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].
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26
Write the time.
O
10
11
7
12
وانيه
Answer is 5:30.. Hope it Helps
if there are 15 cubs and 4 lionesses, what is the ratio of cubs to lionesses?
Answer:
15 : 4
Step-by-step explanation:
Given that,
→ 4 lionesses
→ 15 cubs
Then the ratio of cubs to lionesses,
→ x = No. of cubs : No. of lionesses
→ [ x = 15 : 4 ]
Hence, the ratio is 15 : 4.
Please Help!
Find the dimensions of an American football field. The length is 200ft. more than the width, and the perimeter is 1,040ft. Find the length and width. Use the perimeter formula P=2L+2W
The width and length of the field are 160ft and 200ft respectively
When both the given variables are related to each other, we are required to consider one variable as x and the other as a function of x to solve accordingly
Let the width of the football field be 'x' ft.
then according to given data,
length= 200 ft more than width= (x+200)ft
According to given,
Perimeter of the given field =2L+2W=1040
where L is length and W is the width
Now putting the values of length and width earlier derived, we get:
2(x)+2(x+200) =1040
2x+2x+400=1040
4x+400=1040
4x=1040-400
4x=640
x=160ft
Now, the width of the field= x=160ft
length of the field= x+200=160+200=360ft
Hence the length and the width of the field are 160ft and 360ft
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Evaluate the given function as required. (round your answer to two decimal places.) f(x) = x 6 x2 1 at x = 5 f(5) =
The value of the function for f(5) is 15,651.
The given function is [tex]f(x)=x^{6}+x^{2} +1[/tex].
We need to find the value of f(5).
What is the function?Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math.
Now, put x=5 in the function [tex]f(x)=x^{6}+x^{2} +1[/tex] and simplify.
That is, f(5)=[tex]5^{6} +5^{2} +1[/tex]
=15,625+25+1
=15,651
Therefore, the value of the function for f(5) is 15,651.
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*PLS HELP*
A student is given the rectangle and the square shown. The student states that the two figures have the
same perimeter. Is the student correct? Complete the explanation to explain your reasoning.
X+4
X
X+2
X+2
The student is (select) The perimeter of a figure is found by (select)
For the rectangle, the perimeter is
. For the square, the perimeter
is
the lengths of its sides.
Answer:
The student is correct. The perimeter of a figure is found by adding the length of it's sides. For the rectangle, the perimeter is 4x+8. For the square, the perimeter is 4x+8
Step-by-step explanation:
Perimeter for rectangle:
2(x+4) + 2x
2x + 8 + 2x
4x + 8
Perimeter for the square:
4(x+2)
4x + 8
A 9-foot roll of plastic wrap costs $4.41. What is the price per yard?
Answer:
$1.47 per yard
Step-by-step explanation:
3 feet = 1 yard
9 feet = 3 yards
set up a proportion
[tex]\frac{3}{4.41} = \frac{1}{x}[/tex]
cross multiply; 3x = 4.41 * 1
3x = 4.41
divide both sides by 3
x = 1.47
$1.47 per yard
Is it possible to have a function f defined on [ 4 , 5 ] and meets the given conditions? f is continuous on [ 4 , 5 ], is non-constant, and takes on only integer values.
No, It is not possible that f is continuous on [ 4 , 5 ] is non-constant, and takes on only integer values.
Here,
A function f defined on [ 4 , 5 ].
We have to find, is it possible to f is continuous on [ 4 , 5 ], is non-constant, and takes on only integer values.
What is Intermediate value theorem?
Intermediate value theorem states that if “f” be a continuous function over a closed interval [a, b] with its domain having values f(a) and f(b) at the endpoints of the interval, then the function takes any value between the values f(a) and f(b) at a point inside the interval.
Now,
A function f defined on [ 4 , 5 ].
Assume that the function,
f : [ 4 , 5 ] → Z is a non constant continuous function.
Then, f(4) and f(5) both are integers and not equal to each other.
By, Intermediate value theorem;
Function f takes all real numbers between f(4) and f(5) at least once.
These would contain all non integers rational and irrational number between f(4) and f(5), contradicting the assumption that function takes only integer values.
Hence, It is not possible that f is continuous on [ 4 , 5 ] is non-constant, and takes on only integer values.
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Write a function rule for the table
The function rule for the table is y = 25/4 x
Equation of a linear functionThe standard expression for a linear function is expressed as y =mx + b
where
m is the slope
b is the y-intercept
Using the coordinate points (4, 25.00) and (8, 50.0)
Determine the slope
Slope = 50-25/8-4
Slope = 25/4
Determine the y-intercept
50 = 25/4(8) + b
50 = 25(2) + b
50 = 50 + b
b = 0
Hence the function rule for the table is y = 25/4 x
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can someone solve this please, thank you
Answer:
110
Step-by-step explanation:
13x - 20 + 7x = 180
20x -20 = 180
20x = 200
x = 10
13(10) - 20
=110
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. the amount of snowfall in december in city a
The function is a continuous random variable. The correct option is B.
What is a continuous random variable?Continuous random variables are those that have a large number of uncountable possible values. There are countless possible values. In this illustration, there is no limit to the range of possible values for the height of a giraffe in meters, such as 10.5m, 15.22m, 12.0m, etc. There are countless options.
Discrete Variables that have a finite number of possible outcomes are known as random variables. When a dice is rolled, for example, the outcomes could be 1, 2, 3, 4, 5, or 6. There are only six possible values, with nothing in between.
Therefore, the function is a continuous random variable. The correct option is B.
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PLS Help.............................
Answer:
Top to bottom
1
30
9
45
Step-by-step explanation:
each problem, create a table
Write an equation, in slope-intercept form, to model each situation.
1. You rent a bicycle for $20 plus $2 per hour.
Y=2x120
Answer:
You have a fixed cost ($20) and a variable cost ($2*number of hours you rent the bike)
Cost = Variable Cost + Fixed Cost
Let y = your Cost and x = the number of hours you rent the bike. The fixed cost is $20.
y = ($2 per hour)*(x hours) + $20
y = 2x + 20
− 2|5 − 1| − 3 =− 11 Pls help
The lines mean absolute value.
Not sure what the question is, but both sides are equal to each other. -11=-11, so if the question is if both sides are equal, then it's true
Jack takes 10 minutes to ride his stakeboard down the hill to his friend's house and 20 minutes to ride up the hill from his friend's house. he goes to his friend's house monday through friday. how many minutes does he spend riding his stakeboard to and from his friend's house in two weeks? write an equation to model your work.
Jack spends 300 minutes in two weeks riding his skateboard to and from his friend's house Monday through Friday.
Time taken by Jack to ride his skateboard down the hill to his friend's house = 10 minutes
Time taken by Jack to ride his skateboard up the hill to his friend's house = 20 minutes
Total time combined = 30 minutes
Total days in a week Monday through Friday= 5 days
Total days in 2 weeks = 10 days
Therefore, time spent by jack riding his skateboard up and down the hill to his friend's house in two weeks Monday through Friday = 10*30 = 300 minutes
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Name a pair of adjacent complementary angles.
4. Name a pair of adjacent supplementary angles.
5. Name a pair of nonadjacent complementary angles.
6. Name a pair of nonadjacent supplementary angles.
3. A pair of adjacent complementary angles is: ∠LJM and ∠NJM.
4. A pair of adjacent supplementary angles is: ∠KJL and ∠NJL
5. A pair of nonadjacent complementary angles is: ∠EGF and ∠NJP
6. A pair of nonadjacent supplementary angles is: ∠FGH and ∠LJM
What are Complementary and Supplementary Angles?Supplementary angles have a sum that is equal to 180 degrees, while complementary angles equal 90 degrees.
What are Adjacent Angles?Angles that share the same side and vertex are adjacent angles.
3. m∠LJM + m∠NJM = 56 + 34 = 90°
A pair of adjacent complementary angles is: ∠LJM and ∠NJM.
4. m∠KJL + m∠NJL = 90 + (56 + 34) = 180°
A pair of adjacent supplementary angles is: ∠KJL and ∠NJL
5. m∠EGF + m∠NJP = 41 + 49 = 90°
A pair of nonadjacent complementary angles is: ∠EGF and ∠NJP
6. m∠FGH + m∠LJM = 124 + 56 = 180°
A pair of nonadjacent supplementary angles is: ∠FGH and ∠LJM
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Name:
1.
O
a) Is the graph linear?
b) What is the domain?
c) What is the range?
d) What are the x and y intercepts?
e) Does the graph have symmetry? Type?
f) What are the extrema and end behavior? 20 points
The Graph is not linear.
To graph f, we graph the equation y = f(x). To this end, we use the techniques outlined in Section 1.2.1. Specifically, we check for intercepts, test for symmetry, and plot additional points as needed. To find the x-intercepts, we set y = 0. Since y = f(x), this means f(x) = 0. f(x) = x2−x−6 0 = x2−x−6 0 = (x−3)(x+2) factor x−3=0 or x+2=0 x = −2,3 So we get (−2,0) and (3,0) as x-intercepts. To find the y-intercept, we set x = 0. Using function notation, this is the same as finding f(0) and f(0) = 02 − 0 − 6 = −6. Thus the y-intercept is (0, −6). As far as symmetry is concerned, we can tell from the intercepts that the graph possesses none of the three symmetries discussed thus far. (You should verify this.) We can make a table analogous to the ones we made in Section 1.2.1, plot the points and connect the dots in a somewhat pleasing fashion to get the graph below on the right. y x f(x) (x, f(x)) −3 6 (−3,6) −2 0 (−2,0) −1 −4 (−1,−4) 0 −6 (0, −6) 1 2 3 4 5 6 7 −3−2−11 2 3 4 1 −6 (1, −6) 2 −4 (2, −4) 3 0 (3, 0) 4 6 (4, 6)
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millimeters
Equal 15 centimeters 4 millimeters
154mm
we know that 1cm = 10 mm
therefore 15cm= 10*15 mm
= 150 mm
and 4 mm
we get total mm= 15cm +4mm
= 150mm+4mm
= 154 mm
mm stands for millimeters and cm stand for centimeters
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mathhhhhhhhhhhhhh._ help plsssssss
Answer:
[tex](-4,-\frac{1}{2})[/tex]
Step-by-step explanation:
The midpoint of a line segment can be found using the midpoint formula below:
[tex]\boxed{\text{Midpoint}=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )}[/tex]
Note that [tex](x_1,y_1)[/tex] is the 1st coordinate and [tex](x_2,y_2)[/tex] is the 2nd coordinate of the end points.
Let's identify the coordinates of the two end points, A and B.
On both axes, a square represents 1 unit.
A(-5, -4) and B(-3, 3)
Applying the midpoint formula,
midpoint
= [tex](\frac{-5-3}{2} ,\frac{-4+3}{2} )[/tex]
= [tex](\frac{-8}{2},\frac{-1}{2} )[/tex]
= [tex]\bf{(-4,-\frac{1}{2}) }[/tex]
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Which polynomial does not have an absolute maximum?
A. 2nd degree
B. 3rd degree
C. 4th degree
Reason:
Odd degree polynomials do not have an absolute max nor absolute min. The curve stretches forever upward and downward. The range is the set of all real numbers.
Even degree polynomials on the other hand do have a highest point or lowest point, depending on the leading coefficient. If the leading coefficient is negative, then the curve has a highest point. If the leading coefficient is positive, then the curve has a lowest point.
Example: y = x^3 does not have an absolute max, but y = -x^2 does.
write 196 as a product of primes.
use index notation when giving your answer
Answer:
The prime factorization of 196 is 196 = 2 × 2 × 7 × 7 and can be represented as 196 = 2 2 × 7 2 using exponents.
Answer:
2² × 7² = 196
Step-by-step explanation:
The product of 5 and a number minus 7 is 23
Answer:
6
Step-by-step explanation:
5*6 is 30 - 7 is 23
work backwards
The table shows the distance traveled by 4 cycleists. Sort the speeds of the riders, in miles per hour, from slowest to fastest.
The speed from slowest to the fastest is Julio; Elana; Kevin; Lorena.
Given that a table shows the distance traveled by 4 cyclists as shown in attached images.
Speed is defined as . The rate at which an object changes position in any direction. Speed is measured as the ratio between distance and time traveled.
Firstly, we will calculate the speed of Elena.
The given distance is 20(1/2) mi or it can be written as 41/2mi and the time is 2(1/4) hr or 9/4hr.
Now, substitute the values in speed formula that is
Speed=Distance/Time
Speed=(41/2)/(9/4)
Speed=(41/2)×(4/9)
Speed=82/9 mi/hr.
Now, we will calculate its speed of Julio.
The given distance is 12(1/4) mi or it can be written as 49/4mi and the time is 1(1/2) hr or 3/2hr.
Now, substitute the values in speed formula that is
Speed=Distance/Time
Speed=(49/4)/(3/2)
Speed=(49/4)×(2/3)
Speed=49/6 mi/hr.
Further, we will calculate the speed of Kevin.
The given distance is 20(2/3) mi or it can be written as 62/3mi and the time is 1(2/3) hr or 5/3hr.
Now, substitute the values in speed formula that is
Speed=Distance/Time
Speed=(62/3)/(5/3)
Speed=(62/3)×(3/5)
Speed=62/5 mi/hr.
Furthermore, we will calculate the speed of Lorena.
The given distance is 33(1/4) mi or it can be written as 133/4mi and the time is 2(1/3) hr or 7/3hr.
Now, substitute the values in speed formula that is
Speed=Distance/Time
Speed=(133/4)/(7/3)
Speed=(133/4)×(3/7)
Speed=57/4 mi/hr.
Hence, the speeds from slowest to fastest from the given table is Julio; Elana; Kevin; Lorena.
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What number makes the expression equivalent? 1/2 (-14m+4)= blank m+2
In linear equation, -7 m - 2 is number makes the expression equivalent.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Given expression is 1/2 (-14m+ 4 )
To simplify this expression 1/2 (-14m+ 4 ) we get equivalent expression.
Multiply and Divide the expression by two.
⇒ -14m/2 + 4/2
To simplify the expression again, we get,
⇒ -7 m - 2
So, we found the coefficient of m is -7
The missing number is -7
Hence, –0.7 makes the expression equivalent.
Therefore,1/2 (-14m+4) = -7 m - 2
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pls helpp que 3d and 3g
Answer:
Step-by-step explanation:
d)
[tex]\displaystyle\\\frac{h}{2h+5} +\frac{5}{6} =\\\\\frac{h*6+5*(2h+5)}{(2h+5)*6} =\\\\\frac{6h+2h(5)+5(5)}{2h(6)+5(6)} \\\\\frac{6h+10y+25}{12h+30} =\\\\\frac{16h+25}{12h+30}[/tex]
g)
[tex]\displaystyle\\\frac{3n}{(2n-1)^2} -\frac{5}{2n-1} =\\\\\frac{3n*1 -5*(2n-1)^}{(2n-1)^2}=\\\\\frac{3n(1)-2n(5)-1(-5)}{(2n-1)^2}=\\\\\frac{3n-10n+5}{(2n-1)^2} =\\\\\frac{-7n+5}{(2n-1)^2}[/tex]
In the year 2000, a company made $2.2 million in profit. for each consecutive year
after that, their profit increased by 13%. how much would the company's profit be in
the year 2003, to the nearest tenth of a million dollars?
The company's profit in the year 2003 is $3.1 million
Profit is defined as the amount of revenue generated after deduction of all the liabilities.
Given that in the year 2000 profit = $2.2 million
Each year increase in profit = 13% =0.13
Total number of year = 2003-2000=3 years
Profit is denoted by
[tex]profit=initial profit(1+each.year.increase)^{years}[/tex]
Substituting the values we get
profit=[tex]2.2(1+0.13)^3[/tex]
=[tex]2.2(1.13)^3=2.2*1.442897[/tex]
=3.174373
=3.1 million
Therefor , the company's profit in the year 2003 is $3.1 million
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(50 Points!!!)
Gwen is finding the area of the shaded sector in the given circle, which has a circumference of 6 units.
Identify the step where Gwen first made an error.
A. Step 5
B. Step 6
C. Step 3
D. Step 7
The step in which Gwen made an error for the area of the shaded region in the circle is given by:
A. Step 5.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by:
C = 2π r.
For this problem, the circumference is of 6π units, hence the radius is given as follows:
6π = 2π r.
r = 6/2.
r = 3 units.
What is the area of a circle?The area of a circle of radius r is given by pi multiplied by the radius squared, as follows:
A = πr².
The entire area of the circle englobes 360º, but we want only the area at an angle of 72º, hence it is given by:
A = (72/360) πr².
Which is where Gwen made an error, at Step 5, hence option A is correct.
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Eve and her mom are volunteering at an emergency relief center. To help prepare in case of a flood, they pack emergency kits with food and water. Eve puts 5 water bottles into each kit they pack. In all, she packs 125 water bottles.
Which equation can you use to find the number of emergency kits k Eve packs?
Answer:
Step-by-step explanation:
no. of emergency kits = x
bottles per kit = 5
total no. of bottles = 5x
which means,
5x = 125
125/5 = x
x = 25
Does the mapping diagram represent a function? Why or why not? X -6 2- 3 y 10 5 4 A. No; the input value x = 3 pairs with two different output values. B. No; two output values pair with two different input values. C. No; each input pairs with only one output. D. Yes; each input pairs with only one output.
Answer:
A. No; the input value x=3 pairs with two different output values.
Step-by-step explanation:
For this to be a function, each of the x values should have only one output value.
Hope this helps!
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11 = −5+y
Solve for Y
Answer:
y=16
Step-by-step explanation:
11 = −5+y
Solve for Y
Add 5 to each side
11+5 = -5+y+5
16 = y
y=16
Find a and b so that f(x) is continuous for all values of x f(x)={x^2-4/x-2 if x<2 ax^2-bx+3 if 2<=x<3 2x-a+b if x>=3
The values a = 1/3 and b = 1/6.
Given function is, f(x) =
[tex]\frac{x^2-4}{x-2}\ \ \ if\ x < 2 \\ax^2-bx+3 \ \ \ if\ 2\leq x < 3\\2x-a+b\ \ \ if\ x\geq 3[/tex]
The interval in which the function is defined is broke down into three. They are: x<2, 2≤x<3 and x≥3.
Now the function [tex]\frac{x^2-4}{x-2}[/tex] is continuous except at x = 2. But this function is defined in the interval x>2. The other two function are defined as polynomial, so are continuous any way.
So for the whole function f(x) to be continuous, we need to check the continuity at x = 2, x = 3.
When x = 2, [tex]\frac{x^2-4}{x-2}[/tex] =[tex]\frac{(x+2)(x-2)}{x-2}=x+2 = 4[/tex] and [tex]ax^2-bx+3[/tex] = 4a-2b+3
⇒ 4a-2b+3 = 4
⇒4a- 2b-1 = 0, for the function to be continuous at x = 2.
When x = 3, [tex]ax^2-bx+3[/tex] = 9a-3b+3 and 2x-a+b = 6-a+b
⇒ 9a-3b+3 = 6-a+b
⇒ 10a -2b-3 = 0, for the function to be continuous at x = 3.
On solving 4a-2b-1 = 0 and 10a -2b-3 = 0 by subtracting the two,
we get, -6a+2 = 0
⇒ a = 1/3 and therefore, b = 1/6
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