n applicant receives a job offer from two different companies. Offer A is a starting salary of $58,000 and a 3% increase for 5 years. Offer B is a starting salary of $56,000 and an increase of $3,000 per year.
Part A: Determine whether offer A can be represented by an arithmetic or geometric series and write the equation for An that represents the total salary received after n years. Justify your reasoning mathematically. (3 points)
Part B: Determine whether offer B can be represented by an arithmetic or geometric series and write the equation for Bn that represents the total salary received after n years. Justify your reasoning mathematically. (3 points)
Part C: Which offer will provide a greater total income after 5 years? Show all necessary math work. (4 points)
Answers
The amount provided by each offer after each year depends on the first
salary and the added amount or percentage series.
Part A: Offer A can be represented by a geometric seriesThe salary received after n years is Aₙ = 58,000·1.03⁽ⁿ ⁻¹⁾Part B: Offer B can be represented by an arithmetic seriesThe equation for the salary after n years is Bₙ = 58,000 + (n - 1)×3,000Part C: The offer that will provide a greater income after 5 years is offer B, with an income of $70,000Reasons:
The given parameters of the job offers are;
Starting salary of offer A = $58,000
Amount by which the salary increases for 5 years = 3%
The starting salary offer B = $56,000
Amount by which the salary increases per year = $3,000
Part A: The salary amount received in the first month = $58,000
The salary in the second month, aₙ = 58,000 × (1 + 0.03)
a₂ = 58,000 × (1 + 0.03) = 58,000 × (1.03)
The salary in the third month is given as follows;
a₃ = a₂ × (1.03) = 58,000 × (1.03) × (1.03) = 58,000 × (1.03)²
The salary on the nth month is therefore;
aₙ = 58,000 × (1.03)⁽ⁿ⁻¹⁾
The above formula is in the form of the geometric series formula, which is presented as follows;
aₙ = a·r⁽ⁿ⁻¹⁾
Where;
a = The first term = 58,000
r = The common ratio = 1.03
n = The number of years
Therefore;
Offer A can be represented by an arithmetic series
Part B: The first year salary for offer B = $58,000
The salary on the second year, B₂ = 58,000 + 3,000 = 61,000
Salary on the third year, B₃ = 58,000 + 3000 + 3000 = 58,000 + 2 × 3,000
Therefore;
Salary on the nth year, Bₙ = 58,000 + (n - 1)×3,000
The above equation is in the form of aₙ = a + (n - 1)·d
Where;
a = The first term = 58,000
n = The number of years
d = The common difference = 3,000
Therefore;
Offer B can be represented by an arithmetic series
Part C: The income gained on offer A after 5 years, a₅, is given as follows;
a₅ = 58,000 × (1.03)⁽⁵ ⁻ ¹⁾ = 58,000 × 1.03⁴ ≈ 65,279.51098
The income gained on offer A after 5 years ≈ $65,279.51098
On offer B, we have;
a₅ = 58,000 + (5 - 1) × 3,000 = 70,000
The income gained on offer B after 5 years = $70,000
Therefore;
After 5 years, the income offered by offer B is greater than the income offered by offer A.Learn more about arithmetic and geometric series here:
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Related Questions
What reaction did Pocahontas's people have to her helping the Jamestown colonists?
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Answer:
They were very angry about her helping the colonists.
Step-by-step explanation:
Match the expression to the method needed to evaluate (will give brainlest)
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Answer:
See image
Step-by-step explanation:
This is to help you practice exponent rules. The rules are short cuts, which are good bc they're faster but bad bc they take away the meaning of the work. If you're trying to remember a rule, think through the meaning. See image.
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The Add exponents rule and Subtract are 100% correct.
The expressions are matched to the method needed to evaluate as shown below.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The first expression is 5³ × 5³.
Multiplication rule of exponents states that,
xᵃ × xᵇ = xᵃ⁺ᵇ
That is we add the exponents.
So, 5³ × 5³ = 5³⁺³ = 5⁶
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So, here, multiply the exponents.
(7²)³ = 7⁶
(4x³)⁵
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That is write is as product of the powers.
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A small tree was planted at a height of 8 feet. The tree has been planted for 15 months, and is now 50 feet tall. Which equation could be used to find x, the average number of feet the tree grew each month?
Answers
Answer:
y=42/15x+8
Step-by-step explanation:
We can get the change in height with 50-8, or 42. Now we divide, so 42/15. I'm assuming this is a slope question, so it would be y=42/15x + 8. Let me know if this is the way you want the answer.
Answer:
x=8+(number of feet/number of months)
Step-by-step explanation:
Pls look at the picture for the question.
Answers
Answer:
10
Step-by-step explanation:
each tick mark is worth 5
there is the -10, then one to the right is -5, next is 0, next is 5, next one (the one where the x is) 10, next 15, next 20.
Which of the following is a right triangle based on the given figure?
Answers
Answer:
BDE
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs, In the figure, lines H and KL are parallel. TH K E G D Match each angle relationship with the appropriate reason. Vertical angles theorem Alternate exterior angles theorem linear pair Alternate interior angles theorem Corresponding angles theorem same-side interior angles m_HED = m_FE) mKFE = m_FEJ MZLFG = MADEH
Answers
The angle relationship and their reasons are:
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∠HED and ∠FEJ are directly vertically opposite each other, therefore, they are equal based on the vertical angles theorem.
m∠HED = m∠FEJ ---> Vertical angles theorem∠KFE and ∠FEJ are alternate interior angles, therefore, they are equal based on the alternate interior angles theorem.
m∠KFE = m∠DEH ---> Alternate interior angles theorem∠LFG and ∠FEJ are alternate exterior angles, therefore, they are equal based on the alternate exterior angles theorem.
m∠LFG = m∠DEH ---> Alternate exterior angles theorem∠JEF and ∠LFE are interior angles on same side of the transversal, therefore, the sum of both angles equal 180 degrees based on the same-side interior angles theorem.
m∠JEF + m∠LFE = 180° ---> same-side interior angles theorem∠DEJ and ∠EFL are corresponding angles, therefore, they are equal based on the corresponding angles theorem.
m∠DEJ = m∠EFL ---> Corresponding interior angles theorem∠LFG and ∠GFK are angles on a straight line, therefore the sum of both angles will equal 180 degrees because they are a linear pair.
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If I take 1 hour to cook a batch of cookies and I have 15 ovens working 24 hours a day every day for 5 years, how long does it take me to make 6000000 batches of cookies?
Answers
Answer:
Approximately 40,069 days
What is the gradient of the graph shown?
Give your answer in its simplest form.
Answers
Answer:
m = —1/3
Step-by-step explanation:
There are two clear points shown on the graph
point 1: (0;3)
point 2: (6;1)
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]m = \frac{1 - 3}{6 - 0} [/tex]
[tex]m = - \frac{2}{6} [/tex]
[tex]m = - \frac{1}{3} [/tex]
Factor the expression. 63a - 42b
Answers
Answer:
21(3a-2b)
Step-by-step explanation:
Answer:
21(3a-2b)
Step-by-step explanation:
63a - 42b
21(3a-2b)
22) A corporate charter specifies that the company may issue up to 20 million shares of stock. The company sells 12 million shares to investors and later buys back 3 million shares. The current number of shares of treasury stock after these transactions have been accounted for is:
Answers
Answer:
11 million
Step-by-step explanation:
20 -12 +3 = 11
There will be 11 million shares of stock in the treasury.
The mean time it takes a certain pain reliever to begin reducing symptoms is 20 minutes with a standard deviation of 4.39 minutes.
Assuming the variable is normally distributed, find the probability that it will take the medication less than 25 minutes to begin to work.
A. 0.8729
B. 0.3708
C. 0.8708
D. 0.3729
Answers
Enter your answer and show all the steps that you use to solve this problem in the space provided.
The ratio of boys to girls in Mrs. Williams’s class is 2 to 5. There are 15 girls in the class. What is the total number of students in Mrs. Williams’s class?
Answers
Answer:
It seems like the answer would be 21 students.
Step-by-step explanation:
5 times 3 is 15 so 15 girls
2 times3 is 6 so 6 boys
15+6=21
I hope this helps :))
Daisy had 2 3/4
bags of mulch to put in her yard. Each bag will cover 235.5 ft2
. How much square feet will she be able to cover is she uses all of the bags of mulch?
help me plsssssss
Answers
Answer:
mmmmmmm
Step-by-step explanation:
n
Daisy will cover a total area of 647.625 square feet, if she uses all of the bags of mulch.
The amount of mulch is given as:
[tex]Bag = 2\frac 34[/tex]
The area covered by each bag is given as:
[tex]Area = 235.5ft^2[/tex]
If she uses all bags, the total area covered by the bags is:
[tex]Total = Bag \times Area[/tex]
So, we have:
[tex]Total = 2\frac 34 \times 235.5ft^2[/tex]
Rewrite the fraction as an improper fraction
[tex]Total = \frac {11}4 \times 235.5ft^2[/tex]
This gives
[tex]Total = \frac {2590.5}4 ft^2[/tex]
[tex]Total = 647.625 ft^2[/tex]
Hence, she will be able to cover a total area of 647.625 square feet
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Solve for the value of x
Answers
Answer:
x=9
Step-by-step explanation:
To solve for x, you can set up a proportion between the 2 triangles we see.
The small triangle can be written as [tex]\frac{16}{20}[/tex], and the large triangle can be written as [tex]\frac{16+12}{20+2x-3} = \frac{28}{2x+17}[/tex].
Set both proportions equal to each other.
[tex]\frac{16}{20}=\frac{28}{2x+17}[/tex]
Cross multiply and solve for x.
[tex]16(2x+17)=(28)(20)[/tex]
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32x=288
x=9
write the equation of the line that passes through the points ( 1, -1) and (0, 5)
Answers
Answer:
y=-6x+5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(5-(-1))/(0-1)
m=(5+1)/-1
m=6/-1
m=-6
y-y1=m(x-x1)
y-(-1)=-6(x-1)
y+1=-6(x-1)
y=-6x+6-1
y=-6x+5
A restaurant is making hamburgers. The cooks use 2/3 pounds of beef for each hamburger. If the cooks have 44 and 2/3 pounds of beef,how many hamburgers can they make?
Answers
Answer:
67 hamburgers
Step-by-step explanation:
In order to find the answer to this question, you must do the following equation:
44÷2/3. The answer to this is 66.
Then, you add 1 to 66, because 2/3 divided by 2/3 = 1!
So, the cook can make 67 hamburgers.
PLZ HELP ME WITH MY MATH HOMEWORK!!!!!! SHOW WORK
Answers
Answer:
Step-by-step explanation:
-(4q+8) + 6q = 12q - 5/6(18q + 6)
Open brackets:
<=> - 4q - 8 + 6q = 12q - 5/6*18q - 5/6*6
<=> - 4q - 8 + 6q = 12q - 15q - 5
Put q in one side and non q in one side:
<=> - 4q + 6q - 12q + 15q = 8 - 5
<=> 5q = 3
<=> q = 3/5
3. A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded annually. (a) Write an equation to represent the amount of money in the account as a function of time in years. (b) Find the amount of time it takes for the account balance to reach $800. Show your work. Answer:
Answers
Answer:
31.334... years
Step-by-step explanation:
Initial value = $500
r = 1.5%
t = ?
A = (500)[tex]e^{.015*t}[/tex]
I was unsure if the question was asking to express the equations in terms of t =, but i did those steps anyway just in case.
A/500 = [tex]e^{.015*t}[/tex]
ln A/500 = ln[tex]e^{.015*t}[/tex]
ln A/500 = .015*t
ln(A/500)/.015 = t
t = ln(A/500)/.015
To find the amount of time it takes for the account balance to reach $800, we plug in $800 for A in the equation that solves for t.
t= ln(800/500)/.015 = 31.334...(rounded) years
We also could have solved by plugging in $800 into the original equation and then solving for t, but i found it to be easier to find the equation for t prior to solving. Hope this helps!
Find the next four terms in the sequence.
1,-4, 16, -64, ...
Answers
Answer:
256, -1024, 4096, -16384
i think that's it
it's being multiplied by -4 (geometric)
Help please hhjhhkkkki
Answers
Answer:
000
Step-by-step explanation:
000
Answer:
[tex]$\lim_{x\to 0^+} \tan(x) - \frac{1}{x^2} = -\infty$[/tex]
Step-by-step explanation:
[tex]$\lim_{x\to 0^+} \tan(x) - \frac{1}{x^2} = \lim_{x\to 0^+} \tan(x) - \lim_{x\to 0^+} \frac{1}{x^2} $[/tex]
and
[tex]$\lim_{x\to 0^+} \tan(x) = \tan(0) = 0$[/tex]
[tex]$\lim_{x\to 0^+} \frac{1}{x^2} = +\infty$[/tex]
Therefore,
[tex]$\lim_{x\to 0^+} \tan(x) - \frac{1}{x^2} = -\infty$[/tex]
someone please help meeeeee
Answers
Answer:
B. (5,0)
Step-by-step explanation:
hope this helps
Answer:
B. (5,0)
Step-by-step explanation:
Place all the coordinates on the graph and then its pretty much self-explanatory after that. you just see which is closest to the subject. which, in this case, was the school.
You need to buy bananas at the store, but you realize you only have $2. How many bananas could you buy if they each cost 30 cents?
Answers
Answer:
6 bananas
Step-by-step explanation:
2 ÷ 0.30 = 6.6 repeating so 6 bananas
What is 6.995 to a decimal, fraction, and percent?
Answers
Answer:
1399/200 699.5%
Step-by-step explanation:
1. 6.995 is already a decimal.
2. As a fraction it is [tex]\frac{1399}{200}[/tex] and as an improper fraction it would be 6 [tex]\frac{199}{200}[/tex].
3. As a percent it would be 669.5%.
Six points are plotted on the number line.
Which points on the number line are opposites?
Answers
Answer: P and U
Step-by-step explanation:
.
Simplify.
{[2 + 3(−3 – 4) – 3] – 2} ÷ 23
Answers
Answer:
-0.2
Step-by-step explanation:
pls give me brainliest if possible
If Justin raves his Chevy Camaro south down 1-540 for 2560 meters in 60 seconds, what is his velocity?
Answers
I need this answer answed ASAP please..work out the area of the shaded shape
Answers
Answer:
Step-by-step explanation:
A = 8(14) - 5(14 - 5 - 2) = 77 m²
Answer:
77m (squared)
Step-by-step explanation:
13,22,31,...
Find the 31st term.
Find the 31st term.
Answers
Answer:
The 31st term is 283
Step-by-step explanation:
The sequence has a common difference therefore, it is an arithmetic sequence
[tex]an = a1 + (n - 1)d[/tex]
a31 = 13 + ( 31-1 ) 9
a31 = 13 + 270
a31 = 283
Help on this algebra 2 question look at the pic. Is it’s A, B or C
Answers
Answer:
A is correct
Step-by-step explanation:
perimeter is twice the sum of the two adjacent sides
p = 2(x + (2x³ - 3x + 4))
p = 2(2x³ - 2x + 4)
p = 4x³ - 4x + 8
given the function below, which of the following values will result in f(x)=10
f(x)=1/2x+8
Answers
Answer: x=4
Step-by-step explanation:
1/2x+8=10
Subtract 8 from 10
Multiply 2 to 2
x=4
Step-by-step explanation:
1/2(10)+8=
1/20+8=
161/20=
8.05