How much money will be in an account with an annual interest rate of 7.5% compounded annually, if $5300 was deposited 7 years ago? Be sure to write your answer as money.​

To graph a sequence, let a term's position number [tex]n[/tex] in the sequence be [tex]x[/tex]value.

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.

Starting with a number and repeatedly adding a fixed constant (d) to it is an easy technique to create a series. An arithmetic sequence is this kind of sequence.

Definition: A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence.

The term [tex]a_{n}[/tex] is the corresponding y value

Plot the ordered pairs

Make a table then plot the ordered pairs ([tex]n, a_{n}[/tex])

Position, [tex]n[/tex]                                   Term, [tex]a_{n}[/tex]                                    ([tex]n, a_{n}[/tex])

     1                                                  -15                                        (1, -15)

     2                                                  0                                          (2, 0)

     3                                                  15                                         (3, 15)

     4                                                  30                                        (4, 30)

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Answer: 15.164

Step-by-step explanation:

2. The distance traveled by the remote control car each second is given as follows: C. 3 feet.

3. The equation of the linear function is given as follows: y = -2.5x + 80.

This distance is the rate of change of the output variable relative to the input variable of the linear function, hence it is the slope of the linear function.

Two points on the graph are given as follows:

(0,0) and (1,3).

Then the slope is calculated as the change in the output divided by the change in the input, as follows:

m = (3 - 0)/(1 - 0) = 3.

Meaning that option C is correct.

The linear function in this problem is defined in slope-intercept format, as follows:

y = mx + b.

In which the coefficients are given as follows:

When x = 0, y = 80, hence the intercept is given as follows:

b = 80.

When x increases by 8, y decayed by 20, hence the slope is calculated as follows:

m = -20/8 = -2.5.

This means that the equation is given as follows:

y = -2.5x + 80.

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The slope of the graph of the line is 40.

The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.

Taking any to points on the line point (5, 200) and (10, 400)

Slope = change in y-coordinates / change in x-coordinates

change in y-coordinate = 400 - 200 which is 200

change in x-coordinate = 10 - 5 = 5

slope = 200/5 which is 40

In conclusion the slope of the straight line graph is 40

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When two angles that are located between two co-planar lines on the same side of the transversal are called Alternate external angles.

Alternate External Angles

The pairs of angles outside the two lines and on either side of a transversal that cuts two lines are referred to as the alternate external angles.

In the given diagram below, the alternate exterior angles are:

∠2 and ∠8

∠1 and ∠7

Hence, when two angles that are located between two co-planar lines on the same side of the transversal are called Alternate external angles.

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-464 is the 23rd term of sequence 20,-2,-24

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The sequence is  20,-2,-24...

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is always the same.

In the sequence first term is 20

and common difference is -2-20 is -22

The general term of arithmetic sequence is aₙ=a+(n-1)d

We need to find 23rd term

a₂₃=20+(23-1)(-22)

=20+22(-22)

=20-484

=-464

Hence, -464 is the 23rd term of sequence 20,-2,-24

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Revenue is a calculation or estimation of periodic profits primarily based totally on a particular popular accounting practice or the policies mounted via way of means of a central authority or authorities agency.

The required details for revenue in given paragraph.

What is revenue?

Revenue is simply the profit you earn from your business

Solution;

The number of positive revenues were generated is 6 years

The number of negative revenues were generated in 3 years

smallest revenues were in 2013

Largest revenue was generated in 2020

Actually we are just comparing the data from all previous years and we are also comparing the revenues from them so that we can analyze them and do accounting further

accordingly to multiply the revenues

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The addition of equality states that "if you add on one side, you must add the same number to the other side."

The third term is

-2(3) +5 = -6+5 = -1

The fourth term is

-2(4) + 5 = -8+5 = -3

The fifth term is

-2(5) +5 = -10 +5 = -5

Add these 3 terms together

-1+-3+-5 = -9

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The simplification of the following expression, are;

21. 5t(2)(3) = 30t

24. 9(8n)= 72n

22. 7(a-b+5)= 7a - 7b + 35

25. 3k+ 6k-12 = 9k - 12

23. 9y+ 15y-10y = 14y

26. 2t + 5m+7t-4m = m + 9t

The procedure in mathematics to utilize and analyze the function or expression to make the function or expression uncomplicated or more coherent is called simplifying and the process is called simplification.

We are given the following expression, we need to simplify all of them;

21. 5t(2)(3)

= 30 t

24. 9(8n)

= 72n

22. 7(a-b+5)

= 7a - 7b + 35

25. 3k+ 6k-12

= 9k - 12

23. 9y+ 15y-10y

= 14y

26. 2t + 5m+7t-4m

= m + 9t

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The following constructions are crucial in drawing inscribed circles:

Construct an angle bisector

Construct perpendicular lines

What is the procedure to follow in drawing inscribed circles on an equilateral triangle?

An inscribed circle is a circle drawn in a triangle. An equilateral triangle is a triangle with three equal sides and angles.

The procedure to follow in drawing inscribed circles in such an equilateral triangle is as follows:

You need to construct an angle bisector at each angle of the triangle

Where they meet at the center, is the center of the inscribed circle.

Construct a straight perpendicular line, from the center to one side of the triangles

Set the compass just on the center point, you can change the length to where the perpendicular intersects the triangle to fit in, and construct your inscribed circle.

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Answer:

2

Step-by-step explanation:

After reviewing the derivative of the tangent double , the correct order of the derivative is (a) .

In the question ,

the derivative of the  double tangent is given ,

we have to select the correct order of the derivative .

the function is tan(2x) .

Step 4:   tan(2x) = Sin(2x)/cos(2x)

Step 3 :

expanding sin(2x) and cos(2x) using identity ,

we get ,

= 2sinxcosx/(cos²x - sin²x)

Step 5 :

dividing the numerator and denominator by cos²x .

= [2sinxcosx/cos²x]/[cos²x/cos²x - sin²x/cos²x]

Step 1 : simplifying further,

we get ,

= [2sinx/cosx]/[1 - sin²x/cos²x]

Step 2 : writing sinx/cosx = tanx

we get ,

tan2x = 2tanx/(1 - tanx)

Therefore , the correct order for the given derivative is (a) 4, 3, 5, 1, 2  .

The given question is incomplete , the complete question is

Review the following derivation of the tangent double angle identity. The steps are not listed in the correct order

(a) 4, 3, 5, 1, 2

(b) 4, 5, 3, 1, 2

(c) 3, 4, 5, 1, 2

(d) 3, 4, 1, 5, 2

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Answer:

176366843 / 50000000000

Answer:

[tex]\frac{-2}{567}[/tex]

Step-by-step explanation:

Perimeter of triangles is 6x + 12, 18x + 12, 12x - 9 and 14x - 4.

What is perimeter of a triangle?

The perimeter of any two-dimensional figure is defined as the distance around the figure. Therefore, perimeter of a triangle is sum of three sides of a triangle.

According to the given question:

Perimeter of given triangles is

1) Sum of all sides of triangle 1

  = (x + 6) + (3x + 2) + (2x + 4)

  = 6x + 12

2) Sum of all sides of triangle 2

  = (6x + 4) + (7x + 1) + (5x + 7)

  = 18x + 12

3) Sum of all sides of triangle 3

 = (4x - 3) + (3x) + (5x - 6)

 = 12x - 9

4) Sum of all sides of triangle 4

 = (6x - 8) + (3x + 7) + (5x - 3)

 = 14x - 4

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The value of x will be;

⇒ x = 8 1/4

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ - 1/3 (x + 1 1/2) = - 3 1/4

Now,

Since, The expression is,

⇒ - 1/3 (x + 1 1/2) = - 3 1/4

Solve for x as;

⇒ - 1/3 (x + 3/2) = - 13/4

⇒ x + 3/2 = 13/4 × 3/1

⇒ x + 3/2 = 39/4

⇒ x = 39/4 - 3/2

⇒ x = 39/4 - 6/4

⇒ x = 33/4

⇒ x = 8 1/4

Thus, The value of x will be;

⇒ x = 8 1/4

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we find the restrictions after finding the reciprocal

A division is a process of splitting a specific amount into equal parts.

The values that give a value of 0 in the denominator are the restrictions.

To divide rational expressions, multiply by the reciprocal of the divisor.

The restrictions to the domain of a product consist of the restrictions to the domain of each factor.

To solve this we changes to reciprocal

The reciprocal rule of division method is “Multiply the dividend by the reciprocal of the divisor”.

Hence, we find the restrictions after finding the reciprocal

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The subset of real numbers √3 belong to is irrational numbers

What is a subset ?

If all of the items in a set A are also in a set B, then the sets A and B are subsets of one another. To put it another way, the set A is contained within the set B. A and B stand for the subset connection.

When all the components of Set A are also present in Set B, Set A is said to be a subset of Set B. Alternatively said, Set B contains Set A. Example: If set A contains X and Y and set B contains X, Y, and Z, then set A is a subset of set B because set B also contains X and Y.

As √3 is irrational number

∴it is a  subset of real numbers √3 belong to is irrational numbers

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The value of x which will make the equation 8 + x = 32 true will be 24 thus, option (B) is correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

The equation must be constrained with some constraints.

As per the given equation,

8 + x = 32

Put x = 4

8 + 4 = 12 ≠ 32

Put x = 24

24 + 4 = 32 (so it will be the solution)

Hence "The value of x which will make the equation 8 + x = 32 true will be 24".

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Answer: You are correct

Step-by-step explanation: You are correct with both answers because 9x + 7 and 7 + 9x will equal the same thing. Here's an example

X=3

9(3) + 7

27+ 7

34

7 + 9(3)

7+27

34

34=34

It only equals 34, no matter the order. So, it has one solution.

I hope this helps!

Answer:

Equivalent

Step-by-step explanation:

The expressions 9x+7 and 7+9x are equivalent .The equation has infinite many solutions

The probability that we dealt with two queens as private cards is = 0.0046 .

In the question ,

it is given that ,

the two cards are drawn as private cards,

we have to find the probability that you are dealt with two queens .

the total number of cards in deck is = 52 ,

total number of queens in the deck is = 4 ,

So , the number of ways 2 queens can be drawn from 4 queens is = ⁴C₂ ways .

So , the total number of ways 2 cards can be drawn is = ⁵²C₂

So , the required probability is = ⁴C₂ / ⁵²C₂ .

= 6/1326

= 0.0046

Therefore , the required probability is 0.0046  .

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Consider presenting a particle moving through three dimensions as an illustration. Several x, y, and z-based equations could be used to describe its path.

There are two kinds of parametric equations which are frequently encountered in practical applications.

Circular  Motion:

In parametric equations that model circular motion, sine and cosine have periodic functions for x and y.

Projectile Motion:

The vertical component of projectile motion is quadratic, and the horizontal component is linear.

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Using mathematical operations, we know that the total number of workers in the company is 3,800.

A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.

There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.

Parentheses, Exponents, Multiplication, Division, and Addition Subtraction are also known as PEMDAS (from left to right).

So, we know that 80% of all workers are women.

760 people who work for the company are not women.

Which means:
80% = x

20% = 760

Now, calculate the total workers as follows:

80/x = 20/760

20x = 80 * 760

x = 80 * 760/20

x = 3,040 (Women workers)

Total workers: 3040 + 760 = 3,800 workers

Therefore, using mathematical operations, we know that the total number of workers in the company is 3,800.

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The equation that shows that his hypothesis is wrong is:-

x²+ y²=  25

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

Remove parentheses from each side of the equation and combine similar terms to make it simpler.

To separate the variable term on one side of the equation, use addition or subtraction.

To find the variable, use division or multiplication.

Vladas said that the equation with a squared term is never a function of x.

According to the Pythagorean Theorem, the square of two natural numbers is the third number. When these numbers are used to create a triangle, a right-angled triangle is formed, with a 90° angle between the two smaller sides.

Among the four provided hypotheses:

Option (C) is true since x2+y2=25.

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Answer:

  $13.60

Step-by-step explanation:

You want to evaluate the rental cost function C(x) = 12.00 +0.08x for x = 20.

Put the value for x where x is in the cost function and do the arithmetic.

  C(x) = 12.00 +0.08x

  C(20) = 12.00 +0.08·20 = 12.00 +1.60

  C(20) = 13.60

The total rental cost if Josh drives 20 miles is $13.60.

Answer:

The First One and the last one

Answer:

45

Step-by-step explanation:

it's very easy to do if u know

Answer:

--------------------------

The nth term is visible in the sum:

Apply n = 10 to find the 10th term:

The matching choice is C.