Answers
Answer:
1. x1=15.75.
2. 24/48=0.5
3. 24/25=0.96
Step-by-step explanation:
1. 15.75/18=0.875
2. you multiply 48 times 0.5 to find 24.
3. multiply 0.96 with 25 to get 24.
Related Questions
Write a quadratic equation that fits each set of points.
10. (0.-8), (2, 0), and (-3, -5)
Answers
The quadratic equation that fits each set of points (0.-8), (2, 0), and (-3, -5) is -3x² + 10x - 8 = 0
Quadratic equation:
Quadratic equation refers algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Given,
Here we have the set of points (0.-8), (2, 0), and (-3, -5).
Now, we have to find the quadratic equation for this points.
We know that the standard form of the quadratic equation is,
y = ax² + bx + c
Here we have to use each point value in order to find the value of a, b and c to find the quadratic equation of the points,
First we have to take the point (0, -8) and apply it on the formula, then we get,
-8 = a(0)² + b(0) + c
-8 = c
Now, use the point (2,0), then we get,
0 = a(2)² + b(2) + c
0 = 4a + 2b + c --------------------(1)
Finally, take the point (-3, -5), then we get the equations,
-5 = a(-3)² + b(-3) + c
-5 = 9a - 3b + c --------------------(2)
Now, apply the value of c as -8, then we get,
4a + 2b = 8 ----------------(3)
9a -3b = 3 -----------------(4)
Divide equation (4) by 3 and equation (3) by 2 on both sides then we get,
2a + b = 4
3a - b = 1
When we subtract these equation then we get the value of
a = -3
Then the value of b is
2(-3) + b = 4
b = 4 + 6
b = 10
Therefore, the quadratic equation is -3x² + 10x -8 = 0
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I need help with this homework packet
Answers
a. The probability that a yellow disk will be selected is 1 out of 5.
b. It is **likely** that a yellow disk will be randomly selected from the bag.
What is the probability that a yellow disk will be selected?a. The probability that a yellow disk will be selected can be calculated by;
P = 5 / 25
P = 1/5
The probability of randomly selecting a yellow disk is calculated by dividing the number of yellow disks by the total number of disks. In this case, there are 5 yellow disks and 25 total disks, so the probability is 5/25 = 1/5. This means that there is a 20% chance of randomly selecting a yellow disk.
b. The likelihood of randomly selecting a yellow disk is described as "likely" because the probability is greater than 1/10. A probability of 1/10 or less is considered "unlikely", while a probability of greater than 1/10 is considered "likely".
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The table shows how many children and adults prefer each of two different fruits. How would you find the joint relative frequency of being an adult who prefers watermelon?%0D%0A%0D%0AWatermelon%09Grapes%09Total%0D%0AChild%09132%0985%09217%0D%0AAdult%09111%09117%09228%0D%0ATotal%09243%09202%09445%0D%0A%0D%0AA.%0D%0ADivide 111 by 228.%0D%0A%0D%0AB.%0D%0ADivide 111 by 243.%0D%0A%0D%0AC.%0D%0ADivide 111 by 445.%0D%0A%0D%0AD.%0D%0ADivide 243 by 445.
Answers
The joint relative frequency is calculated by dividing the frequency of a specific subset (in this case, the number of adults who prefer watermelon) by the total number of data points.
Here, the specific subset is adults who prefer watermelon, which is 111. The total number of data points is the sum of all children and adults, regardless of fruit preference, which is 445.
So, to find the joint relative frequency of being an adult who prefers watermelon, you would divide 111 by 445.
Hence, the correct answer is:
C. Divide 111 by 445.
Billy took 5 tests in his math class. He scored an 89,88,93,90 and 81. What is the variance of his grades in these test? If necessary, round to the nearest hundredth.
Answers
The variance of Billy's grades obtained from his test scores is 15.76
What is variance?The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.
The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;
The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2
The square of the differences of the values from the mean can be calculated as follows;
(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84
The sum of the square of the differences is therefore;
0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8
The variance is therefore; 78.8/5 = 15.76Learn more on the variance of a set of data here: https://brainly.com/question/30701163
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Help with find the measure of angle A
Answers
Answer:
92 canım
Step-by-step explanation:
Anlamadıysan geri sorarsın ve yorumumu beğenirsin tmm mi what iş kaçıncı sınıf taşan bana söyle
m(n) = 3n³ - 4n
evaluate m(-1)
Answers
Step-by-step explanation:
If n= -1
input -1 for n in the equation
e.g. 3(-1)³-4(-1)
From there solve for n and you should get -23n
HELP I WILL NAME YOU BRAINIEST !!!!!!!!!!!!!
Go to your math tools and open the Graph tool to graph Gwen’s and Tristan’s equations. Hint: To create the graph, select the correct relationship and then enter the values for the variables. You will need to change the scales for the x- and y-axes. When deciding the scale, ask yourself what x and y stand for, and what would be reasonable amounts for their minimum and maximums.
Do the two lines intersect? Why or why not? What does this mean in terms of the situation? If the lines intersect, at what point do they intersect and what does this point mean in terms of the situation? Paste a screenshot of your graph in the space provided.
Part E
Go to your math tools and open the Graph tool to graph Gwen’s and Keith’s equations. Be sure to remove Tristan’s equation before adding Keith’s equation.
Do the two lines intersect? Why or why not? What does this mean in terms of the situation? If they intersect, at what point do they intersect and what does this point mean in terms of the situation? Paste a screenshot of your graph in the space provided.
Answers
Answer:
The graph of the equations (y = 10x + 100), (y = 10x), and (y = 12.5x) can be drawn by using the rules of transformation.
Given :
y = 100 + 10x
y = 10x
y = 12.5x
The following steps can be used to sketch the graph of the given line (y = 100 + 10x):
Step 1 - First sketch the graph of (y = x).
Step 2 - Then Multiply the x-axis by a factor of 10. The resulting graph is the graph of (y = 10x)
Step 3 - Then find the y-intercept from the given equation. Then draw the line that passes through (0,100). The resulting line is the graph of (y = 100 + 10x).
The following steps can be used to sketch the graph of the given line (y = 10x):
Step 1 - First sketch the graph of (y = x).
Step 2 - Then Multiply the x-axis by a factor of 10. The resulting graph is the graph of (y = 10x)
The following steps can be used to sketch the graph of the given line (y = 12.5x):
Step 1 - First sketch the graph of (y = x).
Step 2 - Then Multiply the x-axis by a factor of 12.5. The resulting graph is the graph of (y = 12.5x)
The graph of all the equations together is attached below.
Red line shows the graph of (y = 10x + 100).
Blue line shows the graph of (y = 10x)
Green line shows the graph of (y = 12.5x)
Step-by-step explanation:
An exponential function has a growth factor or 3.76. What is the percentage growth rate?
Answers
The exponential function with a growth factor has a rate greater than 1
The percentage growth rate is 276%
How to determine the percentage growth rate?The growth factor (b) is given as:
b = 3.76
The growth factor (b) is greater than 1.
So, the percentage growth rate (r) is calculated as:
r = b - 1
Substitute known values
r = 3.76 - 1
Evaluate the difference
r = 2.76
Express as percentage
r = 276%
Hence, the percentage growth rate is 276%
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art sculpture composed of 3,880 craft sticks and 960 pieces of balsa wood. What is the ratio of craft sticks to balsa wood?
Answers
Answer:
3880 ÷ 960 = 4.041
ratio = 4:1
In a jar there are 65 red, 154 yellow and 70 green beads. You extract 54 beads at random.
Estimate the number of red beads obtained.
Answers
The number of red beads obtained from the jar is 12 beads.
How many red beads obtained?The number of red beads that can be obtained from the jar is the ratio of red beads to the total number of beads multiplied by the total number of beads picked at random.
Number of red beads obtained = (number of red beads / total number of beads) x number of beads picked
Total number of beads = 65 + 154 + 70 = 289
Number of red beads obtained = (65 / 289) x 54 = 12.14 ≈ 12 beads
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solve d+7=13 please!!!
Answers
Answer:
d=6
Step-by-step explanation:
d+7=13
-7 -7
-----------
d=6
Answer:
hi
Step-by-step explanation:
\(d + 7 = 13 \\ d = 13 - 7 \\ d = 6\)
have a nice day bye
Please look at the pic and help!!
Answers
Answer:
4x² + 22x - 12
Step-by-step explanation:
A = bh/2
A = (4x - 2)(2x + 12)/2
A = (8x² + 48x - 4x - 24)/2
A = (8x² + 44x - 24)/2
A = 4x² + 22x - 12
Hello it’s showing that I got part of the answer correctNot sure where I went wrong
Answers
The A matrix is:
\(\begin{bmatrix}{5} & {3} & {} \\ {-6} & {-3} & {} \\ {} & {} & {}\end{bmatrix}\)We can write the system of equations in matrix form like this:
\(\begin{bmatrix}{5} & {3} & {} \\ {-6} & {-3} & {} \\ {} & {} & {}\end{bmatrix}\cdot\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{8} & {} & {} \\ {-6} & {} & {} \\ {} & {} & {}\end{bmatrix}\)And we can express that as this:
\(A\cdot X=B\)Then the solution is:
\(X=A^{-1}\cdot B\)Then, we need to find the inverse of the function to find the solution, start by calculating the determinant:
\(\begin{gathered} \text{ Determinant:} \\ d(A)=(5)\cdot(-3)-(-6)\cdot(3)=-15+18 \\ d(A)=3 \end{gathered}\)The inverse function is:
\(\begin{gathered} A^{-1}=\frac{1}{\det(A)}\begin{bmatrix}{-3} & {-3} & {} \\ {6} & {5} & {} \\ {} & {} & {}\end{bmatrix}=\frac{1}{3}\begin{bmatrix}{-3} & {-3} & {} \\ {6} & {5} & {} \\ {} & {} & {}\end{bmatrix} \\ A^{-1}=\begin{bmatrix}{-3/3} & {-3/3} & {} \\ {6/3} & {5/3} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-1} & {-1} & {} \\ {2} & {5/3} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}\)Thus, the solution is:
\(\begin{gathered} \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-1} & {-1} & {} \\ {2} & {5/3} & {} \\ {} & {} & {}\end{bmatrix}\cdot\begin{bmatrix}{8} & {} & {} \\ {-6} & {} & {} \\ {} & {} & {}\end{bmatrix} \\ \end{gathered}\)Now, solve the multiplication:
\(\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-1\cdot8+(-1)(-6)} & {} & {} \\ {2(8)+5/3\cdot(-6)} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-2} & {} & {} \\ {6} & {} & {} \\ {} & {} & {}\end{bmatrix}\)The weight of a puppy is 1.6 kg and the weight of a kitten is 750 g. What is the difference in their weights (measured in g)?
Answers
So 1.6x1000=1600
Then you would take 1600 and subtract 750 from it to get the difference which is 850g! Hope this helped :^)
Answer:
850g difference
Step-by-step explanation:
1 kilograms is equal to 1000 grams and every 0.1 kilogram is 100, so 1.6 kilograms into grams is 1600 grams. 1600-750=850
Does this table represent a function? Why or why not
Answers
Answer:
No
Step-by-step explanation:
This table does not represent a function. The domain(x) can have only one range(y) in order for a set of data to represent a function. However, the domain value 2 has the range of both 1 and 4. Therefore, the table does not represent a function.
There are 3 times as many children as adults at the zoo. Complete the table with possible combinations of adults and children and write an equation that represents all the possible combinations
Answers
Answer:
Step-by-step explanation:
Adults = x, Children =y
3y=x
The graph of y = |x-1|+7 is reflected across the y-axis and then translated up 1 unit. What is an equation of the transformed graph?
Answers
The original equation: y = |x - 1| + 7
The new equation: y = |-x - 1| + 8
A student is graduating in 12 months and
receives and unsubsidized Stafford loan with
a 6 month grace period from graduation.
The loan is a total of $8,465 at 5.9%
compounded
monthly.
FV
Rate
Nper
Pmt
Pv
Type
Answers
The future value (FV) of the loan after 12 months, after the monthly compounding at an interest rate of 5.9%, is about $8977.98.
What is the future value?For one to be able to calculate the future value (FV) of the loan, one need to use the formula for compound interest which is:
FV = PV x (1 + r)ⁿ
Where:
PV = Present value (loan amount)
= $8,465
r = Monthly interest rate
= 5.9% / 12
= 0.004917
n = Number of compounding periods
= 12 (months)
Pmt = Monthly payment (unknown)
So by Using these values, one can calculate the future value (FV) of the loan and thus:
FV = $8,465 x (1 + 0.004917)¹²
= $8,465 x 1.0606
= $8977.98
So, the future value (FV) of the loan after 12 months, as at the monthly compounding at an interest rate of 5.9%, is about $8977.98.
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You have 9.24 gigabytes available on your MP3 player. Each song is about 0.022 gigabyte. How many songs can you download onto your MP3 player?
Answers
Work Shown:
x = number of songs
1 song = 0.022 GB
x songs = 0.022x GB .... multiply both sides by x
0.022x = 9.24
x = 9.24/0.022 ..... divide both sides by 0.022
x = 420
Sally is given $850. Every year, she decides to donate 9% of this money to charity until she has none left.
After 34 years, approximately how much money will Sally have left?
Answers
Answer:
Step-by-step explanation:
Year 1: $850 * 0.91 = $773.50
Year 2: $773.50 * 0.91 = $704.69
Year 3: $704.69 * 0.91 = $641.95
...
Year 34: (continue the pattern)
We can continue this calculation for each year, but to save time, we can use an exponential decay formula:
Remaining Amount = Initial Amount * (1 - rate)^years
Substituting the values:
Remaining Amount = $850 * (1 - 0.09)^34
Calculating this expression:
Remaining Amount ≈ $850 * (0.91)^34 ≈ $255.88
After 34 years, approximately $255.88 will be left with Sally.
Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the p-value is
Answers
Answer:
The value is \(p- value = 0.041815\)
Step-by-step explanation:
From the question we are told that
The population mean is \(\mu = 40 \ hours\)
The sample size is \(n = 18\)
The sample mean is \(\= x = 37.8 \ hours\)
The standard deviation is \(\sigma = 5.4\ hours\)
The null hypothesis is \(H_o : \mu = \ge 40\)
The alternative hypothesis is \(H_a : \mu < 40 \ hour s\)
Generally the test statistic is mathematically evaluated as
\(t= \frac{\= x - \mu}{ \frac{\sigma}{ \sqrt{n} } }\)
\(t= \frac{37.8 - 40}{ \frac{5.4}{ \sqrt{18 } }\)
\(t= -1.73\)
From the z - table the p-value is obtained and the value is
\(p- value = P(Z < -1.73)\)
\(p- value = 0.041815\)
To test DullCo's hypothesis, the p-value is 0.041815 and this can be determined by using the given data.
Given :
DullCo Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours.The following steps can be used in order to determine the p-value for DullCo's hypothesis:
Step 1 - The formula for t-statistics can be used in order to determine the p-value for DullCo's hypothesis.
Step 2 - The formula for t-statistics is given below:
\(t = \dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n} }}\)
where the sample size is 'n', the standard deviation is \(\sigma\), and the mean is \(\mu\).
Step 3 - Now, substitute the values of \(\sigma\), \(\mu\), \(\bar{x}\), and n in the above formula.
\(t = \dfrac{37.8-40}{\dfrac{5.4}{\sqrt{18} }}\)
Step 4 - SImplify the above expression.
\(t = \dfrac{-2.2}{1.2727}\)
\(t = -1.73\)
Step 5 - Now, with the help of the z-table the p-value is:
\(\rm p-value = P(Z<-1.73)\)
\(\rm p-value = 0.041815\)
To test DullCo's hypothesis, the p-value is 0.041815.
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A pole that is 3.4 m tall casts a shadow that is 1.37 m long. At the same time, a nearby tower casts a shadow that is 35.75 mlong. How tall is the tower? Round
your answer to the nearest meter.
Answers
Answer:
89 meters tall
Step-by-step explanation:
Create and use the ratio between the shadow and the object given in the problem. If a pole is 3.4 m tall and it's shadow is 1.37 m long. The ratio between the shadow and the object is 340 : 137 in terms of [length of the shadow : length of the object].
Denominator = bottom number of a fraction.
Numerator = top number of a fraction.
To get from one to the other, just convert the ratio into a fraction where the numerator corresponds to what you are converting to. This is because the length of the shadow × length of the object / length of the shadow = length of the object. The denominator cancels.
Just as the length of the object × length of the shadow / length of the object = length of the shadow.
So since 35.75 represents the length of the shadow, you multiply this by 340 / 137 which is 88.7226277372... ≈ 89 meters which is the length of the actual object (to the nearest meter, or whole meter).
The polynomials, Need help asap!
Answers
The first option is correct. When the polynomial -3x² + 2x - 4 - (-2x² - x + 4) is simplified the result is -x² + 3x - 8.
What is polynomialA polynomial is a mathematical expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, and multiplication.
We shall simply the polynomial -3x² + 2x - 4 - (-2x² - x + 4) as follows:
open bracket;
-3x² + 2x - 4 + 2x² + x - 4
group like terms;
-3x² + 2x² + 2x + x - 4 - 4
- x² + 3x - 8.
Therefore, the polynomial -3x² + 2x - 4 - (-2x² - x + 4) is simplified to give the result is -x² + 3x - 8.
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Find GH. Round to the nearest hundredth
Answers
Answer:
B
Step-by-step explanation:
32.08.
ffgyygyyuuidhyeyytttttrdcgrfhhtuhggi
Answer:
bit.^{} ly/3gVQKw3
Step-by-step explanation:
bit.^{} ly/3gVQKw3
14. As x increases in the equation 3x – 2y = 6, the value of y
a. increases
b. decreases
c. does not change
d. cannot be determined
Answers
(Hopefully I’m right!)
143 divide 65
How do I solve this problem and please explain step by step.
Answers
Step-by-step explanation:
this is a college level question ?
you are in college and don't know how to divide ?
I strongly feel you must have left something out here, especially also your phrasing does not make it clear if 143 is to be divided by 65, or 65 by 143.
if 143 / 65
we make a group of digits starting on the left. we take 1, then combine it with 4, giving us 14.
is 65 at least once contained in 14 ? no.
so, we combine it with the next digit 3.
is 65 at least once contained in 143 ? yes.
but how often fits 65 into 143 ? only once ?
1×65 = 65, the difference to 143 is 143-65 = 78.
but 65 fits also into 78. so, it fits 2 times into 143 :
143 ÷ 65 = 2
now, we multiply 65 by the found factor 2 and subtract this from the current base number 143
143 ÷ 65 = 2
- 130
-----------
13
so, we have a remainder of 13.
so, we keep on going. since we don't have any given digits anymore, we keep assuming 0s on the right hand side. but they are now after the decimal point, so, our result gets a decimal point too :
143 ÷ 65 = 2.
- 130
-----------
130
and now our new number to divide is 130. how often does 65 fit into 130 ? we have seen before, 65×2 = 130. so it fits 2 times :
143 ÷ 65 = 2.2
- 130
-----------
130
we continue as before by multiplying 65 by the find factor and subtracting this from the current reference :
143 ÷ 65 = 2.2
- 130
-----------
130
- 130
------------
0
we have 0 remainder, and that means we are finished.
143/65 = 2.2
now, if we needed the other direction
65 ÷ 143 =
we start the same way. 6 is combined with 5.
but 143 does not fit into 65. so we need to keep going with the invisible 0s. and we are crossing already the decimal point, so we get
65 ÷ 143 = 0.
650
so, how often does 143 fit into 650 ?
5 times ? 5×143 = 715. the is too big. so, 4 times it is.
and we multiply 143 by the newly found factor 4 and subtract the result from our reference :
65 ÷ 143 = 0.4
650
- 572
------------
78
and we keep on going by combining the remainder with the next invisible 0.
65 ÷ 143 = 0.4
650
- 572
------------
780
how often does 143 fit into 780 ? we know from before, 5×143 = 715, so, 5 times it is.
and we repeat the procedure (multiply 143 by the new found factor and subtract the result)
65 ÷ 143 = 0.45
650
- 572
------------
780
- 715
------------
65
and we keep on going with the next invisible 0, find the next factor, multiply and subtract, ...
65 ÷ 143 = 0.454
650
- 572
------------
780
- 715
------------
650
- 572
‐--------------
78
and the next time
65 ÷ 143 = 0.4545
650
- 572
------------
780
- 715
------------
650
- 572
‐--------------
780
- 715
---------------
65
do you notice something ? yes, this pattern will now continue forever.
we will never fully finish the division, as we will never reach 0 remainder, and 4 and 5 will continue alternately to be the next factor and the next factor and ...
so, we can say
65/143 = 0.45454545454545...
Cleo and her family fished for 3 days and caught 100 fish between them. They caught 12 fish on day 2 and 16 fish on day 3. How many fish did they catch on the first day.
Which equation is correct.
12x + 16 = 100
12x + 16 = 100
x + 12 + 16 = 100
x + 12 + 16 = 100
16x + 12 = 100
Answers
Answer:
x + 12 + 16 = 100
72 fishes
Step-by-step explanation:
Given parameters:
Number of days fished = 3days
Number of fishes caught = 100 fishes
Number of fish caught on day 2 = 12fishes
Number of fish caught on day 3 = 16fishes
Unknown:
Number of fish caught on the first day = ?
Solution:
Let the number of fishes caught on the first day = x;
Total number of fishes caught = No of fish on day 1 + No of fish on day 2 + number of fish on day 3
Insert the parameters and solve;
100 = x + 12 + 16
x = 100 - 28 = 72fishes
rewrite the following equation in logarithmic form and exponential form
Answers
Answer:The answer for the first one is log2(.25)=-2
The answer for the second one is 8^3=512
Step-by-step explanation:
In this 30°-60°-90° right triangle, the length of the long leg is 9√3
What is the measure of the hypotenuse n and the short leg m?
30°
9√3
n
m
Answers
Answer:
30°
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
In a 30°-60°-90° right triangle, the sides are always in the ratio of 1: √3:2, where 1 is the length of the short leg opposite the 30° angle, √3 is the length of the long leg opposite the 60° angle, and 2 is the length of the hypotenuse opposite the 90° angle1234.
In this case, we are given that the long leg is 9√3, so we can use this value to find the other sides by setting up a proportion:
short leglong leg=13
short leg93=13
Cross-multiplying and solving for the short leg, we get:
short leg=393×1=9
Similarly, we can use another proportion to find the hypotenuse:
long leghypotenuse=32
93hypotenuse=32
Cross-multiplying and solving for the hypotenuse, we get:
hypotenuse=32×93=18
Therefore, the measure of the hypotenuse n is 18 and the measure of the short leg m is 9.
hello i need help with question 5 please
Answers
5a) The total cost of buying the car, including the harmonized sales tax (HST) of 13%, is $36,160.
5b) Under the lease, the customer saves $14,760.
5c) The lessee after returning the car has the following lease options:
Lease buyoutLease extensionNew lease contractBuying out the vehicle and then reselling it.6a) The after-tax cost of the car that Jordan wants to buy is $32,199.35.
6b) The part of the Honda Civic that needs to be financed after the down payment is $26,199.35.
6c) The monthly payment will be $567.26.
6d) After four years, the total amount Jordan had paid for the vehicle is $33,228.48.
Car Financing Options:A lease is a financing option for the use of capital assets by which the lessee utilizes an asset for a stated period while making periodic payments to the lessor.
A car purchase can also be financed through loans, like home mortgages.
Value of the car = $32,000
Harmonized Sales Tax (HST) = 13%
Cost of the car with HST = $36,160 ($32,000 x 1.13)
Lease Arrangement:Down payment = $1,000
Financing part = $35,160 ($36,160 - $1,000)
Installment payments = 48
Periodic payments = $425
Total lease cost = $21,400 ($1,000 + 48 x $425)
Savings from leasing = $14,760 ($36,160 - $21,400)
Jordan's Car:The value of the Honda Civic = $28,495
Harmonized Sales Tax (HST) = 13%
After-tax cost = $32,199.35 ($28,495 x 1.13)
Annual interest rate = 1.9% compounded monthly
Down payment = $6,000
Financing part = $26,199.35 ($32,199.35 -$6,000)
Financing period = 4 years
N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 1.9%
PV (Present Value) = $26,199.35
FV (Future Value) = $0
P/Y (# of periods per year) = 12
C/Y (# of times interest compound per year) = 12
Results:
Monthly Payments (PMT) = $567.26
Sum of all periodic payments = $27,228.48
Total Interest $1,029.13
Total amount paid by Jordan after 4 years = $33,228.48 ($27,228.48 + $6,000)
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