1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
FromTheMoon [43]
3 years ago
12

If your starting salary is $40,000 and you  receive a 4.2% raise every year, how much  TOTAL money will you make in 15 years?

Mathematics
1 answer:
Oliga [24]3 years ago
5 0
The first year, the amount is 40,000

the second year is 40000 + 4.2% of 40000, or 0.042 * 4000, so 40000+(0.042*4000)
common factoring that  we get 40000(1 + 0.042), or just 40000(1.042)

in short, the starting amount is 40000, and to get the next term's value you'd use the "common ratio" of 1.042, namely the multiplier of 1.042.

for the third year it'll be 40000(1.042) + (0.042 *40000(1.042) ), again, common factoring that

40000(1.042)(1 + 0.042) or 40000(1.042)(1.042) or 40000(1.042)²

therefore,

\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=40000\\
r=1.042\\
n=15
\end{cases}
\\\\\\
S_{15}=40000\left( \cfrac{1-1.042^{15}}{1-1.042} \right)\implies S_{15}\approx 40000\left( \cfrac{-0.8536}{-0.042} \right)
\\\\\\
S_{15}\approx 812951.42
You might be interested in
Need help ASAP will mark brainliest
nalin [4]

Answer:

  5x -7y = 21

Step-by-step explanation:

A sketch can convince you that BC is a transversal perpendicular to parallel lines AB and CD. The question asks for an equation for CD, so we just need to write the equation of a line through D that is parallel to AB.

One way to do this is to equate the slopes of the parallel lines:

  ∆y/∆x for AB = ∆y/∆x for CD

  (y2 -y1)/(x2 -x1) = (y -2)/(x -7) . . . . . . where (x1, y1) = A; (x2, y2) = B; (7, 2) = D

  (4 -(-1))/(1 -(-6)) = (y -2)/(x -7)

  5(x -7) = 7(y -2) . . . . . . . . . . . . . cross multiply

  5x -7y = 21 . . . . . . . . . . . . . . . . add 35 -7y, simplify

_____

Note that the graph shows the line CD is named "b", and its equation is shown at upper left. Multiplying that equation by -1 gives the one shown here.

6 0
3 years ago
Jim and Em baked 33 macaroons.
bearhunter [10]

Answer: 19 macaroons

Step-by-step explanation:

Let's create an equation to represent this situation. Let x represent the number of macaroons that Em made.

33=x+x+5

33=2x+5

33-5=2x+5-5

28=2x

28/2=2x/2

14=x

This means that Em made 14 macaroons.

14+5=19

Therefore, Jim baked 19 macaroons.

4 0
3 years ago
Please can someone help
Fofino [41]

Answer:

a) 0

b) 1

c) 0

Step-by-step explanation:

These are common values from the unit circle but you could also just check with your calculator. Just be sure to set it to degree mode and not radian mode.

6 0
3 years ago
A=L times W
Dovator [93]
A= 30ft, because you only have to multiply LxW= A that is equal to 2x15=30ft
8 0
3 years ago
how do you write the equation of a line in slope-intercept form when given two points on the line? the two points are (-4,4) and
Feliz [49]
Y=7x+ 32 you find slope and y intercept
6 0
3 years ago
Other questions:
  • State what additional information is required in order to know what the triangles are congruent by SSS
    6·1 answer
  • What's 2/3 of 17 as a fraction
    6·1 answer
  • Point S is on line segment RT. Given RT<br> 15 and ST = 3, determine the<br> length RS.
    9·1 answer
  • Y = x – 6
    8·1 answer
  • Choose the product. -6 p3 (3 p2 + 5 p - 1)
    12·1 answer
  • 7x2+49x+84=0<br> by completing the square method
    6·1 answer
  • Right triangles 1-2 and 3 are given with all their angle measures and approximate side lengths.
    13·2 answers
  • Give the value of x. Explain how you got your answer OR which theorem you used.
    9·1 answer
  • Write 63/16 as a improper fraction
    8·2 answers
  • How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!