From the given recurrence, it follows that
[tex]a_{n+1} = 2a_n + 1 \\\\ a_{n+1} = 2(2a_{n-1} + 1) = 2^2a_{n-1} + 1 + 2 \\\\ a_{n+1} = 2^2(2a_{n-2}+1) + 1 + 2 = 2^3a_{n-2} + 1 + 2 + 2^2 \\\\ a_{n+1} = 2^3(2a_{n-3} + 1) + 1 + 2 + 2^2 = 2^4a_{n-3} + 1 + 2 + 2^2 + 2^3[/tex]
and so on down to the first term,
[tex]a_{n+1} = 2^na_1 + \displaystyle \sum_{k=0}^{n-1}2^k[/tex]
(Notice how the exponent on the 2 and the subscript of a in the first term add up to n + 1.)
Denote the remaining sum by S ; then
[tex]S = 1 + 2 + 2^2 + \cdots + 2^{n-1}[/tex]
Multiply both sides by 2 :
[tex]2S = 2 + 2^2 + 2^3 + \cdots + 2^n[/tex]
Subtract 2S from S to get
[tex]S - 2S = 1 - 2^n \implies S = 2^n - 1[/tex]
So, we end up with
[tex]a_{n+1} = 4\cdot2^n + S \\\\ a_{n+1} = 2^2\cdot2^n + 2^n-1 \\\\ a_{n+1} = 2^{n+2} + 2^n - 1 \\\\\implies \boxed{a_n = 2^{n+1} + 2^{n-1} - 1}[/tex]
Can anyone solve the circled numbers?If not just please solve whatever you can.Im so tired
Answer:
36. The absolute value of |97| is 97. Remember, the absolute value of a number is how far away the number is from zero.
40. I think that says |-23/56| .... if so, I'm pretty sure you can just say 23/56... not too sure though. Because, yes, technically this number is 23/56 away from zero... just not sure if that is the final way you should answer.
44. Answer: Wayne, MI (-0.2)
Explain: Wayne, MI had the least percent change in pop. because it is the closest option to 0, it only decreased 0.2 percent.
48.
|43-4a| + 51
|43-4(6)| + 51
|43-24| + 51
|19| + 51
19 + 51
=70
52.
7.4 + |y-2.6|
7.4 + |3.2-2.6|
7.4 + |0.6|
7.4 + 0.6
=8
56.
|-c| + (2+1/2)
|-5/4| + (2+1/2)
|5/4| + (2+1/2)
|1 1/4| + (2+1/2)
1 1/4 + (2+1/2)
1 1/4 + (2 1/2)
1 1/4 + 2 1/2
1 1/4 + 2 2/4
=3 3/4
That is all I can do for you! I hope I helped :)
A manufacturer makes tshirts where the quantity of tshirts sold is a function of (is dependent on) the price in which they can sell the tshirts. The linear model for this is Q(p) = -100p + 2500 where p represents the price of each tshirt and Q(p) represents the quantity sold.
Answer:
Revenue function: The revenue R(x) from selling x units is the product of price per unit p and the number of items sold x (demand). R(x) = px
Step-by-step explanation:
TRANSLATING SENTENCES INTO EQUATIONS PLEASE HELP
Two more than the quotient of a number and 5 equals 7.
Use the variable x for the unknown number.
Answer:
[tex]\frac{x}{5}[/tex] + 2 = 7
Step-by-step explanation:
The quotient of x and 5 is [tex]\frac{x}{5}[/tex] and 2 more is [tex]\frac{x}{5}[/tex] + 2 , then
[tex]\frac{x}{5}[/tex] + 2 = 7
Answer:
2+ (x/5) = 7
You can also write it as (x/5) + 2 = 7
Step-by-step explanation:
x/5 just means x divided by 5. (Quotient is the answer to a division problem!)
Two more than means plus 2 because you are adding 2 more.
:)
:D
The probability of having a head in a single toss of a coin is?
Answer:
probability will be 1/2 because when you toss a single coin then there will be 2 outcomes: a head and a tail that is 2 possible outcomes so, the probability of getting a hard in a single toss of coin will be 1/2
explanation:
hope it helps
-8(5n+3)=-4(-8n+6)
solve equation
Answer:
0
Step-by-step explanation:
-8(5n+3)=-4(-8n+6)
- 40n - 24 = 32n - 24
- 24 + 24= 32n +40n
72n =0
n = 0
The point V is plotted on the coordinate grid below. Plot the point V′, the reflection of
V over the y-axis.
The difference of a number divided by 2 and six is the same as -12
a 18-inch candle is burning at the rate of 1 inch per hour and 1 15-inch candle is burning at half of an inch per hour. How long will it take for the two candles to be the same height?
Suppose that G(x) = F(x) + 6. Which statement best compares the graph of
G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of Fx) shifted 6 units down.
B. The graph of G(X) is the graph of F(x) shifted 6 units to the left.
C. The graph of G(X) is the graph of F(x) shifted 6 units up.
D. The graph of G(x) is the graph of F(x) shifted 6 units to the right.
I need helpp
Answer:
C) Shifted 6 units up
Graphed:
If f(3) =5 and f(4)=8...
f(5)=___ f(6)=____ recursive function
Answer:
f(5)=11
f(6)=14
Step-by-step explanation:
Hope this helps
Write a formula for perimeter and area of a circle
Thank you !
Answer:
Perimeter of a circle = 2 π r = π D.
Area of a circle is pi times the radius squared (A = π r²).
Help!! Will give Brainiest
Answer:
add all the rest of the angles, and then subtract the sum from 1080, and that's your ans mate
Answer:
147
Step-by-step explanation:
If you add up all the angles you have, you get 933. Since an octagon has 1080 degree angles the last angle must be added to 933 to make it equal to 1080. If you subtract 933 from 1080, you get the remaining angle 147.
Simplify 12 + 16 ÷ 4 · 5 - 8
Step-by-step explanation:
12 + 16 ÷ 4 × 5 - 8
12 + 4 × 5 - 8
12 + 20 - 8
32 - 8
24
Answer: 24
Step-by-step explanation:
Given expression
12 + 16 ÷ 4 · 5 - 8
Simplify by division
=12 + 4 · 5 - 8
Simplify by multiplication
=12 + 20 - 8
Simplify by addition
=32 - 8
Simplify by subtraction
=[tex]\boxed{24}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
need helppppppppppppppppp
-1/5>-10
help and explain please!
Answer:
q=x-10=10
Step-by-step explanation:
add 10 10 10 to both sides
What’s 3-5*2x+79/ 3 12/14 =
Answer: −10x+23 13/27
Step-by-step explanation: -(5)(2x) -10x 3+79/ 3 12/14 3+ 79 / 3 6 /7 3+ 79 / 27 /7 3+ 553 /27 634 /27 23 13 /27 −10x+23 13/27
who wants to sign up for this apartment for me online I will reward you with points no more than 500
Answer:
The first of Aristotle's three elements of persuasion
Ethos also means persuasion, which is what other people do
To believe what you're saying, second, Pathos,
Emotional influence refers to other people
Why it feels like what you're saying is personal,
And Logos, the way of reasoning.
Step-by-step explanation:
Use the equation below to find y, if m=4, x= 9, and b = -1.
y=mx+b
35
Step-by-step explanation:
Here,
m=4
x=9
b= -1
Now to find : y=mx+b
Let's substitute the value,
y=mx+b
=4×9+(-1)
=36-1
=35
0.00002468 round to the nearest hundred
Question 16 of 25
Suppose that Ax) = x2 and G(x) = 2/5 x2?.Which statement best compares the
graph of G(x) with the graph of Fx)?
Step-by-step explanation:
.......................................................:<
10/11 as a rational number
Javiver has $15 to spend On action figures.If it’s bigger cost two dollars what is the greatest number of action figures he can buy
how much can 23 go into 162?
Answer:
7 times
Step-by-step explanation:
You will divide 162 by 23 to find out how many times 23 goes into 162.
162 / 23 = 7.0
The estimated probability of a football player scoring a touchdown during a
particular game is 43%. If several simulations of the football player playing
two games were performed, in what percentage of the simulations would the
football player be most likely to get a touchdown in each of the two games?
A. 12%
B. 86%
C. 43%
D. 18%
a file that is 262 megabytes is being downloaded if the download is 19.2% complete how many megabytes has been download round your awnser to the nearest tenth
Downloaded = 50.3 megabytes (MB)
Now we have to,
find the megabytes has been download.
The question states that,
→ 19.2% of 262 mb
The value of the percentage is,
→ 19.2/100
→ 0.192
Let's find the solution,
→ 262 × 0.192
→ 50.304
→ 50 {nearest tenth}
Hence, 50 mb has been download.
someone please help me with this
8 = 2-h / 7 [h]
Answer: h=-42
Step-by-step explanation:
8=7x2/7 + -h/7
8=7x2-h/7
8=14-h/7
8=-h+14/7
7x8=7(-h+14/7)
7x8=-h+14
56=-h+14
56-14=-h+14-14
42=-h
42/-1=-h/-1
h=-42
An appliance store bought a clothes dryer and marked it up 20% from the original cost of $866.71. Later on, Jackie purchased the dryer and paid 4% sales tax. How much, including tax, did she pay for the dryer?
Answer:
$1081.65
Step-by-step explanation:
866.71/5 gives you 173.34 as 20 percent
add that to the original fir an upmarket and it will be 1040.05.
4 percent of that is $41.60 so add that again and you get 1081.65 as the total amount paid.
The amount Jackie paid for the clothes dryer is $1081.65.
What does mark up and tax mean?Mark up means that the price of an item was increased by a certain percentage. Tax is a compulsory sum levied on the purchase of goods and services. Taxes increase the price of products.
What is the amount paid by Jackie?The mark up price of the clothes dryer = 1.20 x $866.71 = $1040.05
Amount paid by Jackie = 1.04 x $1040.05 = $1081.65
To learn more about taxes, please check: https://brainly.com/question/25311567
What is the distance between these two points?
Part B:if (7^2)^x=1 what is the value of x? Explain your answer.(10 points) Part B: if (7^0)^x=1 what are the possible values of x? Explain your answer. (How did u get your answer)
Answer:
Step-by-step explanation:
7^2 = 49
49^ x = 1 only when x =0
Now 7^0 = 1
Then (7^0)^x = 1^x id equal to 1 for any x.
Is 5y + 27 factorable or prime
explain
Answer:
Prime
Step-by-step explanation:
As there is no common between 5y and 7 except 1 as factor.Hence its not factorable