If two names are given for the same quantity then we can use algebra
to solve the equation thus option (C) is correct.
What is the equation?There are many different ways to define an equation.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
In another word, the equation must be constrained with some constraints.
If we have a problem in word formate.
And the same quantity is used two times with two different names.
Then by algebra, the variable defines the quantity remains the same but the value of the variable changes according to the given value.
By this the problem can be easily solved.
Hence "If two names are given for the same quantity then we can use algebra to solve the equation".
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Solve by multiplying digits of value and filling in zeros: 25 x 10⁴
Answer: 250000
Step-by-step explanation:
multiple 10 4 times then multiply 25 at the end
If you are dealt 3 cards from a shuffled deck of 52 cards, find the probability of getting one queen and two kings.
The probability is
(Round to six decimal places as needed.)
Answer:
0.000348 (rounded)
Step-by-step explanation:
Please tell me if this is wrong.
y + 2x2 + 14x = 36
help meee I need help
Answer:
ubtract
36
from both sides of the equation.
x
2
+
14
x
=
−
36
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of
b
.
(
b
2
)
2
=
(
7
)
2
Add the term to each side of the equation.
x
2
+
14
x
+
(
7
)
2
=
−
36
+
(
7
)
2
Simplify the equation.
Tap for more steps...
x
2
+
14
x
+
49
=
13
Factor the perfect trinomial square into
(
x
+
7
)
2
.
(
x
+
7
)
2
=
13
Solve the equation for
x
.
Tap for more steps...
x
=
±
√
13
−
7
The result can be shown in multiple forms.
Exact Form:
x
=
±
√
13
−
7
Decimal Form:
x
=
−
3.39444872
…
,
−
10.60555127
…
Step-by-step explanation:
Suppose $18,000 is deposited into an account paying 8.5% interest, compounded continuously. How much money is in the account after 10 years if no withdrawals or additional deposits are made?
This question requires you to find simple interest. Total money in the account after 10 years is $189,000
The total money can be calculated as follows:
First, multiply all the things known from the question, deposit, interest, and years of saving.Given,
=Deposit×Interest×Year
=18,000×8.5%×10
=18,000×[tex]85/100[/tex]×10
=$171,000
Next, we need to add up the deposit above with the initial deposit=$171.000+$18.000
=$189,000
Hence, the simple interest or total money in the account after 10 years without any withdrawals of additional deposits is $189,000.
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The amount of money in the account after 10 years will be $42113.64.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
As per the given,
Principle amount P = $18000
Rate of interest r = 8.5% = 0.085
Time t = 10
By continuous compounding interest formula,
P = (18000)[tex]e^{0.085\times10}[/tex]
P = $42113.64
Hence "The amount of money in the account after 10 years will be $42113.64".
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Need help with question
When the radius is 9cm, it increases at a rate of 0.06 cm per second.
How fast is the radius increasing?We assume the ballon is a perfect sphere. Remember that the volume of a sphere as a function of the radius is given by:
V = (4/3)*3.14*(R)³
When the radius is R = 9cm, the volume is:
V = (4/3)*3.14*(9cm)³ = 3,052.08 cm³
Isolating the radius as a function of the volume, we get:
R = ∛((3/4*3.14)*V)
And we know that the volume increases at a constant rate of 6cm³/s, if we assume that the initial volume is 3,052.08 cm³ then we can write the radius as a function of time as:
R(t) = ∛((3/4*3.14)*(3,052.08 cm³ + 6cm³/s*t))
Where t is the time in seconds.
Now we need to differentiate this and evaluate in t = 0.
R'(t) = (1/3)*(3/4*3.14)*(3,052.08 cm³ + 6cm³/s*t)^(-2/3)* (6cm³/s*3/4*3.14)
Evaluating in t = 0 we get:
R'(0) = (1/3)*(3/4*3.14)*(3,052.08 cm³ + 6cm³/s*0)^(-2/3)* (6cm³/s*3/4*3.14)
= (1/3)*(3/4*3.14)*(3,052.08 cm³)^(-2/3)* (6cm³/s*3/4*3.14) = 0.06 cm/s
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Deondra read 18 pages in 2/5
of an hour. At what rate, in pages per hour, did she read?
First, reason down from 2/5
to 1/5 . Enter all values as fractions (proper or improper) or whole numbers. You will need to convert mixed numbers to improper fractions.
Deondra read at rate 40 pages per hour.
What is the meaning of the rate?
The rate at which something occurs or changes, as well as the quantity or frequency with which it does so over a period of time.
What is the unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given that, Deondra read 18 pages in 2/5 of an hour.
Use unitary method to calculate the required value:
In 2/5 hour, she read 18 pages.
In 1 hour, she read 18/(2/5) pages.
In 1 hour, she read 18 × (5/2) pages = 40 pages.
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ABC has a right angle at C, BC = 7.7 centimeters, and mA = 41°.
What is CA?
The length of side CA is right triangle ABC, 8.86 centimeters
In this question, we have been given triangle ABC has a right angle at C.
This means, AB is the hypotenuse of right triangle ABC.
measure of angle A = 41 degrees
and the length of side BC = 7.7 centimeters
We need to find length of CA
Consider sine of angle A.
sin(A) = opposite side/hypotenuse
sin(41°) = BC/AB
0.6561 = 7.7 / AB
AB = 7.7/0.6561
AB = 11.74
Applying Pythagoras theorem,
AB² = BC² + AC²
11.74² = 7.7² + AC²
AC² = 11.74² - 7.7²
AC = √(78.53)
AC = 8.86 centimeters
Therefore, the length of side CA is right triangle ABC, 8.86 centimeters
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How does knowing how ACT essays are scored help
you with writing your own?
Answer:
Generally, more selective schools may require or recommend a writing score, while less selective ones may not (though there certainly are exceptions). It's worth noting that most schools no longer require the ACT with Writing, though many schools recommend it.
Step-by-step explanation:
Yvonne's credit car has an apr of 17.79 percent and a 30 day billing cycle. Between the previous balance method and the daily balance method
Between the previous balance method and the daily balance method, the method of calculating Yvonne's June finance charge that will result in a greater finance charge is:
c. The previous balance method will have a finance charge $0.45 greater than the daily balance method.What is the previous balance method?Using the previous balance method to compute the finance charge, the beginning balance is added to purchases minus payments. Then the APR is applied to the sum.
What is the daily balance method?The daily balance method ensures that an average daily balance is computed for the billing cycle and then the APR is applied to the average to compute the finance charge.
Date Transaction Amount ($) Balance Daily Balance
6/1 Beginning balance 925.43 $925.43 $5,552.58 ($925.43 x 6)
6/7 Payment 62.74 $862.69 3,450.76 ($862.69 x 4)
6/11 Purchase 28.27 $890.96 8,909.60 ($890.96 x 10)
6/21 Purchase 50.00 $940.96 9,409.60 ($940.96 x 10)
Total $27,322.54
Average daily balance = $910.75 ($27,322.54)
APR = 17.79%
MPR = 1.4825% (17.79%/12)
Finance Charges:Previous balance method = $13.95 ($940.96 x 1.4825%)
Average daily balance = $13.50 ($910.75 x 1.4825%)
Difference = $0.45 ($13.95 - $13.50)
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Question Completion:The following table details her credit card transactions in the month of June.
Date Transaction Amount ($)
6/1 Beginning balance 925.43
6/7 Payment 62.74
6/11 Purchase 28.27
6/21 Purchase 50.00
Between the previous balance method and the daily balance method, which method of calculating Yvonne's June finance charge will result in a greater finance charge, and how much greater will it be?
a. The daily balance method will have a finance charge $0.21 greater than the previous balance method.
b. The daily balance method will have a finance charge $0.53 greater than the previous balance method.
c. The previous balance method will have a finance charge $0.45 greater than the daily balance method.
d. The previous balance method will have a finance charge $0.40 greater than the daily balance method.
Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.
(−2,3) , (−3,2)
The equation (in slope-intercept form) of the line passing through the points with the given coordinates (−2,3) , (−3,2) is y = x + 5
How to find equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slope of the lineb = y-interceptHence, let's find the slope of the line using the coordinates (-2, 3) and (-3, 2).
Therefore,
m = 2 - 3 / -3 + 2
m = - 1 / -1
m = 1
Therefore, lets find the y-intercept using (-2, 3)
y = x + b
3 = -2 + b
b = 3 + 2
b = 5
Hence, the equation of the line in slope intercept form is y = x + 5
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The quilt has 5 parallelograms. Each parallelogram has a base of 10 inches and a height of
7 inches. What area of the quilt is covered by the parallelograms?
Answer:
350 in. squared
Step-by-step explanation:
PLEASE HELPP!!! QUICK!!!!!!!
To find the distance between the points shown we subtract each point and the x-axis
What is the distance between two points?Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2– x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
Since the two points are on the same coordinate on the x -axis
To find the distance between the two points we subtract the y coordinates of the two points and the x axis.
In conclusion the distance between the two points is found by subtracting the two points and the x -axis
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A water tank holds a total of 5,600 gallons in the tank has three pipe through which water drains what water is drained from the tank pipe B drains twice as much as pipe a pipe C drain 65 gallons more than pipe B how many gallons of water does each pipe
The amounts drained by each pipe, considering a system of equations, are given as follows:
Pipe A: 1107 gallons.Pipe B: 2214 gallons.Pipe C: 2279 gallons.What is the system of equations?The variables to the system of equations are presented as follows:
Variable x: amount of water drained by Pipe A.Variable y: amount of water drained by Pipe B.Variable z: amount of water drained by Pipe C.A water tank holds a total of 5,600 gallons, hence:
x + y + z = 5600.
Pipe B drains twice as much as pipe A, hence:
y = 2x.
Pipe C drains 65 gallons more than pipe B, hence:
z = 65 + y = 65 + 2x.
Replacing the last two equations into the first, the amount drained by Pipe A is obtained as follows:
x + y + z = 5600.
x + 2x + 65 + 2x = 5600
5x = 5535
x = 5535/5
x = 1107 gallons.
Hence the remaining amounts are given as follows:
Pipe B: y = 2x = 2 x 1107 = 2214 gallons.Pipe C: z = y + 65 = 2214 + 65 = 2279 gallons.More can be learned about a system of equations at https://brainly.com/question/24342899
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I need help plssss
-3(2x-11)_>8x-9
The Linear inequality holds true for 21 ≥ x;
What is Linear Inequality?
The mathematical expression with unequal sides is known as inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to a symbol (), less than or equal to a symbol (), or not equal to a symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics. The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities.
In the given question, the given inequality given is:
-3(2x-11) ≥ 8x-9;
Solving the Inequality:
⇒-6x + 33 ≥ 8x - 9;
⇒33 + 9 ≥ 8x - 6x;
⇒ 42 ≥ 2x;
⇒ 21 ≥ x;
Hence,
The Linear inequality holds true for 21 ≥ x;
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Part A
A model car is for sale online. Beginning on day one, the owner discounts the price by 5% each day until it sells. On the third day the car sells.
If the original price of the model car was $40, how much did the car sell for to the nearest cent?
Part B
What percent discount does this represent from the original price? Round to the nearest whole percent.
The car was sold for 3429.5 cents and the percent discount from the original price is 14.265%.
According to the question,
We have the following information:
Beginning on day one, the owner discounts the price by 5% each day until it sells. On the third day the car sells. And the original price of the model car was $40.
The first day:
40*5/100
200/100
2
The price on the first day = $38
The second day:
38*5/100
190/100
1.9
The price on the second day = 38-1.9
The price on second day = 36.1
The third day:
36.1*5/100
180.5/100
1.805
The price on third day = $34.295 (36.1-1.805)
1 dollar = 100 cents
Price of car in cents = 3429.5 cents
B) Percent discount from the original price:
Let's take it to be x.
40 - (40x/100) = 34.295
-40x/100 = 34.295-40
-40x/100 = -5.705
40x = 570.5
x = 570.5/40
x = 14.265%
Hence, the car was sold for 3429.5 cents and the percent discount from the original price is 14.265%.
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A standard deck of cards has 52 cards of four different suits (diamonds, spades, hearts, clubs). Each suit
consists of numbered cards 1 (Ace) to 10, followed by Jack, Queen and King (face cards). Express all your
answers as a percent rounded to the nearest tenth of a percent, if necessary. If one card is drawn randomly from a deck, what is the probability that it is not a face card?
If one card is drawn randomly from a deck, then the probability that it is not a face card is 76.9%
Probability
Probability refers the possible way of getting the required event.
Given,
A standard deck of cards has 52 cards of four different suits (diamonds, spades, hearts, clubs). Each suit consists of numbered cards 1 (Ace) to 10, followed by Jack, Queen and King (face cards).
Here we need to find the probability of getting not a face card and we have to round off the resulting value to the tenth percent.
We know that,
Total number of cards = 52
Number of suits = 4
Number of cards in each suit = 13
Number of face cards in each suit = 3
Therefore, the total number of face cards in the deck is calculated s,
=> 3 x 4
=> 12
Therefore, the probability of getting not a face card is
=> (52 - 12)/52
=> 40/52
When we simplify this one then we get,
=> 0.7692
When we convert this into percent and round of to the nearest tenth then we get the probability of getting not a face card is
=> 76.9%.
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Estimate the following using the Range Method:
$8.94+2.16
+ 9.02
The estimated sum of the given numbers using the range method is 20.1.
We are given three numbers. The numbers are 8.94, 2.16, and 9.02. All the given numbers are decimal numbers. We need to estimate the sum of all the numbers. The approximate value of each number is calculated below.
8.94 ≈ 8.9
2.16 ≈ 2.2
9.02 ≈ 9.0
Let the estimated sum of the given number be represented by the variable "E".
E = 8.9 + 2.2 + 9.0
E = 20.1
The actual sum of the given numbers is given below.
A = 8.94 + 2.16 + 9.02
A = 20.12
We can see that the estimated sum is very accurate as compared to the actual sum.
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A is the point with coordinates(5,9)B is the point with coordinates (d,15) The gradient of the ab line is 3 Work out the value of d.
The gradient will only be equal to 3 if the value of d is 7.
How to find the value of d?
If we have two points (a, b) and (c, d), the gradient of the segment with these endpoints is:
G = (d - b)/(c - a)
Here the endpoints are (5, 9) and (d, 15), and the gradient is 3, so we can write the equation:
3 = (15 - 9)/(d - 5)
3*(d - 5) = 6
3d - 15 = 6
3d = 15 + 6 = 21
d = 21/3
d = 7
The value of d is 7.
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Jose flies a kite 17 1/2 ft above the ground. He increases its elevation by 4 3/4 ft by letting out some strung. Then he reels in the string and changes its elevation by - 15.8 ft. After jose reels in the string, what is the kite's elevation relative to the ground?
The kite's elevation relative to the ground is 6.45 feet.
What is elevation?Elevation simply means the height above sea level.
In this case, Jose flies a kite 17 1/2 ft above the ground and he increases its elevation by 4 3/4 ft by letting out some strung. and then changes its elevation by - 15.8 ft.
This will be illustrated as:
= 17.5 + 4.75 - 15.8
= 6.45 ft
The elevation is 6.45 feet.
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what is the diffrence of 256,805 - 136.667
256 805 - 136.667 ≈ 256 668.333
The difference is approximately 256 668.333
Write an equation for the nth term of the arithmetic sequence
The equation for the nth term of the arithmetic sequences are:
a_n = -11 + 4n and a_n = -10 + 2n where n is an positive integer.
What is the arithmetic sequence?
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.
The formula of nth term of an arithmetic sequence is a_n = a + (n-1) d
The arithmetic sequence is -7, -3, 1, ....
The first term is a = -7.
The common difference is d = (-3)-(-7) = 1 - (-3) = 4.
The nth term of an arithmetic sequence is
a_n = -7 + (n-1) 4
a_n = -7 + 4n -4
a_n = -11 + 4n
The arithmetic sequence is -8, -6, -4, ....
The first term is a = -8.
The common difference is d = (-6)-(-8) = -4 - (-6) = 2.
The nth term of an arithmetic sequence is
a_n = -8 + (n-1) 2
a_n = -8 + 2n - 2
a_n = -10 + 2n
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Ann and Ben translate documents from German into English.
A set of documents that would take Ann 10 days would take Ben 12 days.
Ann starts to translate the documents
After 2 days Ann and Ben both work or translating the documents.
How many MORE days will it take to complete the work?
Give answer in mixed fraction
The additional number of days that is required to complete the rest of the work in mixed fraction is equal to 4 4/11 days.
How to determine the additional number of days?First of all, we would determine the number of work left for Ann after two (2) working days:
In one (1) day, the amount of work that would be done by Ann alone is given by 1/10 days. Therefore, the amount of work that would be done by Ann alone in two (2) days is given by 2/10 or 1/5 days.
For the number of work left, we have:
Work left = 1 - 1/5
Work left = 4/5 days.
Similarly, the amount of work that would be done by Ben alone in one (1) day is given by 1/12 days.
Therefore, the combined work rate of both Ann and Ben is given by:
Combined work rate = 4/5 + 1/12
Combined work rate = 11/60
For the additional number of days required to complete the rest of the work, we have:
Additional days = 4/5 ÷ 11/60
Additional days = 4/5 × 60/11
Additional days = 4 × 12/11
Additional days = 48/11
Additional days = 4 4/11 days.
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Here is a list of numbers. 6724669533 Work out the median.
Answer:
Median: 5.5
Mean: 5.1
jessie needs to borroe 12,000 from northwestern bank. they offeted her a 5 year loan with an apr of 4.98%. how much will she pay interest over the life of the loan?
Answer:
1580.40----------------------------------
GivenLoan amount P = 12000,Rate r = 4.98% = 0.0498,Time t = 5 years,Number of compounds n = 12.Find the monthly payment[tex]M=\dfrac{P(r/n)(1+r/n)^{nt}}{(1+r/n)^{nt}-1}[/tex][tex]M=\dfrac{12000(0.0498/12)(1+0.0498/12)^{12*5}}{(1+0.0498/12)^{12*5}-1} =226.34[/tex]Find the total amount paid226.34*60 = 13580.40Find the amount of interest13580.40 - 12000 = 1580.40Answer:
$1580.69
Step-by-step explanation:
Monthly Payment Formula
[tex]\sf PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}[/tex]
where:
PMT = Monthly payment.P = Loan amount.i = Interest rate per month (in decimal form).n = Term of the loan (in months).Given:
P = $12,000i = 0.0498/12 = 0.00415n = 5 years = 60 monthsSubstitute the values into the formula to calculate the monthly payment:
[tex]\implies \sf PMT=\dfrac{12000(0.00415)\left(1+0.00415\right)^{60}}{\left(1+0.00415\right)^{60}-1}[/tex]
[tex]\implies \sf PMT=\dfrac{49.8\left(1.00415\right)^{60}}{\left(1.00415\right)^{60}-1}[/tex]
[tex]\implies \sf PMT=\dfrac{63.84764727}{0.2820812705}[/tex]
[tex]\implies \sf PMT=226.3448656[/tex]
Therefore, the total payments over the life of the loan is the monthly payment multiplied by the total number of months:
[tex]\implies \sf 226.3448656 \times 60=\$13580.69[/tex]
To calculate how much interest Jessie pays over the life of the loan, subtract the original loan amount from the total payments amount:
[tex]\implies 13580.69-12000=\$1580.69[/tex]
Therefore, the interest Jessie will pay over the life of the loan is $1580.69.
Write 531.246 in expanded form.
Answer:
Step-by-step explanation:
Answer: 500 + 30 + 1 + 0.2 + 0.04 + 0.006
|-2x|>8 how would i do this problem about absolute inequalities
Answer:
x < - 4 or x > 4
Step-by-step explanation:
given an inequality of the type| x | > a , then the solution is in the form
x < - a or x > a
thus
- 2x < - 8
divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.
x > 4
OR
- 2x > 8
divide both sides by - 2, reversing the symbol
x < - 4
solution is x < - 4 or x > 4
Answer:
The answer can be expressed in two types of forms.
INEQUALITY FORM: x < -4 or x > 4
INTERVAL NOTATION: ( –∞, –4) (4, ∞ )
Step-by-step explanation:
1. Isolate the variable "x" by dividing each side by factors that do not contain the variable "x."
2. Write |-2x|>8 as a piece:
TOP: {-2x > 8 x ≤ 0 / BOTTOM: {2x > 8 x > 0}
3. Divide each term by -2, then simplify.
x < -4
4. Divide each term by 2, then simplify.
x > 4
5. Find the union of the solutions.
Determine the period.
The time period of the given waveform is 2 units time
From the waveform,
Each units represent one units
The time period is the time taken for waveform to complete one cycle.
Here we have to find the time taken for the given wave to complete one cycle.
Here at t = 0 the wave reaches its positive peak point
At t = 1, the wave reaches its negative peak point
At t = 2, the wave reaches its positive peak point again
Therefore, in this waveform, the wave took 2 units time to complete one cycle
The time period = 2 units time
Hence, the time period of the given waveform is 2 units time
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Toni runs a restaurant that receives a shipment of 200200200 oranges every day. According to the supplier, approximately 11\%11%11, percent of the population of these oranges is overripe. Suppose that Toni calculates the daily proportion of overripe oranges in her sample of 200200200. We can assume the supplier's claim is true, and that the oranges each day represent a random sample.
What will be the shape of the sampling distribution of the daily proportions of overripe oranges?
The shape of the sampling distribution of the daily proportions of overripe oranges is approximately normal.
The correct answer option is option C
What is sampling distribution?Sampling distribution refers to a probability distribution in which samples are drawn from a population which is taken from a larger population.
Types of sampling
Simple random sampling, Systematic sampling, Stratified sampling, and Cluster sampling.Shapes of sampling distribution:
SymmetricSkewed leftSkewed right Uniform distributionNormal distributionNumber of oranges Toni's restaurant receives everyday = 200
Population of overripe oranges = approximately 11%
Therefore, it the supplier's claim is true of overripe oranges is true, shape of the sampling distribution is approximately normal.
Complete question:
Toni runs a restaurant that receives a shipment of 200 oranges every day. According to the supplier, approximately 11% of the population of these oranges is overripe. Suppose that Toni calculates the daily proportion of overripe oranges in her sample of 200. We can assume the supplier's claim is true, and that the oranges each day represent a random sample. What will be the shape of the sampling distribution of the daily proportions of overripe oranges?
Choose 1 answer:
Skewed to the left
Skewed to the right
Approximately normal
Uniform
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A pilot is flying over the ocean. She determines that the angles of depression to two ships are 74° and 48°, as shown in the figure below. The plane is 5 miles
from the ship located at point A. How far apart are the ships? Round your answer to the nearest tenth of a mile.
According to the given depression angle, ship is 4.4 miles apart from ship B.
Depression angle:
Depression angle refer an angle that is formed with the horizontal line if the line of sight is downward from the horizontal line.
Given,
A pilot is flying over the ocean. She determines that the angles of depression to two ships are 74° and 48°, as shown in the figure below. The plane is 5 miles from the ship located at point A.
Here we need to find the distance between the two ships.
Here we know the following,
Distance between plane and Ship A = 5 miles.
And the depression angle = 74°, 48°
Let us consider the following, that they sit on a line,
So under this situations,
=> 80 - 48 - 74 = 58 degrees.
The next thing we have to do is bring this 74 degree angle inside the diagram. Because it is congruent to this interior angle because they are alternate.
Then it can be written as,
=> x = sin 74°/5
=> x = 4.4
Therefore, the two ships are 4.4 miles apart from each other.
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A young executive is going to purchase a vacation property for investment purposes. She needs to borrow $81,000.00 for 27 years at 6.8% compounded monthly, and will make monthly payments of $546.61. (Round all answers to 2 decimal places) What is the unpaid balance after 12 months? During this period, how much interest did she pay?
1. The unpaid balance after 12 months of paying $546.61 for borrowing $81,000 for 27 years at 6.8% is $79,915.29.
2. During this period, the interest she paid was $5,474.61.
How is the unpaid balance determined?The total payment made, including interest and principal, for 12 months is the product of the monthly payments and 12 months.
From the amortization schedule from an online finance calculator at month 12, we can deduce that the loan balance is $79,915.29.
When this balance is subtracted from the loan, the difference is the principal repayment so far.
N (# of periods) = 324 months (27 years x 12)
I/Y (Interest per year) = 6.8%
PV (Present Value) = $81,000
PMT (Periodic Payment) = $-546.61
Results:
Sum of all periodic payments = $-6,559.32 ($546.61 x 12)
Total Interest for six months = $5,474.61
Amortization Schedule:1 $81,000.00 $-546.61 $459.00 $-80,912.39
2 $80,912.39 $-546.61 $458.50 $-80,824.28
3 $80,824.28 $-546.61 $458.00 $-80,735.68
4 $80,735.68 $-546.61 $457.50 $-80,646.57
5 $80,646.57 $-546.61 $457.00 $-80,556.96
6 $80,556.96 $-546.61 $456.49 $-80,466.84
7 $80,466.84 $-546.61 $455.98 $-80,376.21
8 $80,376.21 $-546.61 $455.47 $-80,285.06
9 $80,285.06 $-546.61 $454.95 $-80,193.40
10 $80,193.40 $-546.61 $454.43 $-80,101.22
11 $80,101.22 $-546.61 $453.91 $-80,008.52
12 $80,008.52 $-546.61 $453.38 $-79,915.29
Total payment at $546.61 x 12 months = $6,559.32
Principal repayment for 12 months = $1,084.71 ($81,000 - $79,915.29)
Interest paid for 12 months = $5,474.61 ($6,559.32 - $1,084.71)
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