Answers
Answer:
Option 2: 1 + 1/2 + 1/4 + 1/8+...
Step-by-step explanation:
When a geometric series converges, it has a common ratio that is in between -1 and 1. We can start by finding the common ratios of all the options and then see which one converges.
In the first option, each term is 3 times the term before it, meaning it has a ratio of 3. 3 does not fit in the range we defined, so this series does not converge.
In the second option, each term is half the term before it. This means the common ratio is 1/2. 1/2 is in the range, so this series converges.
In the third option, we can see that the common ratio is -4 since it is the number being brought to a power. -4 does not fit in the range we defined, so this series does not converge.
In the fourth option, we can see the common ratio is 2 since it is the number you multiply by tone more time to get the next term. 2 does not fit in the range we defined, so this series does not converge.
From this, we can see the second option(1 + 1/2 + 1/4 + 1/8+...) is the solution.
The geometric series [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex] converges by the rule of convergence. Thus, the option [tex]2[/tex] from the given options is correct.
When a geometric series converges, it has a common ratio that is in between [tex]-1[/tex] and [tex]1[/tex].
The convergence of the geometric series depends on the common ratio [tex]r[/tex]. When [tex]r[/tex]>1, then the series diverges.When [tex]r[/tex]<1, then the series converges, and when [tex]r[/tex] = 1, then the series oscillates.
The common ratio [tex]r[/tex] of the series [tex]\dfrac{1}{81} +\dfrac{1}{27} +\dfrac{1}{9} +\dfrac{1}{3}[/tex] is greater than [tex]1.[/tex] So, the series diverges.
For the series, [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex] , the common ratio [tex]r[/tex] is [tex]\dfrac{1}{2}[/tex], which is less than [tex]1[/tex] . So, the series converges.
For the series, [tex]\sum 7(-4)^n[/tex] , here the common ratio is [tex]-4[/tex] which does not lie in the range of convergence. Thus the given series is not convergent.
For the series,[tex]\sum \dfrac{1}{5}(2)^{n-1}[/tex] the common ratio is 2. So, the series is not convergent.
The geometric series is [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex].
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Related Questions
Simplify the expression using order of operation (11 - 8)^3 - 2 x 6
Answers
Answer:
500
Step-by-step explanation:
(11-3)^3-2x6
first evaluate 11-3-->8
then cube it-->8^3=512
then multiply 2x6-->12
then subtract the two-->512-12=500
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\huge\textsf{Just do PEMDAS}[/tex]
[tex]\huge\textsf{Parentheses}[/tex]
[tex]\huge\textsf{Exponents}[/tex]
[tex]\huge\textsf{Multiplication}[/tex]
[tex]\huge\textsf{Division}[/tex]
[tex]\huge\textsf{Addition}[/tex]
[tex]\huge\textsf{Subtraction}[/tex]
[tex]\mathsf{(11 - 8)^3 - 2\times 6}[/tex]
[tex]\mathsf{11 - 8 = \boxed{\bf 3}}[/tex]
[tex]\mathsf{3^3 - 2 \times 6}[/tex]
[tex]\mathsf{3^3 = 3\times 3\times 3 = 9\times 3 = \boxed{\bf 27}}[/tex]
[tex]\mathsf{27 - 2 \times6 }[/tex]
[tex]\mathsf{2\times 6 = \boxed{\bf 12}}[/tex]
[tex]\mathsf{27 - 12}[/tex]
[tex]\boxed{\mathsf{\bf= 15}}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 15}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Solve for xx. Round to the nearest tenth, if necessary.
Answers
Step-by-step explanation:
S+T+U=180°{sum of angle of triangle}
68°+90°+U=180°U=180-158°U=22°sin theta= p/h
sin22°=x/83
o.37=x/83
x=0.37×83
x=30.71
x=31
stay safe healthy and happy.
What is the equivalent radian measure for the angle 53?
Answers
9514 1404 393
Answer:
D (53π)/180
Step-by-step explanation:
There are π/180 radians in 1 degree, so in 53°, there are ...
53(π/180) radians = (53π)/180 radians
Third one (Probably two or one more left)
Answers
6×25= 150
17×5= 85
150+85= 235
the answer is 235 :3
help very easy math!!
Answers
Answer:
[tex]y = x - 5[/tex]
Step-by-step explanation:
GIVEN :-
Slope of the line = 1y-intercept of the line = -5TO FIND :-
Equation of the line in slope-intercept formFACTS TO KNOW BEFORE SOLVING :-
Lets say there's a line whose slope is 'm' & y-intercept is 'c'. So, the equation of line in slope-intercept form is → [tex]\boxed {y = mx + c}[/tex]
SOLUTION :-
By using the basic idea of slope-intercept form , the equation of line given in the question is :-
[tex]y = (1 \times x) + (-5)[/tex]
[tex]=> y = x - 5[/tex]
you have it $15 for the movie the cost of a movie ticket is $3 write an inequality to show how much money you can spend on treats.
Answers
Answer:
$3+x is less than or equal to $15
Step-by-step explanation:
I can't write the sign but it's < with a line under it
Step-by-step explanation:
y≥15-3
I am not sure
Mikos family drove at a constant speed as they left home and traveled to the restaurant where they stopped for lunch. Does the relationship between hours elapsed x and distance traveled y represent a proportional relationship? Explain why or why not
(100 points and brainliest)
Answers
Answer:
yes,
distance = time * speed
the more hours you spend in the road, the longer distance you took
Step-by-step explanation:
Answer:
Yes, the relationship between hours elapsed x and distance traveled y represent a proportional relationship.
Step-by-step explanation:
This is because he continuously stayed at a constant speed and didn't change. Once you stay at a constant speed then it will always be a proportional relationship.
if there 10 students and 2/5 play soccer how many students play soccer?
Answers
Answer:
4
Step-by-step explanation:
2 out of 5 play so if there is 10 students 10*2/5 = 4 students
Answer:
4 students would play soccer
Step-by-step explanation:
To make the total students 10 instead of 5 we multiply the information by 2. 2/5 times 2 equals 4/10. So 4 out of 10 studento play soccer
The weights of 11 swimmers in the team were recorded by the coach and the average
weight was 86 pounds. Three swimmers whose weights were 88 pounds, 79 pounds,
and 83 pounds left the team. What was the new average?
Answers
Answer:
87
Step-by-step explanation:
87 x 11= 946
946-88-79-83=696
696/8 = 87
I need help badly and don't send no links or you will be reported
Answers
Answer: - 3/2
Step-by-step explanation:
Use this formula to find the slope for any two given points.
(4, 3) and (6, 0)
↓ ↓ ↓ ↓
x1 y1 x2 y2
y2 - y1 0 - 3
--------- = ---------- = -3/2
x2 - x1 6 - 4
Hope this helped! :)
A cylindrical can is to be constructed for 80 cents. The cost of the material used for the top and the bottom is 3 cents per square inch, and the cost of the material used for the curved side is 2 cents per square inch. Express the volume of the can as a function of its radius. (Recall the volume of a cylinder is V
Answers
Answer:
V = r(40 - 3πr²)/2
Step-by-step explanation:
We know the area of a cylinder, A = 2πr² + 2πrh where r = radius and h = height.
Now, 2πr² = area of top and bottom and 2πrh = curved surface area
Since the cost of material for the top and bottom is 3 cents per square inch, the total cost of the materials for top and bottom = cost of material × area = 3 × 2πr² = 6πr²
Also, the cost of material for the curved is 2 cents per square inch, the total cost of the materials for the curved side = cost of material × area = 2 × 2πrh = 4πrh
The total cost of material = 6πr² + 4πrh
Since the total cost of material = 80 cents,
6πr² + 4πrh = 80
3πr² + 2πrh = 40 (1)
Now, the volume of a cylinder, V = πr²h
From (1), making h subject of the formula, we have
3πr² + 2πrh = 40
2πrh = 40 - 3πr²
h = (40 - 3πr²)/2πr
Substituting h into V, we have
V = πr²h
V = πr² (40 - 3πr²)/2πr
V = r(40 - 3πr²)/2
Select the correct answer.
What is the product of ?
A.
B.
C.
D.
Answers
Answer:
c the answer is c
Step-by-step explanation:
Answer:
C
I hope this helps
4) A bowl contains 8 red balls and 7 blue balls. One is drawn at random
and not replaced. A second ball is then drawn. What is the probability
that the first ball is blue and the second is red?
Answers
Second red: 8/14
PLEASE HELP!!!!1!1!1! suppose one particular pyramid in egypt has a square base of side length 280 meters and a perpendicular height of 144 meters what is the surgace area of the pyramid?
Answers
Answer:
Pyramid Surface Area = .5 * Perim of Base * Slant Height
Slant Height^2 = 144^2 + 140^2
Slant Height^2 = 20,736 + 19,600
Slant Height^2 = 40,336
Slant Height = 200.8382433701
Surface Area = .5 * perim of base * slant height
Surface Area = .5 * 1,200 * 200.8382433701
Surface Area = 120,503 square meters
Source = www.1728.org/volpyrmd.com
Step-by-step explanation:
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using Minitab, resulting in the accompanying output.
Variable N Mean St Dev SEMean Z P -Value
lifetime 50 738.44 38.20 5.40 -2.14 0.016
What conclusion would be appropriate for a significance level of .05? A significance level of .01? What significance level and conclusion would you recommend?
Answers
What is today date please tell me
The spinner has 8 congruent sections. What is the probability of
spinning a number divisible by 3 two times in a row?
Answers
Answer:
1/16 or 0.0625
Step-by-step explanation:
There are two numbers on the chart that are divisible by 3.
So the odds of spinning and getting one of those on the first try would be 2/8 or 1/4.
The odds are then multiplied by the chance of spinning it again on the second try, which would still be 1/4.
To get: 1/16
Lin drew this set of axes and plotted the points A=(1,2), B=(-3, -5), C=(5,7), D=(-4, -3), and E=(-4, 6) on them. Identify her mistakes! Which points were plotted incorrectly?
Answers
Answer:
B=(-3, -5)
Step-by-step explanation:
HELP ASAP will give brainist
Answers
what is the probability that the third spinner lands on a perfect square or a gray space?
6/12 or 1/2
Answer:
There are 6 gray spaces (12, 2, 4, 6, 8, 10) and 3 perfect squares (4, 9, 1). However, 4 is repetitive (it is gray and a perfect square) so there are only 8 we want. There are 12 numbers/spaces in total. The probability formula is (# of desired outcomes)/(# of total outcomes). In this case, there are 8 desired outcomes and 12 total outcomes. So, our answer is 8/12, or 2/3.
The profit, P, realized by a company varies directly as the number of products it sells. If a company makes a profit of $7800 on the sale of 325 products, what is the profit when the company sells 5000 products?
A.80000
B.100000
C.120000
D.60000
Answers
Answer:
C) 120,000
Step-by-step explanation:
Let's use fractions.
7800 = x
---------- -------- . 325 5000 What we are going to do is multiply 325 times x and 7800 times 5000 . 7800 times 5000 equals 39,000,000. 325 times x equals 325x. The reason why we put the info this way is because we are trying to find the profit for a certain number of products . If we were trying the number of products we would put 5000 on top and the x on the bottom of the fraction the n croos multiply but this is not the case.
39,000,000 = 325x
----------------- --------
325 325
Next, we are going to divide 325 on both sides to get x ( in this case x equals the answer) by itself.
39,000,000 /325 = 120,000
325x / 325 = x
x = 120,000
Jamal borrowed $316 for nine months. He paid it off by paying $38.27 monthly.
What will he pay in finance charges?
Answers
The finance charge payed by Jamal is $28.43.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Amount borrowed by Jamal for nine months = $316
His monthly payment = $38.27
Total amount payed by Jamal for nine months = [tex]9(38.27)[/tex]
⇒ [tex]\$344.43[/tex]
Thus his finance charge = [tex]344.43-316[/tex]
⇒ [tex]\$28.43[/tex]
Hence we can conclude that the finance charge payed by Jamal is $28.43.
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Charles is reading about computers. He learns that a computer processor can perform one command in approximately 0.000000016 nanoseconds. What is this number expressed in scientific notation?
Answers
Answer:
1.6 * 10^{-8}
Step-by-step explanation:
Given the following data;
Time = 0.000000016 nanoseconds
To express in standard scientific notation;
Scientific notation is a standard way of expressing very large numbers in powers of 10.
0.000000016 nanoseconds = 1.6 * 10^{-8} nanoseconds.
Note: count the number of zeros (0s) before 1 and write it to the power of 10.
Answer:
the correct answers are 1.6E-8 and 1.6 × 10-8
3 9 26
a. Use eoch digit once, make the smallest 4-digit number:
b. Use each digit once, moke the largest 4-digit number :
c. You can use one diga twice, make the smallest 4-digit number:
c. You con use one digit twice make the largest 4-digit number
.
Answers
b. 9632
c. 2236
d. 9963
prove that 1-cosA/sinA=cosecA-cotA
Answers
Answer:
See the proof below
Step-by-step explanation:
prove that 1-cosA/sinA=cosecA-cotA
Starting from RHS
cosecA-cotA
From trig identty
cosec theta = 1/sintheta and cot theta = cos theta/sin theta
Hence;
cosecA-cotA
= 1/sinA - cosA/sinA
FInd the LCM
= 1-cosA/sinA (LHS)
If Rashid faces north and then turns clockwise half a turn, in which direction does he face
Answers
Answer:naneeeeee
Step-by-step explanation:
What is the value of n in the equation shown below?
2² x 21 = (24)3
Answers
Answer:
4
Step-by-step explanation:
i hope this helped :]
will give brainliest ASAP PLEASE HELP!
Answers
Answer:
7k+7
41
Step-by-step explanation:
Distribute the 7 -
7(k+1)
7 * k = 7k
7*1 = 7
so 7k + 1
Insert 3 instead of x, so it reads -
[tex]5[/tex][tex](3)^{2}[/tex] - 4
[tex]3^{2} = 9[/tex]
9 * 5 = 45
45 - 4 = 41
Help with Math Question 1
Answers
Answer:
Step-by-step explanation:
X is also 67° Like the interior angle
6th grade, the problem solving is on the image
Answers
Answer:
y = x + 3
Step-by-step explanation:
Equation of the line can be written as y = mx + b (slope-intercept form)
Let's find the slope (m) and the y-intercept (b)
Slope (m) = change in y/change in x
Using two points on the line, (0, 3) and (1, 4),
Slope (m) = (4 - 3)/(1 - 0) = 1/1
m = 1
y-intercept (b) = 3 (the coordinate of the point where the y-axis is intercepted by ye line)
To write the equation, substitute m = 1 and b = 3 into y = mx + b
y = 1(x) + 3
y = x + 3
find the slope of the line
(2,5) and (0,5)
Answers
Answer:
y=5
Step-by-step explanation:
Plugging in the two points.
(2,5). y=mx+b or 5=0 × 2+b, or solving for b: b=5-(0)(2). b=5.
(0,5). y=mx+b or 5=0 × 0+b, or solving for b: b=5-(0)(0). b=5.
Hence, equals to y=5
I’m confused can somebody answer this?
Answers
14 is the asnwer because sqaure root of 200 is 14.14213562 and if you round that it is 14