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
Soloha48 [4]
3 years ago
6

Which of the following geometric series converges?

Mathematics
1 answer:
Mars2501 [29]3 years ago
8 0
All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is

Multiply both sides by r :

Subtract the latter sum from the first, which eliminates all but the first and last terms:

Solve for :

Then as gets arbitrarily large, the term will converge to 0, leaving us with

So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18
You might be interested in
The varsity basketball team started selling T-shirts online in 1994. The number of T-shirts sold online, s, is modeled by the gr
-Dominant- [34]

(PART-A): s-intercept in this case represents the y-intercept of the graph, whereas the t-intercept in this case represents the x-intercept of the graph.

Always remember that y-intercept represents the value of y where the curve (or line) crosses the y-axis, and x-intercept represents the value of x where the curve (or line) crosses the x-axis.

In the graph attached with the question, at point (0,6) the curve crosses the y-axis. Therefore, the <em>y-intercept (s-intercept) in this case is 6</em>. It means that in year 2000 (t=0), 6 hundred shirts were sold.

However, there is no point on the graph where the curve crosses the x-axis, meaning there is <em>no x-intercept (t-intercept)</em>. It means that there is <em>not</em> a single year when the number of shirts sold is 0.


(PART B): As you can see in the graph (attached with the question) that the <em>f(t)</em> is increasing (exponentially) with the increase in <em>t. </em>Therefore, we can safely say that as t increases without bound, the f(t) increases (also). In this context, it means that the sale of shirts increases as the years go by. Hence, the correct blank is "increases."


(PART C): The average rate of change is actually the slope. To find the slope, we can use the following formula:

slope = \frac{y_2 - y_1}{x_2 - x_1} --- (X)

Given points: (5, 12.5) and (7, 22). Plug the values in equation (X),

slope = \frac{22-12.5}{7-5} = 4.75

Hence, the average rate of change for the function between t=5 and t=7 is 4.75 (answer).


(PART D): This part is bit tricky. Therefore, read the explanation carefully!

You can see in the graph that number of Shirts sold is in <em>hundreds. </em>It means that 1 unit (of y-axis in a graph) represents 100 shirts. Therefore, as in the question it is mentioned that there are 1000 T-shirts sold, it will become 10 units (since 10*100 = 1000). So, the function g(t) will become the following:

g(t) = f(t) + 10 --- (Y)

Why did I add f(t)? Because in the question, the word "<em>and</em>" is underlined. It means that g(t) represents not only 1000 T-shirts (10*100 = 1000) sold at the basketball games each year, but it also has the number of T-shirts sold ONLINE, which is f(t).

Now insert f(t) in (Y) and solve:

g(t) = f(t) + 10\\g(t) = (1.5)^t + 5+ 10\\g(t) = (1.5)^t + 15

Hence, g(t) is (1.5)^t + 15

8 0
3 years ago
Read 2 more answers
Need some help with this soon!
Lena [83]

Answer:

f(x)=|x+6|

Step-by-step explanation:

because it is moving the function without changing the slope

5 0
3 years ago
Please help! I will give brainliest to the best answer!
Ahat [919]

Answer:

A

Step-by-step explanation:

y < 1/2x + 1

7 0
3 years ago
In order to have 6,000,000 in 40 years with a 5.75% rate. how much should be deposited each month?
PSYCHO15rus [73]

Answer:

Step-by-step explanation:

This is an Annuity question. It is asking for recurring monthly payment(PMT).  <em>You can use a financial calculator to solve it. I am using (Texas Instruments BA II plus)</em>

Since the payments occur monthly , adjust the interest rate to monthly rate and multiply  40 years by 12 since we have 12 months in a  year<em>.</em>

Total duration of investment ; N = 40*12 = 480

Interest rate; I/Y = 5.75% /12 = 0.4792%

Future value; FV = 6,000,000

Present value ; PV = 0

then CPT PMT = 3,222.912

Therefore $3,222.91  should be deposited each month to achieve the goal.

4 0
3 years ago
Simplify. -7 square root
OverLord2011 [107]
The square root of -1 is i. So you can simplify it to 7(sqrt)-1, which becomes 7i.
8 0
3 years ago
Other questions:
  • Convert to the given unit <br><br> 35 mm = ____ cm
    11·1 answer
  • A kite has vertices at (2, 4), (5, 4), (5, 1), and (0, –1).
    12·1 answer
  • How do i find 3/4 of 460
    5·2 answers
  • Please help, I dont know where to start​
    8·1 answer
  • Polygon ABCD is translated to create polygon A’B’C’D’. Point A is located at (1,5) and point A’ is located at (-2,3). Which expr
    9·2 answers
  • Find the value of x in The parallelogram.
    15·2 answers
  • Use &lt;, &gt;, or = to fill in the blanks.<br> -7----- 0<br> Please help me!
    15·1 answer
  • What is the probability of rolling a number greater than 4 on a standard die?<br> 01<br> Oy<br> 0
    13·1 answer
  • an owl travels 8 1/3 miles an hour and a seagull travels 12 1/2 miles in 2/3 hour. which animal is faster?
    8·2 answers
  • Find the geometric mean of 4 and 8? please i will give you good rating
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!