Answers
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
The geometric series that converges is II. 0.3 + 0.12 + 0.048 + 0.0192 ( Option A).
To determine whether a geometric series converges, we need to check if the common ratio (r) of the series lies between -1 and 1 (inclusive). If the absolute value of r is less than 1, the series converges; otherwise, it diverges.
Let's check each series:
I. 2.9 - 3.19 + 3.509 - 3.8599
To find the common ratio, we divide each term by the previous term:
r = (-3.19) / 2.9 ≈ -1.1 (diverges)
II. 0.3 + 0.12 + 0.048 + 0.0192
To find the common ratio, we divide each term by the previous term:
r = 0.12 / 0.3 = 0.4 (converges)
III. 4 - 16 + 64 - 256
To find the common ratio, we divide each term by the previous term:
r = -16 / 4 = -4 (diverges)
So, the convergent geometric series is II. 0.3 + 0.12 + 0.048 + 0.0192.
To know more about geometric series, refer here:
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Related Questions
Express and simplest radical form.
Answers
Answer:
4 square root 5 is the answer
root(20*4)
2 × root(5×4)
4×root(5)
please help me on this will give you brainliest!!
Answers
Answer:
bc= 6
Step-by-step explanation:
since the triangles are similar, the sides are in a ratio
xz/ac = 20/4 (5:1)
yx/ba = 15/3 (5:1)
yz/bc = 5:1 = 30/6
Hope this helps
Have a great day/night
PLS HELP WILL GIVE BRAINLIEST!
if the diameter of a circle changes from 8 cm to 4 cm, how will the circumfrence change?
A.) multiplies by 1/2
B.) multiplies by 2
C.) increases by 6
D.) decreases by 6
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What is the slope of the line that passes through the points (-4,5) and (0, -5)? Choose the BEST answer!
m = -10/4
m = -5/2
m= 0
m = 5/2
Answers
Answer:
m= -5/2
Step-by-step explanation:
formula for slope(m) : ΔY/ΔX (change in y coordinates - change in x coordinates)
change in y coordinates: 5-(-5) = 10
change in x coordinates: -4-(0) = -4
10/-4 = -5/2= -2.5
Help me pleaseeeeeeeeeeeeewe
Answers
Answer:
no its x = - 4
Step-by-step explanation:
hi hi help math please ill give brainliest too the person whom gets it right :))))))))))))
Answers
Answer:
4/1
Step-by-step explanation:
The slope of the line is y/x or rise/run. The line increases in height (y) by 4, while it only travels (x) 1. The line travels 4y in the time it takes to travel 1x. 4/1 (or just 4)
please help 20 points !!!! right answers please
Answers
Answer:
0.6 inch
Step-by-step explanation:
The volume of a sphere is calculated through the equation,
V = 4πr³/3
Which means that the radius is calculated by the equation,
(3V/4π)^(1/3) = r
Substituting,
Sphere A, (3x30/4π)^(1/3) = r = 1.927 in
Sphere B, (3x10/4π)^(1/3) = r = 1.336 in
When we subtract the radius, we get an answer of 0.59 inch. Therefore, the answer to this item is approximately 0.6 inch.
This is to help me study for a math exam. Anyone that takes advantage of the points will be reported. Thank you!
Answers
Answer:
2) (see image below)
3) x = 8
side(s) = 74
4) x = 10
EF = DE = 67
base = 31
Step-by-step explanation:
For No. 2, if you draw out two triangles with the corresponding angles, you can make it a lot easier. See the image below:
For No. 3, it is given that it's an equilateral triangle, meaning all sides and angles are congruent. So:
12x – 22 = 10x – 6 = 7x + 18
Instead of using all three at once, you can use any two. I'll be using:
12x – 22 = 10x – 6
2x = 16
x = 8
Plugging x in, we can get all the sides, because this is an equilateral triangle:
12x – 22
12(8) – 22
96 – 22
74
For No. 4, it is given that the triangle is an isosceles triangle where DE ≅ EF, so:
8x – 13 = 5x + 17
3x = 30
x = 10
Plugging in x for one of the congruent sides and the base, you can get your needed side length values:
8x – 13
8(10) – 13
80 – 13
67
x + 21
10 + 21
31
Write the linear equation in slope-Intercept form passing through the point with the glven slope. 1. (0, 3): slope = -2
2. (-5,-3); slope = -3/5
3. (-8,6); slope 1/4 Write the linear equation in slope-intercept form that passes through the given points.
4. (1,3) and (-3,-5)
5. (1,4) and (6.-1)
6. (-12, 14) and (6,-1)
Answers
Answer:
1)y=-2x+3
2)Y=-3/5x-6
3)y=1/4x+8
4)M=2
5)y=5x-1
6)M=-5/6
Step-by-step explanation:
In EFG, L is the centroid. If LJ=9 find EL.
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Answer:
LG=LE=LF since it is the centroid. So I think it would also be 9.
PLEASE HELP ME Please!!!
Answers
Answer:
8m would be the answer to your question
Answer:
Depending on the expression you are looking for,
8 times M could be an answer.
8xM
Product is the example of multiplication.
~Hope this helps~
Alex is y years old. His sister Bella is 4 years older than him. Carla is double Alex's age. The sum total of their ages is 32 form and solve an equation to work out the ages of the three children
Answers
Answer:
I dont understand what this question is trying to say, but you should just use a calculator.
Step-by-step explanation:
Sorry!
Help me with this one!
Answers
Answer:
It’s A
Step-by-step explanation:
Cuz it’s just the numbers are replaced in different places but when u multiply u get the same ans ig
PLZZ ANSWER FAST!! (WITH EXPLANATION)Mrs. Evans took a poll of which students in her class have a dog. If 24 students (4/5 of her entire class) have a dog, then how many total students are in Mrs. Evans' class?
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6s + 3 = - 27 s=___ help
Answers
3=-33s divide both sides by 3
s=-11
Answer:
[tex]6s + 3 = - 27 \\ 6s = - 27 - 3 \\ = - 30 \\ s = \frac{ - 30}{6} \\ s = - 5[/tex]
Are the following equations parallel, perpendicular, or neither?
help me
Answers
Answer:
Neither
because parallel equations often have the same exact slop but different y- intercept and nor is it perpendicular because slop must be flipped over 1 and negative so its not evident there.
Hope it helps:))
Step-by-step explanation:
Select the correct answer.
Look at the graph below.
Which of the following statements are true, based on the graph?
A. The number of hours depends on the number of boxes manufactured.
B. The number of boxes manufactured depends on the number of hours.
C. The number of pens depends on the number of boxes manufactured.
D. The number of pens depend on the number of hours.
Answers
Answer:
B. The number of boxes manufactured depends on the number of hours.
Step-by-step explanation:
The graph shows that as more time passes, more boxes are being manufactured. Therefore, the number of boxes relies on the number of hours.
Hope this helps :)
please help(: ( 8th grade lesson)
Answers
Step-by-step explanation:
Since angle 1 is on a straight line and we know that angle 4 is 160, and a straight line has a sum of 180 degrees, simply subtract 160 from 180 to get angle 1.
Angle one would be 180-160 = 20
Since the sum of angles in a triangle is 180 and we already know 2 of them, angle 1 is 20 and angle 3 is 30, just add them together and then subtract that from 180. 20 + 30 = 50, and 180 - 50 = 130.
So in conclusion:
Angle 1 is: 20
Angle 2 is: 130
A toy store sells accessories to go with the latest action figure. The store projects that it will sell a certain number of accessories for every box of a dozen action figures it orders. Let d represent one box of a dozen action figures.
Use the table to write an expression to represent the actual number of each accessory sold per box of action figures.
Accessory Turbo JET Pack X-Ray Vision Glasses Invisible SHIELD
Word Description Six times the number of boxes plus seven Five less than two times the number of boxes One more than ten times the number of boxes
Answers
The expression for the turbo jet pack is 6d+7, the equation for the x-ray vision glasses is 2d-5, and the equation for the invisible shield is 10d+1.
How to write an expression?The steps to write an expression are:
Identify the variables or factors involved.Write the factors by relating them correctly using symbols such as +, -, x, etc.What is the expression for the turbojet back?The expression is 6d (six times the boxes) + 7 (plus seven).
What is the expression for the x-ray vision glasses?The expression is 2d - 5 (two times the number of boxes minus five.
What is the expression for the invisible shield?The expression is 10d + 1 (ten times the number of boxes plus one).
Learn more about x ray in: https://brainly.com/question/2833441
b = -4g + 52
Hi can u help me thanks
Answers
Answer:
54wy35syrdhtrd
Step-by-step explanation:
oy86t4s2r4ssuc78t87y8ma769798bowss668768
How far is the portion of her route from H to A? Round to the nearest whole number. Explain. PLS HELP ME I NEED IT BY TONIGHT
Answers
Answer:
2089
Step-by-step explanation:
if you spin the spinner 40 times, how many 4'
Answers
Answer:
10
Step-by-step explanation:
Answer:
Your prediction would be eight 4's
Step-by-step explanation: I just solved it!
pls help how many terms r there?
Answers
Answer:
3
Step-by-step explanation:
Match the description to the graph:
help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help pls help. I will mark you as Brainly if you help me, also I will also very thank to u.
Answers
Answer:
1.)B 2.)C 3.)D
Step-by-step explanation:
sanaakantulong please give me brainlist
#carry on schoolAnswer:
The first distance is b. The second distance is c. And the last distance is d.
Step-by-step explanation:
For the first one it is b because she does not stop walking from one place to the other and same with d. But c is different because she did not get to her destination and ran back home so she did not complete the trip.
Need help on these please
Answers
Answer:
1)16(x+y) is not equal to 4x+12y, it is equal to 16x+16y
2)2x^2-y+5+3 is not equal
3)3x & 3y
4)15x+15
5)commutative
PLZ HELP PLZ HELP WHATS THE ANSWER
Seven times the first number plus six times the second number equals 31.
- Three times the first number minus ten times the second number is 29.
WHAT ARE THE TWO NUMBERS
Answers
Then for the second equation, well... there’s multiple answers:
First would be 3 and -2 because 3(3)-10(-2) simplifies to 9+20=29.
Another one would be 23 and 4 because 3(23)-10(4) simplifies to 69-40=29.
Hopefully this helps :D
The first number will be [tex]\frac{11}{2}[/tex] and the second number will be [tex]-\frac{5}{4}[/tex].
Let the first number be x and the second number be y.
According to the question,
Since seven times the first number plus six times the second number equals 31. So,
[tex]7x+6y=31.......(1)[/tex]
Similarly,Three times the first number minus ten times the second number is 29.So,
[tex]3x-10y=29.......(2)[/tex]
Multiplying equation (1) by 3 and equation (2) by 7, we get
[tex]21x+18y=93[/tex]
[tex]21x-70y=203[/tex]
Now subtracting both the equations we get,
[tex]88y=-110[/tex]
[tex]y=-\dfrac{110}{88}[/tex]
[tex]y=-\dfrac{5}{4}[/tex]
putting the value of x in equation (1) we get,
[tex]7x+6\times-\dfrac{5}{4} =31[/tex]
[tex]7x-\dfrac{15}{2}=31\\[/tex]
[tex]7x=31+\dfrac{15}{2}[/tex]
[tex]7x=\dfrac{77}{2}[/tex]
[tex]x=\dfrac{11}{2}[/tex]
Hence the first number is [tex]\frac{11}{2}[/tex] and the second number is [tex]-\frac{5}{4}[/tex].
For more details on solving linear equation in two variables follow the link:
https://brainly.com/question/10270150
If I was asked to think of a number and multiply it by 2, I could write this algebraically as 2x.
Write the following algebraically using x as your unknown.
“I think of a number, multiply it by 2, subtract 3 and multiply the result by 4”
Answers
Answer:
8x - 12
Step-by-step explanation:
Let the number be x
multiply by 2
= x * 2 = 2x
Subtract 3 ;
2x-3
Multiply result by 4
=
4(2x -3) = 8x-12
5(a-6) in expanded form?
Answers
Answer:
5a - 30
Step-by-step explanation:
Answer:
5a - 30
Step-by-step explanation:
Distributive property: a(b + c) = a*b + a*c
5(a - 6)= a * 5 - 6*5
= 5a - 30
The length of a rectangle is 1 foot less than 3 times the width. The area is 310 ft². Find the dimensions of the rectangle.
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brainly pleaseee
show step by step......
Answers
Answer:
Step-by-step explanation:
Amount paid for first 100 watches = (65% of 80) *100
[tex]=\frac{65}{100}*80*100\\\\= 65*80\\= 5200[/tex]
Amount paid for next 50 watches = (55% of 80) * 50
[tex]= \frac{55}{100}*80*50\\\\= 55 * 8 * 5\\\\= 2200[/tex]
Remaining watches = 280 -(100+ 55)
= 280 - 155 = 125
Amount paid for 125 watches = (45% of 80) *125
[tex]= \frac{45}{100}*80*125\\\\= 45 * 20 * 5\\\\= 4500[/tex]
Amount received by the watch maker = 5200 + 2200 + 4500
= £ 11900