The difference in interest paid between the two loans is the answer is option (c) $14,515.43.
What is the interest?
Calculate simple interest, and multiply the principal amount by the interest rate and the time. The formula written out is "Simple Interest = Principal x Interest Rate x Time." This equation is the simplest way of calculating interest.
First, we need to calculate the monthly payment for the loan at 15%:
PV = $40,000
i = 0.15/12 = 0.0125
n = 6 years * 12 months/year = 72 months
Using the formula for minimum monthly payment for an amortized loan, we get:
[tex]P = i * PV / (1 - (1 + i)^{(-n)})[/tex]
= 0.0125 * $40,000 / (1 - (1 + 0.0125)⁻⁷²) = $797.95
So Jenny's monthly payment is $797.95 for the 6-year term of the loan.
The total amount paid over the life of the loan at 15% is:
Total paid = P * n = $797.95 * 72 = $57,471.44
The interest paid at 15% is:
Interest paid = Total paid - PV = $57,471.44 - $40,000 = $17,471.44
Now, let's repeat the same calculation for the loan at 5%:
PV = $40,000
i = 0.05/12 = 0.0041667
n = 6 years * 12 months/year = 72 months
Using the same formula, we get:
P = i * PV / (1 - (1 + i)^(-n)) = 0.0041667 * $40,000 / (1 - (1 + 0.0041667)^(-72)) = $630.48
So Jenny's monthly payment would have been $630.48 for the 6-year term of the loan if she did not have a bankruptcy.
The total amount paid over the life of the loan at 5% is:
Total paid = P * n = $630.48 * 72 = $45,434.56
The interest paid at 5% is:
Interest paid = Total paid - PV = $45,434.56 - $40,000 = $5,434.56
The difference in interest paid between the two loans is:
$17,471.44 - $5,434.56 = $12,036.88
Therefore, The difference in interest paid between the two loans is the answer is option (c) $14,515.43.
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How do I find the lengths of sides that are cut by an altitude? (right triangle, the sides that the arrows are pointing at)
The length of line JC is 20 miles.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental concept in geometry that states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of sides of triangle.
To find the length of line JC, which is the hypotenuse of the right triangle JSC, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).
In this case, we have:
JS² + SC² = JC²
Substituting the given values, we get:
12² + 16² = JC²
144 + 256 = JC²
400 = JC²
Taking square root both sides, we get:
JC = √400
JC = 20
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2. Big Money Bank has an offer for new customers: if you deposit
$5,000 in a savings account, you will earn 6.5% simple interest
over the first 10 years.
C. At the town savings bank a new customer earns $2950 in simple interest on a $5000 deposit over the first 10 years what rate of interest does that bank pay
Answer:
We can use the simple interest formula to find the rate of interest that the town savings bank pays:
Simple Interest = Principal x Rate x Time
where Principal is the initial deposit, Rate is the interest rate, and Time is the time period.
We know that the Principal is $5000, the Simple Interest earned over the first 10 years is $2950, and the Time is 10 years. Substituting these values into the formula, we get:
$2950 = $5000 x Rate x 10
Simplifying the equation, we get:
Rate = $2950 / ($5000 x 10)
Rate = 0.059 or 5.9%
Therefore, the town savings bank pays an interest rate of 5.9% on its savings accounts.
What is the value of sin−1(−3√2)
Answer:
The value of sin^-1(-3√2) is an angle whose sine is -3√2.
Since the sine function is an odd function, sin(-θ) = -sin(θ), we can find the reference angle by taking the inverse sine of the positive value 3√2, which gives:
sin^-1(3√2) ≈ 80.06°
The sine function is also negative in the third and fourth quadrants of the unit circle. Since the given value is negative, the angle must lie in either the third or fourth quadrant.
To determine in which quadrant the angle lies, we can use the fact that sine is negative in the third and fourth quadrants. Since sin^-1(-3√2) gives a positive value, the angle must lie in the third quadrant where the sine is negative.
Therefore, sin^-1(-3√2) = -80.06° (rounded to two decimal places).
Step-by-step explanation:
Attempts 1
12. Order of operations
A set of three scores consists of the values 3, 7, and 2.
Σ(3X - 1) =
(2x)² =
Hint: Remember to follow the order of mathematical operations.
The sigma notations when evaluated are Σ(3X - 1) = 33 and Σ(2X)² = 248
How to evaluate the sigma notationFrom the question, we have the following parameters that can be used in our computation:
3, 7, 2
The notation Σ(3X - 1) can be represented as
Σ(3X - 1) = (3(3) - 1) + (3(7) - 1) + (3(2) - 1)
Evaluate
Σ(3X - 1) = 33
Using the above as a guide, we have the following operation
Σ(2X)² = (2 *(3))² + (2 * (7))² + (2 * (2))²
Evaluate
Σ(2X)² = 248
Hence, the value of Σ(2X)² is 248
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In Accounting if the balance in the Allowance for Doubtful accounts account is $2,000, and im adding $500 to the Allowance for doubtful Accounts account and im ONLY DOING A GENERAL JOURNAL ENTRY does the previous Allowance for doubtfull accounts come in play at all?
Answer: The journal entry to record the addition of $500 to the Allowance for Doubtful Accounts account would be:
Debit Allowance for Doubtful Accounts account: $500
Credit Bad Debt Expense account: $500
The resulting balance in the Allowance for Doubtful Accounts account would be $2,500.
Step-by-step explanation:
Yes, the previous balance in the Allowance for Doubtful Accounts account does come into play when you add $500 to the account. The Allowance for Doubtful Accounts account is a contra asset account that is used to offset the Accounts Receivable account. It represents an estimate of the amount of accounts receivable that are expected to be uncollectible.
The balance in the Allowance for Doubtful Accounts account is based on the estimated amount of uncollectible accounts, which is typically a percentage of the total accounts receivable balance. When you add $500 to the account, you are increasing the estimated amount of uncollectible accounts.
To record this journal entry, you would debit the Allowance for Doubtful Accounts account for $500 and credit an expense account (such as Bad Debt Expense) for the same amount. The previous balance of $2,000 would also be included in the account balance and would be reflected in the new balance of $2,500.
The journal entry to record the addition of $500 to the Allowance for Doubtful Accounts account would be:
Debit Allowance for Doubtful Accounts account: $500
Credit Bad Debt Expense account: $500
The resulting balance in the Allowance for Doubtful Accounts account would be $2,500.
The graph below shows line A and point P.
The linear equation on the graph can be written as:
y = (3/4)*x - 1
How to write the linear equation?Here we have the graph of a linear equation, these are written as:
y = mx + c
Where m is the slope and c is the y-intercept.
On the graph we can see that the line intercepts the y-axis at y = -1, then we can write:
c = -1
So the linear equation is:
y = mx - 1
Looking at the graph we can see that the line also passes through the point (4, 2).
Replacing that in the linear equation we will get:
2 = m*4 - 1
2 + 1 = m*4
3 = m*4
3/4 = m
Then the linear equation on the graph is:
y = (3/4)*x - 1
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Determine the percent decrease in total principal and interest paid between a 30-year term mortgage and a 15-year mortgage with a principal balance of $242,300.00 and a 6.5% APR. Round the final answer to the nearest tenth. (4 points)
30.0%
31.1%
45.0%
45.1%
The percentage decrease in total principal and interest paid between a 30-year term mortgage and a 15-year mortgage with an APR of 6.5% and a principal balance of $242,300.00 is about 31.1%
What is an APR?An APR is an acronym for the Annual Percentage Rate, which is the interest on al loan amount expressed as a percentage of the amount on loan annually.
The loan amount, the annual percentage rate, and the term of the loan are presented as follows;
Loan amount, P = $242,300.00
Term of the loan, t = 30 years and 15 years
Annual Percentage Rate (APR), r = 6.5%
The amount of the loan after the period can be obtained by using the formula;
A = P·(1 + r)^t
The amount of each loan can therefore be calculated as follows;
The monthly payment is; M = P·(r·(1 + r)^t)/((1 + r)^t - 1)
M = 242,300×((0.065/12) × (1 + (0.065/12))^(30×12))/((1 + ((0.065/12)))^(30×12) - 1) ≈ 1531.5
The total payment on the 30-year loan ≈ 360 × 1531.5 = 551,340
The monthly payment for the 15-year loan is therefore;
M = 242,300×((0.065/12) × (1 + (0.065/12))^(15×12))/((1 + ((0.065/12)))^(15×12) - 1) ≈ 2110.7
The total payment on the 15-year loan ≈ 360 × 2110.7 = 379962
551,340
The percentage change is therefore;
((551,340 - 379962)/551,340) × 100 ≈ 31.1%
The percentage decrease in the total principal and interest paid between the 30-year term mortgage and a 15-year mortgage is about 31.1%
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You are conducting a study testing whether depression symptoms are lower after participating in therapy compared to before. Given this information, complete the hypotheses in symbols:
H o: [tex]\mu_{post[/tex] - [tex]\mu_{pre[/tex] = 0 This is the null hypothesis, which states that there is no difference in the mean depression symptoms before and after therapy.
What is hypothesis?A hypothesis is a proposed explanation for a phenomenon. It is a testable statement about the relationship between two or more variables that can be used to generate further investigation and research. Hypotheses are developed from research questions and provide a basis for predicting outcomes and testing theories. Hypotheses are not guesses or hunches; rather, they are educated statements that are backed up by evidence.
Ha: [tex]\mu_{post[/tex] - [tex]\mu_{pre[/tex] ≠ 0 This is the alternative hypothesis, which states that there is a difference in the mean depression symptoms before and after therapy.
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The figure consists of a right triangle and an eighth of a circle. Find the area of the shaded region. 22/7 for pie.
The area of the shaded region of the composite shape is: 21.03 cm²
How to find the area of the shaded region?The formula for the area of a triangle is:
Area = ¹/₂ * base * height
Thus:
Area of given triangle = ¹/₂ * 14 * 14 = 98 cm²
Area of sector is given by the formula:
θ/360 * πr²
Area of sector = 45/360 * π * 14 * 14
= 76.97 cm²
Thus:
Area of shaded portion = 98 cm² - 76.97 cm² = 21.03 cm²
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Mrs lam worked a total of 180 hours in 9 months she worked 5 days each month she worked the same number of hours each day how many hours did mrs lam work each day draw a bar diagram and write and equations to help you solve
If Mrs lam worked a total of 180 hours in 9 months she worked 5 days each month then, Mrs. Lam worked 4 hours each day.
What is a bar diagram?Bar graphs or bar charts are visual depictions of groups of data that are made up of vertical or horizontal rectangular bars with lengths that are equal to the data's measure.
The variable quantity is shown on one of the axes, and the drawn bars are all of the same width. Moreover, the other axes show the variable's measure. These graphs are also used to compare different numbers since the heights or lengths of the bars represent the value of the variable. Bar charts make it simple to grasp the data and show frequency distribution tables, which facilitates computations.
Let us suppose the number of hours worked each day = x.
Given that, Mrs lam worked a total of 180 hours in 9 months she worked 5 days.
Thus,
Total hours = 180 = 5 * 9 * x
180 = 45x
x = 4
Hence, Mrs. Lam worked 4 hours each day.
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HELP ASAP WILL GIVE 100 POINTS AND BRAINLYEST IF YOU DON"T ANSWER WITH THE INTENT TO ANSWER CORRECTLY I WILL REPORT YOU
Evaluate the following sum.
∑k=252(3)k
The sum of the series is approximately -2.977069 x 10³⁷.
What is the sum of the series?The sum of the series is calculated by applying the following methods as shown below.
We can write the sum as:
∑k=252(3)k = 3^252 + 3^253 + 3^254 + ...
Notice that this is an infinite geometric series with first term a = 3^252 and common ratio r = 3.
To find the sum of an infinite geometric series, we use the formula:
S = a/(1-r)
Applying this formula, we get:
S = 3^252/(1-3) = 3^252/(-2)
So the sum of the series is -0.5 times 3 raised to the power of 252, which is a very large negative number.
Specifically, it is approximately equal to: -2.977069 x 10³⁷.
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A group of 140 young adults were asked if they use a grocery delivery app instead of going to the grocery store themselves.
According to the table, what is the probability that arándome chosen young adult does not use a grocery delivery app give that they are male? Give your answer in the simplest fraction form.
The probability that a randomly chosen young adult who are male do not use a grocery delivery app is 16.39%.
What is the probability?The probability refers to the chance or likelihood that an expected outcome, event, or success occurs given that there are many possible outcomes, events, or successes.
Probability is a fractional value that lies between zero and one depending on the degree of certainty or otherwise.
The total number of young adults surveyed = 140
The total number of young adults who do not use the app = 78
The number of male young adults who do not use the app = 5
The total number of male young adults surveyed = 17
The probability of a young adult not using the app = 78/140
The probability of a male young adults not using the app = 5/17
Thus, the probability that a randomly chosen young adult who are male do not use a grocery delivery app = 5/17 x 78/140 = 16.39%.
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how to complete borrowings in a cash budget
what continues the pattern, 324,256,196,144, ?
is the answer 100
Answer:
Step-by-step explanation:
324-68=256
256-60=196
196-52=144
144-44=100
Yep...you were correct!
Pascals triangle is named after the French mathematician Blaise Pascal despite the fact that its documented existence pre-dated him by over 600 years. Though he did not invent Pascals triangle he did invent a type of machine in 1642 that would end up being historically significant. What was this invention?
Answer:
Blaise Pascal is known for inventing the mechanical calculator, also called Pascaline, in 1642. The Pascaline was a type of mechanical calculator that could perform addition and subtraction by using a series of gears and wheels. It was one of the first machines capable of performing arithmetic operations automatically and quickly, without the need for manual calculations. The invention of the Pascaline was a significant contribution to the field of mathematics and engineering, and it paved the way for the development of more advanced calculating machines in the future.
Step-by-step explanation:
What is the surface area of the rectangular prism below?
Answer:
72 cm^2
Step-by-step explanation:
2(3 x 2) + 2(6 x 3) + 2(6 x 2) = 2(6) + 2(18) + 2(12)
= 12 + 36 + 24 = 72 cm^2
6 of 8
? Work out the area of the shaded shape.
5m
3m
T
6m
2m
2m
The graph represents a relation where x represents the independent variable and y represents the dep -5 -4 -3 -2 5 4 3 2 1 -1 0 -1 -2 -3 -4 -5 What is the domain of the relation? 1 2 3 4 5
The set representing the domain of the relation is given as follows:
{-4,-2,0,3,5}.
How to find the domain and the range of a function?The domain of a function is the set that contains all the values assumed by the input of the function, hence on a graph it is given by the values of x assumed by the graph.The range of a function is the set that contains all the values assumed by the output of the function, hence on a graph it is given by the values of y assumed by the graph.For the relation in this problem, the x-coordinates of each point are given as follows:
x = -4.x = -2.x = 0.x = 3.x = 5.Hence the set representing the domain of the relation is given as follows:
{-4,-2,0,3,5}.
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Will mark brainliest answer!
What's the best place to eat at? (Restaruant, Fast Food, Buffet, Cafe, etc.)
Answer:
Step-by-step explanation:
Me personally, I think buffets are the best because you can take as music food as you much, without being charged for much! But thats only for some buffets. If you go to a chinese buffet, they might lower the price allowing you to get as much food as you please!
HELP!!
show you're work please...
The height of the trapezoid with an area of 21 square centimeters is equal to 3 cm.
How to evaluate for the height of the trapezoidarea of a trapezoid is calculated using the formula: 1/2 × (A + B) × height where A is and B are the parallel bases.
we shall represent the height of the trapezoid with the letter h so that:
21 cm² = 1/2 × (5 + 9) cm × h
21 cm² = 1/2 × 14 cm × h
21 cm² = 7 cm × h
divide through by 7 cm
h = 21 cm²/7 cm
h = 3 cm
Therefore, the height of the trapezoid with an area of 21 square centimeters is equal to 3 cm.
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solve for x: 2(3x-3)=-18
Answer:
[tex]\huge\boxed{\sf x = -2}[/tex]
Step-by-step explanation:
Given equation:2(3x - 3) = -18
Distribute 2 to 3x and 36x - 6 = -18
Add 6 to both sides6x = -18 + 6
6x = -12
Divide both sides by 6x = -12/6
x = -2[tex]\rule[225]{225}{2}[/tex]
Answer: x=-2
Step-by-step explanation:
Step 1. Multiply the 2×3x and 2×3 which would make the problem 6x-6=-18
Step 2. Add the -6 to the -18 and multiply that answer of -12 by 6 to get your final answer of x=-2
Solve the system
y=2x-2
y=2x+9
Answer:
y=2 x=-13
Step-by-step explanation:
PLEASE HELP!!!
Aidan is 5.5 ft tall and casts a shadow that is 9 ft long. He notices that a nearby tower casts a shadow that is 305 ft long.
What is the height of the tower (h)?
The height of the tower (h) is approximately 186.4 feet.
What is the height (h) of the tower?A ratio is simply the relation between two amounts showing how many times a value is contained within another value.
Given the data in the quesion;
Aidan's height = 5.5ftlength of Aidan's shadow = 9ft height of the tower = ?length of the tower's shadow = 305ftWe can set up a proportion to solve for the height of the tower:
Aidan's height / length of Aidan's shadow = height of the tower / length of the tower's shadow
Plugging in the values we know, we get:
5.5 / 9 = h / 305
To solve for h, we can cross-multiply and simplify:
9h = 5.5 × 305
9h = 1667.5
h = 1667.5 / 9
h = 186.4 ft
Therefore, the value of h is 186.4 feet.
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Which matrix represents the system of equations shown below?
6x +11y = -4
5x-9y=1
Answer: I took the test and got it right
Tthe matrix representing this system of equations is:
[6 11 | -4]
[5 -9 | 1]
The equations in the image can be expressed as a matrix as follows:
[6 11] [x] [-4]
[5 -9] * [y] = [1]
The constants on the right-hand side of each equation are represented by the matrix on the right, while the coefficients of the variables x and y are represented by the matrix on the left. We use square brackets to surround the coefficients matrix and vertical bars to demarcate the variables and constants in order to represent this in matrix form. As a result, the matrix used to describe this set of equations is:
[6 11 | -4]
[5 -9 | 1]
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The store sold 25% of its books over the holiday, and now it has 600 books in stock.
How many books the store had before holidays?
Answer: If the store sold 25% of its books during the holiday, that means it has 75% of its books left in stock after the holiday. Let's represent the original number of books with the variable "x".
So, if 75% of x is equal to 600 books, we can write an equation:
0.75x = 600
To solve for x, we can divide both sides by 0.75:
x = 600 / 0.75
x = 800
Therefore, the store had 800 books before the holiday.
Step-by-step explanation:
Please answer this for me quick i have another one
The value of the fraction x/y is 3/25 and option b is the correct answer.
What are fractions?An expression for a portion of a whole is a fraction. In general, the whole can be any particular object or value, and the fraction might be a piece of any quantity out of it.
The top and bottom numbers of a fraction are explained by the fundamentals of fractions. The bottom number reflects the entire number of components, while the top number represents the number of chosen or coloured portions of the whole.
The given equation is:
5x + y / y = 8/5
Divide the terms individually at the left side of the equation:
5x/y + y/y = 8/5
5 (x/y) + 1 = 8/5
5 (x/y) = 8/5 - 1
5 (x/y) = 3/5
x/y = 3/25
Hence, the value of the fraction x/y is 3/25 and option b is the correct answer.
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Please Help ASAP - 100 pts + Brainliest if the answer is correct!
Answer:
a. aₙ=(aₙ₋₁ x 0.98) + 1150
Suppose a recent government report indicates that 6% of the labor force is Asian. Of the individuals in the labor force who are Asian, 5% are unemployed. Among the individuals in the labor force who are not Asian, 6% are unemployed. Let be the event that a randomly selected member of the labor force is Asian and let be the event that a randomly selected member of the labor force is unemployed. Determine (∣) , the probability that a randomly selected member of the labor force is Asian given that he or she is unemployed. Express your answer as a percentage with no decimal places.
Answer:
The probability that a randomly selected member of the labor force is Asian given that he or she is unemployed is 4.98%
Step-by-step explanation:
We want to find the probability that a randomly selected member of the labor force is Asian given that he or she is unemployed, which can be written as P(A|U). Using Bayes' theorem, we have:
P(A|U) = P(U|A) * P(A) / P(U)
We are given P(A) = 0.06 (6% of the labor force is Asian), P(U|A) = 0.05 (among Asians in the labor force, 5% are unemployed), and P(U|not A) = 0.06 (among non-Asians in the labor force, 6% are unemployed).
To find P(U), we can use the law of total probability:
P(U) = P(U|A) * P(A) + P(U|not A) * P(not A)
We know P(A) = 0.06, so P(not A) = 1 - P(A) = 0.94.
Therefore,
P(U) = 0.05 * 0.06 + 0.06 * 0.94 = 0.0602
Now we can substitute all the values into Bayes' theorem:
P(A|U) = 0.05 * 0.06 / 0.0602 = 0.0498
So the probability that a randomly selected member of the labor force is Asian given that he or she is unemployed is 4.98% (rounded to the nearest percentage with no decimal places).
4. Solve the right triangle: B = 72°; b = 24 cm.
Answer:
The right triangle has sides of approximately 7.86 cm, 24 cm, and 24.88 cm, and angles of 90°, 72°, and 18°.
Answer:
A=18 degrees
a=7.80cm
C=24.54cm
Step-by-step explanation: