Answer:
Step-by-step explanation:15
Kelly bought a new SUV for $28,000. She made a down payment of $11,000 and has monthly payments of $332.63 for 5 years. She is able to pay off her loan at the end of 36 months. Using the actuarial method, find the unearned interest and payoff amount.
The unearned interest and the payoff amount is $11,022.12 and $18,784.87 respectively
Given data ,
Kelly bought a new SUV for $28,000. She made a down payment of $11,000 and has monthly payments of $332.63 for 5 years.
She is able to pay off her loan at the end of 36 months.
Now , Total interest = (monthly payment x number of months) - loan amount
Total interest = ($332.63 x 60) - $17,000
Total interest = $19,957.80
Next, we need to calculate the interest that has already been paid over the first 36 months of the loan. We can use the formula:
Interest paid = (monthly payment x number of months) - (loan amount - down payment)
Interest paid = ($332.63 x 36) - ($28,000 - $11,000)
Interest paid = $8,935.68
The unearned interest is the difference between the total interest and the interest paid so far:
Unearned interest = total interest - interest paid
Unearned interest = $19,957.80 - $8,935.68
Unearned interest = $11,022.12
To find the payoff amount, we need to add the remaining principal balance to the unearned interest:
Payoff amount = remaining balance + unearned interest
To calculate the remaining balance, we can use the formula for the present value of an annuity:
Remaining balance = monthly payment x (1 - (1 + r)^-n) / r
Where r is the monthly interest rate and n is the number of remaining months. We can solve for r by using the total interest calculated earlier:
r = (Total interest / loan amount) / 12
r = ($19,957.80 / $17,000) / 12
r = 0.0986%
Using this interest rate and n = 24 (the remaining 24 months of the loan), we can calculate the remaining balance:
Remaining balance = $332.63 x (1 - (1 + 0.0986%)^-24) / 0.0986%
Remaining balance = $7,762.75
Payoff amount = $7,762.75 + $11,022.12
Payoff amount = $18,784.87
Hence , the interest is solved
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A graph is shown.
6987654321
10
0 1 2 3 4 5 6 7 8 9 10
Which ordered pair describes a point that should be removed from the graph so that the graph represents a function?
An ordered pair that describes a point that should be removed from the graph so that the graph represents a function include the following: A. (1, 1).
What is a function?In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
Based on the graph shown below, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values);
3 → 1
1 → 1
In this context, we can reasonably infer and logically deduce that either (3, 1) or (1, 1) must be removed from the graph in order to represent a function.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
What is the measure of Zx?
Angles are not necessarily drawn to scale.
H
A
45
63
I
K
Applying the triangle sum theorem, the measure of angle x is calculated as: m<x = 72 degrees.
What is the Triangle Sum Theorem?In a triangle, when all of its interior angles are added together, the triangle sum theorem states that we will get a sum of 180 degrees.
Therefore, we have:
m<AHI = 63 degrees [based on the corresponding angles theorem]
Considering triangle AHI, applying the triangle sum theorem, we will have the following:
m<x + m<AHI + m<A = 180°
Substitute:
m<x + 63 + 45 = 180°
m<x + 108 = 180°
m<x = 180 - 108 [subtraction property of equality]
m<x = 72 degrees.
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when the sun is 35° above the horizon. how long is the shadow cast by a building 15 metres high?
Therefore , the solution of the given problem of trigonometry comes out to be approximately 21.424 metres long when the sun is 35 degrees above the horizon.
What is trigonometry?Some people assert that the growth of astrophysics was influenced by the merging of various fields. Many metric problems can be solved or the result of a calculation can be ascertained with the use of exact mathematical techniques. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They go by many other names and acronyms, including sine, variance, direction, and others. (csc).
Here,
When the sun is at a 35° elevation angle and the structure is 15 metres tall, we want to determine the length of the shadow (on the next side).
Let x represent the desired shadow's length. Next, we have
=> tan 35° = 15/x
When we multiply both sides by x, we obtain:
=> x tan 35° = 15
By dividing both sides by 35° of tan, we obtain:
=> x = 15 / tan 35°
We may calculate the value of the tangent of 35 degrees using a calculator:
=> tan 35° ≈ 0.7002
Next, we have
=> 15x/0.702x=21.424 metres
Consequently, a building 15 metres high will create a shadow that is approximately 21.424 metres long when the sun is 35 degrees above the horizon.
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given h(t)=4t and k(t)=t+5t−1 , determine the expressions that are equal to these combinations of h(t) and k(t) . h(t)+k(t) h(t)−k(t) h(t)+k(t)h(t)−k(t) t2+t+4t2+9t−4 −t2+9t−4t2+t+4 t2+4t+4t2−1 −t2+t+4t2−t −t2+4t−6t2−1 t2+9t−4t2−t
The expressions are written as;
h(t)+k(t) = 10t - 1
h(t)−k(t) = -2t + 1
How to determine the expressionsNote that algebraic expressions are described as expressions that are made up of coefficients, variables, terms, constants and factors.
These expressions are made up of arithmetic operations, which includes;
AdditionMultiplicationDivisionBracketParenthesesSubtractionFrom the information given, we have that;
h(t)=4t
k(t)=t+5t−1
To determine the value of h(t) + k(t), we have;
4t + t + 5t - 1
add the like terms, we get;
10t - 1
To determine h(t) = k(t)
4t- t - 5t + 1
add like terms
-2t + 1
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Emma brought $23.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4.50 left over after buying these items.
Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.
How to solve for the costB = 1/4 * S
S = 2/3 * P
B + S + P = 23.75 - 4.50
Emma spent 23.75 - 4.50 = $19.25 on the brush, sketchbook, and paint set.
Now we have the equation:
B + S + P = 19.25
Substitute the expressions from relationships 1 and 2 into the equation:
(1/4 * S) + S + (3/2 * S) = 19.25
Now combine the terms:
(1/4 * S) + (4/4 * S) + (6/4 * S) = 19.25
(11/4 * S) = 19.25
Now, to solve for S, multiply both sides of the equation by the reciprocal of the fraction (4/11):
S = (4/11) * 19.25
S = 7
The sketchbook cost $7. Now we can find the costs of the brush and the paint set using relationships 1 and 2:
B = 1/4 * S = 1/4 * 7 = 1.75
P = 3/2 * S = 3/2 * 7 = 10.5
Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.
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Complete question
Emma brought $23.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4.50 left over after buying these items. What is the total cost for each item
Help pleaseee
Expand the logarithm as much as possible
logy^10
The expanded form of log y^10 is either 10 log y or 10 ln y
Expanding the logarithmAssuming that the base of the logarithm is not specified, we can use the change of base formula to expand the logarithm:
log y^10 = log (y^10) / log (base)
Since the base is not specified, we can use any base we like. For example, we can use base 10 or base e (natural logarithm).
Using base 10:
log y^10 = log (y^10) / log 10
= 10 log y / 1
= 10 log y
Using natural logarithm:
log y^10 = log (y^10) / log e
= 10 log y / 1
= 10 ln y
Therefore, the expanded form of log y^10 is either 10 log y or 10 ln y, depending on the base used.
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I need help please
here is the picture is about Row Ops
The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
Reducing row matricesFrom the question, we are to perform the given row operation on the given matrix
From the given information, the given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]
We are to carry out the operation
Add -4(row 1) to row 3
This means we should multiply row 1 by -4
-4 × [ 1 2 1 | -5
-4 -8 -4 | 20
Now, we will add the result to row 3
4 -1 6 | -8
-4 -8 -4 | 20
------------------------
0 -9 2 | 12
Hence,
The resulting matrix becomes
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
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For the graph of a function y=f(x) shown to the right, find the absolute maximum and the absolute minimum, if they exist. Identify any local maxima or local minima.
Answer:
B) There is no absolute max for y=f(x)
Step-by-step explanation:
There is no absolute max as the function increases infinitely
However there is an absolute minimum at x=0
x+2y=5
4x+8y=20
I need help asap
Answer:
(x, -1/2x + 5/2) or infinitely many solutions
Step-by-step explanation:
We can solve the system of equations using substitution. We can start by isolating x in the first equation. Then, we can plug in the entire equation made from isolating for x in the second equation, which will allow us to find y:
Isolating:
x = -2y + 5
Plugging in and solving for y:
4(-2y + 5) + 8y = 20
-8y + 20 + 8y = 20
20 = 20
We see that we get a constant equal to another constant. Whenever you get this as a solution to a system of equations, this means that there are infinitely many solutions. We can express the general rule for the solution in coordinate form by isolating y in at least one of the equations:
y = -1/2x + 5/2
Thus, the general rule for the solution to the system of equations is
(x, -1/2x + 5/2), so you can either put this general rule as the answer or write solution = infinitely many solutions
You can see that there are infinitely many solutions by plugging in any number for x into the two equations and see that you get 5 for the equation and 20 for the second equation. Let's try 4 for x and 0 for x:
4 for x in first equation:
4 + 2(-1/2(4) + 5/2) = 5
4 + 2(0.5) = 5
4 + 1 = 5
5 = 5
4 for x in the second equation
4(4) + 8(-1/2(4) + 5/2) = 20
16 + 8(0.5) = 20
16 +4 = 20
20 = 20
0 for x in the first equation:
0 + 2(-1/2(0) + 5/2) = 5
0 + 2(2.5) = 5
5 = 5
0 for x in the second equation:
4(0) + 8(-1/2(0) + 5/2) = 20
0 + 8(2.5) = 20
20 = 20
Help please connect the left to the right for each component
f(x) = the total cost for detailing the car. x = the number of minutes it takes to detail the car. m = The cost per minute for the detailing in car. b = the flat fee for detailing the car.
What is a linear equation?An algebraic equation is said to be linear if the maximum power of the variable is 1. In other words, it is an equation that, when plotted on a coordinate plane, defines a straight line. A linear equation with a single variable has the general form:
ax + b = 0, where a and b are constants and x is the variable. A single value of x that causes the equation to be true is the answer to this equation.
The given situation can be expressed in the form f(x) = mx + b.
Where,
f(x) = the total cost for detailing the car.
x = the number of minutes it takes to detail the car.
m = The cost per minute for the detailing in car.
b = the flat fee for detailing the car.
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Which expression is equivalent to (x-3)(2x^(2)-3x-1)
The "Expression" which is considered equivalent to this expression "(3x-1)-2(x+2)' is (c) x-5.
In mathematics, an algebraic expression is a combination of numbers, variables, which are joined by arithmetic operations (such as addition, subtraction, multiplication, and division).
We have to find the equivalent-expression for (3x-1)-2(x+2);
⇒ (3x-1)-2(x+2),
⇒ (3x - 1) - 2x - 4,
Combing the like-terms together in the above expression,
We get,
⇒ 3x - 2x -1 - 4,
⇒ x - 5,
Therefore, the correct equivalent expression is Option (c).
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The given question is incomplete, the complete question is
Which of the following expression is equivalent to (3x-1)-2(x+2)?
(a) x+3
(b) x+1
(c) x-5
(d) x-3
Help Please The sum of two even numbers is even. The sum of 6 and another number is even. What conjecture can you make about the other number?
A) The other number is odd.
B) The number is even.
C) Not enough information.
D) The number is 8.
Answer:
the number is even
Step-by-step explanation:
an even number plus an even number will aalways be even. adding 6 to an odd number will never be even. Therefore the number will be even
El perímetro de un campo rectangular es 300 m . Si la longitud del campo es 88 , ¿cuál es su anchura?
Based on the above, the width of the field is 62 meters.
What is the width?Based on the question, Let's say that the width of the field is denoted with 'w'.
Note that the formula for the perimeter (P) of a rectangle is:
P = 2(l + w)
where"
l = length
w = width.
Fixing the values into the equation, it will be:
300 = 2(88 + w)
So, Divide both sides by 2:
150 = 88 + w
Subtract 88 from both sides:
w = 150 - 88
w = 62
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Se text below
The perimeter of a rectangular field is 300 m. If the length of the field is 88 , what is its width?
Transactions on Furnell's credit card are shown for the month of June. The interest rate is 1.4% per month.
June 1 Balance $352.12
June 4 Sears $331.89
June 8 eBay $81.58
June 15 Outback $30
June 18 Payment $200
Find the average daily balance $
184.89
Find the interest for the month $
Find the balance for the following month $
The balance for the following month is $598.18.
How to solveThe average daily balance for June is $184.89.
To calculate the interest for the month, multiply the average daily balance by the interest rate: $184.89 * 1.4% = $2.59.
To find the balance for the following month, add the initial balance, transactions, and interest, then subtract the payment: $352.12 + $331.89 + $81.58 + $30 + $2.59 - $200 = $598.18.
The balance for the following month is $598.18.
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The hanger image below represents a balanced equation. Select an equation that represents the image. Choose 1 answer: (Choice A) 45 = 3 + � , equals, 3, plus, z A 45 = 3 + � , equals, 3, plus, z (Choice B, Checked) 45 = 3 � equals, 3, z B 45 = 3 � equals, 3, z Find the value of � z that makes the equation true. � z, equals
The balanced equation of the hanger is 3z = 45 and the solution is z = 15
Selecting an equation that represents the imageFrom the question, we have the following parameters that can be used in our computation:
The hanger image
On the hanger image, we have the following
One side = z + z + z
The other side = 45
The expressions on either sides must be equal to have a balanced equation
So, we have
z + z + z = 45
Evaluate the like terms
3z = 45
Divide both sides of the equation by 3
z = 15
Hence, the balanced equation is 3z = 45 and the solution is z = 15
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What's the answer to this problem
The function shows that the chairs and sofas the manufacturer should produce to earn that profit is C. (6, 12) P= 1,260
How to explain the functionThe profit function is P = 50x + 80y.
In order to find the optimal production quantities that will maximize the profit function, we need to determine which vertex yields the highest profit.
From the given vertices, we can see that the profit at (0,0) is 0. The profit at (0,15) is 1,200, and the profit at (6,12) is 1,260.
Therefore, the manufacturer should produce 6 chairs and 12 sofas to earn a profit of 1,260.
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Encik Halim bought 108 lemons to sell at his grocery shop. He packed 3 lemons in small packets and sold at the price of RM6.80 per packet. If he made a total profit of RM88.20, calculate the price of each lemon bought by him.
Answer:
the price of each lemon bought by Encik Halim is RM1.45.
Step-by-step explanation:
Encik Halim bought 108 lemons and packed them into packets of 3 lemons each. So he made a total of 108/3 = 36 packets.
Let's assume that the cost of each lemon bought by Encik Halim is x RM.
The total cost of 108 lemons would then be 108x RM.
Encik Halim sold each packet at a price of RM6.80, so the total revenue he earned from selling 36 packets would be 36 x RM6.80 = RM244.80.
We are told that Encik Halim made a profit of RM88.20 from the sale of these packets, so his total cost would be:
Total cost = Total revenue - Profit
Total cost = RM244.80 - RM88.20
Total cost = RM156.60
We know that Encik Halim bought 108 lemons, so we can write:
Total cost = Number of lemons bought x Cost per lemon
RM156.60 = 108x
Therefore, the cost per lemon bought by Encik Halim is:
x = RM156.60/108
x = RM1.45
So the price of each lemon bought by Encik Halim is RM1.45.
A solution has a total mass of 400 g. If the solvent has a mass of 236 g of the total mass, what is the strength of the drug?
In a case whereby A solution has a total mass of 400 g. If the solvent has a mass of 236 g of the total mass, the strength of the drug can be expressed as 41%.
How can the strength of the drug be calculated?From the question, the total mass =400 g
The solvent mass = 236 g
Then the mass of the drug = 400-236
= 164
Then the mass percentage of the drug can be calculated as 164/400 * 100
= 41%
Therefore, the strenght of the drug can be expressed as 41%
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In the diagram below, BE intersects AD at C, AB | DE. If CD = 4.2 and AB = 9.6, what is the length of
BC to the nearest tenth of a centimeter?
Dont mind the writing
The length of BC, to the nearest tenth of a centimeter, is calculated as: 12.6 centimeter.
How to Find the Length of the Indicated Side?Recall that two similar triangles will always have side lengths that are proportional in length. The triangles shown are similar to each other, therefore, the proportion below would be true:
AC/CE = BC/CD
Given the following:
AC = 7.2 units
CE = 2.4 units
CD = 4.2 units
BC = ?
Plug in the values:
7.2/2.4 = BC/4.2
Cross multiply:
BC = 7.2 * 4.2 / 2.4
BC = 12.6 cm
Thus, the length of side BC in the similar triangles shown is approximately 12.6 cm.
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Girish left his home at 7 45 and travelled to Muar, which was 120 km away. He arrived
at Muar 2 h later. After staying 1 2/3 hours in Muar, he travelled from Muar back to his home
along the same route at a speed which was 20 Km/h slower than his previous speed.
At what time did Girish reach home?
Answer:
2:35
Step-by-step explanation:
it takes 2 hours to get to Muar so 9:45
he spends 1 hour 40 in muar so 11:35
he went at 60 Km/h before so he returns at 40Km/h so it takes 3 hours so 2:35
Suppose a city with population 500,000 has been growing at a rate of 4.3% per year. If this rate continues, find the population of this city in 10 years
In the Show Your Work box, must have the following:
- 1 pt- Formula used
- 1 pt- Variables and what they stand for
- 3 pts- Full solving process
Answer:
t = time in years
p(t) = population at time t
[tex]p(t) = 500000( {1.043}^{t} )[/tex]
[tex]p(10) = 500000( {1.043}^{10}) = 761751 [/tex]
The teacher gave a true and false quiz where P(true) = 0.5 for each question. Interpret the likelihood that the first question will be true.
Likely.
Unlikely.
Equally likely and unlikely.
This value is not possible to represent probability of a chance event.
The likelihood that the first question will be true is equally likely and unlikely.
Interpreting the likelihood that the first question will be true.From the question, we have the following parameters that can be used in our computation:
The teacher gave a true and false quiz where P(true) = 0.5 for each question.
This means that
P(true) = 0.5
As a percentage,, we have
P(true) = 50%
When the probability of an event is 50%, then the event is equally likely and unlikely.
Hence, the liikelihood is (c) qually likely and unlikely.
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Consider the function f(x)=−4.6|x+2|+7.
About what line is the graph of the function symmetric?
Enter your answer in the box.
The graph of the function f(x)=−4.6|x+2|+7 is symmetric at x = -2
About what line is the graph of the function symmetric?From the question, we have the following parameters that can be used in our computation:
The function f(x)=−4.6|x+2|+7.
The function f(x)=−4.6|x+2|+7 is an absolute value function
An absolute value function is represented as
f(x) = a|x - h| + k
Where the line of symmetry is
x = h
Using the above as a guide, we have the following:
Line of symmetry: x = -2
Hence, the graph of the function is symmetric at x = -2
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With workings please
The probability that he passes Math and does not pass Physics is given as follows:
0.28 = 28%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The probabilities for each event is given as follows:
Passes Math: 0.7.Does not pass Physics: 1 - 0.6 = 0.4.The events are independent, hence the probability that he passes Math and does not pass Physics is given by the multiplication of the probabilities of each event, as follows:
0.7 x 0.4 = 0.28 = 28%.
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How do you leave 6.92820323 in three significant numbers
Answer:
6.92
Step-by-step explanation:
When ever there are also of decimal places you must at least write the first 2 only.
Hope this helps
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I NEED HELP WITH STATISTICS
The median of this data set is equal to 9.
The mean of this data set is equal to 13.7.
The number of mode that this data set have is zero modes.
How to calculate the mean for the set of data?In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:
Mean = [F(x)]/n
For the total number of data, we have;
Total, F(x) = 26+ 0 -1 + 33 + 2 + 31 + 10 + 21 + 7 + 8
Total, F(x) = 137
Mean = 137/10
Mean = 13.7.
Median = (8 + 10)/2
Median = 18/2
Median = 9.
In conclusion, the mode of the data set is non-existent or zero modes because all of the number have the same frequency.
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Which of these expressions is equivalent to log (128^)?
OA. log (8) - log (12)
OB. 8 log (12)
C. log (8) log (12)
D. log (8) + log (12)
.
Line g has an equation of y = 2x + 1. Line h includes the point (-5, 2) and is perpendicular
to line g. What is the equation of line h?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Submit
5^-2 x ³√8
answer as a decimal
Answer: We can start by simplifying the cube root of 8:
³√8 = 2
Next, we can rewrite 5^-2 as 1/5^2:
1/5^2 x 2 = 1/25 x 2 = 2/25
So the answer, as a decimal, is 0.08 (or 0.08 rounded to two decimal places).
