The solution of the given function is x < 3 + 4a.
What is a function?
A function is uniquely represented by the set of all pairings (x, f (x)), known as the function graph, which is a popular way of visualizing the function. When the domain and codomain are real number sets, each pair may be thought of as the Cartesian coordinates of a point in the plane. Functions are frequently employed in science, engineering, and the majority of mathematical areas. Most disciplines of mathematics say that functions are "the major subjects of investigation." If the domain and codomain set of two functions f and g are the same and their output values agree over the whole domain, they are equivalent.
The solution of the given function is
-4(-x+a)+5<8
or, 4x - 4a + 5 < 8
or, x < 8 - 5 + 4a
or, x < 3 + 4a
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Determine the remainder if
(x3 + 4x - 24) is divided by
(x - 2).
When [tex]x^3[/tex]+4x-24 is divided by x-2 then the remainder is -8.
What is remainder theorem?
Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that when a polynomial P(x) is divided by a factor (x - a), which isn't really an element of the polynomial, a smaller polynomial is produced along with a remainder. The remainder theorem asserts that when a polynomial p(x) is divided by (x - a), the remainder equals f. (a). Using Euclid's Division Lemma, this may be demonstrated. To put it another way, p(x) = q(x) (x - a) + r if q(x) is the quotient and 'r' is the remainder.
Here the given [tex]x^3[/tex]+4x-24 and x-2
When a function f(x) is divided by x+a, then the remainder is given by f(−a):
So, in this case remainder will be f(2) .
=> f(x)= [tex]x^3[/tex]+4x-24
put x=2 then
=> f(2)= [tex]2^3[/tex]+4(2)-24
=> f(2) =8+8-24
=> f(2) = 16-24 =-8
Hence the remainder is -8.
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Find the sum of all positive integers such that their expression in base 7 digits is the reverse of their expression in base 16 digits. Express your answer in base 10.
The sum of all positive integers such that their expression in base 7 digits is the reverse of their expression in base 16 digits is 58.
What is meant by positive integer?Natural numbers are numbers used in mathematics for counting (as in "there are six coins on the table") and ranking (as in "this is the third largest city in the country"). Cardinal numbers are used for counting, and ordinal numbers are used for ordering. Natural numbers, which have no mathematical features, are sometimes employed as labels.
When the number is a 1 digit number (1 digit number in base 7)- the numerals 0, 1, 2, 3, 4, 5, and 6
When the number is a 2 digit number=a×7+b=b×16+a / subtract (a+b) a×6=15×b / divide by 3 2a=5b indicating an is divisible by 5 meaning a=5 (since if a=0 then b=0 and the phrase ab is not defined because the digit that indicates the highest number in a given number cannot be 0) meaning b=2. So there is just one two-digit number=52 (in base 7)=37. (in base 10).
When the number is three digits, subtract (a+c+7b) 48a=255c+9b / divide by three 16a=85c+3b. c cannot be 0 because this indicates that the expression cba is not defined.
If c=1, 16a=85+3b
There are no answers to that problem. If c>1, this suggests that 16a=85c+3b>=170, implying that a>6. This, however, is not possible! As a result, there is no solution.
As a result, the sum of all positive integers is 58.
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A popular act command $250,000 for a ingle appearance plu 20% of ticket ale and 10% of conceion receipt. If ticket ale are $1,250,000 and conceion receipt are $400,000, what will the act be paid for their performance?
Answer:
$540,000
Step-by-step explanation:
250000 + .2(1250000) + .1(400000)
250000 + 250000 + 40000
540,000
Solve the system of equation and choose
4x+5y=22
2x+3y=12
Answer:The equation of the solution 4x + 5y = 22 and 2x + 3y = 12 will be (3, 2).
What is the solution of the equation?
The solution of the equation means the value of the unknown or variable.
The equations are given below.
4x + 5y = 22 …1
2x + 3y = 12 …2
The degree of the equation is one, then the equations will be the linear equation.
Multiply the equation 2 by 2, then subtract the equation 1 from 2. Then the equation will be
4x + 6y = 24
–4x – 5y = –22
6x - 5y = 24 – 22
Then simplify the equation, then the equation will be
y = 2
Substitute the value of y in equation 1, then the value of x will be
4x + 5(2) = 22
4x + 10 = 22
4x = 22 – 10
4x = 12
x = 12 / 4
x = 3
Then the equation of the solution will be (3, 2).
Step-by-step explanation:
40 POINTS PLEASE HELP ASAP!!! Will give Brainliest if correct. Please show some work.
The answer shown is incorrect as it doesn't follow the rules of indices? Unless that was your attempt?
A power outside the bracket should multiply with the inner powers not add, so the first part should be
(3 x^2 y^5)^4
= 3^4 x^(2*4) y^(5*4)
= 81 x^8 y^20
Then you have
81 x^8 y^20 + x^6 y^9 - 12 x^8 y^20
The powers that equal can be taken away to give
69 x^8 y^20 + x^6 y^9
I hope it's clear enough
a particular 12 -hour digital clock displays the hour and minute of a day. unfortunately, whenever it is supposed to display a 1 , it mistakenly displays a 9. for example, when it is 1 : 16 pm the clock incorrectly shows 9 : 96 pm . what fraction of the day will the clock show the correct time?
1/2 fraction of the day will the clock show the correct time when it is supposed to display a 1 , it mistakenly displays a 9.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Here,
=2/3(1-15/60)
=2/3(3/4)
=2/4
=1/2
When the clock should be displaying a 1, but instead shows a 9, the correct time will be displayed for 1/2 of the day.
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Mg(OH)2 + NaCl ® MgCl₂ + NaOH
How many hydrogen atoms are on the reactant side?
1
2
4
8
The hydrogen atoms are on the reactant side in the reaction is 2 atoms.
What is reaction?Reaction is defined as when atoms' chemical bonds are created or ruptured. The substances that start a chemical reaction are known as reactants, and the compounds that are produced as a result of the reaction are known as products. Now that the chemicals had been combined, bonds would be rearranged, resulting in the production of a new product.
We are aware that one of the requirements for formulating a balanced chemical reaction equation is that the quantity of each element's atoms on the reactant side must match the quantity of that element's atoms on the products side. By performing an atom count, we may determine the number of hydrogen atoms present on the reactants side of the reaction when we examine the reaction as it is proved to be balanced.
Thus, the hydrogen atoms are on the reactant side in the reaction is 2 atoms.
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Find the nth term of this quadratic sequence
2, 8, 18, 32, 50,
Answer:
Step-by-step explanation:
From the series, 2, 8, 18, 32, 50,...
By observation and by trial and error.
The first term, n = 1 = 2*1*1 = 2
Second term, n =2, = 2*2*2 = 8
Third, n =3, = 2*3*3 = 18
Third term, n = 4, = 2*4*4 = 32
Fourth term, n =5, 2 * 5* 5 = 50
For nth term, 2 *n *n = 2n²
Therefore nth term = 2n²
I hope this helps.
What are 3 congruent segments?.
The same circle's radii. parallelogram, rectangle, square, and rhombus opposite sides, sides of a triangle with equal sides.
What is congruent segments?
Segments of the same length are said to be congruent. Collinear points are those that share a line. A mathematical assertion that can be validated is known as a theorem. A point that divides a segment into two congruent segments is the segment's midpoint.
Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments.
When two lines are the same length, they are said to be congruent. Superimposable figures that entirely enclose each other when stacked one atop the other are congruent segments.
The congruent segments continue to be congruent even after being turned, flipped, or rotated. Congruence between any two congruent line segments is represented by the symbol.
the same circle's radii.parallelogram, rectangle, square, and rhombus opposite sides.sides of a triangle with equal sides.Look at the illustration below that shows congruent line segments:
Here, the double vertical bars on each line segment, PQ and XY, represent their equality, resulting in the line segment PQ ≅ XY.
We shall examine the congruent line segments' qualities in order to learn more about them. Congruent lines in geometry possess the following characteristics:
(i) Reflexive
(ii) Symmetric
(iii) Transitive
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By putting suitable signs + , − , × , ÷ , ( , ) in-between the digits 4 4 4 many numbers can be generated, for example, 4 − (4 ÷ 4) = 3. Which of the following numbers can be generated this way?
These are the numbers that can be generated which are 3, 5, 4, 1/4, -11, 20, -8, 64, 1/2, etc.
What is arithematic operartions?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
We have,
signs + , − , × , ÷ , ( , )
the digits 4 4 4
By putting suitable signs + , − , × , ÷ , ( , ) in-between the digits 4 4 4
4 − (4 ÷ 4) = 3.
4 + (4 ÷ 4) = 5.
4 × (4 ÷ 4) = 4.
4 ÷ (4 × 4) = 1/4.
4 - (4 × 4) = -11.
4 + (4 × 4) = 20.
4 - (4 + 4) = -8.
4 × (4 + 4) = 64.
4 ÷ (4 + 4) = 1/2.
Hence, these are the numbers that can be generated which are 3, 5, 4, 1/4, -11, 20, -8, 64, 1/2, etc.
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Please Help ASAP!!!!
The ordered pair that is a solution of the system of inequalities:
4x + 2y > 8
x - y ≥ 2
is (7, 2)
Which ordered pair is a solution for the system of inequalities?Here we have the following system of inequalities:
4x + 2y > 8
x - y ≥ 2
The points (x, y) are solutions only if make both inequalities true. For example let's use the first pair (2, 4)
Replacing that in the inequalities we get:
4*2 + 2*4 > 8
2 - 4 ≥ 2
Simplify the left side:
16 > 8
-2 ≥ 2
The second inequality is false, so (2, 4) is not a solution.
The correct option is the second one, (7, 2), evaluating the inequalities we get:
4*7 + 2*2 = (32) > 8
7 - 2 = 5 ≥ 2
You can see that both are true.
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To promote your basket business, you plan to give away 10 baskets. Your price is $60 and your normal gross margin percentage is 50%. How much will the giveaway cost you in direct product costs?.
The giveaway cost is $600 and the direct product cost is $300 .
In the question ,
it is given that ,
number of baskets that are planned to give away = 10 basket
price = $60
gross margin percentage = 50%
The give away cost is calculated using the formula
give away cost = number of basket × price
give away cost = 10 × 60 = $600.
the direct product cost can be calculated using the formula
direct product cost = Number of basket x Price x (1-margin%)
direct product cost = 10 × 60 × (1-50%)
= 10 × 60 × 0.5
= 600 × 0.5
= 300
Therefore , The giveaway cost is $600 and the direct product cost is $300 .
The given question is incomplete , the complete question is
To promote your basket business, you plan to give away 10 baskets. Your price is $60 in your normal gross margin percentage is 50%. How much will the give away cost you and direct product costs ?
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1. A judge is sentencing a man for speeding. He plans to charge him $30 for every mile over the speed limit that he was driving. If the speed limit was 35 and the man was driving 52.7 miles per hour, what will be the amount he owes for the ticket? Show your work and/or explain your answer.
Answer:
The amount of the ticket will be $531.
Step-by-step explanation:
If the driver is charged $30 for every mile above the speed limit, than :
diff = 52.7 - 35
= 17.7 miles
which leads to say that he owes 17.7 * $30 = $531
Work out the values of A and B in these equivalent ratios.
A: 6:7 = 8:24: B
A =
B =
The value of A is 32.
The value of B is 28.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
A : 6 : 7 = 8 : 24 : B
This means,
6 units = 2432
1 units = 24/6
1 units = 4
Now,
The value of A.
A = 8 units
1 unit = 4
8 units = 8 x 4 = 32
The value of B.
B = 7 units
1 unit = 4
7 units = 7 x 4 = 28
Thus,
A = 32
B = 28
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A bag contains 6 blue marbles, 5 red marbles, 3 green marbles, and 2 yellow marbles. If 2 marbles are removed from the bag one at a time, without being replaced, what is the probability of selecting 2 red marbles in a row?
The probability of selecting 2 red marbles in a row is 1/12.
A bag contains 6 blue marbles, 5 red marbles, 3 green marbles, and 2 yellow marbles. Two marbles are removed from the bag one at a time without being replaced. We need to find the probability of selecting 2 red marbles in a row. Let the probability be represented by the variable "P".
The probability that the first selected marble will be red is given below :
P1 = 5/(6 + 5 + 3 + 2) = 5/16
The probability that the second selected marble will be red is given below :
P2 = 4/(6 + 4 + 3 + 2) = 4/15
The probability that both of the selected marbles will be red is given below :
P = P1*P2 = (5/16)*(4/15) = 1/12.
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Average rate of change from x=2 to x=6
The average rate of change from x=2 to x=6 is 0.
What is the average rate of change?
The average rate of change is a measurement of how much the function changed on average per unit during that time period.
The average rate of change of function f over the interval a≤x≤b, is less than or equal to, x, is less than or equal to, b is given by this expression:
[tex]f'(x) = \frac{f(b)-f(a)}{b-a}[/tex]
Given, for x = 2 to x = 6 , we get a = 2 and b = 6
Then, from the figure,
f(a) = f(2) = -2
f(b) = f(6) = -2
Now,
Average rate of change = [tex]\frac{f(6)-f(2)}{6-2}[/tex] = [tex]\frac{-2-(-2)}{4}[/tex] = 0
Hence, the average rate of change is 0.
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What is the sequence in Pascal's Triangle?.
The triangle-shaped array of numbers known as Pascal's triangle has a top number of 1 and a line of 1s going down each of the other two sides. Each new number is situated between two other numbers and below them; its value is the product of the numbers immediately above it.
What is Pascal's Triangle?
The triangle-shaped array of numbers known as Pascal's triangle has a top number of 1 and a line of 1s going down each of the other two sides. Each new number is situated between two other numbers and below them; its value is the product of the numbers immediately above it.What is the purpose of Pascal's triangle?
In probability theory, combinatorics, and algebra, Pascal's triangle is frequently employed. In general, Pascal's triangle can be used to determine the coefficients of a binomial expansion, the likelihood that a coin will land on its heads or tails, the probabilities of various combinations, etc.Learn more about Pascal's Triangle
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What is parallel line class 4?.
Coplanar, straight lines that just don't cross at any point are considered parallel lines in geometry. Parallel planes were also planes that never cross each other in the same three-dimensional space.
What are lines that are parallel and perpendicular?If two lines are in the same plane and never cross, they are said to be parallel. They are equidistant lines, which means that their separation is constant. The symbol || is used to depict parallel lines. For instance, the symbol AB || CD denotes the parallelism of the line segments AB and CD. On the other hand, two straight lines are said to be perpendicular if they cross at a 90° angle.
A description line is what?A line has length but no breadth, making it a one-dimensional object. A line is made up of several points that continue indefinitely in opposing directions. His two points in a 2D plane serve as the basis for this. Collinear points are two points that are located on the same line.
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thirty seconds after a bowl begins to leak, the bowl is losing 0.28 ounces of liquid per second. let l(t) represent the amount of liquid that has leaked at any given time, and let t be measured in seconds. which of the following expressions represents this scenario?
The expression that represents this scenario would be l(t) = 0.28t. This expression states that the amount of liquid that has leaked at any given time is equal to 0.28 times the number of seconds that have passed.
What are linear equations?Linear equations are mathematical equations of the type y = mx + b, with and x and y being variables. These equations represent a straight line on a graph and are referred to be "linear" since the maximum power of the variable is 1. For example, the equation y = 2x + 3 is a linear equation since the maximum power of the variable x is 1. Linear equations are useful for representing a broad range of real-world events, such as the link between the distance an object travels and the time it takes to traverse that distance. They are a common tool in many disciplines, including physics, engineering, and economics. They are also quite simple to answer.
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The winner of an egg-eating contest ate 132 eggs in 11 minutes
What is the unit rate?
Answer:
12 eggs
Step-by-step explanation:
divide 132 by 11. hope this helped :)
Answer:
12 eggs per minute
Step-by-step explanation:
To find the unit rate, take the number of eggs and divide by the number of minutes
132eggs / 11 minutes
12 eggs per minute
Which of the following is equivalent to 1.92?
1.92%
19.2%
twenty five over twenty three
one and twenty three twenty fifths
Answer: The answer is d 1 23/25
Step-by-step explanation: if you where to rewrite 1.92 as a improper fraction you would get 48/25 so the next step would be to rewrite 48/25 as a mixed number then you would get 1 23/25 there you go :))
What is the graph of y-2=-3(x-1)?
The graph of y-2=-3(x-1) is shown in the figure below;
How to plot a graph of given function?Graphing functions is the process of drawing the graph (curve) of the corresponding function. Graphing basic functions like linear, quadratic, cubic, etc is pretty simple, graphing functions that are complex like rational, logarithmic, etc, needs some skill and some mathematical concepts to understand.
Given;
y-2= -3(x-1)
When x=0
y-2= -3(0-1)
y-2=0
y=0
When y=0
0-2= -3(x-1)
x=1.667
Hence, the graph of these coordinates is as follows;
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Use mental math to solve the equation. x - 15 = 19
Answer: x = 34
Step-by-step explanation:
Add 19 and 15 in your head. 9 + 5 = 14. Now, add 10 + 10 + 14. This gives 34.
What is the equation of the line that is perpendicular to the given line and passes through the point (2,6).
The equation of the line passing through the point (2,6) and perpendicular to the given line is y = 6.
Given data;
The line is horizontal, and the slope of the line is infinity.
The slope of the line perpendicular will be expressed as [tex]\frac{-1}{∞}[/tex] = 0
To get the equation of the line and passes through the point (2,6),
A line's equation in point-slope form is written as;
[tex]m = \frac{y-yo}{x-xo}[/tex]
As m is the slope of the line then,
The required equation will be:
y - 6 = 0*(x-2)
y - 6 = 0
y = 6
Hence, the equation of the line that is perpendicular to the given line and passes through the point (2,6) is y = 6.
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Mo has $90.00 already saved and has a job making $8.00 per hour. Merv already has $50.00 saved and has a job making $8.50 per hour. They both want to save enough money to buy a pair of airpods for $130.00.
Task 1 - Analyze Mo’s Story
Write Mo’s financial situation expressing their total dollar amount saved as a linear function of time (hours) in Slope Intercept Form. In a few sentences interpret what the slope represents in this situation. Interpret what the y-intercept means in terms of Mo’s financial story.
Task 2 - Analyze Merv’s Story
Write Merv’s financial situation expressing their total dollar amount saved as a linear function of time (hours) in Slope Intercept Form. In a few sentences interpret what the slope represents in this situation. Interpret what the y-intercept means in terms of Merv’s financial story.
Task 3 - Evaluate and Compare
Calculate who will reach their financial goal of purchasing the airpods if they both work 8 hours this week. Provide a full Algebraic solution and a paragraph explaining your reasoning. Make sure you use topic sentences to make a claim and transition words to support the claim, creating clear focus and logical order to your reasoning..
The total dollar amount saved by Mo is y = $90 + $8h. The y-intercept is the amount of money he has already saved, $90. The slope is the rate at which the amount saved would increase, $8.
The total dollar amount saved by Merv is y = $50 + $8.50h. The y-intercept is the amount of money he has already saved, $50. The slope is the rate at which the amount saved would increase, $8.50.
Mo would reach the goal. Because the total amount of money he would have saved is $154.
Who would reach the goal?A linear equation is an equation that has a single variable that is raised to the power of one. When drawn on a graph, a linear equation is a straight line.
The general form of a linear equation is:
y = mx + b
Where:
m = slope b = y-interceptThe equation that would be used to represent the total amount of money saved is:
Equation that represents the amount that should be saved by Mo:
y = $90 + $8h
Substitute h with 8
y = $90 + $8(8)
y = $90 + $64 = $154
The total dollar amount saved by Merv is:
y = $50 + $8.50h
Substitute h with 8
y = $50 + (8.50 x 8)
y = $50 + 68
y = 118
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The vertices of a triangle are L(0,1), M(1, - 2), and N(-2,1). Draw the figure and its image after the translation (x-3,y-4)
The coordinates of the translated of the image is as below
(-3, -3), (-2, -6), and (-5,-3)
What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Translation refers to a type of transformation that involve a linear movement.
Movements as seen in translation includes
leftrightupdownThe up and down movements are on the vertical direction controlled by the y coordinate. While the left and right movements are on the horizontal direction controlled by the x coordinate.
Applying the translation rule (x-3, y-4) the coordinates of the image is calculates as below
(0, 1) ⇒ (0-3, 1-4) ⇒ (-3,-3)
(1, -2) ⇒ (1-3, -2-4) ⇒ (-2,-6)
(-2, 1) ⇒ (-2-3, 1-4) ⇒ (-5, -3)
preimage image
(0, 1) (-3, -3)
(1, -2) (-2, -6)
(-2, 1) (-5, -3)
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What is the slope of the line that passes through the points (9, 5) and (21, -5)? Write your answer in simplest form.
Answer:
-5/6
Step-by-step explanation:
1. Label X1 AND Y1 and X2 AND Y2 (9(x1),5(x2)) (21(x2),-5(y2))
2. Use this formula [tex]\frac{y2-y1}{x2-x1}[/tex]=slope
3. Plug the numbers into the formula [tex]\frac{-5-5}{21-9}[/tex][tex]= - \frac{10}{12}[/tex]
4. Find the simplest form.
[tex]slope= - \frac{5}{6}[/tex]
Yaritza and her children went into a restaurant that sells hamburgers for $5 each and tacos for $2.50 each. Yaritza has $60 to spend and must buy at least 14 hamburgers and tacos altogether. If x represents the number of hamburgers purchased and y represents the number of tacos purchased, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities is
x + y ≥ 14
5x + 2.5y ≤ 60
Given, that Yaritza and her children went into a restaurant that sells hamburgers for $5 each and tacos for $2.50 each.
Yaritza has $60 to spend and must buy at least 14 hamburgers and tacos altogether.
As, x represents the number of hamburgers purchased and y represents the number of tacos purchased
Now, according to the question
x + y ≥ 14
as, she must buy at least 14 hamburgers and tacos altogether.
Now, 5x + 2.5y ≤ 60
as, she has $60 to spend.
So, we have two inequalities
x + y ≥ 14
5x + 2.5y ≤ 60
Hence, the system of inequalities for the given problem is
x + y ≥ 14
5x + 2.5y ≤ 60
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Use the five digits in an equation that has the answer of 42: 8 1 3 6 5
To pay for a home improvement project that totals $16,000, Genesis is choosing between taking out a simple interest bank loan at 8% for 3 years or paying with a credit card that compounds monthly at an annual rate of 15% for 7 years. Which plan would give Genesis the lowest monthly payment?
A. The monthly credit card payment would be $511.11, which is lower than the monthly payment on the bank loan.
B. The monthly payment on a bank loan would be $480, which is lower than the monthly credit card payment.
C. The monthly payment on a bank loan would be $551.11, which is lower than the monthly credit card payment.
D. The monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.
The monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.
What is simple interest?The simple interest earned can be calculated by using this formula
A = P(1 + rt)
A is the future value.
P is the principal value.
r is the interest rate.
t is the time.
Now Substituting the values into the formula, we have,
A = 16,000[1 + (0.08 × 3)]
A = 16,000[1 + 0.24]
A = 16,000× 1.24
Future value, A = $19,840.
Following that, we will compute the monthly payment over a 36-month period as follows:
Monthly payment = Future value/Time
Monthly payment = 19,840/36
Monthly payment = $551.11
Similarly, we will compute the credit card's compound interest:
A = 16000[1 + (0.15/12)]⁽¹² ˣ ⁷⁾
A = 16000[1 + 0.025]⁸⁴
A = 16000× 1.025⁸⁴
A = 9000 × 3.49258954
Future value, A = $45425.80
Following that, we will compute the monthly payment over an 84-month period as follows;
Monthly payment = Future value/Time
Monthly payment = 45425.80/84
Monthly payment = $540.78.
Thus, the monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.
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