Answer:
The nth term is aₙ = 5n - 6-------------------------------------
Given sequence:
-1, 4, 9, 14, ...We observe that it has a linear increase and common difference of terms is 5:
4 - (-1) = 9 - 4 = 14 - 9 = 5So d = 5, a₁ = - 1, find the nth term:
aₙ = a₁ + (n - 1)daₙ = - 1 + (n - 1)*5 = - 1 + 5n - 5 = 5n - 6write a statement that associates s with a set that contains the following elements: 23, 42, -11, 89.
A statement that associates s with a set that contains the following elements: 23, 42, -11, 89 is s = set ( [ 23 , 42 , -11 , 89 ] )
Given :
a statement that associates s with a set that contains the following elements: 23, 42, -11, 89.
Statement :
A statement is an instruction that the Python interpreter can execute.
We have seen two kinds of statements: print and assignment.
When you type a statement on the command line, Python executes it and displays the result, if there is one. The result of a print statement is a value.
we can write :
s = set ( [ 23 , 42 , -11 , 89 ] )
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how many degrees was the figure rotated; rotate the point (-3,-4) around the origin 180 degrees; rotate the point (7 8) around the origin 90 degrees; rotate the point (7 8) around the origin 90 degrees counterclockwise; if you were to rotate abcd 180; rotate the point (-3,-4) around the origin 180 degrees. what is the image of the point?; if you were to rotate abcd 90 degrees counterclockwise; what is the angle of rotation for this counterclockwise rotation about the origin
a) 270° counter clockwise rotation of figure 1
b) The image of point (-3,-4) is (3,4).
c) The new image of point (7,8) is (8,-7) after 90° degree clockwise rotation.
d) The new image of point (7,8) is (-8,7) after 90° degree anticlockwise rotation
e) The fig. abcd will moves to second quardent after 90° counter clockwise rotation.
f) The rotation angle of figure is 270° , in the counterclockwise direction about origin.
A rotation is an isometric transformation that turns every point of a figure through a specified angle and direction about a fixed point.
To describe a rotation, you need three things:
Direction (clockwise or counterclcokwise.
Angle in degreesCenter point of rotationRotations About The Origin90 Degree Rotation:
When rotating a point 90 degrees counterclockwise about the origin of a point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
180 Degree Rotation :
When we rotating a point 180 degrees counterclockwise about the origin a point A(x,y) it becomes A'(-x,-y). So all we do is make both x and y negative.
We have given that,
a) The given figure is rotated aoround 90° clockwise or 270° counter clockwise.
b) A point (-3,-4) is rotated around the origin 180 degrees , then the new point or position after the rotation is (3,4).
c) Rotate the point (7 , 8) around the origin 90 degrees , the new point or image of (7,8) is ( 8,-7).
d) If a point (7,8) is rotate around the origin 90 degrees counterclockwise then new point is (-8,7).
e) If you were to rotate abcd 90 degrees counterclockwise then the image of figures abcd will enter in quadrent 2nd with all coordinate changes.
f) when a figure is rotated in counterclockwise rotation about the origin the angle of rotation is 270 degrees.
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use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 y2/3
The equation of the tangent line to the curve at the given point (−3, 3, 1) (asteroid) is y-[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}(x+3)[/tex]
Applying implicit differentiation, the equation of the tangent line is given by:
y - [tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex] (x+3)
The equation of a line tangent to a function f(x) at a point (x0, y0) is given by:
y-y0 = f'(x0,y0)(x-x0)
In this problem, point (-3, [tex]\sqrt{3}[/tex]), thus x0 = -3, y0 = [tex]\sqrt{3}[/tex]
The function is:
[tex]x^{2} /3+ y^{2}/3 = 4\\[/tex]
To find the derivative, we have to apply implicit differentiation, thus:
[tex]2x/3* dx/dx + 2y/3*dy/dx = 0[/tex]
[tex]2y/3*dy/dx = -2x/3[/tex]
[tex]dy/dx = -x/y[/tex]
Thus:
[tex]f(-3, \sqrt{3)} = -(-3/\sqrt{3} * \sqrt{3}/\sqrt{3})[/tex] = [tex]\sqrt{3}[/tex]
Then, the equation to the line tangent is:
y-y0 = f'(x0,y0)(x-x0)
y-[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}(x+3)[/tex]
Refer to this complete question:
Use implicit differentiation to find an equation of the tangent line to the curve at the given point x2/3 + y2/3 = 4 (−3, 3, 1) (asteroid).
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Bob the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 3 clients who did Plan A and 8 who did Plan B. On Tuesday there were 5 clients who did Plan A and 2 who did Plan B. Bob trained his Monday clients for a total of 15 hours and his Tuesday clients for a total of 8 hours. How long does each of the workout plans last?
The number of hours that plan A last is 1 hour and the number of hours that plan B last is 1 1/2 hours.
How long does each workout last?The first step is to form a system of equations using the information in the question:
3a + 8b = 15 equation 1
5a + 2b = 8 equation 2
Where:
a = length of plan A b = length of plan BThe elimination method would be used to determine the required values
In order to determine the value of a, multiply equation 2 by 4
20a + 8b = 32 equation 3
Subtract equation 1 from equation 3 :
17a = 17
Divide both sides of the equation by 17
a = 17/17
a = 1 hour
Substitute for a in equation 1 :
3(1) + 8b = 15
3 + 8b = 15
8b = 15 - 3
8b = 12
b = 12 / 8
b = 1 4/8 = 1 1/2 hours
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2. Mateo graphs quadrilateral EFGH and then reflects it across the
line y = 2. How are the x-coordinates of corresponding points in
the image and the preimage related?
After reflecting the quadrilateral EFGH across the line y = 2, the x-coordinates of the corresponding points in the image and the preimage will be the same.
What is Reflection?Generally, Reflection is an isometry, which means that it preserves distance and angles. Therefore, the x-coordinates of the points in the image and the preimage will not be changed by the reflection. The y-coordinates will change since the reflection flips the points over the line of reflection.
For example, if quadrilateral EFGH has a vertex at (x, y), then the corresponding vertex in the image will be at (x, 2 - y). The x-coordinate remains the same, but the y-coordinate is reflected across the line y = 2.
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prove that the composition of two isometries is an isometry and the inverse of an isometry is an isometry.
The composition of two isometries is an isometry.
Proof:
Let T1 and T2 be isometries. T1(A) = A' and T1(B) = B'. Therefore by isometry T1, AB = A'B'
T2(A) = A'' and T2(B) = B''. Therefore by isometry T2, AB = A''B''
T2 º T1 = T2(T1(A)) = T2(A') = A'''. T2 º T1 = T2(T1(A)) = T2(B') = B'''. Therefore under composition AB = A'''B''' and distance is preserved.
The inverse of an isometry is an isometry.
Proof:
Given T and isometry. This means T(A) = A' and T(B) = B' with AB = A'B'
The inverse of T, T⁻¹maps A' to A and B' to B, so A'B' maps to AB.
But A'B' = AB and so the inverse is an isometry
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I need help with this problem
Answer:
Point slope: y - 115 = 2(x -30)
Slope intercept: y = 2x + 55
Step-by-step explanation:
I choice the first point to write the equation in the point slope form of a line.
(30,115)
Slope is the change in y over the change in x. I see that the y's are increasing by 10, while the x's are increasing by 5
10/5 = 2
The slope is 2
y = y = m( x + x)
y - 115 = 2(x - 30)
Slope intercept form of a line
We already found the slope to be 2. Use the slope and the point (30,115) to find x
y = mx + b
115 = 2(30) + b
115 = 30 + b Subtract 30 from both sides
55 = b
y = 2x + 55
How many square feet is a 20×20 room?
Answer:
400 square feet
Step-by-step explanation:
Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of 4.2 telephone orders per hour. (a) Find the median waiting time until the next telephone order. (b) Find the upper quartile of waiting time before the next telephone order. (c) What is the upper 10 percent of waiting time until the next telephone order? Show all calculations clearly.
a) The median waiting time until the next telephone order is of: 2.91 minutes.
b) The upper quartile of waiting time before the next telephone order is of: 5.82 minutes.
c) The upper 10% of waiting time until the next telephone order is of: 9.67 minutes.
What is the exponential distribution?The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The mean for this problem is of:
m = 4.2.
Hence the decay parameter is of:
[tex]\mu = \frac{1}{4.2} = 0.2381[/tex]
The mass function is then given as follows:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
Hence:
[tex]P(X \leq x) = 1 - e^{-0.2381x}[/tex]
The median time is the value of x for which P(X < x) = 0.5, hence:
[tex]0.5 = 1 - e^{-0.2381x}[/tex]
[tex]e^{-0.2381x} = 0.5[/tex]
[tex]\ln{e^{-0.2381x}} = \ln{0.5}[/tex]
-0.2381x = ln(0.5)
x = -ln(0.5)/0.2381
x = 2.91 minutes.
The upper quartile is the value of x for which P(X < x) = 0.75, hence:
[tex]0.75 = 1 - e^{-0.2381x}[/tex]
[tex]e^{-0.2381x} = 0.25[/tex]
[tex]\ln{e^{-0.2381x}} = \ln{0.25}[/tex]
-0.2381x = ln(0.25)
x = -ln(0.25)/0.2381
x = 5.82 minutes.
The upper 10% is the value of x for which P(X < x) = 0.9, hence:
[tex]0.9 = 1 - e^{-0.2381x}[/tex]
[tex]e^{-0.2381x} = 0.1[/tex]
[tex]\ln{e^{-0.2381x}} = \ln{0.1}[/tex]
-0.2381x = ln(0.1)
x = -ln(0.1)/0.2381
x = 9.67 minutes.
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Irlene invested $3,500 in a high-interest savings account for three years. For the first year, the interest rate was 9% compounded semi-annually. For the second year the rate became 5.25% with the same compounding period. For the third year the rate remained the same but it was compounded quarterly. What was the value of the investment at the end of the third year? For full marks your final answer should be rounded to the nearest cent.
Rounded to the nearest cent, the final value of Irlene's investment at the end of the third year is $4,431.78.
What is the easiest way to define interest rate?A percentage of the principal, or the amount loaned, is what a lender charges a borrower as interest. The annual percentage rate, or APR, is the usual unit used to express the interest rate on a loan (APR).
To calculate the value of Irlene's investment at the end of the third year, you can use the formula for compound interest:
FV = PV * (1 + r/n)^(n*t)
Where:
FV is the future value of the investment (what you want to find)
PV is the present value of the investment (the initial amount, $3,500)
r is the annual interest rate (the rate for the third year is 5.25%)
n is the number of compounding periods per year (for the first year it was 2, for the second year it was 2, and for the third year it was 4)
t is the number of years the money is invested (3 years in this case)
Plugging the values into the formula, you get:
FV = $3,500 * (1 + 5.25%/2)^(23) * (1 + 5.25%/4)^(41)
= $3,500 * (1.0263)^6 * (1.0131)^4
= $3,500 * 1.1496 * 1.0534= $4,431.77
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suppose that and use phasors to reduce the sum to a single term of the form draw a phasor diagram, showing and state the phase relationships between each pair of these phasors
Answer:
I hope the best for you
Step-by-step explanation:
have a good day :)!!
What is the answer for this question?
The percentage of having a probability of a non-vowel letter is 44%
What is ProbabilityProbability is the measure of the likelihood that an event will occur in a given set of circumstances. It is a quantifiable measure of the chance of something happening. Probability is expressed as a number between 0 and 1 (or 0% to 100%) where the higher the number, the more likely the event is to occur.
The probability to select a vowel letter is = 15 + 22 + 11 + 6 + 2 = 56%
The probability of selecting any vowel is 56%
In the English alphabet, we have 26 letters and 5 vowel letters.
The probability of not having a vowel letter is calculated as;
26 - 5 = 21
P = 21 / 28
In percentage, we can simply say the probability of having a non-vowel is 100 - 56 = 44
The percentage of having a non-vowel is 44%
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n april 1, the men's furnishings department had an opening inventory of $168,000 at cost with a markup of 48.5%. during the month the buyer purchased additional merchandise which cost $80,000 with a 52.5% markup. determine the cumulative markup percent for the department at the end of
Cumulative markup percent for department at the end is 23.1%.
The men's furnishing department had an opening inventory of $168,000 at cost with a markup of 48.5%
Cumulative markup is the difference between the total wholesale cost and total retail price of all merchandise handled during a given period of time.
cumulative markup dollars are the total markup dollars on all merchandise for a selected selling period. To calculate cumulative markup dollars and cumulative markup percent, the following formulas are utilized by the retailer:
Cumulative Markup $ = Total Retail $ - Total Cost $
Cumulative Markup % = Cumulative Markup $ ÷ Cumulative Retail $
Steps for calculating cumulative markup percentage for the specified period of time:
Step 1. Calculate the unknown retail value for either opening inventory or purchases.
Step 2. Calculate total retail of opening inventory and purchases.
Step 3. Calculate the unknown cost value for either opening inventory or purchases.
Step 4. Calculate total cost of opening inventory and purchases.
Step 5. Calculate total markup dollars.
Step 6. Calculate cumulative markup percent for the specified period of time.
For opening inventory
retail = $168,000
cost = 168,000*48.5/100 = $81480
For purchases
retail = 80,000*52.5/100 = $42000
cost = $80,000
total retail of opening inventory and purchase =
168,000+42000 = $210000
total cost of opening inventory and purchase =
81480+80,000 = $161480
total markup = total retail - total cost
total markup = 210000-161480 = 48520
cumulative markup percent = (total markup/ total retail)
= (48520/210000)*100
= 0.23104761904*100
=23.1%
So cumulative markup percent for department at the end is 23.1%.
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Cos(75) using cos(a+b)
Answer:
[tex]\sqrt{6}[/tex]/4 – [tex]\sqrt{2}[/tex]/4
Step-by-step explanation:
cos(a + b) = cos (a) cos(b) – sin (a) sin (b)
cos(75) =
cos(45 + 30) = ==> break it down into more solvable angles
cos (45) cos(30) – sin (45) sin (30) =
[tex]\sqrt{2}[/tex]/2 * [tex]\sqrt{3}[/tex]/2 – [tex]\sqrt{2}[/tex]/2 * 1/2 = ==> simplify
([tex]\sqrt{2}[/tex]*[tex]\sqrt{3}[/tex])/(2*2) – ([tex]\sqrt{2}[/tex]*1)/(2*2) =[[tex]\sqrt{6}[/tex]/4 – [tex]\sqrt{2}[/tex]/4]
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1 out of 35 students is going on a field trip. What is the ratio of the number of students who are staying at school to the number of students who are going on the field trip?
Answer:
35:1 because that is the most likely answer
What are the 5 properties of rhombus and rectangle?
1. Opposite angles are equal in measure.
and
2. Diagonals bisect each other.
3. Any two adjacent angles add up to 180 degrees.
Properties of rhombus:
1. All sides are equal in length.
2. Opposite angles are equal.
3. Diagonals bisect each other at 90°.
4. Diagonals are respective angle bisectors.
5. Any two adjacent angles add up to 180 degrees.
6. The area of the rhombus is a product of the lengths of the 2 diagonals divided by 2.
Properties of rectangle:
1. Opposite sides are equal in length.
2. All the angles are 90°.
3. Diagonals bisect each other.
4. Any two adjacent angles add up to 180 degrees.
Hence, the common properties are
1. Opposite angles are equal in measure.
and
2. Diagonals bisect each other.
3. Any two adjacent angles add up to 180 degrees.
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64% of all vehicles examined at a certain emissions inspection station pass the inspection. assuming that successive vehicles pass or fail independently of one another, calculate the probability that exactly one of the next three vehicles fail. (give your answer as a decimal number with 3 digits of precision.)
The probability that exactly one of the next three vehicles fail is 0.737 .
Given :
64% of all vehicles examined at a certain emissions inspection station pass the inspection. assuming that successive vehicles pass or fail independently of one another .
probability that exactly one of the next three vehicles fail is :
P = 1 - probability that all of the next three vehicles passes .
= 1 - 64 % * 64 % * 64 %
= 1 - 64/100 - 64/100 - 64/100
= 1 - 0.64 * 0.64 * 0.64
= 1 - 0.4096 * 0.64
= 1 - 0.262
= 0.737
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A radioactive substance decays according to A=A0e−0.0037t, where A0 is the initial amount and t is the time in years. If A0=740 grams, find the time for the radioactive substance to decay to 373 grams. Round your answer to two decimal places, if necessary.
The time is taken by the substance to decay, if A radioactive substance decays according to [tex]A = A_o \times e^{-0.0037t}[/tex] Where A₀ is the initial amount and t is the time in years. If A0=740 grams is 185.18 years.
What are radioactive substances?Atoms in radioactive materials naturally decay. They are capable of emitting gamma radiation, beta radiation, and alpha radiation. They cannot be turned off, so controlling them is more challenging than controlling X-ray sources.
Given:
The initial amount, A₀ = 740 g,
The final amount, A = 373 g,
Calculate the time by using the formula given below,
[tex]A = A_o \times e^{-0.0037t}[/tex]
373 = 740 [tex]\times e^{-0.0037t}[/tex]
[tex]e^{-0.0037t}[/tex] = 373 / 740
[tex]e^{-0.0037t}[/tex] = 0.504
Taking log on both sides,
㏑ 0.504 - ㏑ 0.0037 = t
t = 185.18
Therefore, the time taken by the substance to decay if A radioactive substance decays according to A=A0e−0.0037t, where A0 is the initial amount and t is the time in years. If A0=740 grams is 185.18 years.
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What value of x satisfies the equation x^2+2x/x+2=2
Answer: X= -2
Step-by-step explanation:
francisco makes garlic bread qith 1/6 pound of garlic and 2/5 pounds of butter. how much garlic and butter is on the bread?
Answer:17/30 lbs
Step-by-step explanation:
Which of the following is true of protecting classified data?
True statement for Protecting classified data is classified material must be appropriately marked.
Classified information being transmitted from one commission office to another shall be protected with a classified document cover sheet and hand delivered by an appropriately cleared person to another appropriately cleared person.
Classified information is material that a government body deems to be sensitive information that must be protected. Access is restricted by law or regulation to particular groups of people with the necessary security clearance and need to know, and mishandling of the material can incur criminal penalties.
Data classification is broadly defined as the process of organizing data by relevant categories so that it may be used and protected more efficiently. Data classification involves tagging data to make it easily searchable and trackable.
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The T distribution :
A) assumes the population is normally distributed
B) approaches the normal distribution as sample size increase
C) has more area in the tails than normal distribution
D) all the above
According to the T distribution, the correct option is (d) All the above
T distribution:
In statistics, t-distribution is used in all forms of t-tests. Where the T-tests are all classified as inferential statistical tests and will follow all of the same steps required to complete the process of null hypothesis significance testing. And it defines the exact shape of the t-distribution is governed by the degrees of freedom. And the t-distribution is associated with a degrees of freedom equal to the sample size minus a value of 1.
Given,
Here we need to find the correct option according to the T distribution.
As per the given options, the correct answer is best represented by option D. All of the above are correct.
Because, the t-distribution, along with the normal distribution, both assume data is normally distributed in the population.
When the sample size increases towards 30, the t-distribution will resemble the normal distribution, provided the data in the population is normally distributed.
If it is correct to state that the tails of the t-distribution are thicker compared to the normal distribution.
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WILL GET 100 POINTS DUE SOON AND I NEED HELP!!!
The restriction on the variables x and y are given as follows:
x ∈ W, y ∈ W.
What are the sets of numbers?The three sets of numbers that appear in this problem are given as follows:
Whole numbers: non decimal and non negative numbers.Integer numbers: non decimal numbers that can be either negative or positive.Real numbers: numbers that can be positive or negative, and can also assume decimal values.The number of tickets sold cannot assume decimal values, hence we know two things:
There is a restriction.x belongs either to the whole numbers or to the integer numbers.The number of tickets also assumes only values of zero or positive numbers, they cannot be negative, hence it is a whole number and the second option is correct.
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Evaluate the expression 5(7 − 4)2 ÷ 3 + 11.
3
14
26
33
Answer:
26
Step-by-step explanation:
8. If f(x) = 3x - 4 and g(x) = 4x - 3, what is f. g? A f(x) · g(x) = 7x - 7 B f(x) · g(x) = 12x + 12 Of(x) · g(x) = 7x² - 14x - 7 D f(x) · g(x) = 12x2 25x+12
Answer:
D: f(x) · g(x) =12x^2-25x+12
Step-by-step explanation:
we multiply the 2 equations
(3x-4)(4x-3)
12x^2-9x-16x+12
12x^2-25x+12
so d is the answer
hopes this helps please mark brainliest
Questionaire below Image
Answer: the first one is 30 ml
Would someone be so kind as to lend a helping hand to me in solving this question?
Answer:
a) Provider B would be cheaper
b) [tex]10m^3[/tex]
Step-by-step explanation:
a) Input 6 into both equations and solve. For Provider A, it would go like this: [tex]y = 6 + 15[/tex]. For Provider B, it would be this: [tex]y = 2(6) + 5[/tex]. The first provider adds up to £21 Pounds ($25.56 USD). The second provider adds up to £17 Pounds ($20.69 USD).
b) All you really need to do is just plug in numbers until both equations contain the same answer. The way I did it was: [tex]x + 15 = 2x + 5[/tex]. If your teacher asks how you got the answer, follow these steps:
[tex]x+15=2x+5\\x-5=2x-5\\x+10=2x[/tex]
A man jogs 2 miles on Monday. Every day he jogs one-half mile farther. Write an equation for the nth term of the arithmetic sequence.
An equation for the nth term of the arithmetic sequence is 2 + 0.5n.
What is an arithmetic sequence?
An arithmetic sequence is a set of integers where each term (except the first) is created by adding a fixed amount to the term before it.
Given, initial distance = 2 miles
Let n be each day on which he jogs one-half (1/2 = 0.5) mile.
Then, according to the question,
nth term = 2 + 0.5n
Hence, an equation for the nth term of the arithmetic sequence is 2 + 0.5n.
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60% of the monthly housing and food budget is for rent. 10% of the budget is for utilities. 30% is for food. What is Amy’s budget for rent? What is the budget for utilities? What is it for a food?
a) Amy's monthly budget for Rent based on the total budget for housing and food is $853.
b) Amy's monthly budget for Utilities based on the total budget for housing and food is $142.
c) Amy's monthly budget for Food based on the total budget for housing and food is $427.
The total budget for Housing, Utilities, and Food for nine months = $12,798
Rent = 60%
Utilities = 10%
Food = 30%
Budget period = 9 months
Budget for rent = $7,679 ($12,798 x 60%)
Monthly budget for Rent = $853 ($7,679/9)
Budget for utilities = $1,280 ($12,798 x 10%)
Monthly budget for Utilities = $142 ($1,280/9)
Budget for food = $3,839 ($12,798 x 30%)
Monthly budget for Food = $427 ($3,839/9)
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Lee Associates borrowed $60,000. The company plans to set up a sinking fund that will pay back the loan at the end of 12 years. Assuming a rate of 8% compounded semiannually, the amount to be paid into the fund each period is):
Multiple Choice
$1,350
$1,535.21
$1,653
$5,163
The required amount to be paid into the fund each period is $1535.21. which the correct answer would be option (B).
Lee Associates borrowed $60,000 in total. The corporation intends to establish a sinking fund to repay the debt after 12 years.
Assuming a semiannual compounding rate of 8%,
As per the given information, the required solution would be as:
Amount to be paid into the fund each semi-annual period will be
= Loan Amount/((1+r/2)²ⁿ⁻¹)/(r/2))
= 60000/(((1+8%/2)²ˣ¹²⁻¹)/(8%/2))
= $1535.21
Thus, the required amount to be paid into the fund each period is $1535.21.
Hence, the correct answer would be an option (B).
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