Answers
Answer:486
Step-by-step explanation:
V=a*a*a=729
a=9
S=6a*a=6*81=486
Answer:
486
hope this helps
Related Questions
The graphic shows 2 lines and 2 rays that intersect at a point 0 to create 6 angles. What are TWO equations that can be used to find m∠3 if the measures of the other angles are known? Responses m∠1 + m∠2 + m∠3 = 180° m∠1 + m∠2 + m∠3 = 180° m∠2 + m∠3 + m∠4 = 180° m∠2 + m∠3 + m∠4 = 180° m∠3 + m∠4 + m∠5 = 180° m∠3 + m∠4 + m∠5 = 180° m∠1 + m∠2 + m∠3 + m∠4 = 180° m∠1 + m∠2 + m∠3 + m∠4 = 180° m∠3 + m∠4 + m∠5 + m∠6 = 180°
Answers
Accοrding tο the angle sum prοperty οf a triangle, m∠1 + m∠2 + m∠3 = 180° and m∠3 + m∠4 + m∠5 = 180° these twο equatiοns can be used tο find m∠3.
What is the angle sum prοperty οf a triangle?The angle sum prοperty οf a triangle is a fundamental geοmetric prοperty that states that the sum οf the interiοr angles οf a triangle is always equal tο 180°. In οther wοrds, fοr any triangle, the sum οf the measures οf its three interiοr angles is always 180°.
This prοperty hοlds true fοr all triangles, regardless οf their size οr shape. It is an impοrtant cοncept in geοmetry and is used in variοus prοοfs and calculatiοns invοlving triangles.
One cοmmοn applicatiοn οf the angle sum prοperty οf a triangle is tο find the measure οf an unknοwn angle in a triangle if the measures οf the οther twο angles are knοwn. This can be dοne by subtracting the sum οf the knοwn angles frοm 180°.
The twο equatiοns that can be used tο find the measure οf angle 3 (m∠3) if the measures οf the οther angles are knοwn are:
m∠1 + m∠2 + m∠3 = 180°
This equatiοn can be used if the measures οf angles 1 and 2 are knοwn. We can find the measure οf angle 3 by subtracting the sum οf angles 1 and 2 frοm 180°.
m∠3 + m∠4 + m∠5 = 180°
This equatiοn can be used if the measures οf angles 4 and 5 are knοwn. We can find the measure οf angle 3 by subtracting the sum οf angles 4 and 5 frοm 180°.
Thus, m∠1 + m∠2 + m∠3 = 180° and m∠3 + m∠4 + m∠5 = 180° these twο equatiοns can be used tο find m∠3.
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What is the greatest common factor of 53 and 11?
Answers
Answer:
1
Step-by-step explanation:
Both of those numbers are prime, so their GCF's are 1
Please help me with this question. Thanks :)
Answers
Answer:
26
Step-by-step explanation:
Total pupils 60
32 boys and girls will be 28 (60-32)
Cola 12 boys
Water 4 boys 9 girls
Milk 21 pupils
Total results 12 + 4 +9+ 21 = 46
Outstanding girls will be 60 - 46
Girls who like coke 14
If 14 girls liked cola and 12 boys liked cola, total will be 14 + 12
Calculate the money you will have in the following accounts after 5 years assuming you earn simple interest,
51. you deposit $700 in an account with an annual interest rate of 4%
54. you deposit $1800 in an account with an annual interest rate of 3.8%
Answers
We will have $840 and $2142 respectively. The solution has been obtained by using simple interest.
What is simple interest?
Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest.
We know that amount after simple interest is given by
A = P (1 + rt)
We are given that $700 are deposited in an account with an annual interest rate of 4%.
Here,
P = $700
r = 4%
t = 5 years
On substitution, we get
⇒A = 700 (1 + (0.04 * 5))
⇒A = 700 (1 + 0.2)
⇒A = 700 (1.2)
⇒A = $840
Similarly, in the second case,
P = $1800
r = 3.8%
t = 5 years
On substitution, we get
⇒A = 1800 (1 + (0.038 * 5))
⇒A = 1800 (1 + 0.19)
⇒A = 1800 (1.19)
⇒A = $2142
Hence, we will have $840 and $2142 respectively.
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Alicia spun a spinner 100 times, and the results are shown in the following table. What is the relative frequency for the spinner to land on number 1?
Responses
Answers
Answer:
3/25
Step-by-step explanation:
Find the ratio of squares to circles
Answers
I believe the ratio of circle to square is 2:3
6 A farmer has 2 400 sheep. He loses 32 and a half % due to the drought. After that he loses 15% due to sickness. How many sheep does he have now?
Answers
Answer: The farmer has 1377 sheeps.
Step-by-step explanation:
Farmer loses sheeps due to drought = 32½% of 2400
32½% of 2400
= 65 × 2400 × 1
2100
After cutting it will be,
65×12
=780
Number of sheeps that are left with him = 2400 - 780
=1620
After that,
The farmer loses due to sickness = 15% of 1620
15% of 1620
= 15 × 1620
100
After cutting it will be,
3 × 81
= 243
Total amount of sheeps that the farmer loses = 780 + 243
= 1023
Now the number of sheeps he has is 2400-1023
= 1377
At westville highschool there are 315 seniors and 389 juniors 65% of the seniors have parking passes and 42% of the juniors have parking passes the statistics teacher selects an SRS of 30 seniors and a seperate SRS of 30 juniors
Answers
The probability of selecting a senior who has a parking pass and a junior who has a parking pass is 0.2730.
At Westville Highschool, there are 315 seniors and 389 juniors. 65% of the seniors have parking passes and 42% of the juniors have parking passes. The statistics teacher selects an SRS (Simple Random Sample) of 30 seniors and a separate SRS of 30 juniors.
To determine the probability of selecting a senior who has a parking pass and a junior who has a parking pass, first the probability of selecting a senior who has a parking pass must be calculated. Since 65% of the seniors have parking passes, the probability of selecting a senior with a parking pass is 0.65. Secondly, the probability of selecting a junior with a parking pass must be calculated. Since 42% of the juniors have parking passes, the probability of selecting a junior with a parking pass is 0.42.The probability of selecting a senior who has a parking pass and a junior who has a parking pass can be found by multiplying the two probabilities. 0.65 x 0.42 = 0.2730.
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The pharaoh's outfitters, 'Cloaks and
Crowns', sell cloaks and crowns in 3
sizes - prince, king and emperor (in
increasing size order).
He wants to kit out his three sons for the
forthcoming festival of Ra. Ahmose
chooses a bigger cloak than Kamose,
but a smaller crown than Thutmose.
Both Thutmose's cloak and crown are
larger than Kamose's, but the size of
Thutmose's crown matches the size of
Kamose's cloak.
Which sizes did the
pharaoh's sons each get?
Answers
Please Help!
Drag each label to the correct location on the equation. Not all labels will be used.
Picture is linked below.
Answers
After answering the given query, we can state that Expression: A group variable of words, divided by signs for addition or subtraction.
What is a Variable?In the context of a mathematical idea or experiment, a variable is something that can be altered. Frequently, a single symbol is used to symbolize a variable. Variables are frequently represented by the letters x, y, and z as abstract symbols. A wide variety of values can be assigned to characteristics known as variables. These factors include, among others, your size, age, wealth, place of birth, scholastic standing, and type of residence. Both numerical and categorical methods can be used to divide variables into two primary groups.
Here are where the labels should be placed based on the illustration:
Coefficient, label one
2nd label: variable
Label 4: the equals symbol Label 3: constant
5th label: term
Expression 6th label
The definition of each term is broken down as follows:
A integer multiplied by a variable in a term of an algebraic expression is referred to as a coefficient.
Variable: A symbol for a quantity that is subject to shift or variation.
A fixed, unchanging number is referred to as a constant.
The equals sign: Shows that the expressions on the left and right are equivalent.
Term: A grouping of variables multiplied by a coefficient and denoted by addition or subtraction marks.
Expression: A group of words, divided by signs for addition or subtraction.
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Help I do not know how to do this and now I’m stuck
Answers
Answer:
okay the answer is b[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
If you have the right answer I will give you brainilest!!!
Answers
Explanation:
The figure can be split into 3 smaller shapes; a rectangle a square and a triangle.
The rectangle's area is found by multiplying its width by its height:
6 x 8 = 48sq km.
The square's area is found by multiplying its width and height:
2 x 2 = 4sq km.
The triangle's area can be found using the formula (base x height) / 2. The height is given as 7km, the base is given as 8 plus an unknown amount. That unknown amount can be found by noticing that the length of the top 6km of the top rectangle plus the 2km distance of the top of the small square add up to the same distance as the 5km side plus the unknown amount.
From this, we see that 6 + 2 = 5 + unknown distance, so the unknown distance must be 3 (8 = 5 + 3).
Now by adding this 3km to the known 8km of the triangles base, we get a base of 11km.
From here we use the formula (base x height) / 2 to find the triangle's area:
(11 x 7) / 2 = 77/2 = 38.5sq km.
Now by adding up every separate shapes area, we get the final area of the figure.
38.5 + 48 + 4 = 90.5sq km.
List three sides to a right triangle. Explain how you can use the Pythagorean theorem to know that your three sides will create a right triangle.
Answers
Answer: Three sides of a right triangle are the lengths of its legs and the length of its hypotenuse.
To know that three given sides will create a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Symbolically, if a, b, and c are the lengths of the sides of a right triangle, with c being the hypotenuse, then:
c^2 = a^2 + b^2
Therefore, if we are given the lengths of three sides, we can square the lengths of the legs, add them together, and then take the square root to find the length of the hypotenuse. We can then compare the squared length of the hypotenuse to the sum of the squares of the legs. If they are equal, the three sides form a right triangle. If the squared length of the hypotenuse is greater than the sum of the squares of the legs, the three sides form an obtuse triangle. If the squared length of the hypotenuse is less than the sum of the squares of the legs, the three sides form an acute triangle.
Step-by-step explanation:
PLEASE SHOW WORK!!!!!
Answers
The correct answer is D. Only statements I and III are true for pi < theta < 3.
What are trigonometric functions?
Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle. They are commonly used in geometry, physics, and engineering to solve problems involving triangles and periodic phenomena. The six basic trigonometric functions are:
Sine (sin): the ratio of the length of the side opposite an angle to the length of the hypotenuse of the triangle.
Cosine (cos): the ratio of the length of the side adjacent to an angle to the length of the hypotenuse of the triangle.
Tangent (tan): the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle.
Cosecant (csc): the reciprocal of the sine function.
Secant (sec): the reciprocal of the cosine function.
Cotangent (cot): the reciprocal of the tangent function.
To answer this question, we need to analyze the given range of values for theta, and determine the signs of the trigonometric functions involved.
For pi < theta < 3, we know that theta is in the second quadrant, where sine is positive and cosine is negative.
Therefore, statement I is true, since sine is positive for values of theta in this range.
Statement II is false, since cosine is negative in the second quadrant, and 2 cos theta is also negative.
Statement III is true, since tangent is negative in the second quadrant, and (1/3) tan theta is also negative.
So, the correct answer is D. Only statements I and III are true for pi < theta < 3.
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I NEED THIS FAST PLEASEEE!!
The population of Cirque City was 43,129 in 1999 and was 56,780 in 2010. If the population was growing exponentially, what was the growth rate?
Answers
Answer:
Step-by-step explanation:
If we call 1999 year 0, then 2010 would be year 11. This makes the coordinates for our problem (0, 43129) and (11, 56780). That means that the initial value, a, is 43129 and we can use that to solve for b.
[tex]56780=43129(b)^{11[/tex]
Divide both sides by 43129 to get
[tex]1.31651557=b^{11[/tex] and take the 11th root on your calculator to get that
b = 1.025314051
Not sure how you need to round that.
(Worth 20 points, will give brainliest if right)
If (r, s) is the solution to the system of equations, what is the value of r?
−8r − 8s = 100
r − 2s = 10
Answers
The price of a jumper is reduced by 17% in a
sale. The sale price is £62.25.
What was the original price of the jumper?
Give your answer in pounds (£).
SALE
17% off!
Original price = £
Sale price = £62.25
Answers
Answer: it is $51.67 in dollars
Step-by-step explanation:
Answer:
£75
Step-by-step explanation:
To find the original price of the jumper using a formula, we can use the following formula:
Sale Price = Original Price - (Discount Rate x Original Price)
Where Sale Price is the price of the jumper after the 17% discount, Discount Rate is the percentage discount applied, and Original Price is the price of the jumper before the discount.
We know that the Sale Price is £62.25, and the Discount Rate is 17%, so we can substitute these values into the formula:
£62.25 = Original Price - (0.17 x Original Price)
Simplifying this equation, we get:
£62.25 = Original Price - 0.17Original Price
£62.25 = 0.83Original Price
Dividing both sides by 0.83, we get:
Original Price = £75
Therefore, the original price of the jumper was £75
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
Answers
Answer:
b d
Step-by-step explanation:
Gretchen is refinishing her gazebo that is in the shape of a regular octagon. The length of one side is 3 feet and the apothem is 3. 5 feet. What
is the area that Gretchen will be refinishing?
Answers
Answer:
10.5
Step-by-step explanation:
you just have to multiply 3 feet by 3.5 feet.
14. Find the measures of all the angles in the rectangle. 1 2 3 5 32 4
Answers
[tex]90^{0} - 32^{0} = 58^{0}[/tex]
1 = 4 = 90°
2 = 32°
3 = 5 = 58°
Answer:
∠1 = ∠4 = 90°∠2 = 32°∠3 = ∠5 = 58°Step-by-step explanation:
You want the measures of the marked angles in the rectangle, given one of the acute angles is 32°.
Complementary anglesThe corner angles of a rectangle are all 90°. That's part of the definition of a rectangle:
∠1 = ∠4 = 90°
That make angles 5 and 32° be complementary angles:
∠5 = 90° -32° = 58°
The angles at the opposite end of the diagonal are complementary to these, as the sum of angles in a triangle is 180°.
∠2 = 90° -58° = 32°
∠3 = 90° -32° = 58°
__
Additional comment
You may have noticed that angles on opposite sides and opposite ends of the diagonal have the same measure. This is no coincidence. These are called "alternate interior angles". As such, they are always congruent where a diagonal meets parallel lines. (The sides of a rectangle are parallel.)
please help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
3/8
Step-by-step explanation:
Solve by Elimination:
5x+2y=−3
2x+3y=−10
Answers
Answer:
Multiplying the second equation by 2, we get:
4x + 6y = -20
Now we can subtract the first equation from this to eliminate x:
4x + 6y = -20
-(5x + 2y = -3)
-x + 4y = -17
Now we have one equation with only y. Solving for y:
-x + 4y = -17
4y = x - 17
y = (1/4)x - 17/4
Now we can substitute this expression for y into either equation to solve for x. Let's use the first equation:
5x + 2y = -3
5x + 2((1/4)x - 17/4) = -3
5x + (1/2)x - 17 = -3
(11/2)x = 14
x = 28/11
So the solution is (x,y) = (28/11, -17/11).
Step-by-step explanation:
Please ASAP Help
Will mark brainlest due at 12:00
Answers
Answer: -5
Step-by-step explanation:
Which expression is NOT equivalent to the others?
Answers
The expression [tex](2+7)^2[/tex] is not equivalent to the others as it is an exponential expression, while the others are all linear expressions.
The expression [tex](2+7)^2[/tex] is not equivalent to the others as it is an exponential expression, while the others are all linear expressions. An exponential expression is a mathematical expression that contains a variable in an exponent, meaning it is raised to a certain power, while a linear expression is a mathematical expression that contains two or more variables, where each has an exponent of 1. For example,[tex](2+7)^2[/tex] can be written as[tex]9^2[/tex]which is equal to 81. In contrast, the other expressions can be written as 2x+7y+3z which is equal to 2x+7y+3z. This means that the two expressions are not equivalent. To illustrate further, we can use a simple example. Let's say x=2, y=3, and z=4. Then the linear expression 2x+7y+3z would be equal to 2(2)+7(3)+3(4) = 22. The exponential expression[tex](2+7)^2[/tex] would be equal to [tex](2+7)^2 = 9^2 = 81[/tex]. We can see here that the two expressions are not equivalent.
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Which expression is NOT equivalent to the others?
A) 2 + 4
B) 6 - 2
C) 8 ÷ 4
D) 3 x 2
Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8. 11 and a standard deviation of 1. 46. Using the empirical rule, what percentage of American women have shoe sizes that are at least 11. 3
Answers
About 1.5% of American women have shoe sizes that are at least 11.3, using the empirical rule and a standard normal distribution table.
To use the empirical rule, we assume that the shoe sizes follow a normal distribution. We can then convert the shoe size 11.3 to a z-score using the formula:
z = (x - μ) / σ
where x is the shoe size, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
[tex]z = (11.3 - 8.11) / 1.46 = 2.17[/tex]
This tells us that a shoe size of 11.3 is 2.17 standard deviations above the mean.
The empirical rule enables us to determine that, with a normal distribution:
About 68% of the data falls within one standard deviation of the mean
The data is within two standard deviations of the mean for about 95% of the time
About 99.7% of the data falls within three standard deviations of the mean
Since 11.3 is more than two standard deviations above the mean, we know that fewer than 5% of women will have a shoe size this large. To find the exact percentage, we can use a standard normal distribution table (also known as a z-table) or a calculator to find the area under the curve to the right of z = 2.17.
Using a calculator or a table, we find that the area to the right of z = 2.17 is approximately 0.015, or 1.5%. Therefore, we can say that about 1.5% of American women have shoe sizes that are at least 11.3.
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Question at position 5 The sum of two numbers is 15. If the second number is twice the other, what is the working equation for this problem as well as the values of the two numbers?
Answers
The two numbers are 5 and 10 and the working equation for this problem is:x + 2x = 15
The sum of the two numbers is 15. If the second number is twice the other, then the working equation for this problem as well as the values of the two numbers according to the given question is the second number y is twice the first number x.
Therefore,y = 2x
Also, the sum of these two numbers is given as 15.
Therefore,x + y = 15
Substituting the value of y in terms of x, we get x + 2x = 15
Simplifying the above equation, we get:3x = 15x = 5
Substituting this value of x in the equation y = 2x, we get:y = 2(5)y = 10
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Miranna teaches gymnastics lessons at summer camp. She is paid $12. 50 per hour.
A. If Miranna were offered a raise of 100% per hour, what would her new hourly rate be? What percent of her original pay would she be paid?
B. Miranna is offered a raise of 75% of her hourly rate to reach a private lesson. How much per hour would she be paid for the private lesson?
C. What is the relationship between the percent raise that Miranna gets her new pay as a percent of her original pay? How is she related to the scale factor (multiplier) between her original pay and her new pay?
Answers
Miranna is offered a 75% raise of her hourly rate to reach a private lesson, which would make her hourly pay $21.88.
This is calculated by taking the original hourly rate of $12.50 and multiplying it by 1.75 (the percent raise she is getting).
The relationship between the percent raise and Miranna's new pay is the same as the relationship between her original pay and her new pay. The percent raise (75%) is equal to the scale factor (1.75) between her original and new pay. In other words, the percent raise is a measure of the degree of increase between her original pay and her new pay.
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Construction company A is determining whether it should submit a bid for a new shopping center. In the past, their main competitor, construction company B, has submitted bids 70% of the time. If company B does not bid on a job, the probability that company A will get the job is 0.20 . If company B bids on a job, the probability that company A will get the job is 0.15 . a. If company A gets the job, what is the probability that company B did not bid? b. What is the probability that company A will get the job?
Answers
a. The probability that company B did not bid given that company A got the job is 0.375 or 37.5%.
b. The probability that company A will get the job, we can use the law of total probability is 0.16 or 16%.
What is Probability?Probability is a measure of the likelihood or chance of an event occurring. It is used to quantify the uncertainty of an outcome, and is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
What is Bayes' Theorem?Bayes' theorem is a mathematical formula that describes the probability of an event based on prior knowledge or information. It is named after the 18th-century English mathematician Thomas Bayes, who first formulated the theorem.
In the given question,
a. To find the probability that company B did not bid given that company A got the job, we can use Bayes' theorem:
P(B did not bid | A got the job) = P(A got the job | B did not bid) * P(B did not bid) / P(A got the job)
We know that P(A got the job | B did not bid) = 0.20, P(B did not bid) = 1 - 0.70 = 0.30, and P(A got the job) = P(A got the job | B did not bid) × P(B did not bid) + P(A got the job | B bid) × P(B bid) = 0.20 × 0.30 + 0.15× 0.70 = 0.16.
Therefore,
P(B did not bid | A got the job) = 0.20 × 0.30 / 0.16 = 0.375 or 37.5%.
b. To find the probability that company A will get the job, we can use the law of total probability:
P(A got the job) = P(A got the job | B did not bid) * P(B did not bid) + P(A got the job | B bid) × P(B bid)
We know that P(A got the job | B did not bid) = 0.20, P(B did not bid) = 0.30, P(A got the job | B bid) = 0.15, and P(B bid) = 0.70. Plugging these values in, we get:
P(A got the job) = 0.20× 0.30 + 0.15 × 0.70 = 0.16 or 16%.
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What is the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week
Answers
Answer:
Without more information about the specific survey and population being surveyed, it is difficult to provide a precise answer to this question. However, I can provide some general information on how probabilities can be calculated in surveys.
Assuming that the survey is a representative sample of college students and that the question about difficulty falling asleep is a binary (yes/no) question, we can calculate the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week as follows:
1. Determine the total number of surveyed college students who answered the question about difficulty falling asleep.
2. Determine the number of surveyed college students who reported having a hard time falling asleep on 3 or more days in the last week.
3. Divide the number of surveyed college students who reported having a hard time falling asleep on 3 or more days in the last week by the total number of surveyed college students who answered the question about difficulty falling asleep.
For example, if 1,000 college students were surveyed and 800 of them answered the question about difficulty falling asleep, and 200 of those 800 reported having a hard time falling asleep on 3 or more days in the last week, then the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week would be 200/800, or 0.25, or 25%.
18. John's car was purchased for $32,451. He put a down payment of $3,500 and financed the rest with a 5.5% annual interest rate compounded monthly.
a.) How much with his payments be if he takes the loan out for 6 years?
b.) The dealership has a special of a 4.75% rate for 4 years. How much more will John have to pay each month?
c) How much will John end up saving by going with the special?
d.) John decides to go with the special financing John's car depreciates at a continuous rate of 6% annually. How much will his car be worth when he finishes paying off his loan?
e.) At the end of the 4-year loan, how much did John actually lose?
Answers
a) Monthly payment = $489.77
b) John will paying $163.69 less per month
c) John will end up saving $3,943.28
d) John's car will be worth approximately $23,142.58
e) John actually lost $8,182.86 at the end of the 4-year loan.
What is the interest rate?The interest rate is the percentage of the amount of money borrowed, lent or invested that is charged or earned as a fee or return over a certain period of time. It is usually expressed as an annual percentage rate (APR) and can be fixed or variable depending on the type of loan or investment.
a) To calculate John's monthly payments, we need to use the formula for the present value of an annuity, which is:
PMT = P*(r/12)/(1-(1+r/12)^(-n*12))
Where PMT is the monthly payment, P is the principal amount (the amount financed after the down payment), r is the monthly interest rate, and n is the number of years.
So, we have:
P = 32,451 - 3,500 = 28,951
r = 0.055/12
n = 6
PMT = 28,951*(0.055/12)/(1-(1+0.055/12)^(-6*12)) = $489.77
Therefore, John's monthly payments would be $489.77.
b) Using the same formula, we can calculate John's monthly payments with the special financing:
P = 28,951
r = 0.0475/12
n = 4
PMT = 28,951*(0.0475/12)/(1-(1+0.0475/12)^(-4*12)) = $653.46
So, John's monthly payments with the special financing would be $653.46.
Difference in monthly payments between the above options is:
$653.46 - $489.77 = $163.69
Therefore, John would have to pay $163.69 more per month with the special financing.
c) To calculate how much John will save by going with the special financing, we need to calculate the total cost of each option.
For the original financing, the total cost can be found by multiplying the monthly payment by the number of payments:
Total cost = $489.77 * (6 * 12) = $35,268.72
For the special financing, the total cost is:
Total cost = $653.46 * (4 * 12) = $31,325.44
Therefore, John will save:
$35,268.72 - $31,325.44 = $3,943.28
So, John will end up saving $3,943.28 by going with the special financing.
d) To calculate the value of John's car when he finishes paying off his loan, we need to use the formula for continuous compounding:
A = P*e^(rt)
Where A is the final amount, P is the initial amount (the purchase price of the car), e is the mathematical constant e (approximately 2.71828), r is the annual interest rate, and t is the time in years.
The car depreciates at a continuous rate of 6%, which means that the value of the car decreases by 6% every year. So, the effective annual rate of depreciation is:
r = e^(-0.06) - 1 = -0.0589
Note that we use a negative value for r, since the value of the car is decreasing.
John will finish paying off his loan in 4 years. So, the time t is 4 years.
Therefore, the value of John's car when he finishes paying off his loan is:
A = 32,451e^(-0.05894) = $23,142.58
So, John's car will be worth $23,142.58 when he finishes paying off his loan.
e) To calculate how much John actually lost at the end of the 4-year loan, we need to subtract the value of his car at the end of the loan from the total amount he paid:
Total amount paid = $653.46 * (4 * 12) = $31,325.44
Value of car at end of loan = $23,142.58
Amount lost = Total amount paid - Value of car at end of loan
= $31,325.44 - $23,142.58 = $8,182.86
Therefore, John actually lost $8,182.86 at the end of the 4-year loan.
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