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
natali 33 [55]
3 years ago
15

Marco makes 36,000 a year. if he receives a 5% raise, how much more money will he be getting each year?

Mathematics
2 answers:
grandymaker [24]3 years ago
8 0
He'll be making 1,800 more money per year
NikAS [45]3 years ago
4 0

Answer:

f(n)= 36,000(0.05) + 36,000 (0.05)² + 36,000 (0.05)³ +...+ 36,000 (0.05)ⁿ =

f(n)= 36,000(0.05) ( 1 +0.05 + 0.05² + ...+ 0.05ⁿ⁻¹)

Step-by-step explanation:

The problem tells us that Marco makes 36,000 dollars a year, if he receives a 5% raise, we will need to multiply the current amount by 0.05 to know how much more is he getting:

(36000)(0.05)= 1800

However the problem doesn't end up there because <u>on the second year he will get a 5% of the amount he will be making after the first 5% raise</u>. So after the first year <u>he will be getting (36,000 + 1800 = 37800) and he will get a 5% raise</u>, so he will get a raise of

37800 (0.05)

We can write this as a function in terms of the numbers of years that have passed,

for year 1 we have that the raise will be:

f(1) = 36,000(0.05)

for the second year we will have

f(2) = 36,000 (0.05) + 36,000 (0.05)²

so for the nth year, the amount of raise will be

f(n)= 36,000(0.05) + 36,000 (0.05)² + 36,000 (0.05)³ +...+ 36,000 (0.05)ⁿ

= 36,000(0.05) ( 1 +0.05 + 0.05² + ...+ 0.05ⁿ⁻¹)

You might be interested in
If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24
VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let r be the radius and \theta be the angle of a circle.

According with the graph, the area of the sector is given by

A=\frac{1}{2}r^2\theta

The arc lenght of a circle with radius r and angle \theta is r \theta

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

2r+r\theta=24 \:in

We need to express the area as a function of one variable, to do this we use the above equation and we solve for \theta

2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}

Next, we substitute this equation into the area equation

A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2

The domain of the area is

0

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r

12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6

To check if r=6 is a maximum we use the Second Derivative test

if f'(c)=0 and f''(c), then f(x) has a local maximum at x = c.

The second derivative is

\frac{d}{dr} A'(r)=\frac{d}{dr} (12-2r)\\A''(r)=-2

Because A''(r)=-2 the largest slice is when r = 6 in.

The diameter of the pizza is given by

D=2r=2\cdot 6=12 \:in

A 12 in diameter will reward you with the largest slice of pizza.

3 0
2 years ago
5. The combined perimeter of a circle and a square is 16. Find the dimensions of the circle and square
charle [14.2K]

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaq

8 0
2 years ago
Are all squares trapezium?
Rina8888 [55]

Answer:

yes

Step-by-step explanation:

In a square, there are always two pairs of parallel sides, so every square is also a trapezoid. TRAPEZOID i said

But this is a US response so if this is from another country then the answer is no

8 0
2 years ago
Determine whether the graphs of y=-2x-7 and -y=2x+13 are parallel, perpendicular, coincident, or none of these.
Elden [556K]
It's parallel. Definitely true

3 0
3 years ago
Read 2 more answers
Find the minimum and maximum possible areas of a rectangle measuring 6 km by 11 km.
ExtremeBDS [4]
Assuming your numbers are rounded to the nearest km, the minimum area will be ...
  (5.5 km)·(10.5 km) = 57.75 km² . . . minimum

And the maximum area will be ...
  (6.5 km)·(11.5 km) = 74.75 km² . . . maximum

_____
When a number is rounded to 6 km as the nearest km, its value may actually be anywhere in the range 6 km ± 0.5 km. If you really want to get technical about it, the ranges of possible dimensions are [5.5, 6.5) km and [10.5, 11.5) km, and the range of possible areas is [57.75, 74.75) km².
3 0
3 years ago
Other questions:
  • A company sells desks for $155 each. To produce a batch of x desks, there is a cost of $83 per desk and a fixed or setup cost of
    14·1 answer
  • A car rental company offers two plans for renting a car. plan
    11·1 answer
  • What is the domain and range of the graph below in interval notation? If union is needed, use Capital U. If infinity is needed u
    15·1 answer
  • As a pendulum swings the angle theta that it makes with the vertical changes through its swing. The force of gravity pulling on
    15·2 answers
  • What is the relationship between the value of the digit 8 in the tens place and the value of the digit 8 in the ones place in th
    12·2 answers
  • To solve e4 – 3x = (4/3)x + 9 by graphing, which equations should be graphed?
    13·2 answers
  • I don't know the answer to this
    9·1 answer
  • Find the derivative of f(x) = -2x2 + 11x at x = 9.
    5·1 answer
  • On the coloring sheet, thd a ratio<br> is equivalent to 3/10.
    7·1 answer
  • Help Please! :) Fast as you can!
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!