

First, we multiply the Xs together.

[tex]x*x=x^2[/tex]

Next, is the Outer values.

[tex]x*6=6x[/tex]

Third, we multiply the Inner values.

[tex]6*x=6x[/tex]

Finally, we can multiply the Last values.

[tex]6*6=36[/tex]

Now, we can put it all together.

[tex]x^2+6x+6x+36[/tex]

We still have one more step left.  Add like terms.

[tex]x^2+12x+36[/tex]

The answer is [tex]x^2+12x+36[/tex].

The length of the line QR is 3 units. Options A

The properties of a pentagon is expressed as;

From the image shown, we have that;

The point from Q to R are (-8, -5)

To determine the distance, we have that;

-8-(-5)

-8 + 5

Add the values

-3

Hence, the number  is 3

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The value of the x in the circle is 17.

'

The angle measure of the central angle is congruent to the measure of the intercepted arc.

Therefore, let's find the value of x.

Hence,

180 - 3x(angle on a straight line) = 7x + 10

180 - 3x = 7x + 10

add 3x to both side of the equation

180 - 3x = 7x + 10

180 - 3x + 3x = 7x + 3x + 10

180 = 10x + 10

180 - 10 = 10x

170 = 10x

x = 170 / 10

x = 17

Therefore,

x = 17

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The square of the monomial 0.16x^2y^2 can be expressed as:

(0.16x^2y^2)^2 = 0.16^2 * x^2 * y^2 * x^2 * y^2 = 0.0256x^4y^4

hope it helps

Answer:Angle 6 and Angle 5, Angle 3 and Angle 2

100% correct don't worry ;)

Step-by-step explanation:

Answer:10%

Step-by-step explanation:

For number one its a decrease equaling 10%

The mean (μ) and standard deviation (σ) represent the parameters of a normal distribution, so in this case, the parameters of the distribution are: μ = 80 transactions and σ = 10 transactions

A normal distribution, also known as a Gaussian distribution, is a continuous probability distribution that has a bell-shaped curve. This type of distribution is often used to model real-world phenomena that are expected to be distributed in a symmetrical fashion around a central value.

The central value of a normal distribution is the mean (μ), which represents the average of all the observations in the distribution. The spread or dispersion of the distribution is measured by the standard deviation (σ), which indicates how much the observations deviate from the mean.

In the given problem, the distribution of the number of transactions per day at an ATM is assumed to be normal with a mean of 80 transactions and a standard deviation of 10 transactions.

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The maximum number of students the school can add if it wants to maintain a ratio of student to teachers 20 : 1 is 210.

Ratio defines the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of student to teachers now = 150 : 18

Ratio of student to teachers to maintain = 20 : 1

For 1 teacher , number of students needed = 20

For 18 teachers, number of students needed = 20 × 18 = 360

Present number of students for 18 teachers = 150

Maximum number of students who can be added = 360 - 150 = 210

Hence school can add a maximum of 210 students in order to maintain a ratio of student to teachers 20:1.

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The solution is, the nth term of the arithmetic sequence 4,7,10,13 is 1 + 3n.

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

The nth term of AP : a_n = a + (n – 1) × d

here, we have,

the arithmetic sequence 4,7,10,13

so. we get,

1st term = 4 = a

common difference = 3 = d

i.e.  the nth term of the arithmetic sequence is, a_n = 4+(n-1)3

                                                                                      =1+3n

Hence, The solution is, the nth term of the arithmetic sequence 4,7,10,13 is 1 + 3n.

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To choose that a matrix is neither a diagonal matrix and are not scalar multiples of each other. The matrices will be as:

A = [ 2 1 ; 1 2 ]

B = [ -2 1 ; 1 2 ]

The matrices shown above can be used to find invertible matrices. The sum of A and B is [0 2; 2 4], which has a non-zero determinant and is therefore invertible. This choice of A and B satisfies the given conditions because they have different eigenvalues, ensuring they are not scalar multiples of each other, and are also not diagonal matrices.

The key idea behind this choice was to use matrices with the same trace and determinant, which guarantees that their sum will have the same determinant as well. This method allows us to construct examples of invertible matrices that satisfy the given conditions.

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The value of x is x= π/8

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

2tan x/1-tan² x= 1

We know that tan π/4= 1

So, 2tan x/1-tan² x= tan π/4

Also, we know that tan 2x=  2tan x/1-tan² x

Again, 2tan x/1-tan² x= tan π/4

tan 2x= tan π/4

Now comparing we get

2x= π/4

x= π/8

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The simplified expression of p^8/p^7 is given as follows:

p.

The expression for this problem is defined as follows:

p^8/p^7.

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the subtraction of the exponents is given as follows:

8 - 7.

Meaning that the simplified expression of p^8/p^7 is given as follows:

p.

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