Which of the following is equal to the rational expression when x -2 or 3? A. B. C. D.

The relative frequency table shows the distribution of the data with respect to all 140 people.

Frequency refers to how often something occurs over a given period of time. It can be used to describe the rate of oscillations of a wave, the number of occurrences of a given event, or the rate at which a signal is processed. Frequency is typically measured in hertz (Hz), which is the number of occurrences per second. Frequency can also be expressed in terms of cycles per second (cps), revolutions per minute (rpm), or vibrations per second (vps). Frequency is an important concept in many fields such as physics, engineering, and mathematics.

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Table is attached below:

Answer:

either the exponent is "negative" or else the base is between 0 and 1.

Step-by-step explanation:

Answer: Yes, but it's also exponential decay if the base if between 0 and 1.

Step-by-step explanation: I hope this helps!

A polynomial equation is an equation that consists two or more algebraic terms including at least one variable and constants through the algebraic operation ( addition, substraction, and multiplication).

A polynomial is defined as an equation that has at least one algebraic term with at least one variable and all exponents are integers greater than or equal to 0. The polynomial equation is expressed in the form of aₙ(x), here a is the coefficient, x is the variable and n is the exponent and expanded form is ; F(x) = aₙxₙ + aₙ₋₁ xₙ₋₁ + …….. + a₁x +a₀ = 0

Types of Polynomial Equation : A polynomial equation has mainally four types;

Example of polynomial equations are the following: 1) 3y² + 5y + 20 = 0

2) 5x² - 6x + 9 = 0

3) x² - 3x + 2 = 0

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Fairfax is 15.94 miles more in distance to Manchester than to Hillsboro

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the distance between Manchester and Newton be = 10.94 miles

Let the distance between Newton and Fairfax be = 13.57 miles

Let the distance between Fairfax and Hillsboro be = 8.57 miles

Now , the distance between Manchester and Fairfax = distance between Manchester and Newton + distance between Newton and Fairfax

Substituting the values in the equation , we get

The distance between Manchester and Fairfax = 10.94 + 13.57

The distance between Manchester and Fairfax = 24.51 miles

So , the difference between the distances A = distance between Manchester and Fairfax - distance between Fairfax and Hillsboro

Substituting the values in the equation , we get

The difference between the distances A = 24.51 - 8.57

The difference between the distances A = 15.94 miles

Hence , the distance is 15.94 miles

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Answer:

55%

Step-by-step explanation:

11/20=0.55

0.55 is the same as 55% since 55/100 is 0,55.

[tex]\textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\\\\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\log_2(x-3)+\log_4(x) \\\\[-0.35em] ~\dotfill\\\\ \log_4(x)\implies \stackrel{\textit{change of base rule}}{\cfrac{\log_2(x)}{\log_2(4)}}\implies \cfrac{\log_2(x)}{\log_2(2^2)}\implies \cfrac{\log_2(x)}{2}\implies \cfrac{1}{2}\log_2(x) \\\\[-0.35em] ~\dotfill\\\\ \log_2(x-3)+\log_4(x)\implies \log_2(x-3)+\cfrac{1}{2}\log_2(x)\implies \log_2(x-3)+\log_2(x^{\frac{1}{2}}) \\\\\\ \log_2(x-3)+\log(\sqrt{x})\implies {\Large \begin{array}{llll} \log_2( ~~ \sqrt{x}(x-3) ~~ ) \end{array}}[/tex]

The side with length 5 cm is the hypotenuse.

The given lengths of the sides are 3 cm,4 cm and 5 cm

3²=3×3=9;

4² =4×4=16;

5² =5×5=25;

We found that

9+16=25

3²+4²+5²

Therefore, the triangle is a right-angled triangle.

Note : In any right-angled, triangle the hypotenuse happens to be the longest side.

In this example the side with length 5 cm is the hypotenuse.

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To simplify a complex fraction, we use the following steps:

1- Use various rules of fractions to simplify both the numerator and denominator into a simple fraction. Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator.

2- Use the following rule to evaluate the result.

3- If needed, simplify the rational expression.

A complex fraction in mathematics is one that has another fraction in either the numerator, the denominator, or both. Simplifying difficult fractions is frequently helpful when working with them. This may be accomplished by utilizing a few straightforward procedures and different fractional rules.

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The order of the numbers from least to greatest is given by 0.003,1/5³,3/8,4/7,√5

A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32, etc.

Given here: The numbers are 1/5³ , 4/7,√5,3/8,0.003

To get a clarity of the magnitude of the numbers lets convert every number into decimal numbers.

Now we know To convert a fraction to a decimal, we'll just divide the numerator...by the denominator.

Thus 1/5³=1/125

              =0.008

4/7=0.5714

3/8=0.375

√5=2.2361

and 0.003

Now arranging the numbers from in ascending order we get

0.003,0.008,0.375,0.5714,2.2361

Hence, The order of the numbers from least to greatest is given by 0.003,1/5³,3/8,4/7,√5

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Any complex number can be divided into four categories based on the characteristics of the real component and imaginary part:

Complex numbers are those that are expressed as a+ib, where a and b are actual numbers and I is a fictitious number called a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im).

The real and imaginary halves of a complex number are represented by the first and second values, respectively, of the complex data type in Python.

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Answer:no

Step-by-step explanation:

Let's start with the first method: converting the fractions to the same denominator. First, we'll set up 5/8 and 1/2 side by side so they are easier to see:

Converting Denominator

5

8

&

1

2

Our denominators are 8 and 2. What we need to do is find the lowest common denominator of the two numbers. This is the smallest number that can be divided by both 8 and 2. In this case, the lowest common denominator is 8.

If we multiply the first denominator (8) by 1 we will get 8. If we multiply the second denominator (2) by 4 we will also get 8. We also need to multiply the numerators above the line by the same amounts so that the fraction values are correct:

5 x 1

8 x 1

1 x 4

2 x 4

This is what 5/8 and 1/2 look like with the same denominator:

5

8

&

4

8

Now that these fractions have been converted to have the same denominator, we can clearly see by looking at the numerators that 5 is NOT less than 4 which also means that 5/8 is NOT less than 1/2.

Answer:

in what order are the sides in?

Answer:

No

Step-by-step explanation:

According to the triangle rule, the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side. Let's check this condition:

5 + 15 > 20 ? -> No

So such a triangle cannot exist. And the sides can't be that lengths.

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There are 11649 solutions for the given binomial series x¹ + x² + x³ + x⁴ + x⁵ = 21.

x¹ + x² + x³ + x⁴ + x⁵ = 21, where xi, i = 1, 2, 3, 4, 5, is a non-negative integer such that: 0≤ x1 ≤10 and x², x³, x⁴, x⁵ can range in between 0 to 21.

Now we have to choose the coefficient of x²¹ in the following expression

(1 + x + x² + x³.....+ x¹⁰) (1 + x + x² + x³.......+x²¹)(1 + x + x² + x³.....+ x²¹)(1 + x + x² + x³.....+ x²¹)(1 + x + x² + x³.....+ x²¹)

also we can extend term of x², x³, x⁴, x⁵ from x²¹ upto infinty because it didn't  change the value of x²¹ coefficient . 

(1 + x + x² + x³.....+ x¹⁰) (1 + x + x² + x³.......∞)(1+ x + x² + x³.....+ ∞)(1 + x + x² + x³.....+ ∞)(1 + x + x² + x³.....+ ∞)

(1 - x¹¹)/(1 - x)[1/(1 - x)⁴]

(1 - x¹¹) [1/(1 - x)⁵]

now we have to find only the coefficient of x²¹ for which we consider the coefficient of x²¹ and x¹⁰ in [tex]1-x^{-5}[/tex]

general term of the binomial coefficient is [tex]\binom{n+r-1}{r}[/tex]

[tex]\binom{5+21-1}{21}-\binom{5+10-1}{10}[/tex] = 12650-1001 = 11649

--The given question is incomplete; the complete question is

"How many solutions are there to the equation x¹ + x² + x³ + x⁴ + x⁵ = 21,

where xi, i = 1, 2, 3, 4, 5, is a nonnegative integer such that: 0≤ x¹≤ 10?"--

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Answer:

x = 2

y = 5

Step-by-step explanation:

Brainly doesn't provide online graphing tools, so I will try to walk you through what to do.

First put both equations in slope-intercept form:

y + x = 7  →  y = -x + 7

3y - 6x = 3   →   3y = 6x + 3  →  y = 2x + 1

These are easy to graph now.  

For equation (1), place a point on the y-intercept (0,7), then draw a line with a slope of -1  (down one, over one, down one, over one, etc.).  The x-intercept is (7,0).

For equation (2), the y-intercept is point (0,1).  Draw a line with a slope of 2 (up 2, over 1, up 2, over 1, etc.)  The x-intercept is (-1/2, 0).

Where the 2 lines intersect is the solution.  They should intersect at point (2,5).

The principal of interest 3415 naira, rate = 5% and time 4 yrs and 3 months​ is 4017.64 naira.

In the context of borrowing, principal refers to the initial sum of a loan; it can also refer to the balance still owed on a loan. For instance, the principal of a $50,000 mortgage is $50,000. If you pay off $30,000, the remaining $20,000 constitutes the principal balance.

The principal of a loan determines how much interest you will pay. When you pay a loan off each month, the amount first goes to pay off the interest that has accumulated; only then is the remaining amount applied to the principal. The only way to lower the monthly interest payment is to reduce the loan's principal.

given

I=3415

r=5%

time=4yrs 3 months

=4.25 yrs

we know,

p=Ix100/tr

= 3415x100/4.25x0.05

=4017.64 naira

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Answer: 300

Step-by-step explanation: if ur dividing and you don’t know the divisible, you multiply the answer by the number you divide with, so 10(30) equals 300.

Answer: The smallest critical value is -5

Step-by-step explanation:

Critical values occur at critical points(they give you important information).

In all rational functions, x-intercepts(zeros) and discontinuities need to be considered. So the critical values here are -5, -3, and -2.

Proof by contradiction is a kind of proof that demonstrates the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction.

More broadly, proof by contradiction is a form of argument that shows a statement by arriving at a contradiction, even when the initial assumption is not the disproof of the statement to be proved. In general, proof by contradiction is also known as indirect proof.

A mathematical proof utilising proof by contradiction usually proceeds as follows:

1. The proposition to be proved is P.

2. We consider P to be false, i.e., we assume ¬P.

3. It is then shown that ¬P implies falsehood. This is typically accomplished by deriving two mutually contradictory assertions, Q and ¬Q, and appealing to the Law of noncontradiction.

4. Since assuming P to be false leads to a contradiction, it is concluded that P is, in fact, true.

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The probability that fewer than 58% of the residents in the sample enjoy riding roller coasters is b) 0.433.

What is probability ?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

The mean value is 0.62

Z value formula is

z = (x' -mean)/([tex]\sqrt{n}[/tex])

Substituting the given values, we get -

sigma = Sqrt {[tex](x'-mean)^2[/tex]/n}

Sigma = sqrt { [tex](0.58-0.62)^2[/tex]/75} = 0.09

z = (0.58-0.62)/(0.09)

z = -0.433

Hence , The probability that fewer than 58% of the residents in the sample enjoy riding roller coasters is b) 0.433.

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The likelihood that less than 58% of the sample's residents enjoy going on roller coasters is 0.433.

Probability is the possibility that something will occur. The total number of conceivable outcomes.

The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.

The average is 0.62.

The formula for the Z value is

Z = (x' – mean) ([tex]\sqrt{n}[/tex])

By substituting the provided values, we get -

Sigma Equals [tex]\sqrt{\frac{(x' - mean)^2}{n} }[/tex]

Sigma is equal to sqrt {[tex]{(0.58-062)^2/75[/tex]} = 0.09

z = (0.58-0.62)/(0.09) (0.09)

z = -0.433

Therefore, the likelihood that less than 58% of the sample's residents enjoy riding roller coasters is 0.433.

Option B is the proper response, thus.

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Answer:

6.4166

Step-by-step explanation:

77/12 = 6.41666666667

The length of each side of the triangle is 3 2/3 units

An equilateral triangle can be defined as a type of  triangle having all three sides of equal length.

It is also known as a regular triangle.

Unlike other triangles, an equilateral triangle is one having not only two sides equal like an isosceles triangle but all of its sides equal in length.

The formula for perimeter of an equilateral triangle is expressed as;

P = 3x

Where;

Substitute the values

12x + 33 = 3x

collect like terms

12x - 3x = 33

substract the like terms

9x = 33

Make 'x' the subject

x = 33/9

x = 3 2/3 units

Hence, the value is  3 2/3 units

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Algebraic expressions involving radicals are known as radical expressions.  The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both).

The main symbol attached to any algebraic expression is  x. Each radical expression consists of three separate components: first the "square root" sign itself serves as the radical sign.

The component of the expression inside the radical is known as the radicand

The degree outside the root indicates which root the radical refers to. Expressions without degree symbols have a degree of 2. A cube root is indicated by a degree of 3, a fourth root is shown by a degree of 4, and so on.

Now according to the above expression here, under the root can be any variable like,  2 , 28 , 25, or y7.

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Using the percentage, the amount raised in the first three months is $840

How can I calculate the money raised in three months?

By the conclusion of the academic year, the Helping Hands Student Club hoped to have raised $3,000 for a project.

It has attained 28 percent of its objective after three months.

The following formula can be used to determine how much was raised within the first three months:

amount raised = 28% × 3000

amount raised = 28 / 100 × 3000

amount raised = 84000 / 100

Therefore,

the amount raised in the first three months = $840

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Answer: 16.6667

Step-by-step explanation:

(48 × p) / 100 = 8

((48 × p) / 100) × 100 = 8 × 100

48p = 800

48p / 48 = 800 / 48

p = 16.6666666666667

Percent Increase ≈ 16.6667

A parallelogram and a semicircle both have an area of 264 and 628 square metres, respectively. A = 892 is the total area.

We have a half-circle and a parallelogram.The parallelogram's area is A=basis*height. [tex]A = r^2[/tex], where r is the radius, is the formula for a circle's area (half of diameter). As a result, the half circle's area is equal to

[tex]$A=\frac{\pi r^2}{2}$[/tex]

parallelogram:

b=12

h=22

A=12 × 22

A=264

Half circle:

r=20

A=(3.14 × 20²)/2

A=628

Total Surface Area of the Figure:

A=264 + 628

A=892 .

Half of a circle's surface area makes up a semicircle. As a circle's area is [tex]r^{2}[/tex], Therefore, a semicircle's area is equal to 1/2([tex]r^{2}[/tex]), where r is its radius. 3.14, or 22/7, is the value of.

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Step-by-step explanation:

1. Draw the diagonal BD of length 6 cm as base.

2. Draw perpendicular bisector of DB which intersects DB at O.

3. Take O as centre and draw an arc of 3 cm above and below the line segment BD.

4. Join A, B, C and D.

square.

see attachment....

When a line L is perpendicular to two lines on the plane that intersects line L , then line L is perpendicular to the plane.

We know that two lines are perpendicular to each other if they intersects and these two lines are inclined at angle 90° (right angle)

Perpendicular lines are intersecting lines.

Mathematically, the perpendicular lines are represented by the symbol, ‘⊥‘.

When a line is perpendicular to two lines on the plane then it is perpendicular to the plane.

We can say that when the line L is perpendicular to every line in the plane that intersects line L, then we can say that a line and a plane are perpendicular.

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Dilation is the process by which rectangle ABCD becomes another rectangle ABCD.

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Answer:

The number 25 is not a prime number