Answers
Answer:
a) -7/9
b) 16 / (n² + 15n + 56)
c) 1
Step-by-step explanation:
When n = 1, there is only one term in the series, so a₁ = s₁.
a₁ = (1 − 8) / (1 + 8)
a₁ = -7/9
The sum of the first n terms is equal to the sum of the first n−1 terms plus the nth term.
sₙ = sₙ₋₁ + aₙ
(n − 8) / (n + 8) = (n − 1 − 8) / (n − 1 + 8) + aₙ
(n − 8) / (n + 8) = (n − 9) / (n + 7) + aₙ
aₙ = (n − 8) / (n + 8) − (n − 9) / (n + 7)
If you wish, you can simplify by finding the common denominator.
aₙ = [(n − 8) (n + 7) − (n − 9) (n + 8)] / [(n + 8) (n + 7)]
aₙ = [n² − n − 56 − (n² − n − 72)] / (n² + 15n + 56)
aₙ = 16 / (n² + 15n + 56)
The infinite sum is:
∑₁°° aₙ = lim(n→∞) sₙ
∑₁°° aₙ = lim(n→∞) (n − 8) / (n + 8)
∑₁°° aₙ = 1
Related Questions
The owner of Sandy’s Boat House advertises the cost to rent a canoe is $15 per hour for trips on the Red Cedar River. He is also willing to adjust the $15 per hour if a customer rents for only a part of an hour.
The manager suggests another deal for customers. She uses the equation cmanager = 0.15t + 2.50 to find the charge c in dollars for renting a canoe for t minutes.
Which option would you choose, the manager’s equation or the owner’s cost of $15 per hour? Explain.
Answers
Answer:
1 dollar
Step-by-step explanation:
If he charges 15 dollars an hour for a canoe, that means that if she rents for 0.15 hours she pays 1 dollar. Hope this helps :)
I need help really quickly with this one!
Answers
Answer: A (y = 1)
Step-by-step explanation:
when dividing, dividing by 0 equals an undefined fraction, therefore, if y was equal to 1, it would cancel out the y - 1, making it 0. I hope that's right :0
Which expression uses the associative property to make it easier to evaluate
8(1/4 x 3/5)?
A. (8 x 5/3) 1/4
B. 4(1/8 x 3/5)
C. 8(3/5 x 1/4)
D. (8 x 1/4)3/4
Answers
Answer: D
Step-by-step explanation:
Using associative property, [tex]8(\frac{1}{4}*\frac{3}{5}) \\[/tex] can be evaluated as 6/5 = 1.2.
What is associative property?The associative property states that the sum or the product of three or more numbers does not change if they are grouped in a different way.
(A × B) × C = A × (B × C).
[tex]=8(\frac{1}{4}*\frac{3}{5}) \\\\=(8*\frac{1}{4}) *\frac{3}{5}\\ \\ = 2* \frac{3}{5} = \frac{6}{5} = 1.2[/tex]
Learn more about associative property here
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Each big square below represents one whole.
Answers
Answer:
[tex]51.5%[/tex]%
Step-by-step explanation:
We can see that each big square is made up of 10 x 10 = 100 small squares.
And we have one whole big square, plus 3 small squares shaded.
So we have 103 shaded squares out of 200.
Therefore percentage is [tex]103 / 200 * 100[/tex] = [tex]51.5%[/tex]%
Answer:
103%
Step-by-step explanation:
if you have 1 100 shaded thats 100% and the 3 on the other representes 3% so 100 plus 3 equals 103
Turner's bookshelf has 6 shelves. Each shelf has 17 books. How many books are on the bookshelf?
Answers
Answer:
102 books
Step-by-step explanation:
Answer:
102 Books
Step-by-step explanation:
Multiply 6 by 17
Without multiplying, determine the sign of the product (−247,634) × (183,758).
Answers
What is the solution of a - 3 = -7
Answers
Answer:
-4
Step-by-step explanation:
take -3 to other side or add 3 to both sides
So, a=-7+3
=-4
2.72981366 rounded to nearest hundredth
Answers
Answer:
I would say 2.73 or 2.72 l can never remember which it is
Step-by-step explanation:
Sorry if it’s wrong!!!
Answer:
2.73
Step-by-step explanation:
Solve the system of equations
y= 2x + 3
y = x - 5
Answers
Answer:
This might be the answer- x=−8 y=−13
Step-by-step explanation:
Answer:
x = 2.66 repeating or 2[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
substitute y for x - 5
y = 2x + 3
x - 5 = 2x + 3
subtract 3 from both sides of the equation
x - 5 - 3 = 2x
x - 8 = 2x
subtract x from both sides of the equation
-8 = 2x - x
-8 = -3x
divide both sides of the equation by -3
-8/-3 = x
2.66 repeating = x
What is the weight in pounds of the tank, as in the above case, if the tank itself weighs 20 lbs per ft of height? A. 63,424 lbs B. 42,241 lbs C. 16,151 lbs D. 10,605 lbs.
Answers
The cost of a pair of shoes was reduced from $60 to $45.
By what percent did the cost of the pair of shoes decrease?
A 2.5%
B 25%
C 30%
D 35%
Answers
Answer:
B. 25%
Step-by-step explanation:
25 percent of 60 would be 15, then if you subtract 15 from 60, you end up with 45, meaning that 25 percent was subtracted.
The percentage is the ratio of change with respect to the original thus cost of a pair of shoes has been reduced by 25% thus option (B) will be correct.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The initial cost of a pair of shoes = $60
Final cost of a pair of shoes = $45
Change in cost = 60 - 45 = 15
The percentage change = change / initial value
Percentage = 15/60
⇒ 0.25 × 100 = 25%
Hence "The cost of a pair of shoes has been reduced by 25%".
For more about the percentage,
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Points J, K, and L are collinear one, and JL: LK = J is located at (-3,5), K is located at (1,-10) and Lis located at (x, y). What are the values of x and y?
Answers
9514 1404 393
Answer:
L = (x, y) = (1/5, -7)
Step-by-step explanation:
The given relation tells you ...
(L -J)/(K -L) = 4/1
Cross-multiplying, we have ...
L -J = 4(K -L)
5L = 4K +J . . . . add 4L+J
L = (4K +J)/5
L = (4(1, -10) +(-3, 5))/5 = (4-3, -40+5)/5
L = (x, y) = (1/5, -7)
Tasha started her homework at 3:45 pm she spent an hour and 20 minutes completing her homework. What time did she finish her homework
Answers
Money that is collecting interest in a bank account doubles in value every 8
years.
When the account was opened, it had 8, or 23 dollars in it. After 32 years, the
account balance has doubled 4 times, increasing by a factor of 24,
It now has a balance of 23. 24. Expressed as a power, how much money, in
dollars, is in the account after 32 years?
A. 24
d
B. 27
C. 212
D. 47
Answers
Answer:
2 to the power of 7
Step-by-step explanation:
add the powers when it is multiplication
Need help ASAP on a timer
Answers
Answer:
1/2
Step-by-step explanation:
use point slope form to write an equation of the line with the given slope that passes through the given point.
Answers
Answer:
A. y - 0 = 2 ( x + 2 )
Step-by-step explanation:
First you have to isolate y, by using A, the 0 can simply be forgotten about. Next, you must expand the equation, thus with 2 ( x + 2 ), it expands to:
y = 2x + 4
With this in mind, the b value is 4, and with a slope of 2, you can see that the equation eventually crosses the y-axis at 4.
A waterfall is n times the height of its picture on a postcard.
Which equation represents the height, y, of the waterfall if
the picture is 6 cm tall?
A y = 6+n
y = 6+n
y = 6n
y=n-6
Answers
Answer: y=6n
Step-by-step explanation:
4/7+2/3=??
Please explain to :)
Answers
Answer: 1 5/21
Step-by-step explanation: change 4/7 into 12/21 and 2/3 into 14/21. Now that you have a common denominator, add the numerators. 26/21. Simplify into 1 5/21
In the diagram g|| h, m<1=(4x+36) and m<2=(3x-3)
What is the measure of <3
Answers
Answer:
60°
Step-by-step explanation:
Since g||h the sum of angle 1 and angle 2 must be equal to 180
4x + 36 + 3x - 3 = 180
7x + 33 = 180
7x = 147
x = 21
The sum of angle 1 and angle 3 is equal to 180 because they are complementary angles
m<1 = 4x + 36 ➡ 4 × 21 + 36 = 120° so angle 3 = 60°
$39.70 + 6% tax equals????
Answers
Answer:
39.70 + 6 equals, (45.7)
Step-by-step explanation:
By simply adding them is how you get your answer.
A car travels at 60 mph for 2 minutes. How far does the car travel?
Answers
Answer:
2 miles
Step-by-step explanation:
Car travels at 60 miles/1 hour
1 hour has 60 minutes
Car travels at 60 miles/60 minutes, which can be reduced to 1 mile/1 minute
In 2 minutues, the car travels two miles
Bre works 12 hour shifts 3 days a week and makes $25.64 per hour. How much does Bre make in 1 week?
Answers
Answer:
923.04 $
Step-by-step explanation:
1 hour: 25.64 $
36 hour: x
x=36×25.64
x=923.04$
Answer:
Bre makes $923.04 in one week.
Step-by-step explanation:
First you have to multiply the 12 hours and the $25.64
25.64x12=307.68 Then if that equals $307.68 then Bre makes $307.68
in on day so then you take $307.68 and multiply it with the 3 days
307.68x3=923.04 So that equals $923.04 then Bre makes $923.04
a week. For (maybe) an easier way to figure this out you can just multiply
12 and 3 first 12x3=36 then you can multiply $25.64 and 36. 25.64x36=923.04 and you will still get the same answer.
Hope this helps:).
Have a nice day:).
Plz mark me brainliest:).
P.S. What kind of job is Bre working that she make almost a thousand dollars
in three days lol.
Dan’s number is three times more than Michael’s. The sum of their numbers is 48. What are their numbers?
Answers
Answer:
michael's number is 12, therefore Dan's is 36.
Step-by-step explanation:
48= michael's number+ 3 times Michael's number
48= m+3m
48= 4m
48÷4= 12 = michael's number
since Dan's is 3 times Michael's, his number is 36.
Answer: Michale's number is 12 and Dan's is 36
Step-by-step explanation:
Using ratios you can create 3:1 which is Dan's ratio to Michale.
You add 3 and 1, which gives you 4.
Divide 48 by 4, which gives you 12.
Michale's part of the ratio is 12 as he has three times less than Dan.
Which concludes that Dan has 36 and Michale has 12.
Please help me with this
Answers
Answer:
300
Step-by-step explanation:
If M
the m
А
B
D.
С
E
Answers
is 0.83 equal to 83/100
Answers
Answer:
Yes.
Step-by-step explanation:
83/100=0.83 : )
Answer:
Yes
Step-by-step explanation:
0.83 means that it's out of 100, if it was 1.0 that means that it would be 100, a full number.
83/100 means that it's out of 100 as well. If it were to be a whole number it would be 100/100
The circumference of a circle can be found using the formula C = 2tr.
Answers
Answer:
r = c/2pi
Step-by-step explanation:
Round the numbers to the highest place value.
2 398-
56 254-
71 563-
33 021-
9 645-
Answers
Answer:
[tex]2398 = 2000[/tex]
[tex]56254 = 60000[/tex]
[tex]71563 = 70000[/tex]
[tex]33021 = 30000[/tex]
[tex]9645 = 10000[/tex]
Step-by-step explanation:
Given
[tex]2398[/tex]
[tex]56254[/tex]
[tex]71563[/tex]
[tex]33021[/tex]
[tex]9645[/tex]
Required
Round up to highest place value
[tex]2398[/tex]
Highest place value here is thousand.
So:
[tex]2398 = 2000[/tex], when approximated
[tex]56254[/tex]
Highest place value here is ten thousand.
So:
[tex]56254 = 60000[/tex], when approximated
[tex]71563[/tex]
Highest place value here is ten thousand.
So:
[tex]71563 = 70000[/tex] when approximated
[tex]33021[/tex]
Highest place value here is ten thousand.
So:
[tex]33021 = 30000[/tex] when approximated
[tex]9645[/tex]
Highest place value here is ten thousand.
So:
[tex]9645 = 10000[/tex] when approximated
Given the following statement, what conclusion can be drawn using law of detachment?
If two angles are vertical, then they are congruent. Angles ABC and DBE are vertical.
Answers
Answer: Angles ABC and DBE are congruent
Last year the original prices of Emma's and Sophie's phones were $560 and $640. Now the prices reduced in ratios 7:6 and 4:3 respectively. What is the difference of the current prices?