The time complexity is O(1) as the recurrence reduces to a constant.
T(n) = 2T(n/2) + n/log n
T(1) = 1
T(2) = 2T(1) + 2/log 2
= 2 + 2/log 2
T(4) = 2T(2) + 4/log 4
= 2(2 + 2/log 2) + 4/log 4
T(8) = 2T(4) + 8/log 8
= 2(2(2 + 2/log 2) + 4/log 4) + 8/log 8
T(n) = 2^k T(1) + (2^k + 2^(k-1) + ... + 2 + 1)*n/log n
= 2^k + (2^k + 2^(k-1) + ... + 2 + 1)*n/log n
= 2^k + n*Σ_(i=1)^k▒2^i/log n
= 2^k + n/log n*(2^(k+1) - 1)
= 2^k + n/log n*(n/2 - 1)
= (2^k + n/2 - n/log n)*n/log n
= (2n - n/log n)*(log n/n)
= 2 - 1/log n
The time complexity is O(1) as the recurrence reduces to a constant.
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Guys please help
Find the intersection of y = 2(x+2) and y = 4(x-4).
Answer:
(10, 24)
Step-by-step explanation:
First equate both the equations,
2(x+2) = 4(x-4)
Then expand the brackets,
2x + 4 = 4x - 16
Collect like terms in each sides,
4 + 16 = 4x - 2x
Simplify and solve,
20 = 2x
20 ÷ 2 = x
x = 10
Then substitute 10 for x in one of the equations,
y = 2(x + 2)
y = 2(10 + 2)
y = 24
Therefore, the point of interssection is (10, 24).
you can solve this using the simultaneous equation
so y = y
4(x-4) = 2( x + 2)
4x - 16 = 2x +4
4x - 2x = 4+16
2x/2=20/2
therefore x=10
y=2 (x+2)
y=2(10+2)
y=2(12)
y=24
2y8x = 20
y = [?]x +
80% of 25$
…………………….
$20
there is two ways to solve this.
ratio form:
80% / 100% = X / $25
---> 2000 / 100 = X
---> X = 20
Decimal form:
80% --- move decimal two places to the left.
80% = 0.8 --- now multiply decimal by total value
0.8 x 25 = 20
$20.
a large Ghirardelli bar is 30cm long and 12cm wide. a smaller Ghirardelli bar is 10cm long. If the bars are similar, what is the width of the smaller Ghirardelli's bar?
Answer:
Step-by-step explanation:
if the bars are similar, they are proportional.
make a proportion: length = 30 = 10
width 12 x
cross multiply: 12 times 10 = 120
divide by the number that ids left - 120 ÷ 30 = 4 cm
The width of the smaller bar is 4 cm.
Pleeeeeeeeeeeease answer this for me I’ll give brainly pls pls pls pls
Answer: S=V cubed
Step-by-step explanation:
Answer: A. S = cube of V
Step-by-step explanation:
Cube both sides of the equation to single s out
Find the solution to the linear system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3:
The solution of the system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3 is given by:
[tex]$x(t) = e^{at} (5 \cos(bt) + 3 \sin(bt))$[/tex]
[tex]$y(t) = e^{ct} (5 \sin(bt) - 3 \cos(bt))$[/tex]
Let x(t) and y(t) be the solution of the linear system of differential equations:
[tex]$\frac{dx}{dt} = ax + by$[/tex]
[tex]$\frac{dy}{dt} = cx + dy$[/tex]
with initial conditions x(0)=5 and y(0)=3.
The general solution of the system of differential equations can be written as:
[tex]$x(t) = e^{at} (X0 \cos(bt) + Y0 \sin(bt))$[/tex]
[tex]$y(t) = e^{ct} (X0 \sin(bt) - Y0 \cos(bt))$[/tex]
where X0 = 5 and Y0 = 3.
Therefore, the solution of the system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3 is given by:
[tex]$x(t) = e^{at} (5 \cos(bt) + 3 \sin(bt))$[/tex]
[tex]$y(t) = e^{ct} (5 \sin(bt) - 3 \cos(bt))$[/tex]
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Find three consecutive positive integers such that
twice the product of the first and third is 2 less
than twenty times the second.
The three consecutive positive integers satisfying the statement are
9, 10, and 11.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, The three numbers be n, (n + 1), and (n + 2).
Therefore, the numerical expression of the given statement is,
2(n)(n + 2) + 2 = 20(n + 1)
2n² + 4n + 2 = 20n + 20.
2n² - 16n - 18 = 0.
n² - 8n - 9 = 0.
n² - 9n + n - 9 = 0.
n(n - 9) + 1 (n - 9) = 0.
(n - 9)(n + 1) = 0.
n = 9 is the positive integer.
So, The numbers are 9, 10, and 11.
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Find the slope and y-intercept of the graph of the equation.
Answer:
The slope: 4
Y-intercept: 9
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
In this case y = 4x + 9
m = 4
b = 9
So,
The slope: 4
Y-intercept: 9
Answer:
Slope: 4/1 or 4
Y-Intercept: 9
Step-by-step explanation:
y = mx + b is the Slope Intercept Formula. 'm' in the formula stands for rate of change in y/x, which is practically slope. 'b' in the formula is where the line crossed the y line. It's where it intercepts with y.
PLEASEE HELPPP LOOK AT IMAGE
Answer:
y = 3(2)^x
Step-by-step explanation:
If we look at the x and y values, we see that the xs' increase by 1 each time, while the ys' double (12*2 = 24, 24 *2 = 48 etc.).
Because the value doubles each time, we know that this is an exponential equation, and the base (b) is 2.
The general form (as shown) is y = a(b)^x, where a is the initial value (y-intercept or value of y when x = 0) and b is the base.
We can find a by plugging in one x and y coordinate and 2.
For example, we can use (1, 6) to solve for a:
[tex]y=a(b)^x\\6=a(2)^1\\6=a(2)\\3=a[/tex]
Mrs Ananaya is buying pencils in packs of 12, notebooks in packs of 16, and red pens in packs of 20. She needs to buy the same number of pencils, notebooks, and red pens. What is the least number of packs of each item that she can buy?
Answer:
Below
Step-by-step explanation:
You need to find the LCD of 12 16 and 20
Using Prime Factorization:
12 = 2 * 2 * 3
16 = 2 * 2 * 2 * 2
20 = 2 * 2 * 5
2 2 2 2 3 5 so LCD will be 2 * 2 * 2 * 2 * 3 * 5= 240
so she will need 240 / 12 = 20 packs of pencils
240 / 16 = 15 packs of notebooks
240 / 20 = 12 packs of pens
The population of the Vatican is 10-4 million and the population of India is 10³ million. How many times more is the population of India than the Vatican? Leave your answer in the form a^b. times more
Answer:
10²
Step-by-step explanation:
assume you typed 10.4 million
so 10³/10.4 ≈ 10²
While visiting your friend in the city, you see two roads that intersect as shown. Your friend tells you that the angle between the roads on the north side is 69° and the angle between the roads on the south side is (3x)°. Find the value of x.
Answer and Step-by-step explanation:
Let's call the angle between the roads on the south side "y" for simplicity. Since the two roads intersect, the sum of the two adjacent angles on one side must add up to 180 degrees. Therefore, we can set up an equation:
y + 69 = 180
Solving for y, we get:
y = 180 - 69 = 111
We also know that y is equal to 3x, so we can set up another equation:
3x = 111
Solving for x, we get:
x = 37
Therefore, the value of x is 37.
Hope it helps! : )Do u know what this is
Answer:
248
Step-by-step explanation:
Find the volume of each box, then add them up.
Volume = l x w x h
Top: 5 x 2 x 5 = 50
Middle: 6 x 4 x 3 = 72
Bottom: 9 x 7 x 2 =126
Total = 50 + 72 + 126 = 248 cubic feet
A motorboat can maintain a constant speed of 23 miles
per hour relative to the water. The boat makes a trip
upstream to a certain point in 52 minutes; the return trip
takes 40 minutes. What is the speed of the current?
The speed of the current is
mile(s) per hour.
the cost of living increased by 2% one year. the next year it increased by 3%. work out the total percentage increase over these two years
Answer:
5.06%
Step-by-step explanation:
x = cost of living....then increase it 2 %
1.02 x = new cost of living now increase this 3 %
(1.03) 1.02x = 1.0506x which equates to 5.06% increase in 2 years
pls help meeeeeee with this problem
Answer:
9
Step-by-step explanation:
this is the explanation 6×3=18 18÷2=9
which number completes the sequence
Answer:
6
Step-by-step explanation:
The number completes the sequence is 6
Can someone please explain how to solve this step by step so I could learn how to do this, if I don’t figure this out I’m literally gonna shoot myself
[tex]2x+2y=-8 \implies x+y=-4 \implies y=-4-x[/tex]
We can substitufe this result into the second equation.
[tex]-10x-5(-4-x)=-5 \\ \\ -10x+20+5x=5 \\ \\ -5x+20=5 \\ \\ -5x=-15 \\ \\ x=3 \implies y=-4-3=-7[/tex]
[tex]\therefore[/tex] The solution is [tex](3,-7)[/tex].
Mark bought s sheets of stickers. There are 9 stickers on each sheet. Write an expression that
shows how many stickers Mark bought.
The expression to find the total number of stickers bought by Mark is x = 9s.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The number of sheets of stickers Mark bought is denoted by the variable = s.
The number of stickers on each sheet is = 9
Let the total number of stickers be x.
Use the arithmetic operation of multiplication.
Then the expression will be -
Total number of stickers = Number of sheets of stickers × Number of stickers on each sheet
Substitute the values into equation -
x = s × 9
x = 9s
Therefore, the expression is obtained as x = 9s
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HELP PLS AND FAST!!!
Answer:
The correct equation you're looking for is the first choice: [tex]\frac{240 miles}{5 hours}[/tex] = 48 miles per hour.
Step-by-step explanation:
The formula to show the relationship between rate, time, and distance is [tex]rt=d[/tex], where [tex]r[/tex] represents the rate of change, [tex]t[/tex] represents time, and [tex]d[/tex] represents the total distance. Since you are given the distance and time, and are looking for the rate of change, then you need to divide the total distance traveled by the time it took to travel that distance, so the correct equation is [tex]\frac{240miles}{5hours}[/tex] = 48 miles per hour.
Have a great day! Feel free to let me know if you have any more questions :)
(5x + 14)°
(8x-10)
Pls help me
I am stoopid
7. Noah edits the school newspaper. He is planning to print a photograph of a
flyer for the upcoming school play. The original flyer has an area of 576
square inches. The picture Noah prints will be a dilation of the flyer using a
scale factor of What will be the area of the picture of the flyer in the
newspaper? (Lesson 5-4)
On solving the provided question, we can say that the area of the picture of the flyer in the newspaper is = 36 square inches.
What is area?The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.
he original flyer has an area of = 576 square inches.
The Picture Noah prints will be a dilation of the flyer using a scale factor of 1/4.
Scale factor k=1/4
So the area of the picture of the flyer in the newspaper is
A = 576 X k^2
A = 576*1/4*1/4
A = 36 sq in.
the area of the picture of the flyer in the newspaper is = 36 square inches.
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A salesman sold 75 percent of his first shipment of 800 units. How many of his next shipment of 600 units must he sell in order to have sold 80 percent of all of the units?
He must sell 520 units from the second shipment in order to have sold 80 percent of all of the unit.
This is mathematical equations.
The salesman sold 75% of 800 units, so he sold 0.75 * 800 = 600 units from the first shipment.
The salesman wants to sell 80% of all the units, which is a total of 0.80 * (800 + 600) = 0.80 * 1400 = 1120 units.
To find out how many units he must sell from the second shipment, we subtract the number of units he has already sold from the number of units he wants to sell:
1120 units - 600 units = 520 units.
Therefore, the salesman must sell 520 units from the second shipment in order to have sold 80% of all the units.
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In the xy-plane, a line with equation 2y = 4.5 intersects a parabola at exactly one point. If the parabola has equation y = −4x2 + bx, where b is a positive constant, what is the value of b ?
Answer: b=6
Step-by-step explanation:
Marcus bought a plant that originally cost $40. All plants were discounted 35%. What did Marcus pay for the plant after the discount
pls help, geometry !!!!!! NEED HELP ASAP
Step-by-step explanation:
what is the question ?
without an actual question I can only "daydream" things about this information.
EB is the diameter, FB is therefore the radius.
since FB = 3 units, EB = 2×FB = 2×3 = 6 units.
the arc angle AB = 120°.
if you need to express the angle in radians, remember :
360° (the full circle) = 2pi
120° = 360/3 = 2pi/3
the arc angle AE is the supplementary angle to AB (both together have 180° or 2pi/2 = pi).
180 = AB + AE = 120 + AE
AE = 180 - 120 = 60°
60° = 360/6 = 2pi/6 = pi/3
the arc angle BC = 45°.
45° = 360/8 = 2pi/8 = pi/4
the arc angle CD = 30°
30° = 360/12 = 2pi/12 = pi/6
the arc angle ED is the supplementary angle to BC and CD.
180 = ED + BC + CD = ED + 45 + 30 = ED + 75
ED = 180 - 75 = 105°
105° = pi - pi/4 - pi/6 = 12pi/12 - 3pi/12 - 2pi/12 = 7pi/12
the sum of
AB + BC + CD = 2pi/3 + pi/4 + pi/6 =
= 4×2pi/12 + 3pi/12 + 2pi/12 =
= 8pi/12 + 3pi/12 + 2pi/12 = 13pi/12
so, nothing fits to any of your answers.
again, I am not sure what problem you need to solve here.
maybe you can build your answer out of the various pieces I gave you here.
which expression is equivalent to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a
The equivalent expression of 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a is 136/120a + 107/120b.
One common way to simplify an expression is to use the unitary method, which involves finding a common denominator and then canceling out like terms.
In this case, we'll use the unitary method to find an equivalent expression to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a.
To start, we'll find a common denominator for all the terms in the expression.
The least common multiple of 5, 3, 8, 6, and 5 is 120. Now, we can convert all the fractions to have a denominator of 120.
Next, we'll simplify each term by dividing the numerator and denominator by their greatest common factor.
96/120a can be simplified to 8/10a by dividing both the numerator and denominator by 8. 80/120b can be simplified to 2/3b by dividing both the numerator and denominator by 40. And so on.
Finally, we'll rearrange the terms and simplify them using the unitary method. We'll start by canceling out like terms, which have the same variable and the same sign.
So, 8/10a and 96/120a are both positive and have the variable a, so we can simplify them to 104/120a.
Similarly, we can simplify 2/3b and 105/120b to 107/120b. We'll then add up all the positive terms and subtract all the negative terms.
The final equivalent expression is
=> 104/120a + 107/120b + 15/120 - 90/120
=> (104 + 107 + 15 - 90)/120a + (107/120)b
=> 136/120a + 107/120b.
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25 POINTS. HELP W THE EQUATION TYSM
Step-by-step explanation:
cubing on both sides,
(-4)³= ³√(9x-1)³
-64=9x-1
-64+1=9x
-63=9x
-63/9=x
x=-7
explain in your own words why it takes more to prove that quadrilaterals are similar
Proving that quadrilaterals are congruent takes more because all quadrilaterals are polygons of four sides and they all have a sum angle of 360°
Explaining quadrilaterals?
With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals' internal angles add up to a constant 360 degrees.
What is quadrilateral formula?
When the diagonal and the sum of the lengths of the perpendiculars drawn from the remaining two vertices are known, the area of the quadrilateral can be determined as follows Area of quadrilateral = (12) diagonal length sum of the lengths of the perpendiculars drawn from the remaining two vertices.
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The complete question is -
Explain in your own words why it takes more to prove quadrilaterals congruent. Include examples demonstrating how ""just angles"" or ""just sides"" is not enough.
The ratio of a rectangle's length to the rectangle's width is 6:11. If
the perimeter of the rectangle is 510 units, then what is the length of
the rectangle?
Answer:
Step-by-step explanation:
90
By solving the equation 510 = 2(6x + 11x), we know that the length of the given rectangle is 90 units.
What are equations?
It primarily consists of a variable, sometimes with a numerical constant in addition.
Take the following illustration into consideration to quickly grasp this idea. 3x – 4 = 5. It is a simple equation of class 7.
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
So, we know that the ration is 6:11 and the perimeter is 510 units.
Then, form and solve the equation as follows:
510 = 2(6x + 11x)
510 = 12x + 22x
510 = 34x
x = 510/34
x = 15
Then, the length will be:
6x
6(15)
90 units
Therefore, by solving the equation 510 = 2(6x + 11x), we know that the length of the given rectangle is 90 units.
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