Someone solve all of these for 30 points, I will report if you do not answer and just spam something.

The given recurrence relations and O (in big-O notation) bound are:

a. T(n) = 2T(n/3) + 1; O(nlog3 2)

b. T(n) = 5T(n/4) + n; O(nlog4 5)

c. T(n) = 7T(n/7) + n; O(n)

d. T(n) = 9T(n/3) + n; O(n²)

e. T(n) = 8T(n/2) + n³; O(n³log2n).

a. T(n) = 2T(n/3) + 1

Applying the master theorem, we have

a = 2, b = 3 and f(n) = 1

Now, logb a = log3 2 = 0.63 > f(n) = 1So, T(n) = O(nlog3 2).

b. T(n) = 5T(n/4) + n

Applying the master theorem, we have

a = 5, b = 4 and f(n) = n

Now, logb a = log4 5 = 1.16 > 1 = f(n)So, T(n) = O(nlog4 5).

c. T(n) = 7T(n/7) + n

Applying the master theorem, we have

a = 7, b = 7 and f(n) = n

Now, logb a = log7 7 = 1 = f(n)

So, T(n) = O(n).

d. T(n) = 9T(n/3) + n

Applying the master theorem, we have

a = 9, b = 3 and f(n) = n

Now, logb a = log3 9 = 2 > f(n)

So,

T(n) = O(n2).

e. T(n) = 8T(n/2) + n³

Applying the master theorem, we have

a = 8, b = 2 and f(n) = n³

Now, logb a = log2 8 = 3 > 3 = f(n)

So, T(n) = O(n³log2n).

Thus, the given recurrence relations and O (in big-O notation) bound are:

a. T(n) = 2T(n/3) + 1; O(nlog3 2)

b. T(n) = 5T(n/4) + n; O(nlog4 5)

c. T(n) = 7T(n/7) + n; O(n)

d. T(n) = 9T(n/3) + n; O(n²)

e. T(n) = 8T(n/2) + n³; O(n³log2n).

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N = 4. The digit N represents 4. The five-digit number is 68364.

To determine if a number is divisible by 9, the sum of its digits must be divisible by 9. In this case, we know that the five-digit number 6836N is divisible by 9, so we can add up the digits to see what value N must be.

6 + 8 + 3 + 6 + N = 23 + N

For 23 + N to be divisible by 9, N must be equal to 4,

The sum of all the digits in the number should be 27 as 23 + 4 = 27, which is divisible by 9. Therefore, the digit N represents the value of 4.

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Answer:

There is a linear relationship between costumes and fabric. The rate of change is 3 1/2 yards per costume.

Step-by-step explanation:

The second possible answer is correct,

3 and 1/2

brailiest would be appreciated :]

Answer:  The correct answer is B. There is a linear relationship between the number of costumes and fabric. The rate of change is 3.5 yards per costume.

Step-by-step explanation:

Divide the Fabric yards by the number of costumes:

7 / 2 = 3.5

14 / 4 = 3.5

21 / 6 = 3.5

28 / 8 = 3.5

Since they are all 3.5 yards per costume, the relationship is LINEAR

Answer:

Step-by-step explanation:

(x , -2)  & (-4, 5)

\(Slope = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

\(\dfrac{5-[-2]}{-4-x}= \dfrac{7}{-11}\\\\ \dfrac{5+2}{-4-x}= \dfrac{7}{-11}\\\\ \dfrac{7}{-4-x}= \dfrac{7}{-11}\)

Cross multiply,

7*(-11) = 7*(-4-x)

-77 = -28 - 7x

Add 28 to both sides,

-77 + 28 = -7x

-49 = -7x

Divide both sides by (-7)

-49/-7 = x

x = 7

Answer:

C

Step-by-step explanation:

I think

For every graph G on 11 or more vertices, at most one of G and its complement G can be planar. An example of such a graph is a complete bipartite graph K3,3.

The statement is asserting that if a graph G has 11 or more vertices, then it is not possible for both G and its complement G to be planar.

To prove this, we can use the fact that a planar graph can have at most 3v - 6 edges, where v is the number of vertices.

If both G and G were planar, their combined number of edges would be at most 3v - 6 + 3v - 6 = 6v - 12. However, the complete graph on v vertices (the complement of G) has v(v-1)/2 edges.

Setting up the inequality 6v - 12 ≥ v(v-1)/2, we can simplify and rearrange it to v^2 - 13v + 24 ≥ 0. By factoring or using the quadratic formula, we find that the roots of this quadratic equation are 3 and 8.

This means that for v ≥ 11, the quadratic v^2 - 13v + 24 is non-negative.

Therefore, if G has 11 or more vertices, the inequality holds, indicating that it is not possible for both G and its complement G to be planar.

To provide an example of a graph G on 11 or more vertices where both G and its complement G are nonplanar, we can construct a graph with a structure similar to the complete bipartite graph K3,3.

Consider a graph with 6 vertices on one side, labeled A1, A2, A3, A4, A5, A6, and 6 vertices on the other side, labeled B1, B2, B3, B4, B5, B6.

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After 2 years, the amount in the bank account will be approximately £2,121.21, considering a 3% compound interest per year.

To calculate the compound interest, we use the formula:

A = P(1 + r/n)^(n*t)

Where:

A = the final amount

P = the principal amount (initial deposit)

r = annual interest rate (in decimal form)

n = number of times interest is compounded per year

t = number of years

Given that the principal amount (P) is £2,000, the annual interest rate (r) is 3% (or 0.03 in decimal form), and the duration (t) is 2 years, we need to determine the final amount (A).

Plugging in the values, we have:

A = £2,000(1 + 0.031)^(1*2)

Simplifying the equation, we get:

A = £2,000(1 + 0.03)^2

Calculating the exponential part, we have:

A = £2,000(1.03)^2

A ≈ £2,000(1.0609)

A ≈ £2,121.21

Therefore, after 2 years, the amount in the bank account will be approximately £2,121.21 with a 3% compound interest per year.

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Step-by-step explanation:

The coordinate of A is 0. It is given that AR = 17. AR represents the distance from point A to point R. Remember that distance is always positive. So, from here we have two possibilities.

Point R is on Right side of A i.e. at coordinate 17

Point R is on Left side of A i.e. at coordinate -17

In both of these cases AR which is the distance from A to R will be 17.

So, if R is on Right side of A, the midpoint of AR would be:

0+17

  ÷      =  17/2  = 8.5

  2

Or if R is on Left side of A, the midpoint of AR would be:

0-17

  ÷      =  -17/2  = -8.5

  2

Thus, the possible coordinates of the midpoint of AR are 8.5 and -8.5

Answer:

1) To calculate length of fringe, we need to find the perimeter

The question does not clearly say how much is length and width

Assuming length = 245 and width = 234 inches

P = 2(length + width)

P = 2 ( 245 + 234)

P = 2 (479)

P = 958 inches

2) To calculate length of fringe, when length is increased by 33 inches

P = 2 ( l + w)

P = 2 (278 + 234)

P = 2 x 512

P = 1024 inches

The amount of tile that would be used to cover the pedestal is equal to the area of the pedestal

The area of an object is the amount of two-dimensional space it occupies.

It is a measure of the size of a surface and is typically expressed in square units, such as square meters or square inches.

The area can be determined for various shapes including squares, rectangles, circles, triangles, and more complex shapes.

for a rectangle it is calculated by the formula

length  * width

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Answer:

As far as I know

Mode: The most frequent number—that is, the number that occurs the highest number of times. Example: The mode of {4 , 2, 4, 3, 2, 2} is 2 because it occurs three times, which is more than any other number.

The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

The student whο scοred 428 will nοt be admitted tο the schοοl because their scοre did nοt fall in the tοp 30% οf the distributiοn.

The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.

Tο find the z-scοre οf the student whο scοred 428, we can use the fοrmula:

z = (x - μ) / σ

where x is the student's scοre, μ is the mean οf the distributiοn (400 in this case), and σ is the standard deviatiοn οf the distributiοn (60 in this case).

Plugging in the values, we get:

z = (428 - 400) / 60 = 0.467

Since the z-scοre οf the student is less than 0.524, which is the z-scοre cοrrespοnding tο the tοp 30% οf the distributiοn, we can cοnclude that the student did nοt scοre in the tοp 30%.

Therefοre, the student will nοt be admitted tο the schοοl based οn the admissiοn criteria οf scοring in the tοp 30%.

Hence, the student whο scοred 428 will nοt be admitted tο the schοοl because their scοre did nοt fall in the tοp 30% οf the distributiοn.

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The solution to the system of linear equations is x = -3 and y = -2

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

y = 3x + 7------------------1

-x + 4y = -5 -----------------2

substitute y = 3x + 7 in equation 2

-x + 4(3x + 7) = -5

multiply out

-x + 12x + 28 = -5

11x = -28 - 5

11x = -33

x = -33/11

x = -3

substitute x = -3 in equation 1

y = 3(-3) + 7

y = -9 + 7

y = -2

In conclusion the values of x and y are -3 and -2 respectively.

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Step-by-step explanation:

Hey, there!!

While simplifying the algebraic expression, you must be very careful about the signs.

Here,

(6x-4) (9x-2)

Multiply 2nd expression by 1st expression,

= 6x ( 9x - 2) -4 ( 9x - 2)

\( = (54 {x}^{2} - 12x) - (36x - 8)\)

Opening brackets,

\( = 54 {x}^{2} - 12x - 36x + 8\)

Simplifying them we get,

\( = 54 {x}^{2} - 48x + 8\)

Therefore, the answer is 54x^2 - 48x +8.

Hope it helps..

The probability that the household contains 3 people must be 0.16

The probability of finding 3 people in a household is the same as the probability of finding 4 people.

The probability = Number of favorable outcomes / Total number of outcomes

The probability is the occurrence of the random event. The value of the probability varies from 0 to 1

Therefore if we add all the probability together, the result will be one

Also The probability of finding 3 people in a household is the same as the probability of finding 4 people.

Consider the probability of finding 3 people = Probability of finding 4 people = x

Then the equation will be

0.25 + 0.32 + x + x + 0.07 + 0.03 + 0.01 = 1

Add the terms

0.68 + 2x = 1

2x = 1 - 0.68

2x = 0.32

x = 0.32 / 2

x = 0.16

Hence, the probability that the household contains 3 people must be 0.16

The complete question is:

In government data, a household consists of all occupants of a dwelling unit. choose an American household at random and count the number of people it contains. here is the assignment of probabilities for the outcome. the probability of finding 3 people in a household is the same as the probability of finding 4 people. what is the probability of finding 3 people in the household ?

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Careful consideration and statistical analysis should be undertaken to determine the appropriate variables to include in a regression model.

By including another variable in a regression analysis, several outcomes are possible. Let's consider the statements you provided one by one:

1. Decrease the regression R^2 if that variable is important:

  - If the added variable is important and has a meaningful relationship with the dependent variable, it can increase the explanatory power of the regression model, thereby increasing the R^2.

However, if the added variable is not relevant or has a weak relationship with the dependent variable, it can decrease the R^2.

2. Decrease the variance of the estimator of the coefficients of interest:

  - Including additional variables in a regression model can sometimes help to reduce the variance of the coefficient estimators for the variables of interest.

This is because including more relevant variables can help to explain some of the variance in the dependent variable, leaving less unexplained variance for the coefficients of interest.

3. Eliminate the possibility of omitted variable bias from excluding that variable:

  - Omitted variable bias can occur when an important variable is not included in the regression model.

Including all relevant variables in the model can help reduce the risk of omitted variable bias, as it allows for a more comprehensive analysis of the relationship between the dependent variable and the independent variables.

4. Look at the t-statistic of the coefficient of that variable and include the variable only if the coefficient is statistically significant at the 1% level:

  - The t-statistic measures the statistical significance of a coefficient. Inclusion of a variable in a regression model is often based on its statistical significance.

If the coefficient of the variable is statistically significant at the desired significance level (e.g., 1%), it suggests that the variable has a meaningful impact on the dependent variable and can be included in the model.

It is important to note that the effect of including an additional variable in a regression model depends on various factors such as the relationship between the variables, sample size, multicollinearity, and the specific research context.

Therefore, careful consideration and statistical analysis should be undertaken to determine the appropriate variables to include in a regression model.

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Answer:

the inclination of the line will decrease

Step-by-step explanation:

If Cassandra changes the amount she deposits from 18 to 14, the slope changes to 14. So the new equation is M=14n + 224. The 224 is still the same, because that is the initial amount, and the new situation hasn't said anything about changing that, so it will not have any vertical translations. With that being said, as a result the slope will be less, so you can see it as "less vertical", so the inclination of the line will decrease

Let a and b be the two numbers. Then

a + b = -4

a b = -2

Solve the second equation for b :

b = -2/a

Substitute this into the first equation:

a - 2/a = -4

Multiply both sides by a :

a² - 2 = -4a

Move 4a to the left side:

a² + 4a - 2 = 0

Use the quadratic formula to solve for a :

a = (-4 ± √(4² - 4(-2))) / 2

a = -2 ± √6

If a = -2 + √6, then

-2 + √6 + b = -4

b = -2 - √6

In the other case, we end up with the same numbers, but a and b are swapped.

Step-by-step explanation:

General line equation: y = mx + c

When x = 0, y = 3. => (3) = m(0) + c, c = 3.

When x = -4, y = 5. => (5) = m(-4) + c,

5 = -4m + (3), -4m = 2, m = -0.5.

Hence the answer is y = -0.5x + 3.

Answer:

y=-\(\frac{1}{2}\)+3

Step-by-step explanation:

To write the equation of the line in slope-intercept form, first calculate the slope of the line (m)

m=\(\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\)

=\(\frac{5-3}{-4-0}\)

=2/-4

=-\(\frac{1}{2}\)

next, calculate b by substituting a point (0, 3) into the equation

y=mx+b

3=(-1/2)(0)+b

b=3

final equation of line is: y=-\(\frac{1}{2}\)+3

Answer:

A or B I think

Step-by-step explanation:

Not entirely sure of it but ummm

Answer:

4 square root 2

Step-by-step explanation:

i just know

the equation \(\[\frac{1}{\sqrt{2}} +\frac{3}{\sqrt{8}} + \frac{6}{\sqrt{32}}.\]\) can be written as 2√2

A collection of numbers and operations is an expression in mathematics. The following are the parts of a math expression that do a math operation:

Operator: An operator is a symbol that denotes a math operation, such as:

division, addition, subtraction, and multiplication.

Given an equation \(\[\frac{1}{\sqrt{2}} +\frac{3}{\sqrt{8}} + \frac{6}{\sqrt{32}}.\]\\\)

Simplifying this equation

=>  1/√2 + 3 / 2* √2  + 6 /4√2

taking 1/√2 Common

=> 1/√2 (1 + 3/2 + 6/4)

=> 1/√2 (4)

=> 4/ √2

=> 2√2

therefore, the given equation can also be written as 2√2.

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The simplest form of the expression is a⁴ b¹/₂ which is option (B)   .

We have given an expression  (a²/¹ b¹/⁴)² .

On simplifying , we get

(a²/¹ b¹/⁴)² = \(a^{2\times2} \ \ b^{2/4}\)

                 = a⁴ b¹/₂

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The complete question is given below :

What is the simplified form of (a²/¹ b¹/⁴)²?

(A) a⁴/₅ b⁹/₁₆ (B) a⁴ b¹/₂ (C) a b (D) (a b)¹⁷/₆

To find dy/dt, we can differentiate the given equation y^3 = 2x^4 + 81 with respect to t using implicit differentiation.

Differentiating both sides of the equation with respect to t, we get:

3y^2 * dy/dt = 8x^3 * dx/dt

Substituting the given values dx/dt = 4, x = 5, and y = 11 into the equation, we can solve for dy/dt:

3(11)^2 * dy/dt = 8(5)^3 * 4

363 * dy/dt = 8 * 125 * 4

363 * dy/dt = 4000

Dividing both sides by 363, we find:

dy/dt = 4000 / 363

Simplifying this expression, we get:

dy/dt = 400/33

Therefore, the value of dy/dt is 400/33.

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Answer:

p(d) = 24p + 500d

Step-by-step explanation:

p(d) = 24p + 500d

hopefully this helps ;)

Can you answer my question pleaseeee?

The function that represents P (the number of pages) that Mario left to read after d days is:

P = 500 - 24d

Given,

Mario has a 500-page novel that he is required to read over summer break for his upcoming language arts class.

Mario read 24 pages each day.

We need to write a function to represent the number of pages that Mario left to read p after d days.

A function has an input and an output.

Example: f(x) = x + 1

x = 1

f(1) = 1 + 1 = 2

Input = 1

Output = 2

We have,

Total number of pages = 500

Pages read each day = 24

Write a function to represent  P the number of pages that Mario left to read after d days.

P = 500 - 24d

Where d must be less than 20 or equal to 20.

i.e d ≤ 20.

Thus the function that represents P (the number of pages) that Mario left to read after d days is:

P = 500 - 24d

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Answer:

Step-by-step explanation:

(x, y) ----> (- x, y)

J(4, 1) ------> J' (- 4, 1)

K(1, 0) -----> K' (- 1, 0)

L(2, - 4) ----> L' (- 2, - 4)

Dodie's triangular plot with 160 rose plants will have 12 rows.

To solve it,

Assigning a variable to the number of rows we want to find. Assume that this variable is "n".

Since there are 5 more plants in each row than in the previous row,

We can use an arithmetic sequence to represent the number of plants in each row.

Specifically, the first row will have 1 plant, and the second row will have

1 + 5 = 6 plants, the third row will have 1 + 5 + 5 = 11 plants, and so on.

The formula for an arithmetic sequence is,

an = a1 + (n-1)d

Where an is the nth term of the sequence,

a1 is the first term,

And d is a common difference.

Using this formula, we can write an expression for the total number of plants in all n rows,

160 = n/2 (2 + (n-1)5)

Simplifying this equation, we get,

160 = 2.5n² + 2.5n - 5

Now we can solve for n using the quadratic formula,

n = (-2.5 ± √(2.5²+ 4(2.5)(165)))/(2(2.5))

After simplifying this equation, we get two solutions,

n = -13.2 and n = 12.2.

Since we can't have a negative number of rows, we'll take the positive solution, n = 12.2.

Now, since we can't have a fraction of a row, we'll round down to the nearest integer.

Therefore, Dodie's plot will have 12 rows.

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Answer:

D

Step-by-step explanation:

Answer:

B. -3

Got It Right On The Test