21. ALGEBRA Kim and Sarah Carson applied for a $120,000 mortgage loan at an 8.25%
annual interest rate. The loan is for 30 years, and the Carsons will repay it in equa
monthly payments that include interest. Find the (a) monthly payment using the
formula, (b) amount paid, and (c) total interest charged.

Answer:

30

Step-by-step explanation:

15/3=5

5 x 5 = 25

25 + 5 = 30

Answer:

C

Step-by-step explanation:

Given

5² + (x ÷ 3) ← substitute x = 15 into the expression

= 25 + (15 ÷ 3)

= 25 + 5

= 30 → C

well, we know it's centered at (-2 , 1) and it passes through (-4 , 1), if it passes through there, that means that the distance from the center to (-4 , 1) must be its radius.

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-4 - (-2)]^2 + [1 - 1]^2}\implies d=\sqrt{(-4+2)^2+0^2}\implies d=2\)

\(\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-2}{ h},\stackrel{1}{ k})\qquad \qquad radius=\stackrel{2}{ r} \\\\\\\ [x-(-2)]^2+[y-1]^2=2^2\implies (x+2)^2+(y-1)^2=4\)

Answer:

3x(2x - 3)

Step-by-step explanation:

Given

y = 6x² - 9x ← factor out 3x from each term

  = 3x(2x - 3)

To determine the loan amount Molly needs, subtract the down payment and cash allowance from the total cost of the car.

Loan amount = Total cost - Down payment - Cash allowance

To calculate Molly's monthly payment, use the Loan Calculator with the loan amount, loan term in months, and the APR of 1.9%.

To find the total interest paid, subtract the loan amount from the product of the monthly payment and the loan term.

To calculate the total cost of the car, add the down payment, cash allowance, loan amount, and total interest paid.

To calculate the loan amount Molly needs, we subtract the down payment and cash allowance from the total cost of the car. Let's assume the total cost is $X.

Loan amount = Total cost - Down payment - Cash allowance = X - $2500 - $500 = X - $3000.

To calculate Molly's monthly payment using the Loan Calculator and the 1.9% APR offer, we need to know the loan amount, the loan term in months, and the APR. Let's assume the loan term is Y months.

Using the Loan Calculator, we can determine the monthly payment based on the loan amount, loan term, and APR.

To calculate the total interest Molly will pay using this plan, we can multiply the monthly payment by the loan term in months and subtract the loan amount. This will give us the total interest paid.

Total interest = (Monthly payment * Loan term) - Loan amount.

To calculate the total cost of the car for Molly using this plan, we add the down payment, cash allowance, and the total interest paid to the loan amount.

Total cost = Loan amount + Down payment + Cash allowance + Total interest.

Please provide the values of X and Y to calculate the specific amounts.

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The equation of the graph passing through the points (-6, -3) and (6, -7) is:

y = (-1/3)x - 5.

To find the equation of a linear graph passing through two given points, we can use the slope-intercept form of a linear equation, which is given by:

y = mx + b

Where:

y and x are the coordinates of any point on the line.

m is the slope of the line.

b is the y-intercept (the point where the line intersects the y-axis).

First, let's calculate the slope (m) using the given points (-6, -3) and (6, -7):

m = (y2 - y1) / (x2 - x1)

m = (-7 - (-3)) / (6 - (-6))

= (-7 + 3) / (6 + 6)

= -4 / 12

= -1/3

Now that we have the slope (m), we can substitute it into the slope-intercept form along with one of the given points to find the value of the y-intercept (b).

Let's use the point (-6, -3):

-3 = (-1/3)(-6) + b

-3 = 2 + b

b = -3 - 2

b = -5

Therefore, the equation of the graph passing through the points (-6, -3) and (6, -7) is:

y = (-1/3)x - 5

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Answer:

declares that human rights are universal – to be enjoyed by all people, no matter who they are or where they live

Step-by-step explanation:

The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

P(B/A) = P(B) P(A and B)

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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-3× - 5= 10+5

-3×=15

15÷-3 = -5

x= -5

The general solution of the given second-order linear differential equation, using reduction of order, is determined based on the given function y1(x) = x^(-1).

In reduction of order, we assume a second solution in the form of y2(x) = u(x)y1(x), where y1(x) is the given first solution. By substituting this into the differential equation, we get:

x(u''(x)y1(x) + 2u'(x)y1'(x) + u(x)y1''(x)) + (2 + 2x)(u'(x)y1(x)) + 2(u(x)y1(x)) = 0.

Simplifying and rearranging terms, we have:

xu''(x)y1(x) + 2xu'(x)y1'(x) + xu(x)y1''(x) + 2u'(x)y1(x) + 2xu'(x)y1(x) + 2u(x)y1(x) = 0.

This can be further simplified to:

xu''(x)y1(x) + (4xu'(x) + 2u(x) + 2xu'(x))y1(x) + xu(x)y1''(x) = 0.

Now, since y1(x) = x^(-1), we can substitute the derivatives of y1(x) into the equation above. Solving the resulting equation for u(x) will give us the general solution.

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The statements that apply to the relative use of dot plots and histograms are Dot plots show the relative frequency of data values and Dot plots are most useful for small data sets.


1. Dot plots are a graphical representation of data that show the relative frequency of data values. Each dot in a dot plot represents one data point, and the position of the dot on the axis represents the value of the data point. Histograms, on the other hand, show the frequency distribution of data values in a bar graph format.

2. Dot plots are most useful for small data sets because they allow for the easy visualization of individual data points and their distribution. Histograms, on the other hand, are more useful for large data sets as they provide a summary of the data distribution in a more concise manner. Dot plots can become cluttered and difficult to read when used with large data sets.

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Answer:

79.5

Step-by-step explanation:

10^7 = 10^6 * 10

then 10*7.95 = 79.5

Answer:

L = 4πa²b

Step-by-step explanation:

Multiply both sides by 4πa²b.

radius : A straight line extending from the center of a circle or sphere to the circumference or surface

In geometry, circles and spheres are two-dimensional and three-dimensional shapes, respectively, that possess unique characteristics. One important concept associated with circles and spheres is the notion of a line extending from their centers to their circumferences or surfaces. This line has a specific name and serves as a fundamental element in understanding these geometric shapes. In this detailed explanation, we will explore the term used to describe this line and delve into its significance.

The line extending from the center of a circle to its circumference, or from the center of a sphere to its surface, is called a "radius." The term "radius" refers to a straight line segment that connects the center of the circle or sphere to any point on its circumference or surface. It is important to note that the term "radius" is used exclusively when referring to circles and spheres and not to other shapes or objects.

Let's examine the properties and significance of the radius in both circles and spheres:

1. Circle:

In a circle, the radius is a fundamental element that defines the size and shape of the circle. It is the distance between the center of the circle and any point on its circumference. Notably, all radii of a circle are equal in length. In mathematical formulas and calculations involving circles, the radius is often denoted by the letter "r."

The radius plays a crucial role in determining various properties of the circle, including its area, circumference, and relationships with other geometric elements, such as chords and tangents.

2. Sphere:

In a sphere, which is a three-dimensional object analogous to a circle, the radius serves a similar purpose. It extends from the center of the sphere to any point on its surface. Like in a circle, all radii of a sphere are equal in length. In mathematical formulas and calculations involving spheres, the radius is typically denoted by the letter "r."

The radius of a sphere is essential in determining properties such as its volume, surface area, and relationships with other geometric elements like great circles or diameters.

The radius is a foundational concept in the study of circles and spheres. It provides a measure of distance from the center to the outer edge and is used in various mathematical calculations and geometric analyses. Moreover, the radius plays a crucial role in determining the symmetry, proportions, and relationships between different parts of circles and spheres.

It is worth mentioning that the concept of the radius is closely related to other geometric elements in circles and spheres. For instance, diameters are lines that pass through the center of a circle or sphere and have endpoints on the circumference or surface, respectively. The diameter is always twice the length of the radius. Additionally, chords are segments within a circle or sphere that connect any two points on the circumference or surface.

The radius bisects any chord that passes through the center, dividing it into two equal segments.

In conclusion, the line extending from the center of a circle to its circumference or from the center of a sphere to its surface is called a "radius." The radius is a fundamental element that defines the size, shape, and proportions of circles and spheres. It plays a crucial role in calculating various properties, such as area, circumference, volume, and surface area.

Understanding the concept of the radius is essential in geometry and provides insights into the symmetrical and proportional relationships within circles and spheres.

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Answer:

for the median its 7

for the mean its 6.

the mode is 9

Step-by-step explanation:

Also sorry for not saying anything for the past many days been busy.

Happy bday

hope you have fun on your trip

Answer:

2

Step-by-step explanation:

If you subtract 8from20 there's 11 memeber student councilors left which then you subtract another 8from the remaining 11 students and there would be 3 student councilors left which means

there can only be 2.5 different committees because you can't subtract 3 from 8

Answer:

125790 different committees can be chosen.

Step-by-step explanation:

The principal would like to assemble a committee of 8 students from the 20-member student council.

We need to find How many different committees can be chosen?

Since the order is not important, so we use Combinations to solve the question.

The formula used is: \(^nC_r=\frac{n!}{(n-r)!r!} \\\)

In the question given: we have n = 20 and r = 8

Putting values and finding the number of ways committees can be chosen:

\(^nC_r=\frac{n!}{(n-r)!r!} \\\\^{20}C_8=\frac{20!}{(20-8)!8!} \\^{20}C_8=\frac{20*19*18*17*16*15*14*13*12!}{12!8!} \\^{20}C_8=\frac{20*19*18*17*16*15*14*13}{8!} \\^{20}C_8=\frac{20*19*18*17*16*15*14*13}{8*7*6*5*4*3*2*1} \\^{20}C_8=\frac{5079110400}{40320}\\^{20}C_8=125970\)

So, 125790 different committees can be chosen.

Thales of Miletus is believed to be the first person who claimed that natural phenomena could be described by mathematics.

Thales of Miletus was a Greek philosopher, mathematician, and astronomer who lived around 624 BCE to 546 BCE. He is widely regarded as one of the Seven Sages of Greece and is known for his contributions to various fields, including geometry, astronomy, and philosophy.

Thales believed that everything in the universe could be explained by natural causes rather than the actions of gods or other supernatural forces. He also believed that these natural phenomena could be described mathematically. For example, Thales was able to predict an eclipse of the sun using his knowledge of geometry and astronomy.

Therefore, Thales of Miletus is often regarded as the first scientist in history because of his emphasis on using reason and evidence to explain the natural world.

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Answer:

Could have been 12, 13, or 14

Step-by-step explanation:

If you add 2 to 12 it's 14. 14 isn't less than 14 or more than 16.

If you add 2 to 13 it's 15. 15 isn't less than 14 or more than 16.

If you add 2 to 14 it's 16. 16 isn't less than 14 or more than 16.

Answer:

A

Step-by-step explanation:

well the one on the bottum is nonliinneir so no and the top is lienier and proprtional

Answer:

(x - 4)² + (y + 3)² = 4

Remember the circle formula:

(x - h)² + (y - k)² = r²

h = X center point  

k = Y center point

In this case your center point is (4,-3) and your radius is 2

If u plug everything in and simplify you should get this:

(x - 4)² + (y - (-3))² = 2²

(x - 4)² + (y + 3)² = 4

(a) The total expected payoffs for Tech when going for one point are (0.98)($7.2 million) + (0.02)(-$1.7 million) = $7,014,000 (0.02)(0.20)($7.2 million) + (0.02)(0.80)(-$1.7 million) = -$108,000 Therefore, based on the expected payoffs, Tech should go for one point.

(b)  Tech’s probability of winning the game in overtime should be 76.82% to make Tech indifferent to going for either 1 or 2 points.

Decision tree analysis is a graph with different decision options and their potential consequences. Tech can go for two points or one point, and if one point is successful, it will go over time. The decision tree analysis is as follows: The following probabilities and outcomes will be used for decision tree analysis if Tech goes for two points: Probability of winning = 0.33 The payoff for a win is $7.2 million The payoff for a loss is -$1.7 million The probability of losing is 0.67 The payoff for a win is -$1.7 million The payoff for a loss is -$1.7 million If Tech goes for one point, the following probabilities and outcomes will be used: Probability of winning = 0.98 The payoff for a win is $7.2 million The payoff for a loss is -$1.7 million The probability of losing is 0.02 The payoff for a win is -$1.7 million The payoff for a loss is -$1.7 million If it goes for one point and loses, it will have a 20% chance of winning in overtime. Therefore, the probability of going for one point and winning is 0.98, while the probability of going for one point and losing is 0.02. If Tech goes for one point and goes to overtime, the probability of winning in overtime is 0.20. The total expected payoffs for Tech when going for two points are: (0.33)($7.2 million) + (0.67)(-$1.7 million) = $1,386,000 The total expected payoffs for Tech when going for one point are: (0.98)($7.2 million) + (0.02)(-$1.7 million) = $7,014,000 (0.02)(0.20)($7.2 million) + (0.02)(0.80)(-$1.7 million) = -$108,000 Therefore, based on the expected payoffs, Tech should go for one point.

(b) Let P be the probability that Tech will go for one point, and 1 – P be the probability that Tech will go for two points. Then, the overall probability of Tech winning the game is given by: P(Tech wins) = P(Tech wins, goes for one point) + P(Tech wins, goes for two points)Let A denote the event that Tech goes for one point and wins, B denote the event that Tech goes for two points and wins, and C denotes the event that Tech goes for two points and loses. Then we have: P(Tech wins) = P(A) + P(B) = 0.98P + 0.33(1 – P)If Tech goes for one point, there is a 0.98 probability of winning, and if Tech goes for two points, there is a 0.33 probability of winning. Let D denote the event that the game goes into overtime. Then: P(A) = P(Tech wins | A)P(A) = 0.98P(1 – 0.2)P(B) = P(Tech wins | B)P(B) = 0.33P(C) = P(Tech loses | C)P(C) = 0.67(1 – P)Hence: P(Tech wins) = P(A) + P(B) = 0.98P + 0.33(1 – P)If Tech is indifferent between going for one point and going for two points, it follows that the payouts for the Sugar Bowl and the Gator Bowl must be equalized. We have: P(Tech wins) = P(Tech wins, goes for one point) + P(Tech wins, goes for two points) = $7.2 million x P(A) + $7.2 million x P(B) + $1.7 million x P(C)Now we can solve for P as follows:0.98P + 0.33(1 – P) = $7.2 million x P(A) + $7.2 million x P(B) + $1.7 million x P(C)0.98P + 0.33 – 0.33P = $7.2 million x 0.98P + $7.2 million x 0.33P + $1.7 million x 0.67(1 – P)0.65P = $7.2 million x 0.98P + $7.2 million x 0.33P + $1.139 million – $1.139 P0.481P = $7.2 million x 0.98P + $7.2 million x 0.33P + $1.139 millionP = $1.139 million/$1.4815 millionP = 0.7682, or 76.82%Therefore, Tech’s probability of winning the game in overtime should be 76.82% to make Tech indifferent to going for either 1 or 2 points.

Sam drove the truck for 247 miles. The solution has been obtained by using the arithmetic operations.

Let's assume that Sam drove the truck for "x" miles. According to the given information, there was a base fee of $16.95 and an additional charge of 98 cents for each mile driven. Therefore, the total cost for renting the truck can be calculated by adding all which gives us the following:

Total cost = Base fee + (Additional charge per mile * Number of miles driven)

From the information given, we know that Sam had to pay $259.01 when he returned the truck. By substituting the values into the equation, we can solve for the number of miles driven:

$259.01 = $16.95 + (0.98 * x)

Rearranging the equation, we have:

0.98x = $259.01 - $16.95

0.98x = $242.06

Dividing both sides of the equation by 0.98, we get:

x = $242.06 / 0.98

x ≈ 247.02

Therefore, Sam drove the truck for approximately 247 miles.

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The approximate expected real rate of interest is find by subtracting the approximate expected inflation rate from the yield of the Treasury bill. In this case, the approximate expected real rate of interest is around 1.5%.

To calculate the approximate expected real rate of interest, we can use a simplified formula that involves subtracting the approximate expected inflation rate from the nominal interest rate. In this scenario, the nominal interest rate is 4.5%, and the expected inflation rate is 3%.

Using the simplified formula, we subtract the approximate expected inflation rate of 3% from the nominal interest rate of 4.5% to get an approximate expected real rate of interest of 1.5%.

It's important to note that this calculation provides an approximation of the expected real rate of interest and may not account for all factors and variations in inflation. For a more precise calculation, additional considerations and data would be required.

Therefore, the approximate expected real rate of interest in this case is around 1.5%. This suggests that after adjusting for an expected inflation rate of 3%, the investor can anticipate an approximate real return of 1.5% on their investment in the one-year Treasury bill.

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a) The range is 14.

b) The sample variance is 20.78.

c) The sample standard deviation is 4.56.

a) Range

The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:

Range = maximum value - minimum value

Range = 15 - 1

Range = 14

b) Sample variance

To calculate the sample variance, follow these steps:

1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:

n = 9

∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75

X = ∑x/n = 75/9 = 8.33

2. Subtract the sample mean from each data value, square the result, and add up all of the squares:

(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23

3. Divide the sum of squares by one less than the total number of values to get the sample variance:

s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78

Therefore, the sample variance is 20.78 (rounded to two decimal places).

c) Sample standard deviation

To calculate the sample standard deviation, take the square root of the sample variance:

s = √s² = √20.78 = 4.56

Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).

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The book value of the building in 2014 was $3.96 million. The book value of the building in 2028 will be $2.28 million.

a) The book value of the building in 2014 can be calculated as follows:

Book Value = Original Cost - (Depreciation Rate * Years Depreciated)

Depreciation Rate = Original Cost / Number of Years

Depreciation Rate = 6 million / 50 years = $120,000 per year

Years Depreciated = 2014 - 1997 = 17 years

Book Value = 6 million - (120,000 * 17) = 6 million - 2.04 million = $3.96 million

So, the book value of the building in 2014 was $3.96 million.

b) The book value of the building in 2028 can be calculated in a similar manner:

Years Depreciated = 2028 - 1997 = 31 years

Book Value = 6 million - (120,000 * 31) = 6 million - 3.72 million = $2.28 million.

So, the book value of the building in 2028 will be $2.28 million.

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Answer:

She can make 2 bags of 4, and she will have 3 bananas left.

Step-by-step explanation:

4 + 4 + 4 = 12; that is 1 banana too many since she only has 11 bananas.

She has 11 bananas, so she has 4 + 4 + 3 = 11.

She can make 2 bags of 4, and she will have 3 bananas left.

188.4 cm²  is the surface area of the cone .

What is known as a cone?

given   r = 4 cm

           l = 15 cm

the curved surface area = πrl

                                     = 3.14 * 4 * 15

                                      = 188.4 cm²

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Answer: 76 cm2

Step-by-step explanation:

I Did it trust

The x-intercept for the graph of y is found to be at x = 2.

The quadratic equation given is

y = x² - 4x + 4

Put y = 0

0 = x² - 4x + 4

It becomes perfect square for (x - 2).

It can be written as;

(x - 2)² = 0

Take square root on the both sides

x - 2 = 0

x = 2

Thus, the x-intercept for the graph of y is found to be at x = 2.

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The correct question is-

What is the x-intercept of the graph of y = x² - 4x + 4?

Answer:

C. 39/48 = 81%

Step-by-step explanation:

To determine the percentage of females who only said they like cats using the given two-way table, we need to find the number of females who selected "cats" only and divide it by the total number of females surveyed. We can then multiply the result by 100 to get the percentage.

According to the provided two-way table:

Number of females who only said they like cats = 39

Total number of females surveyed = 48

To calculate the percentage:

Percentage of females who only said they like cats = (Number of females who only like cats / Total number of females surveyed) * 100

Percentage of females who only said they like cats = (39 / 48) * 100 ≈ 81.25%

Therefore, the correct option is:

C. 39/48 = 81%