what is 83497/3659+3845x264748 i have literally no idea

Answers

Answer 1

Answer:

1017956082.82

Step-by-step explanation:

m a t h


Related Questions

Three professors at a university did an experiment to determine if economists are more selfish than other people. They dropped 64 stamped, addressed envelopes with $10 cash in different classrooms on the campus. 42% were returned overall. From the economics classes 58% of the envelopes were returned. From the business, psychology, and history classes 32% were returned. • R = money returned • E = economics classes • O = other classes1. ) Write a probability statement for the overall percent of money returned.

2. ) Write a probability statement for the percent of money returned out of the economics classes. 3. ) Write a probability statement for the percent of money returned out of the other classes.

Answers

According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

What is meant by probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

At one classroom for economics and another for other topics, they dumped 122 stamped envelopes with addresses and $20 bills inside each.

Let the money returned = R

economics classes = E

other classes = O

a). The following gives the probability statement for the overall percentage of the money returned: 100.P (R)

b). The probability statement that the percentage of money recovered from economics classes is 100.P(R|E)

c). The probability statement that displays the percentage of money returned from the other classes is 100.P(R|O).

d). No, because P(R) is not equal to P(R|E), the money returned is not independent of the classes.

e).  According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

The complete question is:

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 122 stamped, addressed envelopes with $20 cash in two different classrooms (one economics, one not) on the George Washington campus. Of these, 42% were returned overall. From the economics class 51% of the envelopes were returned. From the other class 36% were returned.

From

the business, psychology, and history classes 31% were returned.

Let: R = money returned; E = economics classes; O = other classes

a. Write a probability statement for the overall percent of money returned.

b. Write a probability statement for the percent of money returned out of the economics classes.

c. Write a probability statement for the percent of money returned out of the other classes.

d. Is money being returned independent of the class? Justify your answer numerically and explain it.

e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to justify your answer.

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please help. Will give BRAINLIEST!!!!!

please help. Will give BRAINLIEST!!!!!

Answers

Answer:

√13

Step-by-step explanation:

if you try Pythagorean's theorem for each one, you should get that √13 doesn't work.

Answer:

13

Step-by-step explanation:

f the pattern in the table is extended to represent more equivalent ratios for 2:6, which pair of numbers would be in the columns? A multiplication table. In the column labeled 2, the numbers 2, 4, 6, 8, 10, 12, 14, 16, and 18 are highlighted. In the column labeled 6, the numbers 6, 12, 18, 24, 30, 36, 42, 48, and 54 are highlighted. 20 would be in the column for 2, and 60 would be in the column for 6. 20 would be in the column for 6, and 60 would be in the column for 2. 20 would be in the column for 2, and 56 would be in the column for 6. 20 would be in the column for 6, and 56 would be in the column for 2. please hurry im in a rush

Answers

The pair of numbers that would be in the columns, considering the proportional relationship, is given as follows:

20 would be in the column for 2, and 60 would be in the column for 6.

What is a proportional relationship?

A proportional relationship is a special linear function, with intercept having a value of zero, in which the output variable is obtained with the multiplication of the input variable and the constant of proportionality k, as shown as follows:

y = kx

The table is extended to represent more equivalent ratios for 2:6, hence the constant of the relationship is given as follows:

k = 6/2 = 3.

Hence the equation is:

y = 3x.

The values given by each column are given as follows:

Column 2: values of x.Column 6: values of y.

When x = 20, the numeric value of the relationship is of:

y = 3 x 20 = 60.

Hence the first option is correct.

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An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 160 engines and the mean pressure was 5.5 pounds/square inch (psi). Assume the population variance is 0.36. If the valve was designed to produce a mean pressure of 5.4 psi, is there sufficient evidence at the 0.02 level that the valve performs above the specifications

Answers

The required answer is: Yes, there is sufficient evidence at the 0.02 level that the valve performs above the specifications. The given problem can be solved by hypothesis testing. The null hypothesis and alternate hypothesis are as follows:Null hypothesis (H0): μ = 5.4 psi .

Alternate hypothesis (H1): μ > 5.4 psiSince the sample size (n) > 30, we can use the z-test to test the hypothesis.The z-statistic is given as follows:z = (x - μ) / (σ / √n)where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.z = (5.5 - 5.4) / (0.6 / √160)z = 4.95Since the alternate hypothesis is one-tailed, the p-value is given by:p-value = P(Z > 4.95) = 4.58 x 10^-7Since the p-value is less than the level of significance (0.02), we can reject the null hypothesis. Hence, there is sufficient evidence at the 0.02 level that the valve performs above the specifications.

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(c) Use the result obtained from part (b) to solve the following initial value problem y"+y' = 2t with y(0)=1 and y'(0)=0. (7 Marks)

Answers

(b)To solve the differential equation, we have to find the roots of the characteristic equation. So, the characteristic equation of the given differential equation is: r² + r = 0. Therefore, we have the roots r1 = 0 and r2 = -1. Now, we can write the general solution of the differential equation using these roots as: y(t) = c₁ + c₂e⁻ᵗ, where c₁ and c₂ are constants. To find these constants, we need to use the initial conditions given in the question. y(0) = 1, so we have: y(0) = c₁ + c₂e⁰ = c₁ + c₂ = 1. This is the first equation we have. Similarly, y'(t) = -c₂e⁻ᵗ, so y'(0) = -c₂ = 0, as given in the question. This is the second equation we have.

Solving these two equations, we get: c₁ = 1 and c₂ = 0. Hence, the general solution of the differential equation is: y(t) = 1. (c)Now, we can use the result obtained in part (b) to solve the initial value problem y" + y' = 2t with y(0) = 1 and y'(0) = 0. We can rewrite the given differential equation as: y" = 2t - y'. Substituting the general solution of y(t) in this equation, we get: y"(t) = -e⁻ᵗ, y'(t) = -e⁻ᵗ, and y(t) = 1. Therefore, we have: -e⁻ᵗ = 2t - (-e⁻ᵗ), or 2e⁻ᵗ = 2t, or e⁻ᵗ = t. Hence, y(t) = 1 + c³, where c³ = -e⁰ = -1. Therefore, the solution of the initial value problem is: y(t) = 1 - t.

Part (b) of the given question has been solved in the first paragraph. We have found the roots of the characteristic equation r² + r = 0 as r₁ = 0 and r₂ = -1. Then we have written the general solution of the differential equation using these roots as y(t) = c₁ + c₂e⁻ᵗ, where c₁ and c₂ are constants. We have then used the initial conditions given in the question to find these constants.

Solving two equations, we got c₁ = 1 and c₂ = 0. Hence, the general solution of the differential equation is y(t) = 1.In part (c) of the question, we have used the result obtained from part (b) to solve the initial value problem y" + y' = 2t with y(0) = 1 and y'(0) = 0. We have rewritten the given differential equation as y" = 2t - y' and then substituted the general solution of y(t) in this equation. Then we have found that e⁻ᵗ = t, which implies that y(t) = 1 - t. Therefore, the solution of the initial value problem is y(t) = 1 - t.

So, in conclusion, we have solved the differential equation y" + y' = 2t and the initial value problem y" + y' = 2t with y(0) = 1 and y'(0) = 0.

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1 0points pls solve this small math​

1 0points pls solve this small math

Answers

Answer:

your answer should be A

have a good day:)

Step-by-step explanation:

Answer: A.

Step-by-step explanation: I did all of the work in my notebook this is too easy have a good rest of your day.

Math Help, due soon (homework)

Math Help, due soon (homework)

Answers

Hey there!

First, we are given:

\(\frac{1\frac{1}{4}}{1\frac{3}{8}}\)

To make this easier, I am going to change the fractions in to decimals.

\(\frac{1.25}{0.375}\)

To get the unit rate, we can use proportions:

\(\frac{1.25}{0.375} = \frac{x}{1}\)

Using cross products, we know that...

\(1.25 * 1 = 0.375 * x\)

Now, we solve for \(x\):

\(1.25 * 1 = 0.375 * x\\ 1.25 = 0.375x\\ 3 \frac{1}{3} = x\)

Therefore, the unit rate is \(\frac{3\frac{1}{3} }{1}\)

Now, do the same with the other problem, and the unit rate is \(\frac{1\frac{4}{5} }{1}\)

Have a terrificly amazing day!!!

outside temperature over a day can be modeled as a sinusoidal function. suppose you know the temperature is 55 degrees at midnight and the high and low temperature during the day are 71 and 39 degrees, respectively. assuming t is the number of hours since midnight, find an equation for the temperature, d, in terms of t.

Answers

The equation for the temperature, d, in terms of t (the number of hours since midnight), is:  d = 16 × sin((π/12) × t) + 55

To find an equation for the temperature, we need to determine the amplitude, period, phase shift, and vertical shift of the sinusoidal function.

The amplitude is half the difference between the high and low temperatures, which is (71 - 39) / 2 = 16 degrees. The period is the number of hours in a day, which is 24 hours. Since the temperature is at its highest point at 12:00 PM (midday), there is no phase shift. The vertical shift is the average of the high and low temperatures, which is (71 + 39) / 2 = 55 degrees.

Putting these values together, the equation for the temperature, d, in terms of t can be written as:

d = 16 × sin((2π/24) × t) + 55

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100%
A package of balloons contains 4 red, 6 blue, 3 yellow, and 5 orange balloons, Javier will randomly choose one balloon from the package to
blow up. He then will randomly choose a second balloon to blow up.
What is the probability that Javier chooses an orange balloon and then a yellow balloon?

Answers

Answer:

44.4%

Step-by-step explanation:

FIND THE TOTAL NUMBER OF BALLOONS

4 red +6 blue +3 yellow +5 orange =18

( ORANGE +YELLOW /TOTAL × 100 %)

8/18 × 100%= 44.4 % CHANCE

help pls bc im so bad at math

help pls bc im so bad at math

Answers

Answer:

x = 3

Step-by-step explanation:

sum of all angles of a quadrilateral = 360

76 + 104 + 104 + 25x + 1 = 360

25x + 285 = 360

25x = 360 - 285

25x = 75

x = 75/ 25

x = 3

ull get better at math soon:)

How much interest will you pay if you borrow $850 for 2 years at 4% interest?

Answers

Answer:

If you're being charged annually, you would end up paying $918.

Step-by-step explanation:

850 * 0.04 (or 4%) = 34

34 * 2(years) = 68

850 + 68 = 918

You would end up paying $68 in interest.

Answer:

Its $68

Step-by-step explanation:

just got it right.

the procedure of comparing different instrumental variables estimates of the same parameter is an example of testing . (a) overidentifying restrictions (b) endogeneity (c) heteroskedasticity (d) heteroskedasticity

Answers

The procedure of comparing different instrumental variables estimates of the same parameter is an example of testing over identifying restrictions

Testing the over identifying restrictions is the procedure of comparing different instrumental variables estimates of the same parameter. It is a method used to assess the validity of a set of instruments in a two-stage least squares (2SLS) regression model. In this method, the same parameter is estimated in two different ways using different sets of instruments. The difference between these two estimates is then tested to see if they are statistically different. If they are statistically different, then this indicates that the instruments are not valid and need to be revised.



The over identifying restrictions test is typically used in cases where there is a large number of instruments and the researcher wants to be sure that the instruments are appropriate for the regression model.

This test is also useful for assessing homogeneity, which is when the independent variable is correlated with the error term in the regression model. Heteroscedasticity is another potential issue in regression models, where the variance of the error term is not constant across all observations. The over identifying restrictions test can be used to detect this issue as well.


In summary, the procedure of comparing different instrumental variables estimates of the same parameter is an example of testing over identifying restrictions. It is a method used to assess the validity of a set of instruments in a 2SLS regression model, and can also be used to detect issues such as homogeneity and heteroscedasticity.

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If you roll two fair six-sided dice, what is the probability that the dice show the same number

Answers

Answer:

6/36  

Step-by-step explanation:

Trust me I got it right on Khan academy :)

Answer:

6/36

Step-by-step explanation:

I got it right too on khan academy

find an equation of the tangent line to the curve at the given point. y = 4ex cos(x), (0, 4)

Answers

The equation of the tangent line to the curve at the given point, y = 4ex cos(x), (0, 4) as calculated is y' = 0.

In order to find the equation we will have to differentiate y = 4ex cos(x)

On differentiating we get the differential as ,

y' = - 4eˣsin(x)

given the value of x as 0 and y as 4

y' = -4e⁰sin(0)

  = 0   because sin( 0 ) = 0

Therefore ,the required equation is , y' = 0.

Differentiation is a technique which is used to find the derivative of a  function . Differentiation is a mathematical procedure it determines the rate of change of a function based on one of its variables.

Other than differentiation calculus also has a branch known as integration.

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Find the value of x in the following parallelogram

Find the value of x in the following parallelogram

Answers

Answer:

Step-by-step explanation:

If the figure is a parallelogram then the angles opposite one another are equal

2x - 30 = x + 40                    Subtract x from both sides.

2x - x - 30 = x - x + 40         Combine

x - 30 = 40                             Add 30 to both sides

x - 30 + 30 = 40 + 30           Combine

x = 70

Find y as a function of t if 5y^n+30y=0,
y(0) = 7 y’(0) = 5
y(t) =

Answers

The differential equation is \(5y^n+30y=0\). The initial conditions are y(0) = 7 and y’(0) = 5.

The differential equation is:\(5y^n+30y=0\). First, we solve for n which is the exponent of y.
We get:n = -1When n = -1, the differential equation becomes:5(1/y)+30y=0
Rearranging terms, we get:5(1/y) = -30y
Dividing both sides by 5y, we have:-1/y² = -6
This yields: y(t) =  \(\sqrt{6}\)/t The initial conditions are:y(0) = 7 and y’(0) = 5
We can now apply the first initial condition to find the value of C_1.C_1 = 7/ \(\sqrt{6}\)
When we apply the second initial condition to solve for C_2, we get: C_2 = 5 \(\sqrt{6}\)
Now, we can write the final answer: y(t) = 7cos(t \(\sqrt{6}\)) + 5 \sqrt{6}sin(t \(\sqrt{6}\))
Thus, the function of y as a function of t is y(t) = 7cos(t \(\sqrt{6}\)) + 5 \sqrt{6}sin(t \(\sqrt{6}\)) which is generated by the differential equation \(5y^n+30y=0\)  and initial conditions y(0) = 7 and y’(0) = 5.

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Which is the ground-state electron configuration of gas- phase Co²+? (A) 1s²2s²2p 3s²3p64s²3d (B) 1s²2s22p 3s²3p64s²3d5 (C) 1s²2s²2p 3s²3p64s²4d5 (D) 1s²2s²2p 3s²3p 3d

Answers

Ground-state electron configuration of gas-phase Co²+ is [Ar] 3d⁷. Answer: (E) [Ar] 3d⁷.Explanation: First of all, we need to find the electron configuration of Cobalt (Co).

The electron configuration of Cobalt (Co) is 1s²2s²2p⁶3s²3p⁶4s²3d⁷.Now, we can remove the electrons to get the electron configuration of gas-phase Co²+ .Co: 1s²2s²2p⁶3s²3p⁶4s²3d⁷Co²+: 1s²2s²2p⁶3s²3p⁶3d⁷The full electron configuration of Co²+ will be [Ar] 3d⁷. Therefore, the answer is (E) [Ar] 3d⁷.

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sooo what about this 200+204-100x3+1

Answers

Answer:

105

Step-by-step explanation:

PEMDAS

Hey there!

ANSWER: \(105\)EXPLANATION:

\(200+204-100*3+1\)

Let's start from multiplication because you have to use the order of operations(PEMDAS).

\(100*3=300\)

Now move on to addition.

\(300+1=301\)

Now add 200+204.

\(200+204=404\)

Now we have to subtract it with the other side.

\(404-301-105\\105(ANSWER)\)

Hope this helps!

\(\text {-TestedHyperr}\)

find the curve in the xy-plane that passes through the point (9,8) and whose slope at each point is 3x

Answers

The equation of the curve that passes through the point (9,8) and has a slope of 3x at each point is:

y = (3/2)x²  - 94.5

To find the curve in the xy-plane that passes through the point (9,8) and whose slope at each point is 3x, we can use calculus to solve for the equation of the curve.

First, we integrate the given slope function with respect to x to obtain the expression for the curve's vertical position y:

dy/dx = 3x

dy = 3x dx

Integrating both sides:

y = (3/2)x²  + C (where C is the constant of integration)

Next, we can use the given point (9,8) to find the value of the constant C:

8 = (3/2)(9)²  + C

C = 8 - (3/2)(81) = -94.5

Therefore, the equation of the curve that passes through the point (9,8) and has a slope of 3x at each point is:

y = (3/2)x - 94.5

We can graph this equation to visualize the curve.

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Find angle cad. Show your work.

Hurry plsssss!!!!!​

Find angle cad. Show your work. Hurry plsssss!!!!!

Answers

Answer:

°

3/2x + 20°+2× =90°

3×\2 + 2× + 20 =90°

5×\2 +20_20 =90°_20

2x5×/2. = 70x2

5×\5=140/5

X =28°

how can we solve for the degree of a polynomial which has more than one variable

Answers

Answer:

It is the highest degree among all the terms.

For example, in the polynomial, \(5x^{5} +9y^7+32xy+58\), the degree is the highest degree among the four terms which is 7 (in \(9y^7\\\)).

Hope this helps :)

Which of the following is equal to the expression below?

(625x48)^1\4

Answers

Answer:

Step-by-step explanation:

Factorize 625 & 48

625 = 25 * 25 = 5 * 5 * 5 * 5 = 5⁴

48 = 16 * 3 = 2 * 2 * 2 * 2 *3 = 2⁴ * 3

\(\sqrt[4]{625*48} = \sqrt[4]{5^{4} * 2^{4} * 3}=5*2\sqrt[4]{3}\) =\(10\sqrt[4]{3}\)

1. When publishing a script from the MATLAB Editor, the resulting document contains section headers derived from the MATLAB code. What is the source of these headers?
a. Section titles(lines starting with %% followed by a space and then a title)
b. An option set in the publishing configuration
c. Command lines that contain no executable code (lines starting with %)
d. Comment lines with the markup HEADER (lines starting with %HEADER)
e. The H1 line
2. Which of the following statements about the purpose of code in the MATLAB Editor is not true?
a. Identify and summarize related blocks of code in a large file.
b. Automatically pause code execution at the start of each section when running a script.
c. Interactively evaluate a single block of code independently.
3. GIven a non scalar matrix X, which commands return a matrix of the same size as x?
a. mean(x)
b. sin(x)
c. log(x)
d. sum(x)
e. std(x)
f. sqrt(x)

Answers

1. (A)  Section titles  (lines starting with %% followed by a space and then a title).

2. (B)  Automatically pause code execution at the start of each section when running a script. (This is not a purpose of code in the MATLAB Editor.)

3. All these functions operate element-wise on each element of the matrix X and return a matrix of the same size.

The source of the section headers in the resulting document when publishing a script from the MATLAB Editor is:

a. Section titles (lines starting with %% followed by a space and then a title).

The statement that is not true about the purpose of code in the MATLAB Editor is:

b. Automatically pause code execution at the start of each section when running a script. (This is not a purpose of code in the MATLAB Editor.)

3. The commands that return a matrix of the same size as x, given a non-scalar matrix X, are:

a. mean(x)

b. sin(x)

c. log(x)

d. sum(x)

e. std(x)

f. sqrt(x)

All these functions operate element-wise on each element of the matrix X and return a matrix of the same size.

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Can you tell me the answer to (−7c+8d)0.6

Answers

Answer:

-4.2c+4.8d

Step-by-step explanation:

(−7c+8d)0.6

Distribute

-7c*.6 + 8d * .6

-4.2c+4.8d

Answer:

-4.2c + 4.8d

Step-by-step explanation:

We would like to distribute the 0.6 in the expression (-7c + 8d) * 0.6.

Remember that when distributing, we multiply the "outside number" (0.6 in this case) by each of the "inside numbers" (-7c and 8d) and then add those products.

So, the first product will be: 0.6 * (-7c) = -4.2c. The second product will be: 0.6 * 8d = 4.8d. Add these together: -4.2c + 4.8d.

The answer is thus -4.2c + 4.8d.

~ an aesthetics lover

If snow falls at a rate 2 and 1/2 inches each hour how many hours of snow fall would it take to get 2 and 1/2 feet of snow?

Answers

Answer:

12 hours

Step-by-step explanation:

set up a proportion:  2.5 inches / 1 hour  equals  30 inches / x

cross-multiply to get 2.5x = 30

divide 30 by 2.5 to get 12

Makayla leans a 26-foot ladder against a wall so that it forms an angle of 69∘
with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest tenth of a foot if necessary.

Answers

Answer:

Step-by-step explanation:

bc=12.605

The horizontal distance between the base of the ladder and the wall is  8.9 feet.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

If we draw a right triangle with the ladder being the hypotenuse, the angle between the ladder and the ground is given as 69 degrees.

We can use trigonometric functions to solve for the horizontal distance between the base of the ladder and the wall.

Let x be the horizontal distance between the base of the ladder and the wall.

cos(69°) = x/26

Solving for x, we get:

x = 26 cos(69°)

Using a calculator, we find that cos(69°) ≈ 0.342, so:

x ≈ 26 × 0.342 ≈ 8.892

Therefore, the horizontal distance between the base of the ladder and the wall is approximately 8.9 feet.

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a baseball is thrown upward from a rooftop 60 feet high. the function h(t)= -16t²+68t+60 describe the ball's height above the ground h(t) in feet t seconds after it is thrown. how long will it take for the ball to hit the ground?

Answers

Therefore, it will take the ball approximately 5 seconds to hit the ground. To find the time it takes for the ball to hit the ground, we need to determine when the height h(t) becomes zero.

Given the function h(t) = -16t^2 + 68t + 60, we set h(t) equal to zero and solve for t:

-16t^2 + 68t + 60 = 0

To simplify the equation, we can divide the entire equation by -4:

4t^2 - 17t - 15 = 0

Now, we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. In this case, factoring is the most efficient method:

(4t + 3)(t - 5) = 0

Setting each factor equal to zero:

4t + 3 = 0 --> 4t = -3 --> t = -3/4

t - 5 = 0 --> t = 5

Since time cannot be negative, we discard the solution t = -3/4.

Therefore, it will take the ball approximately 5 seconds to hit the ground.

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Help me figure out this piecewise question!! 60 points!

Help me figure out this piecewise question!! 60 points!

Answers

Check the picture below.

Help me figure out this piecewise question!! 60 points!

Which expeession can be simplified as 1/n¹⁸ ?

(n²)⁹

\(( {n}^{ - 9}) ^{ - 2} \)
\((n^{ - 6}) ^{ - 3} \)
\((n^{ - 3}) ^{6} \)

Answers

Step-by-step explanation:

the last one is the correct answer

Solution:

\( \frac{1}{ {n}^{18} } \\ = {n}^{ - 18} \\ = {n}^{( - 3 \times 6)} \\ = ( {n}^{ - 3} ) ^{6} \)

Answer:

\(( {n}^{ - 3} ) ^{6} \)

Transform the given function f(x) as described and write the resulting function as an equation.

compress horizontally by a factor of 3
translate left 1 unit

compress horizontally by a factor of 2
translate right 2 units

translate left 2 units
translate down 2 units

translate right 1 unit
translate up 3 units

expand vertically by a factor of 3
reflect across the x-axis

translate left 2 units
translate down 3 units

reflect across the x-axis
translate left 1 unit

compress vertically by a factor of 2
translate down 3 units

Answers

The given function, after applying the series of transformations, results in the following equation:

y = -3 * f(3(x + 1)) - 2 * f(2(x - 2)) - 2 - 3 * f(x + 1) + 3 - 3 * |f(x + 2)| - 1 * |f(x)| / 2 - 3

The series of transformations can be summarized as follows:

(1) Compress horizontally by a factor of 3 and translate left 1 unit: f(3(x + 1)).

(2) Compress horizontally by a factor of 2 and translate right 2 units: f(2(x - 2)).

(3) Translate left 2 units and translate down 2 units: f(x + 1) - 2.

(4) Translate right 1 unit and translate up 3 units: -3 * f(x + 2) + 3.

(5) Expand vertically by a factor of 3 and reflect across the x-axis: -3 * |f(x + 2)|.

(6) Translate left 2 units and translate down 3 units: -3 * |f(x + 2)| - 1.

(7) Reflect across the x-axis and translate left 1 unit: -1 * |f(x)| / 2.

(8) Compress vertically by a factor of 2 and translate down 3 units: -1 * |f(x)| / 2 - 3.

The resulting equation combines all these transformations to describe the final function.

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