How many gallons of 25% alcohol solution and 40% alcohol solution must be mixed to get 6 gallons of 30%
alcohol solution?

The required set for Au(BnC) is \(\{2,3,5,8\}\)

Given the following set A={2,3,5,8}, B= {3,5,7} and C= {2,4,8}

We are to find the following expression:

\(An(BuC)\)

First, we need to find BUC

BUC = {2, 3, 4, 5, 7, 8}

Taking the intersection between A and BUC, this is expressed as;

\(An(BuC)= \{2,3,5,8\}\)

Hence the required set for Au(BnC) is \(\{2,3,5,8\}\)

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On the assumption that each curve has only real roots, the quartic function is the graph C.

In this question we have four choices of graphs of polynomials, that is algebraic expressions of the form:

p(x) = Σ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., m - 1, m}

Where m is the grade of the polynomial.

The factor form of the polynomial is described below:

p(x) = a · Π (x - rₙ), for n = {0, 1, 2, 3, ..., m - 1, m}

If we consider that each choice has real roots, then the grade of the polynomial coincides with the number of times that the curve pass through the x-axis. Then, the graph C represent a quartic function, that is, a polynomial with grade 4 with the special feature that is a function of the form f(x) = a · x² · (x - r₁) · (x - r₂).

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x+y=10

225x+70y=1165 where x represents the quantity of sliders in the combo.

The quantity of chicken wings in the combo is given by y.

An equation is an expression of one or more variables equated to a constant or another expression. Equations are used in mathematics to describe the relationship between two or more variables and often involve operations such as addition, subtraction, multiplication, division, and exponents. Equations can also be used to describe physical phenomena and other phenomena such as chemical reactions, motion, and electricity.
Let x represent the number of sliders in the combination meal and let y represent the number of chicken wings in the combination meal. The system of equations used to determine the number of sliders and chicken wings in the combination meal is given by:
Equation 1: 225x + 70y = 1165
Equation 2: x + y = 10
This system of equations can be used to find the number of sliders and chicken wings in the combination meal. To solve this system, the equations must be manipulated to isolate one of the variables. For example, if we subtract 70y from both sides of Equation 1, we obtain 225x = 1165 - 70y. We can then divide both sides by 225 to obtain x = (1165 - 70y)/225. This expression can then be substituted into Equation 2 to obtain a single equation in one variable.
Therefore, the system of equations given by Equation 1 and Equation 2 can be used to determine the number of sliders and chicken wings in the combination meal.
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x+y=10

225x+70y=1165 where x represents the quantity of sliders in the combo.

The quantity of chicken wings in the combo is given by y.

An equation is an expression of one or more variables equated to a constant or another expression. Equations are used in mathematics to describe the relationship between two or more variables and often involve operations such as addition, subtraction, multiplication, division, and exponents. Equations can also be used to describe physical phenomena and other phenomena such as chemical reactions, motion, and electricity.
Let x represent the number of sliders in the combination meal and let y represent the number of chicken wings in the combination meal. The system of equations used to determine the number of sliders and chicken wings in the combination meal is given by:
Equation 1: 225x + 70y = 1165
Equation 2: x + y = 10
This system of equations can be used to find the number of sliders and chicken wings in the combination meal. To solve this system, the equations must be manipulated to isolate one of the variables. For example, if we subtract 70y from both sides of Equation 1, we obtain 225x = 1165 - 70y. We can then divide both sides by 225 to obtain x = (1165 - 70y)/225. This expression can then be substituted into Equation 2 to obtain a single equation in one variable.
Therefore, the system of equations given by Equation 1 and Equation 2 can be used to determine the number of sliders and chicken wings in the combination meal.
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Research has shown that competent communicators achieve effectiveness by adjusting their behaviors to the person and situation (option e).

Effective communication involves being adaptable and responsive to the specific context, individual preferences, and the needs of the situation.

Competent communicators recognize that different people have different communication styles, preferences, and expectations. They understand the importance of tailoring their communication approach to effectively connect and engage with others.

This may involve using appropriate language, tone, non-verbal cues, and listening actively to understand the needs and perspectives of others.

By adapting their behaviors, competent communicators can build rapport, foster understanding, and promote effective communication exchanges. They are mindful of the social and cultural dynamics at play, and they strive to communicate in a way that is respectful, inclusive, and conducive to achieving mutual goals.

In summary, competent communicators understand that effective communication is not a one-size-fits-all approach. They adjust their behaviors to the person and situation, demonstrating flexibility and adaptability in order to enhance communication effectiveness.

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Competent communicators achieve effectiveness mostly by adjusting their behaviors to suit the person they are communicating with and the situation they find themselves in. While other factors, like having a broad vocabulary or giving feedback, play a part in effective communication, the former is considered the most crucial.

Research suggests that competent communicators achieve effectiveness mostly through adjusting their behaviors depending on the person they are communicating with and the situation they are in. This is option e. of your question. Communicating effectively involves behaviors like active listening, understanding the other person's point of view, being able to express thoughts and ideas clearly, and being polite and respectful. While a broad vocabulary (option b.) can be useful, it is not as crucial as adapting your behavior to fit the situation. Moreover, giving feedback (option d.) is a part of effective communication but not the sole defining factor. Apologizing when offending others (option c.) is also important but it doesn't necessarily make one a competent communicator. Using the same type of behavior in various situations (option a.) might not always work, as different situations and individuals require different communication styles.

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Answer:

see the attachment!

The amount of money that Lisa would have after 9 years is equal to $5,183.2.

Mathematically, compound interest can be calculated by using this formula:

A(t) = P(1 + r/n)^{nt}

Where:

Substituting the given parameters into the compound interest formula, we have;

Future value, A(t) = 4,000(1 + 0.029/2)^{2 × 9}

Future value, A(t) = 4,000(1 + 0.0145)^{18}

Future value, A(t) = 4,000(1.0145)^{18}

Future value, A(t) = 4,000(1.2957968642629875)

Future value, A(t) = $5,183.2.

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Answer:

x < -41/6 or x > -13/6.

Step-by-step explanation:

5/2+x>1/3

x > 1/3 - 5/2

x > 2/6 - 15/6

x > -13/6

x+2 < -29/6

x < -29/6 - 2

x < -41/6

The answer is     x < -41/6 or x > -13/6.

Answer:

x > -13/6 or x < -41/6

Step-by-step explanation:

5/2+x>1/3 or x+2 < -29/6

x > 1/3 - 5/2 or x < -29/6 - 2

x > 2/6 - 15/6 or x < -29/6 - 12/6

x > -13/6 or x < -41/6

Answer:

8 inches

Step-by-step explanation:

Use Pythagorean theorem,

Base² + altitude² = hypotenuse²

15²+ altitude² = 17²

225 + altitude² = 289

           altitude² = 289 - 225 = 64

altitude = √64 = 8 in

Answer:

The altitude of triangle is 8 in.

Step-by-step explanation:

Solution :

Here, we have given that the two sides of triangle are 17 in and 15 in.

Finding the third side of triangle by pythagoras theorem formula :

\({\longrightarrow{\pmb{\sf{{(Base)}^{2} + {(Altitude)}^{2} = {(Hypotenuse)}^{2}}}}}\)

Substituting all the given values in the formula to find the third side of triangle :

\(\begin{gathered}\qquad{\longrightarrow{\sf{{(Base)}^{2} + {(Altitude)}^{2} = {(Hypotenuse)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(15)}^{2} + {(Altitude)}^{2} = {(17)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(15 \times 15)} + {(Altitude)}^{2} = {(17 \times 17)}}}}\\\\\quad{\longrightarrow{\sf{{(225)} + {(Altitude)}^{2} = {(289)}}}}\\\\\quad{\longrightarrow{\sf{{(Altitude)}^{2} = {(289)} - (225)}}}\\\\\quad{\longrightarrow{\sf{{(Altitude)}^{2} = 289 - 225}}}\\\\\quad{\longrightarrow{\sf{{(Altitude)}^{2} = 64}}}\\\\\quad{\longrightarrow{\sf{Altitude = \sqrt{64}}}}\\\\\quad{\longrightarrow{\sf{Altitude = 8 \: in}}}\\\\\quad{\star{\underline{\boxed{\sf{\red{Altitude = 8 \: in}}}}}}\end{gathered}\)

Hence, the altitude of triangle is 8 in.

\(\rule{300}{2.5}\)

By considering the given information that angles 21 and 23 are supplementary and analyzing the properties of supplementary angles and parallel lines, we have proven that segment HI is parallel to segment JK.

To prove that segment HI is parallel to segment JK based on the given information that angles 21 and 23 are supplementary, we can utilize the properties of supplementary angles and parallel lines.

First, let's examine the given figure and information.

We have a capital letter A with serifs, where segment HI represents one of the serifs, and segment JK represents a horizontal line within the letter A.

To begin the proof, we'll make use of the fact that angles 21 and 23 are supplementary.

Supplementary angles are defined as two angles whose measures sum up to 180 degrees.

We can observe that angle 21 is an interior angle of triangle AHI, and angle 23 is an interior angle of triangle AJK.

Since angles 21 and 23 are supplementary, their sum is equal to 180 degrees.

Now, let's assume that segments HI and JK are not parallel.

In this case, if we extend lines HA and JA, they will eventually intersect at point P.

Since the angles formed at the point of intersection are supplementary (angle 21 + angle 23 = 180 degrees), it would imply that angle 21 and angle PJK, as well as angle 23 and angle PHI, are also supplementary.

However, this leads to a contradiction. In the original figure, we can observe that angle 21 and angle PJK do not form a supplementary pair since angle PJK is a right angle (90 degrees) in the letter A.

Therefore, our assumption that segments HI and JK are not parallel must be incorrect.

Consequently, we can conclude that segment HI is indeed parallel to segment JK.

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Answer:

its called a calculator division and multiplication

Step-by-step explanation:

Answer:

m=-7 and h=-12

Step-by-step explanation:

-3m + 9 + 8m=- 26

5m + 9 = -26

add -9 both sides

5m +9 -9 = -26 -9

5m = -35

5m/5 = -35/5

m= -7

5h+18=3(h-2)

5h+18=3h -6

add -3h and -18 both sides

5h+18 -18- =3h -6 -18 -3h

2h = -24

2h/2 = -24/2

h= -12

Hope this helps ^-^

The laplace transform of f(t) is \(F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\) and it's values exists for \(s=w\pm\sqrt{3}wi\).

Given,

\(f(t)=sin^2(wt)\\\\\therefore sin^2x=\frac{1-cos2x}{2}\\\\f(t)=\frac{1-cos2wt}{2}\)

applying laplace transform on both sides,

\(L[f(t)]=L[\frac{1-cos2wt}{2}]\\\\F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\)

The range for values of s for which F(s) exists is when F(s)≥0

\(\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)} \geq0\\\\\frac{1}{2s} \geq\frac{2w}{2(s^2+4w^2)}\\\\2(s^2+4w^2) \geq 2sw\\\\s^2-2sw+4w^2 \geq0\)

using formula to find roots,

\(s=\frac{-(-2w)\pm\sqrt{(-2w^2)-4(4w^2)}}{2}\\\\s=\frac{-(-2w)\pm\sqrt{(12w^2}}{2}\\\\s=w\pm\sqrt{3}wi\)

Thus,  the laplace transform of f(t) is \(F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\) and it's values exists for \(s=w\pm\sqrt{3}wi\).

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The solution of x in the equation 3^(x -4) = 6 is x = 5.63

The equation is given as

3^(x -4) = 6

Apply the law of indices on the expression 3^(x -4) to rewrite it

So, we have

3^x/3^4 = 6

The above equation becomes

3^x = 6 * 3^4

Evaluate the product

So, we have

3^x = 486

Take the logarithm of bot sides

xlog(3) = log(486)

Divide both sides by log(3)

x = log(486)/log(3)

Evaluate

x = 5.63

Hence, the solution of x in the equation 3^(x -4) = 6 is x = 5.63

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The confidence intervals created using the percentile method and the standard error method are not exactly the same for two reasons:

First, the two methods are based on different assumptions about the population distribution of the sample. Second, the percentile method and the standard error method use different formulas to compute the confidence intervals. The standard error method assumes that the population is normally distributed, while the percentile method does not make any assumptions about the distribution of the population. As a result, the percentile method is more robust than the standard error method because it is less sensitive to outliers and skewness in the data. The percentile method calculates the confidence interval using the lower and upper percentiles of the bootstrap distribution, while the standard error method calculates the confidence interval using the mean and standard error of the bootstrap distribution.

Since the mean and percentiles are different measures of central tendency, the confidence intervals will not be exactly the same.

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Answer:

44.80

Step-By-Step Explanation:

Ap3x

Answer:

Step-by-step explanation:

The domain and range of all linear functions is the set of real numbers.

Answer:

The answer is -135

Step-by-step explanation:

We can do 160 times 3 which is 480 for the 3 times he withdrew $160 from his total. (Withdraw means taking, so subtraction).

Then, we do 480 minus 354 which is -135.

The greatest possible value for n(AUB) can be determined by finding the union of sets A and B, considering the maximum number of elements that can be in the union.

The notation n(A) represents the number of elements in set A. Given that n(U) = 16, it indicates that the universal set U contains 16 elements. Set A has 7 elements, and set B has 12 elements. To find the greatest possible value for n(AUB), we consider the maximum number of elements that can be in the union. The union of two sets combines all the elements from both sets without duplicating any common elements.

In this case, the greatest value for n(AUB) occurs when all the elements from both sets A and B are combined without duplication. Therefore, the greatest value for n(AUB) is the total number of elements in both sets A and B, which is 7 + 12 = 19.

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Hello !

\(a - (a - b) - b - (b - a)\\\\= a - a + b - b - b+a\\\\\boxed{= a - b}\)

Answer:

Step-by-step explanation:

a - ( a - b ) - b - ( b - a )

= a - a + b - b - b + a

= a - b

The options that represent an amount and price of gas that Pedro purchased are 19 gallons of gas for $52.25, 16 gallons of gas for $44. So options C and D are correct.

To calculate the amount of gas and the total price that Pedro purchased, we need to use the formula:

Price = Cost per gallon * Number of gallons

Dividing the total price by the cost per gallon will give us the number of gallons purchased. We can then compare this with the given options to see which one(s) match.

Using the given cost per gallon of $2.75, we can check each option:

a) 13.75 gallons of gas for $41.25

Price = $2.75/gallon * 13.75 gallons = $37.81

This option does not match the total price of $41.25, so it is not correct.

b) 22 gallons of gas for $71.5

Price = $2.75/gallon * 22 gallons = $60.50

This option does not match the total price of $71.5, so it is not correct.

c) 19 gallons of gas for $52.25

Price = $2.75/gallon * 19 gallons = $52.25

This option matches the total price of $52.25, so it is correct.

d) 16 gallons of gas for $44

Price = $2.75/gallon * 16 gallons = $44

This option matches the total price of $44, so it is correct.

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Complete question is:

Pedro fills up his truck with gas he paid $2.75 a gallon which of these represents an amount and price of gas that Pedro purchased select all that apply.

a) 13.75 gallons of gas for $41.25

b) 22 gallons of gas for $71.5

c) 19 gallons of gas for $52.25

d) 16 gallons of gas for $44

1. The area of square C is 625 ft². 2. The perimeter of square C is 46 ft. 3. The area of square B is 1456 ft². 4. The length of square A is 4√15 ft.

A key idea in geometry that connects the lengths of a right triangle's sides is known as the Pythagorean Theorem. It says that the hypotenuse's square length, which is the side that faces the right angle, is equal to the sum of the squares of the lengths of the other two sides in a right triangle. It has the following mathematical expression:

a² + b² = c²

1. The area of square C can be found using the Pythagorean Theorem:

a² + b² = c²

Using the area the side is calculates as follows:

Side length of A = √225 = 15 ft

Side length of B = √400 = 20 ft

Now,

15² + 20² = c²

225 + 400 = c²

625 = c²

c = √625 = 25 ft

So the area of square C is:

Area of C = 25² = 625 ft²

2. The perimeter of square C can be found by adding up the side lengths of all three squares:

Perimeter of A = 36 ft, so each side length of A is 9 ft.

Perimeter of B = 48 ft, so each side length of B is 12 ft.

Perimeter of C = Side length of A + Side length of B + Side length of C

Perimeter of C = 9 + 12 + c

We found earlier that c = 25 ft, so we can substitute that in:

Perimeter of C = 9 + 12 + 25 = 46 ft

3. The area of square B can be found using the fact that the areas of squares A, B, and C are related by the equation:

Area of A + Area of B = Area of C

We know the area of A and the area of C, so we can solve for the area of B:

Area of A = 15² = 225 ft²

Area of C = 1681 ft²

Area of A + Area of B = Area of C

225 + Area of B = 1681

Area of B = 1456 ft²

4. Perimeter of B = 64 ft

Side length of B = 64 / 4 = 16 ft

Now we can use the Pythagorean Theorem to find the side length of C:

a² + b² = c²

a = 15 ft (side length of A)

b = 16 ft (side length of B)

c = √(a² + b²) = √(15² + 16²) = √481 = 22 ft

Finally, we can use the Pythagorean Theorem again to find the side length of A:

a² + b² = c²

b = 16 ft (side length of B)

c = 22 ft (side length of C)

a = √(c² - b²) = √(22² - 16²) = √240 = 4√15 ft

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Answer: See explanation

Step-by-step explanation:

x=-(2-2*the square root of 6)/5, about 0.58

or

x=-(2+2*the square root of 6)/5, about -1.38

The values of the x from equation  \(5x^2+4x-4=0\) are  x = 0.5798 and -1.38.

Given that:

Equation:  \(5x^2+4x-4=0\)

To find the values of x that satisfy the equation \(5x^2+4x-4=0\), use the quadratic formula:

\(x = \dfrac{ -b \± \sqrt{b^2 - 4ac}}{ 2a}\)

Compare the equation with \(ax^2 + bx + c = 0\).

Here, a = 5, b = 4, and c = -4.

Plugging in the values to get,

\(x = \dfrac{-4 \± \sqrt{4^2 - 4 \times 5 \times (-4)}}{2 \times 5} \\x = \dfrac{-4 \± \sqrt{16 +80}}{10} \\x = \dfrac{-4 \± \sqrt{96}}{10}\\x = \dfrac{-4 \± {4\sqrt6}}{10}\)

So the solutions for x are calculates as:

Taking positive sign,

\(x = \dfrac{-4 + {4\sqrt6}}{10}\\x = \dfrac{-4 + {9.798}}{10}\\\)

x = 5.798/10

x = 0.5798

Taking negative sign,

\(x = \dfrac{-4 - {4\sqrt6}}{10}\\x = \dfrac{-4 - {9.798}}{10}\\\)

x = -13.798/10

x = -1.38

Hence, the exact solutions for the equation  \(5x^2 + 4x - 4 = 0\)  are x = 0.5798 and -1.38.

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Answer: - 8

Step-by-step explanation:

x/4 - 5 = -7

=> x/4 = -2

=> x = -8

Answer:

x=−8

Step-by-step explanation:

Add 5 to both sides

x/4-5+5=-7+5

x/4=-2

4x/4=4(-2)

x=-8

Using Trigonometry, the BC is 4-√2.

The following trigonometric calculations are performed on a right-angled triangle: To go against the grain or hypotenuse. opposing side/hypotenuse = cos. The word "tan" is short for the bordering or adversarial side. Calculating height and distance is one of the most crucial applications for trigonometry in daily life. The principles of trigonometry are frequently applied in a variety of disciplines, such as criminology, marine biology, aviation, and navigation.

The relationship is represented by the sides' ratio, which is a trigonometric ratio. There are six trigonometric ratios: sine, cosine, tangent, cotangent, secant, and cosecant.

In right angle triangle ABGC by trigonometry

\(sin B = \frac{GC}{ BC}\)

⇒\(sin 45 = \frac{4}{ BC}\)

\(BC = 4\sqrt{2 }\) units

Hence, BC = 4√2

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Answer:

y=m+p

Step-by-step explanation:

take the p to the other side.

p crosses = sighn and becomes +

hence ans = y=m+ p

There are 3 balanced strings in set T.

To count the number of balanced strings in the set T={0, 1, 2}, we can establish a bijection between the set of balanced strings and T itself. A balanced string is defined as a string in which the sum of its digits is a multiple of 3.

We can define a function f: T" -> T that maps each string in T" to T by preserving the balanced property. If a string in T" is already balanced, f returns the string itself. If the string is not balanced, f replaces the last digit with digit that makes the sum a multiple of 3.

By showing that this function is both injective (one-to-one) and surjective (onto), we establish a bijection. The bijection rule states that if two sets have a bijection between them, they have the same cardinality. Therefore, the number of balanced strings is equal to the number of elements in T, which is 3.

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We can write the probabilities as -

P{yellow} =  0.2

P'{yellow} = 0.8

P{yellow} + P'{yellow} = 1

Given is to find the probability of landing on yellow.

Area covered by yellow = {72°/360°} x πr²

Total area =  πr²

We can write the probability as -

P{yellow} =  {72/360} x πr²/πr²

P{yellow} =  {72/360}

P{yellow} =  0.2

P'{yellow} = 1 - P{yellow}

P'{yellow} = 1 - 0.2

P'{yellow} = 0.8

P{yellow} + P'{yellow}  = 0.2 + 0.8 = 1

P{yellow} + P'{yellow} = 1

Therefore, we can write the probabilities as -

P{yellow} =  0.2

P'{yellow} = 0.8

P{yellow} + P'{yellow} = 1

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Converges; the series is a constant multiple of a geometric series. Option A

The given series can be written as:

\(\sum n=1 to \infty 4^{(n+1)} * 5^{(-n)\)

= \(4 * \sum n=1 to \infty (4/5)^n\)

This is a geometric series with first term a=4 and common ratio r=4/5. The series converges if and only if |r| < 1. Here, |r| = 4/5 < 1, so the series converges.

The sum of a convergent geometric series with first term a and common ratio r is given by:

sum = a / (1 - r)

Applying this formula, we get:

sum = 4 / (1 - 4/5) = 4 * 5 = 20

Therefore, the given series converges to 20.

The correct answer is option (a) Converges; the series is a constant multiple of a geometric series.

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Answer:

5. 3\(x^{4}\)

6. id k this one