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
PtichkaEL [24]
2 years ago
14

20 POINTS PLEAE HELP!!!!!!!!!!!!!!!

Mathematics
2 answers:
Alina [70]2 years ago
5 0
His first payment is $100, thus a₁ = 100.

the next "term", month will be 1.1 times more than the one before, namely r = 1.1, the common ratio.

\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=100\\
r=1.1\\
n=20
\end{cases}

\bf \sum\limits_{i=1}^{20}~100(1.1)^{i-1}\qquad \qquad\qquad  \qquad S_{20}=100\left( \cfrac{1-1.1^{20}}{1-1.1} \right)
\\\\\\
S_{20}=100\left( \cfrac{1-\stackrel{\approx}{6.727499949}}{-0.1} \right)\implies S_{20}\approx 100(57.27499949)
\\\\\\
S_{20}\approx 5727.4999493256

is the serie divergent or convergent?

well, to make it short, when the common ratio is 0 < | r | < 1, namely a fraction between 0 and 1, only then the serie is convergent, namely it reaches a fixed value, now in this case, 1.1 is a value larger than anything between 0 and 1, so no dice.
frozen [14]2 years ago
5 0
The easiest way to get the answer is to use a spreadsheet. That will allow you to look at ways of getting the answer if you are not certain.

Step One
This is an exponential function and as such you have to make a built in correction factor. To get tn you need to use
tn = 100* [(1.1)^(1/20) ] ^ (20*(n - 1) )
1.1^(1/20) = 1.004776882
tn = 100 * (1.004776882)^(20*(n - 1) )  So if you want the 18th term, you do it like this.
t18 = 100*(1.004776882)^(20*(18 - 1)) 
t18 = 100*(1.004776882)^ 340
t18 = 100 * 5.0545
t18 = 505.45  Does that agree with what the spreadsheet gives? Amazingly enough it does!

Now we have to figure out how to get the sum of all those terms. 
Oddly, you go back to 1.1

\frac{100*(1 - (1.1)^{20})}{1 - 1.1} The answer can be made closer by using the adjustment we used for each term, but as you can see, the sum is within pennies of agreement.

I don't know how to represent this using sigma notation. I could if I knew the latex for it.

It is definitely a divergent series.

You might be interested in
Nathan needs to order some new supplies for the restaurant where he works. The restaurant needs at least 571 forks. There are cu
Step2247 [10]

Answer:

The inequality representing  s, the number of sets of forks Nathan should buy is

s ≥ 21

Step-by-step explanation:

From the question, the restaurant needs at least 571 forks, i.e., if n represents the number of forks the restaurant needs, then

n ≥ 571

Also from the question, there are currently 361 forks. If y represents the number of forks the restaurant needs to buy, then

y ≥ 571 - 361

y ≥ 210

Also, each set on sale contains 10 forks. if s represents the number of sets of forks Nathan should buy, then

s ≥ 210/10

s ≥ 21

Hence, the inequality representing  s, the number of sets of forks Nathan should buy is

s ≥ 21

3 0
3 years ago
Solve the system of linear equations by substitution x-y=-4 2x+y=4
mylen [45]

Answer:

Given:

x-y=-4

2x+y=4

Step-by-step explanation:

x-y=-4

2x+y=4

add both the equation, we get

⇒  x-y=-4

  2x+y=4

⇒3x=-4+4

⇒3x=0

⇒x=0

∴ to find the value of y, put the value of x in any one equation

⇒x-y=-4

⇒0-y=-4

⇒-y=-4

⇒y=4

∴ x=0, y=4

3 0
3 years ago
Tickets for a concert cost $2 each for children and $5 each for adults.A group of 30 people consisting of children and adults pa
noname [10]
Let,
the no. of adults be "x"
then, the no. of childern = total people - total adults 
                                   = (30 - x)
Now,
According to the quesiton,
2 (30 - x) + 5x = 87
60 - 2x + 5x = 87
60 + 3x = 87
3x = 87 - 60
3x = 27
x = 27 / 3
x = 9

So, there were 9 adults in the group

3 0
2 years ago
Can someone solve this question?​
iren2701 [21]
It’s 26 bc it’s says it right there
5 0
2 years ago
Helpppppp huwdhdidcvqicgqe8ygc
lana [24]
YESSS USE THATTTTTTTTTTTT
6 0
2 years ago
Other questions:
  • Which is the minimum or maximum value of the given function? a. The function has a minimum value of -2 b. The function has a min
    5·1 answer
  • Find the solution of the equation. 2(2x + 3) = -4 + 2(2x + 5)
    14·2 answers
  • 32 is 40% of what is the answer
    14·1 answer
  • Solve correct to 2 Demi meal places<br><br><br><br> 8(6)^x=111<br><br> x=
    6·1 answer
  • A beverage is made by mixing two parts of water with three part of fruit juice. How many parts of water are mixed with one part
    5·2 answers
  • The Hiking Club plans to go camping in a state park where the probability of rain on any given day is 0.66. What is the probabil
    14·1 answer
  • Select the correct answer. Thank you
    7·1 answer
  • Need a Quick answer please
    5·1 answer
  • A children's ride at an amusement park has a rule that a person must be shorter than 4 feet tall to ride it.
    8·1 answer
  • On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), c
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!