given that log x = 3, log y=7
PLEASE HELP SOLVE 20 PTsS

Value of indicated point is 2.

In mathematics, a straight line is a geometric object that extends infinitely in both directions and is perfectly straight, meaning that it does not curve or bend. A straight line is defined by any two points on the line, which can be connected by a line segment that lies entirely on the line.

The equation of a straight line can be written in various forms, such as slope-intercept form, point-slope form, or standard form, but they all describe the same line. The equation of a straight line is y = mx + b in slope-intercept form.

Given equation;

3x-y=1

Given coordinate (1,y)

Putting the value of coordinate in equation, we get

3-y=1

3-1=y

y=2

Hence, value of indicated point is 2.

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A polynomial function of least degree with rational coefficients, so that P(x)=0 has the given roots is P(x) = x^2 - 6x - 16.

If the roots of P(x) are -2 and 8, then the factors of P(x) are (x+2) and (x-8), since if we plug in -2 or 8 for x, one of these factors will be equal to zero, making the whole expression equal to zero.

To find the polynomial with these roots, we can multiply these factors together:

P(x) = (x+2)(x-8)

Multiplying this out, we get:

P(x) = x^2 - 6x - 16

Therefore, the polynomial function of least degree with rational coefficients that has roots of -2 and 8 is:

P(x) = x^2 - 6x - 16

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The polynomial function of least degree with rational coefficients and roots at x=-2 and x=8 is P(x) = x² - 6x - 16.

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using only the operations of addition, subtraction, and multiplication, and in which the variables appear only with positive integer exponents. The degree of a polynomial is the highest power of the variable in the expression.

Roots refer to the values that satisfy an equation, making it equal to zero.

Using the zero product property, we know that a polynomial with roots at -2 and 8 can be written as:

P(x) = (x + 2)(x - 8)

Expanding this expression, we get:

P(x) = x² - 6x - 16

Therefore, the polynomial function of least degree with rational coefficients and roots at x=-2 and x=8 is P(x) = x² - 6x - 16.

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Answer:

634538

Step-by-step explanation:

Add 4+2 since in the rest of the columns, we have to add 0 to all of the rest of the numbers.

4+2=6

0+(3, 4, 5, 3, and 8 will equal the same thing)

0+3=3

0+4=4

And so on.

400000

+ 234538

_______

  634538

I hope this has helped!

Nora covered a total distance of 13 miles during these sessions.

The parameter is represented by the line plot.

We can find the following frequency table from the line plot:

Distance   Frequency

0                    0

1/2                  4

1                     3

1 1/2               1

2                    2

2 1/2               1

3                    0

The overall separation from the line plot is then shown as

Total distance = sum of the distance-frequency product

The following equation can be found in mathematics.

Total distance = (0 * 0) + (1/2 * 4) + (1 * 3) + (1 1/2 * 1) + (2 * 2) + (2 1/2 * 1) +

(3 * 0)

Rank the total number of products

Total distance = 13

The total distance is therefore 13 units.

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Answer:

hope this will help you...

The expression that has the greatest value when n is equal to 4 is option B, n + 30, with a value of 34.

To determine which mathematical expression has the greatest value when n is equal to 4, we can simply substitute 4 for n in each expression and compare the results.

A. 5n = 5(4) = 20

B. n + 30 = 4 + 30 = 34

C. 50 - n = 50 - 4 = 46

D. 80 ÷ n = 80 ÷ 4 = 20

The complete question is: Which expression has the greatest value when n is equal to 4? A. 5n B. n + 30 C. 50 – n D. 80 ÷ n

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Answer:

(3x + y)(2x + 3)

Step-by-step explanation:

6x² = 2 * 3 * x * x

2xy = 2*x * y

Common factor = 2x.

        9x = 3 * 3 * x

        3y = 3 * y

Common factor = 3

Take out the common factor 2x from the first and second term & take out the common factor 3 from third and fourth term.

6x² + 2xy + 9x + 3y = 2x(3x + y) + 3(3x + y)

                              = (3x + y)(2x + 3)

Answer: The area of the door can be calculated as:

Area of door = width x height

= 0.9 m x 2.1 m

= 1.89 square meters

The area of one window can be calculated as:

Area of window = width x height

= 1.5 m x 1.2 m

= 1.8 square meters

Since there are four windows, the total area of the four windows is:

Total area of four windows = 4 x Area of window

= 4 x 1.8 square meters

= 7.2 square meters

Therefore, the total area of the door and the four windows is:

Total area = Area of door + Total area of four windows

= 1.89 square meters + 7.2 square meters

= 9.09 square meters

Hence, the total area of the door and the four windows is 9.09 square meters.

Step-by-step explanation:

The area of ΔSTU is approximately 6358 cm², to the nearest square centimeter.

We can find the area of ΔSTU using the given side and angles by applying the formula:

Area = (1/2)ab x sin(C)

Where a and b are the lengths of two sides of the triangle and C is the angle between them.

We have one side, s, which is 210 cm. We also have two angles, ∠S = 115° and ∠T = 23°. We can find the third angle, ∠U, by using the fact that the sum of angles in a triangle is 180°:

∠U = 180° - ∠S - ∠T

∠U = 180° - 115° - 23°

∠U = 42°

Now, we have ∠S = 115°, ∠T = 23°, and ∠U = 42°. We can use the Law of Sines to find the other two sides of the triangle. Let side t be opposite ∠T and side u be opposite ∠U. Then:

s / sin(S) = t / sin(T) = u / sin(U)

We can now find t and u using the known values:

t / sin(23°) = 210 / sin(115°) = 90.5

S = 1/2 x 90.5 x 210 x sin  42°

=6358 cm²

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Answer:

0.222

Step-by-step explanation:

2 divided by 9 is:

0.222 (rounded to the nearest thousandth)

The probability that y is between 5.1 and 5.7 is approximately 0.4292.

Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes an inevitable one.

Since the sample size is large (n = 70), we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean as normal with mean μ = 5 and standard deviation σ/sqrt(n) = 2/sqrt(70) ≈ 0.24.

Now we want to find the probability that y, the sample mean, is between 5.1 and 5.7. We can use the standard normal distribution to do this by standardizing y:

z = (y - μ) / (σ / sqrt(n)) = (y - 5) / 0.24

The probability that y is between 5.1 and 5.7 is equivalent to the probability that z is between:

z1 = (5.1 - 5) / 0.24 ≈ 0.42

and

z2 = (5.7 - 5) / 0.24 ≈ 2.92

Using a standard normal distribution table or calculator, we can find that the probability of z being between z1 and z2 is approximately 0.4292.

Therefore, the probability that y is between 5.1 and 5.7 is approximately 0.4292.

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Answer:

Step-by-step explanation:

40 de grese

Answer:

52°

Step-by-step explanation:

The angle between two secants drawn from the point outside the circle is half the difference of the intercepted arcs.

    [tex]\sf \boxed{\bf \angle \ Y =\dfrac{far \ arc - near \ arc}{2}}[/tex]

     [tex]\sf \angle Y = \dfrac{m\overset{\frown}{GK} - m\overset{\frown}{CE}}{2}\\\\50 = \dfrac{152-m\overset{\frown}{CE}}{2}[/tex]

    [tex]50*2 = 152 - m\overset{\frown}{CE}\\\\100 = 152 - m\overset{\frown}{CE}[/tex]     

 [tex]100 + m\overset{\frown}{CE} = 152\\\\[/tex]  

           [tex]\sf m\overset{\frown}{CE}= 152 - 100\\\\m\overset{\frown}{CE} = 52^\circ[/tex]

A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

How to determine the amount of carpet needed for a rectangular room?

To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.

The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),

18 feet ÷ 3 feet/yard = 6 yards

So the dimensions of the room in yards are 10 yards by 6 yards.

To find the total area of the room, we need to multiply the length and width,

10 yards × 6 yards = 60 square yards

Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

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From given box plot that represents average minute time per night spent on homework 

Min = 0

Q1 = 20

Q2 = 48

Q3 = 60

Max = 190

7.  percent of the sophomores spend more than 60 minutes on homework per night= 25% because 60 represent the Q3 that is 75th percentile , so above that 25 % are remains.

8. range of times that the middle 50% of the sophomores spend on homework per night= 20 to 60 minutes Middle 50% that is from Q1 to Q3

60 - 20 = 40

9. No of  sophomores do not do homeworkHere given box plot is for average Time sophomores spend on homework per night. So it not gives the information about number of students. So we can not identify No of  sophomores do not do homework  from box plot .

10. percent of the sophomores spend less than 20 minutes per night on  homework = 25% because 20 represents the Q1 that is 25th percentile so below that value 25% of data are fall.

7)25%

8)40

9) can not decide 

10)25%

7. Sophomores that spend more than 60 minutes are 25%. 8. The range of times that the middle 50% of the sophomores spend on homework per night = 40.

A box plot, also called a box-and-whisker plot, is a statistical graph that shows how a dataset is distributed. As it enables a visual comparison of their median, range, and distribution, it is very helpful when comparing several datasets.

Two whiskers extend from a rectangular box that makes up a box plot. The whiskers reflect the minimum and maximum values that are not outliers, while the box represents the interquartile range (IQR), which is the middle 50% of the data. Each solitary point outside the whiskers represents an outlier.

From the given box plot that the five number summary can be calculates as follows:

Min = 0

Q1 = 20

Q2 = 48

Q3 = 60

Max = 190

7.  Now, the percent of the sophomores that spend more than 60 minutes on homework per night= 25%.

As 60 represent the Q3 that is 75th percentile. Above this the remaining value is 25%.

Thus, sophomores that spend more than 60 minutes are 25%.

8. The range of times that the middle 50% of the sophomores spend on homework per night= 20 to 60 minutes

Middle 50% that is from Q1 to Q3

60 - 20 = 40

9. Time sophomores spend on homework per night is not given. So we can not identify number of sophomores do not do homework from box plot .

10. The percent of the sophomores spend less than 20 minutes per night on homework = 25%

As 20 represents the Q1 that is 25th percentile so below that value 25% of data are fall.

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The owner can advertise 400 different sound systems. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers can be explained using the four fundamental operations, generally known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.

We are given that the owner of a stereo store carries 5 different CD players, 8 different receivers, and 10 different speakers and each sound system consists of one of each item.

So, the different sound systems that the owner can advertise is obtained by using the multiplication operation, which gives:

⇒ Different sound systems = 5 * 8 * 10

⇒ Different sound systems = 400

Hence, the owner can advertise 400 different sound systems.

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It will take 4.645 months to pay off the loan, which rounds up to 5 months.

Interest rate is the percentage of the principal amount charged by a lender or creditor for the use of borrowed money. In other words, it is the cost of borrowing money, usually expressed as an annual percentage rate (APR) or as a periodic rate for a specific time period.

Given:

Total amount of the loan (A) = $70,000

Monthly interest rate (i) = 0.25% = 0.0025

Monthly payment (P) = $250

We need to find the number of monthly payments (N) needed to pay off the loan.

Using the given formula:

N = (-log(1 - i×A/P))/(log(1+i))

Substituting the values we get:

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

N = (-㏑(0.72))/(㏑1.0025))

N = (-(-0.337))-4.308

N = 4.645 (approx.)

Therefore, it will take approximately 4.645 months to pay off the loan, which rounds up to 5 months.

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Therefore , the solution of the given problem of sequence comes out to be the sequence's roughly 10th term is 0.049 (rounded to the closest thousandth).

A sequence is a grouping of range numbers, or "terms." There are phrases like 2, 5, but choose 8. Certain narrative arcs can be made to go on forever by choosing to capitalise on a certain pattern that they exhibit. Use the designs 2, 5, 8, and then 3 to lengthen it. In a list of words for words, there exist formulas that show where to look. In mathematics, a sequence is a group of items that are ordered in some way.

Here,

The first three terms in the given sequence are 15, 9, and 27/5.

We must determine the pattern or rule that underlies the sequence in order to determine the tenth word.

=>  9 = 15 * (27/5) / 15

=>  27/5 = 9 * (27/5) / 9

Thus, each term is obtained by multiplying the constant value by (27/5) / 15, which may be written as 9/25.

In order to get the next phrase in the series, we can keep multiplying the preceding term by 9/25 using this constant value:

=>  9 * (9/25)⁷

When we compute this expression, we obtain:

=>  (Rounded to the closest thousandth) 9 * (9/25)⁷

As a result, the sequence's roughly 10th term is 0.049 (rounded to the closest thousandth).

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Answer: The formula for compound interest is:

A = P(1 + R/100)^t

where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.

Here, P = Rs. 3,500, R = 8%, and t = 2 years.

So, the amount after 2 years will be:

A = 3,500(1 + 8/100)^2

= 3,500(1.08)^2

= 3,892.32

Therefore, the compound interest for 2 years will be:

CI = A - P

= 3,892.32 - 3,500

= 392.32

Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.

Step-by-step explanation:

The BEST group for Ryan to survey would be the 25 fifth grade boys since they are the specific group that he is interested in studying.

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 gather data from a sample or population and to draw conclusions or make predictions based on that data.

There are two main branches of statistics: descriptive statistics and inferential statistics. Descriptive statistics is the process of summarizing and presenting data in a meaningful way, such as by calculating measures of central tendency (e.g. mean, median, mode), variability (e.g. range, variance, standard deviation), and correlation. Inferential statistics involves using probability theory to make inferences about a larger population based on a sample of data.

Statistics is used in a wide variety of fields, including business, economics, psychology, social sciences, medicine, and engineering. It is often used to test hypotheses, identify trends, and make predictions based on data. The field of statistics has evolved over time, with the development of new techniques and technologies for collecting and analyzing data.

The BEST group for Ryan to survey would be the 25 fifth grade boys since they are the specific group that he is interested in studying. Surveying a larger group of fifth grade students or every teacher at the school would not be as effective since it would include girls and boys who are not in the fifth grade, and teachers who may not have as much knowledge about the specific video game preferences of fifth grade boys. Surveying every boy who will pass to fifth grade next year would also not be as effective since they are not currently in the fifth grade and their preferences may change by the time they reach that grade. Therefore, surveying the 25 fifth grade boys would provide the most relevant and accurate data for Ryan's study.

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The complete question is:

Ryan wants to find the favorite video game of the fifth grade boys at his school. Which group would be BEST for Ryan to survey? 25 fifth grade boys 25 fifth grade students every teacher at his school every boy who will pass to fifth grade next year

Answer:

(-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52

Step-by-step explanation:

i literally just learned this today so here we go:

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

(x - h)^2 + (y - k)^2 = r^2

We are given the center of the circle as (-7, -4), so we can substitute these values for h and k:

(x - (-7))^2 + (y - (-4))^2 = r^2

(x + 7)^2 + (y + 4)^2 = r^2

We also know that the circle contains the point (-1, -8).

We can substitute these values for x and y, and solve for r:

(-1 + 7)^2 + (-8 + 4)^2 = r^2

36 + 16 = r^2

r^2 = 52

Substituting this value of r^2 into the equation for the circle, we get:

(x + 7)^2 + (y + 4)^2 = 52

Therefore, the equation of the circle with center (-7, -4) containing the point (-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52

Answer:

mean: 20mins

Step-by-step explanation:

add them all together to get 240

then divide by how many there are

240÷12=20

so the mean is 20mins

The reduced radical forms of the expressions provided are as follows:

1.  3^(4/9m)

2. -11√7

3. a^(1/2) * b^6

4.  2x^(9/4) * y^3

5. 16 - ^3√24

6. 4p^(9/10)q^(7/10)

A reduced radical form is a way of simplifying expressions that contain radicals such as square roots and cube roots, as much as possible. In a reduced radical form, the radical is simplified to its lowest possible terms.

To obtain the reduced radical forms of the expresions, we can proceed with the workings:

1. 3^(√4/9m^2) = 3^(2/3 * 1/3√4m^2) (since √4 = 2)

= (3^(2/3))^(1/3√4m^2)

= (3^(2/3))^(2/3m)

= 3^(4/9m)

2. √63 = √(9 * 7) = 3√7

√700 = √(100 * 7) = 10√7

√112 = √(16 * 7) = 4√7

√63 - √700 - √112 = 3√7 - 10√7 - 4√7

= -11√7

3. (a^2b^8/a^1/3)^3/4 = (a^2/1/3√a)^3/4 * b^8^3/4

= (a^(2/3))^3/4 * b^6

= a^(1/2) * b^6

4. ^4√1024x^9y^12 = (^4√1024) * (^4√x^9) * (^4√y^12)

= 2 * x^(9/4) * y^(12/4)

= 2x^(9/4) * y^3

5. 4^3√81 = 4^3 * 3 = 64

2^3√72 = 2^3 * 2√9 = 16√9 = 48

^3√24 can't be simplified any further

4^3√81 - 2^3√72 - ^3√24

= 64 - 48 - ^3√24 or  16 - ^3√24.

6. ^5√2pq^6 • 2 √2p^3q

= 2p^(3/5)q^(6/5) * 2p^(3/2)q^(1/2)

= 4p^(9/10)q^(7/10)

So, the results are the simplified or reduced forms of the expressions.

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Answer: What is the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic?

Let's call the number of pulled-pork sandwiches "P" and the number of barbeque chicken sandwiches "C". According to the problem, the organizers are making 2 pulled-pork sandwiches for every 5 barbeque chicken sandwiches. This means that:

P/C = 2/5

To simplify this ratio, we can multiply both sides by a common factor that will make the denominators the same. In this case, the smallest common multiple of 2 and 5 is 10, so we can multiply both sides by 10:

10(P/C) = 10(2/5)

Simplifying this expression, we get:

2P = 4C

Dividing both sides by 2, we get:

P/C = 2/4

Simplifying this fraction, we get:

P/C = 1/2

Therefore, the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic is 1:2.

Step-by-step explanation:

The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.

Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.

Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.

In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.

The statements that provide support for Chloe's claim are:

A. A<0 because A is to the left of zero.

F. B>0 because B is to the right of zero.

Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.

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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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The absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3

What is an absolute value equation?

An absolute value equation can be written as |expression| = value

To have -8 and -2 as the solution set, we need an absolute value equation that produces these two values when the expression inside the absolute value is either positive or negative.

We can write,

|x + 5| = 3

To solve for x, we have two cases,

Case 1: x + 5 is positive

If x + 5 is positive, then the equation becomes x + 5 = 3

Solving for x,

x = -2

This matches one of the solutions we want.

Case 2: x + 5 is negative

If x + 5 is negative, then the equation becomes -(x + 5) = 3

Solving for x,

x = -8

This also matches the other solution we want.

Therefore, the absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3.

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It would take approximately 1,980 minutes (33 hours) for the tester to eat all possible cheeseburgers.

Nick's monthly mortgage payment is $482.16.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To calculate Nick's monthly mortgage payment, we first need to find out the amount he borrowed from the bank, which is 75% of the purchase price:

$145,500 x 0.75 = $109,125

Next, we need to calculate the monthly interest rate. We can do this by dividing the annual interest rate (3.15%) by 12:

3.15% / 12 = 0.002625

Now we can use the following formula to calculate Nick's monthly payment:

M = P [ [tex]i(1 + i)^{n}[/tex] ] / [ [tex](1 + i)^{n}[/tex] – 1]

Where:

M = Monthly payment

P = Loan amount (principal)

i = Monthly interest rate

n = Number of payments (in months)

Plugging in the values we have:

M = $109,125 [ 0.002625 [tex](1 + 0.002625)^{360}[/tex] ] / [ [tex](1 + 0.002625)^{360}[/tex] – 1]

M = $482.16

Therefore, Nick's monthly mortgage payment is $482.16.

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Mohal will be able to paint 9 bookcases for the amount of paint.

An expression for a portion of a whole is a fraction. It is represented by the numerator above the denominator, with a horizontal line separating the two numbers. In mathematics, fractions are used to represent fractions of a whole or values that are not whole numbers. Like whole numbers, they can be multiplied, split, added, and subtracted. Ratios and proportions, which are crucial ideas in many branches of mathematics and science, are also represented by fractions.

Given that, he has 1 1 /8​ gallons of paint.

Thus, number of bookcases are:

1 1/8 ÷ 1/8 = (9/8) ÷ (1/8) = 9

Hence, Mohal will be able to paint 9 bookcases for the amount of paint.

Learn more about fraction here:

https://brainly.com/question/10354322

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