What is the graph of g?

To find the derivative of f(x) = (2e^(3x) + 2e^(-2x))^4, we can use the chain rule and the power rule.

First, we need to find the derivative of the function inside the parentheses, which is:

g(x) = 2e^(3x) + 2e^(-2x)

The derivative of g(x) is:

g'(x) = 6e^(3x) - 4e^(-2x)

Now, using the chain rule and power rule, we can find the derivative of f(x):

f'(x) = 4(2e^(3x) + 2e^(-2x))^3 * (6e^(3x) - 4e^(-2x))

Simplifying this expression, we get:

f'(x) = 24(2e^(3x) + 2e^(-2x))^3 * (e^(3x) - e^(-2x))
To find the derivative of f(x) = (2e^(3x) + 2e^(-2x))^4, we can use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Let u = 2e^(3x) + 2e^(-2x). Then f(x) = u^4.

First, find the derivative of the outer function with respect to u:
df/du = 4u^3

Next, find the derivative of the inner function with respect to x:
du/dx = d(2e^(3x) + 2e^(-2x))/dx = 6e^(3x) - 4e^(-2x)

Now, use the chain rule to find the derivative of f with respect to x:
df/dx = df/du * du/dx = 4u^3 * (6e^(3x) - 4e^(-2x))

Substitute the expression for u back into the equation:
df/dx = 4(2e^(3x) + 2e^(-2x))^3 * (6e^(3x) - 4e^(-2x))

This is the derivative of f(x) with respect to x.

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A planet's radius is approximately 2,812 mi. About two-thirds of the planet's surface is covered by water. An estimate for the land area on the planet is 33 million mi²

The surface area of a sphere is given by the formula:

S = 4πr²

where S is the surface area and r is the radius.

Substituting the given radius, we get:

S = 4π(2,812)²

S ≈ 99,392,252.4 mi²

Since two-thirds of the planet's surface is covered by water, we can estimate the land area as one-third of the total surface area:

Land area ≈ (1/3) x 99,392,252.4

Land area ≈ 33,130,750.8 mi²

Rounding this to the nearest million, we get an estimate of 33 million mi² for the land area on the planet.

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The function that would best represent this is given as p(t) = 1150 (0.8769)^t

An exponential function is a mathematical function of the form f(x) = a^x, where "a" is a constant called the base and "x" is the variable. The base is usually a positive number greater than 1, but it can also be a fraction between 0 and 1, or even a negative number.

Exponential functions are characterized by the fact that the variable "x" appears as an exponent. As a result, these functions grow or decay very rapidly as "x" increases or decreases, depending on the value of the base "a".

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The total area of the first floor of the tiny house is 121 square feet

The total area of the first floor of the tiny house can be expressed as the sum of the areas of each room. The area of a rectangle is calculated by multiplying the length by the width. Therefore, we can write:

Total area = Area of kitchen + Area of bathroom

The area of the kitchen is given by the product of the length and the width of the kitchen, which is 11 feet and 7 feet, respectively. Therefore, the area of the kitchen can be written as:

Area of kitchen = 11 x 7 = 77 square feet

Similarly, the area of the bathroom is given by the product of the length and the width of the bathroom, which is 11 feet and 4 feet, respectively. Therefore, the area of the bathroom can be written as:

Area of bathroom = 11 x 4 = 44 square feet

Substituting these expressions into the equation for the total area, we get:

Total area = Area of kitchen + Area of bathroom

= 77 + 44

= 121 square feet

Therefore, the total area of the first floor of the tiny house is 121 square feet, which can also be expressed as the sum of the areas of the kitchen and bathroom.

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By using  sum , difference , product , quotient and one that involves at least two operations that have the value of -3/4.

Now, We have to find the five expressions :

Expression for sum is -

1/4 + (-1) = -3/4

Expression for difference is -

(1/4 - 1) = -3/4

Expression for product is -

(-3/2)(1/2) = -3/4

Expression for quotient is -

(1 - 4)/4 = -3/4

Expression that involves at least two operations is -

-(1/4 + 2/4) = -3/4

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Answer:

search them up it should give you the answers

Step-by-step explanation:

the intersection point is approximately (2.215421, 3.256684). For the first question, the initial value problem is given by the differential equation f'(u) = 5(cost - sinus) with the initial condition f(3xN) = 3.

To solve this problem, we can separate the variables and integrate both sides as follows:

f'(u) = 5(cosu - sinu)
∫ f'(u) du = ∫ 5(cosu - sinu) du
f(u) = 5sinu + 5cosu + C

Using the initial condition f(3xN) = 3, we can solve for the constant C:

f(3xN) = 5sin(3xN) + 5cos(3xN) + C = 3
C = 3 - 5sin(3xN) - 5cos(3xN)

Thus, the solution to the initial value problem is given by:

f(u) = 5sinu + 5cosu + 3 - 5sin(3xN) - 5cos(3xN)

For the second question, we are asked to find the intersection points of the two curves y = 16/* and y = x + 1 using Newton's method. To applyhttps://brainly.com/question/2228446 we need to find the function f(x) that represents the difference between the two curves:

f(x) = 16/x - (x + 1)

The intersection points correspond to the roots of f(x), which can be found using Newton's method:

x_{n+1} = x_n - f(x_n)/f'(x_n)

where x_n is the nth approximation of the root. We start with an initial guess of x_0 and iterate until we reach a desired level of accuracy. For example, if we start with x_0 = 1, the iterations are as follows:

x_1 = 1 - (16/1 - (1 + 1))/(16/1^2 + 1) = 2.5
x_2 = 2.5 - (16/2.5 - (2.5 + 1))/(16/2.5^2 + 1) = 2.267857
x_3 = 2.267857 - (16/2.267857 - (2.267857 + 1))/(16/2.267857^2 + 1) = 2.219208
x_4 = 2.219208 - (16/2.219208 - (2.219208 + 1))/(16/2.219208^2 + 1) = 2.215430
x_5 = 2.215430 - (16/2.215430 - (2.215430 + 1))/(16/2.215430^2 + 1) = 2.215421

Thus, the intersection point is approximately (2.215421, 3.256684).

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There are 1140 different predictions possible for this game of chance.

In this scenario, customers have an opportunity to predict three numbers out of 20, which will be drawn from a bin. The order in which the numbers are selected does not matter, which means the same set of numbers in different orders will be considered as the same prediction.

To solve this problem, we can use the formula for combinations, which is

=> [tex]^nC_x = \frac{n!}{ x! \times (n-x)!}[/tex]

where n is the total number of items, and x is the number of items to be selected.

In this case, we have 20 balls, and we want to select three balls without replacement. So, the formula becomes

=> [tex]^{20}C_3 = \frac{20!} { 3! \times (20-3)!}[/tex]

Using a calculator or simplifying the equation, we get:

[tex]= > ^{20}C_3 = \frac{201918} { 321} = 1140[/tex]

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Any function of the form [tex]y = \sqrt[3]{x + a}[/tex] is a translation left a units of the graph of [tex]g(x) = \sqrt[3]{x}[/tex], which has one x-intercept.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The function in this problem has a single x-intercept, hence a translation left only moves the function laterally, meaning that it would also have only one x-intercept.

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The maximum altitude the object reaches is approximately 0.459 meters, and it takes approximately 0.612 seconds for the object to hit the ground after being shot upwards from ground level.

To find the maximum altitude and the time at which the object hits the ground after being shot upwards from ground level with an initial velocity of 3 meters per second and subject only to the force of gravity,

we can use the following steps:

1. Calculate the time it takes to reach its maximum altitude:

To do this, we can use the formula vf = vi - gt, where vf is the final velocity (0 m/s at the peak), vi is the initial velocity (3 m/s), g is the acceleration due to gravity (9.81 m/s²), and t is the time. Rearranging and solving for t:

0 = 3 - 9.81t

t = 3 / 9.81 ≈ 0.306 seconds

2. Calculate the maximum altitude:

We can use the formula h = vit - 0.5gt², where h is the maximum altitude. Plugging in the values:

h = (3 m/s)(0.306 s) - 0.5(9.81 m/s²)(0.306 s)²

h = 0.459m

3. Calculate the time it takes to hit the ground:

Since the object will take the same amount of time to fall from its maximum altitude to the ground as it took to reach the maximum altitude, the total time to hit the ground is double the time it took to reach the maximum altitude:

total time = 2 × 0.306 s ≈ 0.612 seconds

So, the maximum altitude the object reaches is approximately 0.459 meters, and it takes approximately 0.612 seconds for the object to hit the ground after being shot upwards from ground level.

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The 99% confidence interval of the true mean weight of minivans with 4150 pounds is CI = (3950, 4350).

The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.

Most of the time, the confidence level is chosen before looking at the data. 95% confidence level is the standard degree of assurance. Nevertheless, additional confidence levels, such as the 90% and 99% confidence levels, are also applied.

Point estimate is the sample mean, which is 4150 pounds. It is the best "guess" one has.

selected minivans was 4,150 pounds,

(z < 0.99) = 2.58

99% CI = ±2.58

Standard Error of the mean.

It is the = [tex]\frac{standard \ deviation}{\sqrt{sample \ size} }[/tex]

SE = [tex]\frac{490}{\sqrt{40} }[/tex]

SE = 77.475

To the nearest decimal ,

z x SE = ±200

CI = (3950, 4350) units are pounds.

Therefore, the confidence interval of the true mean weight of minivans is (3950, 4350).

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The triangle is a right triangle.

Any given triangle in which one of its internal angles measures 90^o is said to be a right angle. Thus there is a common relations among the three sides of the triangle which is shown by the Pythagorean theorem.

The Pythagorean theorem states that;

For a right triangle, this relation holds among its three sides;

/Hyp/^2 = /Adj/^2 + /Opp/^2

Considering the given diagram, we have;

/Hyp/^2 = /Adj/^2 + /Opp/^2

             = 4^2 + 3^2

             = 16 + 9

             = 25

so that;

Hyp = 25^1/2

       = 5

Therefore the given triangle is a right triangle.

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The derivative of f(x) = sinº (4x) is f '(x) = 4cos (4x).

To find the derivative of f(x) = sinº (4x), we can use the chain rule.

First, we need to find the derivative of the outer function, which is sinº (4x). This can be done using the derivative of the sine function:

f '(x) = cos (4x)

Next, we need to multiply this by the derivative of the inner function, which is 4.

f '(x) = cos (4x) * 4

Simplifying this expression, we get:

f '(x) = 4cos (4x)

Therefore, the derivative of f(x) = sinº (4x) is f '(x) = 4cos (4x).

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The amount of more sauce needed is 5/12.

Thus we are given that the total amount of sauce required for making the pizza is 2/3 cup.

Thus we already have 1/4 cup of tomato sauce present.

Hence, for making the recipe the leftover amount of sauce will be the difference in the sauce we have got to the sauce required.

Tomato sauce required= Total tomato sauce needed - Sauce already present

Therefore,

Tomato sauce required= 2/3-1/4

Thus we have to make the denominators qual by taking their LCM as the denominator.

The LCM of the denominators comes out to be 12.

Therefore,

[tex]=\frac{8-3}{12}[/tex]

[tex]=\frac{5}{12}[/tex]

Therefore, the amount of sauce required is 5/12.

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The density of the object is 0.0018 g/mL.

To calculate the density of the object, we need to use the formula:

Density = Mass / Volume

Given that the mass of the object is 4.70g and the volume is 2.55L, we can substitute these values into the formula:

Density = 4.70g / 2.55L

We need to convert the units of mass and volume to a consistent unit. Let's convert the volume from liters to milliliters (1L = 1000mL):

Density = 4.70g / 2550mL

Now we can simplify by dividing both the numerator and denominator by 10:

Density = 0.47g / 255mL

Finally, we can express the answer in units of g/mL:

Density = 0.0018 g/mL

Therefore, the density of the object is 0.0018 g/mL.

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Answer:

Yes they are mutually exclusive

Step-by-step explanation:

You cannot both be a rational number and an irrational number

(a) The least squares regression equation that models the data is: y = 0.091x + 1.125, where x is the time in years since 1995 and y is the price per gallon.

(b) To estimate the price per gallon in 2030, we need to find the value of y when x = 35 (2030 - 1995). Substituting x = 35 in the equation, we get: y = 0.091(35) + 1.125 = 4.22 dollars per gallon. Therefore, the estimated price per gallon in 2030 is 4.22 dollars.

(a) The least squares regression equation is used to model the relationship between two variables, in this case, time and gasoline price. It calculates the line that best fits the data points and can be used to estimate the value of the dependent variable (gasoline price) for any given value of the independent variable (time).

(b) To estimate the price per gallon in 2030, we simply need to substitute the value of x = 35 in the equation and solve for y. The equation shows that the price per gallon increases by 9.1 cents every year since 1995.

However, this is just an estimate based on the data available, and other factors such as changes in supply and demand, government policies, and global events can also influence gasoline prices in the future.

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2(2.5) + 5(23) = 150

3(2.5) + 4(23) = 144.5

Both equations are satisfied, so our solution is correct.

To solve the problem, let's first assign some variables. Let x be the cost of one pine tree and y be the cost of one hydrangea bush. We can then use these variables to set up a system of equations:

2x + 5y = 150 (equation 1)

3x + 4y = 144.5 (equation 2)

We can solve this system of equations using various methods. Here, we will use the substitution method.

From equation 1, we can solve for x in terms of y:

2x = 150 - 5y

x = (150 - 5y)/2

We can then substitute this expression for x into equation 2:

3((150 - 5y)/2) + 4y = 144.5

Multiplying both sides by 2 to eliminate the fraction:

3(150 - 5y) + 8y = 289

Expanding and simplifying:

450 - 15y + 8y = 289

-7y = -161

y = 23

We can now substitute this value for y into either equation 1 or 2 to solve for x:

2x + 5(23) = 150

2x = 5

x = 2.5

Therefore, one pine tree costs $2.50 and one hydrangea bush costs $23.

To check our work, we can substitute these values into both equations:

2(2.5) + 5(23) = 150

3(2.5) + 4(23) = 144.5

Both equations are satisfied, so our solution is correct.

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Answer:

70 dogs

Step-by-step explanation:

sum the parts of the ratio , 5 + 2 = 7 parts

divide total by 7 to find the value of one part of the ratio

98 ÷ 7 = 14 ← value of 1 part of the ratio , then

5 × 14 = 70 ← number of dogs

Last week, the ratio of bananas sold to watermelons sold was 4 : 3.

This ratio means that for every 4 bananas sold, the number of watermelons sold was 3.

Since there were 48 bananas sold, we can find the number of watermelons sold by subtracting 12 from 48:

48 bananas - 12 = 36 watermelons

Now, we can determine the ratio of bananas sold to watermelons sold. The ratio would be:

Bananas : Watermelons = 48 : 36

To simplify this ratio, we can divide both numbers by their greatest common divisor (GCD), which in this case is 12:

48 ÷ 12 = 4
36 ÷ 12 = 3

So, the simplified ratio is:

4 : 3

This ratio means that for every 4 bananas sold, the number of watermelons sold was 3. In other words, out of every 7 fruits sold (4 bananas + 3 watermelons), 4 were bananas and 3 were watermelons. This provides an easy way to understand the proportion of each type of fruit sold at Jun's fruit stand last week.

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The simplification of the given algebraic expression is: -3x - 9y

Algebraic expressions are defined as the idea of expressing numbers with the aid of letters or alphabets without really specifying their actual values.

Now, the algebraic operations are known by the acronym PEMDAS which denotes:

P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.

We want to find the sum of the algebraic expressions given as (-10x - 4y) and (7x - 5y) in simplest form.

Thus, we have:

(-10x - 4y) + (7x - 5y)

= -10x - 4y + 7x - 5y

= -3x - 9y

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Complete question:

Find an expression which represents the sum of (-10x - 4y) and (7x - 5y) in simplest terms.

Answer: x² - 2x - 3

Step-by-step explanation:

      What is FOIL? The FOIL method is used to multiply two binomials.

F ➜ First
O ➜ Outer
I ➜ Inner
L ➜ Last

      Let us break it down into each piece by multiplying, following the pattern.

F ➜ x * x ➜ x²
O ➜ x * 1 ➜ x
I ➜ x * -3 ➜ -3x
L ➜ -3 * 1 ➜ -3

      Lastly, we add these pieces together.

x² + x - 3x - 3 = x² - 2x - 3

The probability that more than 2 minutes pass before a sale is completed is approximately 0.895 or 89.5%.

The CDF of the exponential distribution is given by:

F(x) = 1 - e^(-λx)

where λ is the rate parameter, which is the reciprocal of the mean, λ = 1/18 in this case. The variable x is the time it takes for a sale to be completed.

To find the probability that more than 2 minutes pass before a sale is completed, we need to find the complement of the probability that a sale is completed within the first 2 minutes. That is:

P(X > 2) = 1 - P(X ≤ 2)

Substituting into the CDF formula:

P(X > 2) = 1 - F(2) = 1 - [tex](1 - e^{(-\lambda_2)} = e^{(-\lambda_2)}[/tex]

Plugging in the value of λ:

P(X > 2) = [tex]e^{(-(1/18)\times2)}[/tex] ≈ 0.895

This means that there is a high chance that it will take more than 2 minutes for a sale to be completed on the phone.

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The values on the relative frequency table indicates;

Part A; 55%

Part B; 20%

Part C; There is an association between passing the exam and completing the exam review

The relative frequency table shows the mode of a dataset, from the sample obtained from a population.

The data in the table can be expressed as follows;

[tex]{}[/tex]                                           Passed exam Did not pass exam Row totals

Completed exam review [tex]{}[/tex]            55%        10%                         65%

Did not completed exam review[tex]{}[/tex] 20%       15%                          35%

Column Total [tex]{}[/tex]                               75%        25%                         100%

Part A; The above table indicates that the percentage who passed the exam given that they completed the exam review is 55%

Part B; The percentage that passed the exam given that they did not complete exam review is 20%

Part C; The conditional percentages of passing the exam and completing the exam review are very different indicating that there is an association between passing the exam and completing exam review

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Answer:  [tex]\frac{x-4}{x-7}[/tex]

Step-by-step explanation:

[tex]\frac{x^{2}-5x+4 }{x^{2} -8x+7}[/tex]    

factor the top and bottom by finding numbers that multiply to the last term but add to middle

for top part:

-4 and -1   multiply to +4 and add to -5

for bottom part:

-7 and -1 multiply to to +7 and add to -8

Those are your factored numbers, put into factored form

[tex]\frac{(x-4)(x-1)}{(x-7)(x-1)}[/tex]    now cross off same factors from top and bottom only

[tex]\frac{x-4}{x-7}[/tex]

Answer:

Step-by-step explanation:

16 - (y^2/sqrt(49)) +12

at y = -5

16 - ( (-5)^2 / sqrt(49)) +12    

16 - ( 25 / 7) + 12

28 - (25/7)

(28*7 - 5) / 7    (LCM)

(196 - 5) / 7

(191/7)

27.2857 = Ans

Jones would save $20 over 2 months by choosing Texas Bank over Lone Star Bank for his online banking needs.

To answer this question, we need to know the fees and charges associated with online banking at Texas Bank and Lone Star Bank. Without this information, it's impossible to accurately calculate how much Jones would save by choosing one bank over the other.

Assuming we have this information, we can use the following steps to calculate Jones' potential savings:

Calculate the fees and charges associated with 40 transactions per month at each bank.

Subtract the total fees and charges at Texas Bank from the total fees and charges at Lone Star Bank to determine the difference.

Multiply the difference by 2 to determine how much Jones would save in 2 months by choosing Texas Bank over Lone Star Bank.

For example, let's say that the fees and charges at Lone Star Bank for 40 transactions per month total $20, while the fees and charges at Texas Bank for the same number of transactions total $10. In this case, the difference would be $10 per month.

To calculate Jones' potential savings over 2 months, we would multiply $10 by 2, giving us a total potential savings of $20.

So, in this hypothetical scenario, Jones would save $20 over 2 months by choosing Texas Bank over Lone Star Bank for his online banking needs.

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Answer is:

For the south region, the proportion of sales from current stores is approximately 58 %.

because this proportion is relatively close to the sales director's statistical model, the data is consistent with the model.

The given information states that the proportion of sales from current stores in the South region is approximately 58%. This value falls within the range of the sales director's statistical model, which could be an estimated value or a range of values based on past data or other sources. Since the proportion of sales falls within the expected range, the data is consistent with the model. This means that the actual value observed is not significantly different from the expected value, and there is no evidence to suggest that the model needs to be revised or updated.

Therefore, the answer to the second drop-down menu is "consistent". If the actual proportion of sales from current stores in the South region was significantly different from the expected value in the sales director's statistical model, then the answer would be "inconsistent". However, since the observed proportion is relatively close to the expected value, the data is consistent with the model.

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