What is the quotient of the rational expression below?

The value of n(B) in the set is 23

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

n(A) = 108, n(A ∪ B) = 160, and n(A ∩ B) = 43,

The value of n(B) is calculated as

n(A u B) = n(A) + n(B) - n(A n B)

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

160 = 108 + n(B) - 43

This gives

n(B) = 160 + 43 - 180

Evaluate

n(B) = 23

Hence, the solution is 23

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The step-by-step process of making simplified algebraic expressions are shown below

Below are six simplified algebraic expressions with step by step solutions:

1. Simplify: 2x + 3x

Step 1: Combine like terms: 2x + 3x = 5x

Step 2: Simplified expression: 5x

2. Simplify: 7x - 4x

Step 1: Combine like terms: 7x - 4x = 3x

Step 2: Simplified expression: 3x

3. Simplify: 5y + 2y + 3y

Step 1: Combine like terms: 5y + 2y + 3y = 10y

Step 2: Simplified expression: 10y

4. Simplify: 8z - 6z

Step 1: Combine like terms: 8z - 6z = 2z

Step 2: Simplified expression: 2z

5. Simplify: 4a + 6a - 3a

Step 1: Combine like terms: 4a + 6a - 3a = 7a

Step 2: Simplified expression: 7a

6. Simplify: 9b - 7b + 5b

Step 1: Combine like terms: 9b - 7b + 5b = 7b

Step 2: Simplified expression: 7b

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Answer:

Answer: 0, 1, 1, 2, 2, 4, 5, 6, 7, 0, 8, 9

Step-by-step explanation:

1. Start by writing five digits less than 3: 0, 1, 1, 2, 2

2. Then write four digits greater than 3: 4, 5, 6, 7

3. Finally, add three more digits of any value: 0, 8, 9

Answer: False.

Step-by-step explanation:

A concave polygon is a polygon that has at least one interior angle greater than 180 degrees. This means that the polygon has a "cave" or indentation on its interior. However, the fact that a polygon is concave does not automatically mean that one of its diagonals will be drawn outside the polygon. Whether a diagonal is drawn inside or outside the polygon depends on the specific arrangement of the vertices, and cannot be determined solely based on the fact that the polygon is concave.

The answer is 9:2 or 2:9. It depends if there is 9 women and 2 men or 2 women and 9 men.

Mark me branliest. :D

A straight line can be drawn through all the points, and the line passes through the origin. Option C

We know that a relationship is proportional when we can be able to find an association between the variables. It is either the variables are increasing or that the variables are decreasing.

here, we have,

Thus, we would notice that if there is an association between the variables then the graph would be a straight line graph and the graph would have to pass through the origin.

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The value of the function f(g(4)) is C) 4.

The diagram shows that f(1) = 0, f(2) = 1, f(3) = 4, and f(4) = 9. Therefore, the value of f(g(4)) is equal to f(9) = 4.

The other options are incorrect. Option A is incorrect because f(0) is not defined. Option B is incorrect because f(4) is not equal to 0. Option D is incorrect because f(1) is not equal to 9.

Here is the solution in steps:

The diagram shows that f(1) = 0, f(2) = 1, f(3) = 4, and f(4) = 9.

Therefore, the value of f(g(4)) is equal to f(9) = 4.

The other options are incorrect. Option A is incorrect because f(0) is not defined. Option B is incorrect because f(4) is not equal to 0. Option D is incorrect because f(1) is not equal to 9.

Therefore, the answer is C. 4.

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The measure of the angle K is equal to 12.2° approximately to the nearest tenth, using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

For the triangle KLM, by sine rule;

k/sinK = m/sinM = l/sinL

We first derive the angle K as follows:

5.8/sin28° = 2.6/sinK

sinK = (2.6 × sin28°)/5.8

sin K = 0.2105

K = sin⁻¹(0.2105)

K = 12.1517

Therefore, the measure of the angle K is equal to 12.2° approximately to the nearest tenth, using the sine rule.

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The graph will be piecewise. Then the graph of the function is given below.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

S(n) = 0.50n + 3.5, if 1 ≤ n ≤ 14

S(n) = 0                 , if n ≥ 15  

The graph will be piecewise. Then the graph of the function is given below.

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Solution set for y < 3/2 x – 4 is represented by Graph D.

In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal.

Given inequality,

y < 3/2x - 4

Since there is less than sign, the region should be shaded below dotted line.

Equation for the dotted line

y = 3/2x - 4

comparing it with Slope intercept equation,

y = mx + c

slope m = 3/2

y - intercept = - 4 unit.

Only graph D has the shaded part below dotted line.

Hence, Graph D represents  y < 3/2 x – 4.

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The solution of system of equations x is 1 and value of y is 6.

Two or more expressions with an Equal sign is called as Equation.

The  system of equations are y = 2x² - 5x+9 and y = 2x² + 5x - 1

Subtract both the equations

y-y=2x² - 5x+9 -2x² - 5x +1

0=-10x+10

10x=10

Divide both sides by 10

x=1

Now plug in x value in any of the equation.

y=2(1)² - 5(1)+9

y=2-5+9=6

Hence, the solution of system of equations x is 1 and value of y is 6.

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The cost of the cloth to cover the top surface of the box is 1,750.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

Given the rectangular wooden box,

length = 7 m

breadth = 5 m

the top surface of the box is in the shape of a rectangle, to cover the surface with cloth we need to calculate the area of the surface to find the total cloth needed to cover,

area of rectangle = l*b

l = length, b = breadth

A = 7*5

A  = 35 m²

area of the cloth needed  is 35 m²

cost of 1 square meter = 50

cost for 35 m² cloth = 50*35

cost for 35 m² cloth =  1,750

Hence the required cost is 1,750.

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Answer:

5.2

Step-by-step explanation:

8.6 Pounds + P = 14.2 Pounds

-8.6 Pounds -8.6 Pounds

P = 5.2

Rufus gained 5.6 pounds between his first and second visits to the veterinarian.

We have,

To find the number of pounds Rufus gained between visits, we need to subtract his initial weight from his weight at the second visit.

Therefore, we have:

pounds gained = weight at second visit - weight at the first visit

p = 14.2 - 8.6

p = 5.6

Therefore,

Rufus gained 5.6 pounds between his first and second visits to the veterinarian.

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Due to length restrictions, we kindly invite to read the explanation for further details on how to go across the maze with linear functions.

In this problem we find a maze formed by representations of linear functions on Cartesian plane, of which we must determine the slope of each line until finish is reached. This can be done by understanding the following instructions based on results from secant line formula:

The procedure to go across the maze is shown below:

FAIL

SUCCESS

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20(2/5x+3/4y-1/2) = 2(2x+7), 3x-2x+0.5x = 1/2 (16x+30y-20) corresponding expression from column B for each expression in column A

It is necessary to multiply, distribute, add, or take in mathematics. The following is the way an expression is put next to each other: Number, expression, and logical operator The ingredients of a mathematical expression include numerals, variables, and equations (such as addition, subtraction, multiplication or division etc.) It is conceivable to contrast statements with phrases. An phrase, often known as an arithmetic operation, is any logical statement that abstract, numbers, and a mathematical operation between those. For instance, the word m in the formula given is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the phrase 4m + 5.

given

3x-2x+0.5x  =  1/2 (16x+30y-20)

6(x+4)-2(x+5)  =  1.5%

3(x+4)-2(x+4) +0.5(x+4) =  1.5

20(2/5x+3/4y-1/2) = 2(2x+7)

20(2/5x+3/4y-1/2) = 2(2x+7), 3x-2x+0.5x = 1/2 (16x+30y-20) corresponding expression from column B for each expression in column A .

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The set of pairs for which x and y vary inversely is given as follows:

{(-1, -2/7), (4, 1/14), (6, 1/21)}

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse relation, the relation is modeled as follows:

y = k/x.

Meaning that when x increases, y decreases at a constant rate.

The constant is then given as follows:

k = yx.

Hence the third relation is then the relation for which x and y vary inversely, as:

k = -1 x -2/7 = 4 x 1/14 = 6 x 1/21.

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Answer:

5

Step-by-step explanation:

The surface area of the pyramid is 300 square inches.

The surface area of a square pyramid can be calculated by:

The area of the square base is

10 inches * 10 inches = 100 square inches.

Based on the given parameters:

The area of each triangular face is:

(10 inches * 10 inches) / 2 = 50 square inches.

So, the total surface area of the pyramid is:

100 square inches + 4 * 50 square inches = 300 square inches.

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Answer:

D: ( - ∞, 5)

R: [- 3, ∞)

Step-by-step explanation:

The domain is the set of possible x values. The function has values from below five while not including 5(as shown by the open circle). Therefore the domain would be ( - ∞, 5). (Open brackets are non-inclusive while closed brackets are inclusive).

The range is the set of possible y values. The minimum of this graph seems to be at y = -3, and there is not a maximum as while the x values decrease, the y-values infinitely increase. Therefore, the range is [- 3, ∞)

The proportional relationship modeling the number of eggs needed to make x pies is given as follows:

y = 3x.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

3 large eggs, hence the constant of the proportional relationship is given as follows:

k = 3.

Then the equation of the proportional relationship is given as follows:

y = 3x.

Which is a linear function with a slope of 3 and an intercept of zero.

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The equation the line is, y = 3/8 *x - 23/8, equation of the line in POINT-SLOPE form that passes through the given points (5,-1) and (-3,-4).

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have to points (5,-1) and (-3,-4)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

now, solving we get,

3x-8y = 23

equation of the line in POINT-SLOPE form is,

y = 3/8 *x - 23/8

Hence, the required equation is, y = 3/8 *x - 23/8

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The given equation would be, 5(6b-3) - 3b = 0 and b can take infinite number of values to make the equation true.

What equation system has an infinite number of solutions ?

The prerequisite for a situation in which an equation has an endless number of solutions is that the right and left sides of the equation are equal.

The equation is already complete and has infinitely many solutions.

The unknown variable is b, and there are an infinite number of values that b can take to make the equation true.

5(6b-3) - 3b = 0

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Answer:

The range is -11,-4,3,10

Step-by-step explanation:

Answer:

b, education

Sana makatulong

Answer:B. 1.50(5) + 2.00m ≤ 19.00

Step-by-step explanation:This inequality can be used to determine the maximum number of milkshakes that Donna can buy with her $19.00. The expression on the left side of the inequality represents the total cost of her purchase and the expression on the right side of the inequality represents the amount of money she has to spend. Since she must buy 5 ice cream cones, that is represented by the 1.50(5) term. The 2.00m term represents the cost of the milkshakes she can buy, with m representing the number of milkshakes. The inequality states that the total cost of her purchase must be less than or equal to the amount of money she has to spend, so the maximum number of milkshakes she can buy can be determined by rearranging the expression.

If Donna buys 5 ice cream cones, that adds up to, £10.00.

She is then left with £9.00.

9 divided by 1.50 = 6.

She is able to buy 6 milkshakes with the money she has left. However, she is now left with no money.

The answer would be B.1.50(5) +2.00m≤19.00

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Therefore , the solution of the given problem of percentage comes out to be $387.704 is the weekly unemployment amount.

In mathematics, a percentage is any amount that can be stated as a proportion of 100. Also occasionally used are the abbreviations "pct.," "pct," or "pc." But the "%" mark is usually used to indicate it. The proportional amount is flat and lacks any dimensions. Since percentages have a numerator of 100, they can be thought of as fractions. A number should be preceded by the percent sign (%) to denote it is a percent.

Here,

Given :

A weekly unemployment amount is calculated using the following three components:

1. Determine the quarterly wage total (consecutive)

2. Multiply the sum by 26.

3.Multiplying by the rate of unemployment

Calculate the total of a quarterly salaries first:

=> (12950.80 + 12250.10) / 26

=>  25,200.9/26

=> 969.26 * 40 %

=> 387.704

Therefore , the solution of the given problem of percentage comes out to be $387.704 is the weekly unemployment amount.

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You invested $12,000 in the company when you originally started it. Additionally, you borrowed $12,000 for a five-year (long-term) loan and paid back $2,018 of it.

Businesses, a noun in plural. a group of people who are connected or who have joined together. a guest or guests: We're having people over for dinner. a collection of individuals together for social purposes. association, camaraderie, and fellowship She is a lot of joy to be around.

The Old French word "compagnie," which was first used in the Salic code and meaning "one who eats bread with you," is where the English word "company" originates. To describe a "society, friendship, closeness, or body of troops," it was first used in 1150.

You invested $12,000 in the company when you originally started it. Additionally, you borrowed $12,000 for a five-year (long-term) loan and paid back $2,018 of it.

Total Amount to be when start the company is $12000 + $12000

= $24000

Out of which company owns land and a building worth $8,878 and equipment worth $4,230 and have retained $1,291 in earnings to be reinvested in the company, and you decided to put $1,000 of it aside for a long-term investment.

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Answer:

40

Step-by-step explanation:

Assign the variable x to Devaughn's age. If Devaughn is 7 years older than Sydney, then Sydney must be 7 years younger than him, so the expression x - 7 can represent Sydney's age.

The sum of their ages would be x + x - 7 or 2x - 7 which is also said to equal  87. Therefore, this can be written as an equation and be solved accordingly:

2x - 7 = 87

2x = 94

x = 47

Therefore, Devaughn is 47 and Sydney, who is 7 years younger, is 40.

Sydney's age is determined by setting up and solving a simple algebraic equation based on the information provided. The equation that represents this situation is S + (S + 7) = 87, which leads to the conclusion that Sydney is 40 years old.

Devaughn is 7 years older than Sydney. Given that the sum of their ages is 87, we can represent this situation with algebra. Let's denote Sydney's age as S.

Considering Devaughn is 7 years older, we can represent his age as S + 7. Given that the sum of their ages is 87, we can write down this equation: S + (S + 7) = 87.

Solving this equation will help us find Sydney's age. First, simplify the left side: 2S + 7 = 87. Then, subtract 7 from both sides: 2S = 80. Finally, divide both sides by 2 to solve for S, yielding Sydney's age: S = 40.

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Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]\angle B=180^{\circ}-115.5^{\circ}-27.2^{\circ} \longrightarrow \boxed{\angle B=37.3^{\circ}}[/tex]

Using the Law of Sines:

[tex]\frac{AC}{\sin 37.3^{\circ}}=\frac{76.0}{\sin 115.5^{\circ}}\\\\\boxed{AC=\frac{76\sin 37.3^{\circ}}{\sin 115.5^{\circ}} \text{ ft}}[/tex]

[tex]\frac{BC}{\sin 27.2^{\circ}}=\frac{76.0}{\sin 115.5^{\circ}}\\\\\boxed{BC=\frac{76\sin 27.2^{\circ}}{\sin 115.5^{\circ}} \text{ ft}}[/tex]

sin(A) / a = sin(B) / b = sin(C) / c

where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.

The parrot was 12.5 miles from its nest 30 minutes ago.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

Average speed = distance/ time

Since the parrot can fly 5 miles in one hour,

So it can fly 5/2 = 2.5 miles in 30 minutes. (apply the division operation)

So 30 minutes ago, the parrot was 15 - 2.5 = 12.5 (apply the subtraction operation)miles from its nest.

Thus, the parrot was 12.5 miles from its nest.

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