The radius of convergence, R, of the series ∑[infinity]n=1 xn8n-1 is 1/8. The interval of convergence, I, is (-1/8, 1/8) or (-1/8 ≤ x ≤ 1/8).
To find the radius of convergence, we can use the ratio test. Let's apply the ratio test to the given series:
lim |xn+1 × 8n / (xn × 8n-1)| as n approaches infinity.
Simplifying the expression, we get:
lim |x × 8n / 8n-1| as n approaches infinity.
Since the absolute value of x does not affect the limit, we can simplify further:
lim |8x| as n approaches infinity.
For the series to converge, the limit must be less than 1. Therefore, we have: |8x| < 1.
Solving for x, we find: -1/8 < x < 1/8.
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Could someone please tell me what this means? Like is it a/6 - 1/6?
Answer:
Yes, this is similar to [tex]\frac{a}{6} - \frac{1}{6}[/tex]
Answer:
yes
Step-by-step explanation:
Given
[tex]\frac{a-1}{6}[/tex]
Then each term on the numerator is divided by 6, that is
= [tex]\frac{a}{6}[/tex] - [tex]\frac{1}{6}[/tex]
Omar rented a truck for one day. There was a base fee of $15.99, and there was an additional charge of 74 cents for each mile driven. Omar had to pay
$166.95 when he returned the truck. For how many miles did he drive the truck?
[tex]15.99 + 0.74(m)[/tex]
[tex]15.99 + 0.74(m) = 166.95[/tex]
[tex]15.99 - 15.99 + 0.74(m) = 166.95 - 15.99[/tex]
[tex]0.74m = 150.96[/tex]
[tex] \frac{0.74m}{0.74} = \frac{150.96}{0.74} [/tex]
[tex]m = 204[/tex]
He drove 204 miles.
The formula V = s3 gives the volume V of a cube with side length s. The volume of a cube that has a side length of 7 inches
The volume of a cube with a side length of 7 inches is 343 cubic inches.
To find the volume of a cube with a side length of 7 inches, we can use the formula [tex]V = s^3[/tex], where V represents the volume and s represents the side length.
Substituting the given side length into the formula, we have:
[tex]V = 7^3[/tex]
To simplify the expression, we raise 7 to the power of 3, which means multiplying 7 by itself three times:
V = 7 * 7 * 7
V = 343 cubic inches
Therefore, the volume of a cube with a side length of 7 inches is 343 cubic inches.
The complete question is
The formula V = s3 gives the volume V of a cube with side length s. The volume of a cube that has a side length of 7 inches is equal to ____.
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What is the change in temperature from -8°F to 14°F?
-6°F
6°F
0
-22°F
22°F
Which scenario could be represented by the value −8 ? Select each correct answer. A puppy gains 8 pounds. The temperature is 8 degrees below 0. The elevation of a hot air balloon is 8 meters. A student's class average decreases by 8 points.
plzz help ill give brainliest
Answer:
- The temperature is 8 degrees below 0
- A student's class average decreases by 8 points.
Answer:
The temp is 8 degrees below 0, a student's class average decreases by 8 points
Step-by-step explanation:
a puppy gaining 8 pounds is positive
the temp is 8 degrees below 0 which is negative
the elevation of a hot air balloon is 8 meters above the ground
A student's class average decreases by 8 points = negative
The value -8 is negative and it doesn't say you have to only select one answer
I really need someone's help please!
Answer:
Felipe subtracted 3x from both sides of the equation.
Answer:
-2
Step-by-step explanation:
first, you will subtract the 2x from 3x then take 6 away from - 8 so it would be 8 and subtract it from 6 because of where the = is and get your answer
In an arithmetic sequence, a17 = -40 anda28 = -73. Explain how to use this information to write a recursive formula for this sequence.
Answer:
–73 – (–40) = –33.
Step-by-step explanation:
7.1 added to a number equals 10.3?
The answer is 3.2. If you subtract 10.3 and 7.1, then you get 3.2.
graph x<2/9 on a number line
Answer:
The line should begin on the right side 2 dashes (the small lines tht go throught the number line. There are 9 dashes between each whole number.)
Then the line should go left because it says x is less than 2/9. (which is right)
The line segment you should choose is the one with the open circle with an arrow going to the left.
<---O (looks like this lol.)
Which of the following options have the same value as 40%, percent of 84?
Please Answer ASAP
Answer:
40% of 84 is 33.6
Step-by-step explanation:
I really need help with this one or I fail
PLEASE PLEASE HELP HELP PLEASE
Answer:
1. product 2. difference 3. quotient 4. sum 5. dividend
pls answer the following questions i will give brainilest if u get them right
4 × 0.75=?
4 ÷ 0.65 = ?
2.8 × 1.42 = ?
2.75 ÷ 1.30 = ?
Answer:
1. 3
2. 6.15
3. 3.976
4. 2.11
Step-by-step explanation:
Hope this helped:)) Plz mark Brainliest :))
(sat prep) find the value of x
Answer:
120 degrees
Step-by-step explanation:
RSM boi
but you actually have to get the values of the angles on the other side so
180-70=110
180-50=130
pretty simple from there
Answer:
120 deegress
Step-by-step explanation:
x + y = z
70 + 50 = x
x = 50+70 = 120
Help would be appreciated thanks .
Answer:
my answer was wrong and cannot help
pls help! marking brainliest!!
Answer:
x = 52
Step-by-step explanation:
∡RQS = 180 - (90 + 34)
∡RQS = 56°
∡PQS + ∡RQS = 180°
∡PQS = x + 72
x + 72 + 56 = 180
x + 128 = 180
x = 52
9 x 3/9 is greater than less than or equal to 9?
Answer:
9 x 3/9 is less than 9
Step-by-step explanation:
Answer:
No because when multiplyin a fraction your outcome is less than the orginal
number most likely
Step -by-step explanation:
simplify - 5 1/4 - (- 7 1/2)
Answer:
Hey! Your answer is, 9/4
Step-by-step explanation:
Hope this hepls! :)
Have a nice day!♥
Brainliest?
Answer:
Exact Form:
91/20
Decimal Form:
4.55
Mixed Number Form:
4 11/20
Step-by-step explanation:
011
Question Help
in a race, 16 out of the 25 bicyclists finished in less than 30 minutes. What percent of bicyclists
finished the race in less than 30 minuten Write an equivalent fraction to find the percent
Answer:
[tex]\frac{16}{25}[/tex] x [tex]\frac{4}{4}[/tex] = [tex]\frac{64}{100}[/tex] = 64%
Step-by-step explanation:
9. found the answer.... Find the function rule.
y=4x+3
Write a rule for the linear function in the table.
I NEED HELP PLEASE!!!!!
A. f(x) = –4x – 3
B. f(x) = x + 3
C. f(x) = 1/4x + 3
D. f(x) = 4x + 3
Answer:
The answer is "Choice D"
Step-by-step explanation:
In this question, given equation "[tex]y=4x+3[/tex]" is similar the choice d, and its values matches the given table, that can be defined as follows:
choice:
[tex]\to f(x)=4x+3\\\\ when \ x=0\\\to f(0)=4\times 0+3=0+3=3 \\\\ when \ x=3\\\to f(3)=4\times 3+3=12+3=15 \\\\when \ x=6\\\to f(6)=4\times 6+3=24+3=27 \\\\when \ x=9\\\to f(9)=4\times 9+3=36+3=39 \\\\[/tex]
~!¡! Attributes !¡!~
~I'm new to this~
Find the mode of the following data: 5, 0, 5, 4, 12, 2, 14
Answer:
5
Step-by-step explanation:
To solve the problem we must know about Mode.
What is the mode?Mode is the data point that repeats the most number of times in a given data set.
The mode of the data set is 5.
Given to us
Data set: {5, 0, 5, 4, 12, 2, 14}As in the given data points {5, 0, 5, 4, 12, 2, 14}, number 5 repeats twice, therefore, 5 is the mode of the given data set.
Hence, the mode of the data set is 5.
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Half of Ethan string is equal to 2/3 of Kayla stream the total length of the string is 10 feet how much longer is Ethan string Kayla string
Answer:
10/7 feet
Step-by-step explanation:
Let e = Ethan
k = Kayla
The following equations can de derived from the equation :
1/2 e = 2/3k
multiply both sides of the equation by 2
e = 4/3k --- 1
e + k = 10 --- 2
Substitute for e in equation 2
4/3k + k = 10
7/3k = 10
multiply both sides of the equation by 3/7
k = 30/7
Substitute for k in equation 1
e = (4/3) x 30/7 = 40/7
difference in length = 40/7 - 30/7 = 10/7
How many liters of 70% acid solution must be mixed with a 15% acid solution to get 550L of a 60% acid solution
9514 1404 393
Answer:
450 L
Step-by-step explanation:
Let x represent the number of liters of 70% solution needed. Then the amount of 15% solution needed is (550-x), and the total amount of acid in the mixture is ...
0.70x + 0.15(550-x) = 0.60(550)
0.55x + 82.5 = 330 . . . . simplify
0.55x = 247.5 . . . . . . . . . subtract 82.5
x = 450 . . . . . . . . . . . divide by 0.55
450 liters of 70% acid solution must be used.
New York City is approximately 205 miles from Washington, D.C. How far apart will these cities appear on a map with the scale 1 in: 50 miles?
Answer: 4.1 inches
Step-by-step explanation:
From the question, we are informed that New York City is approximately 205 miles from Washington, D.C.
The distance that these cities will appear on a map with the scale 1 in: 50 miles will be represented by x.
Therefore, x:205 = 1:50
Cross multiply
x/205 = 1/50
50x = 205
x = 205/50
x = 4.1 inches
The answer is 4.1 inches
Which expression has a value closest to 1? (Use 3.14 as the value of 1.)
A.
77
V10
B. 75-V74
O C.
V37-V26
3V5 – V20
D.
Answer:
C: √37 - √26
Step-by-step explanation:
√37 = 6.083
√26 = 5.1
6.083 - 5.1 = 0.983
Answer:
C
Step-by-step explanation:
The sales tax in one state is 6%. Write a function rule for finding the total cost of an item with selling price x. Then find the total cost of a CD player with a selling price of $160.
f(x) = 0.06x; $9.60
f(x) = 6 + x; $161.06
f(x) = x – 6; $158.94
f(x) = 1.06x; $169.60
Answer: brainly.... D. f(x) = 1.06x; $169.60
sales tax = 6% or 6/100.
assuming tax is added onto the item:
total cost function f(x) = price + tax
however, assuming the cost price = sales price - tax, then:
f(x) = sales price - tax
This is not really a business or accounting forum, its a maths forum, so you need to be clearer about business or accounting terms such as total cost, selling price, selling cost.
Step-by-step explanation: brainly
if y= the item after tax
y=x+(x*6%) or y=x+6%
and then for the answer you would go:
y=160+6% or 160+(160*6%)= $169.60
Answer: f(x)=1.06x; $169.60
Step-by-step explanation: pearson
The relationship between the postage rate and the weight of a letter can be defined by a piecewise function. The graph shows the 2018 postage rates for using regular service to mail a letter. Kiran and Mai wrote some rules to represent the postage function, but each of them made some errors
Kiran equation is incorrect because there are two rates when the weight is 1,2, and 3 ounces, also, the first symbol is incorrect; on the other hand, Mai is incorrect because the prices for 1, 2, and 3 ounces are not correctly expressed.
What is a function?A function is an expression that shows how two factors, in this case, rate and weight are related. These functions are usually created based on specific data and they should relate the data correctly.
What was Kiran's mistake?1. There are two rates for 1, 2, and 3 ounces: The use of symbols Kiran used to explain the rate for 1, 2, and 3 ounces is incorrect. Let's examine an example:
0.71 1 ≤ w ≤ 20.92 2 ≤ w ≤ 3It seems the rate for 2 pounds can be both 0.71 and 0.92 because in the first line if the weight is less or equal to 2, the rate is 0,71 and this also happens in the second line.
2. The first symbol he used is incorrect because it seems like there is a charge even if the weight is 0, which is impossible.
0.50 0 ≤ w ≤ 1 (The rate if the weight is less or equal to 0 is 0.50)What is Mai's mistake?1. Similarly to Kiran she did not express the rate and the pounds correctly. Let's look at one example:
0.71 1 < w < 2 (if the weight is less than 2 the rate is 0.71, which is incorrect because the rate is 0.71 if the weight is less or equal to 2)Note: This question is incomplete; here is the missing section:
Identify the error in each person's work:
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The table gives the costs for organizing Field Day at a Middle School. Thirty-two students will attend the event.
Expense:
Total Cost ($):
Supplies
$272.64
Announcer
$168.84
Refreshments
$113.40
What is the cost per student for this event?
What is the cost per student for supplies only?
If you eat 4 medium strawberries, you get 36% of your daily recommended amount of vitamin C.
What fraction of your daily amount of vitamin C do you still need? Enter your answer in simplest form
You still need
amount of the daily recommended amount of vitamin C.
Answer:
16/25
Step-by-step explanation: