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m_a_m_a [10]
3 years ago
15

1. What is the relationship of ratios and proportions? Give an example of a proportion.

Mathematics
1 answer:
shepuryov [24]3 years ago
3 0
Ratio is the comparison of sizes of two quantities of the same unit. Proportions are the equality of two ratios. A/b =c/d
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After lunch, you need to buy new shoes. You bought a pair last year and they cost $79.00. Now, the same shoes cost $86.00. By wh
valentina_108 [34]

Answer:

The main answer: $4.84

Step-by-step explanation:

County A: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!

$75 * 0.0725 = $5.4375

Add the original price and the sales tax.

$75 + $5.4375 = $80.4375

County B: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!

$70 * 0.08 = $5.6

Add the original price and the sales tax.

$70 + $5.6 = $75.6

Then take the difference.

80.4375 – 75.6 = 4.8375

Round to the nearest hundredth: $4.84

8 0
3 years ago
Will give 30 points!<br> What is a expanded notation?
gavmur [86]

Answer:

It is the number written out to show each digit

Step-by-step explanation:

Let's say you have the number 459

you write out the hundredths place, which is 4 times 100

you write out the tenths place which is 5 times 10

and you write out the oneths place which is 9 times 1

the full thing written out is 459 = 100×4 + 5×10 + 9 × 1

4 0
3 years ago
Imagine that you would like to purchase a $275,000 home. Using 20% as
vfiekz [6]

Answer:

The mortgage chosen is option A;

15-year mortgage term with a 3% interest rate because it has the lowest total amount paid over the loan term of $270,470

Step-by-step explanation:

The details of the home purchase are;

The price of the home = $275,000

The mode of purchase of the home = Mortgage

The percentage of the loan amount payed as down payment = 20%

The amount used as down payment for the loan = $55,000

The principal of the mortgage borrowed, P = The price of the house - The down payment

∴ P = $275,000 - 20/100 × $275,000 = $275,000 - $55,000 = $220,000

The principal of the mortgage, P = $220,000

The formula for the total amount paid which is the cost of the loan is given as follows;

Outstanding \ Loan \ Balance = \dfrac{P \cdot \left[\left(1+\dfrac{r}{12} \right)^n -  \left(1+\dfrac{r}{12} \right)^m \right] }{1 - \left(1+\dfrac{r}{12} \right)^n }

The formula for monthly payment on a mortgage, 'M', is given as follows;

M = \dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot \left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}

A. When the mortgage term, t = 15-years,

The interest rate, r = 3%

The number of months over which the loan is payed, n = 12·t

∴ n = 12 months/year × 15 years = 180 months

n = 180 months

The monthly payment, 'M', is given as follows;

M =

The total amount paid over the loan term = Cost of the mortgage

Therefore, we have;

220,000*0.05/12*((1 + 0.05/12)^360/( (1 + 0.05/12)^(360) - 1)

M = \dfrac{220,000 \cdot \left(\dfrac{0.03}{12} \right) \cdot \left(1+\dfrac{0.03}{12} \right)^{180} }{\left(1+\dfrac{0.03}{12} \right)^{180} - 1}  \approx 1,519.28

The minimum monthly payment for the loan, M ≈ $1,519.28

The total amount paid over loan term, A = n × M

∴ A ≈ 180 × $1,519.28 = $273,470

The total amount paid over loan term, A ≈ $270,470

B. When t = 20 year and r = 6%, we have;

n = 12 × 20 = 240

\therefore M = \dfrac{220,000 \cdot \left(\dfrac{0.06}{12} \right) \cdot \left(1+\dfrac{0.06}{12} \right)^{240} }{\left(1+\dfrac{0.06}{12} \right)^{240} - 1}  \approx 1,576.15

The total amount paid over loan term, A = 240 × $1,576.15 ≈ $378.276

The monthly payment, M = $1,576.15

C. When t = 30 year and r = 5%, we have;

n = 12 × 30 = 360

\therefore M = \dfrac{220,000 \cdot \left(\dfrac{0.05}{12} \right) \cdot \left(1+\dfrac{0.05}{12} \right)^{360} }{\left(1+\dfrac{0.05}{12} \right)^{360} - 1}  \approx 1,181.01

The total amount paid over loan term, A = 360 × $1,181.01 ≈ $425,163

The monthly payment, M ≈ $1,181.01

The mortgage to be chosen is the mortgage with the least total amount paid over the loan term so as to reduce the liability

Therefore;

The mortgage chosen is option A which is a 15-year mortgage term with a 3% interest rate;

The total amount paid over the loan term = $270,470

8 0
3 years ago
Write an equation for slope of -2/3 and y-intercept of 5
goldenfox [79]

Answer:

y=-2/3x+5

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Solve the following equation.<br> Round to the nearest tenth.<br> 8x -1 = -9 + 2x
motikmotik

Answer:

8x-2x=1-9

6x=-8

x= -4/3

6 0
3 years ago
Read 2 more answers
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