A new homeowner is purchasing a living room set for $2,975 and must decide between two financing offers.

Offer 1: $250 down payment, 24.90% interest rate, compounded monthly, for 3 years, with no payments due for 6 months and then fixed payments of $139.05 for the remainder of the loan term

Offer 2: $400 down payment, 22.90% interest rate, compounded monthly, for 3 years, with no payments due for 12 months and then fixed payments of $165.76 for the remainder of the loan term

Part A: What is the total cost of offer 1? Explain which technology you used to solve and each step of your process. (3 points)

Part B: What is the total cost of offer 2? Explain which technology you used to solve and each step of your process. (3 points)

Part C: Which financing offer should the new homeowner choose? Explain your reasoning. (4 points)

\(\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_{3}(y+5)+\log_3(6)~~ = ~~\log_3(66) \\\\[-0.35em] ~\dotfill\\\\ \log_3[(y+5)\cdot 6]=\log_3(66)\implies (y+5)6=66 \\\\\\ y+5=\cfrac{66}{6}\implies y+5=11\implies \boxed{y=6}\)

Answer:

Step-by-step explanation:

24

\(x^2 -8x-2=0\\\\x^2 -8x=2\\\\x^2 -8x+16=18\\\\(x-4)^2 =18\\\\x-4=\pm \sqrt{18}\\\\\boxed{x=4 \pm \sqrt{18}}\)

Step-by-step explanation:

200m:1.4km

200m:1400m

1:7

The decimal representation of the given sequence is 4,063.21.

The given sequence can be interpreted as follows: "63 ones, 21 hundredths, 4 thousand." To convert this sequence into decimal form, we need to understand the place value of each digit.

Starting from the left, we have "63 ones." This means we have 63 units, which can be represented as 63.

Next, we have "21 hundredths." Since there are two digits after the decimal point, the number becomes 0.21.

Finally, we have "4 thousand." Considering the place value, 4 thousand would be written as 4,000.

Putting it all together, we have 63 + 0.21 + 4,000, which equals 4,063.21. Therefore, the decimal representation of the given sequence is 4,063.21.

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Answer:

6 benches are needed

Step-by-step explanation:

3/4= 6/8

1/8 goes into 6/8, 6 times so,

6 benches are needed on the 3/4 mile trail

Answer:

\(280000\)

Step-by-step explanation:

Given the following question:

\(7372\times39\)

To estimate by rounding each number so it only has one nonzero digit, we have to round the number that is the furthest on the left.

\(7372\times39\)

\(7372\)

\(3<5\)

\(7000\)

\(39\)

\(9>5\)

\(40\)

\(7000\times40=280000\)

\(=280000\)

Hope this helps.

Answer:

\(m=\frac{5}{3}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph

Point (-2, 0)

Point (1, 5)

Step 2: Find slope m

The output value of (g/f)(x) is 9x/(7x + 28).

The domain of g/f is (-∞, -4) U (-4, ∞)..

In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;

(g/f)(x) = (9/(x + 4)) ÷ 7/x

By rearranging the mathematical expression using the multiplication operation, we have the following:

(g/f)(x) = (9/(x + 4)) × x/7

(g/f)(x) = 9x/(7x + 28)

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

7x + 28 ≠ 0

7x ≠ -28

x ≠ -4

Domain = (-∞, -4) U (-4, ∞).

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Answer: serbia

Step-by-step explanation:

They will be when they pass each other at 44 4/9 mins.

This is a classic question on Speed, time, & distance.

1. When time traveled in each segment is constant, then average speed is simple mean of speeds.

2. When distance traveled in each segment is constant, then average speed is reciprocal of simple mean of reciprocal of speeds. It is basically called Harmonic mean.

So this question falls in the category of 2.

=> So, average speed = Reciprocal of mean of reciprocals of 40 & 50.

=> Average speed = Reciprocal of mean of 1/40 & 1/50.

=> Average speed = Reciprocal of (1/40 + 1/50)/2

= Reciprocal of (5+4)/400

= 44 4/9 mins

Hence, they will be when they pass each other at 44 4/9 mins.

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Answer:

  ∠DQE = 65°

Step-by-step explanation:

You want to know the measure of Angle DQE in the given figure.

Triangle ADE is inscribed in a semicircle, so is a right triangle. That makes acute angle AED complementary to acute angle EAD. The latter is given as 50°, so ...

  ∠AED = 90° -50° = 40°

We know that tangent line QE is perpendicular to diameter AE, so angle AEQ is a right angle. Segment ED divides that right angle into complementary angles, so ...

  ∠DEA +∠DEQ = 90°

  ∠DEQ = 90° -∠DEA = 90° -40° = 50°

A.pex angle DEQ in isosceles triangle DEQ being 50° means that the base angles QDE and DQE will have measure ...

  ∠DQE = (180° -50°)/2 = 130°/2

  ∠DQE = 65°

__

Alternate solution

Let angles DQE and QDE be represented by x. Then the sum of angles in quadrilateral ADQE is 360°:

  50° +(90+x)° +x° +90° = 360°

  230° +2x = 360° . . . . . . simplify

  x = 130°/2 = 65° . . . . . solve for x

Answer:

B. Sigma Subscript p hat Baseline = 0.032 In SRSs of size 100, the sample proportion of women in this town giving birth to twins typically varies 0.032 from the true proportion, p = 0.12.

Step-by-step explanation:

took the quiz

The correct calculation and interpretation of the standard deviation of the sampling distribution of p hat is the sample proportion of women in this town giving birth to twins typically varies 0.032 from the true proportion, 0.12.

Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.

The standard deviation of the sampling distribution of p hat is given as,

\(\sigma_{ \hat p}=\sqrt\dfrac{p(1-p)}{n}\)

Here, p is the proportion and n is the number of sample.

The proportion of twins born in a town is p = 0.12. Now there is randomly select 100 women from this town who give birth in the next year.

\(\sigma_{ \hat p}=\sqrt{\dfrac{0.12(1-0.12)}{100}}\\\sigma_{ \hat p}=\sqrt{0.001056}\\\sigma_{ \hat p}=0.032\)

Thus, the correct calculation and interpretation of the standard deviation of the sampling distribution of p hat is the sample proportion of women in this town giving birth to twins typically varies 0.032 from the true proportion, 0.12.

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Answer:

I believe it would be 1400

Step-by-step explanation:

If it is multiple choice this would probably be the best choice

Hailey goes to a store an buys an item that price of a dollars, so the expression that represents the total amount that Hailey paid at the register in terms of a is 0.702a.

The amount of discount that Hailey receives is 35% of the original price, which is 0.35a. Therefore, the discounted price she pays is a - 0.35a = 0.65a.

The amount of tax that is added to the discounted price is 8% of the discounted price, which is 0.08(0.65a) = 0.052a.

So the total amount that Hailey paid at the register is the discounted price plus the tax:

total amount = discounted price + tax

total amount = 0.65a + 0.052a

Simplifying this expression, we get:

total amount = 0.702a

Therefore, the expression that represents the total amount that Hailey paid at the register in terms of a is 0.702a.

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Answer:

300,000 8,000 800 i think sorry if i got it wrong

Step-by-step explanation:

Answer:

1 x 300,000 + 8 x 1,000 + 8 x 100

Step-by-step explanation:

On solving the provided question we can say that The following is the data table of the function.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

the provided functions that can be formed are

           x            -infinity < x < -10

f(x) =    2x + 10          -10 < x < 10

           4X - 10       10 < x < infinty

The following is the data table of the function.

x              y

-20          -20

-15          -15

-10          -10

-5             0

0              10

5               20

10              30

15              50

20              70

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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.

A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.

Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The following is the data table of the function.

x               y

-20          -20

-15           -15

-10           -10

-5              0

0              10

5              20

10              30

15              50

20             70

The provided functions that can be formed are

\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

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Answer:

she was 13.1 meters below sea level in 1 minute

Step-by-step explanation:

make it into a fraction 5/65.5 (after 5 minutes, she is 65.5 meters underwater)

divide the numerator (representing the minutes) by 5 to get 1 minute

5÷5= 1

then divide the denominator (representing the meters below sea level) by 5 as well to get her position she is at after 1 minute

65.5÷5= 13.1

after dividing you should get 1/13.1 (after 1 minute, she is 13.1 meters underwater)

Answer:

30 dollars. I think

Step-by-step explanation:

3x5=15

15+15=30

Note: Deposit means to put in!
The correct answer is 30 dollars.

How did I get my answer? Well I did:
$3 per day times 5 days which is $15. I then added that $15 to the $15 it already contained which was $30

—————

Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

—————

Answer:

$2.20

Step-by-step explanation:

44 divided by 20.

=2.2

=2.20

=$2.20

Answer:

$2.20 per wing

Step-by-step explanation:

Take the total cost and divide by the number of wings to determine the cost per wing

$44.00 / 20 wings

$2.20 per wing

Answer:

C (-8-i)

Step-by-step explanation:

The sum of the -8 and -i will be option C. (-8-i).

In mathematics, the sum can be defined as the result or answer we get on adding two or more numbers or term.

So here we need to calculate the sum of -8 and -i. For this, we will do a sum operation.

\(Sum = (-8)+(-i)\)

As we know that minus and plus together become minus so

\(Sum= -8-i\)

Hence the sum of the -8 and -i will be option C. (-8-i).

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Answer:

x=2

x=-4

Step-by-step explanation:

\( |x + 1| = 3\)

\(x + 1 = 3 \\ x + 1 = - 3\)

therefore

\(x = 2 \\ x = - 4\)

Saving for a down payment was worth it for Isabel. It reduces the total amount paid for the car by lowering the loan amount, resulting in less interest paid over time.

When evaluating whether saving for a down payment on a car was worth it for Isabel, we need to consider the difference in the total amount paid for the car in two scenarios: with a down payment and without a down payment. Let's analyze the two scenarios to make a judgment.

Scenario 1: With a down payment

In this scenario, Isabel saved up and made a down payment on the car. As a result, her monthly loan payment fits within her budget. By making a down payment, she reduces the principal amount borrowed and, subsequently, the interest charged on the loan.

The benefits of saving for a down payment include:

Lower loan amount: By making a down payment, Isabel reduces the total amount borrowed from the lender.

Reduced interest: With a lower loan amount, the interest charged on the loan is also reduced.

Shorter loan term: A down payment can help Isabel secure a shorter loan term, reducing the overall interest paid over time.

Scenario 2: Without a down payment

In this scenario, Isabel does not make a down payment and finances the entire purchase price of the car. As a result, her monthly loan payment may be higher, as she is borrowing a larger sum and potentially paying more interest over the loan term.

The drawbacks of not saving for a down payment include:

Higher loan amount: Without a down payment, the entire purchase price is financed, leading to a higher loan amount.

Increased interest: With a higher loan amount, more interest may accumulate over the loan term, resulting in a higher total cost of the car.

By comparing the two scenarios, we can assess the impact on the total amount paid for the car. Generally, having a down payment reduces the loan amount, decreases interest charges, and may result in a shorter loan term. This, in turn, can lead to substantial savings in the long run.

To determine the exact difference in the total amount paid for the car in each scenario, we would need specific details such as the purchase price of the car, the interest rate, and the loan term. With these figures, we could calculate the total cost of the car, including interest, in both scenarios and compare the results. Based on this analysis, we can then determine if saving for a down payment was worth it for Isabel.

In conclusion, saving for a down payment on a car can offer financial benefits such as lower loan amounts, reduced interest charges, and potentially shorter loan terms. Considering the potential cost savings and improved financial stability, it is generally advisable for Isabel to save for a down payment, making it worth the effort and consideration.

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Question

The down payment makes the monthly loan payment fit into Isabel's budget. Besides this benefit, do you think saving for a down payment on the car was worth it for Isabel? Use each monthly payment with and without a down payment) to find the difference of the total amount paid for the car in each scenario to justify your answer.

Answer:

m = -3/4

Step-by-step explanation:

Calculation of the Slope of a line

The information provided about the line is that the line passes through the points  (-8, 9) to (-4,6)

Therefore, the first step consists in computing the slope. The formula for the slope is:
\(m=\frac{y_2-y_1}{x_2-x_1}\)

Now, by plugging the corresponding numbers is , we get that the slope is:

\(m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-9}{-4-(-8)} =\frac{6-9}{-4+8} =-\frac{3}{4}\)

So then, we find that the slope is \(m=-\frac{3}{4}\) and that the line passes through the point  \((-8,9)\).

The time it will take for your account balance to reach $10,000 is given as follows:

t = 10.8 years.

The balance of an account after t years, using continuous compounding, is given as follows:

A(t) = A(0)e^(kt).

In which:

The parameters for this problem are given as follows:

A(0) = 6500, k = 0.04.

Hence the time needed for a balance of $10,000 is obtained as follows:

10000 = 6500e^(0.04t)

e^(0.04t) = 10000/6500

0.04t = ln(10000/6500) -> ln is the inverse operation of the exponential

t = ln(10000/6500)/0.04

t = 10.8 years.

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Answer:

  see attached

Step-by-step explanation:

You want to know the valid row operations that may be applied to the given matrix.

A row operation will be valid if it does not change the solution set of the equations the matrix represents.

In general, any row may be replaced by a linear combination of that row and any other row. Replacing a row by some combination of other rows will result in making the equations dependent. A row may not be replaced by zeros or by some nonlinear function of its elements.

Two rows may be swapped.

The attachment shows the valid row operations.

Working down the left column, the unchecked operations are invalid because ...

Working down the right column, the unchecked operations are invalid because ...

<95141404393>

Answer:

Given that sin(θ) = -2√13/13 and θ is in quadrant III, we know that sin(θ) is negative and cos(θ) is also negative. We can use the Pythagorean identity to solve for cos(θ):

cos²(θ) + sin²(θ) = 1

cos²(θ) = 1 - sin²(θ)

cos(θ) = ±√(1 - sin²(θ))

Since cos(θ) is negative in quadrant III, we take the negative square root:

cos(θ) = -√(1 - sin²(θ))

Substituting sin(θ) = -2√13/13, we get:

cos(θ) = -√(1 - (-2√13/13)²) = -√(1 - 4/13) = -√9/13 = -3√13/13

Therefore, cos(θ) = -3√13/13.

Answer:

1/4

Step-by-step explanation:

Q=event of pulling a quarter (25 cents)

D=event of pulling a dime (10 cents)

N=event of pulling a nickel (5 cents)

P=event of pulling a penny (1 cent)

Simon needs to pull out the penny last, so that the first three coins add up to $0.40.

We assume the coins are wrapped so it is a random choice.

For the first coin, probability of NOT pulling a penny is 3/4,

similarly, for the second coin, probability of NOT pulling a penny is 2/3,

for the third coin, probability of NOT pulling a penny is 1/2,

For all this to happen, we use the multiplication rule

P(3 coins but no penny) = (3/4*2/3*1/2) = 1/4

Answer:

Circumference

Step-by-step explanation:

Answer:

circumference

Step-by-step explanation:

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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