Answer:
See belowStep-by-step explanation:
1. Arithmetic: Add 3,500
The annual raise of 3,500 means add 3,500 to the previous year's salary
60,000 + 3,500 = 63,500
63,500 + 3,500 = 67,000
67,000 + 3,500 = 70,500
70,500 + 3,500 = 74,000
74,000 + 3,500 = 77,500
Geometric: Multiply by 1.05
The annual raise by 5% of his current salary means multiply by 1.05.
60,000 x 1.05 = 63,000
63,000 x 1.05 = 66,150
66,150 x 1.05 = 69,457.50
69,457.50 x 1.05 = 72,930.38 rounded
72,930.375 x 1.05 = 76,576.89
The first sequence is arithmetic because we add the same number (3,500) to the preceding term. The second sequence is geometric because we multiply the preceding term by the same number always (1.05.)
2a. Arithmetic - New salary is $3,500 greater each year than last year's salary
S = 60,000 + 3500(n-1)
Geometric - New salary is 5% more each year than last year's salary
60,000 + (1.05)^(n-1)
2b. Arithmetic Earnings over 3 years
60,000 + 63,500 + 67,000 = 190,500
Geometric Earnings over 3 years
60,000 + 63,000 + 66,150 = 189,150
There is a 1,000 dollar difference. In this case, the arithmetic increase of 3,500 dollars would be better for Mr. Nicholson. 1,000 dollars may or may not be considered a big difference. In my opinion, I'd say there is a slight difference between the two
3.Arithmetic
a(9) = 3,500 + a(9-1)
a(9) = 3,500 + 89,000
a(9) = 92,500
Geometric
a(9) = 1.05 x a(9-1)
a(9) = 1.05 x 84,425.90
a(9) = 88,647.20
4. In this case, both the 3 year and 9 year time frames favor the arithmetic increase of $3,500. At 3 years, he would have 190,500 compared to the geometric salary of 189,150. However, this is a small difference. If he is going to be at the company for 9 years, then definitely he should choose the first opportunity. 92,500 is significantly more money than 88,647.20. So, longer time frames only make the first opportunity, which is better to begin with, shine even more.
I'm always happy to help :)
The problem analyses two salary options: a regular increase (arithmetic sequence) and a percentage increase (geometric sequence). It involves using recursive models to calculate potential earnings over a specified period. Over the long term, the geometric sequence provides a greater total income.
Explanation:The subject is about Mr. Nicholson's two different salary options. An arithmetic sequence series represents option a) where Mr. Nicholson's salary increases by a steady $3,500 per year. The difference, or increase, remains constant.
On the other hand, option b) represents a geometric sequence where Mr. Nicholson's salary increases by 5% of his current salary each year. The ratio, or multiplier remains constant at 1.05 (current salary * 5%).
To calculate his earnings for the first three years using the recursive model: Option a) Year 1: $60,000 Year 2: 60,000 + 3,500 = $63,500, Year 3: 63,500 + 3,500 = $67,000. Option b) Year 1: $60,000, Year 2: 60,000 * 1.05 = $63,000, Year 3: 63,000 * 1.05 = $66,150.
For a period of 9 years, continually apply the recursive model for each year. It becomes apparent that with the geometric sequence (option b), the amount of raise will increase per year because it is based on a percentage of his increasing salary, providing a higher total over time compared to the arithmetic sequence (option a).
Learn more about Arithmetic and Geometric Sequences here:https://brainly.com/question/32028384
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What is the volume if something measures 6.2 cm x 13.7 cm x 26.9 cm?
The calculated volume is 2284.886 cubic centimeters.
The volume of a rectangular prism (or box) is calculated using the formula:
Volume = length x width x height
For the given measurements:
Length (l) = 6.2 cmWidth (w) = 13.7 cmHeight (h) = 26.9 cmPlug the values into the formula:
Volume = 6.2 cm x 13.7 cm x 26.9 cm
First, calculate the product of the length and width:
6.2 cm x 13.7 cm = 84.94 cm²
Next, multiply this result by the height:
84.94 cm² x 26.9 cm = 2284.886 cm³
Therefore, the volume of the object is 2284.886 cubic centimeters.
You were assigned to read 5⁄8 of your book. how many sixteenths is that? fraction
Jesse ate 100 donughts i 5 days each day she ate 6 more then the day before how many did she eat each day
Segment AB is rotated to form A'B'¯¯¯¯¯¯¯ . The coordinates of point A are (1, 5) and the coordinates of point B are (−6, 4) . Which clockwise rotation around the origin results in the transformation of AB¯¯¯¯¯ to form A'B'¯¯¯¯¯¯¯ ?
Merry and pippin were working on a project in carpentry class. they needed to cut 4 lengths of 1 5/8 feet from a board. how long must the board be to allow this?
Answer:
Hence, the length of board is:
6.5 feet
Step-by-step explanation:
Merry and pippin were working on a project in carpentry class.
They needed to cut 4 lengths of 1 5/8 feet from a board.
That means each of the piece is of length 1 5/8 feet which could be written in fraction as:
[tex]1\frac{5}{8}=\dfrac{13}{8} feet[/tex]
Hence, the otal length of the board is addition of length of each board.
i.e.
[tex]\dfrac{13}{8}+\dfrac{13}{8}+\dfrac{13}{8}+\dfrac{13}{8}=4\times \dfrac{13}{8}=\dfrac{13}{2}feet=6.5feet[/tex]
Hence, the length of board is:
6.5 feet
Please help with these questions thank you.
Four people are painting a house. Zachary paints 1/5 of the house, Alyssa paints 33% of the house, Chloe paints 0.3 of the house, and Nicholas paints 0.17 of the house. Which choice lists the people in order from least to greatest by the amount of the house each painted?
Answer:
Nicholas, Zachary, Chloe, Alyssa.
Step-by-step explanation:
Given that Four people are painting a house. Zachary paints 1/5 of the house, Alyssa paints 33% of the house, Chloe paints 0.3 of the house, and Nicholas paints 0.17 of the house.
As such we cannot compare their works to order from least to greatest
Hence we can convert each portion into a decimal thus enabling comparison easier.
Zachary paints [tex]\frac{1}{5} =0.20[/tex] of the house
Alyssa paints [tex]33%=\frac{33}{100} =0.33[/tex] of the house
Chloe paints 0.3 of the house and
Nicholas paints 0.17 of the house.
In ascending order these can be written as
0.17, 0.2, 0.3, 0.33
Hence Nicholas, Zachary, Chloe, Alyssa.
The total number of people at a football game was 5600. field-side tickets were 40 dollars and end-zone tickets were 20 dollars. if the total amount of money received for the tickets was 132000 how many of each kind of ticket were sold.
Find the 31st term of the following sequence.
9, 15, 21, ...
Notice that the above sequence is arithmetic because the common difference: d is constant.
d = second term - first term.
= 15 - 9
= 6
The general term of an arithmetic sequence is,
a_{n} =a_{1} +(n-1)d
Where , nth term = [tex] a_{n} [/tex]
[tex] a_{1} [/tex] = First term
and d = common difference.
The given sequence is: 9, 15, 21, ...
Here a_{1} = 9,
d = 6
We need to find the 31st term. So, n = 31.
Next step is to plug in these values in the above formula. Therefore,
[tex] a_{31} =9 +(31-1)*6 [/tex]
= 9 + 30* 6
= 9 + 180
= 189
So, 31st term of this sequence is 189.
Hope this helps you.
Answer:
189
Step-by-step explanation:
What is the x-intercept of a line that passes through the point (3, 4) and has a slope of 2?
The function y = h(x) is defined as follows:
h(1) =
and h(4) =
Two integers with the sum of -17 and the product of 52?
PLZ HELPP ME WITH THIS MATH PROBLEM
which ordered pair is a solution of the equation y=x-4
Answer:
Step-by-step explanation:
y = x - 4
there are so many ordered pairs which are the solution of the given equation.
for example,
x = 0, y = -4
x = 1 , y = -3
x = 2, y = -2
x = 3, y = -1
x = 4, y = 0
x = - 1, y = - 5
x = - 2, y = - 6
x = - 3, y = - 7
x = - 4, y = - 8
Which of the sets of ordered pairs represents a function? (4 points)
A = {(−4, 5), (1, −1), (2, −2), (2, 3)}
B = {(2, 2), (3, −2), (9, 3), (9, −3)}
you can do both or neither as well THX
i need someones help please?
The point MegaMarket sold 450 organic pears last season. this season they only sold 360 What was the percent decrease in sales
PLEASE HELP!!!! WILL MARK THE BRAINLIST!!!! PLEASE PLEASE PLEASE PLEASE PLEASE PLEASE
a) The shoe store manager borrowed $17,000.00 from the bank to purchase 1000 pairs of shoes. The bank charges a simple interest rate of 5% per year on a loan to a business. If it takes 3 years to pay back the loan and interest, what is the total amount of interest that the shoe store will pay? (2 points)
b) What is the total amount, including interest, that the shoe store must pay on the loan? (2 points)
c) How could you use estimation to determine if your answer is reasonable? Explain. (2 points)
A) 17000*(1+(0.05*3) = 19550
19550-1700 = $2,550 total interest
B) $19,550 total amount
C) multiply 5 by 3 = 15 than multiply by 17 = 17 * 15 = 255 , then make it a thousands amount by adding a zero at the end
Answer:
A)
p = 17000
r = 5% or 0.05
t = 3
Simple interest formula = p x r x t
Interest paid in 3 years = [tex]17000\times0.05\times3=2550[/tex] dollars
B)
Total amount to be paid = [tex]17000+2550=19550[/tex] dollars
C)
You can first multiply the years and rate that is 5 and 3 to make 15. Then you can multiply by 17. Then put proper decimals as per the values.
Find the sum of all numbers below 1000 that are divisible by 3 or 5
First of all, stop thinking on the number 10001000 and turn your attention to the number 990990 instead. If you solve the problem for 990990 you just have to add 993,995,996993,995,996 & 999999 to it for the final answer. This sum is (a)=3983(a)=3983
Count all the #s divisible by 33: From 33... to 990990 there are 330330 terms. The sum is 330(990+3)/2330(990+3)/2, so (b)=163845(b)=163845
Count all the #s divisible by 55: From 55... to 990990 there are 198198 terms. The sum is 198(990+5)/2198(990+5)/2, so (c)=98505(c)=98505
Now, the GCD (greatest common divisor) of 33 & 55 is 11, so the LCM (least common multiple) should be 3×5=153×5=15.
This means every number that divides by 1515 was counted twice, and it should be done only once. Because of this, you have an extra set of numbers started with 1515 all the way to 990990 that has to be removed from (b)&(c).
Then, from 1515... to 990990 there are 6666 terms and their sum is 66(990+15)/266(990+15)/2, so (d)=33165(d)=33165
The answer for the problem is: (a)+(b)+(c)−(d)=233168(a)+(b)+(c)−(d)=233168
Simple but very fun problem.
Find three consecutive odd integers whose sum is negative 465
465 / 3 = 155
so -153 + -155 + -157 = -465
Given that a line has a slope of -3 and a point on the line is (2,-4),
1.what is the equation of the line in point-slope form?
2.how do we create slope-intercept form?
*please show all work, step by step.
given a line whose slope is, m, is -6/5, and passes through point (-5,3), the graph will?
There are currently 58 million cars in a certain country, increasing exponentially by 5.5% annually. how many years will it take for this country to have 79 million cars? round to the nearest year.
Which of the following properties is 5(3 + 2) = 15 + 10 an example of?
associative property
commutative property
multiplicative identity
distributive property
Answer: Distributive property
Step-by-step explanation:
Associative property states that either in addition or multiplication we can changes the position of parenthesis.
That is, a.(b.c) = (a.b).c or a+(b+c) = (a+b)+c
Commutative property states that in addition or multiplication we can change the order.
That is, a.b = b.a or a+b = b+a
Multiplicative identity is an element that gives the same number after multiplication.
That is, a × 1/a = 1 ⇒ 1/a is the multiplicative identity of a.
Distributive property lets us multiply a sum by multiplying each addend separately and then add the products.
That is, a(b+c) = a.b + a.c
Thus, it is clear that ,
5(3 + 2) = 5× 3+ 5×2 = 15 + 10 is the example of distributive property.
What is the value of N?
-10= N over -0.2
The relation of this set of points is a function. True or false.
{(−2, 6), (4, 5), (3, −3), (6, 9), (4, −4)}
Question 1 options:
True
False
Save
What is the exact value of cos theta = squareroot 2 over 2?
solve this inequality 2(4x-3)≥-3(3x)+5x?
Answer:
x ≥0.5
Step-by-step explanation:
Given : 2(4x-3)≥-3(3x)+5x.
To find : solve this inequality.
Solution : We have given that
2(4x-3)≥-3(3x)+5x.
Distributes 2 over (4x-3) and -3 over 3x.
8x - 6 ≥ -9x + 5x .
8x - 6 ≥ -4x .
On adding both side by 4x
8x + 4x - 6 ≥ 0 .
12 x - 6 ≥ 0
On adding both sides by 6.
12 x ≥ 6.
On dividing both sides by 12.
x ≥ [tex]\frac{6}{12}[/tex] .
x ≥ [tex]\frac{1}{2}[/tex] .
x ≥0.5.
Therefore, x ≥0.5
The table below represents the distance a person runs as a function of time:
Time distance meters
x f(x)
10 60
13 78
16 96
19 114
he average rate of change of the function between x = 10 to x = 16 is m/s and represents the person's speed. (3 points)
Each of ten tickets is marked with a different number from 1 to 10 and put in a box. if you draw a ticket from the box, what is the probability that you will draw 2, 8, or 4?
Answer: [tex]\dfrac{3}{10}[/tex]
Step-by-step explanation:
Given : Each of ten tickets is marked with a different number from 1 to 10 and put in a box.
i.e. The total number of outcomes : 10
Favorable outcomes : 2, 8, or 4
i.e. Number of favorable outcomes = 3
Now, the probability that you will draw 2, 8, or 4 is given by :-
[tex]=\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}\dfrac{3}{10}[/tex]