On a certain hot summers day, 402 people used the public swimming pool. The daily prices are 1. 50$ for children and 2. 00$ for adults. The receipts for admission totaled 648. 50$. How many children and how many adults swam at the public pool that day?

The combined resistance, R, of two resistors with resistances r and s connected in parallel can be calculated using the equation:
[tex]1/R = 1/r + 1/s[/tex]
When an electric current passes through these resistors, the combined resistance depends on the values of r and s. To analyze the behavior of R with respect to r, we can rewrite the equation as:
[tex]R = (rs)/(r + s)[/tex]
R is a function of r and s, and its behavior depends on the values of r and s. If r and s are positive, the function is neither increasing nor decreasing globally, as it depends on both r and s values. However, for specific values of r and s, the function can be either increasing or decreasing locally.
There is no global maximum or minimum for this function because it depends on the specific values of r and s, and it can take any positive value depending on these resistances. So, the answer is none for global maximum or minimum.
In summary, the behavior of the combined resistance R when an electric current passes through two resistors connected in parallel depends on the values of r and s. It is neither globally increasing nor decreasing and has no global maximum or minimum.

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Explanation:

A strain of Mycobacterium tuberculosis that is deficient in nonhomologous end joining repair should be more sensitive to damage by X-rays.

Nonhomologous end joining is a DNA repair mechanism that can join two DNA fragments with little or no homology between them. X-rays, which are high-energy electromagnetic waves, can cause damage to DNA by breaking the strands of the double helix.

This damage can be repaired by mechanisms like nonhomologous end joining, so a strain of Mycobacterium tuberculosis that is deficient in this repair mechanism would be more sensitive to damage by X-rays.

UV radiation, glycosylase, and depurination are not directly related to nonhomologous end joining repair and would not have the same effect.

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The conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts is 4.74%.

The conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, can be calculated using Bayes’ theorem:

P(heart on fourth draw | first three draws are not hearts) = P(heart on fourth draw and first three draws are not hearts) / P(first three draws are not hearts)

To calculate the numerator, we need to find the probability of drawing a heart on the fourth draw and the first three draws being not hearts. Since we are drawing without replacement, the probability of drawing a heart on the fourth draw is 13/49 (there are 13 hearts remaining out of 49 cards remaining). The probability of the first three draws being not hearts can be calculated as:

(39/52) x (38/51) x (37/50) = 0.4372

Therefore, the numerator is:

P(heart on fourth draw and first three draws are not hearts) = (13/49) x (39/52) x (38/51) x (37/50)

P(heart on fourth draw and first three draws are not hearts) =  0.0207

To calculate the denominator, we need to find the probability of the first three draws being not hearts. We already calculated this as 0.4372.

Therefore, the conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, is:

P(heart on fourth draw | first three draws are not hearts) = P(heart on fourth draw and first three draws are not hearts) / P(first three draws are not hearts)

P(heart on fourth draw | first three draws are not hearts) = 0.0207 / 0.4372

P(heart on fourth draw | first three draws are not hearts) ≈ 0.0474

So the probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, is approximately 0.0474 or 4.74%.

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The surface area of the triangular prism is 960 units squared.

The surface area of the triangular prism can be found as follows:

surface area of the triangular prism = bh + l(s₁ + s₂ + s₃)

where

Therefore,

surface area of the triangular prism = 24 × 16  + 9 (20 + 20 + 24)

surface area of the triangular prism = 384 + 9(64)

surface area of the triangular prism = 384 + 576

surface area of the triangular prism = 960 units²

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The exact value of the circle is 36π square feet. Option A

The formula used for calculating the area of a given circle is expressed with the equation;

A = π(d/2)^2

A = πr²

Such that the parameters are;

The formula for radius is given as;

radius = diameter/2

divide the values

radius = 6 feet

Substitute the values

Area = 3.14 ×6²

multiply the values

Area = 36π square feet

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Yuri will spend $ X more on concrete than on soil and wood.

When answering questions on Brainly, it is important to be factually accurate, concise, and professional.

It is also important to provide a step-by-step explanation of how you arrived at your answer.

The question is asking about the cost of materials for a patio, garden, and deck.

Let's break down the information we have.

Area of the patio = enter your response

Here

Cost of concrete = $ enter your response

Here

Area of the garden = enter your response

here

Cost of soil = $ enter your response

here

Total area of the deck = enter your response

here

Cost of wood = $ enter your response

here

Yuri will spend $ enter your response here more on concrete than on soil and wood.

To find the cost of each material, we need to multiply the area by the cost per unit area.

For example, the cost of concrete would be the area of the patio multiplied by the cost of concrete per unit area.

Let's call the cost per unit area for concrete C, the cost per unit area for soil S, and the cost per unit area for wood W.

Area of patio = P

Cost of concrete = C

Area of garden = G

Cost of soil = S

Total area of deck = D

Cost of wood = W

Yuri will spend X more on concrete than on soil and wood.

To find the values of P, C, G, S, D, and W, we need to use the information given in the question.

However, some values are missing.

We can use the given information to create equations that will help us find these values.

For example, we know that the total area of the deck is the sum of the area of the patio and the area of the garden, so we can write:

D = P + G

Similarly, we can write an equation for the cost of each material.

For example, the cost of concrete is the area of the patio multiplied by the cost per unit area for concrete, so we can write:

C = P * C

Similarly, we can write equations for the cost of soil and wood:

S = G * W, W = D * W

Now we have three equations and three unknowns: P, G, and D. We can solve this system of equations to find these values.

Let's solve for P and G first.

We'll use the equation

D = P + G

to eliminate G from the equations.

C = P * CS = G * WP = D - G

Substitute P = D - G into the first two equations.

C = (D - G) * CW = D * W - G * W

Now we have two equations and two unknowns: D and G.

We can solve for these values.

We'll use the equation

W = D * W - G * W

to eliminate W from the equations.

C = (D - G) * CS = G * SD = P + G = 2G - (W / C)

Substitute D = P + G into the first two equations.

C = P * C + G * CS = G * SW = P + G - DC = P * C + (D - P) * C + (W / C) * C = 2P * C + W

We can now solve for P, G, and D.

P = (C + S + W / C) / 2G = (S + W / C) / 2D = P + G = (C + S + W / C) / 2 + (S + W / C) / 2P = enter your response

here

C = enter your response

here

S = enter your response

here

W = enter your response

here

G = enter your response

here

D = enter your response

here

Now we can find the value of X, which is the difference between the cost of concrete and the combined cost of soil and wood.

X = C - (S + W)X = enter your response.

The area of the patio is enter your response here ​, so the cost of concrete is ​$ enter your response here. The area of the garden is enter your response here ​, so the cost of soil is ​$ enter your response here. The total area of the deck is enter your response here ​, so the cost of wood is ​$ enter your response here.

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Question:

Yuri bought a new house. The diagram shows the layout of his backyard. Yuri is designing improvements that he wants to make. Yuri plans to fill the patio with concrete, the garden with a special soil mixture, and the remaining areas that surround the hot tub with a wood deck. The table shows the costs associated with each project. How much more will Yuri spend on concrete than on soil and wood?

Answer:

To calculate the total milk yield in one year, we need to multiply the number of dairy cows by the amount of milk each cow produces per year:

Total milk yield = 2650 dairy cows × 2320 gallons of milk per cow per year

Total milk yield = 6,188,000 gallons per year

To write this answer in scientific notation, we need to express the number 6,188,000 as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point to the left until we have a number between 1 and 10, and counting the number of decimal places we moved. In this case, we need to move the decimal point 6 places to the left:

Total milk yield = 6.188 × 10^6 gallons per year

Therefore, the dairy farm yields 6.188 × 10^6 gallons of milk per year.

The volume of the solid obtained by rotating the region bounded by the given curves about the y-axis is 8π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curves y=x^2, y=0, x=0, and x=2 about the y-axis, we can use the disk method.

The steps are as follows:

STEP 1. Identify the radius of the disk:

Since the solid is obtained by rotating around the y-axis, the radius of the disk is the x-value.

To get the x-value in terms of y, solve the equation

y=x^2 for x: x = sqrt(y).

STEP 2. Set up the volume integral:

The volume of the solid is given by the integral of the cross-sectional area of the disks.

The area of a disk is A = πr^2, where r is the radius. In this case, r = sqrt(y), so A = π(sqrt(y))^2 = πy.

We will integrate this area function along the y-axis, from the lowest to the highest y-value on the curve.

The lowest y-value is y=0, and the highest y-value is given by y = (2)^2 = 4 (since x=2).

STEP 3. Evaluate the integral:

The volume integral is given by V = ∫[0, 4] πy dy.

To evaluate this, we find the antiderivative of πy:

(π/2)y^2.

Now, we apply the Fundamental Theorem of Calculus:
V = [(π/2)(4)^2] - [(π/2)(0)^2] = (π/2)(16) = 8π.

So, the volume of the solid obtained by rotating the region bounded by the given curves about the y-axis is 8π cubic units.

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The measure of angle J, m∠J = 41.2°.

angle mwasurement:

We can use trigonometry to find the measure of ∠J. Since we know the lengths of the two sides adjacent to ∠J (GH and GJ), we can use the tangent function, which is defined as the opposite side divided by the adjacent side:

tan(J) = opposite/adjacent = GH/GJ

We can solve for J by taking the inverse tangent (or arctan) of both sides:

J = [tex]tan^{-1}[/tex](GH/GJ)

Substituting the given values, we get:

J = [tex]tan^{-1}[/tex](14/16)

Using a calculator, we find:

J ≈ 41.186

Rounded to the nearest tenth, the measure of angle J is 41.2°.

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Since Shay's sibling is 7 years younger than twice her age, Shay is therefore 29 years old.

Mathematicians use the unitary method, also referred to as the "single unit technique," to answer problems involving proportional relationships between two or more quantities. The unitary technique entails determining the value of a single unit or quantity and using that value to calculate the values of other quantities in relation to that unit or quantity. Problems requiring ratios, proportions, percentages, and other related ideas can be solved using this approach.

given

Shay's age will be denoted by the letter S, and her sister's age will be referred to as "Sister".

The first claim informs us of the following:

Sibling = 2S – 7

And based on the second assertion, we can infer that:

Sibling + S = 80

The result of putting the first equation into the second equation is:

S + (2S - 7) = 80

When we simplify this solution, we obtain:

3S - 7 = 80

7 added to both edges gives us:

3S = 87

When we multiply both parts by 3, we get:

S = 29

Since Shay's sibling is 7 years younger than twice her age, Shay is therefore 29 years old.

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The statement that creates an array of decimals named miles and assigns the values 27.2, 33.5, 12.8, and 56.4 to its elements is: `double[] miles = {27.2, 33.5, 12.8, 56.4}.

An array is a data structure that contains a group of elements of the same data type. It is a collection of variables with the same data type but with different values assigned to them. To create an array in Java, we specify the data type of the elements in the array and the size of the array.The code that creates an array of decimals named miles and assigns the values 27.2, 33.5, 12.8, and 56.4 to its elements is given as follows: double[] miles = {27.2, 33.5, 12.8, 56.4}: The `double[]` specifies the data type of the elements in the array, which is double. The name of the array is miles, and it contains four elements with values 27.2, 33.5, 12.8, and 56.4 respectively.

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DECIMAL MILES can create array of decimal miles.

In computer science, an array is a data structure consisting of a collection

of elements, of same memory size, each identified by at least one array

index or key. An array is stored such that the position of each element can

be computed from its index tuple by a mathematical formula. Two type of

array are there 2D array and 3D array. The following statement creates an

array of decimals named miles and assigns the values 27.2, 33.5, 12.8, and

56.4 to its elements:

decimal[] miles = {27.2, 33.5, 12.8, 56.4};

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According to Luban, moral injuries and physical injuries are similar in that they share most characteristics except for the pain and suffering caused by physical injuries.

Luban is an American lawyer and philosopher. He is known for his work on just war theory and international law. Luban argues that moral injuries and physical injuries are similar in that they share most characteristics except for the pain and suffering caused by physical injuries.

Moral injuries:

Moral injuries are injuries caused by actions that violate a person's moral or ethical values.

Physical injuries:

Physical injuries are injuries caused by physical trauma, such as a broken bone or a cut.

Moral injuries and physical injuries are similar in many ways. Both can cause pain and suffering, loss of functionality, and disfigurement. Both can also have long-lasting effects on a person's health and well-being.

                     However, moral injuries are different from physical injuries in one important way

they do not cause physical pain and suffering.Moral injuries are caused by actions that violate a person's moral or ethical values.

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The truth regarding the conditions for constructing a confidence interval for a population mean for the real estate market is that E. All conditions have been met.

For a confidence interval to be construction, sample should be randomly selected, sample size should be no more than 10% of the population size, and the sampling distribution should be approximately normal. This can be achieved if the sample size is large (typically n ≥ 30) and the data doesn't have strong skewness or outliers.

The question states that the realtor is working in a large city, and it is reasonable to assume that 100 home sales are less than 10% of all homes sold in the previous 6 months in this large city. So, this condition is met.

The realtor has randomly selected 100 home sales, so the random condition is met. All conditions have therefore been met to construct a confidence interval.

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Options for this question include:

The resolution (n) is an important factor when specifying the smallest ton. If the TPWM (time-proportional width modulation) doubles and the ton (time-on) remains the same, the resolution will also double.

This is because the same amount of time (ton) is distributed over twice the pulses (TPWM).

To better understand this, imagine having 10 slices of a cake and trying to divide them into 2 even halves. You can achieve that by cutting each slice into 2 parts. The same logic applies to TPWM and ton.

TPWM represents the number of “slices” and ton represents the “time” allotted to each slice. When TPWM doubles, resolution (n) doubles as well. This is because twice the number of pulses (TPWM) are spread over the same time (ton), meaning that each pulse gets a smaller amount of time (a higher resolution).

The resolution (n) is inversely proportional to TPWM, meaning that if TPWM increases, resolution decreases, and if TPWM decreases, resolution increases. Thus, when TPWM doubles and ton remains the same, resolution (n) doubles as well.

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The confidence level of the CI is 95%.

The formula for the confidence interval of a normal distribution is

CI = X ± Zα/2 × σ/√n

Where

CI is the confidence interval

X is the sample mean

Zα/2 is the Z-score corresponding to the desired confidence level α/2

σ is the population standard deviation

n is the sample size

We know that the width of the confidence interval is 3.4, so

3.4 = 2 × Zα/2 × σ/√n

We also know that σ = √22 = 4.69, X = 25, and n = 15. Plugging these values into the equation and solving for Zα/2

3.4 = 2 × Zα/2 × 4.69/√15

Zα/2 = 1.96

The Z-score corresponding to a 95% confidence level is 1.96. Therefore, the confidence level of the CI is 95%.

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The equatiοns, 1 unit equals 10 οn the x-axis and 10 οn the y-axis.

Equatiοns are statements in mathematics that have twο algebraic expressiοns οn either side οf the equals (=) sign.

It shοws that the expressiοns printed οn the left and right sides have an equal relatiοnship.

In any mathematical equatiοn, we have LHS = RHS (left hand side = right hand side).

Equatiοns can be sοlved tο find the value οf an unknοwn variable that represents an unknοwn quantity.

If there is nο "equal tο" symbοl, a statement is nοt an equatiοn.

When twο expressiοns have equal values, a mathematical statement knοwn as an equatiοn includes the symbοl "equal tο" between them.

Accοrding tο οur questiοn-

Alsο, cοst οf 4 kg apples and 2 kg οf grapes are ₹ 300. can be represented as,

4x + 2y = 300

2(2x + y) = 300

2x + y = 150  ---  Equatiοn(2)

Therefοre, the algebraic representatiοn fοr equatiοn(1) is:

2x + y = 160

y = 160 - 2x

And, the algebraic representatiοn fοr equatiοn(2) is:

2x + y = 150

y = 150 - 2x

Hence, The equatiοns, 1 unit equals 10 οn the x-axis and 10 οn the y-axis.

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The calculated value of the area of the circle with radius 7 feet is 153.93 square feet.

To find the area of a circle with radius 7 feet, we can use the formula A = πr^2, where A is the area and r is the radius.

Substituting the given value of radius, we get:

A = π(7)^2

Simplifying this expression, we get:

A = 49π square feet

Evauate the expression

So, we have

A = 153.93 square feet

Therefore, the area of the circle with radius 7 feet is 153.93 square feet.

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Complete question

Find the area.

Remember: A = πr²

Round to the nearest hundredth.

Use 3.14 for π

The inequality trigonometry expression 2sin(2x - π/2) ≥ √3 when solved has a solution of x ≥ 5π/12

In the question, we have the following expression

2sin(2x - π/2) ≥ √3

The above expresson is an inequality and a trigonometry expression

So, we have

2sin(2x - π/2) ≥ √3

Divide by 2

sin(2x - π/2) ≥ 1/2√3

Take the arc sin of both sides

2x - π/2 ≥ π/3

Add π/2 to both sides of the expression

2x ≥ π/2 + π/3

Evaluate the like terms

2x ≥ 5π/6

Divide both sides by 2

x ≥ 5π/12

Hence, the solution to the variable x is x ≥ 5π/12

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the perimeter of the door on the scale drawing is 4 centimeters. A scale drawing is a representation of an object that is drawn to a smaller or larger size than the actual object, but the proportions between the dimensions of the object are maintained.

In this case, we are given a rectangular door of a dollhouse with a height of 5 centimeters and a width of 3 centimeters, and we are asked to find the perimeter of the door on a scale drawing that uses the scale 2:8.

The scale 2:8 means that every 2 units on the scale drawing represent 8 units on the actual object. To find the dimensions of the door on the scale drawing, we can divide both the height and the width by 8 and then multiply by 2, since the scale ratio is 2:8. This gives us the following dimensions on the scale drawing:

Height = (5/8) x 2 = 1.25 centimeters

Width = (3/8) x 2 = 0.75 centimeters

Now, we can use these dimensions to find the perimeter of the door on the scale drawing. The perimeter of a rectangle is given by the formula:

Perimeter = 2 x (Length + Width)

In this case, the length and width of the door are the same as the height and width of the door, respectively. So, we can write:

Perimeter = 2 x (Height + Width)

= 2 x (1.25 + 0.75)

= 2 x 2

= 4

Therefore, the perimeter of the door on the scale drawing is 4 centimeters.

In summary, we can find the dimensions of the door on the scale drawing by dividing the actual dimensions by 8 and multiplying by 2, and we can find the perimeter of the door on the scale drawing using the formula for the perimeter of a rectangle.

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It can be proven that a Rubik's cube will return to its original state if you repeat any algorithm for a number of times

To prove that a Rubik's cube will return to its original state if you repeat any algorithm for a number of times, follow these steps,

1. Choose an algorithm, Select any algorithm that can be applied to the Rubik's cube. For example, the R U R' U' algorithm.

2. Apply the algorithm repeatedly, Perform the chosen algorithm on the Rubik's cube multiple times. Keep track of the number of times the algorithm is applied.

3. Observe the cube's state, After each iteration, observe the state of the Rubik's cube to see if it returns to its original state.

4. Identify the cycle length, Eventually, the Rubik's cube will return to its original state after a certain number of repetitions of the algorithm. This number is the cycle length of the algorithm.

5. Generalize the proof, The proof holds true for any algorithm on the Rubik's cube, as every algorithm has a finite cycle length due to the finite number of possible configurations of the cube.

In conclusion, it can be proven that a Rubik's cube will return to its original state if you repeat any algorithm for a number of times, because every algorithm has a finite cycle length due to the finite number of possible configurations of the cube.

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The patient will take 2 tablets of lanoxin each day based on strength of tablets for the measurement.

We need to know the strength of the lanoxin tablets in order to calculate how many the patient will take dail based on measurement. Assume that the amount of lanoxin in each tablet is 0.0625 mg.

Given that 2 * 0.0625 mg = 0.125 mg, we can provide the patient 2 pills to obtain a dose of 0.125 mg. The patient will therefore take 2 lanoxin tablets daily.

It's crucial to remember that in order to make sure the patient receives the proper dosage of medication, we must take the medication's potency and the recommended dose into account while calculating dosages. In this instance, we assumed that each pill contained 0.0625 mg of lanoxin, but it's vital to read the drug label twice or get confirmation from the prescribing healthcare provider before giving the patient the medication. To maintain the patient's safety and wellbeing, it's also critical to adhere to the right pharmaceutical delivery standards.

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The probability of obtaining an increasing (non-decreasing) sequence after 4 draws with replacement from 6 balls labelled 1-6 is 1/15.

To explain the answer, we can first consider the number of possible combinations of four numbers that can be drawn from the six numbers. Since each draw is done with replacement, each draw has the same probability and the same six numbers can be chosen. Thus, there are 6 x 6 x 6 x 6 = 1296 possible combinations.

Next, we can calculate the number of possible increasing (non-decreasing) sequences. If the first number drawn is 1, then the remaining three numbers must be greater than or equal to 1. Thus, the second number can be 1, 2, 3, 4, 5, or 6, the third number can be 1, 2, 3, 4, 5, or 6, and the fourth number must be 6. There are 6 x 6 x 1 = 36 possible increasing sequences if the first number drawn is 1. If the first number drawn is 2, then the second number can be 2, 3, 4, 5, or 6 and the remaining two numbers must be greater than or equal to 2. Thus, the third number can be 2, 3, 4, 5, or 6, and the fourth number must be 6. There are 5 x 5 x 1 = 25 possible increasing sequences if the first number drawn is 2. This process can be repeated for the remaining numbers, 3, 4, 5, and 6. The total number of increasing (non-decreasing) sequences is the sum of these possibilities, which is 36 + 25 + 15 + 6 + 1 = 83.

Therefore, the probability of obtaining an increasing (non-decreasing) sequence after 4 draws with replacement from 6 balls labelled 1-6 is 83/1296 = 1/15.

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Answer:

2=a

Step-by-step explanation:

2a+3+4=11

2a+7=11

2a=11-7

2a=4

a=2

Based solely on statistical probability from demographic studies, the individual who has the greatest likelihood of being a smoker is a male aged between 18 to 24 years old.

According to demographic studies, men are more likely to smoke than women. Besides, the smoking rate increases with age, which means individuals aged between 18 to 24 have a higher likelihood of being a smoker than people of other ages.

Therefore, based solely on statistical probability from demographic studies, a male aged between 18 to 24 years old has the greatest likelihood of being a smoker.

It is important to note that statistical probability from demographic studies only shows what is likely or probable to happen but does not guarantee the actual occurrence of the event.

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The expression 3x-(4-x) is equivalent to 4x-4

The distributive property is a mathematical property that describes the relationship between multiplication and addition or subtraction. It states that when a number is multiplied by a sum or difference of two or more numbers, the result is the same as if we multiplied the number by each of the individual terms inside the parentheses and then added or subtracted the products.

To simplify the expression 3x-(4-x), we can distribute the negative sign to the second term inside the parentheses, which gives:

3x - (4 - x) = 3x - 4 + x

Now we can combine the like terms (3x and x) to get:

3x - 4 + x = 4x - 4

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The given question is incomplete, the complete question is:

Which expression is equivalent to 3x-(4-x)?

In order to have a potential value of $12,000 at a simple rate of interest of 8.0% after 6 years, the current value you must invest is therefore approximately $8,108.11.

A formula called Simple Interest (S.I.) is used to determine how much interest will be charged on a certain principal sum of money at a specific interest rate. For instance, if a person borrows Rs. 5000 for two years at a rate of 10 p.a., they will be compelled to pay S.I. on the whole amount borrowed during those two years.

For simple interest, use the formula:

A = P(1 + rt)

where r is the interest rate, t is the amount of time in years, A represents the future value, P is indeed the present value, and so on.

This formula can be changed to account for P:

P = A / (1 + rt)

By entering the specified values, we obtain:

P = 12,000 / (1 + 0.08 x 6)

P = 12,000 / 1.48

P = $8,108.11

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The value of sides b for different value of a  in a rectangle are;

a=2 and b=7

a=1/3 and b=42

A rectangle is a type of quadrilateral with four sides and four right angles (90-degree angles). It is a two-dimensional shape with opposite sides that are parallel and equal in length. The opposite sides of a rectangle are also perpendicular to each other, which means they meet at 90-degree angles.

A = l x w, where A is the area, l is the length, and w is the width, calculates the area of a rectangle.

In this case, we are given that the area is 14 square units, so we can set up the equation:

14 = a x b

Given;

a=2

Using this value as a replacement in the formula, we obtain:

14 = (2) x b

b=7

Taking another value of a=1/3

Using this value as a replacement in the formula, we obtain:

14=1/3×b

b=42

Therefore, The value of b for different value of a are;

a=2 and b=7

a=1/3 and b=42

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In Triangle ABC, we can draw a circle around each vertex of the triangle.

If the radii of all three circles are equal, then Triangle ABC is an equilateral triangle.

Radii is the plural form of radius. It is half of the diameter and the length of the radius is used to calculate the area and circumference of the circle.

To determine whether a triangle is an equilateral triangle, we can use circles.

In this method, we draw three circles, one around each vertex of the triangle.

We then measure the radii of the circles, ensuring that they are all equal. If the radii of the three circles are equal, then the triangle is an equilateral triangle.

In Triangle ABC, we can draw a circle around each vertex of the triangle. Then, we could use a measuring tool to measure the radii of each circle. If the radii of all three circles are equal, then Triangle ABC is an equilateral triangle.

This method of using circles to determine whether a triangle is an equilateral triangle is simple and efficient. It does not require any complex calculations, and it is easy to understand.

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The 12 of each type of the ring would give max profit for the company.

Let x = number of VIP rings: let y = number of SST rings

:

The total production inequality;

x + y =< 24

y = 24 - x; arranged to plot graph (purple)

:

The labor inequality;

3x + 2y =< 60

2y = 60 - 3x

y = 60/2 - (3/2)x

y = 30 - 1.5x; arranged to plot the graph (red).

From the graph, the 3 corners of the area of feasibility (at or below the lines whichever is lower):

: x/y;.....profit on each type;... total profit

0,24; 40(0) + 35(24) = 0 + 840 = $840

12,12; 40(12) + 35(12) = 480 + 420 = $900

20,0; 40(20) + 35(0) = 800 + 35(0) = $800.

Therefore, the 12 of each type of the ring would give max profit for the company.

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The sum of all positive integers k that satisfy the property is 1800.

To find the sum of all positive integers k that satisfy the property of the least common multiple of k and 720 being 3600, we need to use the concept of prime factorization and LCM. What is LCM?The least common multiple (LCM) of a set of numbers is the smallest number that is a multiple of all the given numbers. It is calculated by taking the common prime factors of the numbers and multiplying them by their highest powers.

Now mentioned in the question that  the LCM of k and 720 is 3600. Let's write 720 and 3600 in prime factorization form. 720 = 2⁴ × 3² × 5¹, 3600 = 2³ × 3² × 5²Let LCM of k and 720 be L. So, L = 2⁴ × 3² × 5²Let k = 2ᵃ × 3ᵇ × 5ᶜ. So, LCM of k and 720 = 2ⁿ × 3ᵐ × 5ᴬ, where, n = max (4, a) , m = max (2, b) , A = max (2, c)Given, LCM of k and 720 = 3600.So, 2ⁿ × 3ᵐ × 5ᴬ = 2⁴ × 3² × 5².

As we know, n = max (4, a) , m = max (2, b) , A = max (2, c)Thus, n = 4, m = 2, A = 2. Since, n = max (4, a) , a = 4 is the only possible solution And, m = max (2, b) , b = 2 is the only possible solution, And, A = max (2, c) , c = 2 is the only possible solution.So, the possible value of k is k = 2⁴ × 3² × 5²i.e. k = 1800. Sum of all possible values of k is 1800.Therefore, the sum of all positive integers k that satisfy the property is 1800.

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