I will mark 1st correct answer as brainliest
Let f(x) = log base 3 of x and g(x) = 3^x.
What is the value of

[f(g(f(f(f(g(27))))))?]

I will mark 1st correct answer as brainliest

Answers

Answer 1

The value of the composite function [f(g(f(f(f(g(27))))))], when f(x) = log₃(x) and g(x) = 3ˣ is 1

How to evaluate the composite function

From the question, we have the following parameters that can be used in our computation:

Let f(x) = log base 3 of x and g(x) = 3^x.

Express the equations properly

So, we have the following representations

f(x) = log₃(x) and g(x) = 3ˣ

Calculating the composite function [f(g(f(f(f(g(27))))))], we have

[f(g(f(f(f(g(27))))))] = [f(g(f(f(f(3²⁷))))))]

Next, we have:

[f(g(f(f(f(g(27))))))] = [f(g(f(f(log₃(3²⁷))))))]

This gives

[f(g(f(f(f(g(27))))))] = [f(g(f(f(27))))))]

For f(27), we have

[f(g(f(f(f(g(27))))))] = [f(g(f(3)))))]

For f(3), we have

[f(g(f(f(f(g(27))))))] = [f(g(1))))]

Calculating g(1), we have

[f(g(f(f(f(g(27))))))] = f(3)

Lastly, we have

[f(g(f(f(f(g(27))))))] = log₃(3)

Evaluate

[f(g(f(f(f(g(27))))))] = 1

Hence, the solution is 1

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Related Questions

What is the area of the red region?

Answers

Answer:

Exact: A = (3.28 + 8π) cm²

Approximate: A = 57.13 cm²

Step-by-step explanation:

The right part of the red figure is a rectangle which is half of the square.

The left half of the red figure is a semicircle.

A = LW + ½πr²

A = (4 cm)(8 cm) + ½(π)(4 cm)²

A = (32 + 8π) cm² (exact)

A = 57.13 cm² (approximate)

PLZ HELP ASAP!!

I got the quadrant part I just need help with 0ther parts​

Answers

Answer:

Step-by-step explanation:

The X intercept is 1 and the y-intercept is 1 aswell.

Answer:

x intercept: 1

y intercept: 1

Step-by-step explanation:

also, where u wrote quad: IIII, four in roman numerals in IV not IIII

There are 6 times as many females as males on the maths course at university. What fraction
of the course are female?
Give your answer in its simplest form.

Answers

Answer:

i hope it helps

thank you

a parallelogram shaped patio has a rectangular rug in the middle jwhat is the area of the patio around the rug?

Answers

Answer:

12" 15"

Step-by-step explanation:

The answer would be 127


Which transformation on triangle XYZ results in a triangle that is similar, but not congruent, to triangle XYZ?
A. a translation 3 units to the right
B. a reflection across the line y = - 2x + 3
C. a rotation 90° clockwise around the origin
D. a dilation centered at the origin with a scale factor of​

Answers

Answer: Choice D

Step-by-step explanation: A dilation would result in a similar triangle because multiplying by the scale factor will create proportional sides. However, this will change the size of the triangle, making it not congruent.

Answer:

D.

Step-by-step explanation:

Congruent means that the triangles are exactly the same in shape and size.

Dilating the triangle is the only answer that will change its size.

A certain United States flag has a perimeter of 58 feet. The length of the flag is 9 feet longer

than the width. What are the dimensions of the flag?

Answers

The dimensions of the flag are:

length = 19 feet and width = 10 feet

Let 'l' be the length of the flag and 'w' be the width of the flag.

The length of the flag is 9 feet longer than the width.

So, we get an equation

l = 9 + w                ............(1)

The flag has a perimeter of 58 feet.

We know that the formula for the perimeter of rectangle:

P = 2(l + w)             ..............(2)

Here, P = 58 feet

Substitute the value of P in equation (2)

58 = 2(l + w)                

29 = (9 + w) + w                      ..........(from (1))

29 - 9 = 2w

2w = 20

w = 10

Substitute this value in equation (1),

l = 9 + 10

l = 19 feet

Therefore, length = 19 ft and width = 10 ft

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A farmer is using a random sample to predict the number of broken eggs in a shipment of 3,000 eggs. Using a calculator, the farmer generates the following random numbers. The numbers 1-250 represent broken eggs. 477 2,704 2,116 900 1,044 238 81 1,672 619 187 755 1,509

Based on this sample, how many broken eggs might the farmer expect?​

Answers

Answer:

238

Step-by-step explanation:

Solve the given differential equation. 3x^2y'' + 6xy' + y = 0

Answers

The solution for given differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)

This is a second-order linear differential equation with constant coefficients. To solve this equation, we can use the method of an auxiliary equation, which is 3r^2 + 6r + 1 = 0. This equation has two complex conjugate roots, r = -3 ± i√3. Therefore, the solution of the differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)cos(√3x^2/2) + c3xe^(-x^3/3)sin(√3x^2/2), where c1, c2, and c3 are arbitrary constants.

The method of an auxiliary equation is a popular way to solve second-order linear differential equations with constant coefficients. It involves finding the roots of an auxiliary equation, which is found by setting the coefficient of the second derivative equal to zero.

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hello! pls help if you can, it will very much be appreciated T-T

Answers

Is it the area or volume you are looking for

Answer:

download algemator then you can find the answer

What is the domain of exponential function f/x )= BX?

Answers

The domain of an exponential function is all real numbers. In the interval notation is (-∞, ∞).

What is interval notation?

A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤ x ≤ 1 .

Given exponential function is f(x) = B^x.

A function with an exponent as the independent variable is called an exponential function. The general form of an exponential function is y = f (x) = B^x, where B > 0 and a > 1, and x is any real number. The function is undefined for -1 < x < 1 if an is negative, which is why a > 0 is true. The function can have a domain that includes all real numbers by limiting a to positive values.

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Problem Solving Quick Check

A recipe for macaroni and cheese takes 3 tablespoons of milk and 2 tablespoons of butter Simon is going to make 5 batches of the macaroni and cheese for a family dinner how many cups of milk are

required? tpoint)

os

o

Answers

0.94 cups of milk is required for 5 batches of the macaroni and cheese.

Given that the recipe for macaroni and cheese takes:

3 tablespoons of milk

and 2 tablespoons of butter

To find: the number of cups of milk required

Let m be the number of cups of milk is required to make 5 batches of the macaroni and cheese.

a batch of the macaroni and cheese require 3 tablespoons of milk .

So by unitary method for 5 batches of the macaroni and cheese,

(5 × 3) = 15 tablespoons of milk is required.

We know that 1 US Cup = 16 US tablespoons

So by unitary method,

m = 15/16 cups of milk

m = 0.94 cups of milk

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PLEASE HELP IF YOU KNOW ALGEBRA AND SPANISH

Answers

I don't know Spanish but I'm reasonably sure I know what the questions are asking. Please correct me if I'm wrong.

a. f(2) = -2^2+4(2)-10 = -4+8-10 = -6.

b. g(6) = 5(6)+1 = 30+1 = 31.

c. f(-1) = -(-1)^2+4(-1)-10 = -1-4-10 = -15.

d. This is saying to solve g(x)=16:

5x+1=16Subtract 1 from each side: 5x=15Divide both sides by 5: x=3.

The answer is x=3.

Homework please help

Answers

Answer:

b. one solution

Step-by-step explanation:

hope this helps :)

Answer:

B. One solution

Step-by-step explanation:

Hope this helps!!

sofia and her brother combined to read a total of 40 books over the summer sofia read four times as many books as her brother how many books did each person read

Answers

The number of books that Sofia read is 32 books and the brother read 8 books.

How to calculate the number of books read?

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

From the information, Sofia and her brother combined to read a total of 40 books over the summer sofia read four times as many books as her brother how many books did each person read

Let the number of books read by the brother = x

Number of books read by Sofia = 4x

Therefore, x + 4x = 40

5x = 40.

Divide

x = 40 / 5

x = 8

The brother read 8 books

Sofia read = 4x

= 4 × 8

= 32 books.

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Find the measure of ∠d. PLEASE HELP

Answers

Answer:

107

Step-by-step explanation:

3x + 16 + 5x - 4 = 180 (Being linear pair)

8x + 12 = 180

8x = 180 - 12

8x = 168

x = 21

3x + 16 = 3 * 21 + 16 = 79

< C = 79 ( being corresponding angles)

< d + < c = 180 ( being linear pair)

< d = 180 - 79

< d = 107

Hope it will Help :)❤

The points (14, –3) and (–10, –3) fall on a particular line. What is its equation in slope-intercept form?

Answers

Answer:

y = -3

Step-by-step explanation:

Slope intercept form is y = mx + c.

"m" is the slope and "c" is the y-interecept.

The slope is calculated by dividing the change in y values by change in x values. However, you can see from these two points that as the value of x changes, the value of y stays the same (-3). This means the slope is zero, as it doesn't move up in the y-direction at all.

This means y = 0x + c

You can substitute 14 for y and -3 for x from the first point to get:

-3 = 0(14) + c

-3 = c

y = 0x + -3

Which is the equation of the line in slope-intercept form.

This is the same as saying y = -3, as for every x value, y will always be -3.

Answer is y= -3
There is no slope

Step by step

Find slope with y2 - y1 over x2 - x1

-3 - -3 over -10 - 14

0/-24 = 0 slope, so it’s a horizontal line at
Y = -3

Slope intercept form

Y-y1 = m (x-x1)
Y - -3 = 0 (x - -10)
Y + 3 = 0 (x + 10)
Y = -3
There is no slope

See attachment


The product of 15 and a number has a result in 15 what is the number

Answers

Answer:

1

Step-by-step explanation:

To find an unknown number we can use properties of equality.

Algebraic Method

Another word to describe an unknown number is "variable". For the equation, I will call this variable x. Any variable can be used, but x is the most common.

We can write an equation to describe the situation. The statement says that the product of 15 and x is 15. This means that 15 * x = 15. Now we can use algebra to solve this equation.

To find x, divide both sides by 15.

x = 1

Identity Property of Multiplication

Additionally, if you know all the properties of equality, you can answer this question without doing any math. One of the properties of equality is the identity property of multiplication. The identity property states:

a * 1 = a

This means that any number multiplied by 1 is itself. So, since the factor and product are equal, the other factor must be 1. If you plug 15 in for a, you can see how this property applies to this situation.

A 2 3/4inch candle burns down in 11 hours. At what rate does the candle A burn, in inches per hour?

Answers

Answer:

0.25 in/h

Step-by-step explanation:

1. change 2 3/4 t0 2.75

2. 2.75/11= 0.25

find f(k-1) when f(x)=5x^2+3x-6

please help its urgent!

Answers

5k^2–7k-4 it says I have to write 20 characters so here

Answer: 5k^2-7k-4

Step-by-step explanation: substitute (k-1) in for the x's

5(k-1)^2+3(k-1)-6

(k-1) * (k-1) = k^2-2k-1

5(k^2-2k-1) = 5k^2-10k+ 5

then do 3(k-1)-6

3k-3-6 (combine like terms)

3k-9

5k^2-10k+5 +3k-9 (combine like terms again)

5k^2-7k-4

hope this helps (^_^)

SOMEBODY PLEASE HELP ME BY GIVING ME ANSWERS AND EXPLANATIONS. I NEED YOUR HELP AS SOON AS POSSIBLE OR I AM GOING TO GET BAD GRADES!

Answers

Answer:

here you go

Step-by-step explanation:

8)10

9)3

10)increase

11) decrease

12)increase

13)constant

Answer this pls I really need it

Answers

Answer:

x = - 6

y = - 2

Step-by-step explanation:

Given,

y = - 2

To find : x = ?

1x - 5y = 4

x - 5 ( - 2 ) = 4

x + 10 = 4

x = 4 - 10

x = - 6

Help me with this plz guys ur my only hope

Answers

Answer:

Pi = 3.14

Diameter (d) = 86 cm

•°• Radius (r) = 86 ÷ 2 = 43 cm (radius is 1/2 of diameter)

Area of the circle = ?

Formula,

[tex]\pi( {r})^{2} [/tex]

Substitute the value of 'r' & pi in the formula.

[tex]\pi(43) {}^{2} \\ = 3.14 \times 43 {}^{2} \\ = 3.14 \times 1849 \\ = 5805.86 \: \: cm {}^{2} [/tex]

⎆ The area of the circle is about 5805.86 cm² (approx.)

Charles and Paul each have a computer repair business.
Charles charges a diagnostic fee of around 60$ plus 12$ per hour spent on computer repairs.
Y= 12x+60
Paul charges a diagnostic fee of 40$ plus 16$ per hour spent on computer repairs.
The situation is graphed in the picture
Y= 16x+40

*Which statement BEST describes the system of equations?

A. For repairs requiring 2 hours of work, the total amount charged by Charles will be 72$ and the total amount charged by Paul will be 84$

B. For repairs requiring 8 hours of work, the total amount charged by Charles will be 168$ and the total amount charged by Paul will be 156$

C. For repairs requiring 5 hours of work, the total amount charged by both Charles and Paul will be 100$

D. For repairs requiring 5 hours of work, the total amount charged by both Charles and Paul will be 120$

(This is just too much to look at for me so If anyone can figure it out I greatly appreciate it)

Answers

For repairs that take five hours to complete, Charles and Paul will each charge a total of $120.

What is the graph's equation?

In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change.

What are the three techniques for graphing equations?

For charting linear functions, there are three fundamental techniques. The first method involves tracing a line through a set of points that have been plotted. The second method makes use of the slope and y-intercept. Applying transformations to the identity function f(x)=x f(x) = x is the third step.

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Find the volume of the composite figure below round your answer to the nearest whole number

Answers

Answer:

1017in^3

Step-by-step explanation:

The scale model of a statue is 1 inch to 11.2 feet. If the model is 5.8 inches, what is the length, in feet, of the actual statue?

Answers

The length of the actual statue in feet would be = 64.96 ft

What is scale model?

A scale model is defined as the the exact type of an object but with a different measurement.

The scale model of a statue = 1 In = 11.2 ft

The length of the model = 5.8 inches

Therefore it length in feet = X ft

That is; 1 in = 11.2 ft

5.8 in = X ft

make X ft the subject of formula;

X ft = 5.8 × 11.2 = 64.96 ft

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It takes 126 cubes that have edge lengths of 1/3 ft to completely fill a plastic bin. What is the area of the base of the bin?​

Answers

The area of the base of the bin is 9 ft^2.

The given information states that the bin is filled with 126 cubes that have edge lengths of 1/3 ft. To determine the area of the base of the bin, we must first determine the total volume of the bin.

Since each cube has a volume of 1/27 ft^3, the total volume of the bin is 126/27 ft^3. Since the volume of a rectangular prism is equal to the length times the width times the height, we can solve for the area of the base of the bin by rearranging the formula to A = V/h, where A is the area, V is the volume, and h is the height.

We can substitute the values given to obtain A = 126/27 ft^3/h. Since the height of the bin is equal to the edge length of the cubes, which is 1/3 ft, we can substitute that value into the equation to get A = 126/27 ft^3/1/3 ft = 9 ft^2. Therefore, the area of the base of the bin is 9 ft^2.

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I’m doing homework and this may be easy for others but I’m not that good at learning quickly. Take ur time it’s fine. Please help

Answers

the statement that "you walk at a constant rate" tells us that the relationship is indeed proportional, namely, there's a value in the input that's consistent or common yielding the output.

Check the picture below.

to get the equation of any straight line, we simply need two points off of it, for the distance "from school" table, let's use those two points in that table

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{0.5})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{1.5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1.5}-\stackrel{y1}{0.5}}}{\underset{\textit{\large run}} {\underset{x_2}{30}-\underset{x_1}{10}}}\implies \cfrac{1}{20}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0.5}=\stackrel{m}{\cfrac{1}{20}}(x-\stackrel{x_1}{10})\implies y-0.5=\cfrac{1}{20}x-\cfrac{1}{2} \\\\\\ y=\cfrac{1}{20}x-\cfrac{1}{2}+0.5\implies y=\cfrac{1}{20}x-\cfrac{1}{2}+\cfrac{1}{2}\implies \boxed{y=\cfrac{1}{20}x}[/tex]

Some epidemiologists are planning a second study to evaluate the PSA screening test. The only difference is that this time, the men from Reno who they randomly sample will be 44-59 years of age. Age is a strong risk factor for prostate cancer. The prevalence of prostate cancer in men 44-59 years of age will be much lower than the prevalence of prostate cancer in men 60-75 years of age. How do you expect the results of the second study will compare with the results from the study conducted among 60-75 year old men

Answers

Answer:

The second test result will be lower and more sensitive to changes than the first test result and it will better test the efficacy of the PSA screening test

Step-by-step explanation:

The evaluation the epidemiologist are planning = Prostrate Specific Antigen, PSA, screening test

The given difference between the first and second study = The age range of the study group

The age range of the first study = 60 to 75 years

The age range of the second study = 44 to 59

The prevalence of prostrate cancer in men 44 to 59 years of age < The prevalence of prostrate cancer in men 60 to 75 years of age

Therefore, due to the low prevalence, the result of the second test will be more sensitive than the result of the first test.

(i) change 234mm into m
(ii) change 876m^2 into square cm

Answers

Answer: (i) 0.234m

(ii) 8760000cm^2

Step-by-step explanation:

234÷1000=0.2234m

876x10^4=8760000cm^

At a benefit concert, fifteen bands have volunteered to perform but there is only enough time for eight of the bands to play. How many lineups are possible?

Answers

On solving the provided question, we can say that  - he need 56  answers he need to get correct if he want a grade of 80 percent on a test with 70 questions

what is percentage?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. It has no measuring systems. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) * 100%.

Assuming that all of the questions are equally weighted, 56 is equal to 80% of 70. (.80)(70)=56 Therefore, 56 out of 70 is the lowest number you may get correct, or 80%.

So, the maximum number of questions you may omit is 14. As an alternative, if you desire 80% accuracy, you can have no more than 20% errors.

20% of 70

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