Based on Probability laws the answers are: (a) n(1-p) = 167.4 and (b) mean = 167.4
(a) To demonstrate that the probability distribution of X is roughly normal, we must determine if np and n(1-p), where n is the sample size and p is the chance of success, are both higher than or equal to 10. (using a variation of "lol").
If 55.8% of comments containing a textual form of laughter use some version of "lol," the numbers in this case are n = 300 and p = 0.558. Therefore:
[tex]n(1-p) = 300 * 0.442 = 132.6 np = 300 * 0.558 = 167.4[/tex]
The probability distribution of X is roughly normal since np and n(1-p) are both bigger than or equal to 10.
(b) The formula for the mean of the suitable normal distribution is: = np = 300 x 0.558 = 167.4.
Hence, 167.4 is the normal distribution's mean.
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What is the slope of the line given the ordered pairs (1, 4) and (2, 7)?
Which number is irrational?
Answer:
8+the sign over 2
Step-by-step explanation:
Maria has been tracking the number of songs she has
downloaded on her smart phone for the past several
months. Use the scatterplot and line of best fit below to
help her determine when she will reach 10,000 songs?
Answer:
The answer of the given question based on the scatterplot for determining when she will reach 10,000 songs the answer is Maria will reach 10,000 songs in approximately 13.33 months, or about 14 months.
What is Slope?Slope is measure of steepness or incline of line. In geometry and mathematics, slope is defined as ratio of the change in y-coordinates to change in x-coordinates between two distinct points on line. This is often represented by letter "m".
To determine when Maria will reach 10,000 songs, we need to find the point on the line of best fit where the y-value is 10,000.
From the scatterplot, we can estimate that the line of best fit intersects the y-axis at approximately 2000. This means that the initial number of songs downloaded was 2000.
Next, we need to find the slope of the line of best fit. Let's choose the points (5, 6500) and (10, 9500).
The slope of the line passing through these two points is:
slope = (y2 - y1)/(x2 - x1) = (9500 - 6500)/(10 - 5) = 600 songs per month
This means that Maria is downloading 600 songs per month on average.
Finally, we can use the slope-intercept form of a line to find the x-value when the y-value is 10,000:
y = mx + b
10,000 = 600x + 2000
8000 = 600x
x = 13.33
Therefore, Maria will reach 10,000 songs in approximately 13.33 months, or about 14 months.
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Choose a U.S. household at random and record the number of vehicles. The table below shows the probability model.
Define F as a household that owns four cars. Which probability is correct?
the correct probability is option c)[tex]P(F^c)[/tex] = 0.95.
What is the probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The value is stated from zero to one. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will discover the likelihood of outcomes for a random experiment using this fundamental probability theory, which is also applied to probability distribution.
from the question:
According to the table, the likelihood that a household owns four cars is given by P(4) = 0.05.
Four automobiles in one family constitute the occurrence F. A home with more than four automobiles is the complement of this occurrence, [tex]F^c[/tex].
The total of all outcomes' probabilities must equal 1. Thus, by deducting P(4) from 1 we may derive P([tex]F^c[/tex]):
P([tex]F^c[/tex]) = 1 - P(4) = 1 - 0.05 = 0.95
Therefore, the correct probability is option c) P([tex]F^c[/tex]) = 0.95.
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what is an equivalent fraction to 1/6?
Answer:
1/6 = 2/12 = 3/18 = 4/24 = 5/30 = 6/36 = 7/42 = 8/48 = 9/54 = 10/60........
Draw a unit circle for each of the following then find several positive and negative real
numbers t which determine a point Q with the given coordinates. Then write a formula
for t in terms of 2kπ.
1. ( 0, 1)
The fοrmula fοr t in terms οf 2kπ is: t = kπ + π/2, where k is an integer.
How tο draw a unit circle?Tο draw a unit circle fοr the given cοοrdinates, we first draw the hοrizοntal and vertical axes intersecting at the οrigin (0,0):
Next, we draw a circle with radius 1 centered at the οrigin:
Tο find pοints οn the circle with y-cοοrdinate 1, we lοοk at the pοint where the circle intersects the vertical axis. This οccurs when x = 0, sο the pοint οn the circle with y-cοοrdinate 1 is (0,1):
(0,1)
Tο find οther pοints οn the circle, we can use the Pythagοrean identity:
sin²(t) + cοs²(t) = 1
Since we want y = sin(t) tο be 1, we can sοlve fοr x = cοs(t)
cοs(t) = sqrt(1 - sin²(t))
Using this fοrmula, we can find several pοsitive and negative real numbers t that determine pοints Q οn the circle with y-cοοrdinate 1:
t = 0 radians (0 degrees): Q = (1,0)
t = π/6 radians (30 degrees): Q = (√3/2, 1/2)
t = π/4 radians (45 degrees): Q = (√2/2, √2/2)
t = π/3 radians (60 degrees): Q = (1/2, √3/2)
t = π/2 radians (90 degrees): Q = (0,1)
t = 7π/6 radians (-150 degrees): Q = (-√3/2, 1/2)
t = 3π/4 radians (-135 degrees): Q = (-√2/2, √2/2)
t = 5π/6 radians (-120 degrees): Q = (-1/2, √3/2)
t = π radians (-180 degrees): Q = (-1,0)
Tο write a fοrmula fοr t in terms οf 2kπ, we can use the inverse sine functiοn:
sin(t) = 1
t = sin⁻¹(1) + 2kπ
Since sin(π/2) = 1, we have:
t = π/2 + 2kπ
Sο the fοrmula fοr t in terms οf 2kπ is:
t = kπ + π/2, where k is an integer.
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Which expression gives the distance between the points (-11, 2) and (5, 2)
Answer:16
Step-by-step explanation:
Determine the length of x in the triangle. Give your answer to two decimal places. most importantly show the steps, please.
Answer:
x=43.85
Step-by-step explanation:
solution Given.
let the given angle be θ: 20 degree.
It's opposite side is 12.
It's hypotenuse is x.
Since
We have
Sin θ= opposite/hypotenuse
Sin20 degree=12/x
0.34202014332=12/x
doing criss cross multiplication
x=12/0.34202014332
therefore x=43.8570660032
in two decimal form x=43.85
How much money should be deposited today in an account that earns 2.5% compounded monthly so that it will
accumulate to $13,000 in 4 years?
i Click the icon to view some finance formulas.
Answer: We can use the formula for the future value of an annuity with monthly compounding to determine how much money should be deposited:
FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)
where:
FV = future value (the amount we want to accumulate, which is $13,000 in this case)
P = periodic payment (the amount we need to deposit each month)
r = annual interest rate (2.5% in this case)
n = number of compounding periods per year (12 for monthly compounding)
t = number of years (4 in this case)
We want to solve for P, so we can rearrange the formula as follows:
P = FV * (r/n) / ((1 + r/n)^(n*t) - 1)
Substituting the given values, we get:
P = 13000 * (0.025/12) / ((1 + 0.025/12)^(12*4) - 1)
Calculating this expression gives us:
P = $279.27 (rounded to the nearest cent)
Therefore, we need to deposit $279.27 each month for 4 years in an account that earns 2.5% compounded monthly in order to accumulate $13,000. Alternatively, if we want to make a single deposit today, we can multiply this monthly amount by 12 and then by 4, which gives us:
P = $13,414.08 (rounded to the nearest cent)
Therefore, we need to deposit $13,414.08 today in an account that earns 2.5% compounded monthly in order to accumulate $13,000 after 4 years.
Step-by-step explanation:
I’m confused, how do I create a dot-plot with only one number in the tens?
The dot represents the data point of 5, and there are no other data points to include on the dot plot.
You can still make a dot plot even if you just have one number in the tens by placing a dot on a number line above the number. If your data point is 5, for instance, you can represent it by placing a dot above the tick mark for 5 on a number line that has tick marks for each integer from 0 to 9. Here is an illustration of how the dot plot might appear:
|
5 •
|
|
|
|
|
|
|
|
+ - - - - - - -
0 1 2 3 4 5 6 7
There are no additional data points to place on the dot plot because the dot in this illustration represents the data point of 5.
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PLEASE HELP!!! THANK YOU
The point slope form of the line that passes through (-2 ,1) and a slope of - 4 is y - 1 = -4(x + 2).
How to represent equation in point slope form?The equation of a line can be represented in point slope form as follows:
y - y₁ = m(x - x₁)
where
m = slope of the linex₁ and y₁ are variablesTherefore, the line passes through (-2 ,1) and a slope of - 4.
The point slope form is as follows:
y - y₁ = m(x - x₁)
y - (1) = -4(x - (-2))
y - 1 = -4(x + 2)
Therefore, the point slope form is y - 1 = -4(x + 2)
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Answer this question please
The possible rotation that transforms the image obtained from the reflection of the square ABCD on the line x = -1, with two vertices of the square remaining invariant is as presented as follows;
A rotation of the image of ABCD 270° counterclockwise, about the point (-2, -1) What is a rotation transformation?A rotation transformation is a transformation in which the preimage coordinate points are turned (in a circular manner) about a point.
The vertices of the square ABCD are; A(1, 4), B(3, 4), C(3, 2), D(1, 2)
The coordinates of the square following the reflection across the line x = -1 are; A'(-3, 4), B'(-5, 4), C'(-5, 2), and D'(-3, 2)
The rotation transformation of the image such that two vertices of the square are invariant (such that they remain the same) can be found as follows;
The rotation of a vertices of the image about the point (-2, -1) indicates the relative points are;
A'(-1, 5), B'(-3, 5), C'(-3, 3), and D'(-1, 3)
The image following a rotation of 270° are;
A''(5, 1), B'(5, 3), C'(3, 3), and D'(3, 1)
The above points relative to the origin are;
A''(5 + (-2), 1 - 1) = (3, 0), B''(5 - 2, -1 + 3) = (3, 2), C';(3 - 2, 3 - 1) = (1, 2), and D''(3 - 2, 1 - 1) = (1, 0)
A''(3, 0), B''(3, 2), C''(3, 4), and D''(1, 4)
The points (1, 2), and (3, 2) are therefore, the same as the points in the preimage and are therefore, invariant
The rotation is therefore;
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The value, V, of a particular automobile (in dollars) depends on the number of miles, m, the car has been driven, according to the function V(m).
A. Interpret the statement, V(70, 000) = 12, 500, in the context of this application. Write a sentence that tells someone what that statement means and include the appropriate
units.
B. In the statement f '(70, 000) = − 15
i. What are the units of the 70, 000?
ii. What are the units of the − 15?
iii. Interpret the statement, f '(60, 000) = − 15, in the context of this application.
In other words, using everyday language, write a sentence that tells someone
what that statement means and include the appropriate units.
Please help will mark Brainly
The function in vertex form is f(x) = 10(x + 2)² - 8.
What is the vertex form of a quadratic equation?In this exercise, you are required to determine the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about this quadratic function, we can reasonably infer and logically deduce that a mathematical expression which quickly reveals the vertex of the quadratic function is given by:
y = a(x - h)² + k
y = 10(x - (-2))² + (-8)
y = f(x) = 10(x + 2)² - 8
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Which property of equality is shown below?
If: –70 =
26 −
y
Then:
–70 +
z
=
26 −
y
+
z
The property of equality shown in the given equation is the addition property of equality.
What are the property of equality?The properties of equality are a set of rules that can be used to manipulate equations while maintaining their truth value, including the reflexive, symmetric, transitive, addition, subtraction, multiplication, and division properties.
which states that if we add the same quantity to both sides of an equation, the equation remains true. In this case, we add z to both sides of the equation –70 = 26 – y to obtain –70 + z = 26 – y + z.
By the addition property of equality, the equation remains true because we have added the same quantity.
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Does anyone know the answer?
Answer: Car tire
Step-by-step explanation:
30 inches is about 2 1/2 feet, about the size of a car tire when taken into consideration.
could somebody please provide me wish an explaination for the textbook example answers:
a) why here is 3 and 4 relevant and what do them being a square number have to do with it?
b) I understand this one
c) why is 5 square rooted
Answer:
Step-by-step explanation:
The number 5 is prime. This implies that the number 5 is pairless and is not in the power of 2. Therefore, the square root of 5 is irrational.
- Notify me if any questions.!
[tex]\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ 9p^2-16q^2\implies 3^2p^2-4^2q^2\implies (3p)^2-(4q)^2\implies (3p-4q)(3p+4q) \\\\[-0.35em] ~\dotfill\\\\ x^2-5\implies (x)^2-\sqrt{5^2}\implies (x)^2-(\sqrt{5})^2\implies (x-\sqrt{5})(x+\sqrt{5})[/tex]
Simplify 7/12 + 5/18 =
Answer:31/36
Step-by-step explanation:
we should find greatest common divisor(GCD) ,
GCD(12,18)=36
7/12=7*3/36=21/36
5/18=5*2/36=10/36
21/36+10/36=31/36
Answer:
31/36
Step-by-step explanation:
1) Find the Least Common Denominator (LCD) of [tex]\frac{7}{12}[/tex], [tex]\frac{5}{18}[/tex]. In other words, find the Least Common Multiple (LCM) of 12, 18.
Method 1: By Listing Multiples1) List the multiples of each number
Multiples of 12: 12, 24, 36, ...
Multiples of 18: 18, 36, ...
2) Find the smallest number that is shared by all rows above. This is the LCM.
LCM = 36
Method 2: By Prime Factors1) List the prime factors of each number.
Prime Factors of 12: 2, 2, 3
Prime Factors of 18: 2, 3, 3
2) Find the union of these primes.
2, 2, 3, 3
3) Multiply these number: 2 x 2 x 3 x 3 = 36. This is the LCM.
LCM = 36
STEP 2: Make the denominators the same as the LCD.
[tex]\frac{7\times3}{12\times3} +\frac{5\times2}{18\times2}[/tex]
3) Simplify. Denominators are now the same.
[tex]\frac{21}{36} +\frac{10}{36}[/tex]
4) Join the denominators.
[tex]\frac{21+10}{36}[/tex]
5) Simplify.
[tex]\frac{31}{36}[/tex]
Thank you,
Eddie.
write 9sinhx+4coshx in terms of e^x and e^-x
Answer:
You can write it as (9/2)e^x + (2)e^-x.
Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
None of the provided equations are direct formulas for finding the lengths of the legs of a triangle.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals symbol ("="). For illustration, 2x - 5 Equals 13.
Here,
5 and 13 are phrases for 2x.
FROM THE QUESTION?
The number of x, which is one of the lengths of a right triangle's legs, can be determined by solving the quadratic equation [tex]0.5(x)(x+2)=24[/tex] . It is not a straightforward method, though, to determine the lengths of the legs.
It is possible to simplify and calculate the quadratic equation [tex]x(x+2)=24[/tex] to determine the values of x, which correspond to the lengths of a rectangle whose area is 24. Once more, there is no simple method for determining the lengths of a triangle's legs.
You can simplify and calculate the equation [tex]x^2+(x+2)2=100[/tex] to determine the value of x, which is one of the lengths of a right triangle's legs. It is not a straightforward method, though, to determine the lengths of the legs.
The lengths of a triangle's legs cannot be determined directly using any of the given formulae.
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i’ve been struggling for hours and i still can’t get it!! someone please help
Answer:
40.1 cm
Step-by-step explanation:
For this problem we will use trigonometry. To find x, we have to remember SOH CAH TOA
Our angle is 55, and the we have the value adjacent to the angle which is 23 cm so we will take that and make an equation because we are missing the hypotenuse:
CAH = adjacent/hypotenuse
cos = ^
cos ( 55 ) = 23/x
multiply x both sides
xcos(55) = 23
divide cos(55) from left
x = 23/cos(55)
input in calculator (make sure in right mode degrees)
23/(cos(55))
x = 40.09927 cm
x = 40.1 cm
1. If the letters of the word "COMPUTER" are arranged in random, what is the probability that O&E are together?
The probability that O and E are together in a randomly arranged word "COMPUTER" is 0.25, or 25%.
What is probability?Statistics and probability theory both make substantial use of probability, which is a measure of the possibility or chance of an event occurring. A number between 0 and 1, where 0 denotes an event that is impossible and 1 denotes an event that is certain, is used to indicate the likelihood of an occurrence.
We must count the number of favourable possibilities—those that match the event of interest—and divide that number by the total number of potential outcomes in order to calculate the probability of an occurrence.
There are 8 letters in the word, so the total number of arrangements is 8! = 40,320.
For O and E to be together we consider it as a sing letter, thus:
There are 7! ways to arrange the letters of new word.
Now, OE can be written as OE or EO thus:
2 x 7! = 10,080
Now, the probability of O and E together is:
Probability = 10,080 / 40,320
Probability = 0.25
Hence, the probability that O and E are together in a randomly arranged word "COMPUTER" is 0.25, or 25%.
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(If A : B = 2:5and B: C = 15: 8 then find A : C.) →
The ratio is given as A:C = 3:4
What is a ratio?A ratio is the number of times one number divides into another or the proportion of one number to the other.
Since we have that the A : B = 2:5 and B: C = 15: 8.
We desire to the ratio find A : C.
We proceed to solve the problem as follows
Since we have that the ratio
A:B = 2:5
This implies that
A/B = 2/5
Also, we have that the ratio
B : C = 15/8
This implies that
B/C = 15/8
Now, the ratio A:C = A/C
= A/B × B/C
So, substituting the values of the variables into the equation, we have that
A/C = A/B × B/C
= 2/5 × 15/8
= 1/1 × 3/4
= 3/4
So, A:C = 3:4
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Which side lengths form a right triangle? Choose all answers that apply: A 5, 6,√30 B 2.5, √18, 5 C √2, 2, √6
Since 6 = 6, these side lengths do form a right triangle.
Therefore, the answer is C: √2, 2, √6.
How are lengths of sides of a triangle calculated?
The Pythagorean theorem, which asserts that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides, can be used to identify which side lengths make up a right triangle.
A) The Pythagorean theorem enables us to deduce that: 52 + 62 = 25 + 36 = 61
[tex]\sqrt{30^{2}[/tex] = 30
These side lengths do not create a right triangle because 61 > 30.
B) The Pythagorean theorem enables us to observe that:
[tex]2.5^2 + \sqrt{18^{2} }[/tex] = 6.25 + 18 = 24.25
Also,
[tex]5^{2}[/tex] = 25
Since 24.25 < 25, a right triangle cannot be formed by these side lengths.
C) The Pythagorean theorem enables us to observe that:
[tex]\sqrt{2^{2} } + 2^2[/tex] = 2 + 4 = 6
[tex]\sqrt{6^{2} }[/tex] = 6
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The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown:
Constraint Television Radio Online
Audience per advertisement 140,000 18,000 30,000
Cost per advertisement $1,500 $200 $550
Maximum media usage 15 19 12
To ensure a balanced use of advertising media, radio advertisements must not exceed 45% of the total number of advertisements authorized. In addition, television should account for at least 15% of the total number of advertisements authorized.
(a) If the promotional budget is limited to $24,100, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter “0”.
the Westchester Chamber of Commerce should run 6 advertisements on television, 17 advertisements on radio, and 12 advertisements online to maximize total audience contact within the budget constraint.
What is cost?The term "cost" generally refers to the amount of resources (such as money, time, effort, or opportunity) that are required to produce or obtain something.
In a business or financial context, cost can refer to the expenses incurred in the production of goods or services, such as materials, labor, and overhead. It can also refer to the price paid for goods or services that are purchased from others.
Given by the question.
Let's denote the number of advertisements to be run on television, radio, and online as x, y, and z, respectively. We want to maximize the total audience, which is given by:
Total Audience = 140,000x + 18,000y + 30,000z
Subject to the following constraints:
Cost constraint: 1500x + 200y + 550z ≤ 24,100
Maximum media usage constraint:
a. x + y + z ≤ 46 (total number of advertisements authorized)
b. y ≤ 0.45(x+y+z) (radio advertisements should not exceed 45% of the total)
Note that we combined the maximum media usage constraints to get a single constraint for the total number of advertisements authorized.
We can now set up the optimization problem:
Maximize Total Audience = 140,000x + 18,000y + 30,000z
Subject to:
1500x + 200y + 550z ≤ 24,100
x + y + z ≤ 46
y ≤ 0.45(x+y+z)
We can solve this problem using a linear programming solver. Here is the solution:
Number of advertisements on TV (x) = 6
Number of advertisements on radio (y) = 17
Number of advertisements online (z) = 12
Total audience = 140,000x + 18,000y + 30,000z = 2,452,000
Total cost = 1500x + 200y + 550z = $22,300
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which uses th GFC to generate an expression equivalent to 2.4x - 12
The GCF (Greatest Common Factor) of 2.4x and 12 is 2.4. Therefore, we can write: 2.4x - 12 = 2.4(x - 5)
What is expression ?
In mathematics, an expression is a combination of symbols and/or numbers that represents a mathematical quantity or relationship. It can be a simple numerical value or a more complex arrangement of terms and operations.
To generate an expression equivalent to 2.4x - 12 using the GCF, we need to find the largest common factor between the terms 2.4x and 12.
First, we can simplify 2.4x by dividing both the numerator and denominator by 0.4, which gives us:
2.4x = 6x
Now, we can find the GCF between 6x and 12, which is 6. We can factor out this GCF from both terms to get:
2.4x - 12 = 6(x - 2)
So, the expression equivalent to 2.4x - 12 using the GCF is 6(x - 2). This expression represents the same quantity as 2.4x - 12, but is simplified and factored.
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Suppose you want to buy a new car that cost 32,700 you have no cash only your old car which is worth 2000 as a trade in the dealer says the interest rate is 3% add on for five years find the total interest
The tοtal interest paid οver the 5-year lοan periοd wοuld be $4,605.
What is Interest?In mathematics, interest is the cοst οf bοrrοwing mοney, usually expressed as a percentage οf the bοrrοwed amοunt. It is calculated based οn the principal amοunt, the interest rate, and the time periοd fοr which the mοney is bοrrοwed.
Assuming that the full purchase price οf the new car is $32,700, and the dealer has οffered a trade-in value οf $2,000 fοr yοur οld car, yοu will need tο finance the remaining balance, which is:
$32,700 - $2,000 = $30,700
If the dealer has οffered a 3% add-οn interest rate fοr a 5-year lοan, we can calculate the tοtal interest paid οver the life οf the lοan using the fοllοwing fοrmula:
Tοtal interest = (Principal × Interest rate × Lοan term) ÷ 2
Substituting the given values intο the fοrmula, we get:
Tοtal interest = ($30,700 × 0.03 × 5) ÷ 2
Tοtal interest = $4,605
Therefοre, the tοtal interest paid οver the 5-year lοan periοd wοuld be $4,605.
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Findthe value of x using trigonometry. Round answer to the nearest tenth
Answer:
x ≈ 20.0
Step-by-step explanation:
using the cosine ratio in the right triangle
cos26° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{18}{x}[/tex] ( multiply both sides by x )
x × cos26° = 18 ( divide both sides by cos26° )
x = [tex]\frac{18}{cos26}[/tex] ≈ 20.0 ( to the nearest tenth )
APR 30-Year Term 20-Year Term 15-Year Term
5.5 $5.68 $6.88 $8.17
6.0 $6.00 $7.16 $8.44
6.5 $6.32 $7.46 $8.71
7.0 $6.65 $7.75 $8.99
7.5 $6.99 $8.06 $9.27
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 term mortgage at an APR of 6.5% and principal of $242,300.00 is about 31.1%
What is a mortgage?A mortgage is a loan used to purchase property.
The principal balance = $242,300.00
The Annual Percentage Rate, APR = 6.5%
The term of the loan = 30-year and 15-year
The monthly payment for the loan per each term can be obtained using the following formula;
M = P·[r·(1 + r)^n]/[(1 + r)^n - 1]
Where;
M = The monthly payment
P = The principal amount of the loan = $242,300.00
r = The monthly interest rate = APR/12 = 0.065/12
n = The the number of periods of payment = 12 × 30 = 360
The monthly payment for the 30-year loan term is therefore;
M₃₀ = 242,300 × [(0.065/12)·(1 + (0.065/12))^360]/[(1 + (0.065/12))^360 - 1] ≈ 1531.5
The total payment for the 30-year term ≈ 360 × 1531.5 = 551,340.3
The total payment for the 30-year term is about $551,340.3The monthly payment for the 15-year loan term is found as follows;
n = 12 × 15 = 180
M₁₅ = 242,300 × [(0.065/12)·(1 + (0.065/12))^180]/[(1 + (0.065/12))^180 - 1] ≈ 2110.7
The total payment in 15 years ≈ 15 × 12 × 2110.7 = 379962
The total payment for the 15-year loan term is about $379,962The percentage decrease, is therefore;
((551,340.3 - 379,962)/551,340.3) × 100 ≈ 31.1%
The percentage decrease is about 31.1%Learn more on mortgage calculations here: https://brainly.com/question/28041674
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