A linear recurrence relation is a function or sequence in which each term is a linear combination of the terms that came before it.
The recurrence relation exists [tex]$T(n)=\Theta\left(3^n\right)$[/tex].
What is meant by "recurrence relation"?Recurrence relations are used to simplify complex problems by reducing them to an iterative process based on simpler versions of the problem.
Using the substitution method, we find out that
[tex]T(n) &=n+3 T(n-1) \\[/tex]
[tex]&=n+3(n-1)+3^2 T(n-2) \\[/tex]
[tex]&=n+3(n-1)+3^2(n-2)+3^3 T(n-3) \\[/tex]
[tex]&=\cdots \\[/tex]
[tex]&=n+3(n-1)+3^2(n-2)+\cdots+3^{n-1}(n-(n-1))+3^n T(0) \\[/tex]
simplifying the above equation, we get
[tex]$&=\frac{3^{n+1}-2 n-3}{4}+3^n T(0) \\[/tex]
[tex]&=\Theta\left(3^n\right)[/tex]
Even without doing the full calculation it is not hard to check that [tex]$T(n) \geq 3^{n-1}+3^n T(0)$[/tex], and so [tex]$T(n)=\Omega\left(3^n\right)$[/tex].
A cheap way to obtain the corresponding upper bound is by considering
[tex]$S(n)=T(n) / 3^n$[/tex], which satisfies the recurrence relation
[tex]$S(n)=S(n-1)+n / 3^n$[/tex].
Repeated substitution then gives
[tex]$\frac{T(n)}{3^n}=\sum_{m=1}^n \frac{m}{3^m}+T(0)[/tex]
Since the infinite series [tex]$\sum_{m=1}^{\infty} \frac{m}{3^m}$[/tex] converges, this implies that [tex]$\frac{T(n)}{3^n}=\Theta(1)$[/tex] and so [tex]$T(n)=\Theta\left(3^n\right)$[/tex]
Therefore, the recurrence relation exists [tex]$T(n)=\Theta\left(3^n\right)$[/tex].
To learn more about recurrence relation, refer to:
https://brainly.com/question/4082048
#SPJ4
The expression 162 models the distance, in feet, that an object falls during the first t seconds after being (1 point)
dropped. Find the distance the object falls in 2 seconds.
O 24 feet
O 64 feet
O 32 feet
O 16 feet
Answer:
64 Feet.
Step-by-step explanation:
First find the expression that describes the distance at t seconds. Which will be 16t^2
Now the distance is t=2.
So...
=16t^2
=16(2)^2
=64.
what is the median of 0,4,8,5,3,5,5,5,1
Answer:
The median is: 5
Hope this helps! <3
Answer:
Step-by-step explanation:
5
Mel makes arm bracelets . she is making one for each arm of her six friends . How
many should she make
Mel should make 12 bracelets.
Here, we are given that Mel makes arm bracelets.
She is making a bracelet for each arm of her 6 friends.
We know that a humans by default have 2 arms each.
We will assume that all of her 6 friends have 2 arms each.
Thus, 6 of her friends will get 2 bracelets each, one for each arm.
This means that the total number of bracelets Mel should make will be given by-
2 + 2 + 2 + 2 + 2 + 2
or we can also write this as
2 × 6
6 times 2 is equal to 12.
Thus, Mel should make 12 bracelets.
Learn more about multiplication here-
https://brainly.in/question/322070
#SPJ9
find the perimeter of the polygon with vertices U (-2,4) V (3,4) and W (3,-4)
So the perimeter of the polygon with vertices U (-2,4) V (3,4) and W (3,-4) is Perimeter = 22.434
Perimeter of any close shape is the total length of the boundary of any closed shape.
We have been given vertices of polygon that are U (-2,4) V (3,4) and W (3,-4)
To find the perimeter we need to find the length of all three sides, and we do that by finding the distance between the points that form the sides:
The formula for the distance between two points is:
[tex]$d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}$[/tex]
side UV:
[tex]$U V=\sqrt{(-2-3)^2+(4-4)^2}=5$[/tex]
side VW:
[tex]$V W=\sqrt{(3-3)^2+(4-(-4))^2}=8$[/tex]
side UW:
[tex]$U W=\sqrt{(-2-3)^2+(4-(-4))^2}=9.434$[/tex]
So the perimeter is:
P=UV+VW+UW
[tex]$P=5+8+9.434=22.434$[/tex]
So the perimeter is: 22.434
To learn more about perimeter visit brainly.com/question/6465134
#SPJ9
What is the value of invar in the base workspace after executing: invar = 1; out1 = plusone(invar);
2 is the value of invar in the base workspace after executing.
What are variables?
A idea or thing that can be numerically, or quantitatively, measured is represented by a variable. Variables can have a wide range of values, which is why they are called variables. Thus, a variable can be thought of as a quantity that can take on different values depending on the circumstances of a given issue.What three categories of variables are there?
Any feature, characteristic, or circumstance that can exist in various amounts or types is considered a variable. Independent, dependent, and controlled variables are typically present in an experiment.
invar = 1;
out1 = plusone(invar);
= 2
Learn more about variables
brainly.com/question/17344045
#SPJ4
Which quantity is best modeled by a linear function?
A the area of a square as a function of the side length
the height of a ball thrown into the air as a function of time
the number of seconds as a function of the number of hours
the height of a reflector on a rotating bike tire as a function of time
The quantity that is best modeled by a linear function is given as follows:
the number of seconds as a function of the number of hours.
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.Another feature of linear functions is uniform behavior, as they are either increasing or decreasing over the entire domain, there are no changes from increasing to decreasing.
Heights increase or decrease over the domain, hence they are not linear, while the area of the square is quadratic, as A = s².
One hour has 3600 seconds, hence the number of seconds in a number of hours is modeled by the following linear function:
S(h) = 3600h.
Hence the quantity that is best modeled by a linear function is given as follows:
the number of seconds as a function of the number of hours.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
When a denominator is greater then numerator does the cutting fraction stop there?or it can still be reduced
Answer:
it can be reduce by turning into a mixed number.
Explain why V8 is
a rational number, but √8 is not a rational
number.
1. (2x - 3)² = 18
2. 2 (5x + 2)² = 64
solve using Quadratic Equation
1) The solution to the given quadratic equation is; x = ¹/₂(3 ± 3√2)
2) The solution to the given quadratic equation is; x = 5/6 or -2
How to find the roots of quadratic equations?
1) (2x - 3)² = 18
To fid the value of x, we can solve by first taking the square root of both sides to get;
√(2x - 3)² = ±√18
Add 3 to both sides using addition property of equality to get;
2x - 3 = ±3√2
2x = 3 ± 3√2
x = ¹/₂(3 ± 3√2)
2) 2(5x + 2)² = 64
To fid the value of x, we can solve by first dividing both sides to get;
(5x + 2)² = 32
Take square root of both sides to get;
(5x + 2) = ±8
Subtract 2 from both sides using subtraction property of equality to get;
5x + 2 = ±8
5x = ±8 - 2
5x = 6 or 5x = -10
x = 5/6 or -2
Read more about Roots of Quadratic equations at; https://brainly.com/question/1214333
#SPJ1
someone please help me with this! i am very confused so explain too :) thank you
Answer: 14/15
Step-by-step explanation:
[tex]9x=10x-x[/tex]
Divide both parts of the equation by 9:
[tex]\displaystyle\\x=\frac{10x-x}{9}\\\\x=0,9333333...\\\\Hence,\\\\x=\frac{10*0,933333...-0,9333333...}{9} \\\\x=\frac{9,333333...-0,933333...}{9} \\\\x=\frac{8,4}{9} \\\\x=\frac{8,4*10}{9*10} \\\\ x=\frac{84}{90}\\\\x=\frac{14*6}{15*6} \\\\ x=\frac{14}{15}[/tex]
2a²-2a-15 at a = 13
Answer: 297
Step-by-step explanation:
2a^2 - 2a - 15
sub a = 13
2 * 13^2 - 2 * 13 - 15
2 * 169 - 2 * 13 - 15
338 - 26 - 15
= 297
Teresa made a circular plywood cover bigger than the mouth of the mixing bowl. it is 20 cm in diameter. but in using the mixer, the cover must have a hole in the middle to insert the mixing tool. if the hole is 10 cm in diameter, what is the final area of the mixer cover?
The final area of the mixer cover is 1650/7 square cm.
Given that:-
Diameter of circular plywood cover = 20cm
Diameter of circular hole in the middle = 10cm
We have to find the final area of the mixer cover after cutting the hole in the middle.
We can find the radius of the circular cover and the circular hole using their respective diameters.
Hence,
Radius of circular plywood cover = 20/2 = 10 cm
Radius of circular plywood cover = 10/2 = 5 cm
We know that,
Area of circle = [tex]\pi r^2[/tex]
Hence,
Area of circular plywood cover = [tex]\frac{22}{7}*(10)^2 =\frac{2200}{7}[/tex]
Area of circular hole = [tex]\frac{22}{7}*(5)^2 =\frac{550}{7}[/tex]
Final area = Area of circular plywood cover - Area of circular hole
Final area = (2200/7) - (550/7) = 1650/7 square cm.
To learn more about area of circle, here:-
https://brainly.com/question/11952845
#SPJ4
4 12 ➗ 1 12
what is the quotient?
The quotient of the fraction 4/12 ÷ 1/12 is 4.
What do we mean by fractions?A fraction is a small part of a larger whole.In arithmetic, the number is expressed as a quotient, which is the numerator divided by the denominator.In a simple fraction, both are integers.A complex fraction has a fraction in the numerator or denominator.In mathematics, there are three major types of fractions.The three types are proper fractions, improper fractions, and mixed fractions.Fractions are terms with a denominator and a numerator.So, evaluation of 4/12 ÷ 1/12:
4/12 ÷ 1/124/12 × 12/1 (Reciprocal)4/1 (12 - 12 cancel)4Therefore, the quotient of the fraction 4/12 ÷ 1/12 is 4.
Know more about fractions here:
brainly.com/question/17220365
#SPJ9
Samuya is multiplying 0.7 by 0.003. how many zeros will be to the right of the decimal point in the product?
After multiplying 0.7 by 0.003 there are two zero to right of the decimal point in the product.
Here,
Samuya is multiplying 0.7 by 0.003.
We have to find, zeros will be to the right of the decimal point in the product.
What is Product?
The product of two numbers is the result you get when you multiply them together.
Now,
Product of 0.7 and 0.003 we get;
0.7 x 0.003 = 0.0021
Clearly, there are two zero to the right of the decimal point in the product.
So, After multiplying 0.7 by 0.003 there are two zero to right of the decimal point in the product.
Learn more about the product visit:
https://brainly.com/question/26587426
#SPJ4
Three times the greater of two consecutive even integers is 26 less than four times the lesser.
Find the integers.
Answer:
-20, -18
Step-by-step explanation:
let x = the smaller number
Let x + 2 = the larger number
3(x +2) -26 = 4x
3x + 6 -26 = 4x
3x -20 = 4x Subtract 3x from both sides of the equation
-20 = x
x + 2
-20 + 2 = -18
Check:
3(-20 + 2) -26= 4(-20)
3(-18) - 26 = -80
-54 -26 = -80
-80 = -80
How do I simplify this?
Find the slope of each of the lines below (-4,-2),(6,1)
2x+15=25 find for x
Answer:
x= 5
Step-by-step explanation:
2x+ 15=25
-15 -15
2x= 10
/2 /2
x=5
Answer:
x = 5
Step-by-step explanation:
2x + 15 = 25
2x + 15 - 15 = 25 - 15 (subtract 15 from both sides)
2x = 10
2x/2 = 10/2 (divide by 2 on both sides)
x = 5
Given a function f(x) = m/x-1 + n, where f(-2) = 1 and f(4) = 3. Find the values of m and n
We get the values of m as 1 and n as 0.
We are given a function:
f(x) = m / (x - 1) + n
We are also given that:
f (-2) = 1 and f (4) = 3
We have to find the value of m and n.
f (-2) = m (2 - 1) + n
1 = m + n
n = 1 - m
f (4) = m / (4 - 1) + n
3 = 3 m + n
3 = 3 m + 1 - m
3 = 2 m + 1
2 m = 3 - 1
2 m = 2
m = 2 / 2
m = 1
m + n = 1
1 + n = 1
n = 0.
Therefore, we get the values of m as 1 and n as 0.
Learn more about function here:
https://brainly.com/question/4025726
#SPJ9
Complete the point-slope equation of the line through (-4,8) (−4,8)
Use exact numbers.
(Point-Slope Equation)
any detailed answer for this??
Answer: y = 8
Step-by-step explanation:
Point-slope form is written as y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]) where m is the slope and ([tex]x_1[/tex] , [tex]y_1[/tex]) are points on the line.
First, we need to find the slope. This can be found with change in y over change in x:
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\displaystyle \frac{8-8}{-4--4}=\frac{0}{-4+4}=\frac{0}{0}=[/tex] undefined
Now, we will plug this undefined slope (0) into the equation below. Anything times 0 is 0, so no matter what (x - [tex]x_1[/tex]) is, the right side of the equation will always be 0.
y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])
y - [tex]y_1[/tex] = (0)(x - [tex]x_1[/tex]) ➜ y - [tex]y_1[/tex] = 0
Lastly, we will take the y-value of 8 and plug it into the equation and simplify.
y - [tex]y_1[/tex] = 0 ➜ y - (8) = 0 ➜ + 8 (y - 8) = (0) + 8
y = 8
See attached for a visual explanation.
He said "l travel a lot in my job change into i direst speech
Step-by-step explanation:
the ratio between two circles vqjoizxcvu g çm
NEED NOW what is (-3, 0) (0, -3) in slope-intercept form
Answer:
y=-x-3
Step-by-step explanation:
Write in slope-intercept form, the equation is y=mx+b .
y=−x−3
he zeros of a quadratic function are 6 and -4. Which of these choices could be the function?
A.
f(x) = (x + 6)(x + 4)
B.
f(x) = (x + 6)(x − 4)
C.
f(x) = (x − 6)(x + 4)
D.
f(x) = (x − 6)(x − 4)
Answer:
C
Step-by-step explanation:
given the zeros x = a and x = b then the corresponding factors are
(x - a) and (x - b)
then f(x) is the product of these factors
given zeros x = 6 and x = - 4 then the factors are
(x - 6) and (x - (- 4)) , that is (x - 6 and (x + 4) , then
f(x) = (x - 6)(x + 4)
which property is shown by 2 + 0 = 2
A. Associative Property of Addition
B. Commutative Property of Addition
C. Distributive Property
D. Identify Property of Addition
The property shown in 2 + 0 = 2 is the Identify Property of Addition
How to name the property shown?The expression is given as:
2 + 0 = 0
The Identify Property of Addition property states that
a * 0 = a
This means that the property shown is the Identify Property of Addition
Hence, the property shown in 2 + 0 = 2 is the Identify Property of Addition
Read more about algebraic property at
brainly.com/question/12956307
#SPJ1
a statistical procedure for analyzing the results of multiple studies to reach an overall conclusion.
A "meta-analysis" is a statistical procedure for combining the findings of multiple studies to reach a single conclusion.
What is meant by meta-analysis?Meta-analyses are more rigorous and quantitative than both kinds of reviews.
Some main points related to meta-analysis are-
These papers, in addition to providing an overview, provide a quantitative assessment of how effectively a treatment works or an evaluate of how significantly more likely a person is to grow a disease if they engage in a certain behavior.Meta-analyses are performed so that research from multiple studies with differing data can be combined to make more informed decisions about effectiveness of a medication on the a person's risk of developing a disease than a Magic 8-ball.The research question is defined first in meta-analyses. A well-defined research topic identifies the population impacted by the intervention as well as the potential treatment outcome(s).To know more about the meta-analysis, here
https://brainly.com/question/14723190
#SPJ4
5. Let p be "an animal is a puppy" and let q be "it is a dog." Write each statemen
in words. Then decide whether it is true or false.
a. the conditional statement p → q
b. the converse q→ p
c. the inverse -p-9
d. the contrapositive -q→ ~P
a. The conditional statement p → q is true
b. The converse q → p is False.
c. The inverse p → ~q is False
d. The contrapositive -q→ ~p is True
How to Interpret Conditional Statements?
We are given the conditional statement;
Let p be "an animal is a puppy" and let q be "it is a dog."
a) The conditional statement p → q which is "If an animal is a puppy, then it is a dog" is true.
b) The converse statement q → p which is "If an animal is a dog, then it is a puppy" is false.
c) The inverse statement p → ~q which is "If an animal is not a puppy, then it is not a dog" is false.
d) The contrapositive statement: q → ~p which is "If an animal is not a dog, then it is not a puppy" is true.
Read more about Conditional Statements at; https://brainly.com/question/11073037
#SPJ1
Which fraction is equivalent to this decimal
Answer:
1/7
Step-by-step explanation:
You can just divide all the possible answers.
1/9 = 0.1111111 (1 repeating
1/7 = 0.142857142857
1/11 = 0.090909090909 (repeating)
1/14 = 0.0714285714286 (repeating)
completa la tabla sobre o debajo segun corresponda
A) el 24 por ciento de los valores queda por _________ del P25
b) el 25 por ciento de los valores queda por __________ del Q3
complete the table above or below as appropriate of segun corresponda.
Spanish 22% English 25% Periodism 18% Physical Education 17% Biology 18%
1. Thirty-five percent of students studied science; hence, 35 (35 = thirty-and-five) = thirty-and-five.
2. One-hundred and thirty-three percent of students studied English or periodical studies — 25+18 = 43 (forty-three = one hundred and thirty-three).
3. One-sixty-five percent of students did not study science — 22+25+18 = 65 (sixty-five = one-sixty-five)
4. Eighty two percent of students did not study biology — 17 + 22 + 25 + 18 = 82 (eighty two Equals eighteen and two).
5. One-quarter and seven percent of students studied either English or Spanish — 25+22 = 47 (quarter and seven = 47).
6. One hundred and three percent of students — 17+18+18 = 53 (one hundred and thirty equals five) — did not study languages.
y tres)
To learn more about segun corresponda Visit : https://brainly.com/question/11159374
#SPJ9
New, larger bottle of shampoo contains 20 ounces. the bottle says you get 33% more than the amount in the original bottle. how many ounces of shampoo were in the original bottle?
Amount of shampoo in the original bottle is 15.0376 ounces.
Larger bottle of shampoo contains = 20 ounces
Let, amount of shampoo in the original bottle = x ounces
33% of amount of shampoo in the original bottle = ((33x)/100)
According to the question, amount of shampoo in the larger bottle is 33% more of amount of shampoo in the original bottle. So, mathematically we can write
20 = x + ((33x)/100)
⇒ 20 = x + 0.33x
⇒ 20 = 1.33 x
⇒ x = 20/1.33
⇒ x = 15.0376
Amount of shampoo in the original bottle is 15.0376 ounces.
To now more about Amount Calculation in mathematical problems refer to the link:
https://brainly.com/question/25186043
#SPJ4
please help me
Here are two expressions whose sum is a new expression, A.
(2x2+5)+(6x□−7)=A
Select all the values that we can put in the box so that A is a polynomial.
Answer:
D, F and G
Step-by-step explanation:
A polynomial must have a negative exponent for the variable term. So we can eliminate A, B and C
Also no fractional exponents so eliminate E
F & G are positive exponents so acceptable
D has the exponent 0 so the term becomes (2x² + 5) + (6x⁰ + 7)
x⁰ = 1 so the expression becomes 2x² + 5 + 6 + 7 = 2x² + 18 which is a polynomial.
