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xz_007 [3.2K]
2 years ago
11

Autumn found a wallet containing $ 900 in the street. She returned the wallet to its owner, who gave her a $ 180 reward. What pe

rcentage of the $ 900 was the reward?
Mathematics
1 answer:
Murljashka [212]2 years ago
4 0

Answer:

\frac{180}{900} = 0.2 × 100 =20

Autumn got a 20% reward of the $900 she found.

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Lenny and Lisa have obtained a 30-year, fixed rate mortgage for $675,250 with a 7.25% interest rate. They purchased 3 points and
Vikentia [17]

Answer:

119 months

Step-by-step explanation:

In this question, we are asked to calculate the amount of time it would take for a break-even point on a mortgage, if there is a factoring in the cost of points.

We proceed to answer the;

Mathematically,

The Break Even Point = Amount Paid for purchasing Discount Points divided by Monthly savings in the interest payments

We lost out the important values given in the question as follows:

Amount of Mortgage - $675,250

Tenure - 30 Years

The Rate of interest without points = 7.25%

The number of points = 3 points

The rate of interest with the 3 points = 6.875%

The amount to be paid for purchasing the discount point is now calculated below;

Since 1 discount point = 1% of mortgage value;

Therefore, 3 discount points = 3% of mortgage value

The amount paid is thus = 3% of $675,250 = $20,257.5

To calculate Monthly payment without points, we use the mathematical formula;

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

Where M

Is monthly payment, r is the interest rate, n is the number of months.

According to the question M = 675,250, r = 7.25% = 7.25/100 = 0.0725 , n= 30 * 12 months = 360 months

M = 675,250[0.0725(0.0725+1)^30/(1+0.0725)^360)-1) = $4606.40

To get the monthly payment with points, we simply use the formula again but this time interest rates will be 6.875% = 0.06875 I.e r = 0.06875

Inputting the terms in the formula will yield a value of $4435.91. This means monthly payment with discount will be $4435.91

Savings in monthly payments after purchasing the discount points = $4,606.40 - $4,435.91 = $170.48

Break Even = Purchase cost of Discount Points / Monthly savings

= $20,257.5 / $170.48

= 119 Months

Hence, the number of months it will take Lisa and Lenny to break-even point on their mortgage will be 119 months

6 0
3 years ago
Find the range of the graph
Alex

Answer:

4,-7 = 11

and

6, -9 = 15

3 0
2 years ago
What is the picture equal to? Help please
amm1812

25(3n - 2) \\  \\ 1. \: 25  \times 3n + 25  \times  - 2 \\ 2. \: 75n + 25 \times  - 2 \\ 3. \: 75n - 50

7 0
2 years ago
Solve the system of equations
Phoenix [80]
The correct answer is letter B, (6,-1).

When you substitute this ordered pair on the equations, you would found out is the correct one.
6 0
3 years ago
Read 2 more answers
For a sample of eight​ bears, researchers measured the distances around the​ bears' chests and weighed the bears. Minitab was us
Karolina [17]

Answer:

Step-by-step explanation:

Given that for a sample of eight​ bears, researchers measured the distances around the​ bears' chests and weighed the bears.

r = linear correlation coeff = 0.952

H_0: r =0\\

H_1 :r\neq 0

(Two tailed test)

r difference = 0.952

n=8

Std error = \sqrt{\frac{1-r^2}{n-2} } =0.12496

Test statistic t = 0.952/0.12496 = 7.618

Alpha = 0.05

df = 6

p value = 0.000267

This implies H0 is rejected.

There exists a linear relation between the variables and r cannot be 0

0.952^2 = 0.906=90.6% of variation in weight can be explained by the linear relationship between weight and chest​ size

3 0
3 years ago
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