The asymptotic bound for the recurrence relation T(n) = 2T(n/2) + n lg n is Θ(n lg² n).
How to solve recurrence relation?To determine the asymptotic bound for the recurrence relation T(n) = 2T(n/2) + n lg n using the Master theorem, we need to compare the function f(n) = n lg n to the function g(n) = [tex]n^log_b[/tex](a).
In this case, a = 2, b = 2, and f(n) = n lg n.
The Master theorem states that if f(n) = O(n[tex]^log_b[/tex](a - ε)) for some ε > 0, where a ≥ 1 and b > 1, then the solution to the recurrence relation is T(n) = Θ(n[tex]^log_b[/tex](a)).
Let's calculate the values:
n[tex]^log_b[/tex](a) = n[tex]^log_2[/tex](2) = n¹ = n
Since f(n) = n lg n and n¹ = n, we need to determine if f(n) satisfies the condition f(n) = O(n(¹ - ε)) for some ε > 0.
We can apply the limit test to check this condition:
lim (n->∞) [f(n) / (n(¹ - ε))] = lim (n->∞) [(n lg n) / (n(¹ - ε))]
= lim (n->∞) [lg n / [tex](n^ε)[/tex]]
Since the limit evaluates to 0, we can conclude that f(n) = O(n(¹ - ε)) for some ε > 0.
According to the Master theorem, the solution to the recurrence relation T(n) = 2T(n/2) + n lg n is T(n) = Θ(n lg n).
To find a tight asymptotic bound using the recurrence tree expansion method, we can visualize the expansion of the recurrence relation as a binary tree.
At each level of the tree, the cost of the nodes is n lg n.
The total number of levels in the tree is log n, since n is a power of two.
Therefore, the total cost of the recurrence relation can be calculated by multiplying the cost per level (n lg n) by the number of levels (log n):
Total cost = n lg n * log n = Θ(n lg² n)
Hence, a tight asymptotic bound for the recurrence relation T(n) = 2T(n/2) + n lg n is Θ(n lg² n).
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i need help!!!! list the factors of -108 that equal to -3
Answer:
9 and -12
Step-by-step explanation:
there's 4 that describe the same function
Answer:
A,B,C,E
Step-by-step explanation:
for a everything is multiplied by 10
for c everything is divided by 6
for b everything is divided by 12
e is the only other one that fits
for a everything is multiplied by 10
for c everything is divided by 6
for b everything is divided by 12
e is the only other one that fits
ABCE is the answer to the question
–4v – 9z – 9v + 2 – 4v find the sum
Answer:
-1x(13v+9z+2)
Step-by-step explanation: try solve this :)
Answer
-17v-9z+2
Step-by-step explanation:
First collect the like terms
-4v-4v-9v-9z+2
-17v-9z+2
Since we can no longer add up due to they are unlike term. Therefore our answer is -17v-9z+2
Find an ordered triple that represents 65 = (2, 6, 8) and Ž = (1, -2, 6).
Answer:
< 40, 28, 72 >
Step-by-step explanation:
Given
y = < 2, 6, 8 > and z = < 7, - 2, 6 > , then
6y + 4z
= 6 < 2, 6, 8 > + 4 < 7, - 2, 6 >
Multiply each component by the scalar quantity
= < 6(2), 6(6), 6(8) > + < 4(7), 4(- 2), 4(6) >
= < 12, 36, 48 > + < 28, - 8, 24 >
Add corresponding components
= < 12 + 28, 36 - 8, 48 + 24 >
= < 40, 28, 72 >
I need help, I don't just need to answer I need to know the steps on how to solve it asap
PLEASE HELP! DUE SOON!
PLEASE HELP ASAP!!
Graph the function
h (x) = -4x-1.
Answer:
Hope this helps!
−12 = −0.6k solve for k
Answer:
-20
Step-by-step explanation:
Step-by-step explanation:
-12=-0.6k
divide both sides by -0.6
k=20
lmk if this is right
Tyrone has 16 model airplanes on his shelf. He has 4 times as many model airplanes as model trains. How many model trains does Tyrone have?
Write multiplication and division equations to model and solve the problem. Use m for the unknown
Step-by-step explanation:
Write multiplication and division equations to model and solve the problem. Use m for the unknown
Find the area of the composite
Figure-someone help plz
Answer:
84
Step-by-step explanation:
The sides of a rectangle have length x+1 and width x-5. which equation below describes the area A of the rectangle in terms of x?
can someone please help? i’ll mark brainliest!!
Answer:
z+5 z+2 Z i think
Step-by-step explanation:
the lenght is longer to shorter
Answer:
angle # > angle * > angle $
Step-by-step explanation:
Since z + 5 > z+ 1 > z
So, angle # > angle * > angle $ (Angle opposite to greater side is greater and opposite to smallest side is smallest)
It usually takes Mary 6 hours to do the cleaning that Jane can do in 5 hours and Ellen can do in 4 hours. If
Jane and Ellen agree to help Mary so that they can all go on a picnic, how long will it take them to do the
cleaning?
Answer:
It will take them about 5 hours to do the cleaning.
Step-by-step explanation:
Since all three of them are going to do it together, you must find the average amount of time between the three of them. To do this you add all of their cleaning times, 6, 5 and 4, and them divide by the amount of people there. 6+5+4= 15, 15/3=5.
Please solve this question
I need help, please solve this math problem. If you don't know the answer please don't answer. You will get reported.
Answer:
I believe it's A 2¹²
Step-by-step explanation:
The answer lies in the question itself.
In the equation, we have
3x - y = 12.
This means 3x = 12 + y.
We have to find 8^x/2^y.
8 can be written as 2^3. Therefore, 8^x = 2^3x.
But 3x = 12 + y, hence can be replaced.
Now we have, in the fraction, 2^(12 + y)/2^y.
This can be written as 2^(12 + y - y) = 2^12.
Idris bought 9 tomato plants for $33.12. How much did each tomato plant cost?
Answer:
9 tomat plant cost= 33.12
each tomato plant cost = 33.12 / 9
answer = 3.68 dalours
Help me solve thank you will give 20 points
Answer:
Natalie bought 500 apples at $0.40 each, then she pays $0.40 500 times, this means that the total cost of the 500 apples is:
Cost = 500*$0.40 = $200
Now she threw away n apples from the 500 apples, then the number of apples that she has now is:
apples = 500 - n
And she sells the remaining apples for $0.70 each.
a) The amount that she gets by selling the apples is:
Revenue = (500 - n)*$0.70
b) We know that she did not make a loss, then the revenue must be larger than the cost, this means that:
cost ≤ revenue
$200 ≤ (500 - n)*$0.70
c) We need to solve the inequality for n.
$200 ≤ (500 - n)*$0.70
$200/$0.70 ≤ (500 - n)
285.7 ≤ 500 - n
n + 285.7 ≤ 500
n ≤ 500 - 285.7
n ≤ 214.3
Then the maximum value of n must be equal or smaller than 214.3
And n is a whole number, then we can conclude that the maximum number of rotten apples can be 214.
What is the volume of the rectangular prism below?
Answer:
V=140
Step-by-step explanation:
5*4=20
20*7=140
Find the surface area of the square pyramid shown in the net below. The surface area of the
figure is
cm. (Round your answer to the nearest tenth.)
4 cm
8.4 cm
Answer:
93 cm
Step-by-step explanation:
In ΔWXY, x = 680 inches, w = 900 inches and ∠W=157°. Find all possible values of ∠X, to the nearest degree.
Given:
In ΔWXY, x = 680 inches, w = 900 inches and ∠W=157°.
To find:
The all possible values of ∠X, to the nearest degree.
Solution:
Law of Sines:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
For ΔWXY,
[tex]\dfrac{w}{\sin W}=\dfrac{x}{\sin X}=\dfrac{y}{\sin Y}[/tex]
Now,
[tex]\dfrac{w}{\sin W}=\dfrac{x}{\sin X}[/tex]
[tex]\dfrac{900}{\sin (157^\circ)}=\dfrac{680}{\sin X}[/tex]
[tex]900\sin X=680\sin (157^\circ)[/tex]
[tex]\sin X=\dfrac{680}{900}\sin (157^\circ)[/tex]
[tex]\sin X=0.295219[/tex]
[tex]X=\sin^{-1}(0.295219)[/tex]
[tex]X=17.17067[/tex]
[tex]X\approx 17[/tex]
Therefore, the value of ∠X is 17 degrees.
d) What would be the total cost of purchasing the number of shirts needed to use your coupon—after your coupon is applied and a 7.5% sales tax is charged on the purchase?
Answer: Multiply 7.5% by the price after subtracting the coupon's value.
Step-by-step explanation:
Let's assume that the cost of the shirts is x. So the coupon would subtract y from x so that's x-y which gives us z. Then to find z, on a calculator just put in 7.5% x z. I used variables since I don't know the value of the coupon or the original price of the shirts.
please help me please
Answer:
2πx - 4
Step-by-step explanation:
C = 2πr
r = (x-2)
C = 2π(x-2)
C = 2πx - 4
The table shows how many hours Sara spent at several activities one Saturday.
Activity "Hours
Soccer practice 2
Birthday party 3
Science project 1
What is the ratio of hours spent at soccer practice to hours spent at a birthday party?
Choose 1 answer:
1 for every 2
B
2 for every 1
2 for every 3
3 for every 2
Answer:
Its2 for every 3
Step-by-step explanation:
(GIVING BRAINILEST) Which characteristic do stable ecosystems tend to have s
Answer:
It will be C
Step-by-step explanation:
This is because ecosystems worh high biodiversity tend to be more stable
Hope this Helped
Answer:
The awnser is c i took the test ( a high amount of bio deversety)
Step-by-step explanation:
Check whether -2 is a zero of the polynomial 3x2 + 4x + 32 .
Answer:
x = - 2 is not a zero
Step-by-step explanation:
If x = - 2 is a zero of the polynomial then f(- 2) = 0
f(x) = 3x² +4x + 32
f(- 2) = 3(- 2)² + 4(- 2) + 32 = 3(4) - 8 + 32 = 12 - 8 + 32 = 36
Since f(- 2) ≠ 0 , then x = - 2 is not a zero of the polynomial
plz I NEEEEED HELP NOWWWW PLZ PLZ PLZ
Angle (p+7)° and angle (3p+1)° are a linear pair so their sum will be equal to 180°.
Which means :
[tex] =\tt 3p + 1 + p + 7 = 180[/tex]
Let us solve that equation to find the value of p and the two angles :
[tex] =\tt 3p + 1 + p + 7 = 180[/tex]
[tex] =\tt 3p + p + 1 + 7 = 180[/tex]
[tex] =\tt 4p + 8 = 180[/tex]
[tex] = \tt4p = 180 - 8[/tex]
[tex] = \tt4p = 172[/tex]
[tex] =\tt p = \frac{172}{4} [/tex]
[tex]\hookrightarrow \tt \color{plum}p = 43[/tex]
Thus, value of p = 43
Measure of angle (p+7)° :
[tex] =\tt 43 + 7[/tex]
[tex]\tt\color{plum}angle \: (p + 7)° =\tt 50°[/tex]
Measure of angle (3p+1)° :
[tex] =\tt 43 \times 3 + 1[/tex]
[tex] = \tt129 + 1[/tex]
[tex]\tt\color{plum}angle \: (3p + 1)° = 130°[/tex]
Thus, the measure of the larger angle = 130°
Therefore, the correct option is (a) 130
what is the sum of 17 and a difference of 5
Answer:
The answer is 12.
~Hoped this helped~
Answer:
please mark me as brainliest answer
Step-by-step explanation:
The sum of two numbers is 17 and their difference is 5. What are the two numbers? Let's start by calling the two numbers we are looking for x and y.
The sum of x and y is 17. In other words, x plus y equals 17 and can be written as equation A:
x + y = 17
The difference between x and y is 5. In other words, x minus y equals 5 and can be written as equation B:
x - y = 5
Now solve equation B for x to get the revised equation B:
x - y = 5
x = 5 + y
Then substitute x in equation A from the revised equation B and then solve for y:
x + y = 17
5 + y + y = 17
5 + 2y = 17
2y = 12
y = 6
Now we know y is 6. Which means that we can substitute y for 6 in equation A and solve for x:
x + y = 17
x + 6 = 17
X = 11
Summary: The sum of two numbers is 17 and their difference is 5. What are the two numbers? Answer: 11 and 6 as proven here:
Sum: 11 + 6 = 17
Difference: 11 - 6 = 5
How do the 6s in 0.96 and 93.601 compare?
The value of the 6 in 0.96 is 100 times the value of the 6 in 93.601.
The value of the 6 in 0.96 is 10 times the value of the 6 in 93.601.
The value of the 6 in 0.96 is 110 the value of the 6 in 93.601.
The value of the 6 in 0.96 is 1100 the value of the 6 in 93.601.
Answer:The value of the 6 in 0.96 is 1/10 the value of the 6 in 93.601. This is because the 6 in 0.9 compared to the 6 in 93.601 which is in the tenths place.
Step-by-step explanation:The value of the 6 in 0.96 is 1/10 the value of the 6 in 93.601. This is because the 6 in 0.96 is in the hundredths place, compared to the 6 in 93.601 which is in the tenths place.
Answer:
The value of the 6 in 0.96 is 110 the value of the 6 in 93.601
Step-by-step explanation:
A 1,000 mL solution of acetic acid contains 26 mL of pure acetic acid. Find the percent concentration of this solution.
Given:
Total solution : 1000mL
Pure acetic acid = 26mL
To find:
The percent concentration of given solution.
Solution:
We know that,
[tex]\text{Percent concentration}=\dfrac{\text{Pure acetic acid}}{\text{Total solution}}\times 100[/tex]
Putting the given values, we get
[tex]\text{Percent concentration}=\dfrac{26}{1000}\times 100[/tex]
[tex]\text{Percent concentration}=\dfrac{26}{10}[/tex]
[tex]\text{Percent concentration}=2.6[/tex]
Therefore, the percent concentration of this solution is 2.6%.
Write Each Ratio as a Percent
1. 14 losses in 50 games
2. 4/5 of the students ride the bus
3. if AB represents 25% what is the length of a line segment that is 100%?
A________________B
5ft
Answer:
28%
80%
20
Step-by-step explanation:
hope this helps