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Using mathematical induction, it can be proven that g(n) ≤ 2n - 4 for n ≥ 4 by establishing a base case and an inductive step, which involves considering a new person calling someone at the start and the end.

To prove g(n) ≤ 2n - 4 for n ≥ 4, we follow these steps:

1. Base case (n=4): g(4) = 2 calls, and 2 ≤ 2(4) - 4, which is true.
2. Inductive hypothesis: Assume g(k) ≤ 2k - 4 for some k ≥ 4.
3. Inductive step (n=k+1): The new person makes a call at the start and end, which adds 2 calls to the total. So, g(k+1) = g(k) + 2.

Using the inductive hypothesis, g(k+1) = (2k - 4) + 2 ≤ 2(k+1) - 4.

Simplifying, we have 2k - 2 ≤ 2k, which is true for k ≥ 4.

Thus, by mathematical induction, g(n) ≤ 2n - 4 for n ≥ 4.

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Answer: (4, -7) (8, 1) (12, 54)

Step-by-step explanation:

A: u = (4, 8), and v = (4, -7)

B: u + v = (4 + 4, 8 - 7) = (8, 1)

C: 5u - 2u = 5(4, 8) - 2(4, -7)

                    = (20, 40) - (8, -14)

                         = (12, 54)

This helped me, so hopefully it helps you! Good luck!

The general solution is y(t) = c1 t⁻⁹ + c2 t² for the Cauchy-Euler equation t² d²y/dt² + 8t dy/dt - 18y.

We can solve this second-order Cauchy-Euler equation by assuming a solution of the form:

y(t) = [tex]t^{r[/tex]

We substitute this solution into the differential equation and find the characteristic equation by solving for the values of r that satisfy the equation:

t² d²y/dt² + 8t dy/dt - 18y = 0

t² [r(r-1) [tex]t^{(r-2)}[/tex]] + 8t [r [tex]t^{(r-1)}[/tex]] - 18[tex]t^r[/tex] = 0

r(r-1) + 8r - 18 = 0

r² + 7r - 18 = 0

(r + 9)(r - 2) = 0

So the roots are r = -9 and r = 2. Therefore, the general solution is a linear combination of the two independent solutions:

y(t) = c1 [tex]t^{(-9)[/tex] + c2 t²

where c1 and c2 are constants to be determined by the initial or boundary conditions of the problem.

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The probability of randomly drawing a vowel is 4/10

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

W, E, L, O, V, E, M, A, T, H

Using the above as a guide, we have the following:

Vowels = 4

Total = 10

So, we have

P(Vowel) = Vowel/Total

Substitute the known values in the above equation, so, we have the following representation

P(Vowel) = 4/10

Hence, the solution is 4/10

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Answer:

acute

Step-by-step explanation:

this is an acute triangle because all angles are less than 90 degrees

it is not obtuse because no angle is over 90 degrees

it is not equiangular because the angles are not equal to each other

and it is not right because there is no right angle

Acute

Triangles can be classified by the size of their angles.

Angle Classification

Angles can be classified into 3 sizes: acute, right, and obtuse.

Triangle Classification

Triangles are classified by their largest angle. If the largest angle is obtuse, then it is an obtuse triangle. If there is a right angle, then it is a right triangle. If the largest angle is an acute angle, then it is an acute triangle. Finally, there is one special classification that technical falls under acute angles. If all of the angles are equal (meaning they are all 60°), then it is an equiangular triangle.

The triangle in the picture has 3 angles that are all under 90°. The largest angle is 76°. Since this is an acute angle, it is an acute triangle.

The most effective graphical representation of the above data would be a histogram.

A histogram is a graphic representation of the distribution of numerical data. In this case, data on the carbohydrate content of ten different tortilla sandwich wraps is acquired. The best option is a histogram because the data is numerical.

For categorical data, which is broken up into several categories and displayed as a fraction or percentage of the whole, a circle chart, also known as a pie chart, is the best option. The information offered is numerical rather than categorical, though.

Each individual data point is shown as a dot on a number line in a dot plot, also called a line plot. It may not be suitable for larger quantities of data, although being advantageous for an.

Numerical data can be arranged and displayed using a stem-and-leaf plot. For just ten data points, it might not be the ideal depiction, though.

Therefore, the most appropriate graphical representation for the provided data would be a histogram.

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a) The distribution for the change in stock price after two trading days is Y ~ {(-2, 1/16), (-1, -1/32), (0, 1/32), (1, 1/32), (2, 1/64)}

b) The probability that the total change in stock price is at most 4.5 after one hundred independent trading days is approximately zero.

(a) To find the distribution for the change in stock price after two independent trading days, we can use the convolution formula, which states that the probability density function of the sum of two independent random variables is the convolution of their individual probability density functions.

Let Y be the change in stock price after two trading days. Then, we have:

P(Y = -2) = P(X = -1) * P(X = -1) = (-1/4) * (-1/4) = 1/16

P(Y = -1) = P(X = -1) * P(X = 0) + P(X = 0) * P(X = -1) = (-1/4) * (1/8) + (1/8) * (-1/4) = -1/32

P(Y = 0) = P(X = -1) * P(X = 2) + P(X = 0) * P(X = 0) + P(X = 2) * P(X = -1) = (-1/4) * (1/8) + (1/8) * (1/8) + (1/8) * (-1/4) = 1/32

P(Y = 1) = P(X = 0) * P(X = 2) + P(X = 2) * P(X = 0) = (1/8) * (1/8) + (1/8) * (1/8) = 1/32

P(Y = 2) = P(X = 2) * P(X = 2) = (1/8) * (1/8) = 1/64

Therefore, the distribution for the change in stock price after two trading days is:

Y ~ {(-2, 1/16), (-1, -1/32), (0, 1/32), (1, 1/32), (2, 1/64)}

(b) To find a normal approximation to the probability that the total change in stock price is at most 4.5 after one hundred independent trading days, we can use the central limit theorem.

The central limit theorem states that the sum of a large number of independent and identically distributed random variables approaches a normal distribution, regardless of the underlying distribution, as the number of variables increases.

Let Z be the total change in stock price after 100 trading days. Then, we have:

E(Z) = 100 * E(X) = 100 * (-1/4 + 0 + 2/8) = 25

Var(Z) = 100 * Var(X) = 100 * [(-1/4 - 25)^2 * 1/4 + (0 - 25)^2 * 1/8 + (2/8 - 25)^2 * 1/8] = 1953.125

Using the normal approximation, we can standardize Z by subtracting the mean and dividing by the standard deviation:

Z' = (Z - E(Z)) / √(Var(Z)) ~ N(0, 1)

Then, we can calculate the probability that Z is at most 4.5 by using the standard normal distribution:

P(Z ≤ 4.5) = P(Z' ≤ (4.5 - 25) / √(Var(Z))) ≈ P(Z' ≤ -18.62) ≈ 0

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The calculated number from the statement is -22

From the question, we have the following statement

Ten more than seven times a number is equal to eight times the sum of the number and four

Express the number as x

So, we have

Ten more than seven times x is equal to eight times the sum x and four

Mathematically, we have

10 + 7x = 8 * (x + 4)

So, we have

10 + 7x = 8x = 32

Evaluate the like terms

This gives

x = -22

Hence, the number is -22

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Exponential function would better model the data because as x increases, the y values change multiplicatively. The common ratio or multiplier or base of this function is approximately 1.02.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

The ratios for this problem are given as follows:

Hence the rate can be rounded to 1.02.

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The basis for the property is stepped-up to $129,360; therefore, none of the $29,568 suspended loss is deductible on Rose's final return or by the beneficiary.

Upon Rose's death, the adjusted basis of the passive activity property is stepped-up to its fair market value at the date of her death. In this case, the fair market value is $129,360. As a result, the suspended losses ($29,568) do not carry over to her final return or to the beneficiary, as the increased basis eliminates the need to deduct the suspended losses.

The stepped-up basis for the property is $129,360, and none of the $29,568 suspended loss is deductible on Rose's final return or by the beneficiary due to the basis adjustment upon her death.

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The given statement "Stack algorithms can never exhibit Belady's anomaly" is True because stack algorithms, including LRU, do not exhibit Belady's anomaly due to their inherent properties that prioritize recently accessed pages and prevent increased page faults when the number of frames is increased.

Belady's anomaly is a phenomenon that occurs in certain page replacement algorithms used in computer systems, where increasing the number of allocated frames for a process can lead to an increase in the number of page faults. This anomaly is usually observed in algorithms like First-In-First-Out (FIFO) and Second Chance.

Stack algorithms, such as the Last-In-First-Out (LIFO) policy and the Least Recently Used (LRU) algorithm, do not exhibit Belady's anomaly due to their properties. In a stack algorithm, the most recently accessed pages are kept close to the top of the stack, while the least recently accessed pages are at the bottom.

The LRU algorithm, in particular, has been proven to be free from Belady's anomaly because it possesses the stack property. When a page is accessed, it is moved to the top of the stack, making it the most recently used page. If a new page needs to be loaded, the LRU algorithm will replace the page at the bottom of the stack, which is the least recently used page. Due to this behavior, adding more frames to the system will not cause an increase in the number of page faults.

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In finance, interest is the cost of borrowing money or the compensation paid to an individual or organization for lending money. It is usually expressed as a percentage of the amount borrowed and is calculated over a specific period of time.

1. To calculate the total interest payment for the first year, follow these steps in Excel:

Step 1: Enter the given values in separate cells.
Loan amount: $250 million in A1
Monthly installment: $5 million in A2
Number of installments: 60 in A3

Step 2: Calculate the monthly interest rate (i) using the RATE function.
In cell A4, type the formula: =RATE(A3, -A2, A1)

Step 3: Calculate the annual interest rate (I) by multiplying the monthly interest rate by 12.
In cell A5, type the formula: =A4*12

Step 4: Calculate the total interest for the first year by multiplying the annual interest rate by the loan amount.
In cell A6, type the formula: =A1*A5
The total interest payment for the first year is approximately $17 million.

2. To calculate the effective interest rate (j12) of the loan, use the following formula in Excel:

In cell A7, type the formula: =(1+A4)^12-1
The effective interest rate (j12) is approximately 7.4% p.a.

3. To calculate the principal repayment during the first year, follow these steps:

Step 1: Calculate the total amount paid in the first year by multiplying the monthly installment by 12.
In cell A8, type the formula: =A2*12

Step 2: Subtract the total interest payment for the first year (calculated in Step 1) from the total amount paid in the first year.
In cell A9, type the formula: =A8-A6
The principal repayment during the first year is approximately $43 million.

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The sequence values in the table and the function for the graph indicates;

The common ratio for the sequence is 3

A sequence is a list of element s or numbers that are ordered.

The constant ratio is the value obtained by dividing the value of a term in the table or graph by the value of the previous term.

Therefore, the common ratio for sequence A is; -18/(-6) = -6/(-2) = 3

The common ratio for the the sequence of terms in the graph can be obtained from the equation for the function of the graph as follows;

The function of the graph is; y = -2·3⁽ˣ ⁻ ¹⁾

The value of the first term, x = 1 is therefore; y = -2·3⁽¹ ⁻ ¹⁾ = -2

The value of the next term is; y = -2·3⁽² ⁻ ¹⁾ = -6

The table of values, therefore, represents the values on the graph

The common ratio is; 2 × 3⁽ˣ ⁺ ¹ ⁻ ¹⁾/(2 × 3⁽ˣ  ⁻ ¹⁾) = 3ˣ/(3ˣ/3) = 3

The common ratio of the graph is 3

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The corporation should deposit $4,298.46 at the end of each month into the sinking fund.

The amount of interest earned over the life of the account is: $47,616.64.

The value of the fund after 2, 4, 6 are $56,243.62, $115,263.54, $178,155.28 respectively.

The interest earned during the second month of the 7th year is $317.13

To determine the amount that should be placed in the sinking fund at the end of each month, we can use the formula for present value of an annuity:

PV = R[(1-(1+i)^(-n))/i]

where:

PV = present value of the sinking fund

R = monthly deposit

i = monthly interest rate

n = number of months

We know that the sinking fund needs to have a future value of $460,000 in 8 years. If we assume monthly deposits and monthly compounding, we have:

PV = 0

FV = $460,000

i = 6.5%/12 = 0.00541667

n = 8 years * 12 months/year = 96 months

Using the formula, we can solve for R:

R = (FV*i)/((1+i)^n - 1) = ($460,000 * 0.00541667)/((1+0.00541667)^96 - 1) = $4,298.46

Therefore, the corporation should deposit $4,298.46 at the end of each month into the sinking fund.

To determine the amount of interest earned over the life of the account, we can subtract the total amount deposited from the total amount in the sinking fund at the end of 8 years:

Total amount deposited = $4,298.46/month * 96 months = $412,383.36

Total amount in sinking fund after 8 years = $460,000

Interest earned = $460,000 - $412,383.36 = $47,616.64

To determine the value of the fund after 2, 4, and 6 years, we can use the formula for future value of an annuity:

FV = R[((1+i)^n - 1)/i]

where:

FV = future value of the sinking fund

R = monthly deposit

i = monthly interest rate

n = number of months

After 2 years, we have:

FV = $4,298.46[((1+0.00541667)^(2*12)) - 1]/0.00541667 = $56,243.62

After 4 years, we have:

FV = $4,298.46[((1+0.00541667)^(4*12)) - 1]/0.00541667 = $115,263.54

After 6 years, we have:

FV = $4,298.46[((1+0.00541667)^(6*12)) - 1]/0.00541667 = $178,155.28

To determine the interest earned during the second month of the 7th year, we can first calculate the total amount in the sinking fund at the beginning of the 7th year:

FV = $4,298.46[((1+0.00541667)^(6*12)) - 1]/0.00541667 = $178,155.28

Then, we can calculate the amount of interest earned during the first month of the 7th year:

Interest earned = $178,155.28 * 0.00541667 = $964.11

Finally, we can calculate the amount of interest earned during the second month of the 7th year by subtracting the interest earned during the first month from the total interest earned during the 7th year:

Interest earned during second month = $47,616.64 * (0.065/12) - $964.11 = $317.13

Therefore, the interest earned during the second month of the 7th year is $317.13

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Area: 2x² + 17x

Perimeter: 6x + 18

      To create an expression for the area, we will break the shape up into two shapes. Then, we will find the area of each of these shapes and lastly add them together. The formula for a rectangle's area is A = LW. I have attached a picture of how I broke this shape up below.

      1st Area:

A = LW

A = (x)(x + 3)

A = x² + 3x

      2nd Area:

A = LW

A = (x + 2)(x + 4)

A = x² + 6x + 8x

      Add them together by combining like terms:

x² + 3x + x² + 6x + 8x

x² + x² + 3x + 6x + 8x

2x² + 17x

      To create an expression for the perimeter, we will add all of the figure's sides together. Since some of the sides are not given, we will add the two congruent sides together to find these sides.

      Adding together:

x + (x + 3) + 2 + (x + 4) + (x + 2) + ((x + 3) + (x + 4))

      Combing like terms:

x + x + 3 + 2 + x + 4 + x + 2 + x + 3 + x + 4

x + x + x + x + x + x + 3 + 2 + 4 + 2 + 3 + 4

6x + 18

The solution to the differential equation with the given initial condition is:

u = (-1/5) ln(-15t² - 75).

To solve the separable differential equation du/[tex]dt[/tex] = ([tex]e^5^u[/tex] + 3t), we can rearrange the terms and separate the variables:

du / [tex]e^5^u[/tex] = (3t) [tex]dt[/tex]

We can integrate both sides:

∫ (du / [tex]e^5^u[/tex]) = ∫ 3t [tex]dt[/tex]

Using u-substitution, let u = 5u and du = 5 du:

(1/5) ∫ (1 / [tex]e^u[/tex]) du = (3/2) t² + C1

(1/5) [tex]e^(^-^5^u^)[/tex] = (3/2) t² + C1

Multiplying both sides by -5:

[tex]e^(^-^5^u^)[/tex] = [tex]-15t^2[/tex] + C2

Now, we can solve for u:

-5u = ln(-15t² + C2)

u = (-1/5) ln(-15t² + C2)

Using the initial condition u(0) = 5, we can find the value of C2:

u(0) = (-1/5) ln(-15(0)² + C2) = 5

C2 = -75

Therefore, the solution to the differential equation with the given initial condition is:

u = (-1/5) ln(-15t² - 75)

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Note that the correct options with regard tot he above transformation are:  are A), C), D), E), G), and l).

To obtain the function g(x) from f(x) = cos(x), the following transformations have been applied:

A) Translation right by 1 unit: (x - 1)

B) Horizontal shrink by a factor of π: πx

C) Vertical shrink by a factor of 1/2: 1/2 cos(x)

D) Vertical translation up by 2 units: 1/2 cos(x) + 2

E) Vertical stretch by a factor of 2: 2(1/2 cos(x) + 2) = cos(x) + 4

F) There is no vertical reflection applied.

G) Translation left by 1 unit: cos(x - 1) + 4

H) There is no horizontal shrink by 1/2 applied.

I) Translation down by 2 units: cos(x - 1) + 2

So the transformations that have been applied to f(x) to obtain g(x) are:

G) Translation right by 1 unit: (x - 1)

C) Horizontal shrink by a factor of π: πx

H) Vertical shrink by a factor of 1/2: 1/2 cos(x)

D) Vertical translation up by 2 units: 1/2 cos(x) + 2

E) Vertical stretch by a factor of 2: cos(x) + 4

A) Translation left by 1 unit: cos(x - 1) + 4

l) Translation down by 2 units: cos(x - 1) + 2

Therefore, the correct options are A), C), D), E), G), and l).

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The total number of groups in the study of one way ANOVA with the given condition of variable and levels is four different groups and number of different factors in one-way ANOVA is equal to one.

In a one-way ANOVA with one independent variable with four levels, there are four different groups in the study.

Each group represents a level of the independent variable.

There is only one factor in a one-way ANOVA.

The factor is the independent variable with the four levels, which is used to classify the groups in the study.

The factor is what the researcher is interested in studying.

And the ANOVA is used to determine if there are any statistically significant differences in the mean scores between the groups.

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Gail would have to pay $3834.06 if she pays the credit card ill in 6 months else, $4600.87 if she pays it in 18 months

Here we are given that Gail's APR is 20%. APR is the Annual Percent rate or the annual interest is 20%

Gail decides to pay it back after months. Now, after 6 months, we will see the credit card value to be compounded.

The formula is

Amount = Principal X (1 + rate)ⁿ

where n is the time

Here,

principal = $3500

rate = 20% = 0.2

time = 6 months = 0.5 years

Hence we will see

Amount = 3500 X (1 + 0.2)⁰°⁵

= $3834.06

Now if Gail pays the credit card bill in 18 months, time is 1.5 years

Hence the bill be

3500 X (1 + 0.2)¹°⁵

= $4600.87

Hence, Gail would have to pay $3834.06 if she pays the credit card ill in 6 months else, $4600.87 if she pays it in 18 months

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Complete Question

Image Attached

| *

| / \

Red | / \

paint | / \

| / \

*-----------*

White

paint

(b) If we need to mix 9 liters of white paint with red paint in the ratio of 2:3, we can use the graph to find the corresponding amount of red paint. We plot 9 on the x-axis and draw a vertical line up to the line representing the 2:3 ratio. From the point where the vertical line intersects the ratio line, we can draw a horizontal line to the y-axis to find the corresponding amount of red paint.

The method of undetermined coefficients cannot be applied to find a particular solution for the given equation because it is not a linear differential equation with constant coefficients.

First, let's write down the given equation:

4xsin²(x) + 4xcos²(x)

To apply the method of undetermined coefficients, we need a nonhomogeneous linear differential equation with a constant coefficient. However, the given equation is not a differential equation, but rather an algebraic expression that combines sine and cosine functions.

Therefore, the method of undetermined coefficients cannot be applied to find a particular solution for the given equation because it is not a linear differential equation with constant coefficients.

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The experimental values are 1.099 x 10^7 m^-1 and 1.096 x 10^7 m^-1, respectively. The averaglevalue is 1.0975 × 10^7 m⁻¹. The literature value of the Rydberg constant is 1.0974 x 10^7 m^-1. The percent error is approximately 0.0091%.

The Rydberg equation for hydrogen is given by:

1/λ = R (1/n1² - 1/n2²)

where λ is the observed wavelength, R is the Rydberg constant, and n1 and n2 are the initial and final energy levels, respectively.

For the first observed wavelength of 474.5 nm:

1/474.5 = R (1/1² - 1/n2²)

Solving for n2, we get:

n2 = 4.02

Rounding to the nearest integer, n2 = 4.

For the second observed wavelength of 657.0 nm:

1/657.0 = R (1/1² - 1/n2²)

Solving for n2, we get:

n2 = 3.03

Rounding to the nearest integer, n2 = 3.

To calculate the experimental value of the Rydberg constant for each wavelength, we can rearrange the Rydberg equation:

R = (1/λ) / (1/n1² - 1/n2²)

Using the values of n2 calculated above, we can solve for R for each wavelength:

For the first wavelength:

R = (1/474.5) / (1/1² - 1/4²) = 1.099 × 10^7 m⁻¹

For the second wavelength:

R = (1/657.0) / (1/1² - 1/3²) = 1.096 × 10^7 m⁻¹

Taking the average of these two values, we get:

Ravg = (1.099 × 10^7 + 1.096 × 10^7) / 2 = 1.0975 × 10^7 m⁻¹

The literature value of the Rydberg constant is 1.0974 × 10^7 m⁻¹, so the % error in our experimental value is:

% error = [(Rlit - Ravg) / Rlit] × 100% = [(1.0974 × 10^7 - 1.0975 × 10^7) / 1.0974 × 10^7] × 100% = 0.0091%

Therefore, our experimental value is very close to the literature value with a very small % error.

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Answer:

0N, balanced

Step-by-step explanation:

There are equal forces on each side.

Hope this helps.

Please mark me Brainliest.

Answer: y=3.33x+20

Step-by-step explanation:

Slope intercept form- y=mx+c

m=slope

c=y-intercept

Slope-

y2-y1/x2-x1

30-20/3-0

10/3

m=3.333333

Y-intercept= 20

So,

y=3.33x+20

Hope this helps! :)

As the sample size increases, the t-distribution appears more and more like a normal distribution. So, the correct answer is A).

This is because the t-distribution approaches the normal distribution as the degrees of freedom (which depend on the sample size) increase. The shape of the t-distribution is not unaffected by the sample size, as its tails become less and less pronounced with increasing degrees of freedom.

Additionally, as the sample size increases, the standard error of the mean becomes smaller and closer to the true value of the population mean, which also contributes to the t-distribution becoming more like a normal distribution. So, the correct option is A).

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The comma-separated list of functions f(x) and g(x) is f(x) = x^5, g(x) = x - 9.

To express the function f(x) = (x - 9)^5 in the form f∘g, we will find two non-identity functions f(x) and g(x) such that f(g(x)) = (x - 9)^5.

Step 1: Choose a suitable function for g(x).
Let's choose g(x) = x - 9.

Step 2: Determine f(x) such that f(g(x)) = (x - 9)^5.
Since g(x) = x - 9, we can replace g(x) with (x - 9) in the f function.
Now, f(g(x)) = f(x - 9).

To obtain (x - 9)^5, let f(x) = x^5.

Step 3: Verify that f(g(x)) = (x - 9)^5.
f(g(x)) = f(x - 9) = (x - 9)^5.

Therefore, the comma-separated list of functions f(x) and g(x) is f(x) = x^5, g(x) = x - 9.

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To express the function f(x) = (x - 9)⁵ in the form f∘g, we can let g(x) be x - 9 and f(x) be x⁵. So, f∘g(x) = f(g(x)) = f(x-9) = (x-9)⁵. The functions are f(x) = x⁵ and g(x) = x - 9.

To understand this composition of functions, consider that g(x) is applied first, which results in x - 9. Then, f(x) is applied to the result of g(x), which means raising the result (x - 9) to the power of 5.

By composing these two functions, we obtain the original function f(x) = (x - 9)⁵. This is how we express the function in the form of f∘g using non-identity functions for f(x) and g(x).

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To evaluate dy for the given values of x and dx, we can use the formula:

dy = (∂y/∂x)dx

Where (∂y/∂x) represents the partial derivative of y with respect to x.

First, let's find the partial derivative of y with respect to x: ∂y/∂x =[tex]√3(2x)/2 = √3x[/tex]

Now we can plug in the given values of x and dx into the formula to find dy: dy = [tex](√3x)(-0.1) = -0.1√3[/tex]

Therefore, when x = 1 and dx = -0.1, the value of dy is [tex]-0.1√3.[/tex]

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The value of the given expression 6/(y-z) - 2/(y-z) is 4/(y-z). Option 3 is the correct answer.

In algebra, like terms are those in which the same variable(s) are raised to the same power (s). Because they both have the same variable (y) raised to the same power, the expressions 2xy and -5y are similar (1). When combining terms that have similar coefficients, it's important to preserve the exponent and variable constants.

The given expression is 6/(y-z) - 2/(y-z).

Simplifying the expression by combining the like terms we have:

(6 - 2)/(y-z) = 4/(y-z)

Hence, the value of the given expression is option 3 4/(y-z).

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The population density of the neighborhood of 1250 people in people per square mile is 1534 people per square mile

Population density is the number of people per unit area of a location.

The population density is the number of people per square mile in the neighborhood

The population of the neighborhood = 1,250 people

The number of city blocks in the neighborhood = 30

The length of each city block = (1/16) mile

The width of each neighborhood = (1/8) mile

The area of each neighborhood = (1/16) × (1/8) = 1/128 square miles

The area of the whole neighborhood = 30 × 1/128 = 15/64 square miles

The population density = 1250/(15/64) = 16,000/3 ≈ 5334 people per square mile (rounding up)

The number of people per square mile, the population density, therefore is 5333 people per square mile

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The number 0.1271 represents the area under the standard normal curve below a particular z-score. To find the z-score, you can use a standard normal (z-score) table or an online calculator. In this case, the z-score is approximately -1.14.

To find the z-score corresponding to the area of 0.1271 under the standard normal curve, you can use a standard normal table or a calculator that can perform inverse normal calculations. When using a standard normal table, you can look up the area of 0.1271 in the body of the table or in the cumulative area column. The corresponding z-score is the value found in the leftmost column or in the row of the table that contains the area.

Alternatively, you can use a calculator to perform the inverse normal calculation. By inputting the area of 0.1271 and specifying that you are working with a standard normal distribution, you can obtain the z-score that corresponds to this area, which is approximately -1.14.

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