HELP FIND THE AVERAGE RATE OF CHANGE

Arithmetic Progression is a recursive mathematical sequence in which the next term is generated by adding the previous term with a fixed number that is called the Common difference represented by 'd'. This is calculated by the difference between any two terms in the given sequence.

The formula to calculate the 12th term of an Arithmetic Progression is :

                                    =>  [tex]a_{12} = a_{(12-1)} + d[/tex]    

Here, a = first term, n = nth term, and d = common difference

In the given question, First term a = 7, n = 12, and calculating d,

                                 => [tex]d = a_{2} - a_{1}[/tex]  => d = 6

But for a12 we need to find out a11, a10, a9, a8, a7, a6 using the same formula we get :

[tex]a_{6} = 37, a_{7} = 43, a_{8} = 49, a_{9} = 55, a_{10} = 61, a_{11} = 67[/tex]

Now for a12 we have a11 = 67, by using formula :

                                  [tex]a_{12} = a_{11} +d[/tex]

                                  [tex]a_{12} = 73[/tex]

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The 7th term of the Arithmetic Progression (AP) is found using the common difference formula.

In Arithmetic Progression, the difference between the two arithmetical orders is just a constant value (AP). Arithmetic Sequence is another name for it.

We'd come across the few key phrases in AP that were denoted as:

As shown below, the AP can also be described in terms of common differences.

Now, according the given condition in the question.

Let the 5th term is defined by 'a₅'.

Let the 6th term is defined by 'a₆'.

Let the 7th term is defined by 'a₇'.

The common difference of the can be calculated as;

d = a₆ - a₅

Now, for the second case, it could be written as;

d = a₇ - a₆

So,

a₇ = d + a₆.

Therefor, the 7th term of an AP can be computed by adding the common difference to the 6th term of an AP.

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We get the following order:

1, 4, 7, 10, ....

Given that each term has a common difference, this is an arithmetic

sequence. In this instance, the next item in the series is obtained by multiplying the preceding term by 3.

The formula for arithmetic series is as follows:

an = a + (n - 1)d

Our first term is now a1 = 1.

Common variation d=3

Therefore, by entering these numbers into the given formula,

an = 1 + (n-1)3

an = 3n - 2

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The value of the 4 is in the hundredth value.

Answer:

Step-by-step explanation:

yes the answer is correct 100 + 30 = 130

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Answer:

it is correct

Step-by-step explanation:

100

+ 30

___

=130

___

The value of c so that cx-d=2x+4 has No Solution is c=2.

In the given question ,

we have

cx-d=2x+4       ....(i)

Given that d = 2 ,

We substitute the value of d=2 in equation (i)

On substituting we get

cx-2=2x+4

Simplifying further we get

cx=2x+4+2

cx=2x+6

cx-2x=6

x(c-2)=6

x=6/(c-2)

For x to have NO SOLUTION the denominator should be 0.

because when denominator becomes 0 the value becomes not defined , hence will have no solution.

Substituting the denominator = 0

we get c-2=0

c=2.

Therefore , the value of c so that cx-d=2x+4 has No Solution is c=2.

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[tex]3^{9} . 2^{12} .5^{11}[/tex]

Power :

An expression that represents repeated multiplication of the same factor is called a power.

Factor: The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.

the expression 5 x 5. This expression can be written in a shorter way using something called exponents.

5⋅5=5^2

An expression that represents repeated multiplication of the same factor is called a power.

The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.

3 to the first power 3

4^2 4 to the second power or 4 squared 4 ∙ 4

5^3 5 to the third power or 5 cubed 5 ∙ 5 ∙ 5

2^6 2 to the power of six

= [tex](3.5)^{4} (2.3)^{5} (2.5)^{7}[/tex]

= [tex]3^{4+5} .2^{5+7} .5^{4+7}[/tex]

=[tex]3^{9} . 2^{12} .5^{11}[/tex]

Ans : [tex]3^{9} . 2^{12} .5^{11}[/tex]

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The property that justifies the following statement, if 7(x-3)=35 then 35=7(x-3) is the symmetric property.

Symmetric property is one of the properties of equality which states that if there is an equality sign (=) between two values or numbers, then the two values will always remain equal even if you change the sides of the values. Therefore if ab = cd, then cd = ab

Hence, according to this property, the left side of the equation can be transferred to the right side and the right side of the equation can be transferred to the left side as the order of the equation can be ignored.

The symmetric property also justifies that if the values on the two sides are not equal, then they will remain unequal even if the sides are changed. That is if ab ≠ cd, then cd ≠ ab.

So, according to the symmetric property, the statement, if 7(x-3)=35 then 35=7(x-3) is valid.

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Answer:

0.714

Step-by-step explanation:

Argument

The total number of cards = 5 yellow. 3 blue and 7 red = 15 cards in all.

The probability of choosing a yellow card first is 5/15 = 1/3.

We are now down to 14 cards

There are 3 blue cards.

P(yellow then blue) = 1/3 * 3/14

P(yellow then blue) = 1/14 = 0.0714

Answer:

The sum of three and xy is equal to 5

or

The difference of xy and 3 is 5

Step-by-step explanation:

[tex]{ \tt{xy = 5 + 3}} \\ [/tex]

Approximately 291 people can attend the party.

Given,

The rent of the meeting room at the convention center = 400

Additional fee for each person who attends the party = 5.50

The amount raised by the senior class for the party = 2000

Now we have to find the number of people can attend the party.

That is,

Amount raised by seniors – rent of meeting room = 2000 – 400 = 1600

Now,

The number of people can attend the party = (Amount raised by seniors – rent of meeting room) / additional fee for each person

= 1600 / 5.50

= 290.91

That is, approximately 291 people can attend the party.

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Answer:

Answer on screen

Step-by-step explanation:

I hope everything is clear

The rate of change of the volume is  9123 . 185   inches³/min.

What is volume of the sphere?

Volume of sphere is

   V = 4/3 π r³

differentiating with respect to time

[tex]\frac{dv}{dt} = \frac{4}{3} \pi . 3r^{2} . \frac{dr}{dt}[/tex]

[tex]\frac{dv}{dt} = 4\pi r^{2} . \frac{dr}{dt}[/tex]

now [tex]\frac{dr}{dt} = 6 inches/min ,[/tex]     when r = 11

[tex]\frac{dv}{dt} = 4\pi (11)^{2} . 6[/tex]

    = 2904 π      cubic inches per minute

    ≅ 9123 . 185   inches³/min

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you would divide both sides by 2. in this case that would be 2x/2 and 5/2.

The difference between average call time on weekdays and average call time on weekends is 2.98 minutes.

What do I know?

What do I need to know?

What operations, drawings, expressions or formula will I use?

Work:

Difference between average call time on weekdays and average call time on weekends = Average call time on weekends - Average call time on weekdays

= 9.38 - 6.4

= 2.98 minutes

Writing:

The difference between average call time on weekdays and average call time on weekends can be found by subtracting average call time on weekdays from average call time on weekends.

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The laws of parallelogram and triangle methods of adding vectors is compared and the differences are stated.

Triangle Law of Vector Addition

Triangle law of vector addition states that when two vectors are represented as two sides of the triangle with the order of magnitude and direction, then the third side of the triangle represents the magnitude and direction of the resultant vector.

Parallelogram Law of Vector Addition:

The Parallelogram law states that the sum of the squares of the length of the four sides of a parallelogram is equal to the sum of the squares of the length of the two diagonals.

Given,

Here we need to compare and contrast the law of  parallelogram and triangle methods of adding vectors.

While we looking at the definition of the both law,

We have identified that both are performing the sum operation, but Triangle law is for two vectors when the second vector deviates from the direction of the first vector. Note here that second vector starts after the first vector.

Where as in parallelogram law, the two vectors start from the same initial point in two different directions.

So, the laws of parallelogram and triangle methods of adding vectors is compared and the differences are stated.

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4600 is the loan's future value, a, or the total amount due at time t.

What Is Simple Interest?

P=$4000

r=5%

t=3 years

Now we have to find th loans future value A.

So

Simple interest me I=prt=(4000)(.05)(3)=600

Total due is Principal + Interest =4000+600= 4600

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Answer:

Step-by-step explanation:

Length of an arc of a circle = rC  where r = radius and r is the angle in radians

So, the answer is 4000(0.54+0.55)

= 3960 miles.

Geometric Progression is a type of recursive  mathematical sequence in which the next term is generated by multiplying the previous term with a fixed number that is called the Common Ratio represented by 'r'.It is calculated by the ratio of two consecutive terms.

The formula to calculate the 12th term of a Geometric Progression is :              

                                   =>       [tex]a_{12} = a.r^{(12-1)}[/tex]

Here a = first term, r = common ratio calculated by => r=(a2/a1), and n = [tex]n^{th}[/tex] term to find

In the given question, First term a = 10, n = 12, and calculating r,

                                   =>  r = (a2/a1) => r = (20/10) = 2

Calculating,

                         [tex]a_{12\\} = (10).(2^{(12-1)})[/tex] => [tex](10).(2048)[/tex]

                         [tex]a_{12} = 20480[/tex]

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Answer:

This is a geometric sequence since there is a common ratio between each term.

Step-by-step explanation:

2592

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by eren hunter

Answer:  the sequence by 6 gives the next term.

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

Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so basically, the mirroring of a function is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.

The function's reflection should be similar in size and shape to the original function.

f(x)=2x-6; y -axis

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A circle chord exists a straight line segment with both endpoints on a circular arc.

SU goes through the center, R, so SU is a diameter.

Any straight line segment that traverses a circle's center and has ends on the circle exists said to have that circle's diameter in geometric terms. It exists even comprehended as the longest chord of the circle. Both definitions apply to the diameter of a sphere.

The line segment joining any two points on a circle's circumference exists known as the chord. A circle's diameter exists described as the lengthiest chord that passes through its center.

A circle chord exists a straight line with circular arcs at both ends. A secant line, or simply secant, is the infinite line extension of a chord. A chord exists a segment of a line that connects two points on a curve, such as an ellipse.

SU goes through the center, R, so SU is a diameter.

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The word that makes given statement sometime true is: quadratic.

The correct answer is an option (I)

We know that, the domain of a function is the set of all possible values for which function is well defined.

And the range of a function is the set of all output values for given input.

We know that the domain of polynomial function is the set of all real numbers but the range of a polynomial function depends on the polynomial.

In case of a logarithmic function, the domain is the set of all non-negative numbers and the range is the set of all real numbers.

For exponential function, the domain of a function is the set of all real numbers and the range is all positive real numbers.

The domain as well as the range of a quadratic function is the set of all real numbers.

So the given statement would be, "The domain and range of a(n) quadratic function is the set of all real numbers."

Therefore, the word that makes given statement sometime true is: quadratic.

The correct answer is an option (I)

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The value of the reverse permutation is F-¹(3) = 5.

An inverse permutation is one in which each number as well as the number of the place it occupies are swapped.

For, the given values in the question;

So, if you remove the last point, (5,3), the inverse is a function because it contains only the points.

F= {(2, 6), (3, 1), (4, 5), and (5,3)}.

Thus, it can be written as;

F: 2 → 3 → 4 → 5

F: 6 → 1 → 5 → 3.

Thus, F-¹(3); 3 →  5.

F-¹(3) = 5.

Therefore, the value of the reverse permutation is F-¹(3) = 5.

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The sequence  1/4, 1, 4, 16,  . . . . is a geometric sequence and its 10th term is 65,536

To determine whether the sequence is an arithmetic or geometric one, we need to check the relation between two consecutive terms.

If it is an arithmetic sequence, then:

 a(n) = a(n-1) + d

where d is the common difference.

If it is a geometric sequence, then:

 a(n) = a(n-1) . r

where r is the common ratio.

The given sequence is:

   1/4, 1, 4, 16,  . . . .

In this sequence:

a(1) = 1/4

a(2) = 1

a(3) = 4

a(4) = 16

Notice that

a(2) : a(1) = 1 : 1/4 = 4

a(3) : a(2) = 4 : 1 = 4

and so on

Since the ratio of consecutive terms are constant, then the given sequence is a geometric sequence. Furthermore, its ratio, r = 4.

To find the 10th term, use the formula:

a(n) = a(1) . rⁿ⁻¹

Substitute n = 10, r = 4, and a(1) = 1/4

a(10) = 1/4 . 4⁹

a(10) = 4⁸  = 65,536

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Answer:

all integers are rational numbers

The percent decrease is 10.16%

Percent decrease can be calculated by dividing the decrease by the original value and multiplying by 100

The first step is to calculate the decrease

= 4.33 - 3.89

= 0.44

The percent decrease can be calculated as follows

= 0.44/4.33 × 100

= 0.1016 × 100

= 10.16

Hence the percent decrease is 10.16 %

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Answer:

(B)  10.16%

Step-by-step explanation:

Correct on my quiz.

The expression which is equivalent to 7 3/4 subtracted by 1/2 will be ( 31 / 4 ) - ( 2 / 4 ).

We are given a statement:

7 3/4 subtracted by 1/2

We need to write an expression to represent the same.

We know that:

7 3/4 can also be written as an improper fraction as:

31 / 4

And 1 / 2 can be written as an equivalent fraction to 2 / 4.

Subtracting the values, we will get the expression as:

( 31 / 4 ) - ( 2 / 4 )

Therefore, the expression which is equivalent to 7 3/4 subtracted by 1/2 will be ( 31 / 4 ) - ( 2 / 4 ).

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The probability that the break will occur within 20 meters of a pole is 12.5%.

Probability:

The term probability refers the possible occurrence of the required event.

Given,

A 320 meter long tightrope is suspended between two poles.

Here we assume that the line has an equal chance of breaking anywhere along its length.

Now, we need to determine the probability that the break will occur within 20 meters of a pole.

From the given question,

The line has an equal chance of breaking anywhere along its length.

The first and last 20meters form,

=> [ (20 + 20) / 320 ] x 100

=> [ 40 / 320 ] x 100

=> [ 1 / 8 ] x 100

=> 12.5 %.

Therefore, the probability that a break will occur within 20 meters of a pole is about 12.5%.

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