Write the next three terms of the geometric sequence. 81, - 27, 9, - 3, ...​

The least integer k such that f(n) is O(nk) for each of the following functions is k = 2.

log (n!) = ln(n!)

First we know ,

[tex]\lim_{n \to \infty} \frac{ln(n!)}{n^{k} } = L[/tex]

where L is a limited number.

then ,

[tex]\lim_{n \to \infty} \frac{ln(n!)}{n^{k} } = L \\\\\lim_{n \to \infty} \frac{ln(n+1)!-ln(n!)}{(n+1)^{k}- n^{k} } = L[/tex]     Stolz's Formula

By solving the upper limit we get k =2

It can make  

[tex]\lim_{n \to \infty} \frac{1}{k} \frac{ln(n+1)}{n^{(k-1)} } _[/tex]

[tex]\lim_{n \to \infty} \frac{1}{2} \frac{ln(n+1)}{n^{} } = 0[/tex]

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain.

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The range of the progress of the construction company's six projects is 0.82.

The range of data is a measure of its spread. To calculate the range, you subtract the smallest value from the largest value.

The data for this problem is:

Project     Progress

 u                0.87

 v                0.31

 w               0.08

 x                0.05

 y                0.19

 z                0.5

In this case, the smallest value is 0.05 (project x) and the largest value is 0.87 (project u), so:

This means that the difference between the most advanced project and the least advanced project is 0.82. The range is an important measure of variability and helps in understanding the distribution of data, in this case, the progress of the construction projects.

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Since Fathi has $1.10 in his printing account, he will have -$59342.28 after printing the 474747-page PDF document.

Let's calculate how much Fathi will spend on printing the 474747-page PDF document.

Since Fathi is printing 2 pages on each side of a sheet, he uses 1/2 sheet of paper per 2 pages. And since each sheet of paper reduces his printing account balance by $0.25, he will spend $0.25 per 2 pages.

So, the cost per page is $0.25 / 2 = $0.125.

Now, we can calculate the total cost of printing the 474747 pages by multiplying the cost per page by the number of pages:

$0.125 * 474747 = $59343.38

Since Fathi has $1.10 in his printing account, he will have $1.10 - $59343.38 = -$59342.28 after printing the 474747-page PDF document.

So, Fathi will not have enough funds in his printing account to print the document and will have to add more money to his account or find another way to print the document.

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Since Fathi has $1.10 in his printing account, he will have -$59342.28 after printing the 474747-page PDF document.

Let's calculate how much Fathi will spend on printing the 474747-page PDF document.

Since Fathi is printing 2 pages on each side of a sheet, he uses 1/2 sheet of paper per 2 pages. And since each sheet of paper reduces his printing account balance by $0.25, he will spend $0.25 per 2 pages.

So, the cost per page is $0.25 / 2 = $0.125.

Now, we can calculate the total cost of printing the 474747 pages by multiplying the cost per page by the number of pages:

$0.125 * 474747 = $59343.38

Since Fathi has $1.10 in his printing account, he will have $1.10 - $59343.38 = -$59342.28 after printing the 474747-page PDF document.

So, Fathi will not have enough funds in his printing account to print the document and will have to add more money to his account or find another way to print the document.

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The third side of triangle is 7/15.

The third side of a triangle must satisfy the triangle inequality, which states that the sum of any two sides must be greater than the third side. For a triangle with sides of 5 and 7 inches, the third side must be less than 5 + 7 = 12 inches. So, the possible lengths for the third side are 5, 6, 7, 8, 9, 10, 11 inches.

There are 15 total possible lengths for the strip, so the probability of randomly selecting a strip that can be used as the third side of a triangle with sides of 5 and 7 inches is 7/15.

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The third side of triangle is 7/15.

The third side of a triangle must satisfy the triangle inequality, which states that the sum of any two sides must be greater than the third side. For a triangle with sides of 5 and 7 inches, the third side must be less than 5 + 7 = 12 inches. So, the possible lengths for the third side are 5, 6, 7, 8, 9, 10, 11 inches.

There are 15 total possible lengths for the strip, so the probability of randomly selecting a strip that can be used as the third side of a triangle with sides of 5 and 7 inches is 7/15.

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After differentiation, The expression will be [tex]y = \frac{10}{9-t}[/tex].

Differentiation is one of the two central concepts in calculus, along with integration. Differentiation is a method for finding a function's derivative. Differentiation is a mathematical technique used to calculate the instantaneous rate of change of a function based on one of its variables. Velocity, or how quickly a distance varies in respect to time, is the most common example. Differentiation's opposite is finding an antiderivative.

If x and y are two variables, then dy/dx gives the rate of change of x in relation to y. A function's derivative is represented universally by the equation f'(x) = dy/dx, where y = f(x) is any function.

dy/dx

Now,

Given right expression is[tex]10(t+1)\frac{dy}{dt}-9y=9t[/tex]

[tex]9(y+t)=(10t-10)\frac{dy}{dt}[/tex]

After differentiation: [tex]\frac{s}{dx} (x^{n}) = nx^{n-1}[/tex]

[tex]9(y+t)=10[/tex]

[tex]y = \frac{10}{9-t}[/tex]

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Answer: cos(L) = 0.3684

Step-by-step explanation:

To solve, we need to identify what its asking first.

It wants us to find the value of the cos L

We know that Cosine is equivalent to the [tex]\frac{adjacent}{hypotenuse}[/tex] sides.

We also know that Cos L is an angle.

If we look at the picture, we first need to locate where L is. Then we need to find the cosine of it.

The adjacent side to L is 7.

The hypotenuse is 19.

we can rewrite this information into an equation:

[tex]cos (L)=\frac{7}{19}[/tex]

Since it wants cos L value to the nearest hundredth, we will use a calculator to divide.

cos(L) = 0.3684

(b) Yes, the experiment has a control group.

(c) The treatments can be randomly assigned to the experimental units by randomly selecting 20 containers and assigning each of the four treatments to 5 containers.

a) Treatments: Four different concentrations of fungus mixtures (0 ml/L, 1.25 ml/L, 2.5 ml/L, and 3.75 ml/L).

Experimental units: 20 individual containers with a group of insects.

Response variable: Number of insects that are still alive in each container one week after spraying.

(b) A control group is used to compare the results of the treatment group to a group that is not exposed to the treatment.

In this experiment, the control group can be the group of insects that are not exposed to any of the fungus mixtures.

c) The treatments can be randomly assigned to the experimental units by randomly selecting 20 containers and assigning each of the four treatments to 5 containers.

This way, each treatment has the same number of units and the assignment of treatments to units is random, which reduces the risk of bias in the experiment.

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Answer:

the Answer is x=5

Step-by-step explanation:

so all you do is 2+5 is 7 example say 2+x=4 what is 2+2=4

What is the question for this so I can answer it?

The area of the region between the curves y=sinx and y=cosx that contains the point (0,0) is 4π.

The area of the region between the curves y=sinx and y=cosx that contains the point (0,0) is the integral of the absolute value of the difference between the two functions. This is expressed mathematically as:

∫|sinx-cosx|dx

Using integration by parts, we can break this integral into two parts:

∫sinx dx - ∫cosx dx

Integrating each of these parts separately and substituting in the limits of integration from 0 to 2π, we get the following:

2π - 0 - (-2π)

Simplifying, this gives us the area of the region as 4π.

Therefore, the area of the region between the curves y=sinx and y=cosx that contains the point (0,0) is 4π.

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The equation of the first and second line is y = 1.5x + 1 and y = 1.5x - 2

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

The slope intercept form of a linear equation is:

y = mx + b

where m is the rate of change and b is the y intercept

The first line passes through the point (0, 1) and (-2, -2). Hence:

[tex]y-y_1=\frac{y_1-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-1=\frac{-2-1}{-2-0} (x - 0)\\\\y=1.5x+1[/tex]

The second line passes through the point (0, -2) and (-2, -5). Hence:

[tex]y-y_1=\frac{y_1-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-(-2)=\frac{-5-(-2)}{-2-0} (x - 0)\\\\y=1.5x-2[/tex]

The equation of the line is y = 1.5x + 1 and y = 1.5x - 2

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Answer:

48

Step-by-step explanation:

48+96 =144

x * (1+2) = 3x = 144

so x = 48

E = 18.1 h will be a proportional equation for e in terms of h that matches the context.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given a table of data about total earnings and working hours,

Since its given that the data is proportional thus we can make an equation in terms of earning and working hours variable.

Let "e" be the earnings of Penelope and " h" be the total working hours

Thus,

e/h = 362/20

e = 18.1h

Therefore, a proportional equation for e in terms of h that matches the context will be  E = 18.1h.

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The limit as x approaches 4 of f(x) is equal to -2 * 4^2 + 3 * 4 - 1 = 15.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example. A function is defined technically as a relation between a set of inputs and a set of potential outputs, where each input is associated to exactly one output. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

The limit of f(x) as x approaches 4 is given by the value of f(4).

For x = 4, the definition of f(x) is:

-2x^2 + 3x - 1 = -2 * 4^2 + 3 * 4 - 1 = 15.

Therefore, the limit of f(x) as x approaches 4 is 15.

So, lim x→ 4 f(x) = 15.

The limit of f(x) as x approaches 4 is equivalent to -2 * 42 + 3 * 4 - 1 = 15.

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The general term for the recurrence T(n) = 3T(n/2) + O(n) is O(nlog3). To get the answer, we should plug in k = log3. For the second recurrence, we cannot use the master theorem since it does not cover this case.

To solve this recurrence, we have to use the substitution method, where we guess a solution of the form T(n) = an^k and then prove that this is indeed a solution. This can be done by substituting the guessed solution back in to the recurrence. If the substitution works, then we have solved the recurrence. If not, we can try different values for a and k until the substitution works.

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Answer:

618.4

Step-by-step explanation:

Based on the given conditions, formulate: 773 x (1 - 20%)

Calculate the sum or difference: 773 × 0.8

Calculate the product or quotient: 618.4

Answer: 618.4

The Rational Root Theorem states that for a polynomial equation with integer coefficients to have a rational solution, that solution must be represented by the a factor of the constant (denoted by the variable p) divided by a factor of the leading coefficient (denoted by the variable q).

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The required integration-by-parts formula of given function is 5x (1/6) sin(6x) - (5/36) cos(6x) + C.

To evaluate the integral using integration-by-parts, we need to find two functions u and dv such that their derivative is equal to the integrated, and such that the anti-derivative of dv can be easily found. The integration-by-parts formula states that:

∫ uv = u(v) - ∫ v du

Let's choose u = 5x and dv = cos(6x) dx. Then, du = 5 dx and v = (1/6) sin(6x).

Using the integration-by-parts formula, we get:

∫ 5x cos(6x) dx = 5x (1/6) sin(6x) - ∫ (1/6) sin(6x) 5 dx

The antiderivative of (1/6) sin(6x) 5 is (5/36) cos(6x), so:

∫ 5x cos(6x) dx = 5x (1/6) sin(6x) - (5/36) cos(6x) + C,

where C is the constant of integration.

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Answer:

Below

Step-by-step explanation:

y = 3/20  *  x        where y is in miles   and x is in minutes

The letters in the actual advertisement will be 25.5 inches tall.

The height of the letters in the sketch is ¾ inch. To find the height of the letters on the actual advertisement, we have to multiply ¾ inch by 34.

So, ¾ inch x 34 = 25.5 inches

Therefore, the height of the letters on the building will be 25.5 inches.

It's important to understand the relationship between the sketch and the actual advertisement. In this case, the sketch serves as a visual representation to plan the design, but the size of the lettering must be adjusted to fit the intended space. In this case, the lettering needs to be 34 times larger in the actual advertisement than it is in the sketch.

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$13320 is the value of the camper after 5 years.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

m=23680-29600/3-2

=-5920

Now let us find the y intercept

37000=-5920(1)+b

b=37000+5920

b=42920

y=-5920(5)+42920

=-29600+42920

y=13320

Hence, $13320 is the value of the camper after 5 years.

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Answer:

False

Step-by-step explanation:

Answer:

Step-by-step explanation:

5x=6x+9 then subtract 6x to get -1x=9. divide by 1 to get x=-9. this make the equation true. Therefore it is open.

The description corresponds to an observational study, which involves gathering data and information to draw conclusions without intervening in the process. Correct answer: letter D.

An experiment would involve manipulating the variables to see the effect of the manipulation. In this case, it would involve changing the caffeine consumption and observing the effect on heart arrhythmias.

In order to better understand the relationship between heart arrhythmias and caffeine consumption, researchers need to consider a variety of factors, including the amount of caffeine consumed, the timing of consumption, and any potential underlying medical conditions that could be influencing the results.

Furthermore, researchers need to ensure that the study population is large enough and diverse enough to accurately reflect the general population. Additionally, researchers need to consider potential confounding variables, such as lifestyle factors, medications, and other dietary components that could be influencing the results.

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The value of y in the given triangle is 5√3. Therefore, option A is the correct answer.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In the given triangle, one of the leg of right tringle is 5 units.

We know that, tanθ= Opposite/Adjacent

tan60° =y/5

√3 =y/5

y=5√3

Therefore, option A is the correct answer.

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Answer:

41/81

Step-by-step explanation:

There are a total of 4 blue marbles, 5 red marbles giving 9 total number of marbles

Let P(B₁) =Probability of getting a blue marble on the first draw

Let P(B₂) =Probability of getting a blue marble on the second draw

Let P(R₁) =Probability of getting a red marble on the first draw
Let P(B₂) =Probability of getting a red marble on the second draw

P(B₁) = Number of blue marbles ÷ total number of marbles = 4/9

Since the marble is replaced before the second draw, the total number of blue marbles and total number of both marbles is the same as for the first draw

P(B₂) = P(B₁) = 4/9 also

Probability of getting 2 blue marbles on 2 consecutive draws= P(B₁B₂)
= 4/9 x 4/9 = 16/81

P(R₁) = Number of red marbles ÷ total number of marbles = 5/9

P(getting a red marble on the second draw) = P(R₁R₂) = 5/9

Probability of getting 2 red marbles on 2 consecutive draws = P(R₁R₂)
= 5/9 x 5/9 = 25/81

Since we are asked the probability of getting 2 of the same color we can rephrase the same question as

P(two of same color) = P(B₁B₂ ∪ R₁R₂) = P(B₁B₂) + P(R₁R₂) = 16/81 + 25/81 = 41/81

Shakita will have enough felt to make 10 banners and she will have 2 yards left over

First, let's calculate how much felt Shakita needs for 10 banners using multiplication

= 10 banners * 1/4 yard per banner

= 2.5 yards

Comparing this with the amount of felt Shakita has:

Shakita has 4.5 yards of felt, and she needs 2.5 yards to make 10 banners, so she will have:

4.5 yards - 2.5 yards = 2 yards of felt left over.

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The distance that would be between the cities on a map that has a scale of 3 inches:17 miles is 9 inches.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The two cities are 51 miles away from each other.

3 inches:17 miles

Now,

17 miles = 3 inches

Multiply 3 on both sides.

17 x 3 miles = 3 x 3 inches

51 miles = 9 inches

Thus,

There would be 9 inches between the cities on the map.

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To find the speed of a roller coaster, measure the distance it travels in a certain amount of time, then divide that distance by the amount of time it took to travel.

To find the speed of a roller coaster, start by measuring the distance it travels in a certain amount of time. This can be done by using a measuring tape to measure the total length of the track. Then, use a stopwatch to measure the amount of time it takes for the coaster to complete one full lap of the track. Once you have both of these measurements, divide the total distance traveled by the amount of time it took to travel. This will give you the speed of the roller coaster, given in units such as meters per second.

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Answer:
look at the image and give me brainliest k thx

Step-by-step explanation:

Answer:

Step-by-step explanation:

7,2 is viable

Answer:

Below

Step-by-step explanation:

the sides of the second figure are 4/3 bigger than the first

4/3 * 4/3 * 100 = 177.78 units^2

   There are two sides involved in calculating area  L x W

        so you have to multiply by 4/3 TWICE