What is meant by continuity of a function explain with an example?

An integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).

This is the value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

Integral is a term derived form the word integration. Integration in calculus is the opposite of differentiation

Integration is used to get the whole by combining combine slices or smaller portions.

Finding areas, volumes, central points, and many other important things may be done with integration. However, it is simplest to begin by calculating the distance between a function and the x-axis.

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Answer: Zero point eighty four lbs

Step-by-step explanation:

The expression for final velocity is;  [tex]v_{f}[/tex] = [tex]v_{i}[/tex] + at

Change of subject of formula.

Subject of formula is a topic which involve expressing a variable in terms of other variables in a given mathematical expression.

Acceleration of an object is its change in velocity divided by change in time.

From the given question;

a = [tex]\frac{v_{f} - v_{i} }{t}[/tex]

cross multiply to have

[tex]v_{f}[/tex] - [tex]v_{i}[/tex] = at

So that;

 [tex]v_{f}[/tex] = at + [tex]v_{i}[/tex]

    = [tex]v_{i}[/tex] + at

Therefore the expression for final velocity in terms of other variables is;

[tex]v_{f}[/tex] = [tex]v_{i}[/tex] + at

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To find the sale price of the item, we need to multiply the regular price by the discount percentage, then subtract the result from the regular price. In this case, the discount is 45% * $85 = $<<45*.01*85=38.25>>38.25. So the sale price of the item is $85 - $38.25 = $<<85-38.25=46.75>>46.75. Answer: \boxed{46.75}.

Answer:

$46.75

Step-by-step explanation:

Original price: $85

Markdown: 45%

Price: 0.55(85)=$46.75

Sale Price: $46.75

The number of milliliters of acetaminophen for a 55 kg child is 11 ml

Since a Pediatricians prescribe 7 milliliters (ml) of acetaminophen for every 35 pounds of a child's weight, we desire to find how many milliliters of acetaminophen will the doctor prescribe for Jocelyn, who weighs 55 pounds.

First, we need to find the number of milliliters of acetaminophen per pound of child, n

n = number of milliliters, L/mass of child, m

Since

So, substituting the values of the variables into the equation, we have

n = L/m

= 7 ml/35 lb

= 1/ml/5 lb

= 0.2 ml/lb

Since we require the number of milliters of acetaminophen required for a 55 pound child.

Since n = L/m

L = mn

Given that

So, susbstituting the values of the variables into the equation, we have

L = mn

= 55 lb × 0.2 ml/lb

= 11 ml

So, the number of milliliters is 11 ml

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The end behavior of the graph will be that it increases without bound as x approaches positive infinity, and decreases without bound as x approaches negative infinity.

The end behavior of a graph is a description of how the graph behaves as the x-values approach either positive or negative infinity. If the highest degree of the function is odd and the leading coefficient is positive, then the end behavior will be that the graph increases without bound as x approaches positive infinity and decreases without bound as x approaches negative infinity. This can be explained by examining the degree of the function. Since the degree is odd, the highest degree of the function must be an odd power, such as x^3. When x is positive and increasing without bound, the value of the function will also be increasing without bound, since the exponent is positive. Similarly, when x is negative and decreasing without bound, the value of the function will also be decreasing without bound, since the exponent is negative.

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Answer:

10 packages

Step-by-step explanation:

153-63=90 since each package has 9, 90/9 is 10 packages

the algebraic version is

(153-63)/9=x

The factored form of 3x² + 14x + 8 is (3x + 4)(x + 2).

Factor is a number that can be divided evenly into another number. Factors are used in mathematics to simplify equations, calculate percentages, and solve problems. Factors can also be used to identify the greatest common factor (GCF) between two or more numbers. Factors can also be used to find the least common multiple (LCM) of two or more numbers.

This is the product of the two binomials (3x + 4) and (x + 2),which are the factors of the equation.

The process of factoring an equation involves breaking it down into its component parts,

which in this case are 3x² + 14x + 8. The factors of this equation are determined by first finding the greatest common factor (GCF) of the terms, which in this case is 3x + 4.

Then, the GCF is divided by each of the terms to determine the other factor. For example, 3x² / 3x + 4 =x + 2.

When the two factors are multiplied together, the result is the original equation.
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Answer:

It is not possible to make both sides of the mathematical equation 2 ≠ 3 equal by using the Properties of Equality. This is because the equation is already in reduced form and there is no way to simplify it further.

If we try to apply the Properties of Equality to this equation, we can see that it is not possible to make both sides equal. For example, if we try to add or subtract a constant or variable to both sides, the result will not be modified. If we try to multiply or divide both sides by a constant or variable, the result will also not be modified.

Therefore, it is not possible to make both sides of the mathematical equation 2 ≠ 3 equal using the Properties of Equality.

The third polygon must have five sides as well, since the interior angles of the three polygons must add up to 360°.

The interior angle of a regular pentagon is 108°. Therefore, the three pentagons must have a total of 3 x 108° = 324°. The remaining 36° must come from the third polygon, which must also have five sides.

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Answer: y=14

Step-by-step explanation: y is directly proportional to x, meaning that multiplying x by a certain factor would also multiply y by that same factor. x=5 and y=7. If x changes to 10, it means that x is multiplied by a factor of (10/5) = 2. Therefore, y is multiplied by this same factor (2). As a result, 7*2=14

The factors are (3x + 2)(x + 5).

Factorization or factoring is the process of breaking down an entity—such as a number, matrix, or polynomial—into a product of another entity—or factors—that, when multiplied together, give the original number, matrix, or other entity.

Given  3x² + 17x + 10

factors of equation is

In order to factorize this expression, we can split the Middle Term.

If we want to factorize an expression like a x² + b x + c using this method, we need to think of two numbers that are like:

n₁.n₂ = a.c = 3.10 = 30

and n₁ + n₂ = b = 17

3x² + 2x + 15x + 10

= x(3x + 2) + 5(3x + 2)

= (3x + 2)(x + 5)

Hence, the factors are (3x + 2)(x + 5).

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The correct question is

Factorize 3x² + 17x + 10

The volume of a rectangular pyramid with a congruent base and the same height is 1 1/2 cu.in.

In this question we have been given the volume of a rectangular prism which is  4 1/2 cu.in.

We need to find the volume of a rectangular pyramid with a congruent base and the same height.

Volume of rectangular pyramid = 1/3 * length * width * height

And the volume of rectangular prism = length * width * height

So, the relationship between the volumes of the rectangular prism and pyramid which have the same height and base:

Volume of rectangular pyramid = 1/3 * Volume of rectangular prism  

In this question we ahve been given volume of a rectangular prism = 4 1/2 cu.in.

First we write improper fraction 4 1/2 as proper fraction.

4 1/2 = 9/2

From above equation,

volume of rectangular pyramid = 1/3 * 9/2

Volume of rectangular pyramid = 3/2

Volume of rectangular pyramid = 1 1/2 cu.in.

Therefore, the volume of a rectangular pyramid = 1 1/2 cu.in.    

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The complete question is:

The volume of a rectangular prism is 4 1/2 cu.in. What is the volume of a rectangular pyramid with a congruent base and the same height?

The two different types of values for a parameter: Default and user given

The correct answer is an option (2)

In this question we need to select the two different types of values for a parameter.

We know that  a parameter is nothing but a special kind of variable which is used in a function to refer to input of the function.

If no argument value is passed during the function call, then  the function argument will take default value.

In PL/SQL, user given values for a parameter can be prompted to input a value using & character.

The ACCEPT command is used to obtain input from the user.

Therefore, default value and user given values are two different types of values for a parameter.

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The complete question is:

What are the two different types of values for a parameter?

1)    Default and System given

2)    Default and user given

3)    System given and user given

4)    Compile time and run time values

The value of "i" multiplied by the cube is

-i = i³

Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.

Among the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.

In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:

√(-1) = i

From this definition, we can know the value of i³, as a multiplication of the following form:

[√(-1)]² = i²

(-1) = i²

i × (-1) = i× i² = i³

-i = i³

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Answer:

1) (i) dan (iii) karena gradiennya sama "4x"

2) gradien = 1/3

3) gradien = 4/7

4) y = 4/9x - 1/3

5) saya tidak tahu

6) (iii) dan (iv) karena gradiennya sama "3x"

7) y = 3x + 2

8) m = 2 c = -3

9) y = -2/3x + 3

10) g = -4/5

Step-by-step explanation:

1) i) y = 4x +10

ii) y = 2x +3

iii) y = 4x+5

iv) y =-2x +5

(i) dan (iii) karena gradiennya sama "4x"

2) g = (6-0)/(-2-0)

g = 6/-2

g =-3

m1 x m2 = -1

m2 = -1 / (-3)

m2 = 1/3 -----> gradien

3) A(0,0)

Hitung kotaknya

7 -----> Baik

4 -----> ke atas

gradient = 4/7

4) y = mx + c

1 = m(3) - 1/3

1 + (1/3) = m(3)

(4/3) / 3

m = 4/9

y = 4/9x - 1/3

5) saya tidak tahu

6) (iii) dan (iv) karena gradiennya sama "3x"

7) g = (6-3) / (-5-4)

g = -1/3

y - y1 = m (x -x1)

y - (3) = -1/3 (x - 4)

y = -1/3x + 4/3 + 3

y = -1/3x + 13/3

m1 x m2 = -1

m2 = -1 / (-1/3)

m2 = 3

y - y1 = m (x -x1)

y - (-4) = 3 (x - (-2))

y = 3x + 6 - 4

y = 3x + 2

8) g = (1-5) / (2-4)

g = 2

y - y1 = m (x - x1)

y - 5 = m (x - 4)

y = 2x - 8 + 5

y = 2x - 3

m = 2 c = -3

9) -2y = 12 - 3x

y = 3/2x - 6

m1 x m2 = -1

m2 = -1 / (3/2)

m2 = -2/3

y - y1 = m (x - x1)

y - (-1) = -2/3 (x - 6)

y = -2/3x + 4 -1

y = -2/3x + 3

10) g = (-20-0) / ( 0-(-25))

g = -4/5

Saya berharap jawaban saya membantu anda.

The value of the new mechanic box is $94.96.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario

Let the mechanic box be x.

Since the sum of all of the transactions was $239.41 on Saturday, this will be illustrated as:

147.50 + 32.47 + x + 25.32 - 50.64 = 249.41

154.65 + x = 249.41

Collect like terms

x = 249.41 - 154.65

x = 94.96

The mechanic box is $94.96

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The number of people still living has a Binomial (n = 5, p = 2/3)

The probability of all five people still living is

P(X = 5) = (2/3)⁵ ≈ 0.1317

The probability of exactly two people living

P(X = 2) = 10 x (2/3)² (1/3)³ ≈ 0.16

The probability of at least three people still living

P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5)

≈ 0.3292 + 0.3292 + 0.1317

≈ 0.790

Probability is simply the probability that something will happen. Whenever  the outcome of an event is uncertain, we can talk about the probability of a particular outcome, i.e. its likelihood. The analysis of events driven by probability is called statistics.

Probabilities can be expressed numerically by the number of desired outcomes, divided by the total number of outcomes.

Properties:

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The required sets of range of the corresponding functions are illustrated in the below solution part.

The range of a function is the set of all possible output values of the function.

To find the range of a function, we need to evaluate the function at every point in its domain and find the set of all possible output values.

For example, we are given the function f(x) = x² - 2x and the domain (-5, -1, 0, 5, 7). To find the range of this function, we need to evaluate it at every point in its domain, which gives us the following values:

f(-5) = (-5)² - 2 × (-5) = 25 + 10 = 35

f(-1) = (-1)² - 2 × (-1) = 1 + 2 = 3

f(0) = (0)² - 2 × (0) = 0

f(5) = (5)² - 2 × (5) = 25 - 10 = 15

f(7) = (7)² - 2 × (7) = 49 - 14 = 35

The range of the function is therefore the set of all possible output values, which are 3, 0, 15, and 35. Therefore, the range of this function is {3, 0, 15, 35}.

We can use the same method to find the range of the other functions in the questions. The ranges of the other functions are:

6) f(x)=x²-2x & Domain= (-5, -1, 0, 5, 7)

Range: {-1, 3, 0, 15, 35}

7) f(x) = -3x+12) & Domain= (-9, -4, 4, 8, 11)

Range: {0, 15, 36, 39, 48}

8) f(x)=x²-(x/2) & Domain = {4, 8, 12, 30)

Range: {2, 30, 102, 942}

9) f(x)= |x-2x & Domain= (-5, -4,-3, 3, 5)

Range: {-4, -3, 0, 3, 4}

10) f(x) = (x²/2) + 30 & Domain = {-4, -2, 6, 8)

Range: {26, 28, 54, 60}

Thus, the required sets of range of the corresponding functions are illustrated in the above solution part.

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Answer:

a) 3(4) + 8 = 20

b) 2(4)(5) = 40

c) 6(4+5) = 54

d) (5)² - (4)² = 9

explanation:

change x and y with the value given.

Answer: a.20

b. 40

c.54

d. 9

Step-by-step explanation:

a. 3x4=2+8+20

b.2x4x5=40

c.6x9=54

d.25-16=9

The expression 2x²y has in its entirety 1 term.

First let's define what algebraic expressions are.

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

The terms of an expression are identified by the fact that they are separated by means of an addition and subtraction operation:

Since 2x²y has neither addition nor subtraction operations, we can clearly state that it has only one term.

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Kelly's estimate cannot be said to be reasonable because it falls below the range of acceptable number of sunglasses from the given amount in each box.

We are told that Kelly bought 4 boxes.

Now, we are told that each box had either 20, 25, or 30 pairs of sunglasses in it.

Thus;

Minimum number of sunglasses = 20 * 4 = 80 sunglasses

Maximum number of sunglasses = 30 * 4 = 120 sunglasses

Now, we are told that Kelly estimates a reasonable number of sunglasses to be 70.

From our previous calculations, the minimum possible can only be 80 and as such her estimate falls lower and we conclude that it is unreasonable.

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Transformations. Transform is the verb form of change. Therefore, to modify a geometric shape would entail to make certain changes to that shape.

Transforming something into another thing is referred to by the verbs transform, metamorphosis, transmute, convert, and transfigure. Transform suggests a significant shift in form, nature, or function. To completely and instantly modify something or someone so that they are considerably better or more beautiful is to transform them. When you move into a new home, quit your job, or become a parent, you are experiencing "change."

"Transition" refers to the process that takes place before to, during, and following the change event. We experience transition on a bodily, emotional, and psychological level, and we change as a result. Mathematicians define a transformation as a geometric shape or formula alteration that transfers the shape or formula from its pre-image, or original position, to its image, or after-transformation position.

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There are no potential remedies for -15y + 7 + 17y = 2y + 70.

Given,

Unknown to us is that equation.

-15y + 7 + 17y = 2y + 70

The quantity of solutions to the given equation must be determined.

-15y + 7 + 17y = 2y + 70

Modify the terms.

-15y + 17y + = 2y + 70

Conjoin similar terms

2y + 7 = 2y + 70

The equality property of subtraction

2y - 2y = 70 - 7

Conjoin similar terms

0 = 61

However, it is not feasible.

As a result, the provided equation has no solution.

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The square root of k is 192 which is an integer.

Define Trigonometric functions

A right-angled triangle's angle can be related to side length ratios using real-world trigonometric functions.

Given expression is,

12 cos 30° + 2 tan 60°

We know,

cos 30° = √3/2

tan 60° = √3

Now, plug in the values

⇒12 * √3/2 + 2 * √3

⇒6√3 + 2√3

⇒8√3

We know, 8 * 8 = 64

The above value in square root form,

⇒√8*8*3

⇒√192

⇒√k  (where, k is 192 an integer)

Hence, the square root of k is 192 which is an integer.

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The mean for a given set of observations is 3.67.

The mean is the average of a set of variables in mathematics and statistics. The mean may be calculated in a variety of methods, including the simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean. A data set's mean (average) is calculated by summing all of the numbers in the set and then dividing by the number of values in the set. When a data collection is arranged from least to largest, the median is the midway value. The mode is the number that appears the most frequently in a data collection.

Here,

given set of observation,

=1,1,2,4,6,8

=(1+1+2+4+6+8)/6

=3.67

The mean for given set of observation is 3.67.

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Using line tangent, the approximation for f(2.1) is 3.95

Given,

The point (a, f(a)) is on the line tangent to the graph of y = f(x) at x = a, which has a slope of f'(a).

The equation be like;

y - f(a) / (x - a) = f'(a)

y = f'(a) (x - a) + f(a)

Using the provided data and a = 2, we can determine that the tangent line to the graph of y = f(x) at x = 2 has equation

y = f'(2) (x - 2) + f(2)

y = -1/2 (x - 2) + 4

To compute a "approximation of f(2.1) using the line tangent to the graph of f at x = 2," one must substitute x = 2.1 for f in the equation for the tangent line (2.1). You get 2.1 when you plug this in.

y = -1/2 (x - 2) + 4

y = -1/2 (2.1 - 2) + 4

y = -1/2 x 0.1 + 4

y = 3.95

That is,

The approximation for f(2.1) using line tangent is 3.95

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The percentage of the company she owns after selling its specific parts is equivalent to 41.66%.

In mathematics →

Given is that an entrepreneur sells of 1/2 her company to one buyer and 1/6 to another buyer.

Assume that the amount of company left in percentage is equivalent to {R%}. Let the complete company be represented by 100%. The remaining percent of company after selling half of it can be written as -

100 - {1/2 x 100} = 100 - 50 = 50%.

The remaining percent of company after selling 1/6 of it can be written as -

{R%} = 50 - {1/6 x 50} = 50 - 8.34 = 41.66%
{R%} = 41.66%

Therefore, the percentage of the company she owns after selling its specific parts is equivalent to 41.66%.

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{Complete question is given below -

An entrepreneur sells 1/2 of her company to one buyer and 1/6 to another buyer. What percent of the company does she have left?}

The values are

Define Rounding Numbers

Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $23.4476 with $23.45, the fraction 312/937 with 1/3.

Round Values to Nearest Tenth :

To round the decimal number to its nearest tenth, look at the hundredth number. If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth's place.

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To prove a congruence statement, you need to demonstrate that two figures are congruent by showing that they have the same size and shape. This can be done by showing that they have the same lengths for corresponding sides and the same measures for corresponding angles. Alternatively, congruence can be proved using transformations, such as translation, rotation, and reflection.

For instance, given that ABCDEF, side AB corresponds to side DE because each is made up of the first two letters, side AC corresponds to side DF because each is made up of the first and last letters, and side BC corresponds to side EF because each is made up of the last two letters.

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