Look at the function and find parts A and B please

Look At The Function And Find Parts A And B Please

Answers

Answer 1

As given by the question

There are given that the function:

\(f(x)=\sqrt[16]{x}\)

Now,

To find the inverse, first interchange the function f(x) to y:

So,

\(\begin{gathered} f(x)=\sqrt[16]{x} \\ y=\sqrt[16]{x} \end{gathered}\)

Then,

Interchange the variable:

So,

\(\begin{gathered} y=\sqrt[16]{x} \\ x=\sqrt[16]{y} \end{gathered}\)

Then,

Solve the above equation for y

So,

\(\begin{gathered} x=\sqrt[16y]{\square} \\ x=(y)^{\frac{1}{16}} \\ (x)^{16}=(y)^{\frac{1}{16}\times16} \\ y=x^{16} \end{gathered}\)

Then,

The inverse function is :

\(f^{-1}(x)=x^{16}\)

Hence, the correct option is (A) and the value is shown below:

\(f^{-1}(x)=x^{16}\)

(B):

For verify, put inverse function into the given function:

So,

\(\begin{gathered} f(x)=\sqrt[16]{x} \\ f(f^{-1}(x))=\sqrt[16]{(x^{16})} \\ f(f^{-1}(x))=(x^{16})^{\frac{1}{16}} \\ f(f^{-1}(x))=x \end{gathered}\)

And,

Put the value of f(x) into the inverse function:

So,

\(\begin{gathered} f^{-1}(x)=x^{16} \\ f^{-1}(f(x))=(\sqrt[16]{x})^{16} \\ f^{-1}(f(x))=(x^{\frac{1}{16}})^{16} \\ f^{-1}(f(x))=x \end{gathered}\)

Hence proved.


Related Questions

quiz 2 : percent and percentage
change the decimal 0.82 to a percent


A. 0.8%
B.82%
C.90%
D. None of these choices are correct​

Answers

Answer:

82%

Step-by-step explanation:

0.82x100=82

=82%

Hope this helps

Answer:

B. 82%

Step-by-step explanation:

.82 can also be written as 82/100 and 82/100 can be turned into 82% because they are all based on 100

Question 1 of 10
Which of these expressions is equivalent to log (9^2)?
A. 2. log (9)
B. log (2) + log (9)
O C. log (2) • log (9)
D. log (2) - log (9)

Answers

Answer:

\(log(9^2) = 2\ log(9)\)

Step-by-step explanation:

Given

\(log(9^2)\)

Required

Select an equivalent expression

To answer this, we apply the following law of logarithm.

\(log(a^b) = b\ log(a)\)

So:

\(log(9^2) = 2 * log(9)\)

\(log(9^2) = 2\ log(9)\)

Hence:

The equivalent expression is (a). \(2\ log(9)\)

select the three expressions that are equivalent to 3/5a + 10
A. 1/5a + 10 + 2/5a
B. a(3/5 + 10)
C. 14 + 3/5a - 4
D. 1/5 (3a + 50)
E. 10 + 2/5a - a + 1/5a

Answers

Answer:

A, C and D

Step-by-step explanation:

Given

\(\frac{3}{5}a + 10\)

Required

Select 3 equivalent expressions

\(\frac{3}{5}a + 10\)

Express 3 as 2 + 1

\(\frac{2 + 1}{5}a + 10\)

Rewrite as:

\(\frac{2a + a}{5} + 10\)

Split

\(\frac{2a}{5} + \frac{a}{5} + 10\) ----- Option (A)

\(\frac{3}{5}a + 10\)

Express 10 as 14 - 4

\(\frac{3}{5}a + 14 - 4\)

Rewrite as:

\(14+\frac{3}{5}a - 4\) --- Option (C)

\(\frac{3}{5}a + 10\)

Factor out 1/5

\(\frac{1}{5}(3a + 50)\) --- Option D

Answer:

Option D

Step-by-step explanation:

You can give the guy/girl above Brainliest ^^

They rlly went out of their way to answer that question for you.

They deserve it!

)The mean voltage of a battery is 15 and S.D 0.2.Find the probability that four such batteries connected in series will have combined voltage of 60.8 or more volts

Answers

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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3+ (-20) + (-20) + (-3) + 40

Answers

Answer:

the answer is 0

Step-by-step explanation:

You weren’t really specific on what u needed to do with this equation but If you’re simplifying the expression it’ll be 0


B=K+L/M
Solve for M

Answers

Step-by-step explanation:

\(b = k + \frac{l}{m} \\ b - k = \frac{l}{m} \\ m = \frac{l}{b - k} \\ thank \: you\)

Anyone wanna give me help on the most easy thing?

Anyone wanna give me help on the most easy thing?

Answers

Answer:

\( 7\frac{5}{12} + 3\frac{7}{12} \\ \frac{14}{3} \\ 4.666\)

Answer:

\( \\ 7\frac{5}{12} + 3 \frac{7}{12} \)

\( \\ = \frac{89}{12} + \frac{43}{12} \)

\( \\ = \frac{132}{12} \)

\( \\ = 11\)

A previous survey reported that 53% of respondents increased their portfolio value over the past 3 years. How large should a sample be if the margin of error is .03 for a 91% confidence interval

Answers

Answer:

A sample of 796 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In this question, we have that:

\(\pi = 0.53\)

91% confidence level

So \(\alpha = 0.09\), z is the value of Z that has a pvalue of \(1 - \frac{0.09}{2} = 0.955\), so \(Z = 1.695\).

How large should a sample be if the margin of error is .03 for a 91% confidence interval

We need a sample of n, which is found when \(M = 0.03\). So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.03 = 1.695\sqrt{\frac{0.53*0.47}{n}}\)

\(0.03\sqrt{n} = 1.695\sqrt{0.53*0.47}\)

\(\sqrt{n} = \frac{1.695\sqrt{0.53*0.47}}{0.03}\)

\((\sqrt{n})^2 = (\frac{1.695\sqrt{0.53*0.47}}{0.03})^{2}\)

\(n = 795.2\)

Rounding up

A sample of 796 is needed.

Solve y+1/2-2y-1/3=4​

Answers

Answer:

y=-23/6

Step-by-step explanation:

Answer:

y=-26

Step-by-step explanation:

multiply each side by 3

Y+1/2-2y-3=12

Multiply each side by 2

Y+1-2y-3=24

Add 3 to each side

Y+1-2y=27

Subtract each side by 1

Y-2y=26

-y=26

Multiply each side by -1

Y=-26

Convert .805 liters to millimeter s

Answers

Wouldn’t it be 805000 millilitres

PLEASE HELP URGENT ASAP DUE TOMORROW PLSSSSS
∫x²cos(2x³)dx

Answers

Answer:

-222

Step-by-step explanation:

can u pls a nd this question​

can u pls a nd this question

Answers

Answer:

B

Step-by-step explanation:

He makes 50 by the pens, and the pencils, but he loses 20 because he loses 2 each time he sells a pencil

Use the given equation to complete the table: s = 16 t squared t (sec) s(ft) 0 1 2 3 Using the points from the table select the graph that best represents the equation. Graph A On a coordinate plane, a parabola opens up. It goes through (negative 1, 16), has a vertex at (0, 0), and goes through (1, 16). Graph B On a coordinate plane, a parabola opens up. It goes through (negative 1, 4), has a vertex at (0, 0), and goes through (1, 4). a. 0, 16, 64, 144; Graph A b. 0, 4, 8, 12; Graph A c. 0, 16, 64, 144; Graph B d. 0, 4, 8, 12; Graph B

Answers

Answer:

a 0, 16, 64,144 graph A edge

Step-by-step explanation:

The graph that best represents the equation is option A.

What is an Equation?

An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.

The equation is

s = 16t²

The table is

s              t

0             16*0 = 0

1              16 * 1 = 16            

2              16 * 4 = 64

3               16 * 8 = 108

The points represents a parabola opening upwards, vertex is at (0,0) and goes through the point (-1,16)

This has been confirmed by the graph plotted for the equation.

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Use the given equation to complete the table: s = 16 t squared t (sec) s(ft) 0 1 2 3 Using the points

A car traveled 281 miles in 4 hours 41 minutes. What was the average speed of the car in miles per hour?

Answers

Answer:

= 60 miles / hour

Step-by-step explanation:

We first convert the time of 4 hours 41 minutes in minutes

4 hours 41 minutes = 4 × 60 + 41 = 281 minutes

Average speed S is given by distance / time. Hence

S = 281 miles / 281 minutes = 1 mile / minute

= 60 miles / hour

41min=41/60h=0.7h

Total distance=281mi

Total time=4.7h

\(\\ \tt\hookrightarrow Avg\:Speed=\dfrac{Total\: distance}{Total\:time}\)

\(\\ \tt\hookrightarrow Avg\:Speed=\dfrac{281}{4.7}\)

\(\\ \tt\hookrightarrow Avg\:Speed=59.78mph\)

thanks i'll mark brainliest ​

thanks i'll mark brainliest

Answers

Answer:

1.

Step-by-step explanation:

If the probability that a vaccine you took will protect you from getting the flu is 0.977, what is the probability that you will get the flu?
Probability that you will get the flu =

Answers

Answer:

Step-by-step explanation:

0.033

Annika is comparing two companies based on the costs for renting a bike for the . Company A charges a $20 rental fee plus $4.50 the bike is rented. Company B charges a 9 rental fee plus $6.50 per hour the bike is rented.

Answers

Answer:

depends on how long u need it for

Step-by-step explanation:

What is the value of 7x (3 + x/4) when x= −8?
A −280
B −170
C −56
D 280
PLEASE HELP ME

Answers

The answer is -56. For future problems, I highly recommend the calculator app “Desmos”, and writing the equation out in the calculator, and then replacing X values with the number (-8).

Answer:

-56

Step-by-step explanation:

Equation = 7x( 3 + x/4)

f(x) = 7x( 3 + x/4)

f(-8) = 7( -8 )( 3+ -8/4 )

f(-8) = -56 ( 3+ ( - 2 ))

f(-8) = -56( 1 )

f(-8) = -56

-Chetan K

10.) Sam makes $9.75 per hour at his job. How much money does he
make in 7.5 hours?

Answers

Answer:$73.12

Step-by-step explanation:

9.75 multiply by 7.5 then you will get $73.12

I don't really know if it correct but if it is then hope this helps.

Sam made $73.12.
You get the answer by simply multiplying the numbers 9.75 and 7.5 together.

Need help please I will give brainliest

Need help please I will give brainliest

Answers

Answer:

i believe your answer would be 5 and 3, FD

Step-by-step explanation:

The 2010 General Social Survey asked the question: "After an average work day, about how many hours do you have to relax or pursue activities that you enjoy?" to a random sample of 1,155 Americans.^41 A 95% confidence interval for the mean number of hours spent relaxing or pursuing activities they enjoy was (1.38, 1.92). Interpret this interval in context of the data. Suppose another set of researchers reported a confidence interval with a larger margin of error based on the same sample of 1,155 Americans. How does their confidence level compare to the confidence level of the interval stated above? Suppose next year a new survey asking the same question is conducted, and this time the sample size is 2,500. Assuming that the population characteristics, with respect to how much time people spend relaxing after work, have not changed much within a year. How will the margin of error of the 95% confidence interval constructed based on data from the new survey compare to the margin of error of the interval stated above?

Answers

Answer:

- How does their confidence level compare to the confidence level of the interval stated above?

Provided all the other parameters involved in the determination of margin of error remains constant, the confidence level of the interval obtained by the second set of researchers (with a larger margin of error) is definitely greater than the confidence of the first stated interval.

- How will the margin of error of the 95% confidence interval constructed based on data from the new survey compare to the margin of error of the interval stated above?

Provided all the other parameters involved in the determination of margin of error remains constant, the margin of error of the confidence interval of data from the new survey will be less than the margin of error of the initially stated interval because the margin of error is inversely proportional to the sample size and the sample size of the new survey (2500) is more than the sample size of the old survey (1155).

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Since the sample sizes are so large, the critical value for this would be obtained from the z-distribution tables.

And critical value increases with higher confidence level.

Which directly translates to margin of error increasing with higher confidence level.

A) Hence, if all other parameters stay the same, the margin of error can only be larger if the confidence level of the second researchers is more than than the confidence level at which the initial research was carried out.

B) In the determination of the margin of error

Margin of Error = (Critical value) × (standard Error of the mean)

Standard error of the mean = σₓ = (σ/√n)

where σ = population standard deviation or sample standard deviation for a sample size that's very large

n = sample size

If the critical value stays the same (the tests in the two years being considered are performed at the same level) and the standard deviation too remain almost the same (the question asks us to assume that the population characteristics, with respect to how much time people spend relaxing after work, have not changed much within a year), the margin of error is obviously inversely proportional to the sample size.

Margin of error = (zσ/√n)

zσ = constant = k

Margin of error = (k/√n)

So, if the sample size increases, the new margin of error that will be obtained will be lesser.

Hope this Helps!!!

rena divides a square into 8 equal part. what unit fraction should she write as a label for each parts?

Answers

Answer =1/8

The unit fraction is 1/8
A unit fractions one with numerator being 1
She divide the square into 8 and took 1 part out
Hence is 1 out of 8 Represented mathematically as 1/8

If rena divides a square into 8 equal part then 1/8 is a unit fraction which she has to write as a label for each parts.

What is Fraction?

A fraction represents a part of a whole.

Given that rena divides a square into 8 equal part.

A division is a process of splitting a specific amount into equal parts.

Let the whole square is divided into eight equal parts.

Which can be represented by 1/8.

Where the numerator 1 represents the whole and eight represents the parts.

The unit fraction for each part is 1/8 because the square is divided into 8 equal parts.

This means each part is one eighth of the whole.

Hence, if rena divides a square into 8 equal part then 1/8 is a unit fraction which she has to write as a label for each parts.

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I3. Antonio is designing a room that is20 feet long and 12 feet wide.Make a scale drawing of the room.Use the scale 0.25 inches = 4 feet.STEP 1: Find the room's length on thedrawing (let x = length)STEP 2: Find the room's width on thedrawing (let w = width)

Answers

Having a scale of 0.25 in = 4 feet means that every 0.25 inches in the model represent 4 feet in the real room. Using this knowledge and the length and width of the actual room we can find the values we need to build the model.

Let's start with the room's length using the rule of three:

4 feet----------0.25 inches

20 feet---------x

According to the rule of three x is given by:

\(x=\frac{20\cdot0.25}{4}=1.25\)

If we make the same process for the model's width:

4 feet----------0.25 inches

12 feet---------w

\(w=\frac{12\cdot0.25}{4}=0.75\)

So for the model we have that x=1.25 inches and w=0.75 inches

sketch the graph of the function. f(x, y) = 9 − 9x2 − y2

Answers

A function is defined as a relation between a set of inputs, each with an output. The sketch of the function f(x,y) = 9 - 9x² - y² is given below.

f(x,y) = 9 - 9x² - y²

Let the given function is equal to 0, Then

           9 - 9x² - y² = 0

                         y²  = 9 - 9x²

The function can be written as

                          y²  = 9 - 9x²

A function is a relationship between inputs, each associated with exactly one output. Each function has a domain and a codomain or scope. Functions are commonly denoted by f(x). x is the input. Here's the technical definition of the function:

A relationship from a set of inputs to a set of possible outputs.

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sketch the graph of the function. f(x, y) = 9 9x2 y2

Compare the best estimate for 1.789/178 and 0.05. Which is less?

Answers

Answer:

The smaller number in 0.01

Step-by-step explanation:

To find this answer, just take the fraction and find the quotient of both numbers.

1.789/178 = 0.01005056179

Now take the quotient and compare it to 0.05.

Is 0.01 larger or 0.05 - the answer is 0.01.

A cruise ship can cover 19 nautical miles in 437 minutes. How many nautical miles will it travel in 345 minutes?

Answers

The cruise ship will travel approximately 15 nautical miles in 345 minutes.

How did we get the value?

Use a proportion to solve this problem. Let "d" be the number of nautical miles the cruise ship will travel in 345 minutes. Then:

19 nautical miles / 437 minutes = d nautical miles / 345 minutes

To solve for "d", cross-multiply:

19 nautical miles x 345 minutes = d nautical miles x 437 minutes

Then, divide both sides by 437 minutes to isolate "d":

d nautical miles = (19 nautical miles x 345 minutes) / 437 minutes

Simplifying this expression, we get:

d nautical miles = 15 nautical miles (rounded to the nearest whole number)

Therefore, the cruise ship will travel approximately 15 nautical miles in 345 minutes.

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Determine the equation of the graph and select the correct answer below.

Determine the equation of the graph and select the correct answer below.

Answers

Answer: y = (x - 1)² - 3

Step-by-step explanation:

y = (1-1)²-3
y=0-3
y=-3

Lesbian Anna close cylinder have the same radius the height of the cylinder is four times the radius what is the ratio of the volume of the cylinder to the volume of the sphere

Lesbian Anna close cylinder have the same radius the height of the cylinder is four times the radius

Answers

The ratio of the volume of the cylinder to the volume of the sphere = 3:1

Let take the volume of a closed cylinder as V1.

And take the volume of a closed sphere as V2.

And the radius of the cylinder = radius of the sphere = r

Height of the cylinder = h

If height of the cylinder is four times the radius of the cylinder  which means h = 4r

Volume of the closed cylinder V1 = π × r^2 × h

if h = 4r

Then V1 = π × r × r × 4r

V1= 4π × r^3

Volume of the closed cylinder V1= 4π × r^3

Volume oh the sphere V2 = 4/3 × π × r^3

The ratio of the volume of the cylinder to the volume of the sphere

= V1 / V2 = V1 : V2

V1 : V2 = (4π × r^3) ÷ (4/3 × π × r^3)

V1 : V2 = 4 ÷ 4/3 = 4/1 × 3/4 = 3/1 = 3 : 1

The ratio of the volume of the cylinder to the volume of the sphere = 3:1

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. You and a friend have dinner at a restaurant . Your meal costs $15.85 and you leave an 18% tip and your friend's meal cost $14.30 and he leaves a 20% tip and 6 % sales tax who spent more on the bill he or she

Answers

Answer:

I slightly rounded my answers so to the nearest hundred.

You Did.

Your bill is 19.65

Their bill is 18.02

Step-by-step explanation:

Match the two lines that are parallel and the two lines that are perpendicular. Then, match the equations.

Match the two lines that are parallel and the two lines that are perpendicular. Then, match the equations.

Answers

Step-by-step explanation:

A and C are parallel. equations G and E.

B and D are perpendicular (standing at a right angle = 90° to each other). equations F and H.

parallel means that both lines have the same slope.

the slope is the factor a of x when the equations look like

y = ax + b (slope-intercept form)

or

y - y1 = a(x - x1) (point-slope form)

"a" being the slope, b being the y-intercept (the y- value when x = 0), (x1. y1) being a point on the line.

the slope is specified as ratio (y coordinate difference / x coordinate difference) when going from one point to another.

the perpendicular slope to y/x is the upside down ratio and the sign is flipped.

e.g. the perpendicular slope to 5/4 is -4/5.

equation E is already in point-slope form.

the slope is 2/3, and the point (-9, -2) must be on the line.

only one line goes through the point (-9, -2) : C.

equation H is already in slope-intercept form.

the slope is 3/2, and the y-intercept is 5, meaning the line goes through the point (0, 5).

only one line goes through that point : D

equation F

2x + 3y = -21

3y = -2x -21

y = (-2/3)×x - 7

the slope is -2/3, which is perpendicular to 3/2 (equation H).

the y-intercept is -7, meaning the line goes through the point (0, -7).

only one line goes through that point : B

equation G

-2x + 3y = -6

3y = 2x - 6

y = (2/3)×x - 2

the slope is 2/3 (parallel to equation E).

the y-intercept is -2, meaning the line goes through the point (0, -2).

only one line goes through that point : A

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