: The given T is a linear transformation from R2 into R2, Show that T is invertible and find a formula for T1. T (x1X2)= (3x1-9x2. - 3x1 +5x2) To show that T is invertible, calculate the determinant of the standard matrix for T. The determinant of the standard matrix is (Simplify your answer.)

If you deposit 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, you will have 347,401.59 in the account in 20 years. You will have 2,545,025.81 if you make deposits for 40 years.

Given that you deposited 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest. Now you have to find out how much money you will have in the account in 20 years and how much will you have if you make deposits for 40 years.

The formula to calculate the future value of an annuity due is:

[tex]FV = PMT \times [(1 + r)^{(n - 1)} / r] \times(1 + r)[/tex]

Where,

FV = Future Value

PMT = Payment (amount) each period

r = Interest Rate per period

n = Number of periods

To find the future value of an annuity due for 20 years:

[tex]FV = 4500 \times [(1 + 0.097)^{(20 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{19} / 0.097] \times (1.097)\\FV = 4500 \times [(6.226)] \times (1.097)\\FV = 347,401.59[/tex]

To find the future value of an annuity due for 40 years:

[tex]FV = 4500 \times [(1 + 0.097)^{(40 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{39} / 0.097] \times (1.097)\\FV = 4500 \times [(38.84)] \times (1.097)\\FV = 2,545,025.81[/tex]

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Answer:15%

Step-by-step explanation:

The pizza would be covered by approximately 100.48 centimeters of the pizza cutter if it is rotated exactly 4 times.

The circumference of a circle can be calculated using the formula:

circumference = π x diameter

where π is approximately equal to 3.14.

Given that the diameter of the pizza cutter is 8 centimeters, we can calculate its circumference as:

circumference = π x diameter

circumference = 3.14 x 8

circumference = 25.12 centimeters

If the pizza cutter is rotated exactly 4 times, it will cover a distance equal to 4 times its circumference:

distance covered = 4 x circumference

distance covered = 4 x 25.12

distance covered = 100.48 centimeters

Therefore, approximately 100.48 centimeters of the pizza would be covered by the pizza cutter if it is rotated exactly 4 times.

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Complete question

The image shows a circular pizza cutter that has a diameter of 8 centimeters. Approximately how many centimeters would the pizza cutter cover if it is rotated exactly 4 times

Answer:

answer is 3

Step-by-step explanation:

Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.

To represent the problem as an equation, we first need to define some variables. Let's let "f" represent the number of fiction books, and "n" represent the number of nonfiction books. We know from the problem that there are 2 times as many nonfiction books as fiction books, so we can write:

n = 2f

We also know that they put the same number of books on each of the 7 bookshelves and put as many as they can on each shelf. Let's call this number "s". We can then write an equation for the total number of books that can fit on the bookshelves:

7s = f + n

Since n = 2f, we can substitute 2f for n in the equation:

7s = f + 2f

Simplifying, we get:

7s = 3f

Finally, we know that any remaining books are put on Ms. Krebs's desk. Let's call this number "r". We can write an equation for the total number of books:

f + n = 7s + r

Substituting 2f for n, we get:

f + 2f = 7s + r

Simplifying, we get:

3f = 7s + r

Now we can solve for "f":

3f = 7s + r

f = (7s + r) / 3

We don't have enough information to solve for "s" or "r", but we can use this equation to find the number of fiction books. For example, if we know that there are a total of 70 books, we can write:

f + n = 70

f + 2f = 70

3f = 70

f = 23.33

Since we can't have a fractional number of books, we would round down to the nearest whole number and get:

f = 23

We could then use the equation f = (7s + r) / 3 to find the number of books on each shelf, assuming there are no books left over:

23 = (7s + 0) / 3

69 = 7s

s = 9.86

Since we can't have a fractional number of books on a shelf, we would round down to the nearest whole number and get:

s = 9

So Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.

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330 litres per hour = 5489.64 millimeter³ per minute.

Given that330 litres per hour needs to be converted into millimeters per minute.

Conversion factor: 1 litre =1000 cubic centimeter 1 cubic centimeter =1 millimeter³

∴ 1 litre=1000 millimeter³

∴ 1 litre per hour=1000 millimeter³ per hour
Also, 1 hour = 60 minutes

∴ 1 hour = 60 × 60 seconds = 3600 seconds

∴ 1 second = 1/3600 hours=0.0002778 hours

Thus, 1 litre per hour =1000/3600 millimeter³ per second =0.2778 millimeter³ per second

Therefore, 330 litres per hour = 330 × 0.2778 millimeter³ per second=91.494 millimeter³ per second

Also, 1 minute =60 seconds

∴ 1 minute = 60 × 60 seconds=3600 seconds

∴ 1 second = 1/60 minutes=0.01667 minutes

Thus, 91.494 millimeter³ per second = 91.494/0.01667 millimeter³ per minute = 5489.64 millimeter³ per minute

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The height of the tree is approximately 76 feet.

What is the angle of elevation?

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

We can use tangent to set up the following two equations based on the given angles of elevation:

tan(62°) = h/x

tan(56°) = h/(x+10)

We can rearrange the first equation to solve for "h":

h = x * tan(62°)

tan(56°) = (x * tan(62°)) / (x+10)

We can solve for "x" by multiplying both sides by (x+10) and rearranging:

x = 10 * (tan(62°) - tan(56°)))

Now we can substitute this value for "x" into either of the two equations we set up earlier to find the height of the tree "h". Using the first equation, we get:

h = x * tan(62°) ≈ 76 feet

Therefore, the height of the tree is approximately 76 feet.

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The correct answer is (A) r² - 2rs +s² which is a square of a Binomial.

What exactly are binomials?

In algebra, a binomial is a polynomial which consists of two terms. The terms may be separated by a plus or minus sign. The general form of a binomial is:

ax + b

where "a" and "b" are constants and "x" is the variable. A binomial can be added, subtracted, multiplied, and divided using algebraic operations. Binomials are commonly used in algebra to represent and solve problems involving two quantities or variables.

Now,

The correct answer is (A) r² - 2rs +s².

This is a perfect square trinomial, which can be written as (r - s)².

Option (B) c² + d² is not a binomial, it is the sum of two squares.

Option (C) 16x² - 25y² is a difference of two squares, which can be written as (4x + 5y)(4x - 5y).

Option (D) d² - de + e² is also a perfect square trinomial, but it cannot be written as the square of a binomial.

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Simplifying this equation gives: [tex](x - 1)^2+(y+5/8)^2=5[/tex].

A circle is a geometrical shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter. The circumference of a circle is the distance around the edge of the circle, and it is calculated as 2 times pi (π) times the radius. Circles are found in many areas of mathematics and the physical world, and they have important applications in geometry, trigonometry, calculus, physics, and engineering, among other fields.

The equation of a circle with center (a, b) and radius r is given by:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

In this case, the center is (1, -5/8) and the radius is √5. So, the equation of the circle is:

[tex](x - 1)^2 + (y + 5/8)^2 = (\sqrt5)^2[/tex]

Simplifying this equation gives:

[tex](x - 1)^2+(y+5/8)^2=5[/tex]

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The solution to the system of equations are (-4, 5), (2, 7), (3, -1), no solution, (-5, 8) and (7, -3)

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

Question 1 and 2

See attachment for the graphs, where we have the solutions to be

System 1: (-4, 5)

System 2: (2, 7)

Question 3 and 4

Here, we solve the system of equation by substitution method.

So, we have

2x - 7y = 13

3x + y = 8

Make y the subject in (2)

y = -3x + 8

Let's substitute the value of y in equation (i)

2x - 7(-3x + 8) = 13

2x + 21x - 56 = 13

23x = 13 + 56

23x = 69

Divide both sides by 23

x = 69 / 23

x = 3

Let's find y

y = -3(3) + 8

y = -9 + 8

y = -1

For system (4), we have

x - 3y = 2

2x - 6y = 6

So, we have

x = 2 + 3y

By substitution, we have

2(2 + 3y) - 6y = 6

4 + 6y - 6y = 6

4 = 6

The system has no solution

Question 5 and 6

Here, we have

x + y = 3

x - 3y = -29

By eliminating x, we have

4y = 32

So, we have

y = 8

This means that

x + 8 = 3

x = -5

So, the solution is (-5, 8)

For system 6, we have

3y = 26 - 5x

6x + 7y = 21

So, we have

5x + 3y = 26

6x + 7y = 21

This gives

30x + 18y = 156

30x + 35y = 105

By elimination, we have

17y = -51

y = -3

This means that

6x + 7(-3) = 21

6x = 42

So, we have

x = 7

So, the solution is (7, -3)

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The relation in which a college student is related to another if and only if they have attended class together is an example of an equivalence relation.

Reflexivity: Every element of the set is related to itself. In this case, every student has attended class with themselves, so the relation is reflexive.

Symmetry: If one element is related to another, then the second element is also related to the first. In this case, if student A has attended class with student B, then student B has also attended class with student A, so the relation is symmetric.

Transitivity: If one element is related to a second, and the second is related to a third, then the first is related to the third. In this case, if student A has attended class with student B, and student B has attended class with student C, then student A has also attended class with student C, so the relation is transitive.

Therefore, the relation in which a college student is related to another if and only if they have attended class together satisfies all three properties of an equivalence relation, and is an example of such a relation.

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The expression g(f(x)) simplifies to -6x + 6, and we can see that the coefficient of x is -6 and the constant term is 6.

A function f(x) is a mathematical relationship that assigns a unique output value (or range value) for every input value (or domain value) from a specified set. In other words, a function takes one or more input values and produces a single output value based on a specific rule or set of rules.

To find g(f(x)), we need to substitute the expression for f(x) into g(x) wherever x appears, since g(x) is being evaluated at the value of f(x). That is, we need to substitute -2x+5 for x in the expression for g(x). This gives:

g(f(x)) = g(-2x+5)

         = 3(-2x+5) - 9

         = -6x + 15 - 9

         = -6x + 6

So, g(f(x)) = -6x + 6.

Therefore, the expression g(f(x)) simplifies to -6x + 6, and we can see that the coefficient of x is -6 and the constant term is 6. Thus, we can express the response as follows:

g(f(x)) = -6x + 6

         = [-6]x + [6]

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According to the given statement, the government is held accountable by the citizens. Citizens are the ones who elect the government and, thus, have the power to hold it accountable. This is a fundamental principle of democracy that ensures that those in power are serving the people's interests.In a democratic society, the government is accountable to the people.

This means that citizens have the right to hold elected officials accountable for their actions. This is achieved through various means such as free and fair elections, the rule of law, and the right to free speech and expression.Government officials are elected to serve the people and carry out their wishes. This means that they must be transparent and open to criticism. They must be willing to listen to citizens' concerns and take action to address them. This is why democratic societies have mechanisms in place to ensure that citizens can hold their government accountable, such as a free press and independent judiciary.In conclusion, citizens are the ones who hold the government accountable in a democratic society. They have the power to elect officials and the right to criticize them if they are not serving their interests. This ensures that those in power are always acting in the best interests of the people.

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The amount of money Mayte can spend on a daily basis is given by $ 111 .

Sellers and purchasers of products and services both accept money as a form of payment. When we purchase goods like food, clothing, a house, groceries, etc., we provide money in exchange. We exchange money for everything we buy. This is a straightforward swap.

In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that can be made. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each. The division sign, "," or occasionally "/," is used in computer code.

Mayte get a total money of  $977 from her parents so,

total = 977

She saves $200 for herself so now the remaining sum is

977 - 200 = 777

The rest she has to distribute in 7 days so, by using the simple dividation rule we get,

777/7 = 111

Therefore, much money can you spend daily is $111.

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Complete question:

Mayte is a foreign student and receives his parents $977 per week. She saves $200 and the rest is distributed among the 7 days of the week, How much money can you spend daily?​

The height of the water column would be 1033.6 cm if the pressure were 1 atm.

SOLUTION:

If a barometer were built using water instead of mercury, and the pressure were 1 atm, the height of the water column would be:
1. First, find the height of the mercury column at 1 atm. The standard height is 760 mm (or 76 cm) for mercury.
2. Since the density of water is 13.6 times lower than that of mercury, the water column needs to be 13.6 times higher than the mercury column to exert the same pressure.
3. Multiply the height of the mercury column (76 cm) by 13.6:

76 cm x 13.6 = 1033.6 cm.

So, the height of the water column would be 1033.6 cm if the pressure were 1 atm.

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The value that makes the expressions equivalent is 6, as 5+6=11, 11+6=15 and 15+6=30.

Value is the worth of something in terms of the amount of other things for which it can be exchanged or in terms of some medium of exchange. It is also seen as a measure of the usefulness or desirability of something. Value is often subjective, based on personal opinion and preferences, and can change over time. Value can also be seen as an intangible quality of a product or service that makes it desirable, such as convenience, reliability, or customer service.

This is known as a linear sequence, where the difference between each number is the same. In this case, the difference is 6. To find the equivalent expression, you must add 6 to each number in the sequence.

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The value that makes the expressions equivalent is 6, as 5+6=11, 11+6=15 and 15+6=30.

Value is the worth of something in terms of the amount of other things for which it can be exchanged or in terms of some medium of exchange. It is also seen as a measure of the usefulness or desirability of something. Value is often subjective, based on personal opinion and preferences, and can change over time. Value can also be seen as an intangible quality of a product or service that makes it desirable, such as convenience, reliability, or customer service.

This is known as a linear sequence, where the difference between each number is the same. In this case, the difference is 6. To find the equivalent expression, you must add 6 to each number in the sequence.

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Complete questions as follows-
What value makes the expressions equivalent?
6(3x+5) and 15x+□+3x

A. 5
B.11
C.15
D.30

Answer:

x ≈ 3.24

Step-by-step explanation:

using the cosine ratio in the right triangle

cos29° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{3.7}[/tex] ( multiply both sides by 3.7 )

3.7 × cos29° = x , then

x ≈ 3.24 ( to the nearest hundredth )

As per the given average, the solution of the breakeven w/ hidden costs is 62% higher.

Let's assume that the costs associated with running a 315-ticket run are $7,592. This means that on average, each ticket needs to sell for $24.10 (($7,592/315) = $24.10) to break even.

Similarly, if we consider the other two runs, we can calculate the average number of tickets needed to break even per show as follows:

For the 323-ticket run, the average number of tickets needed to break even per show is 65. (($7,784/323) = $24.10)

For the 331-ticket run, the average number of tickets needed to break even per show is 56. (($7,977/331) = $24.10)

Furthermore, we can calculate the break-even occupancy percentage for each run, which is the percentage of tickets that need to be sold to break even. The break-even occupancy for each run is as follows:

For the 331-ticket run,

=> 56/331 = 0.17 or 17%,

=> 1-0.17 = 0.83 or 83%,

=> 0.83/0.17 = 4.88,

=> 4.88 x 100% = 488%,

=> 488% x 0.62 = 303%,

=> 303%/4.88 = 62%

Hence the break-even occupancy is 62%.

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Answer:

No.

Step-by-step explanation:

Line XY will be tangent to Circle W when XY is perpendicular to the radius XW. We can test if it is perpendicular by using Pythagoras theorem as it only works on right angled triangle. If the angle WXY is 90 degrees (XY ⊥ WX) then the theorem should work.

[tex](XY)^2=(WX)^2+(XY)^2\\R.H.S = 66^2+54^2 = 7272\\L.H.S = 87^2 = 7569\\R.H.S \neq L.H.S[/tex]

Thus the angle is not 90 degrees since the Pythagoras theorem doesn't work thus the line is not tangent since it is not at 90 degrees with the radius WX.

Answer:

not a tangent

Step-by-step explanation:

if XY is a tangent to the circle then ∠ WXY = 90°

using converse of Pythagoras' identity.

if the square of the longest side is equal to the sum of the squares on the other 2 sides , then the triangle is right.

longest side is WY

WY² = 87² = 7569

WX² + XY² = 66² + 54² = 4356 + 2916 = 7272

since WY² ≠ WX² + XY² , then Δ WXY is not right

then XY is not a tangent to the circle

Answer:The number of minutes m you spend in line is 5 times the number of people p in line. Identify the independent and dependent variables. Then write and graph a function that describes the relationship between p and m.

Step-by-step explanation:

The perimeter of the rectangle is approximately 208.9 meters.

To find the perimeter of the rectangle, we need to know the length of the other side.

Let's use the formula for the area of a rectangle:

area = length x width

We know that the area is 717.8 m^2 and one of the sides (width) is 7.4 m. So we can rearrange the formula to solve for the length:

length = area / width

length = 717.8 / 7.4

length ≈ 97.05 m

Now we have both the length and width of the rectangle, so we can find the perimeter:

perimeter = 2 x (length + width)

perimeter = 2 x (97.05 + 7.4)

perimeter = 2 x 104.45

perimeter = 208.9 m

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The height of first graders in a class, represented by x, would be considered a Continuous variable. Continuous variables can take on any value within a specified range and are often used to measure physical attributes, such as height.

Let x represent the height of first graders in a class. Discrete variables are those that can be measured using whole numbers, such as the number of people in a room, the number of items on a grocery list, or the number of pages in a book. Continuous variables, on the other hand, are those that can take on any value, such as height, weight, and time.Continuous variables are those that can take on any value between two points on a measurement scale. For example, the height of first graders in a class can be measured in inches or centimeters and can take on any value between the smallest and largest heights in the class.

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Answer:

-0.2

Step-by-step explanation:

[tex]\frac{y2-y1}{x2-x1}[/tex]

^This here is how I calculated the slope^

Y2=4

Y1= 2

4-2= 2

X2=-7

x1=3

-7-3=-10

2/-10

or -2/10

Answer:

20/52 or simplified to 5/13

Step-by-step explanation:

The Venn Diagram is provided

Let
n(A) =  number of customers who had syrup
n(B) =  number of customers who had sprinkles

n(A and B) = number of customers who had both syrup and sprinkles = 16
This would be the number in the overlapping region

n(A or B) = number of customers who had either syrup or sprinkles or both
= n(A) + n(B) - n(A and B)
= 48 + 28 - 16
= 60

Therefore number of customers who had neither topping = 80 - 60 = 20

This number is indicated outside both circles but within the rectangle

The number of customers who had only syrup is given by set difference

= No. of customers who had syrup - No. of customers who had both
= n(A) - n(A and B)
= 48 - 16
= 32

This is the figure inside the left circle

Let's consider the statement: Customers who didn't have sprinkles

This would be customers who had only syrup(32) + customers who had neither topping(20)
= 32 + 20 = 52

Number of customers who did not have either topping = 20
P(selected customer doesn't have either topping, given that they don't have sprinkles)
= 20/52
= 5/13

3198 x 750 equals 2,398,500. We may use the distributive approach to solve 3198 x 750 without a calculator by multiplying each digit of one number by each digit of the other number, starting with the rightmost digit.

We may use the distributive approach to solve 3198 x 750 without a calculator by multiplying each digit of one number by each digit of the other number, starting with the rightmost digit.

markdown

3198 \s x 750

23970 (8 x 0), 319800 (9 x 0 + 9 x 5) and 2398500 (9 x 0 + 9 x 7 + 8 x 5) are the numbers.

Because of this, 3198 x 750 equals 2,398,500.

When a problem or question asks to be solved "without using a calculator," it signifies that the answer must be determined by hand without the aid of a calculator or any other electronic instrument. This is frequently used to assess a person's math prowess and to motivate them to hone their problem-solving and mental math ability.

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a) The rate of change of the drug's concentration at 50 minutes is 1.7 mg/min.

b) The rate of change of the drug's concentration at 85 minutes is 0.2 mg/min.

c) The drug's concentration is decreasing at 115 minutes.

a) The central difference approach can be used to calculate the rate of medication change after 50 minutes.

f'(x) = (f(x+h) - f(x-h))/2 × h    ....(1)

As per the question, we have h = 10 and x = 50

Substitute the values of h = 10 and x = 50 in (1),

f'(40) = (f(50+10) - f(50-10))/2 × 10

f'(40) = (89-55)/20

f'(40) = 1.7 mg/min

b) For the rate of change of concentration at 85 minutes:

Here, f(80) = 111 mg and f(90) = 113.

The concentration at 90 minutes is 113 mg.

Rate of change = (f(90) - f(80)) / h

= (113 - 111) /10

= 2 / 10

= 0.2 mg/min

c) Since the concentration at 120 minutes (68 mg) is lower than the concentration at 110 minutes (103 mg), the drug's concentration is decreasing.

Therefore, the drug's concentration is decreasing at 115 minutes.

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The amount of plastic wrap required to cover the entire cone will be 16.575 square inches.

To calculate how much plastic wrap is required to completely cover an ice cream cone with a slant height of 4.25 inches and a diameter of 2 inches, we must use the surface area of the cone.

Here, the ice cream cone can be visualized as a cone-shaped object with an added circular base.

We must use the following formula to calculate the surface area:

Surface area = πr2 + πrl

Where r is the radius and l is the slant height of the cone.

As we know the diameter of the ice cream cone is 2 inches, and its radius can be calculated by dividing it by

2.r = d/2 = 2/2 = 1 inch.

Substitute the values of r and l in the formula, and then calculate the surface area of the cone.

π = 3.14r = 1 inchl = 4.25 inches

Surface area = πr2 + πrl

                     = 3.14 × 1² + 3.14 × 1 × 4.25

                     = 3.14 + 13.435

                     = 16.575 square inches

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We use the formula I = Prt where I is the interest earned, P is the principal, r is the interest rate per year, and t is the time in years. Substituting the values, we find that it will take 4 years for a $5000 balance to reach $6500 with a 7.5% simple interest rate.

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

I = Prt

Where I is the interest earned, P is the principal (initial amount), r is the interest rate per year (as a decimal), and t is the time in years.

In this case, we know that the principal is $5000, the interest rate is 7.5% or 0.075, and we want to find the time required for the balance to reach $6500.

Substituting these values into the formula, we get:

I = $6500 - $5000 = $1500

P = $5000

r = 0.075

t = ?

Solving for t, we get:

$1500 = $5000 * 0.075 * t

t = $1500 / ($5000 * 0.075)

t = 4

Therefore, it will take 4 years for the balance of the account to be $6500 with a 7.5% simple interest rate.

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