If we were constructing a box with length l , width w , and height = 8 cm, where the length of the box is twice the width, which could we use as a volume function?A)V = 16W2B)V =8w2C)V =16I2D)V = 16I

Answer:

Amount originally invested = $700

Step-by-step explanation:

[This answer assumes that the interest is simple interest.]

We are told that upon investing a certain amount of money for 4 years at a rate of 6%, we get $168 in interest. We are then asked to calculate the amount originally invested.

To solve this problem, we have to use the formula for simple interest:

[tex]\boxed{I = PRT}[/tex],

where:

• I ⇒ interest = $168

• P ⇒ principal (original) amount = $?

• R ⇒ interest rate = 6% = 0.06

• T ⇒ time for which the money is invested = 4 years.

Using the above formula and rearranging it to make P the subject of the equation, we can calculate the principal amount:

[tex]I = PRT[/tex]

⇒  [tex]P = \frac {I}{RT}[/tex]

⇒ [tex]P = \frac{168}{0.06 \times 4}[/tex]

⇒ P = 700

Therefore, the amount originally invested was $700.

the two roots of the equation are x1 = -2.5 and x2 = -1.5.

x1 = -2.5;

x2 = -1.5.

Step 1: Calculate the discriminant

b2 - 4ac = (-2)2 - 4(2)(-3) = 4 + 24 = 28

Step 2: Calculate the roots

x1 = (-b + √D) / 2a = (-(-2) + √28) / 4 = (-2 + 5.29) / 4 = -2.5

x2 = (-b - √D) / 2a = (-(-2) - √28) / 4 = (-2 - 5.29) / 4 = -1.5

We start by calculating the discriminant, which is b2 - 4ac. In this case we have b2 = (-2)2 = 4 and ac = 2(-3) = -6, so the discriminant is 4 + 24 = 28. Then we calculate the two roots, x1 and x2, using the formula x1 = (-b + √D) / 2a and x2 = (-b - √D) / 2a. Substituting in the values we have, x1 = (-(-2) + √28) / 4 = (-2 + 5.29) / 4 = -2.5 and x2 = (-(-2) - √28) / 4 = (-2 - 5.29) / 4 = -1.5. Therefore, the two roots of the equation are x1 = -2.5 and x2 = -1.5.

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the solution to the pair of equations is u = (1,1) and v = (1,0).

u + 3v = (2,1)

3u + v = (3,2)

u = (1,1) and v = (1,0)

The first equation can be written as:

u + 3v = (2,1)

We can rewrite this equation as:

u + 3(1,0) = (2,1)

By substituting the values of i and j, we can solve for u:

u + (3,0) = (2,1)

u = (2-3,1) = (-1,1)

Now, we can substitute the value of u in the second equation:

(1,1) + v = (3,2)

By subtracting (11) on both sides, we can solve for v:

v = (3-1,2-1) = (2,1)

Therefore, the solution to the pair of equations is u = (1,1) and v = (1,0).

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The parametrization of the line of intersection of the two planes is <12, -6, 12>

A parametrization is a way of representing a line or a curve using a set of parameters.

First, we can find the normal vectors of the two planes.

For the first plane, the normal vector is given by <3, -6, -2>, and for the second plane, the normal vector is given by <2, 1, -2>.

The line of intersection will be parallel to the cross product of these two normal vectors, which is <12, -6, 12>.

Plugging in the values from the first plane, we get:

3x - 6y - 2z = 3

3x = 6y + 2z + 3

x = 2y + z + 1

Now that we have a point on the line, we can use this to parametrize the line.

We can use the direction vector <12, -6, 12> and the point <1, 0, 0> to find the parametrization of the line:

x = 1 + t * 12

y = 0 - t * 6

z = 0 + t * 12

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Answer: what grade u in?

Step-by-step explanation:

The rate at which the population of the city was growing was an average of 1.5 million people per year, which can be expressed as an integer or reduced fraction as 3/2.

To break this down further, this means that the city's population was increasing by an average of 416,666 people each month or 14,053 people each day.

This is an impressive rate of growth, especially when considering that the city was already quite large at 5.2 million people. This growth can be attributed to a number of factors, including high levels of immigration, a strong economy, and a booming job market.

Moreover, the growth in population can be seen as a testament to the city's quality of life and its ability to attract new residents.

The population of the city in 1980 was 5.2 million and by 1992 it had grown to 7.6 million. This shows that the rate at which the population of the city was growing was an average of 1.5 million people per year, which can be expressed as an integer or reduced fraction as 3/2.

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Best data tools to represent each information with the options from the image;

Scatter plot - 7th, 9th, 10th and 12th

stem-and-leaf plot - 1st, 3rd, 5th

histogram - 4th, 8th

box-and-whisker plot - 2nd, 6th, 11th

The form in which data is stored, processed, and transmitted is referred to as data representation. Scatter plot are graphs that show the relationship between two variables in a data set eg. to plot heights and weights of a group of people.

Stem-and-leaf plot is a table in which each data value is divided into a "stem" (the first digit or digits) and a "leaf" (usually the last digit) like; To show how many A's, B's, C's, D's and F's there were on a test.

Histogram are graphs that uses rectangles to show the frequency of numerical data such as to plot how many students brought lunch at school each month

Box-and-whisker plot is a graphical method of representing variation in a set of data such as to show the medians of quartiles of the grades on the chapter 5 test for 3rd periods and to show the median score of the basket ball games.

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Todd has 48 words to spell for a puzzle, then he earned $7.35 and he spell correctly 39 words and 9 words missed.

Given that,

Todd has 48 words to spell for a puzzle

His mother offers to pay him 20 cents for each word

If Todd will pay her 5 cents for each word he spells incorrectly,

Let x= number of words Todd spells correctly

48-x = number of words that he misses

In order to avoid the decimals, let's solve this in "cents". Does that make "cents" to you, It means that he gets 20 cents for correct words, he pays 5 cents for words missed, and there is a total income of 735 cents. Here is the equation:

[tex]20*x[/tex] -5(48-x) = 735

[tex]20x[/tex] - 240 + [tex]5x[/tex] = 735

[tex]25x[/tex] - 240 = 735

[tex]25x[/tex] = 735 + 240

[tex]25x[/tex] = 975

[tex]x[/tex] = 39 words correct

48-39 = 9 words missed

So,

39*$.20 -9*$.5 =  $7.35

$780-$45 = $735

Therefore,

Todd has 48 words to spell for a puzzle, then he earned $7.35 and he spell correctly 39 words and 9 words missed.

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Todd has 48 words to spell for a puzzle, then he earned $7.35 and he spells correctly 39 words and 9 words missed.

Given that,

Todd has 48 words to spell for a puzzle

His mother offers to pay him 20 cents for each word

If Todd will pay her 5 cents for each word he spells incorrectly,

Let x= number of words Todd spells correctly

48-x = number of words that he misses

In order to avoid the decimals, let's solve this in "cents". Does that make "cents" to you, It means that he gets 20 cents for correct words, he pays 5 cents for words missed, and there is a total income of 735 cents. Here is the equation:

20x -5(48-x) = 735

20x - 240 + 5x  = 735

25x - 240 = 735

25x = 735 + 240

25x = 975

x = 39 words correct

48-39 = 9 words missed

So,

39*$.20 -9*$.5 =  $7.35

$780-$45 = $735

Therefore,

Todd has 48 words to spell for a puzzle, then he earned $7.35 and he spells correctly 39 words and 9 words missed.

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3(x+5)-2 is 3x + 13.

Knowing this information, all you have to do is find an equivalent expression to 3x + 13.

I'll see you in class tomorrow.

I'm kind of disappointed.

You were my favorite student too.

(and yes, I do have a secret undercover teacher account.)

The cumulative percent frequency for students working less than 20 hours per week is 25%.

In statistics, the frequency of the first-class interval is added to the frequency of the second class, and this sum is added to the third class and so on then, frequencies that are obtained this way are known as cumulative frequency (c.f.). A table that displays the cumulative frequencies that are distributed over various classes is called a cumulative frequency distribution or cumulative frequency table. There are two types of cumulative frequency - lesser than type and greater than type. Cumulative frequency is used to know the number of observations that lie above (or below) a particular frequency in a given data set. Cumulative frequency is the total frequencies showcased in the form of a table distributed in class intervals. There are two types of cumulative frequency i.e. lesser than and greater than, let us learn more about both types.

The number of hours frequency is given as follows:

Number of hours   Frequency  Cumulative frequency

0 - 9                          20                20

10 - 19                       80                100

20 - 29                     200               300

30 - 39                     100                400

So, the cumulative percent frequency  for students working less than 20 hours per week is

= (No. of students working less than 20 hours/ total number of students)* 100

= (100/400)*100

= 25%

Thus, the cumulative percent frequency for students working less than 20 hours per week is 25%.

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The pints of white paint molly used to paint her bedroom walls is 5.58 pints.

Quantity of paint molly used for her bedroom walls= 9.3 pints

Fraction of blue paint= 2/5 of 9.3 pints

= 2/5 × 9.3

= 0.4 × 9.3

= 3.72 pints

Quantity of white paint = Quantity of paint molly used for her bedroom walls - Quantity of blue paint

= 9.3 pints - 3.72 pints

= 5.58 pints

Hence, Molly used 5.58 pints of white paint to paint her bedroom walls.

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First, let's determine what (1/3) to the power of 4 is:

1/3 x 1/3 x 1/3 x 1/3 = 1/81

(1 x 1 x 1 x 1 = 1; 3 x 3 x 3 x 3 = 81)

1/81

Now what is 3 as a decimal?

We have to use the same denominator as 1/81 to be able to do a subtraction:

81 x 3 = 243

3 = 243/81

243/81 - 1/81 = 242/81

The answer is D.

Hope this helps! :) If you have any questions, let me know.

for an approximate result, divide the time value by 3.154e+7

so the answer is 31.71 calendar years

There are approximately 31.71 years in 1 billion seconds. The solution has been obtained by using the unit conversion.

What is unit conversion?

A unit conversion is used to express the same attribute in a different unit of measurement. Instead of using hours to represent time, you could use minutes, and instead of using miles to express distance, you could use feet. Measurements are frequently requested in one set of units, such as chains, but are given in another set, such as feet.

We are given 1 billion seconds which are to be converted into years.

We know that 1 second = 3.171e-8 years

So,

⇒1,000,000,000 seconds = 1,000,000,000 * 3.171e-8

⇒1,000,000,000 seconds = 31.71 years

Hence, there are approximately 31.71 years in 1 billion seconds.

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(D) Statistical significance is achieved when the result is very unlikely to occur by chance. Practical significance is related to whether common sense suggests that the treatment makes enough of a difference to justify its use. It is possible for a treatment to have statistical significance, but not practical significance is correct.

Statistical significance is achieved when the result is very unlikely to occur by chance, and is usually determined by a p-value. Practical significance is related to whether common sense suggests that the treatment makes enough of a difference to justify its use, and is determined by the magnitude of the effect, such as the size of the difference between the treatment and control groups.

It is possible for a treatment to have statistical significance, but not practical significance. This means that the result is unlikely to occur by chance, but the magnitude of the effect may be small and not clinically meaningful. Conversely, a treatment can also have practical significance, but not be statistically significant, meaning that the magnitude of the effect is large enough to be considered important, but the result may not be statistically significant due to a large sample size, for example.

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Distinct prime factors does the product of these numbers have 2,3 , and 5 are the three distinct prime factors

Prime factorization is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers.

Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors.

As we know, a composite number has more than two factors, therefore, this method is applicable only for composite numbers and not for prime numbers.

The numbers must be 4,5 , and 6 .

4+5+6=15 and

4*5*6=120

=2^3*3*5

Distinct prime factors does the product of these numbers have 2,3 , and 5 are the three distinct prime factors.

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Distinct prime factors do the product of these numbers have 2,3, and 5 are the three distinct prime factors

Prime factorization is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers.

Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors.

As we know, a composite number has more than two factors, therefore, this method is applicable only to composite numbers and not to prime numbers.

The numbers must be 4,5, and 6.

4+5+6=15 and

4*5*6=120

=2^3*3*5

Distinct prime factors the product of these numbers have 2,3, and 5 are the three distinct prime factors.

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This system of equations has been solved graphically and their solution is equal to the ordered pair (-1, 2).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

x + 2y = 3     ......equation 1.

-x + 3y = 7     ......equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II and it is given by the ordered pair (-1, 2)

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It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.M is  12.

It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.

The equation is referred to as a linear equation in one variable if just one variable is contained in the linear equation.

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

3 + 0.75m = 12

(3/4)m = 9

m=12

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6.5 m far from the airport can Courtney travel for $12.

What is a linear equation?

It is referred to as the relationship between two variables, and a straight line is produced when the linear equation's graph is shown.

If there is just one variable in the equation, it is referred to as a linear equation in one variable.

A linear equation in algebra is one that only contains a constant and a first-order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.

In Houston, taxis charge $3 plus $.75 per mile for an airport pickup.

3  + 75 m = 78

78 m / 12  = 9

m = 78 / 12  =  6.5 m

6.5 m far from the airport can Courtney travel for $12.

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The area of the composite figure that consists of a half circle and a triangle is calculated as  86.24 cm^2.

The composite figure shown is composed of a half circle and a triangle. Therefore:

The area of the composite figure = area of semicircle + area of triangle = pi*r^2 + 1/2(base * height)

r = 4 cm

Base = 2(4) = 8 cm

Height = 9 cm

Area = 3.14 * 4^2 + 1/2(8 * 9)

= 50.24 + 36

Area of composite figure = 86.24 cm^2

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Answer:

24 bricks will cover a 5.15 meter wall

Step-by-step explanation:

1 meter = 1000 mm

5.15 meters = 5150 mm

5150/215 = 23.9534884

23 bricks will not be enough because 23 x 215 = 4945

24 will be the better option because 215 x 24 = 5160

So 24 bricks will cover a 5.15 meter wall

The domains of the relation are (-3, -2, -1, 2, 4)

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The independent variables are the domain of the relation.

Now,

The coordinates from the graph are:

(2, 0), (4, -1), (-1, 1), (-3, 4), and (-2, 0)

Now,

2, 4, -1, and -3 are the independent variables.

The domains are (-3, -2, -1, 2, 4)

Thus,

The domains are (-3, -2, -1, 2, 4)

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The parabola and line's intersection can be easily determined which the area bounded by two curves is most easily found by integrating with respect to y. So the option A is correct.

We can readily locate the area by looking at the following sketches; the first sketch, integrating with respect to x, is in figure one.

The curve in the first illustration is a parabola and a line, as you can see.

The parabola and line's intersection can be easily determined.

The area between the curves is then calculated using the formula

A = integration from a to b [(higher curve) - (lower curve)] dx,

which means that the first sketch represents the right response.

So, the first option A is correct one.

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The complete question is given below:

Answer:

x [tex]\geq[/tex] 21

Step-by-step explanation:

2x - 10 [tex]\geq[/tex] 52
2x [tex]\geq[/tex] 42
x [tex]\geq[/tex] 21

Answer is 5.54 miles. The decimal digit generally refers to the representation of a number in the decimal number system, often referred to simply as a decimal, or less precisely as a decimal.

How far should the visitor run to minimize the time it takes to reach the coral reef?

Assume she runs up to a point that is x miles to the east of the coral reef: distance running =6 -x miles.

distance swimming = root of x^2+5^2= root of x^2+25.

Times: time= distance / speed time running =6-x/8

time swimming =x^2+25/8 Total time

time running + time swimming:  

T=6-x/8+x^2+25/8

The accepted method of representing integers and non-integers is the decimal number system. It is an extension of the Indo-Arabic numeral system to non-integer values. Decimal notation is a term used to describe how numbers are represented in the decimal system.

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Answer is 5.54 miles. The decimal digit generally refers to the representation of a number in the decimal number system, often referred to simply as a decimal, or less precisely as a decimal.

Assume she runs up to a point that is x miles to the east of the coral reef: distance running =6 -x miles.

distance swimming = root of x²+5²= root of x²+25.

Times: time= distance / speed time running =6-x/8

time swimming =x²+25/8 Total time

time running + time swimming:  

T=6-x/8+x²+25/8

The accepted method of representing integers and non-integers is the decimal number system. It is an extension of the Indo-Arabic numeral system to non-integer values. Decimal notation is a term used to describe how numbers are represented in the decimal system.

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Quadrilateral PQRS was translated 8 units to the right and 7 units up to create quadrilateral P'Q'R'S' using the rule is (x, y) ⇒ (x + 8, y + 7)

Transformation is the movement of a point from its initial location to a new location. Transformation can either be rigid like translation, rotation, reflection or it can be non rigid like dilation.

Translation is a rigid transformation because it preserves the shape and size. Translation is the movement of a point either up, left, right or down in the coordinate plane.

Quadrilateral PQRS was translated 8 units to the right and 7 units up to create quadrilateral P'Q'R'S'.

The rule is (x, y) ⇒ (x + 8, y + 7)

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(a) The probability that a passenger who died was in the third class is 528 / 817.

we can find the probability by using the formula:

P(Third Class | Died) = P(Third Class and Died) / P(Died)

Where,

P(Third Class and Died) = the joint probability of a passenger being in third class and dying

P(Died) = the probability of a passenger dying regardless of class.

We can find P(Third Class and Died) by adding the no. of passengers in third class who died (528) and then dividing by the total no. of passengers (1317)

P(Third Class and Died) = 528 / 1317

Now we can find P(Died) by adding the no. of passengers who died (817) and dividing by the total no. of passengers (1317)

P(Died) = 817 / 1317

By using the values we got, we can find P(Third Class | Died):

P(Third Class | Died) = P(Third Class and Died) / P(Died) = 528 / 817

So, the probability that a passenger who died was in the third class is 528 / 817.

(b) The probability that a passenger survived given they were in first class is 201 / 324

we can find the probability by using the formula:

P(Survived | First Class) = P(Survived and First Class) / P(First Class)

Where,

P(Survived and First Class) = joint probability of a passenger surviving and being in first class.

P(First Class) = probability of a passenger being in first class regardless of survival.

We can find P(Survived and First Class) by adding the no. of passengers in first class who survived (201) and dividing by the total no. of passengers (1317)

P(Survived and First Class) = 201 / 1317

Now we can find P(First Class) by adding the no. of passengers in first class (324) and dividing by the total no.of passengers (1317):

P(First Class) = 324 / 1317

By using the values we got, we can find P(Survived | First Class):

P(Survived | First Class) = P(Survived and First Class) / P(First Class) = 201 / 324

So, the probability that a passenger survived given they were in first class is 201 / 324.

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If T is a linear transformation then the standard matrix of T is [tex]\left[\begin{array}{ccc}1&-19\\0&1\end{array}\right][/tex].

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

The transformation is given as - T : IR² → IR²

Take the (x,y) values as x(1,0) and y(0,1)

(x,y) = x(1,0) + y(0,1)

Apply the transformation -

T(x,y) = T[x(1,0) + y(0,1)]

Since T is a linear map then -

T(x,y) = x T((1,0)) + y T((0,1))

Now, substitute the values -

T(x,y) = x Te1 + y Te2

T(x,y) = x [e1 - 19e2] + y [e2]

T(x,y) = x e1 + e2(-19x + y)

Resubstitute the values back -

T(x,y) = x (1,0) + (0,1)(-19x + y)

T(x,y) = (x , -19x+y)

For T : IR² → IR²

T(x,y) = (ax+by , cx+dy)

Then A = [tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex]

So, now the matrix A is -

A = [tex]\left[\begin{array}{ccc}1&-19\\0&1\end{array}\right][/tex]

Therefore, the matrix is  [tex]\left[\begin{array}{ccc}1&-19\\0&1\end{array}\right][/tex].

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Northern Dancer will take 2 2/5 minutes to run the Belmont stakes

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

2 minutes / (1 1/4 miles) = x / (1 1/2 miles)

We transform the mixed fractions into improper fractions and we have:

1 1/4 =

[(4*1)+1])/ 4=

(4+1) / 4 =

5/4

1 1/2 =

[(2*1)+1] / 2 =

(2+1) / 2 =

3/2

Substituting and clearing the value we get:

2 minutes /5/4 miles = x / 3/2 miles

8/5 = 2x/3

2x = 8/5 * 3

2x = 24/5

x = 24/5 / 2

x = 24/10

x = 12/5 = 2 2/5 minutes

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Correctly written question:

A Horse named Northern dancer won the Kentucky derby with a time of exactly 2 minutes. At this rate, how long would it take Northern dancer to run the Belmont stakes? The Kentucky Derby is  1 1/4 miles in the Belmont stakes is 1 1/2 miles.

function (f-1)(2) = 18 because the derivative of f at a = 2 is 18x2 + 10x.

We can find out how a function is changing at a specific point by looking at its derivative. We are required to calculate (f-1) in this scenario (2). We must first get the derivative of the given function, f(x) = 3x3 + 3x2 + 5x2, in order to perform this. The derivative of each term can be used to achieve this, giving us 9x2 + 6x + 10x. The derivative of f at a = 2 is equal to 18x2 + 10x when this is evaluated at a = 2. Now, by putting the derivative equal to 0 and finding x, we may calculate (f-1)(2). Thus, we obtain x = -1/9. Once this value has been entered, the original method returns (f-1)(2) = 18.

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On solving the provided question, we can say that Hence, there are 26 terms in given arithmetic progression.

A series of numbers known as an arithmetic progression is one in which the difference between each term and the term before it stays constant over the course of the sequence. In this mathematical progression, the constant difference is referred to as the tolerance. A series of numbers is arranged in an arithmetic progression (AP) if the difference between any two consecutive integers is a constant value. additionally known as mathematical order. The gap between succeeding terms in an arithmetic progression is always the same. Because the difference between succeeding phrases is always 2, episodes 3, 5, 7, and 9 are examples of arithmetic.

Clearly, the given sequence is an AP with first term a=5 and common difference d=3.

Let there are n terms in this AP. Therefore,

⇒5+(n−1)3=80

⇒(n−1)3=75

⇒n−1=25

⇒n=26

Hence, there are 26 terms in given AP

To know more about arithmetic progression, visit

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