48500 has been invested in total. Total invested at the end: $289,279.40. This exemplifies the need to allow your savings to increase over time.
Why do you use the word "investment"?An investments is a procurement made with both the intention of making money or increasing capital. Appreciate seems to be the term for just an asset's value growing over time. When someone invests in something, they do it with the intention of using it to generate cash later on instead of for current consumption.
Why do individuals invest?Investing is a wise method to use your money and may possibly increase your wealth. When your make intelligent investment choices, your cash can increase in value and outpace inflation.
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Find the following in slope intercept form
The equation of a horizontal line that passes through (4,2)
The equation of a horizontal line that passes through (4,2) in slope intercept form is y = 2.
A horizontal line has a slope of 0, which means that the y-value remains constant while the x-value changes. In slope intercept form, the equation of a line is written as y = mx + b, where m is the slope and b is the y-intercept.
Since the slope of a horizontal line is 0, the equation of a horizontal line can be written as y = 0x + b, or simply y = b. The y-intercept is the value of y when x = 0, which is the same as the y-value of any point on the line.
In this case, the line passes through the point (4,2), so the y-value is 2. Therefore, the equation of the line in slope intercept form is y = 2.
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For
each of the following, find the formula for an exponential function
that passes through the two points given.
a. (-1, 2/3) and (2,18)
f(x) =
b. (-1,7) and (2,4)
g(x) =
(If needed, round to 3 decim
The values of x are 0.732 and -2.732.
Given function:f(x) = g(x)We need to determine the value of x.For, f(x) = g(x), we have the following equation:f(x) = x^2 + 2x + 1 = 2x + 3g(x) = 2x + 3To solve for x, we can substitute the value of g(x) in the first equation:x^2 + 2x + 1 = g(x)Substituting g(x) = 2x + 3 in the above equation:x^2 + 2x + 1 = 2x + 3x^2 + 2x - 2 = 0x^2 + 2x - 2 = 0Applying the quadratic formula, we get:$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$Where, a = 1, b = 2, and c = -2Substituting the values in the formula, we get:$$x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-2)}}{2(1)}$$$$x = \frac{-2 \pm \sqrt{12}}{2}$$$$x = -1 \pm \sqrt{3}$$Therefore, the value of x is x = -1 + √3 or x = -1 - √3.To round off the answer to 3 decimal places, we get:x = -1 + 1.732 = 0.732 or x = -1 - 1.732 = -2.732Hence, the values of x are 0.732 and -2.732.
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Given the matrices A = [3/4 0] and B = [-4 0]
[0 ¾] [0 -4] 2a) Compute AB 2b) Compute BA.
2c) How did your answer in part (a) and part (b) compare? 2d) Will this be true, in general, for any two matrices when you multiply them (assuming their dimensions line up so that they may be multiplied)? If so, explain your reasoning If not, show an example of two matrices C and such that CD+DC.
The matrices A and B are given as:
A = [3/4 0]
[0 3/4]
B = [-4 0]
[0 -4]
2a) Compute AB:
AB = [3/4 0] * [-4 0]
[0 3/4] [0 -4]
= [3/4 * -4 + 0 * 0 3/4 * 0 + 0 * -4]
[0 * -4 + 3/4 * 0 0 * 0 + 3/4 * -4]
= [-3 0]
[0 -3]
2b) Compute BA:
BA = [-4 0] * [3/4 0]
[0 -4] [0 3/4]
= [-4 * 3/4 + 0 * 0 -4 * 0 + 0 * -4]
[0 * 3/4 + -4 * 0 0 * 0 + -4 * 3/4]
= [-3 0]
[0 -3]
2c) How did your answer in part (a) and (b) compare?
The answers in part (a) and (b) are the same. Both AB and BA resulted in the matrix [-3 0] [0 -3].
2d) Will this be true, in general, for any two matrices when you multiply them (assuming their dimensions line up so that they may be multiplied)? If so, explain your reasoning. If not, show an example of two matrices C and D such that CD≠DC.
No, this will not be true in general for any two matrices when you multiply them. The order in which matrices are multiplied matters, and in most cases, AB≠BA. Here is an example of two matrices C and D such that CD≠DC:
C = [1 2]
[3 4]
D = [5 6]
[7 8]
CD = [1 * 5 + 2 * 7 1 * 6 + 2 * 8]
[3 * 5 + 4 * 7 3 * 6 + 4 * 8]
= [19 22]
[43 50]
DC = [5 * 1 + 6 * 3 5 * 2 + 6 * 4]
[7 * 1 + 8 * 3 7 * 2 + 8 * 4]
= [23 34]
[31 50]
As you can see, CD≠DC.
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hiranda T Show all of the work of how you List the correct answer and circle or highlight it. ((7)/(8)+(1)/(2))/(2(1)/(4))
On simplifying ((7)/(8)+(1)/(2))/(2(1)/(4)) the correct answer is 2 3/4.
To solve the problem ((7)/(8)+(1)/(2))/(2(1)/(4)), we can follow these steps:
Step 1: Simplify the expression inside the parentheses in the numerator.
(7/8) + (1/2) = (7/8) + (4/8) = (11/8)
Step 2: Simplify the expression inside the parentheses in the denominator.
2(1/4) = (2/1)(1/4) = (2/4) = (1/2)
Step 3: Divide the simplified numerator by the simplified denominator.
(11/8) ÷ (1/2) = (11/8) × (2/1) = (22/8) = (11/4)
Step 4: Simplifying the final expression, if possible.
(11/4) = 2 3/4
Therefore, the correct answer is 2 3/4.
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In a group of 39 students, 14 study both Art and Biology. 5 study Biology but not Art. 6 study neither subject. How many study Art?
Answer:
11
Step-by-step explanation:
What is the measure of arc IJ?
Check the picture below.
PLSSS HELP IF YOU TURLY KNOW THISSS
Answer:
-8=x
Step-by-step explanation:
-6=x+2
take away 2 from each side
-8= x
Answer:
x = -8
Step-by-step explanation:
To solve for x in equation 3(x - 2) = 4x + 2, we need to simplify the expression on the left side of the equation by using the distributive property. This gives:
3x - 6 = 4x + 2
Next, we need to isolate the variable x on one side of the equation. We can do this by adding 6 to both sides of the equation:
3x - 6 + 6 = 4x + 2 + 6
Simplifying this expression, we get:
3x = 4x + 8
Now, we need to isolate x again by subtracting 4x from both sides:
3x - 4x = 4x + 8 - 4x
Simplifying this expression gives:
-x = 8
Finally, we solve for x by multiplying both sides of the equation by -1:
x = -8
Therefore, the solution to the equation 3(x-2) = 4x + 2 is x = -8.
In a group of 30 students, 12 take Mathematics, 16 take Art, and 18 take History. If each student takes at least one subject and no one takes all three, then what is the number of students taking exactly 2 subjects?
There are 23 students taking exactly 2 subjects.
To find the number of students taking exactly 2 subjects, we can use the formula:
n(A∩B∩C) = n(A) + n(B) + n(C) - 2n(A∩B) - 2n(B∩C) - 2n(C∩A) + 3n(A∩B∩C)
Since we know that no one takes all three subjects, n(A∩B∩C) = 0. We can plug in the values given in the question and solve for n(A∩B), which represents the number of students taking exactly 2 subjects:
0 = 12 + 16 + 18 - 2n(A∩B) - 2(0) - 2(0) + 3(0)
0 = 46 - 2n(A∩B)
2n(A∩B) = 46
n(A∩B) = 23
Therefore, the number of students taking exactly 2 subjects is 23.
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PLEASE HELP ASAP!!!!!!!!!!!
A cylinder has a volume of 1 1/3 and a radius of 1/3 in. What is the height of the cylinder?
the height of the cylinder is 12/π inches. This is an exact value, but if you want an approximate decimal value, you can use a calculator and substitute 3.14 or 22/7 for π. For example, if we use π ≈ 3.14, we get:
h ≈ 12/3.14
h ≈ 3.822 inches (rounded to three decimal places)
what is
1) y=2x
y=x+15
2) 2x+5y=55
-6x+y=-4
(systems of equations
Answer:
53
Step-by-step explanation:
becuas eyou divide it all togtheir and then subtract 42 from 83 and you ga the anwer
please help asap and show work please o
The correct coordinates for N' after a 180° rotation about the origin are (-3, -4).
Ari's likely error was that they incorrectly flipped the signs of the coordinates independently.
How to explain the coordinatesIt should be noted that to rotate a point 180° about the origin, we need to flip the sign of both coordinates of the point. Therefore, the correct coordinates for N' after a 180° rotation about the origin are (-3, -4), not (-4, 3) as Ari claimed.
Ari's likely error was that they incorrectly flipped the signs of the coordinates independently, rather than flipping both signs together. This mistake could have arisen from a misunderstanding of the geometric concept of rotation or a simple arithmetic error.
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A. Write an expression that is equivalent to m + m + m + m that is the product of a coefficient and a variable.
B. Write an expression that is equivalent to m + m + m + m that is the sum of two terms.
The expression that is equivalent to m + m + m + m that is the product of a coefficient and a variable is 4m, where 4 is the coefficient and m is the variable.
What are algebraic expressions?
An algebraic expression is a mathematical phrase that contains one or more variables, numbers, and arithmetic operations (such as addition, subtraction, multiplication, and division). It can also include exponents, roots, and other mathematical symbols.
Algebraic expressions are used to represent mathematical relationships and to solve problems in various areas of mathematics, science, and engineering. Examples of algebraic expressions include 3x + 5, 2y - 7, and 4x² - 3xy + 2.
A. The expression that is equivalent to m + m + m + m that is the product of a coefficient and a variable is 4m, where 4 is the coefficient and m is the variable.
B. The expression that is equivalent to m + m + m + m that is the sum of two terms is 2m + 2m, where 2m is one term and the other term is also 2m.
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There are "D" defective motherboards in a package of 100 motherboards. Two motherboards are randomly selected. Here, D = Last 2 digits of your student ID. Let, Y be the random variable that represents number of defective motherboards selected. a. Find the Probability Mass Function of Y. [3] b. Find the Cumulative Distribution Function of Y. [2] c. Find the mean of Y. [2] d. Find the standard deviation of Y. [3]
The standard deviation of Y is 0.49.
Let's assume that D=20 (the last two digits of your student ID). Therefore, there are 20 defective motherboards in a package of 100 motherboards.
The Probability Mass Function (PMF) of Y is given by:
P(Y=0) = (80/100)*(79/99)
=> 0.64
P(Y=1) = (20/100)*(80/99) + (80/100)*(20/99)
=> 0.32
P(Y=2) = (20/100)*(19/99)
=> 0.04
The Cumulative Distribution Function (CDF) of Y is given by:
P(Y<=0) = P(Y=0)
=> 0.64
P(Y<=1) = P(Y=0) + P(Y=1)
=> 0.64 + 0.32
=> 0.96
P(Y<=2) = P(Y=0) + P(Y=1) + P(Y=2)
=> 0.64 + 0.32 + 0.04
=> 1
The mean of Y is given by:
E(Y) = 0*P(Y=0) + 1*P(Y=1) + 2*P(Y=2)
=> 0 x 0.64 + 1 x 0.32 + 2 x 0.04
= 0.4
The standard deviation of Y is given by:
Var(Y) = SD(Y)
=> [tex]\sqrt{(Var(Y))[/tex]
=>[tex]\sqrt{(0.24)[/tex]
=> 0.49
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2x+5y=5solve for x
3x-2y=9 solve for y
The solution for each expression is given as follows:
2x + 5y = 5 for x -> x = 2.5(y - 1).3x - 2y = 9 for y -> y = 1.5(x - 3).How to solve the expressions?To solve an expression for a variable, we isolate the desired variable applying the inverse operations.
The solution for x of the first expression is obtained as follows:
2x + 5y = 5
2x = 5y - 5
x = 5(y - 1)/2
x = 2.5(y - 1).
The solution for y of the second expression is obtained as follows:
3x - 2y = 9
2y = 3x - 9
2y = 3(x - 3)
y = 3/2(x - 3)
y = 1.5(x - 3).
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5(y+x)-6(x-y)=-8 asses through the point (14,3) and is perpendicular to the given
The equation of the line that passes through the point (14,3) and is perpendicular to the given equation is y = x - 11.
To solve the equation 5(y+x)-6(x-y)=-8, we need to use the distributive property and combine like terms.
5(y+x)-6(x-y)=-8
Distribute the 5 and -6:
5y + 5x - 6x + 6y = -8
Combine like terms:
11y - x = -8
Now, we need to find the slope of the line that passes through the point (14,3) and is perpendicular to the given equation.
The slope of the given equation is -1, so the slope of the perpendicular line is the negative reciprocal, which is 1.
Using the point-slope form, we can write the equation of the perpendicular line:
y - 3 = 1(x - 14)
Distribute the 1:
y - 3 = x - 14
Add 3 to both sides:
y = x - 11
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Please, help I need this done today and show work.
The points (1, 1) and (2, 2) have been used to graph the inequality as shown in the image attached below.
The boundary line is dashed.
The boundary line is shaded below.
What are the rules for writing an inequality?In Mathematics, there are two (2) main rules that are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph and these include the following:
The line on a graph should be a solid line when the inequality symbol is (≥ or ≤).The line on a graph should be a dashed (dotted) line when the inequality symbol is (> or <).Additionally, the point (2, 2) and point (1, 1) are not solutions to the given inequality y < 1/4(x) + 1 because the lie below the boundary line
y < 1/4(x) + 1
2 < 1/4(2) + 1
2 < 3/2 (False)
y < 1/4(x) + 1
1 < 1/4(1) + 1
2 < 5/4 (False)
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19. sin!/2 x cos x – sin5/2 x cos x = cos x/sin x 20. secx(sec x tan x) - sec4 x(sec x tan x) sec5 x tanx -
cosx = cos4x = cos5x.
19. Using the identity sin2x + cos2x = 1, we can rewrite the equation as:
sin2x/2 - sin2x/2 = cosx/sinx
Simplifying both sides: cosx/sinx = 0
Therefore, cosx = 0 and sinx = 0.
20. Using the identities secx = 1/cosx, tanx = sinx/cosx, and sec2x = 1 + tan2x, we can rewrite the equation as:
secx(secx tanx) - sec4x(secx tanx) = sec5x tanx
Simplifying: secx - sec4x = sec5x
Therefore, secx = sec4x = sec5x.
Simplifying further: 1/cosx = 1/cos4x = 1/cos5x
Therefore, cosx = cos4x = cos5x.
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Consider the following all integer linear program
Max 1x1+1x2
s.t.
4x1+6x2 less than or equal to 22
1x1+5x2 less than or equal to 15
2x1+1x2 less than or equal to 9
x1,x2 greater than or equal to 0 and integer
A) graph the constraints of the problem
B) solve the LP relaxation of this problem
C) find the optimal integer solution
A) To graph the constraints of the problem, we need to rearrange each constraint into slope-intercept form (y = mx + b) and plot them on a graph.
For the first constraint, 4x1+6x2 <= 22, we can rearrange it as follows:
6x2 <= -4x1 + 22
x2 <= (-2/3)x1 + (22/6)
For the second constraint, 1x1+5x2 <= 15, we can rearrange it as follows:
5x2 <= -1x1 + 15
x2 <= (-1/5)x1 + (15/5)
For the third constraint, 2x1+1x2 <= 9, we can rearrange it as follows:
1x2 <= -2x1 + 9
x2 <= (-2)x1 + 9
We can now plot these constraints on a graph with x1 on the x-axis and x2 on the y-axis.
B) To solve the LP relaxation of this problem, we can use the simplex method. The objective function is Max 1x1+1x2. The constraints are 4x1+6x2 <= 22, 1x1+5x2 <= 15, 2x1+1x2 <= 9, x1 >= 0, and x2 >= 0.
Using the simplex method, we can find that the optimal solution is x1 = 3 and x2 = 2, with an objective function value of 5.
C) To find the optimal integer solution, we can use the branch and bound method. We start with the LP relaxation solution of x1 = 3 and x2 = 2. Since this is already an integer solution, it is the optimal integer solution. The objective function value is 5.
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Isabella bought a new dress for the Spring Dance that was on sale for 35% off the regular price of $135. 00 The total cost included 8. 5% sales tax. What was the total cost?
The total cost of the dress including sales tax is 95.21.
The amount of discount that Isabella received on the dress is:
35% of 135.00 = 0.35 x 135.00 = 47.25
So, the price she paid for the dress after the discount is:
135.00 - 47.25 = 87.75
To find the total cost including sales tax, we need to add the sales tax to the price of the dress:
Sales tax = 8.5% of 87.75 = 0.085 x 87.75 = 7.46
Total cost = Price of dress after discount + Sales tax
= 87.75 + 7.46
= 95.21
Therefore, the total cost of the dress including sales tax is 95.21.
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help please! giving brainliest and reward for this is 100 points. and if you dont mind giving a explanation to it that is what i mainly need but thanks help please!!1
not completely sure
3x25=75
answer 75
i think so bye
Two students, Stella and Vladimir, completed the conversion
statement 12 feet 8 inches =
inches.
Stella stated that 12 feet 8 inches = 152 inches.
Vladimir stated that 12 feet 8 inches = 9 inches.
Which student is incorrect? Explain.
1. Highlight the measurement to be converted.
2.
Into what units do the students need to convert the given
measurement? Explain.
3.
Is a conversion factor given for the students in the problem? If not,
where could they find it?
4. Circle Stella’s and Vladimir’s answers. Explain how they are different.
5. Which student’s answer is more reasonable? Explain.
6. Should your final answer be a number? Explain.
1. Completing the conversion of 12 feet 8 inches to inches, Stella who stated that 12 feet 8 inches = 152 inches is correct unlike Vladimir who got 9 inches.
2. Stella and Vladimir need to convert the given measurement into inches.
3. No conversion factor is given for the problem. However, the conversion factor could be found online or using the mathematical table.
4. Stella's and Vladimir's answers differ because Vladimir failed to convert the feet into inches.
5. Stella's answer is more reasonable, and it is correct because 12 feet equal 144 inches plus 8 inches, giving 152 inches.
6. The final answer should not just be a number without indicating the unit of measurement.
What is unit conversion?A unit conversion is the mathematical expression of the same property in a different unit of measurement.
For instance, instead of stating distance in kilometers, it can be depicted in miles. Similarly, instead of reporting time in hours, it can be reported in minutes or seconds.
1 foot = 12 inches
12 feet = 144 inches
12 feet 8 inches = 152 inches (12 x 12 + 8)
Thus, in this situation, the measurement to be converted is feet to inches.
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two runners are racing against each other. jeri graphs a linear equation for each runner that shows the runners distance from the starting line over time. the two equations form a system that has infinitely many solutions. describe the intersection points of the lines an situations explain what solution means in this
Answer:If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. the intersection points (-3,3) Since the system is infinite it means there is 1 line on the graph-
Step-by-step explanation:
The answer I choose was wrong I need help choosing the right one
The value of the length WY is 40√3 mm. Option J
How to determine the measure of the lengthThe different types of trigonometric identities are;
cotangenttangentcosinesinesecantcosecantFrom the information given, we have that;
Opposite side = WY
Angle of elevation, θ = 60 degrees
Adjacent side = 40mm
Now, let's use the tangent identity;
tan θ = WY/40
substitute the value
tan 60 = WY/40
cross multiply
WY = 40 × √3
Multiply the values
WY = 40√3 mm
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the cost of a ticket to the circus is $15 for children and $40 for adults. on a certain day ,attendance at the circus was 1,000 and the total gate revenue was $30,000. How many children and how many adults bought tickets?
400 children and 600 adults bought tickets to the circus.
Let's call the number of children who bought tickets "C" and the number of adults who bought tickets "A". We can set up two equations to represent the information given in the question:
C + A = 1000 (the total number of people who bought tickets)
15C + 40A = 30000 (the total gate revenue)
We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for C in terms of A:
C = 1000 - A
Now we can substitute this equation into the second equation to solve for A:
15(1000 - A) + 40A = 30000
15000 - 15A + 40A = 30000
25A = 15000
A = 600
So 600 adults bought tickets. We can use the first equation to find the number of children who bought tickets:
C + 600 = 1000
C = 400
So 400 children bought tickets. Therefore, the answer is that 400 children and 600 adults bought tickets to the circus.
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Town A and Town B are located at the points shown in the diagram. Mr. Peterson
wants to drive from Town A to Town B. He can choose between the route that takes
him through Towns P and Q, or the route that takes him through Town R. Each unit on
the grid equals 1 kilometer.
Answer:
To find the shorter route, we need to calculate the distances for both routes and compare them.
Route through Towns P and Q:
The distance between Town A and Town P is 3 units to the right and 5 units up, so it is √(3² + 5²) = √34 km.
The distance between Town P and Town Q is 2 units to the right, so it is 2 km.
The distance between Town Q and Town B is 4 units to the right and 4 units down, so it is √(4² + 4²) = 4√2 km.
Therefore, the total distance for this route is √34 + 2 + 4√2 km.
Route through Town R:
The distance between Town A and Town R is 5 units to the right and 3 units up, so it is √(5² + 3²) = √34 km.
The distance between Town R and Town B is 5 units to the right and 7 units down, so it is √(5² + 7²) = √74 km.
Therefore, the total distance for this route is √34 + √74 km.
Comparing the distances, we can see that:
√34 + 2 + 4√2 km ≈ 10.2 km
√34 + √74 km ≈ 12.6 km
Therefore, the shorter route is the one that goes through Towns P and Q, which is approximately 10.2 km long.
PLEASE HELP ME ASAP TRIPLE THE BRAINLY!
slope = -1/5
used slope forumula
Sheng has two credit cards. He used his credit card statements to make the summary table that follows. Sheng is also eligible for a debt consolidation loan with an APR of 10.7% that reduces his monthly payments to $179.37. This loan will take six years to pay off, and Sheng will pay a total of $3,414.39 in interest charges. How much more in interest charges will the debt consolidation loan cost Sheng?
The debt consolidation loan will cost Sheng an additional $1,997.69 in interest charges compared to his credit cards.
Calculating how much more in interest the debt consolidation loan will cost ShengFrom question, we are to calculate how much more in interest the debt consolidation loan will cost Sheng
To calculate the interest charges for Sheng's credit cards, we need to use the following formula:
Interest Charges = Balance x APR x Number of Days in Billing Cycle / 365
Using this formula, we can calculate the interest charges for each of Sheng's credit cards:
For Credit Card A:
Interest Charges = $2,500 x 0.19 x 30 / 365 = $4.94
For Credit Card B:
Interest Charges = $3,000 x 0.22 x 30 / 365 = $6.01
So, the total interest charges for Sheng's credit cards are:
Total Interest Charges = $4.94 + $6.01 = $10.95
Now, let's calculate the total cost of the debt consolidation loan:
Total Cost = Total Monthly Payments x Number of Payments - Loan Amount
Total Monthly Payments = $179.37
Number of Payments = 6 x 12 = 72
Loan Amount = ?
To find the loan amount, we need to solve for it using the interest rate and the total interest charges:
Loan Amount = Total Interest Charges / (APR x Number of Payments / 12)
Loan Amount = $3,414.39 / (0.107 x 72 / 12) = $25,000
So, the total cost of the debt consolidation loan is:
Total Cost = $179.37 x 72 - $25,000 = $2,008.64
Therefore, the additional interest charges for the debt consolidation loan compared to Sheng's credit cards are:
Additional Interest Charges = Total Cost - Total Interest Charges
Additional Interest Charges = $2,008.64 - $10.95 = $1,997.69
Hence, the debt consolidation loan will cost him an additional $1,997.69 in interest charges
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Please help and provide steps if you can
Which numbers below are ratonal? (Select all that apply)
A. -7
B. 36.545454....
C. 9.149278643
D. 7/11
E. 10√
F. 25√+ 3
G. 2√+9√
model with a proportion
The decrease in price for notebooks was $1.60, a 40% decrease. What was al original price and what is the new price?
The new price of the notebooks is $2.40.
To find the original price and the new price of the notebooks, we can use a proportion model. Let's call the original price "x" and the new price "y".
The proportion model for this problem would be:
40/100 = 1.60/x
To solve for x, we can cross-multiply:
40x = 100(1.60)
And then divide both sides by 40:
x = 4
So the original price of the notebooks was $4.00. To find the new price, we can subtract the decrease in price from the original price:
y = x - 1.60
y = 4 - 1.60
y = 2.40
So the new price of the notebooks is $2.40.
40/100 = 1.60/4
0.4 = 0.4
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