Question 9 (2 points)
Evaluate the function f(x), if f(x) = 4x - 2, what is the value of f(3)?
Enter your answer in the box below.
f(3) =

Using Equivalent equation, equation in option (b) i.e 2x+3 = 4 is equivalent to equation, 6x + 9 = 12. So, The Correct option is Option (b) .

Equivalent equation (Algebra) :

Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants. Arrange the terms in the same order, usually x-term before constants. Then equivalent equation are algebaric expression which having same roots or solution .

We have given an expression as

6x + 9 = 12 --(1)

we have to find out an equation out of given options which is equivalent to equation(1) .

firstly , we evaluate the given expresion and find out solution i.e x .

6x + 9 = 12

Substracts 9 from both sides

=> 6x = 12 -9 = 3

both sides dividing by 6

=> x = 3/6 = 1/2

so, 1/2 is solution

Now, we check the options one by one

a) x + 9 = 6

solving it we get, x = 6- 9 = -3

=> not equivalent

b) 2x + 3 = 4

=> 2x = 4 - 3 = 1

=> x = 1/2

same solution as solution of given expresion

c) 3x+9 = 6

=> 3x = 6-9 = -3

=> x =-1

i.e not equivalent

d) 6x + 12 = 9

=> 6x = 9-12 = -3

=> x = -3/6 = -1/2

=> not equivalent

Hence, the required expression is 2x + 3 = 4

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Using the Quadratic function,

a) The age of unmarried women with the highet birth rate is 27.1

b) The highet birth rate of unmarried women is 61.42..

Quadratic Function:

A quadratic function is a polynomial function of degree 2 which can be written in the general form, f(x) = ax²+ bx + c

here a, b , c are real numbers and a not equal to zero.

The quadratic function f(x) will have only the maximum value when the the leading coefficient or the sign of 'a' is negative.

when "a" is negative then maximum value of f(x) is -b/2a .

We have given that,

United State ,the birth rate B of unmarried women (birth per 1000 unmarried women) for women whoe age say a modeled function is

B(a) = −0.30a² + 16.26a −158.90 ---(*)

which is a quadratic function .

comparing (*) with ax²+bx +c = 0

we get, a = - 0.30 , b = 16.26, c = - 158.90

we have to find out the age of unmarried women with highest birth rate .

Highest birth rate means B(a) is maximum.

and using above facts , B(a) is Maximum at -b/2a

a) so, the age of unmarried women with highest birth rate = - b/2a = - 16.26/2×(-0.30) = 27.1

b) birth rate will be highest or max. when a = 27.1

the highet birth rate of unmarried women = B(27.1)

= −0.30(27.1)²+ 16.26(27.1) −158.90

= 61.42

Hence, the age of unmarried women with the highet birth rate is 27.1 and the highet birth rate of unmarried women is 61.42..

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[tex]\huge \boxed{\sf 8+4\sqrt{5} }\\\\\\\displaystyle \sf Four\ lines\ are\ equal \\\\BC+CD+EF+FA = 2 \\\\Pythagorean\ theorem \\\\AB = DE= \sqrt{4^2 + 2^2} = 2\sqrt{5} \\\\ The\ sum\ of\ all\ individual\ segments \\\\ (4)2+(2 )2\sqrt{5}=8+4\sqrt{5}[/tex]

The perimeter of the polygon with the given vertices is 16.94 units.

From the graph:

Polygon ABCDEF with vertices A(0,4),B(2,0),C(2,-2),D(0,-2),E(-2,2) and F(-2,4).

Distance between AB = [tex]\sqrt{(2-0)^2+(0-4)^2}[/tex]

= [tex]\sqrt{2^2+4^2}[/tex]

= [tex]\sqrt{20}[/tex]

we know that opposite sides in polygon are equal.

AB = DE = [tex]\sqrt{20}[/tex]

Distance between BC = [tex]\sqrt{(2-2)^2+(-2-0)^2}[/tex]

= [tex]\sqrt{2^2}[/tex]

= [tex]\sqrt{4}[/tex]

= 2 units.

BC = EF = 2

Distance between CD = [tex]\sqrt{(2-0)^2+(-2+2)^2}[/tex]

= [tex]\sqrt{2^2}[/tex]

= 2

CD = FA = 2

The perimeter of polygon = [tex]\sqrt{20}[/tex] + 2+2+2+2+[tex]\sqrt{20}[/tex]

= 8+2[tex]\sqrt{20}[/tex]

= 8+4[tex]\sqrt{5}[/tex]

= 8+8.94

= 16.94 units

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The positive square root of 5⁴ × 7² using index notation 5²×7

Index notation is a way of writing numbers and letters that have been multiplied by themself multiple times e.g 2×2×2 = 2³

Given: 5(to the power of 4) x 7 (to the power of 2). That is 5⁴ × 7²

In order to find the positive square root of 5⁴ × 7² using index notation, we have to separate the number into two identical parts. Thus:

5⁴×7² = 5²×5²×7×7 = ( 5²×7) × ( 5²×7)

Therefore, the positive square root of 5⁴×7² is 5²×7

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The Rate at which she practices piano per day will be 34 minutes.

We know that Proportional relationships are relationships between two variables like x and y when their ratios got equivalent.

For example,  [tex]\frac{a}{b}[/tex] = [tex]\frac{c}{d}[/tex]. This is the proportional relationship between the variables, a, b, c, and d. In this a is equal to c (a = c) and b is equal to d(b = d).

In our question, the proportional relationship between total minutes (m) and the number of days (d) is given by:
m = 34d.

We need to find the rate, which can be defined as the total minutes spent on practice piano per day.

Minutes spent = m
Days = d

Rate = [tex]\frac{m}{d}[/tex]

So, we know, m  = 34d

[tex]\frac{m}{d}[/tex] = [tex]\frac{34}{1}[/tex] = 34

Hence, The rate is 34 minutes per day.

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The last year's salary was Rs 8250 and he is drawing this year Rs 9075.

What is the percentage of a number?

The percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'  known as percentage symbol.

The monthly salary of Mr. Maharjan was Rs 7500 before last year and it was increased by 10% last year.

So, The last year's Salary was 7500 +750 = 8250

Again, it increased by 20% this year.

Then, Drawings of current year = 7500 + 20% of 7500

7500 + 1500 = 9000

8250 + 10% of 8250 = 9075

Drawings of current year = 9075.

Hence, the last year's salary was Rs 8250 and he is drawing this year Rs 9075.

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The equation 2y  = 10x - 16 in standard form is  10x - 2y = 16 where A = 10, B = - 2 and C = 16

Linear equation can be represented in various form such as general form, standard form, slope intercept form and point slope form.

Therefore, linear equation in standard form can be represented as follows:

Ax + By = C

where

Therefore, let's write 2y  = 10x - 16 in standard  form.

2y  = 10x - 16

Hence,

10x - 2y = 16

Therefore,

A = 10

B = - 2

C = 16

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The order of H can be |H| = 84, or |H| = 210 or |H| = 420.

In the mathematical field of group theory, Lagrange's theorem is a theorem that states that for any finite group G, the order (number of elements) of every subgroup of G divides the order of G.

By Lagrange's Theorem, we know |K| divides |H|, so |H| = 42k for some k (bigger than 1 since K is a proper subgroup of H).

Likewise, 42k divides 840, so k divides 840/42 = 20.

Since H is a proper subgroup of G, we know k < 20,

so either k = 2 , k = 5 or k = 10, and

Hence either |H| = 2(42) = 84, or |H| = 5(42) = 210 or |H| = 10(42) = 420.

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For the given average principal $28650 of per student loan at the rate of interest increases from 5.05% to 6.8% , the amount of interest increases for the period of 10 years is equal to $8424 (nearest dollars).

As given in the question,

Principal amount owed by student for student loan 'P' = $28,650

Rate of interest increases from 5.05% to 6.8%

Time period of repayment of student loan 'T' = 10-years

Interest for the first rate of interest 'R' = 5.05%

Interest = P ×( 1+ R/100)^T

             = 28,650 × ( 1 + 5.05/100 ) ^10

             = 28,650 × ( 1 + 0.0505 )^10

             = 28,650 × 1.63667

             = $46,890.6

Interest for the second rate of interest 'R' = 6.8%

Interest = P ×( 1+ R/100)^T

             = 28,650 × ( 1 + 6.8/100 ) ^10

             = 28,650 × ( 1 + 0.068 )^10

             = 28,650 × 1.930689

             = $55,314.2

Increase in interest amount for increase in rate of interest from 5.05% to 6.8%

=  $( 55,314.2 - 46,890.6 )

= $8423.6

=$8424 ( nearest dollar)

Therefore,  for the given average principal $28650 of per student loan at the rate of interest increases from 5.05% to 6.8% , the amount of interest increases for the period of 10 years is equal to $8424 (nearest dollars).

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There is no solution for the given system of equations, 2x-4y = 6 and -4x+8y = -12, by the elimination method.

According to the question,

We have the following system of equations:

2x-4y = 6 ...(1)

-4x+8y = -12 ...(2)

Now, we will multiply equation 1 by 2 and add the obtained result to equation 2:

2(2x-4y) = 2*6

4x-8y = 12

Now, adding this equation to second one (note that the left hand side will be added to only left hand side):

-4x+8y+4x-8y = -12+12

Now, there is no variable left on the left hand side.

Hence, there is no solution for the given system of equations.

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The combined inventory of the two stores  is  [tex]\frac{7g^{2} }{2} -\frac{4g}{5}+\frac{15}{4}[/tex]

A polynomial is an expression that consists of variables and coefficients in which we can perform addition subtraction and multiplication. Let us understand polynomials with one illustration[tex]x^{2}+x-14[/tex] . In the given illustration, their exists three terms: [tex]x^{2}[/tex], x and 14

According to the given information :

Store A :       [tex]\frac{g^{2} }{2} + \frac{7}{2}[/tex]

Store B :       [tex]3g^{2}-\frac{4g}{5} +\frac{1}{4}[/tex]

Now to find the combined inventory of two stores , we need to find the combination of the above polynomials.

Combining polynomials means adding the polynomials.

Combined inventory = [tex]\frac{g^{2} }{2} + \frac{7}{2} + 3g^{2} -\frac{4g}{5} +\frac{1}{4}[/tex]

By combining the like terms,

Combined inventory = [tex]\frac{g^{2} }{2}+3g^{2} -\frac{4g}{5}+\frac{7}{2}+\frac{1}{4}[/tex]

Combined inventory = [tex]\frac{7g^{2} }{2} -\frac{4g}{5}+\frac{15}{4}[/tex]

The combined inventory of the two stores is  [tex]\frac{7g^{2} }{2} -\frac{4g}{5}+\frac{15}{4}[/tex]

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Answer:

95

Step-by-step explanation:

To find the average you take the sum of the scores and then divide it by the number of exams. Let x equal the score Lucy must obtain on the next math test.

[tex]\frac{85+64+76+x}{4} =80[/tex]

Add the scores and multiply both sides by 4

225 + x = 320

Subtract 225 from both sides

x = 95

Because the p-value is less than 0.05, the null hypothesis should be rejected.

Given,

Null Hypothesis;-

The null hypothesis presupposes that any variation in the selected characteristics you observe in a set of data is the result of chance.

Alternative Hypothesis;-

The alternate response to your research question is the alternative hypothesis (Ha). It asserts that the populace is affected. Your research hypothesis and your alternate hypothesis are frequently identical. Alternatively said, it's the assertion that you anticipate or hope will be accurate.

Here,

Because the p-value is less than 0.05, the null hypothesis should be rejected. The allegation that the proportion of ball bearings with dimension values smaller than 2.20 cm in the current manufacturing process is the same as the proportion in the new process is sufficiently refuted by the evidence.

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The maximize revenue the ticket prices should be $5.5.

Consider a stadium that holds 58, 000 spectators, with ticket prices at $10, with an

Average attendance 5, 000.

Suppose the ticket prices were lowered to $8, then the average attendance rise to 15, 000.

Let R be the revenue, x be the average attendance, p(x) demand

The total revenue function R(x) is,

R (x) = p (x) x

=11 -x/5000*

=11x-x²/5000

Differentiate of R(x) with respect to x.

2x

R'(x) =11 - 2x/5000

=11-x/2500

Set R'(x ) = 0 to solve for x.

X = 27500

Therefore, the average attendance of spectators is 27,500 and, 27,500 fans will buy tickets.

Substitute x = 27,500 in p(x) =11-x/5000

p(x) = 5.5

Therefore, the maximize revenue the ticket prices should be $5.5.

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(a) P( Type -I error) = P (rejecting [tex]H_0[/tex] |  when  [tex]H_0[/tex] is true )

(b)  P( Type -II error)= P(not rejecting  [tex]H_0[/tex] |  when  [tex]H_0[/tex] is false )

Given,

In the question:

We are interested in testing whether or not a coin is balanced based on the number of heads Y on 36 tosses of the coin.

To find the:

a) the value of α

b) the value of β if p = .7

Now, According to the question:

Hypothesis Testing:

The hypothesis testing evaluates two mutually exclusive statements about the population parameters to determine which statement is correct among them. There are two types of error :

1. Type -I

2. Type -II

The data is given as:

X ~ Bin(36, p)

[tex]H_0:p = 0.5\\\\H_1:p \neq 0.5[/tex]

(a) P( Type -I error) = P (rejecting [tex]H_0[/tex] |  when  [tex]H_0[/tex] is true )

                               = P(|X- 18| [tex]\geq[/tex] 4 ; p = 0.5)

                               = 1 - {P(14 < X < 22)}

                               = 1 - {P(X < 22) - P(X < 14)}

                                = 1 -  {P(X ≤ 21) - P(X ≤ 13)}

                                = 1 - {0.87851 - 0.066249}

                                = 0.18774

(b)  P( Type -II error)= P(not rejecting  [tex]H_0[/tex] |  when  [tex]H_0[/tex] is false )

                                  = P(|X- 18| [tex]>[/tex] 4 ; p = 0.7)

                                  = P(14< X < 22)

                                  =  P(X < 22) - P(X < 14)

                                  =  P(X ≤ 21) - P(X ≤ 13)

                                  = 0.091662 - 0.018322

                                  = 0.07334

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The model suggests the equation 3x-4 = 6-2x and the solution is x = 2.

What is equation?

In arithmetic, associate equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =

Main body:

According to question,

there are 3 bars for x and 2 bars for -x  so it shows

The equation becomes :

3x - 4 = 6-2x

5x = 10

x =2

Hence the solution to this equation is 2.

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The relevant parameter of interest for this numerical variable would be the average filling weight of all cereal packages.

What is the standard deviation in statistics?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.

If a machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy. in a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. the population standard deviation is known to be 0.06 pounds.

The parameter of interest is the average filling weight of all cereal packages.

Hence, the relevant parameter of interest for this numerical variable would be the average filling weight of all cereal packages.

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Answer:

Step-by-step explanation:

answer is -25

Answer:

-25

Step-by-step explanation:

-15/1 / 3/5

(-15/1)(5/3) Do reciprocal on the second fraction  

(-5)(5) = -25 Cancel out common factors then multiply

For n is positive integer and d is a digit such that gives the numerical value and satisfied all given conditions. We get the base value i.e n is 9

and d = 2 . So, required value n+d = 11 .

We can start by setting up an equation to convert 32d base n to base 10. To convert this to base 10, it would be 3n²+2n+d. Because it is equal to 263, we can set this equation to 263. Finally, subtract d from both sides to get

3n²+2n = 263-d.

We can also set up equations to convert 324 base n and 11d1 base 6 to base 10. The equation to covert 324 base n to base 10 is 3n²+2n+4. The equation to convert 11d1base 6 to base 10 is 6³+ 6²+6d+1.

Simplify , 6³+6²+6d+1 so it becomes 6d+253. Setting the above equations equal to each other, we have3n²+2n+4 = 6d+253. Subtracting 4 from both sides gets 3n²+2n = 6d+249.

We can then use equations

3n²+2n = 263-d

3n²+2n = 6d+249 to solve for d.

Set 263-d equal to 6d+249 and solve to find that d=2.

Plug d=2 back into the equation 3n²+2n = 263-d. Subtract 261 from both sides to get your final equation of 3n²+2n-261 = 0.

We solve using the quadratic formula to find that the solutions are 9 and -10. Because the base must be positive, n=9.

Adding 2 to 9 we get, n+ d = 9+2 = 11

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It says how many standard deviations the sample mean is away from the population mean.

A population is a collection of associated things or events that are important to a certain subject or experiment. A statistical population can be a group of actual objects or a fictitious, potentially infinite group of things developed from experience. The sample mean is the average value throughout the entire sample. The average value across the entire population is known as the population mean. If the sample was large and random, the sample mean would be a close approximation of the population mean. The standard deviation of a population is determined by taking the square root of the variance of the data set. When making judgments, it is used to compute a confidence interval.

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Shelly needs 168 blocks to cover the area of the square gap

A square is a two-dimensional shape quadrilateral with four sides equal and parallel to each other. The angles in this shape are measured as 90 degrees.

The gap is 36 mm deep and it's length is assumed to be 36 mm too

The area of the gap will be calculated using area of square

Area of square = L²

Area of square = 36²

Area of square = 1296mm²

However, the block has a shape of rectangle and the area of rectangle is given as

Area of Rectangle = L * W

Area of the rectangular blocks = 4 * 2 = 8mm²

The number of blocks required to fill the square gap will be

1296 / 8 = 162 blocks

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The function will be designed in the python computing language

Python is an interpreted, object-oriented, high-level, dynamically semantic programming language. Its straightforward syntax prioritizes readability and makes it simple to understand, which lowers the cost of program sustenance.

The code will be -

def main():

number = int(input('Enter a positive integer: '))

finalSum = addition(number)

print("The integral of this number is ", finalSum, ".")

def addition(num):

if num == 1:

return 1

else:

return num + addition(num-1)

main()

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The integer variable bonus is assigned a value based on the value of the integer variable score

score > 100 implies bonus = 10 * score

score between 50 and 100 implies bonus = score

score < 50 implies bonus = 0

First, we need to analyze the conditions:

score > 100 implies bonus = 10 * score

score between 50 and 100 implies bonus = score

score < 50 implies bonus = 0

Writing the above as programming instructions, we have:

if(score > 100){//This represents the first condition

bonus = 2 * score;

}

else if(score >=50 && score<=100){//This represents the second

bonus = score;

}

else{//This represents the last condition

bonus = 0;

}

Hence, if score > 100 implies bonus = 10 * score

score between 50 and 100 implies bonus = score

score < 50 implies bonus = 0

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"Reflection and dilation" are the series of transformations that would produce a square that was comparable to the original square but not congruent.

Reflection:

Reflection is a method of transformation which it flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance as from mirror line as its mirrored point.

Dilation:

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The relationship between m number of songs downloaded  and the total cost of $20 Mariana receives will be represented by inequality :

1.29m ≤ 20.

Given,

The value of gift card which Mariana have $20.

The costs of each downloaded song is $1.29.

Since m represents the number of songs downloaded and she has in total $20, so the inequality represents the given situation is,

1.29m ≤ 2.

Hence the required inequality is 1.29m ≤ 2.

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Answer:

659.375

Step-by-step explanation:

big brain

use a calculator

To use graphing to solve a set of linear equations.

Using the same rectangular coordinate system, graph the second equation.

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Using the triangle inequality theorem, the possible values for x is: x < 11.

The triangle inequality theorem states that two sides of a triangle, when added together must be greater than the length of the third side of the triangle.

Applying the triangle inequality theorem, we have the following inequality statement:

15 + 3 > 2x - 4

18 > 2x - 4

Add both sides by 4

18 + 4 > 2x - 4 + 4

22 > 2x

Divide both sides by 2

22/2 > 2x/2

11 > x

or  x < 11.

The possible values for x is x < 11.

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For

Example 1: Pair of lines are parallel.

Example 2: Pair of lines are perpendicular.

Example 3: Pair of lines are not parallel nor perpendicular.

Example 4: Pair of lines are perpendicular.

Example 5: Pair of lines are parallel.

Example 6: Pair of lines are parallel.

Example 7: Pair of lines are perpendicular.

Example 8:  Pair of lines are not parallel nor perpendicular.

What is the slope of the line in the slope-intercept form of the line?

If y = mx + c line is given then 'm' represents the slope of the line. If any pair of lines are given and if they have the same value of the slopes then we can say that the given pair of lines will be parallel in nature and if the slope of the one line is the negative inverse of the other line then we can say that the pair of lines are perpendicular to each other.

For example 1:

      y = 3x + 4 and y = 3x +7

     The slopes of both lines are equal hence, these pair of lines are parallel.

For example 2:

     y = -4x + 1 and 4y = x + 3

    Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 3:

     y = 2x - 5 and y = 5x -5

   In this, the slopes are not equal so we can say that the graph of this pair of equations is not parallel nor perpendicular.

For example 4:

     y = -1/3x + 2 and y = 3x - 5

     Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 5:

     y = 3/5x - 3 and 5y = 3x - 10

    The slopes of both lines are equal hence, these pair of lines are parallel.

For example 6:

     y = 4 and 4y = 6

     The slopes of both lines are equal hence, these pair of lines are parallel.

For example 7:

     y = 7x + 2 and x + 7y = 8

     Here, the slope of one line is the negative inverse of the other line hence this pair of lines are perpendicular to each other.

For example 8:

     y = 5/6x - 6 and x + 5y = 4

    In this, the slopes are not equal so we can say that the graph of this pair of equations is not parallel nor perpendicular.

Hence,

Example 1: Pair of lines are parallel.

Example 2: Pair of lines are perpendicular.

Example 3: Pair of lines are not parallel nor perpendicular.

Example 4: Pair of lines are perpendicular.

Example 5: Pair of lines are parallel.

Example 6: Pair of lines are parallel.

Example 7: Pair of lines are perpendicular.

Example 8:  Pair of lines are not parallel nor perpendicular.

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Using the formula of compound interest, the amount compounded annually for 30 years at a rate of 7% is $76,122.55

The compound interest is the interest-based on the initial principal amount and the interest collected over the period of time.  The compound interest formula is given below:

A = P(1 + r/n)^nt

Substituting the values into the equation above;

A = 10000(1 + 0.07/1)^1 * 30

A = $76,122.55

The amount at the end of 30 years is equal to $76,122.55

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