Which statement describes ?
The series diverges because it has a sum of 4.
The series converges because it has a sum of 4.
The series diverges because it does not have a sum.
The series converges because it does not have a sum.
Answers
Answer: B
The series converges because it has a sum of 4.
Step-by-step explanation:
The convergence or divergence of a series depends on the sum of the series and its common ratio. The series converges because its sum is b
The series is given as:
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n[/tex]
A geometric series is given as:
[tex]T_n = ar^{n-1}[/tex]
So, we rewrite the series as follows:
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = \sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n[/tex]
Apply law of indices
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = \sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^{n-1} \times (\frac{2}{3})[/tex]
Rewrite
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = \sum\limits^{\infty}_{n=1} 2 \times (\frac{2}{3})(\frac{2}{3})^{n-1}[/tex]
[tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = \sum\limits^{\infty}_{n=1} \frac{4}{3}(\frac{2}{3})^{n-1}[/tex]
So, we have:
[tex]T_n = \frac{4}{3}(\frac{2}{3})^{n-1}[/tex]
Compare the above series to: [tex]T_n = ar^{n-1}[/tex]
[tex]a = \frac{4}{3}[/tex]
[tex]r = \frac{2}{3}[/tex]
The sum of the series to infinity is:
[tex]S_{\infty} = \frac{a}{1 - r}[/tex]
So:
[tex]S_{\infty} = \frac{4/3}{1 - 2/3}[/tex]
[tex]S_{\infty} = \frac{4/3}{1/3}[/tex]
[tex]S_{\infty} = 4[/tex]
i.e. [tex]\sum\limits^{\infty}_{n=1} 2 (\frac{2}{3})^n = 4[/tex]
Also:
The common ratio (r)
[tex]r = \frac{2}{3}[/tex]
[tex]r = \frac{2}{3}[/tex] [tex]< 1[/tex]
When common ratio is less than 1, then such series is convergent.
Hence, (b) is true because it has a sum of 4
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Related Questions
Name an interior angle that is supplementary to <7.
Will give BRAINLIEST!!!!
Answers
Answer:
2, 4, and 6
Step-by-step explanation:
Supplementary angles are angles that add to 180°.
We can see that the angles that make a straight line/straight angle with ∠7 are supplementary to it, because a straight line is 180°.
Those numbers would be be 2, which equals to 4, which equals to 6 and also 8, but that number isn't one of the answers
2,4, and 6
A cube shaped box with 9 centimeter edges is used
for shipping glass figurines. What is the surface
area of the box?
A. 54 in2
B. 108 in2
C. 324 in2
D. 486 in
Answers
2×(c power of 2-5)for c =4
Answers
2/5 x - 3/2 = 1/4 x + 3/5
Answers
Answer:
x = 14
Step-by-step explanation:
Given
[tex]\frac{2}{5}[/tex] x - [tex]\frac{3}{2}[/tex] = [tex]\frac{1}{4}[/tex] x + [tex]\frac{3}{5}[/tex]
Multiply through by 20 ( the LCM of 5, 2 and 4 ) to clear the fractions
8x - 30 = 5x + 12 ( subtract 5x from both sides )
3x - 30 = 12 ( add 30 to both sides )
3x = 42 ( divide both sides by 3 )
x = 14
Ernesto is deep-sea diving with two friends. Alexandra is floating on the surface 6 meters
above Emesto, and Krysta is exploring a coral reef 7 meters in front of Ernesto. How far apart
are Alexandra and Krysta? If necessary, round to the nearest tenth.
Answers
Answer:
Use the Pythagorean theorem. The answer should be 3.61.
Step-by-step explanation:
Help please!! Due in 10 min
Answers
Answer:
Hello Answer: V = 20
Step-by-step explanation:
Hope this helps!
9514 1404 393
Answer:
v = 20 ft
Step-by-step explanation:
The similarity statement tells you the proportional sides:
IH/IK = IG/IJ
v/(10 ft) = (16 ft)/(8 ft)
v = 10 ft × (16 ft)/(8 ft) = 10 ft × 2
v = 20 ft
A student rounds a number to 12.9. Which of the following is a possible value of the original number?
Answers
Answer:
12.85, 12.86, 12.87, 12.88, 12.89, 12.90, 12.91, 12.92, 12.93, and 12.94
Step-by-step explanation:
there is none
11th Grade And Algebra
4g + 13 =54
Answers
Answer:
g = 41⁄4
Step-by-step explanation:
4g + 13 = 54
=> 4g = 54 - 13
=> 4g = 41
=> g = 41⁄4
∴ g = 41⁄4
find the volume if the figure
Answers
Answer:
there aint no figure
Step-by-step explanation:
Answer:
yea there ain't no figure
Step-by-step explanation:
lololololololololol
Convert 400 meters (m) to feet (ft). Round your answer to two decimal places. (1 metre = 3.28084 feet)
Answers
Answer:
1m----------3.28084ft
400m---------xft
x=(400*3.28084)/1
x=1,312.33 ft
Step-by-step explanation:
WVTU is a television station that has 20 thirty-second advertising slots during their regularly scheduled programming each evening. The station is now selling advertising for the first few days in November. They could sell all the slots immediately for $4,500 each, but because November 7 will be an election day, the station manager knows she may be able to sell slots at the last minute to political candidates in tight races for a price of $8,000 each. The demand for these last minute slots is estimated as follows:
8 9 10 11 12 13 14 15 16 17 18 19
Probability 0.03 0.05 0.1 0.15 0.2 0.15 0.1 0.05 0.05 0.05 0.05 0.02
Slots not sold in advance and not sold to political candidates at the last minute can be sold to local advertisers at a price of $2,000.
a. If the station manager sells all the advertising slots in advance, how much revenue will the station receive?
b. How many advertising slots should be sold in advance if the station manager wants to maximize expected revenue?
c. If the station manager sells in advance the number of slots identified in the previous question, what is the probability that the total revenue received will exceed the amount identified in part a where all slots are sold in advance?
Answers
Answer:
a. $90,000
b. 15 advertisement slots
c. 0.53
Step-by-step explanation:
Let the purchase price of the slots, c = 4,500
The salvage value of the slots, s = 2,000
The selling price of the slots, p = 8,000
a. If the store manager sells all the advertising slots in advance, the revenue received, 'R', is given as follows;
R = The number of slots, n × The purchase price for selling immediately, c
∴ R = 20 × $4,500 = $90,000
The revenue the station will receive by selling all the advertising slots in advance, R = $90,000
b. The Cost of Overage, [tex]C_o[/tex] = Purchase price - Salvage value
∴ The Cost of Overage, [tex]C_o[/tex] = 4,500 - 2,000 = 2,500
The Cost of Underage, [tex]C_u[/tex] = Selling price - Purchase price
∴ The Cost of Underage, [tex]C_u[/tex] = 8,000 - 4,500 = 3,500
P; 0.03, 0.05, 0.1, 0.15, 0.2, 0.15, 0.1, 0.05, 0.05, 0.05, 0.05, 0.02
With help of MS Excel, we get the following cumulative frequency
F(Q); 0.03, 0.08, 0.18, 0.33, 0.53, 0.68, 0.78, 0.83, 0.88, 0.93, 0.98, 1
The expected monetary value for the decision to sell the 8th slot at the last minute is given by the following relation;
[tex]C_u[/tex] × [1 - F(Q)] - [tex]C_o[/tex] × F(Q)
Where F(Q) = The cumulative frequency for the 8th stock
Therefore, we have;
3,500 × (1 - 0.03) - 2,500 × 0.03 = 3,300
For the 8th slot, the TV station is expected to make an extra $3,300
Using MS Excel, we get;
For the 9th slot, the profit over the purchase price = $3,020
Fot the 10th slot, the profit over the purchase price = $2,420
The profit over the purchase price for the 11th slot = $1,520
The profit over the purchase price for the 12th slot = $320
The profit over the purchase price for the 13th slot = $(-580)
The 14th = $(-1,180)
15th = $(-1,480)
16th = $(-1,780)
17th = $(-2,080)
18th = $(-2,380)
19th = $(-2,500)
Therefore, to maximize profit, only the 8th, 9th, 10th, 11th, and 12th, slots which are 5 slots should be sold late while 20 - 5 = 15 slots should be sold in advance
c. The probability that the total revenue will exceed the identified amount in part 'a' is the cumulative probability at the 12th slot which is given as follows;
P(D ≤ 12) = F(12) = 0.53.
The probability that the total revenue will exceed the identified amount in part 'a' is the cumulative probability at the 12th slot is 0.53.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
Given information
The demand for these last minute slots is estimated
8 9 10 11 12 13 14 15 16 17 18 19
Probability 0.03 0.05 0.1 0.15 0.2 0.15 0.1 0.05 0.05 0.05 0.05 0.02
The purchase price of the slots = 4,500
The salvage value of the slots = 2,000
The selling price of the slots = 8,000
a. The revenue received
R = The number of slots × The purchase price of the slot
R = 20 × $4,500 = $90,000
The revenue the station will receive by selling all the advertising slots in advance, R = $90,000
b. The Cost of Overage = Purchase price - Salvage value
The Cost of Overage, = 4,500 - 2,000 = 2,500
The Cost of Underage, = Selling price - Purchase price
The Cost of Underage, = 8,000 - 4,500 = 3,500
Probability 0.03, 0.05, 0.1, 0.15, 0.2, 0.15, 0.1, 0.05, 0.05, 0.05, 0.05, 0.02
Cumulative frequency
F(Q); 0.03, 0.08, 0.18, 0.33, 0.53, 0.68, 0.78, 0.83, 0.88, 0.93, 0.98, 1
The expected monetary value for the decision to sell the 8th slot at the last minute
The Cost of Underage × [1 - F(Q)] - × F(Q)
Where F(Q) = The cumulative frequency for the 8th stock
Therefore, we get
3,500 × (1 - 0.03) - 2,500 × 0.03 = 3,300
For the 8th slot, the TV station is expected to make an extra $3,300
For the 9th slot, the profit over the purchase price = $3,020
For the 10th slot, the profit over the purchase price = $2,420
Similarly,
The profit over the purchase price for the 11th slot = $1,520
The profit over the purchase price for the 12th slot = $320
The profit over the purchase price for the 13th slot = $(-580)
The profit over the purchase price for the 14th = $(-1,180)
The profit over the purchase price for the 15th = $(-1,480)
The profit over the purchase price for the 16th = $(-1,780)
The profit over the purchase price for the 17th = $(-2,080)
The profit over the purchase price for the 18th = $(-2,380)
The profit over the purchase price for the 19th = $(-2,500)
Therefore, only the 8th, 9th, 10th, 11th, and 12th slots should be sold in advance to maximize profit.
c. The probability that the total revenue will exceed the identified amount in part 'a' is the cumulative probability at the 12th slot.
P(D ≤ 12) = F(12) = 0.53.
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Phil needs to run at least 30
miles this week for his
training, If he has already run
18 miles this week, then how
mary miles should he run on
each of the 3 remaining days
this week?
I NEED THE INEQUALITIES SOLUTION AND THE GRAPH OF EACH QUESTION
Please please please give me all to each question not just the answer please
IF YOU GIVE ME A LINK I WILL REPORT YOU!
Answers
Answer:
The answers to these equations are 4 for the left math problem, 4 for the middle math problem, and 10 for the right math problem.
Step-by-step explanation:
Answer above.
NO LINKS
what is the answer??
Answers
Answer:
5625 bald eagles
Step-by-step explanation:
Given
[tex]y = 312.5x + 1562.5[/tex]
Required
Predict the numbers in 1998
First, we calculate the value of x
[tex]x = 1998 - 1985[/tex] ---- years since 1985
[tex]x = 13[/tex]
So, we have:
[tex]y = 312.5x + 1562.5[/tex]
[tex]y = 312.5*13 + 1562.5[/tex]
[tex]y = 4062.5 + 1562.5[/tex]
[tex]y = 5625[/tex]
Find the greatest common factor of 6c^3 and 10c^4
Answers
Answer:
2c^3
Step-by-step explanation:
The greatest common divisor of 6 and 10 are 2
The factors that are common to 6c^3, 10c^4 would be 2ccc
Simplify that and you have 2c^3
Write the number six and a half thousand in figures
Answers
Answer:
Step-by-step explanation:
6500 is the correct answer
PLEASE HELP WITH THE SECOND QUESTION!
I'LL MARK BRAINLIEST!
Answers
Answer:
For question #2 about Teresa, it would cost her $1,004.80 to fence all around the circle garden.
Step-by-step explanation:
C = 2πr
C = 2 x 3.14 x 8
C = 50.24 ft.
50.24 x $20 = $1,004.80
Is this model a function?
Explain.
(Someone pls be a decent human being and not send links, all links will be reported)
Answers
Answer:
Yes, that model is a function.
Step-by-step explanation:
A technical definition of a function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
And the model shows that each domain ( x ) only goes to one codomain ( y ) which is what a function is.
Is the graph increasing , decreasing or constant
Answers
Answer: Constant.
The graph does not have an incline and therefore has a slope of 0. This means that the graph is constant.
if lim x-> 4 f(x)=5 lim x-> 4 f g(x)=0 and lim x-> 4 f h(x)=-2, then find lim (fg)(x)
a.1
b.0
c.3
d.does not exist
Answers
Answer:
0
Step-by-step explanation:
Assuming the problem is:
"lim x-> 4 f(x)=5 lim x-> 4 g(x)=0 and lim x-> 4 h(x)=-2, then find lim x->4 (fg)(x)"
lim x->4 (fg)(x)
Since we know the limits of f and g at x=4 exist we can write the limit as:
lim x->4 f(x) lim x->4 g(x) (since fg(x) means f times g of x.)
5(0)
0
if lim x-> 4 f(x)=5 lim x-> 4 f g(x)=0 and lim x-> 4 f h(x)=-2, then lim (fg)(x) 0
What is inequality?inequality the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
Assuming the problem is:
"lim x-> 4 f(x)=5 lim x-> 4 g(x)=0 and lim x-> 4 h(x)=-2, then find lim x->4 (fg)(x)"
lim x->4 (fg)(x)
Since we know the limits of f and g at x=4 exist we can write the limit as:
lim x->4 f(x) lim x->4 g(x) (since fg(x) means f times g of x.)
=5(0)
=0
Hence the lim x-> 4 f(x)=5 lim x-> 4 f g(x)=0 and lim x-> 4 f h(x)=-2, then lim (fg)(x) 0
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Use the drawing tools to form the correct answers on the graph.
Consider this linear function:
y = -23 – 5.
Plot all of the ordered pairs for the values in the domain.
D: {-6, -5, -2,0, 1}
Answers
Answer:
Step-by-step explanation:
Domain of a function defines the input values (x-values) of the function.
Given linear function is,
y = -2x - 5
Domain of the function is,
{-6, -5, -2, 0, 1}
By substituting the values of x in the equation we can get y-values (output values).
Input-output table for the function,
x -6 -5 -2 0 1
y 7 5 -1 -5 -7
Now we can plot these points of the graph.
Two similar solids A and B are shown.
B
А
3 cm
6 cm
Solid A has a volume of 60 cm.
a) Work out the volume of solid B.
Solid B has a total surface area of 140 cm?
b) Work out the total surface area of solid A.
Answers
Answer:
a)
Step-by-step explanation:
a)140cm3-60cm3=60cm of solid C
Answer:
a = 480 b = 35
Step-by-step explanation
:) dont forget correct units
Select all the expressions that are equivalent to –25(15 – 20d + 5c)
Answers
Answer:
-375+500d-125c
-125c+500d-375
Help me out!!!! ASAP!!!!
Answers
Answer:
226 feet
Step-by-step explanation:
264^2 + 900^2= c^2
879696= c^2
938= c
900+ 264= 1164
1164- 938= 226
I think this is right
Which of the following could cause a 32 oz bag of chips to not weigh exactly 32 oz?
Answers
Answer:
you eat 1 chip
Step-by-step explanation:
eat 1 chip and you get 31 oz
The number 4 is what percent of 5? A. 0.8% B. 1.25% C. 80% D. 125%
Answers
Answer:
The answer is C. 80%
Step-by-step explanation:
Hope this helped:)
PLEASE HELP ME GIVING LOTS OF POINTS AND BRAINLIEST TO THE FIRST LEGIT ANSWER!!!
A group of students were surveyed to find out if they like building snowmen or skiing as a winter activity. The results of the survey are shown below:
60 students like building snowmen
10 students like building snowmen but do not like skiing
80 students like skiing
50 students do not like building snowmen
Make a two-way table to represent the data and use the table to answer the following questions.
Part A: What percentage of the total students surveyed like both building snowmen and skiing? Show your work. (5 points)
Part B: What is the probability that a student who does not like building snowmen also does not like skiing? Explain your answer. (5 points)
Answers
Answer: 45.4% of students like both building snowmen and skiing
18.1% of students who do not like building snowmen also do not like skiing
Step-by-step explanation:
__________________________________________________
likes snowmen doesn't like snowmen total
__________________________________________________
likes skiing 50 30 80
__________________________________________________
doesn't like skiing 10 20 30
_________________________________________________
total 60 50 110
help pls Peter bought 9 tickets to a basketball game. He paid a total of $72. Choose the equation that determines whether each ticket cost $6 or $8
Answers
Answer:
Cost of each ticket bought by Peter = $8 for each ticket
Step-by-step explanation:
Given:
Number of ticket bought by Peter = 9 tickets
Amount paid by Peter for tickets = $72
Find:
Cost of each ticket bought by Peter
Computation:
Cost of each ticket bought by Peter = Amount paid by Peter for tickets / Number of ticket bought by Peter
Cost of each ticket bought by Peter = 72 / 9
Cost of each ticket bought by Peter = $8 for each ticket
put in a new
A rectangular garage is 11 yards long and 5 yards wide. It costs $2.00 per square yard
concrete floor. How much would it cost to put a new concrete floor in the garage?
Answers
Answer:
$110
Step-by-step explanation:
The first step would be to multiply 11 and 5 to get the result of 55.
Then, you would multiply 55 by whatever the cost per square yard is, which in this case is $2.
Finally after multiplying 55 and 2 you would get the answer of $110.
Hope this helped! Have a great day! :)
pls help me waaaaaaa
Answers
Answer:
lol lol lol lol lol lol lol lol
Step-by-step explanation:
A researcher was interested in knowing whether the mean weight of the second baby is higher, lower, or about the same as the mean weight of the first baby for women who have at least two children. She selected a random sample of 20 women who had at least two children and asked for the weights of the first two at birth. She found that the mean of the differences (first - second) was 5 ounces, and the standard deviation of the differences was 7 ounces.
Required:
a. Why was the researcher's study design better than taking independent samples of mothers and asking the first sample about the weight of their first baby and the sec_ and sample about the weight of their second baby?
b. Define the parameter of interest. Use appropriate notation.
c. Write the mean of 5 ounces and the standard deviation of 7 ounces using appropriate statistical notation.
d. Find a 90% confidence interval for the parameter that you defined in part (b). Write a sentence or two interpreting the interval.