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Therefore, we can rationalize the denominator of a fraction containing a radical by taking the methods outlined above.

Components of fractions are the numbers in the numerator and denominator (and ratios). The denominator, which is the smallest number, represents the greatest possible number of parts that can be put together to create a whole. You can tell how many parts you have by looking at the numerator, which is the greatest number. It might not be the whole thing! If the denominator is 0, that is bad. Division by zero is prohibited. If the denominator is a 1, our fraction is actually an integer.

Here,

we can rationalize a radical-containing fraction's denominator by doing the following:

Step 1: In order to eliminate the radical from the denominator, multiply the numerator and denominator by a radical.

Verify in step two that all radicals have been streamlined.

Step three is to simplify the fraction, if necessary.

Therefore, we can rationalize the denominator of a fraction containing a radical by taking the methods outlined above.

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The given equation t = s/5 represents a proportional relationship and the value of the constant of proportionality is 1/5.

The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.

Proportional relationships are written in the form y = kx

where k is the constant of proportionality.

The given equation below which is given in the question:

t = s/5

The above equation represents a proportional relationship.

According to the given question, k = 1/5 so the answer is 1/5.

Thus, the value of the constant of proportionality is 1/5.

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So the number of parcels that Helen delivered on Monday ​is 120 parcels.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

An equality of two ratios is a percentage. We use proportions to construct comparable ratios and find solutions to problems involving unknown numbers.

If on Wednesday Helen delivered 50% fewer parcels than on Tuesday, then on Tuesday Helen delivered 72 / (1 - 0.5) = 72 * 2 = 144 parcels.

On Tuesday Helen delivered 20% more parcels than on Monday, so the number of parcels Helen delivered on Monday is (144 / 1.2) = 120

So Helen delivered 120 parcels on Monday.

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The total number of such committees that may be created, divided by the prime numbers that divide N, is 81.

In the scenario presented in this question, a club with 11 men and 12 women must elect a committee from among its members in order for there to be one more woman on the committee than males.

The committee might consist of only 1 person or up to 23 people.

Let N represent the maximum possible number of such committees.

The total number of prime numbers that divide N must be determined.

The number of ladies chosen will be m.

The number of guys who were not chosen would thus be:

11 - (m - 1) = 12 - m

Each pairing of men who were not chosen and women who were chosen represents a committee choice.

Since selecting 12 people from a total of 23 would result in m women and 12 - m males, the committee chose:

making use of a combination formula

N = 23C12

N = 23!/12!(23 - 12)!

N = 1352078

These are the main components of 1352078: 2, 7, 13, 17, 19, and 23.

Consequently, the prime number total would be,

2 + 7 + 13 + 17 + 19 + 23 = 81

The total of the prime numbers is thus 81.

The complete question is:

A club consisting of 11 men and 12 women needs to choose a committee from among its members so that the number of women on the committee is one more than the number of men on the committee. The committee could have as few as 1 member or as many as 23 members. Let N be the number of such committees that can be formed. Find the sum of the prime numbers that divide N.

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yes it  is the same as that of all students at Faber GPAs as 2.32 and lower will mean that a track team athlete will be recommended for extra tutoring and population is 2.3* student number

What is the definition of a population?

In ordinary usage, a population is a distinct group of individuals with shared citizenship, identity, or characteristics. In statistics, a population is a representative sample of a larger group of people (or even things) with one or more characteristics in common.

When the distribution is normal, we use the z-score formula.

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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No, Both will not have the same amount of comic books because they add the same number each month.

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Adrian started with 12 comic books and buys 4 more each month.

Rory started with 8 comic books and buys 4 more each month.

let x be the number of books.

A(x) = 4x+12

Rory starts with 8 comic books and add 4 comic books each month.

R(x) = 4x+8

Hence, Both will not have the same amount of comic books because they add the same number each month. There will be 4 additional comic books for Adrian.

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Answer: 24 bunches of cilantro

Step-by-step explanation:

1. Set a proportion with the given information, which should be 1/1.60 = x/38.40.

2. Cross multiply. Now the equation should 1.60x = 38.40.

3. Divide by 1.60 to get x alone to find out how many bunches of cilantro you can buy with $38.40. This should give you x = 24 bunches of cilantro.

Answer:

24 bunches

Step-by-step explanation:

The person below is correct

Index notations are as follows:

a) 2³

b) 3²

c) 6³ * 8³

d) 3³ * 4²

A number's exponent demonstrates how many times we are multiplying a given number by itself. 3^4, for instance, indicates that we are multiplying 3 by four. 3*3*3*3 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable.

Let's break down the given index notation one by one:

a) 2 is taken 3 times = 2³

Similarly,

b) 3²

c) 6³ * 8³

d) 3³ * 4²

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The number of real solutions of a quadratic equation depends on the sign of the discriminant.We can find discriminant by using discriminant formula.

A real solution in algebra is simply a solution to an equation that is a real number. there can be 0, 1, or 2 solutions to a quadratic equation depending on whether the expression inside the square root sign (b2 - 4ac), is positive, negative, or zero.

When the discriminant value is positive we get two real solutions. When the discriminant value is zero we get one real solution. When the discriminant value is negative we get a pair of complex solutions.

So that we can find real solution of quadratic equation by finding discriminant of given equation.

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By plot in graph, we get Y=6 and x=-1 is perpendicular lines.

Parallel lines are lines in a plane that are always the same distance apart and never intersect. They are coplanar lines that do not intersect each other, and they have the same slope.

Perpendicular lines are lines that intersect at a right angle (90 degrees). In other words, they are lines that are at a 90-degree angle to each other. The slope of perpendicular lines are opposite reciprocals of each other, meaning that if one line has a slope of m, the other line will have a slope of -1/m.

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The evaluation of the expression 2(b + 4) when b = 4 is 18

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

Expression: 2(b + 4)

Values: b = 5

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

2(b + 4) = 2 * (5 + 4)

Evaluate the products

This gives

2(b + 4) = 10 + 8

Evaluate the like terms in the equation

So, we have the following representation

2(b + 4) = 18

Using the above as a guide, we have the following:

The solution is 18

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For the expression to be negative (m + p) < 2.

An expression is a group of terms and mathematical symbols which can be evaluated to a given value.

Since we have the expression -2 + (m + p), we need to determine the value of (m + p) for which the value of the expression is negative.

This implies that the value of the expression is less than zero.

So, we proceed as follows.

Since the expression is -2 + (m + p), for it to be negative, it must be less than zero.

So, -2 + (m + p) < 0

⇒ -2 < -(m + p)

Dividing both sides by -1, we have that

-2/-1 < -(m + p)/-1

2 > (m + p)

(m + p) < 2

So, for the expression to be negative (m + p) < 2.

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The circumference of the circle is 2πr.

The circumference of a circle is the distance around the outside of the circle. It is given by the formula C = 2πr, where C is the circumference, π is the mathematical constant approximately equal to 3.14 and r is the radius of the circle. In other words, the circumference is equal to the diameter times pi.

For the given question,

The formula of the circumference of the circle,

C = 2πr

where r is the radius of the circle.

Hence we can conclude that the circumference of the circle is 2πr.

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The values of x are 16, 15, and 13 respectively after balancing equations 19 - 17 = x - 13, 18 - x = 19 - 16, and 17 - 12 = 18 - x.

It is thought that a number's simplest form is represented by its smallest equivalent fraction. finding the simplest form: what to do. For shared factors, look into the numerator and denominator. Examine a fractional integer to determine if it is a prime number. An equation is a statement that has two equal sides and an equal sign in the middle. In the general form of any equation, the degrees of all the variables are listed in descending order. The common representation of a linear equation is an x + b = 0. x + b y + c = 0 is the general form of a two-variable linear equation (or something similar). Identity or conditional equations are the two categories under which equations fall. An identity holds true regardless of how the variables are valued.

given

balancing equations

a) 19 - 17 = x - 13

x = 16

b ) 18 - x = 19 - 16

x = 15

c) 17 - 12 = 18 - x

x = 13

The values of x are 16, 15, and 13 respectively after balancing equations 19 - 17 = x - 13, 18 - x = 19 - 16, and 17 - 12 = 18 - x.

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Therefore , As a result, y=Sin will be the equation of the sinusoid that answers the supplied equation problem (2x).

An equation is a representation of two equal variables in mathematics, one on each side of a "equals" sign. Common difficulties can be solved using equations. We commonly seek pre algebra help to resolve problems in real life. Pre-algebra lessons address the fundamental concepts of mathematics.

Here,

Given: Maximum: 210

Minimum: 10

Time : 90

In order to create a sinusoid equation:

When x=0, sin(2*0)=sin(0)=0.

If x = 4 then sin(4 / 2) = 1.

Sin(π) = 0 if x =π/2 and

Consequently, the sinusoid's equation will be y=Sin (2x)

Therefore , As a result, y=Sin will be the equation of the sinusoid that answers the supplied equation problem (2x).

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The domain of the equation is (A) All real numbers and the range of the equation is (A) y≥-4.

The range of values that can be plugged into a function is known as its domain. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).

The domain of the equation is (A) All real numbers because the value of x is all real numbers.

and the range of the equation is (A) y≥-4, because the value of variable y is greater than and equal to -4 for all values of x.

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As per the concept of graph, the name of the point where the two axes cross is origin.

Graph in math is defined as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

Here we have to identify the name of the point where the two axes cross.

As we all know that the horizontal axis in the coordinate plane is called the x-axis and the vertical axis is called the y-axis.

Here we have also know that the point at which the two axes intersect is called the origin.

Where the origin is at 0 on the x-axis and 0 on the y-axis.

And these intersecting x- and y-axes divide the coordinate plane into four sections

Finally all these four sections are called quadrants.

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Answer:25.5 divided by 3= answer I think

Step-by-step explanation:

The measure of  angle B is m ∠B = 107°.

What is similar triangles?

Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects include all equilateral triangles and squares with any side length. To put it another way, if two triangles are similar, then their corresponding angles and sides are congruent and equal in size.

Given:   Δ NPZ ~ Δ HBZ

As the triangles NPZ and triangle HBZ are similar that means the corresponding angles are congruent.

⇒ ∠N = ∠H,  ∠P = ∠B,  ∠Z = ∠Z

Since,

∠P = (8x - 37)°,  ∠Z = 42°,  ∠H = (2x - 5)°

⇒ 2x - 5 = ∠H,  ∠B = 8x - 37,  Z = 42°

Since, the sum of three angles of triangle is 180°.

⇒              ∠H + ∠B + ∠Z = 180°

(2x - 5)° + (8x - 37)° + 42° = 180°

                10x - 42° + 42° = 180°

                                  10x = 180°

                                     x = 18°

So,

∠B = (8x - 37)° = 8(18) - 37 = 144 - 37 = 107°.

Hence, the measure of  angle B is m ∠B = 107°.

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The amount he will have at the end of 3 years is $1596.55.

Option B is the correct answer.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

P = $1220

r = 9%

n = 12

t = 3 years

Amount = P [tex](1 + r/n)^{nt}[/tex]

A = 1220 [tex](1 + 9/12)^{36}[/tex]

A = 1220 [tex](1 + 0.75)^{36}[/tex]

A = 1220 x [tex]1.75^{36}[/tex]

A = $1,596.55

Thus,

The amount after 3 years is $1596.55.

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The domain of the function f(x) = ∛x + 2 is all real numbers such that x ≥ 0. This is because the cube root function is defined only for non-negative numbers.

What do a function example's range and domain mean?

A straightforward function, such as f(x) = x2, can have a domain (what goes in) of just the counting numbers 1, 2, 3, etc., and a range (what comes out) of the set 1, 4, 9, etc. Another function, g(x) = x2, may have an integer domain of..., -3, -2, -1, 0... 1, 2, 3, and its range is..., 1, 4, 9,...

For the range, the function f(x) = ∛x + 2 is a monotonically increasing function over the domain, which means that it increases as the input x increases. Therefore the range of f(x) = ∛x + 2 is all real numbers greater than or equal to 2

So the domain is x>=0 and the range is y>=2

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The amount of GI is $35,468.

The amount of taxable income is $23,068.

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Gross income = $35,468

Exemption = $12,400

Deduction = 0

Adjustment = 0

Taxable income.

= Gross income - Exemption

= 35,468 - 12,400

= $23068

Thus,

GI and taxable income are $35,468 and $23,068

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The equation of the straight line in slope - intercept form will be y = (1/4)x - 2.

The slope - intercept form of a line is -

y = mx + c                                                     ... { 1 }

where -

{m} is slope of line.
{c} is y - intercept of the line.

Given is the slope of the line as {m} = 1/4 and the y - intercept as {c} = -2.

From Eq { 1 }, we can write the slope - intercept form as -

y = mx + c

y = (1/4)x - 2

Therefore, the equation of the straight line in slope - intercept form will be y = (1/4)x - 2.

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The matrix C shows the inventory of the three products for the three Sports Equipment Corporation stores at the end of July. The value of the entry represented by c22 is 389, which is the value for Store B for Y in Table B.

Table C: Ending Inventory

Product Store A Store B Store C

X 441 278 546

Y 266 389 360

Z 322 814 330

The value of the entry represented by c22 is 389, which is the value for Store B for Y in Table B.

The maximum possible value that a31 can have is 903, which is the value for Store C for Z in Table A.

The value of the entry represented by c22 in the matrix C that shows the inventory at the end of July is 389, and the maximum possible value that a31 can have is 903.

The matrix C shows the inventory of the three products for the three Sports Equipment Corporation stores at the end of July. The value of the entry represented by c22 is 389, which is the value for Store B for Y in Table B. The maximum possible value that a31 can have is 903, which is the value for Store C for Z in Table A. This value indicates that the maximum number of units of Product Z that can be stored in Store C is 903. In summary, the value of c22 in the matrix C is 389, and the maximum value of a31 is 903.

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The result of the operation between two mixed numbers are listed below:

Mixed numbers are real numbers with special notation to transform improper fractions into a combination of integers and fractions. That is:

a b / c = a + b / c

Where a, b, c are integers and c is a non-zero number.

The procedure to simplify the operation is described below:

Case 1

1 3 / 8 ÷ 1 4 / 9

(1 + 3 / 8) ÷ (1 + 4 / 9)

(11 / 8) ÷ (13 / 9)

(11 / 8) / (13 / 9)

99 / 104

Case 2

2 1 / 3 ÷ 1 3 / 4

(2 + 1 / 3) ÷ (1 + 3 / 4)

(7 / 3) ÷ (7 / 4)

(7 / 3) / (7 / 4)

28 / 21

4 / 3

Case 3

4 1 / 5 ÷ 3 1 / 2

(4 + 1 / 5) ÷ (3 + 1 / 2)

(21 / 5) ÷ (7 / 2)

42 / 35

6 / 5

Case 4

5 1 / 5 ÷ 2 1 / 2

(5 + 1 / 5) ÷ (2 + 1 / 2)

(26 / 5) ÷ (5 / 2)

(26 / 5) / (5 / 2)

52 / 25

Case 5

9 1 / 2 ÷ 9 4 / 6

(9 + 1 / 2) ÷ (9 + 4 / 6)

(19 / 2) ÷ (58 / 6)

114 / 106

57 / 53

Case 6

2 2 / 10 ÷ 6 2 / 3

(2 + 2 / 10) ÷ (6 + 2 / 3)

(22 / 10) ÷ (20 / 3)

(22 / 10) / (20 / 3)

(66 / 200)

33 / 100

Case 7

2 1 / 4 ÷ 4 1 / 2

(2 + 1 / 4) ÷ (4 + 1 / 2)

(9 / 4) ÷ (9 / 2)

(9 / 4) / (9 / 2)

18 / 36

1 / 2

Case 8

2 2 / 3 ÷ 1 2 / 3

(2 + 2 / 3) ÷ (1 + 2 / 3)

(8 / 3) ÷ (5 / 3)

(8 / 3) / (5 / 3)

8 / 5

Case 9

5 3 / 5 ÷ 1 2 / 5

(5 + 3 / 5) ÷ (1 + 2 / 5)

(28 / 5) ÷ (7 / 5)

(28 / 5) / (7 / 5)

28 / 7

4

Case 10

4 2 / 3 ÷ 3 1 / 2

(4 + 2 / 3) ÷ (3 + 1 / 2)

(14 / 3) ÷ (7 / 2)

(14 / 3) / (7 / 2)

28 / 21

4 / 3

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Eight 1/2s are in 4. This can be visualized with pattern blocks, as four triangles (each triangle is 1/2) would be needed to make up a square (4).

Visualization is the process of creating graphical representations of data and information. It can take the form of charts, graphs, diagrams, maps, and other visual representations of data and patterns. Visualization can be used to explore, analyze, and communicate data in an effective and meaningful way, helping to make complex data more accessible and easier to understand. Visualization can also help to uncover trends and relationships that might otherwise be difficult to detect.

b. Three 2/3s are in 2. This can be visualized with pattern blocks, as three hexagons (each hexagon is 2/3) would be needed to make up a rectangle (2).
c. Six 1/6s are in 1. This can be visualized with pattern blocks, as six rhombuses (each rhombus is 1/6) would be needed to make up a hexagon (1).

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The fifth term of the given arithmetic sequence is 36.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d

Given that, in a sequence the first term of 4 and the common difference is 8.

Here, a=4 and d=8

Now, the fifth term is

a₅=4+(5-1)×8

= 4+32

= 36

Therefore, the fifth term of the given arithmetic sequence is 36.

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The angle measure of m∠CAF = 23°.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

The angle measures,

m∠EBG = 23°

m∠CAE = 52°

From  the figure,

m∠EBG = m∠FAE = 23°

So, from the figure,

m∠CAE = m∠CAF + m∠FAE

Substituting the angle measures,

52 =  m∠CAF + 23

m∠CAF = 52 - 23

 m∠CAF = 22°

Therefore, 23° is the angle measure of  m∠CAF.

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Answer:

y = 90°

Step-by-step explanation: