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The exponential function showing the relationship is y = 2300(1 + 0.12)^t

The exponential function showing the relationship between y and t can be written as:

y = 2300(1 + 0.12)^t

where 2300 is the initial number of bacteria cells, 0.12 is the growth rate (12% expressed as a decimal), and t is the time in hours since the start of the study.

This function is obtained by using the formula for exponential growth, which is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is the time.

In this case, a = 2300, r = 0.12, and y represents the amount of bacteria cells after t hours.

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For the given expression a)(f◦g)(4) = 1. b)(g◦f)(2) = -29. c)(f◦f)(1) = 1. d)(g◦g)(0) = -17.5.

An expression refers to a combination of numbers, symbols, and/or operators that represents a mathematical value or relationship. It can be a single term, such as a number or a variable, or a combination of terms connected by operators, such as addition, subtraction, multiplication, division, exponentiation, etc.

A function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain), such that each input is associated with exactly one output.

According to the given information:

(a) To find (f◦g)(4), we need to first substitute g(4) into f(x) in the given expression, and then evaluate f(g(4)).

Given:

f(x) = 3x² - 2

g(x) = 7 - (1/2)x²

Substituting g(4) into f(x):

g(4) = 7 - (1/2)(4²) = 7 - 8 = -1

Now, substituting -1 into f(x):

f(-1) = 3(-1)² - 2 = 3 - 2 = 1

So, (f◦g)(4) = 1.

(b) To find (g◦f)(2), we need to first substitute f(2) into g(x), and then evaluate g(f(2)).

Substituting f(2) into g(x):

f(2) = 3(2)² - 2 = 12

Now, substituting 12 into g(x):

g(12) = 7 - (1/2)(12)^2 = 7 - 36 = -29

So, (g◦f)(2) = -29.

(c) To find function (f◦f)(1), we need to first substitute f(1) into f(x), and then evaluate f(f(1)).

Substituting f(1) into f(x):

f(1) = 3(1)²- 2 = 1

Now, substituting 1 into f(x):

f(1) = 3(1)² - 2 = 1

So, (f◦f)(1) = 1.

(d) To find (g◦g)(0), we need to first substitute g(0) into g(x), and then evaluate g(g(0)).

Substituting g(0) into g(x):

g(0) = 7 - (1/2)(0)² = 7

Now, substituting 7 into g(x):

g(7) = 7 - (1/2)(7)² = 7 - 24.5 = -17.5

So, (g◦g)(0) = -17.5.

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The vertex is (50, 630). The vertex is the peak and correspond with the coordinates of he maximum height of the arch.

The solutions is the base of the arch and this (20, 0) and (80, 0)

vertex form, y = -0.7(x - 50)² + 630

Quadratic equation factored form, y = -0.7 (x - 80) (x - 20)

The equations are the same when plotted on a graph and examined mathematically. physically it looks different.

the domain is (-∞, ∞)

The height of the monument 15 feet from the left side is 472.5 feet

since the zeroes of the quadratic equation is (20, 0) and (80, 0), hence we have that

y = a(x - 20)(x - 80) and the equation pass points (50, 630)

630 = a(50 - 20)(50 - 80)

630 = a * 30 * -30

630 = -900a

a = -0.7

Quadratic equation has a standard vertex form, y = a(x - h)² + k    

y = a(x - h)² + k

vertex (h, k) = (50, 630) and a = -0.7

plugging the values

y = -0.7(x - 50)² + 630

Quadratic equation has a standard factored form, y = a(x - h)² + k    

y = a(x - r2)(x - r1)

where r2 and r1 are the roots r1 = 20 r2 = 80 an a = -0.7

plugging the values

y = -0.7 (x - 80)(x - 20)

The height of the monument 15 feet from the left side is gotten from the graph

this is 15 feet from 20 hence x = 35 feet

from the graph it can traced to be 472.5 feet

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The similes in the story are:

A simile is a figure of speech that compares two things using the words "like" or "as." It is a type of metaphor that helps to create a vivid and engaging image in the reader or listener's mind.

Similes are often used in literature, poetry, and everyday language to make a comparison more relatable and understandable. For example, "He is as brave as a lion" or "She sings like an angel." These similes help to convey a certain quality or trait by comparing it to something else that is well-known or familiar.

Note: It seems there may be a typo in the last sentence of the story, where the word "e" appears instead of "elephant" or another word that would make sense in context.

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The equations that can be used to solve for y are y(y + 5) = 750,  y² – 5y = 750 and y(y – 5) + 750 = 0

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.

The equations that can be used to solve for y, the length of the room are:

1. y(y + 5) = 750

2. y² – 5y = 750

3. y(y – 5) + 750 = 0

Option 1 and 2 are quadratic equations that can be solved by factoring, completing the square, or using the quadratic formula. Option 3 is also a quadratic equation but it requires rearranging to the standard form before applying the same methods. The last option, (y + 25)(y – 30) = 0, is not a quadratic equation but it can be easily solved using the zero product property.

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A. There are 9 sample spaces.

B.  The probability of choosing Chocolate, Fudge, and Rainbow is 1/9

What is meant by sample spaces?

In probability theory, a sample space is the set of all possible outcomes of a random experiment or process. It is used to define the space of events and calculate probabilities.

What is meant by probability?

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. It is calculated by dividing the number of favourable outcomes by the total number of possible outcomes.

According to the given information

A. There are 9 possible combinations (3 ice cream flavors x 3 toppings x 1 sprinkle color), so there are 9 sample spaces.

B.  The probability of choosing Chocolate, Fudge, and Rainbow is 1/9, assuming all combinations are equally likely.

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Answer:

[tex]\frac{64}{25}[/tex]

Step-by-step explanation:

[tex]\frac{4^{3} }{5^{2} }[/tex]

4³ = 64

5² = 25

[tex]\frac{64}{25}[/tex] is already in simplest form, so it is the answer.

Answer:

They are collinear if they are on the same line

The agency made $28,275 in commission on the house.

The agent earned $5,655 in commission on the sale of the house.

We first need to calculate the amount of commission that the agency received.

The commission rate for the agency is 7.5%, so we can find the commission amount by multiplying the sale price of the house by 7.5% in decimal form:

Commission for the agency = $377,000 x 0.075 = $28,275

Therefore, the agency made $28,275 in commission on the house.

To calculate how much the agent earned in commission, we need to find 20% of the commission amount that the agency received:

Commission for the agent = $28,275 x 0.20 = $5,655

Therefore, the agent earned $5,655 in commission on the sale of the house.

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Answer:

do 5x-27+7x-26=10x-23 because sum of two interior angle of a triangle is equal to the sum of one exterior angle and don't forget because it comes daily in exam

The degree measure of the angles are;

1. 5π/3 = 300°

2 3π/4 = 135°

3. 5π/6 = 150°

4. -3π/2 = 90°

A degree is a unit of measurement which is used to measure circles, spheres, and angles while a radian is also a unit of measurement which is used to measure angles.

A circle has 360 degrees which are its full area while its radian is only half of it which is 180 degrees or one pi radian.

therefore π = 180°

1. 5π/ 3 = 5×180/3 = 300°

2. 3π/4 = 3× 180/4 = 540/4 = 135°

3. 5π/6 = 5×180/6 = 150°

4. - 3π/2 = -3 × 180/2 = -270° = 90°

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Step-by-step explanation:

From a z-score table

   z-score = 1 corresponds to  .8413   or  84.13 percentile

     meaning 84 .13 % have a lesser score than you

The x^6y^7 term in the expansion will be 36x^2y^7.

The x^7y^2 term in the expansion will be 36x^7y^2.

In the given problem, we have the binomial expansion of (x - y)^n, which includes the term 126x^5y^4.

We will use the binomial coefficient formula to find the coefficients of the desired terms.

The general term of the binomial expansion is given by:

T(k) = C(n, k) * x^(n-k) * y^k

where C(n, k) is the binomial coefficient and can be calculated as:

C(n, k) = n! / (k!(n-k)!)

From the given term, 126x^5y^4, we have:

126 = C(n, 4)

x^5 = x^(n-4)

y^4 = y^4

Now we can find the value of n:

126 = n! / (4!(n-4)!)

Let's solve for n:

126 * 4! = n! / (n-4)!

504 = n! / (n-4)!

Now, we will find the coefficients of the terms x^6y^7 and x^7y^2.

The x^6y^7 term in the expansion will be:

T(k) = C(n, 7) * x^(n-7) * y^7

Since x^5 = x^(n-4), we have n - 4 = 5, so n = 9.

Substituting the value of n:

T(k) = C(9, 7) * x^2 * y^7

Using the binomial coefficient formula:

C(9, 7) = 9! / (7!2!) = 36

So, the x^6y^7 term in the expansion will be 36x^2y^7.

The x^7y^2 term in the expansion will be:

T(k) = C(n, 2) * x^(n-2) * y^2

We already found that n = 9, so substituting the value of n:

T(k) = C(9, 2) * x^7 * y^2

Using the binomial coefficient formula:

C(9, 2) = 9! / (2!7!) = 36

So, the x^7y^2 term in the expansion will be 36x^7y^2.

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There are 7 books in the stack.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To find the number of books in the stack, we can divide the total mass of the stack by the mass of each book:

Number of books = Total mass of the stack / Mass of each book

In this case, the total mass of the stack is 21 kilograms, and the mass of each book is 3 kilograms.

Number of books = 21 kg / 3 kg/book

Simplifying the right side, we get:

Number of books = 7 books

Therefore,

There are 7 books in the stack.

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Answer:

0

Step-by-step explanation:

0

Answer: 5 * 5 = 20

20 divided by 1 = 20

If there are 5 apples with an apple:orange ratio of 1:4, there are 20 oranges.

The number of people who play only football is |A' ∩ B' ∩ C'| = 25. So, 25 people play only football.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of various methods and techniques to draw conclusions from data and make informed decisions.

The main goal of statistics is to provide a systematic approach to understanding and interpreting data, which can be used in a wide variety of fields, including business, social sciences, engineering, medicine, and many others. Statistics is used to study and analyze various types of data, including numerical, categorical, and ordinal data, as well as time series and spatial data.

Let A, B, and C be the sets of people who play football, baseball, and hockey, respectively. We know that:

|A| = 61, |B| = 65, |C| = 72

We also know that:

|A ∩ B ∩ C| = 22, |A ∪ B ∪ C| = 141, |A' ∩ B' ∩ C'| = 11

where A', B', and C' denote the complements of A, B, and C, respectively.

We can use the principle of inclusion-exclusion to find the number of people who play only two games. This principle states that:

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

Using the given values, we can substitute and simplify to get:

141 = 61 + 65 + 72 - |A ∩ B| - |A ∩ C| - |B ∩ C| + 22

|A ∩ B| + |A ∩ C| + |B ∩ C| = 75

We also know that an equal number of people play only two games, so let x be that number. Then:

|A ∩ B| = |A ∩ C| = |B ∩ C| = x

Substituting into the previous equation, we get:

3x = 75

x = 25

Therefore, 25 people play only two games. To find the number of people who play only football, we need to subtract the number of people who play baseball and hockey from the number of people who play only two games:

|A' ∩ B ∩ C| = x = 25

|A' ∩ B ∩ C'| = 11

|A' ∩ C ∩ B'| = x = 25

|A ∩ B' ∩ C'| = x = 25

|A' ∩ B| = 65 - (25 + 11) = 29

|A' ∩ C| = 72 - (25 + 11) = 36

|A' ∩ B' ∩ C| = 61 - (25 + 11) = 25

|A ∩ B' ∩ C| = 141 - (29 + 25 + 36 + 11) = 40

Therefore, the number of people who play only football is:

|A' ∩ B' ∩ C'| = 25

So, 25 people play only football.

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Answer: The formula for the surface area of a sphere is given by 4πr^2, and since we have half of a sphere, the surface area of a dome (a half sphere) is 2πr^2.

Plugging in the radius r = 12 meters, we get:

Surface area = 2π(12)^2

Surface area = 2π(144)

Surface area ≈ 904.78

Rounding to the nearest whole number, we get the surface area of the dome as 905 meters squared. Therefore, the closest answer choice is 967 meters squared.

So the answer is: 967 meters squared.

Step-by-step explanation:

Answer:

40 m²

Step-by-step explanation:

Area of triangle:

To find the area of triangle, multiply the base and area and then divide it by 2.

      base = b = 8 m

height      = h = 10m

      [tex]\boxed{\bf Area \ of \ triangle = \dfrac{1}{2}*b*h}[/tex]

                                     [tex]= \dfrac{1}{2}*8 * 10\\\\= 4 * 10\\\\= 40 \ m^2[/tex]

The line's equation in point-slope form is shown here. Point (2, 5) is the given point on the line, and slope 2 is the given slope of the line. The slope of this line is -1/2, which is the negative reciprocal of the slope.

A line's point slope form equation is [tex]y - y_1 = m(x - x_1)[/tex]. Consequently, y - 0 = m(x = 0), or y = mx, is the equation of a line passing through the origin with a slope of m.

We require a point on the line and the slope of the line in order to create a line equation in point-slope form. In point-slope form,

[tex]y - y1 = m(x - x1)[/tex]

As an illustration, suppose we want to formulate the equation of the line passing through the coordinates (2, 5) and having a slope of 2. The values can be entered into the point-slope form as follows:

y - 5 = 2(x - 2)Let's say the given line has the equation [tex]y - y1 = m(x - x1)[/tex], where (x1, y1) is a point on the line and m is the slope of the line.

we can use the given point (2, 5). Then we can plug in the values into the point-slope form:

[tex]y - 5 = (-1/2)(x - 2).[/tex]

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With regard to the linear functions,

Part 1:

To find the point where the cost equals the revenue, we need to set the two equations equal to each other and solve for x:

Revenue: y=1.2x

Cost: y = 0.4x+32

1.2x = 0.4x + 32 (substitute y with 1.2x for revenue and y with 0.4x+32 for cost)

0.8x = 32 (subtract 0.4x from both sides)

x = 40 (divide both sides by 0.8)

Now that we have found x=40, we can find y by plugging it into either equation. Let's use the revenue equation:

y = 1.2x

y = 1.2(40)

y = 48

Therefore, the point where the cost equals the revenue is (40, 48).

Part 2:

The point (40, 48) represents the number of batteries that need to be produced in order for the cost to equal the revenue. In other words, if the company produces 40 thousand batteries, they will earn 48 thousand dollars in revenue and spend 32 thousand dollars in costs, resulting in a profit of 16 thousand dollars.

Part 3:

To check if our results from Part 1 correspond with the graph, we can plot the two equations on the same graph and look for the point of intersection.

As we can see from the graph, the two lines intersect at the point (40, 48), which confirms our result from Part 1.

Part 4:

Profit is found by subtracting cost from revenue, so the profit equation would be:

Profit: y = 1.2x - (0.4x + 32)

Simplifying the equation:

y = 1.2x - 0.4x - 32

y = 0.8x - 32

Part 5:

To find the profit from producing 100 thousand batteries, we can plug x=100 into the profit equation we found in Part 4:

y = 0.8x - 32

y = 0.8(100) - 32

y = 48

Therefore, the profit from producing 100 thousand batteries would be 48 thousand dollars.

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Answer: it’s 8.25

Step-by-step explanation: because it’s in between 8 and 8.5. Thank god

The height of the cylinderical can is approximately 1147.8 inches.

What is a cylinder?

A cylinder is a three-dimensional geometric object made up of two parallel and congruent circular bases that are joined by a curving lateral surface. The lateral surface has a uniform circular cross-section and is perpendicular to the bases. A cylinder's height is the perpendicular distance between its bases. Cans, tubes, and pipes are all instances of cylinders. The volume of a cylinder may be computed by multiplying its base area by its height, and the formula for the lateral surface area is 2πrh, where r is the radius of the base and h is the cylinder's height.

Now,

We can start by finding the radius of the can using the given diameter:

radius = diameter/2 = 5/2 = 2.5 inches

The surface area of the can is given by:

Surface area = 2πrh + 2πr²

where h is the height of the can, r is the radius, and π is the mathematical constant pi.

Substituting the given values, we get:

18064 = 2π(2.5)(h) + 2π(2.5)²

Simplifying and solving for h, we get:

18064 = 15.707h + 39.269

18064 - 39.269 = 15.707h

18024.731 = 15.707h

h = 18024.731/15.707

h ≈ 1147.8 inches

Therefore, the height of the can is approximately 1147.8 inches.

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The total net amount the supermarket owes the wholesaler for the order is $231.31.

A discount is a reduction in the price of a product or service. It is often offered by businesses to encourage customers to buy more or to make a purchase they might not otherwise make. A discount can be expressed as a percentage or a specific dollar amount, and it is usually subtracted from the original price of the item or service.

To find the total net amount the supermarket owes the wholesaler for the order, we need to first calculate the cost of each case of soup and baked beans after the 39% trade discount is applied, and then multiply those costs by the number of cases ordered.

The trade discount rate is 39%, which means the supermarket will receive a discount of 39% off the list price of each case of soup and baked beans. To calculate the cost of each case after the discount is applied, we can use the following formula:

Discounted cost = List price - (Discount rate x List price)

For the soup, the discounted cost per case is:

$18.90 - (0.39 x $18.90) = $11.51

For the baked beans, the discounted cost per case is:

$33.50 - (0.39 x $33.50) = $20.42

Now we can calculate the total net amount owed by the supermarket to the wholesaler:

Total net amount = (Number of cases of soup x Cost per case) + (Number of cases of baked beans x Cost per case)

Total net amount = (13 x $11.51) + (4 x $20.42)

Total net amount = $149.63 + $81.68

Total net amount = $231.31

Therefore, the total net amount the supermarket owes the wholesaler for the order is $231.31.

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With given compound interest, it will take 27.25 years to pay off the loan.

What is Compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, the interest that is earned on both the principal amount and any previously accumulated interest. In other words, it is interest that is calculated not only on the original amount of money but also on any interest that has been earned previously. This can result in significant growth of an investment or loan balance over time, as the interest earned on the accumulated interest can compound exponentially. Compound interest can be calculated using a specific formula that takes into account the principal amount, the interest rate, and the compounding frequency.

Now,

First, we need to calculate the total amount of the loan. We round up the tuition and fees cost for 5 years to the nearest thousand dollars:

Total cost = $70,000

Rounded up to nearest thousand = $70,000

So, the amount of the loan is $70,000.

Next, we can use the formula N= (-log⁡(1-i*A/P))/(log⁡(1+i)) to calculate the number of monthly payments needed to pay off the loan.

N = (-log(1-0.0025*70000/250))/(log(1+0.0025))

N = (-log(1.75))/(log(1.0025))

N = 326.45

Rounding up to the nearest whole number, it will take 327 monthly payments to pay off the loan.

So, it will take 327/12 = 27.25 years to pay off the loan.

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The empty set (also known as the null set) is a subset of every set because it does not contain any elements that are not in the set. In other words, if A is any set, then every element of the empty set is also an element of A, since the empty set contains no elements. This satisfies the definition of a subset, which states that for any two sets A and B, A is a subset of B if every element of A is also an element of B. Therefore, the empty set is a subset of every set.

~~~Harsha~~~

Answer:

Option A

Step-by-step explanation:

Solving using quadratic formula:

Use the quadratic formula to determine the coefficient of the quadratic equation.

Option A:

         x² + 6x + 24 = 3x

        x² + 6x + 24 - 3x = 0

         x² + 3x + 24 = 0

Compare with ax² + bx + c = 0,

a = 1 ; b = 3 and c = 24

[tex]\boxed{\bf x= \dfrac{-b \± \sqrt{b^2-4ac}}{2a}}[/tex]

     [tex]= \dfrac{-3 \±\sqrt{3^2-4(1)(24)}}{2(1)}[/tex]

This equation could be solved using the application of the quadratic formula.

Option B:

3x² + 3x + 24 = 3

3x² + 3x + 24 - 3 = 0

3x² + 3x + 21 = 0

a = 3  ; b = 3 and c = 21

Here, co-efficients are different.

Option C:

     x² + 3x - 24 = 3

 x² + 3x - 24 - 3= 0

   x² + 3x - 27    = 0

          a = 1  ; b = 3 and c = -27

Here, co-efficients are different.

Option C:

     x² + 3x + 24 = 3

 x² + 3x + 24 - 3 = 0

    x² + 3x + 21    = 0

             a= 1 ; b = 3  and c = 21

Here, co-efficients are different.

Answer:

AB: y = 2x + 4

Step-by-step explanation:

Line AB is parallel to the line y = 2x + 3

When 2 lines are parallel they have the same coefficient of x.

=> AB: y = 2x + m (1)

Because line AB passes through the point (0, 4)

Replace x = 0; y = 4 into (1) => 2 × 0 + m = 4 => m = 4

So AB: y = 2x + 4

40% of Canadians read at least 10 books a year.

A percentage is a way of expressing a portion or a part of a whole as a fraction of 100. It is represented by the symbol "%". Percentages are often used to compare different quantities or to describe how much of a total is made up by a specific amount or group. For example, if you score 80 out of 100 on a test, your score can be expressed as 80%, meaning you got 80 out of 100 possible points.

If two out of every five Canadians read at least 10 books a year, then we can write this as a fraction:

2/5

We can multiply this fraction by 100 to turn it to a percentage:

(2/5) x 100 = 40%

Therefore, 40% of Canadians read at least 10 books a year.

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Answer:

a) To find out how big of a loan you can afford, we can use the formula for the monthly payment of a mortgage:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]

where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (which is the annual interest rate divided by 12), and n is the number of monthly payments (which is the number of years times 12).

In this case, we know that M = $1,000, i = 0.053/12, and n = 30 x 12 = 360. We want to solve for P, the principal we can afford.

Substituting these values into the formula, we get:

$1,000 = P [ 0.004416(1 + 0.004416)^360 ] / [ (1 + 0.004416)^360 - 1 ]

Simplifying and solving for P, we get:

P = $183,928.72

Therefore, you can afford a loan of approximately $183,928.72.

b) The total money paid to the loan company will be the monthly payment multiplied by the number of payments over the life of the loan. In this case, we have:

Total money paid = $1,000 x 360 = $360,000

Therefore, the total amount of money paid to the loan company will be $360,000.

c) To find out how much of that money is interest, we can subtract the principal from the total amount paid. In this case, we have:

Interest paid = Total money paid - Principal = $360,000 - $183,928.72 = $176,071.28

Therefore, the amount of money paid in interest will be $176,071.28.