The dimensions of the rectangular frame is found as : 12 and 6 inches.
Explain about the Pythagorean theorem?When a triangle is just a right triangle, the hypotenuse square is equal to the sum of the squares of the triangle's legs.
That's a picture frame, therefore pay attention that it must be rectangular.
Hence, the triangle is really a right triangle, and the Pythagorean theorem will eventually be applied.
You are aware that the square of the hypotenuse is 20 and equals 400.
hence, a² + b² = 400 and...
So because length is 4 times more than the breadth, a = b + 4.
This can be resolved if "b + 4" is substituted for "a":
(b + 4)² + b² = 400,
(b + 4)(b + 4) + b² = 400,
b² + 8b + 16 + b² = 400,
2b² + 8b = 384
Further solving;
b² + 4b = 192
b² + 4b - 192 = 0
(b + 16)(b - 12) = 0
Due to the fact that a length cannot be negative, b must therefore be between b - 16 or 12 (negative value not taken)
The second leg is 12 + 4 = 6.
Thus, the dimensions of the rectangular frame is found as : 12 and 6 inches.
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During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the machine recommends that the temperature of the machine part remain below 135°F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by T=-0.005x^2+0.45x+125. Will the temperature of the part ever reach or exceed 135°F? Use the discriminant of a quadratic equation to decide.
Using the discriminant of the quadratic equation, the temperature will part after 50 minutes
Will the temperature of the part ever reach or exceed 135°F?The temperature of the machine part is given by the equation:
T = -0.005x^2 + 0.45x + 125
We need to find out if the temperature will ever reach or exceed 135°F, which means we need to check if there exists a value of x for which T = 135.
Substituting T = 135 in the above equation, we get:
135 = -0.005x^2 + 0.45x + 125
Simplifying the equation, we get:
0.005x^2 - 0.45x + 10 = 0
This is a quadratic equation of the form ax^2 + bx + c = 0, where a = 0.005, b = -0.45, and c = 10.
The discriminant of this quadratic equation is given by:
D = b^2 - 4ac
= (-0.45)^2 - 4(0.005)(10)
= 0.2025 - 0.2
= 0.0025
Since the discriminant is positive, the quadratic equation has two real roots. Therefore, the temperature of the machine part will cross 135°F at some point during the operation.
We can also find the roots of the quadratic equation using the formula:
[tex]x = (-b \± \sqrt(D)) / 2a[/tex]
Substituting the values of a, b, and D, we get:
[tex]x = (0.45 \± \sqrt(0.0025)) / 2(0.005)\\= (0.45 \± 0.05) / 0.01[/tex]
Taking the positive value, we get:
x = 50
Therefore, the temperature of the machine part will cross 135°F after 50 minutes of operation.
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create your own example of a sample of 100 people such that: the two-sided p-value is less than 0.001.
Example of samples of 100 people for two-sided p-value of less than 0.001 represents that the new drug is indeed effective.
Example of a scenario that could lead to a two-sided p-value of less than 0.001 is ,
To investigate whether a new drug reduces blood pressure in patients.
Randomly select 100 patients with hypertension and divide them into two groups.
One group receives the new drug, while the other group receives a placebo.
After a month of treatment, you measure the blood pressure of each patient .
And compute the difference between the pre- and post-treatment measurements.
Assuming that the blood pressure measurements are normally distributed.
Perform a two-sample t-test to compare the mean difference in blood pressure between the two groups.
If the difference is statistically significant at the 0.001 level.
It means that the probability of obtaining such a large difference by chance is less than 0.001.
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A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the
n independent trials of the experiment.
n=9, p=0.4, x$3
The probability of x ≤ 3 successes is
. (Round to four decimal places as needed.)
The probability of x successes in n independent trials of the experiment is given by the Binomial probability formula, where n is the total number of trials and p is the probability of success in each trial.
Since n = 9 and p = 0.4, we can calculate the probability of x ≤ 3 successes as follows:
P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= (9C0)(0.4)^0(0.6)^9 + (9C1)(0.4)^1(0.6)^8 + (9C2)(0.4)^2(0.6)^7 + (9C3)(0.4)^3(0.6)^6
= 0.17496 + 0.41472 + 0.36608 + 0.04320
= 0.99976
Therefore, the probability of x ≤ 3 successes is 0.99976.
Find the value of X using the picture below.
Answer:
x = 7
Step-by-step explanation:
The two angles are equal so the opposite sides are equal.
5x-2 =33
Add two to each side.
5x-2+2 = 33+2
5x=35
Divide by 5
5x/5 =35/5
x = 7
A camera has a list price of
$
579.99
before tax. If the sales tax rate is
7.25
%
, find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary
Answer:
622.04
Step-by-step explanation:
579.99 x 7.25% = 42.049 or 42.05
579.99 + 42.05 = 622.04
The total cost of the camera with sales tax included is $622.04.
What is the sales tax?A sales tax is a government-imposed consumption tax levied upon that purchase of goods and services. A standard sales tax is assessed at the moment of sale, received by the shop, and paid to the government.
Now according to the question;
The Listed price of the camera is $579.99.
The sales tax rate is 7.25%,
[tex]7.25\% \ \text{of} \ \$579.99 = (7.25\times579.99)\div100[/tex]
Sales tax = $42.04
[tex]\text{Total cost of camera = Listed price + sales tax amount}[/tex]
[tex]= \$579.99 + \$42.04[/tex]
[tex]\text{Total cost of camera} = \$622.04[/tex]
Therefore, the total cost of the camera with sales tax included is $622.04.
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In the New York State Numbers Lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $750, which is a profit of $749. If you lose, you lose $1. Your probability of winning is 0.001.
The expected value of playing this game is -$0.251. This means that, on average, you can expect to lose 25.1 cents every time you play this game.
What is outcome?The term "outcome" generally refers to the result or effect of an action, process, or event. It refers to what happens as a consequence of a particular decision, activity, or circumstance.
According to question:To calculate the expected value, we multiply the possible outcomes by their probabilities and then sum them up.
Let's start with the possible outcomes:
If you win, you make a profit of $749, so the outcome is $749.
If you lose, you lose $1, so the outcome is -$1.
The probabilities are:
Probability of winning is 0.001.
Now we can calculate the expected value:
Expected value = (0.001 * $749) + (0.999 * -$1)
Expected value = $0.748 - $0.999
Expected value = -$0.251
Therefore, the expected value of playing this game is -$0.251. This means that, on average, you can expect to lose 25.1 cents every time you play this game.
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2(x-6)²
could you please explain this to me, thanks!
Answer:
expand the square
2(x-6) (x-6)
2(x(x-6)-6(x-6)
2(x²-6x-6(x-6)
2(x²-6x-6x+36)
2(x²-12x+36)
2x²-24x+72
Step-by-step explanation:
hope this helps
The Millers have hired an interior designer to decorate their family room. They want to have a 29" by 29" oil painting framed and incorporated in the design plan. If the designer chooses molding that is 4" wide and is priced at $3.65 per inch, how much will the molding cost (before tax)?
Answer: I really don't know i'm just trying to get a quest done sorry
Please indicate which is the best answer to complete the figure below.
Answer:b
Step-by-step explanation:
Colin buys gas for her car at $4 a gallon. Write an equation using two variables to show the relationship between the number of gallons of gas, g, and the total amount of amount she spends, s.
Answer:
s = 4g ..........................................................
Mr. James is enlarging a logo for printing
on the back of a T-shirt. He wants to enlarge a logo that is 3 inches by
5 inches so that the dimensions are 3 times larger than the original. How
many times as large as the original logo will the area of the printing be?
The area of the enlarged logo will be 9 times larger than the original logo.
When an object is enlarged or scaled up how does it area change ?
When an object is enlarged or scaled up by a factor of [tex]k[/tex], both its length and width are multiplied by [tex]k[/tex]. Therefore, the new length is [tex]k[/tex] times the original length, and the new width is [tex]k[/tex] times the original width.
The area of the new object is the product of the new length and width, which is ([tex]k[/tex] times the original length) multiplied by ([tex]k[/tex] times the original width), or [tex]k^2[/tex] times the original area.
Therefore, the area of an object increases by a factor of [tex]k^2[/tex] when the object is enlarged or scaled up by a factor of [tex]k[/tex].
Calculating how many times larger the area of the enlarged logo will be :
The original logo has dimensions of 3 inches by 5 inches, so its area is 3 x 5 = 15 square inches.
Mr. James wants to enlarge the logo so that the dimensions are 3 times larger than the original. This means the new dimensions will be 9 inches by 15 inches.
To determine how many times larger the area of the enlarged logo will be, we need to compare the areas of the original logo and the enlarged logo. The area of the enlarged logo is 9 x 15 = 135 square inches.
To find out how many times larger the area of the enlarged logo is compared to the original logo, we divide the area of the enlarged logo by the area of the original logo:
135 square inches ÷ 15 square inches = 9
Therefore, the area of the enlarged logo will be 9 times larger than the area of the original logo.
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Change the following equation of a line into slope-intercept form.
y + 4 = 2x
Answer:
Step-by-step explanation:
[tex]y=2x-4[/tex] (slope-intercept form is [tex]y=mx+b[/tex] where m=gradient
and b is where line intercepts y-axis)
A bucket contains three slips of paper. One of the following colors is written on each slip of paper: Red, Blue, and Yellow.
List 1 List 2 List 3 List 4
Red Red, Blue Red, Red Red, Red, Red
Blue Red, Yellow Red, Blue Red, Blue, Yellow
Yellow Blue, Red Red, Yellow Red, Yellow, Blue
Red Blue, Yellow Blue, Blue Blue, Blue, Blue
Blue Yellow, Red Blue, Red Blue, Red, Yellow
Yellow Yellow, Blue Blue, Yellow Blue, Yellow, Red
Red Red Yellow, Yellow Yellow, Yellow, Yellow
Blue Blue Yellow, Red Yellow, Red, Blue
Yellow Yellow Yellow, Blue Yellow, Blue, Red
Which list gives the sample space for pulling two slips of paper out of the bucket with replacement?
List 1
List 2
List 3
List 4
The list that gives the sample space for pulling two slips of paper out of the bucket with replacement is List 4.
What is probability?Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.
According to the given information:The sample space for pulling two slips of paper out of the bucket with replacement means that after drawing the first slip of paper, it is returned to the bucket before drawing the second slip. This means that each draw is independent of the previous draw, and the possible outcomes of each draw remain the same for all subsequent draws.
The possible outcomes for each draw are {Red, Blue, Yellow}, and there are three possible outcomes for each draw.
Since we are drawing with replacement, each draw has the same possible outcomes and the same number of outcomes. So, the total number of possible outcomes for two draws is simply the number of outcomes for a single draw raised to the power of 2:
[tex]3^2 = 9[/tex]
Therefore, the list that gives the sample space for pulling two slips of paper out of the bucket with replacement is List 4.
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I don’t understand please help me with this
Answer:
Greg bought a pack of X jumbo stickers during the back - to - school sale at Crafty's craft store. He ( uses 4 ( -4 ), ( you didn't give options ). There were 8 stickers left in the pack.
Hope this helps!
Step-by-step explanation:
The water bill was $120. It went up 5%. Use two different expressions to find the amount of the new water bill. You may use a calculator.
The new water bill after 5% increase is $126.
Define PercentageThe ratio that may be stated as a fraction of 100 is called as a percentage in mathematics. To compute a percentage of a number, divide it by its whole and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
First Expression:Given bill of water =$120
Increment in percentage=5%
New water bill= 120+120×5/100
=$126
Hence, The new water bill after 5% increase is $126.
2nd Expression% increase = Increase in bill ÷ Old bill × 100.
5%=Increase in bill/120×100
Increase=5×120/100
=6
New bill=Old bill+ increase=120+6=126
hence, the new water bill after 5% increase is $126.
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Which of the following pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p?
Therefore , the solution of the given problem of standard deviation comes out to be option C with n = 1,000 and p near to 1/2 is the right response.
What does standard deviation actually mean?Statistics uses variance as a way to quantify difference. The image of the result is used to compute the average deviation between the collected data and the mean. Contrary to many other valid measures of variability, it includes those pieces of data on their own by comparing each number to the mean. Variations may be caused by willful mistakes, irrational expectations, or shifting economic or business conditions.
Here,
The following algorithm determines the standard deviation of the sampling distribution of a sample proportion p:
=> √((p*(1-p))/n)
where n is the sample size, and p is the population percentage.
For the sampling distribution of a sample proportion p,
the pair of sample number n and population proportion p that would result in the highest standard deviation is:
=>n =1,000, and p is almost half.
Because p=1/2
yields the highest possible value of the expression (p*(1-p)), a bigger sample size will result in a smaller standard deviation.
The standard deviations will be lower for the other choices, which have smaller sample sizes or extreme values of p.
Therefore, (C) with n = 1,000 and p near to 1/2 is the right response.
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Solve using the correct order of
operations.
P
E
MD
AS
15-(4-3) 2= [?]
Enter
Help
Here using the correct order of operations that is PEMDAS, we get the value to be 13.
Define PEMDAS?PEDMAS can be summed up as a mathematical acronym that lists the various arithmetic operations in order of greatest to least practical use.
The letters stand for:
P stands for parentheses.
Exponents are shown as E.
D stands for division.
The letter M stands for multiplication.
A stand for addition.
S stands for subtraction.
Now in the given question,
15 - (4-3)2
First the parentheses
15 - (1)2
Next is exponents.
15 - 2
At last, after subtracting, we get:
13
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true/false. when the population variance is not known (i.e., must be estimated from data), we use a z-statistic instead of a t-statistic for our hypothesis tests.
The given statement " when the population variance is not known (i.e., must be estimated from data), we use a z-statistic instead of a t-statistic for our hypothesis tests. " is false. Because in distribution of sample means, population variance is unknown.
When the population variance is not known and must be estimated from the data, we use a t-statistic instead of a z-statistic for our hypothesis tests.
This is because the distribution of the sample means follows a t-distribution when the population variance is unknown, whereas it follows a standard normal distribution (z-distribution) when the population variance is known.
The t-distribution has fatter tails than the z-distribution to account for the extra uncertainty introduced by estimating the population variance from the sample.
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what is a chord in mathematics
Answer:
a straight line that connects two points on the circumference of a circle
Step-by-step explanation:
Bhujangrao invested Rs. 2,50,590 in shares of F.V. Rs. 10 when M.V. is Rs. 250. [Nov 2020]
Rate of brokerage is 0.2% and GST is 18%, then find:
a. the number of shares purchased,
b. the amount of brokerage paid, and
c. GST paid for the trading
a. The number of shares purchased can be calculated as:
Number of Shares = (Investment Amount / Face Value)
= 25,059/ 10 = 2,505.9 = 2,506 (to the nearest whole number)
b. The amount of brokerage paid can be calculated as:
Brokerage = (Investment Amount x Brokerage Rate)
= 2,50,590 x 0.002 = Rs. 501.18
c. The GST paid for the trading can be calculated as:
GST = (Brokerage Amount x GST Rate)
= 501.18 x 0.18 = Rs. 90.22
when comparing the distribution of the population of individual scores to the distribution of means, the distribution of means will always have
The population distribution of scores has a similar average as the distribution of means.
In a sample distribution of means, the distribution will roughly resemble a normal distribution, the sampling distribution's mean will be equal to the population's mean, and the sampling distribution's standard deviation is based on the Central Limit Theorem.
The central limit theorem (CLT) of probability theory states that the distribution of a sample variable tends towards a normal distribution (i.e., a "bell curve") as the sample size increases, under the premise that all samples are of equal size and regardless of the population's actual distribution shape.
In other terms, the central limit theorem (CLT) is a statistical presumption that the mean of all sampled variables from the same population will be substantially equal to the mean of the entire population, given a large enough sample size from a population with little volatility. These samples likewise resemble a normal distribution in accordance with the law of large numbers, with their variances nearly matching the variance of the population as the sample size rises.
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the actual question is :
When comparing the size of the standard error of the mean with the size of the standard deviation of the underlying distribution of individual scores:
a. the standard error of the mean is always larger
b. the standard error of the mean is always smaller
c. the standard error of the mean is sometimes larger and sometimes smaller, depending on the sample size
d. none of these
Bart's skateboard weighs 3.6 kg. How many grams does Bart's
skateboard weigh?
Answer: 3,600
Step-by-step explanation:
1 kg. = 1000 g.
3.6 X 1000 = 3,600
Students at a virtual school are allowed to sign up for one math class each year. The numbers of students signing up for various math classes for the next school year are given in the following table:
Grade Geometry Algebra I Pre-Calculus AP Statistics Total
A student calculated the joint relative trequency of 10th grade students in geometry as being 71.4%. What did the student actually calculate and what is the correct answer?
A) The student calculated the conditional relative frequency for students who are in 10th grade, given that they are enrolled in Geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 20.7%.
B) The student calculated the conditional relative frequenc for students who are in 10th grade, given that they are enrolled in Geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 29%.
C) The student calculated the marginal relative frequency for 10th grade students in geometry. The correct value of the joint relative trequency of 10th grade students in geometry is 20.7%.
D) The student calculated the marginal relative frequency for 10th grade students in geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 29%
Option C) The student calculated the marginal relative frequency for 10th grade students in geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 20.7%.
How to calculate a relative frequency?Relative frequency is a measure of the proportion or percentage of times an event occurs in a given sample. It is calculated by dividing the frequency of an event by the total number of events in the sample. The formula for relative frequency is given as follows:
Relative frequency = Frequency of an event / Total number of events in the sample
For the joint relative frequency of 10th grade students in geometry, the parameters are given as follows:
Frequency of 10th grade students in geometry: 20.7%.Total number of events in the sample: 100% of students.Hence the joint relative frequency is obtained as follows:
20.7/100 x 100%= 20.7%.
Hence option C is correct.
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Find dz/dt in two ways: by using the Chain Rule, and by first substituting the expressions for x and y to write z as a function of t. Do your answers agree?z= x^2y+xy^2, x = 3t y = t^2
The derivative of the function z= x^2y+xy^2, x = 3t y = t^2 using the chain rule is given by dz/dt = 36t^3 + 15t^4.
Expressions are equals to,
z= x^2y+xy^2
x = 3t
y = t^2
Using the chain rule calculate dz/dt,
which states that if z is a function of x and y,
And x and y are both functions of t, then,
dz/dt = (dz/dx)(dx/dt) + (dz/dy)(dy/dt)
Using these expressions, calculate the value of dz/dt using the chain rule,
z= x^2y+xy^2
This implies,
dz/dx = 2xy + y^2
dz/dy = x^2 + 2xy
x = 3t
⇒ dx/dt = 3
y = t^2
⇒ dy/dt = 2t
Substituting these values into the chain rule formula, we get,
dz/dt = (2xy + y^2)(3) + (x^2 + 2xy)(2t)
= [2(3t)(t^2 ) + (t^2)^2 ]3 + [(3t)^2 + 2(3t)(t^2)](2t )
= [ 6t^3 + t^4 ]3 + [ 9t^2 + 6t^3 ]2t
= 18t^3 + 3t^4 + 18t^3 + 12t^4
= 36t^3 + 15t^4
Substituting the given expressions for x and y into z, we get,
z = (3t)^2(t^2) + (3t)(t^2)^2
= 9t^4 + 3t^5
here also,
dz/dt = 36t^3 + 15t^4
Therefore, the value of the function using the chain rule dz/dt is equals to 36t^3 + 15t^4.
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Zaheer had a set of marbles, he used 2/3 to make a design and he had 14 left. How many did he used to make the design?
Answer: 42
Step-by-step explanation:
1. 1/3=14
2. 14x3=42
30 POINTS, URGENT!! Choose the system of inequalities that best matches the graph below.
Answer: A
y < 2x + 1
y > 1/2x + 2
Prove that the diagonals of rectangle are equal vectorically in easy way
Answer: Imagine a rectangle with its centre (point of intersection of diagonals) situated at the origin of the XY plane and it's each of the sides being aligned with the co-ordinate axis.
A cube of sugar is 2cm wide. Calculate the number of cube in a box 720cm³
Answer:
V=lwh
=2×2×2=8
720÷8=90
90 cubes
A parent donated 36 fruit cups and 24 bananas to fifth grade. The teacher wanted to make field trip snack bags with the donated food and wondered about the ways snacks could be packed. To be fair the teacher wants to make sure that all bags are exactly the same.
A) What is the greatest number of snack bags that the teacher can make, if each bag is identical? How do you know ?
B) What other numbers of snack bags could she make? How do you know?
2) Another parent also donated 24 bananas, so there are 48 bananas total. Now what is the greatest number of snack bags can that can be made?
3) The teacher realized that she miscounted and had only 30 fruit cups. How many snack bags can she make with 48 bananas and fruit cups?
4) What do the different numbers of snack bags that can be made have to do with the number of fruit cups and number of bananas?
4. (Extra Credit) Mason has a credit card debt of $15,600 that he would like to reduce by applying $8,500 of his inheritance money to the b
off the remaining balance in 24 months rather than 60 months. His credit card has an APR of 18%. How much will these changes save
Hint: 1st, subtract 8500 from 15,600 to find the remaining balance he will pay in 24 months. Use the formula
P=PV (1/(1-(1+1)^-n) where PV is the remaining balance, i = 0.18/12, and n = 24 months.
2nd, multiply your answer in step 2 by 24 months to find out the total amount you paid in 24 months.
3rd, find the interest you paid by subtracting 7100 from the amount you found in step 2.
4th, find out how much you would have paid had you not reduced the amount you owed by 8500 (in other words, 15,600). Use the same
months
5th, multiply the answer in step 4 by 60 months to find out how much you paid in total.
6th, to find the interest, subtract the amount in step 5 from 15,600 to find the interest.
Finally, find the difference between step 3 and step 6, and that is how much you saved.
$1,407.04
b. $3,302.59
a.
PSUE
$6,760.96
d. $8,168.40
C.
Mason would save $7,618.32 in interest by paying off $8,500 immediately.
What is compound interest?In other terms, compound interest is interest on principle + interest and refers to the addition of interest to the principal amount of a loan or deposit. Reinvesting interest, or adding it to the lent capital rather than paying it out or requesting payment from the borrower, results in interest being generated on the principle amount plus previously accrued interest in the next month. In economics and finance, compound interest is common.
Comparing compound interest to simple interest, which has no effect on previously accrued interest
Given that, Mason has a credit card debt of $15,600.
Using his original payment plan of 60 months we have:
[tex]I = P * (1 + r/n)^{(n*t)} - P[/tex]
Substitute the values we have:
[tex]I = 15,600 * (1 + 0.18/12)^(12*5) - 15,600\\I = 9,316.84[/tex]
For the new plan:
New balance = $15,600 - $8,500 = $7,100
[tex]I = 7,100 * (1 + 0.18/12)^(12*2) - 7,100\\I = $1,698.52[/tex]
Hence, over the course of 24 months, Mason would pay approximately $1,698.52 in interest.
The difference in interest paid between the two scenarios is:
$9,316.84 - $1,698.52 = $7,618.32
Therefore, Mason would save approximately $7,618.32 in interest by paying off $8,500 immediately.
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