1) Note that the altitude of the top of the hill is -136 feet above sea level.
2) Note that Checkpoint 1 is 3,558 feet higher than Checkpoint 5.
What is the rationale for the above response?Altitude or height is a distance measurement between a reference datum and a point or object, generally in the vertical or "up" direction. The precise definition and reference datum vary depending on the circumstance.
1) Checkpoint 4 has an altitude of -202 feet above sea level. The top of the hill rises 66 feet above Checkpoint 4. Therefore, the altitude of the top of the hill is:
-202 + 66 = -136 feet
So, the altitude of the top of the hill is -136 feet above sea level.
2) To find the difference in altitude between Checkpoint 1 and Checkpoint 5, we need to subtract the altitude of Checkpoint 5 from the altitude of Checkpoint 1.
Altitude difference = Altitude of Checkpoint 1 - Altitude of Checkpoint 5
Substituting the values given in the table, we get:
Altitude difference (AD) = 3,459 - (-99)
AD = 3,459 + 99
Thus, AD = 3,558
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Пожалуйста, напишите вымышленную историю о том, как растут деревья, заранее спасибо.
Answer:
Step-by-step explanation:
К счастью, другое маленькое дерево поблизости заметило растущее дерево и дало несколько интересных советов о том, как удерживать его распускающиеся листья новыми и интересными способами. Было забавно испытать на других маленьких деревьях множество различных способов расположения листьев. Другие маленькие деревья вскоре заметили это и начали поворачивать свои немногочисленные листья под углом. Другие маленькие деревья могли лишь слегка приподнять свои листья.
Растущее дерево решило, что будет немного приподнимать листья на радость другим деревьям. Но, в конце концов, все маленькие деревья начали отращивать больше листьев на ветвях, которые тянулись еще дальше. С каждым сезоном многие листья невозможно было приподнять. Некоторые из растущих деревьев продолжали шептаться, в то время как некоторые научились громко смеяться, некоторым, казалось, нравилось плакать и падать духом, а некоторые росли вдали от группы из-за того, как многие времена года влияли на них и на другие деревья и животных вокруг них.
За прошедшие годы родительские деревья время от времени мельком смотрели вниз, чтобы увидеть, как растут их семена, и они поднимали свои ветви к небу, чтобы пропустить солнечный свет через полог. Все растущие деревья заметят это и поднимут головы, чтобы насладиться солнечным светом. Те, кто не обращал внимания на поведение своего родительского дерева, обычно подражали другим растущим деревьям и умудрялись собирать немного солнечного света. Иногда растущее дерево переставало расти, потому что не могло достичь солнечного света. Его листья не будут такими обильными, а его ветви будут тянуться дальше, чтобы быть ближе к солнечному свету других растущих деревьев. По прошествии многих сезонов растущие деревья становились все выше и теперь можно было видеть, что их место среди кроны деревьев было довольно тесным.
The function f is defined by the following rule.
f(x)=4x+2
Complete the function table.
table
x f(x)
-4 ?
-1 ?
1 ?
2 ?
5 ?
The function table.
table
x f(x)
-4 4(-4)+3 = -16+3 = -13
0 4(0)+3 = 0+3 = 3
2 4(2)+3 = 8+3 = 11
4 4(4)+3 = 16+3 = 19
5 4(5)+3 = 20+3 = 23
What is Function?
A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.
We can complete the function table by substituting the given values of x into the rule for f(x) and simplifying in the following table.
Therefore, the completed function table is as follows.
so final table is
x f(x)
-4 -13
0 3
2 11
4 19
5 23
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Which of the following statements proves the series 250 – 150 + 90 – 54 + … is geometric?
r equals five thirds
r equals three fifths
r equals negative three fifths
The given series is geometric when r equals negative three-fifths.
What is geometric series?
The geometric series refers to the total of terms with a common ratio between every pair of neighbouring terms. Geometric series can be of two different types: finite and infinite. The sequence is of the form {a, ar, ar², ar³, …….} where, a is the first term, and r is the "common ratio".
where, r = ar/a = (second term)/(first term)
Given, the series 250 – 150 + 90 – 54 + …
So, r = (-150)/250 = -3/5
or, r = 90/(-150) = -3/5
Hence, for the geometric series, r should be equal to negative three-fifths.
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Which expressions are equivalent to the given complex number?
45 + 2i
C
(13 + 4i) + (32 - 6i)
000
(13 + 4i) + 2(7 + 2i)(2 -i)
(2 - 8i) + 2(9 + 6i)(1 - i)
4i) + (36
2i)
(2 + 8i) + (30 - 6i)
0 (9 + 4i) + 2(4 + 7i)(1 - 2i)
The equivalent expressions of 45 + 2i are (13 + 4i) + (32 - 6i) and (9 + 4i) + 2(4 + 7i)(1 - 2i)
How to determine the equivalent expressionsFrom the question, we have the following parameters that can be used in our computation:
Complex number: 45 + 2i
Next, we test the options:
(13 + 4i) + (32 - 6i) = 13 + 4i + 32 - 6i
(13 + 4i) + (32 - 6i) = 45 - 2i --- true
(13 + 4i) + 2(7 + 2i)(2 -i) = (13 + 4i) + 2(14 - 7i + 4i - 2)
(13 + 4i) + 2(7 + 2i)(2 -i) = 13 + 4i + 28 - 14i + 8i - 4
(13 + 4i) + 2(7 + 2i)(2 -i) = 37 - 2i --- false
(2 + 8i) + (30 - 6i) = 2 + 8i + 30 - 6i
(2 + 8i) + (30 - 6i) = 32 + 2i--- false
(9 + 4i) + 2(4 + 7i)(1 - 2i) = (9 + 4i) + 2(4 - 8i + 7i + 14)
(9 + 4i) + 2(4 + 7i)(1 - 2i) = 9 + 4i + 8 - 16i + 14i + 28
(9 + 4i) + 2(4 + 7i)(1 - 2i) = 45+ 2i --- true
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An assiatant receies a 10% raise, bringing the salary to 47,585. What was the salary before the raise?
Answer:
Step-by-step explanation:
here's a more detailed explanation:
The assistant received a raise of 10%, which means that their salary increased by 10% of the original salary. The new salary after the raise is given as 47,585.
To find the original salary before the raise, we need to reverse the effect of the raise. To do this, we divide the new salary by the factor that represents the increase, which is 1 plus the raise as a decimal.
The raise as a percentage is 10%, which is equivalent to 0.10 as a decimal. Therefore, the factor that represents the increase is 1 + 0.10 = 1.10.
We can now use this factor to find the original salary by dividing the new salary by the factor:
Original salary = New salary / (1 + Raise as a decimal)
Original salary = 47,585 / (1 + 0.10)
Original salary = 47,585 / 1.10
Original salary = 43,259.09
So the salary before the raise was 43,259.09.
How Many Solutions Does The Equations y=-2x+1 and y=3x-1
Answer:
It has a Unique solution.
Step-by-step explanation:
The equations are:
y=-2x+1 and y=3x-1
subtracting equation 2 from equation 3
we get,
⇒-5x+2=0
⇒5x=2
⇒x=2/5
substitute x in equation 1, then we get
⇒y=-4/5+1
⇒y=1/5
Hence the equations have a Unique solution.
Yoshi swam across a lake but did not know how far he swam. He found that it was 100sqrt(3) feet from point A to point C. Angle C was a right angle and angle A was 30°.
Find the distance he swam across the lake.
Hint: hypotenuse = 2shortleg )
The length of the lake is 100 ft
Finding the length of the lake:Form a right-angled triangle according to the given data in the problem. Chose which trigonometric ratio can be used to find the side that is considered as the side of the lake.
From the trigonometric ratio table,
Tan 30 = 1/√3Here we have
Yoshi swam across a lake but did not know how far he swam.
He found that it was 100√) feet from point A to point C.
Angle C was a right angle and angle A is 30°.
We represent the given scenario in the form of a right angle triangle as shown in the picture.
Let 'B' be the point where Yoshi swam started and BC be the length of the lake.
From the triangle,
Tan A = BC/AC
From the given data,
Tan 30° = BC/100√3
=> BC = Tan 30°(100√3)
=> BC = (1/√3)(100√3)
=> BC = 100 ft
Therefore,
The length of the lake is 100 ft
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The ratio of your age to Jasper is 3:4. If you are 14, how old is Jasper?
Answer:10 1/2
Step-by-step explanation:
Jasper is approximately 18.67 years old as per the given ratio.
What is the ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, the ratio of your age and the age of Jasper is 3:4.
Let's use this ratio to find out how old Jasper is if you are 14.
First, we can set up a proportion:
3/4 = 14/x
where x is Jasper's age.
To solve for x, we can cross-multiply:
3x = 4 * 14
3x = 56
x = 56/3
x ≈ 18.67
So if you are 14 and the ratio of your age to Jasper's age is 3:4, then Jasper is approximately 18.67 years old.
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in 4x to the fifth +1 what would the end behavior of the graph be?[
The end behavior of the given fucntion is [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex].
What is end behavior of function.?End behavior of a equation is defined as behavior of graph of the function at the ends of the x-axis.
Given, [tex]4x^{5} +1[/tex].
We have to find the end behavior of the graph.
The corresponding graphical representation is given below:
From the graph it is clearly known that as,
Value of x increases ⇒Value of y decreases.
That is x approaches positive infinity and y approaches negative infinity.
i.e., [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex]
Hence, the end behavior of the given equation is [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex].
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18. What percentage of R90 is 90c?
The percentage of R90 that will give 90c is 4%
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
1 cent = R0.04
R1 = 1/0.04
R 90 = 90/0.04 = 2,250c
x/100 × 2250 = 90
2250x = 9000
x = 9000/2250
x= 4%
therefore 4 percent of R 90 is 90c
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parallelagram abcd has the angle measures shown
Answer:
Theres nothing shown
Step-by-step explanation:
what is the pattern for each hypotenuse in the pythagorean spiral?
i have:
Hypotenuse = (Triangle # + 1) X 9
(square root the answer)
does this make sense?
The pattern for the hypotenuse in the Pythagorean spiral is √(a² + b²)
How to get the patternThe Pythagorean spiral is formed by drawing squares whose side lengths are given by the Pythagorean triples, which are sets of three positive integers (a, b, c) that satisfy the equation a² + b² = c².
In the Pythagorean spiral, the hypotenuse of each square is the diagonal of the square, which is given by the square root of the sum of the squares of the sides. For a square with side lengths a and b, the hypotenuse (diagonal) is given by:
√(a² + b²)
Since the side lengths of each square in the Pythagorean spiral are given by the Pythagorean triples, the hypotenuse of each square can be calculated using the Pythagorean theorem. Therefore, the pattern for each hypotenuse in the Pythagorean spiral is that it is given by the square root of the sum of the squares of the side lengths, where the side lengths are integers that form a Pythagorean triple.
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help would be appreciated
The perimeter of the parallelogram is 10units
What is perimeter of a parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.
To obtain the perimeter of the parallelogram , we add all the sides together.
P = 2(l+b)
P= 2( c-2+12-c)
P = 2( c-c -2 +12 )
P = 2( 10)
P = 20
therefore the perimeter of the parallelogram is 20
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A guy wire supporting a radio tower is positioned 145 feet up the tower. It forms a 45 angle with the ground. To the nearest tenth, about how long is the wire?.
The approximate length of the guy wire supporting the radio tower, as determined using trigonometry with the given information of a 45 degree angle and a height of 145 feet up the tower, is 145 feet.
We can use trigonometry to solve this problem. Let's call the length of the guy wire "x". The opposite side of the right triangle formed by the guy wire and the ground is 145 feet (the height of the tower where the guy wire is attached), and the angle opposite the guy wire is 45 degrees.
Using the trigonometric function tangent, we can set up the following equation:
[tex]tan(45)[/tex] = opposite / adjacent
where "opposite" is 145 feet and "adjacent" is the length of the guy wire, x. Simplifying this equation, we get:
1 = 145 / x
Multiplying both sides by x, we get:
x = 145
Therefore, the length of the guy wire is approximately 145 feet to the nearest tenth.
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Mr. Mosley ordered pizzas for the volunteers at Highland School's fundraiser event. He ordered 12 large pizzas from the Roman Rounds pizzeria. Since this was a bulk order, Roman Rounds reduced the price of each large pizza by $2. The total came to $192. Which equation can you use to find the amount of money, p, Roman Rounds normally charges for a large pizza?
Roman Rounds normally charges $18 for a large pizza.
What is the equation in one variable?
An equation in one variable is a mathematical statement that uses one variable and an equal sign to relate two expressions. The variable in the equation represents an unknown value, and the goal is often to find the value of the variable that makes the equation true.
Let's use p to represent the normal price of each large pizza charged by Roman Rounds.
Since the price of each pizza was reduced by $2 for the bulk order, the amount Mr. Mosley paid for 12 large pizzas is:
12(p - 2) = $192
We can simplify this equation by first distributing the 12 on the left side:
12p - 24 = $192
Then, we can isolate the variable p on one side of the equation by adding 24 to both sides:
12p = $216
Finally, we can solve for p by dividing both sides by 12:
p = $18
Therefore, Roman Rounds normally charges $18 for a large pizza.
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Select the correct answer. A line t runs downward to the right through two parallel horizontal lines a and b, forming 8 angles numbered from 1 to 8. In the diagram, transversal t cuts parallel lines a and b. Which equation is necessarily true? A. m∠1 = m∠7 B. m∠3 = m∠6 C. m∠5 + m∠8 = 90° D. m∠6 + m∠7 = 180°
Answer:
Step-by-step explanation:
The correct answer is D. m∠6 + m∠7 = 180°.
When a transversal cuts two parallel lines, corresponding angles are equal and alternate interior angles are supplementary. This means that the sum of alternate interior angles is equal to 180°. In this diagram, ∠6 and ∠7 are alternate interior angles, so it is necessarily true that m∠6 + m∠7 = 180°.
The other options are not necessarily true. Option A states that m∠1 = m∠7, but this is only true if the two lines being cut by the transversal are perpendicular. Option B states that m∠3 = m∠6, but this is only true if the two lines being cut by the transversal are parallel. Option C states that m∠5 + m∠8 = 90°, but this is only true if the two lines being cut by the transversal are perpendicular.
What is the y-intercept of the line perpendicular to the line y = 3/4x + 3 that includes the point (3, 1)?
Answer:
Step-by-step explanation:
perp.: -4/3
y - 1 = -4/3(x - 3)
y - 1 = -4/3x + 4
y = -4/3x + 5
y-int: (0, 5)
Question 3 of 5
Solve 3x + 6 = 21.
A. x=7
B. x=5
C. x=8
D. x=9
Answer:
B. x=5
Step-by-step explanation:
3x + 6 = 21
Subtract 6 from both sides.
3x = 15
Divide both sides by 3.
x = 5
Answer: B. X=5
Step-by-step explanation:
3x+6=21
subtract 6 on both sides
3x=15
divide by 3 on both sides
x=5
find an ordered pair (x,y) that is a solution to the equation -x+6y=2
Explanation:
Let's replace y with 0 and solve for x.
-x+6y = 2
-x+6*0 = 2
-x + 0 = 2
-x = 2
x = -2
We have x = -2 pair up with y = 0 to get the ordered pair (x,y) = (-2,0)
This is the x intercept of the graph. It's where the line crosses the x axis. You can use a tool like Desmos or GeoGebra to confirm.
Since we have infinitely many numbers to replace x or y with, we have infinitely many solution points on this line.
Each point is of the form (-2+6k, k) where k is any real number. If k = 0, then it leads to (-2,0) found earlier.
the height is determined by a function F (x)9x2+3x-5 then the height was determined by the function P(x)=6x2-2x+3,write the function that determines the height of the water i a pool if booth hoses are on the same time.
Answer:
Q(x) = 15x^2 + x - 2.
Step-by-step explanation:
To find the height of the water in a pool when both hoses are on, we need to add the values of the two functions, F(x) and P(x), at a given x value. The new function, Q(x), that determines the height of the water in the pool can be expressed as follows:
Q(x) = F(x) + P(x) = 9x^2 + 3x - 5 + 6x^2 - 2x + 3 = 15x^2 + x - 2
So the height of the water in the pool is determined by the function Q(x) = 15x^2 + x - 2.
Need help answering this question
Answer:
24 people
Step-by-step explanation:
German : 4 + (4/2) = 6
Norwegian : 4 + 4 + (4/2) = 10
Italian : 4 + 4 = 8
Add them all :
6 + 10 + 8 = 24
A typical glass of wine contains about 22 grams of alcohol. Consider a 103-pound woman, with approximately 6 liters (6000 milliliters) of blood, who drinks two glasses of wine. Complete parts (a) and (b) below.
If all the alcohol were immediately absorbed into her bloodstream, what would her blood alcohol content be? (Round to two decimal places as needed.) g/100 mL
Answer: The amount of alcohol the woman consumed can be calculated as follows:
Two glasses of wine * 22 grams of alcohol per glass = 44 grams of alcohol
To convert this amount to milliliters, we need to know the concentration of the alcohol, which is typically around 12% for wine. So, 44 grams of alcohol is equivalent to 44 grams / 0.12 g/mL = 367 mL.
Next, we can calculate the woman's blood alcohol content (BAC) using the following formula:
BAC = (Alcohol consumed in mL) / (Blood volume in mL) * 100%
The blood volume for a 103-pound woman with approximately 6 liters of blood can be estimated as follows:
6 liters * 1000 mL/liter = 6000 mL
So, the BAC can be calculated as follows:
BAC = (367 mL) / (6000 mL) * 100% = 0.0612 * 100% = 6.12%
Therefore, the woman's blood alcohol content would be 6.12% if all the alcohol were immediately absorbed into her bloodstream.
Step-by-step explanation:
Let X,X2, ...,X25 denote 25 random draws (with replacement) from the following list of 5 numbers: 0, 1,0,0,0. What is E(X)?
(a) 0.875
(b) 1/3
(c) 0.5
(d) 2.0
As per the probability, the value of E(X) is option (a) 0.8
In statistics, the expected value or mean is a measure of central tendency that represents the average outcome of a random variable over an infinite number of trials.
To find the expected value of X, we need to calculate the probability of each possible outcome and multiply it by its corresponding value. In this case, the possible outcomes are 0 and 1, and their probabilities can be calculated as follows:
The probability of drawing a 0 is 4/5 because there are 4 zeros in the list and 5 total numbers.
The probability of drawing a 1 is 1/5 because there is only one 1 in the list and 5 total numbers.
Using these probabilities, we can calculate the expected value of X as follows:
E(X) = (0 x 1/5) + (1 x 4/5)
The first term in this equation represents the probability of drawing a 0, multiplied by its value (which is 0), and the second term represents the probability of drawing a 1, multiplied by its value (which is 1). Simplifying this equation gives:
E(X) = 4/5 =0.8
Therefore, the answer to this problem is (a) 0.8, since the expected value of X is 0.8 of the possible outcomes.
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Complete the following proof.
Given: WXYZ is a parallelogram with diagonals XZ and WY intersecting at point V.
Prove: XZ bisects WY
The proof of the parallelogram has been given below
How to prove that X bisects WYWe have WXYZ as a parallelogram.
XW = ZY
XW // ZY
such that
M ∠VXW = M VZY (This is alternate interior angles,)
M∠VWX = M ∠VYZ
therefore ΔVXW ≅ Δvzy
wv = yv
Then XZ bisects WY
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PLEASE HELP ME!!!!! CORRECT ANSWER GETS BRAINLIEST
Answer:
So, Darmal needs to work more than 8.96 hours to earn more than $128.
Step-by-step explanation:
The situation represented by the inequality 14.25x > 128 is B. Darmal earns $14.25 per hour at his job. How many hours does he need to work to earn more than $128?
The inequality states that the product of 14.25 and x (representing the number of hours worked) is greater than 128. Solving for x, we can find the number of hours Darmal needs to work to earn more than $128:
14.25x > 128
x > 128 / 14.25
x > 8.96
So, Darmal needs to work more than 8.96 hours to earn more than $128.
What is the surface area of the box?
A. 160 square inches
B. 46 square inches
C. 92 square inches
D. 184 square inches
Answer:
D
Step-by-step explanation:
Front
5x4 = 20
Back
5x4 = 20
Top
5x8 = 40
Bottom
5x8 = 40
Right side
8x4 = 32
Left side
8x4 = 32
Add all the sides
20 + 20 + 40 + 40 + 32 +32 = 184
Q. On Fridays at the ballpark, a cup of soda costs $4, and each refill costs $0.80. If x represents the number of refills, which of the following equations represents the amount a person spends on soda?
A. y = 0.8x + 4.8
B. y = 4x + 4.8
C. y = 4x + 0.8
D. y = 0.8x + 4
Answer:
The correct answer is D.
Step-by-step explanation:
D. y = 0.8x + 4.
identify the range of the following function when given the domain (2,3,10) y=4x-12
Answer: range is (-4,0,28)
Step-by-step explanation:
Graph the line using the slope and the y-intercept, or the points.
The correct answers are:
Slope: 4y-intercept: (0,12)What is a domain?
The word "domain" is used with other related meanings in some areas of mathematics. In topology, a domain is a connected open set. In real and complex analysis, a domain is an open connected subset of a real or complex vector space.
The slope-intercept form is y =mx + b where m is the slope and b is the y-intercept:
→ y = mx + b
Find the values of m and b using the form y = mx + b:
m = 4
b = 12
Therefore, Graph the line using the slope and the y-intercept, or the points.
The correct answers are:
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If a1 = 2 and an = -2an-1 + 3 then find the value of a5.
The value of the fifth term B is 17.
What is a sequence?An ordered list of things is a sequence (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered items (potentially infinite).
Given:
The first term of the sequence is 2.
a₁ = 2
And the explicit formula of the sequence,
aₙ = (-2)aₙ₋₁ + 3.
The value of a₂:
a₂ = (-2)a₁+ 3.
a₂ = -2(2) + 3 = -1
And a₃ = -2(-1) + 3 =5
a₄ = -2(5) + 3 = -7
Now, the value of the fifth term,
a₅ = -2(-7) + 3 = 17.
Therefore, the fifth term is 17.
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You (or your parents) are debating about whether to buy a new car for $19,072.00 or a used car for $15,635.00. Sales tax is 4.5%. You (or your parents) plan to make a down payment of $1,200.00 and your credit rating is fair. What is the difference in interest accrued by the end of the first month?
The difference in the interest accrued by the end of the first month, given the credit rating and the cost is $ 21. 97
How to find the difference ?First, find the amount borrowed to pay for the new car or the used car.
New car :
= ( 19, 072 x ( 1 + 4. 5 % sales tax )) - 1, 200 down payment
= $ 18, 730. 24
The used car :
= 15, 635. 00 x ( 1 + 4. 5 %) - 1, 200
= $ 15, 138. 58
The difference in interest at the first month is :
= ( Amount borrowed for new car x Monthly APR for fair credit rating ) - ( Amount borrowed for old car x Monthly APR for fair credit rating )
= ( 18, 730. 24 x 7. 55 % / 12 ) - ( 15, 138. 58 x 7. 60 % / 12 )
= $ 21. 97
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