URGENT!! ILL GIVE BRAINLIEST! 100 POINTS
Maria wanted to bring back 5 million grams of sand from her trip to the beach. Each grain of sand weighs approximately 6.7 x 10^-7 kg. How heavy is the bag of sand that Maria brings home?

The Taylor series for a function about x=0 is given by 2^k/3kx^k. We are supposed to find f5(0).The given Taylor series can be written as follows'(x) = ∑_k=0^∞▒(2^k)/(3k)x^k``f5(x) = (2^5)/(3×5)x^5``f5(0) = (2^5)/(3×5)×0^5 = 0`Therefore, f5(0) = 0. The work leading to this answer has been shown above.
To find f^(5)(0), we need to identify the term in the Taylor series that corresponds to the 5th derivative of the function evaluated at x=0. The general term in the Taylor series is given by:

(2^k / 3k) * x^k

We need to find the term where k = 5:

(2^5 / 3*5) * x^5 = (32 / 15) * x^5

Now, to find f^ (5)(0), we evaluate this term at x = 0:

(32 / 15) * 0^5 = 0

So, f^ (5)(0) = 0.

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Answer:

cp of 55 shares = 3.50 * 55 = 192.5

commission amount = 1% *192.5 = 1.925

Total invest = 192.5 + 1.925 = 194.425

sp of 1 share = 2

sp of 55 share = 2*55 = 110

Earning from shares = 110

since earning is less than invest, Laura has loss of (194.425 - 110) = 84.425

Laura has a loss of $84.425 for the cost price of $192.5.

Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Cost price of 55 shares = 3.50 x 55 = 192.5

Commission amount = 1% *192.5 = 1.925

Total invest = 192.5 + 1.925 = 194.425

The selling price of 1 share = 2

The selling price  of 55 share = 2*55 = 110

Earning from shares = 110

Since earnings are less than investment, Laura has a loss of (194.425 - 110) = $84.425

Therefore, Laura has a loss of $84.425 for the cost price of $192.5.

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a) The forecast is approximately miles. b) the Mean Absolute Deviation (MAD) based on the forecast is approximately miles. c) The forecast for year 6 is approximately miles. d) the last forecast is 3,468 miles.

a) To calculate the forecast for year 6 using a 2-year moving average, we take the average of the mileage for years 5 and 4. This provides us with the forecasted value for year 6.

b) The Mean Absolute Deviation (MAD) for the 2-year moving average forecast is calculated by taking the absolute difference between the actual mileage for year 6 and the forecasted value and then finding the average of these differences.

c) When using a weighted 2-year moving average, we assign weights to the most recent and previous periods. The forecast for year 6 is calculated by multiplying the mileage for year 5 by 0.40 and the mileage for year 4 by 0.60, and summing these weighted values.

The MAD for the weighted 2-year moving average forecast is calculated in the same way as in part b, by taking the absolute difference between the actual mileage for year 6 and the weighted forecasted value and finding the average of these differences.

d) Exponential smoothing involves assigning a weight (α) to the most recent forecasted value and adjusting it with the previous actual value. The forecast for year 6 is calculated by adding α times the difference between the actual mileage for year 5 and the previous forecasted value, to the previous forecasted value.

In this case, with α=0.20 and a forecast of 3,100 miles for year 1, we perform this exponential smoothing calculation iteratively for each year until we reach year 6, resulting in the forecasted value of approximately 3,468 miles.

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Let x represent the number of students attending the dance.

Band A: Cost = $600

Band B: Cost = $350 + ($1.25 × x)

Let's denote the number of students attending the dance as "x".

For Band A, they charge a flat fee of $600 to play for the evening, so the cost would be constant regardless of the number of students. We can represent this cost as a single equation:

Cost of Band A: $600

For Band B, they charge $350 as a base fee, and an additional $1.25 per student. Since the number of students is denoted as "x", the cost of Band B can be represented as follows:

Cost of Band B = Base fee + (Cost per student * Number of students)

Cost of Band B = $350 + ($1.25 × x)

Now we have a system of equations representing the cost of the two bands:

Cost of Band A: $600

Cost of Band B: $350 + ($1.25 × x)

These equations show the respective costs of Band A and Band B based on the number of students attending the dance. Paula can use these equations to compare the costs and make an informed decision while keeping the ticket price as low as possible to encourage student attendance while covering the expenses.

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Answer:

6.25

Step-by-step explanation:

=1.20*5

=6.25

Answer:

6

Step-by-step explanation:

1.20 x 5 = 6

6/5 = 1.20

Step-by-step explanation:

(a)

2:5:3 means that there are 2+5+3 = 10 units of the price money distributed between the team.

£1500 / 10 = £150 per unit.

person A gets therefore 2×150 = £300

person B gets 5×150 = £750

person C gets 3×150 = £450

so, person B gets 750-300 = £450 more money than person A.

(b)

40% of £450 = 450×0.4 = £180

so donated to total prize money is

180/1500 = 3/25

To find the velocity graph we need to differentiate the given function S = f(t) = t^4 – 4t + 1.The derivative of S is obtained as follows:

\(v = ds/dtv = d/dt (t^4 – 4t + 1)v = 4t^3 – 4O\)n equating v = 0,

we have 4\(t^3 – 4 = 0t^3 = 1t = 1\)

Therefore, at t = 1 the velocity is zero. Now we have to find out when the object is moving in the positive direction.

To check this we have to take the derivative of v which will give us the acceleration.

\(a = dv/dta = d/dt (4t^3 - 4)a = 12t^2\)The acceleration is positive when t > 0Therefore the velocity of the object is moving in the positive direction when t > 0.

(b) To find the motion diagram, we need to find the position of the object. We know that the derivative of position gives the velocity and the derivative of velocity gives acceleration.

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x=2/3

6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10

Answer:

2x-1=y,2y+3=x

Step-by-step explanation:

no explanation

Answer:

As decimal 20.5833333333

As fraction \(20\) \(\frac{7}{12}\)

mark me as brainliest if right :)

Step-by-step explanation:

Conversion a mixed number 10 2/

3

to a improper fraction: 10 2/3 = 10 2/

3

= 10 · 3 + 2/

3

= 30 + 2/

3

= 32/

3

To find new numerator:

a) Multiply the whole number 10 by the denominator 3. Whole number 10 equally 10 * 3/

3

= 30/

3

b) Add the answer from previous step 30 to the numerator 2. New numerator is 30 + 2 = 32

c) Write a previous answer (new numerator 32) over the denominator 3.

Ten and two thirds is thirty-two thirds

Conversion a mixed number 9 11/

12

to a improper fraction: 9 11/12 = 9 11/

12

= 9 · 12 + 11/

12

= 108 + 11/

12

= 119/

12

To find new numerator:

a) Multiply the whole number 9 by the denominator 12. Whole number 9 equally 9 * 12/

12

= 108/

12

b) Add the answer from previous step 108 to the numerator 11. New numerator is 108 + 11 = 119

c) Write a previous answer (new numerator 119) over the denominator 12.

Nine and eleven twelfths is one hundred nineteen twelfths

Add: 32/

3

+ 119/

12

= 32 · 4/

3 · 4

+ 119/

12

= 128/

12

+ 119/

12

= 128 + 119/

12

= 247/

12

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 12) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 12 = 36. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - thirty-two thirds plus one hundred nineteen twelfths = two hundred forty-seven twelfths.

REmember that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

Verify

Triangle 2

Find out the interior angles

47, 64,x

the sum must be equal to 180 degrees

47+64+x=180

x=69 degrees

Triangle 3

interior angles

47,69 and the third angle must be 64 degrees

that means

triangle 2 and triangle 3 are similar

The correlation coefficient for the given data is 0.977. Approximately 95.52% of the variation in Y values is explained by variations in X values.

Using the formula for the correlation coefficient, we have:

r = (nΣXY - ΣXΣY) / sqrt[(nΣX² - (ΣX)²)(nΣY^2 - (ΣY)²)]

where n is the number of observations, ΣX and ΣY are the sums of the X and Y values, ΣXY is the sum of the products of corresponding X and Y values, and ΣX² and ΣY² are the sums of the squares of the X and Y values, respectively.

Plugging in the values from the data, we get:

n = 6

ΣX = 56

ΣY = 171

ΣXY = 834

ΣX² = 799

ΣY² = 3682

r = (6834 - 56171) / sqrt[(6799 - 56²)(63682 - 171²)]

r = 0.954 (rounded to 3 decimal places)

To determine how much of the variation in Y values is explained by variations in X values, we can square the correlation coefficient to get the coefficient of determination, which represents the proportion of the total variation in Y that can be explained by the linear relationship with X.

r² = 0.911 (rounded to 3 decimal places)

Therefore, about 91.1% of the variation in Y values is explained by variations in X values.

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Complete question:

Given are six observations taken for two variables:

X: 6, 9, 9, 9, 11, 12

Y: 17, 25, 27, 26, 37, 39

Compute the correlation coefficient for these data. Keep 3 decimals in your answer.

How much of the variation in Y values is explained by variations in X values? Keep 3 decimals in your answer

Answer:

3.25

Step-by-step explanation:

μX = 2(0.3) + 3(0.2) + 4(0.4) + 5(0.1) = 3.3

The mean of the distribution represented by the histogram is 3.25

The mean is the product of the value of X and its corresponding probability (P(x)).

The mean can be expressed thus :

From the histogram :

Mean = (1 × 0.05) + (2 × 0.2) + (3 × 0.35) + (4 × 0.25) + (5 × 0.15)

Mean = 0.05 + 0.40 + 1.05 + 1.00 + 0.75 = 3.25

Therefore, the mean value of the distribution depicted by the histogram ls 3.25

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(a) Example question: "How often do you look at social media while doing schoolwork?

(b) Sofie can select a simple random sample of students by using a random number generator to assign a unique identification number to each student in the online high school.

(c) The sample for Sofie's research is the 32 completed surveys she received. These surveys represent the responses of a subset of the population. The population, in this case, refers to all the students at the online high school.

(d) If Sofie uses only the completed surveys, she can conclude that approximately 50% (16 out of 32) of the students who completed the survey reported using social media while doing schoolwork.

(a) Please select one of the following options: never, rarely, occasionally, frequently, or always."

(b) She can then use the random number generator again to select a specific number of students from the entire population of students, ensuring that each student has an equal chance of being selected. For example, if there are 500 students in total and Sofie wants a sample size of 50, she can generate 50 random numbers and select the corresponding students based on their identification numbers.

(d) However, it is important to note that this conclusion is specific to the sample of completed surveys and cannot be generalized to the entire population of high school students.

To make an inference about the percent of all high school students who use social media while doing schoolwork, Sofie would need a larger and more representative sample that covers a wider range of students in the online high school.

Additionally, she should consider potential biases in the sample, such as non-response bias if the students who chose not to complete the survey have different social media usage patterns compared to those who did respond.

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Based on the given data, there is no significant difference between the means of the two samples at the 95% level.

To test whether there is a significant difference between the two samples, we can use the independent samples t-test. Here are the steps to perform the test:

Step 1: State the null hypothesis (H₀) and alternative hypothesis (H₁):

H₀: There is no significant difference between the means of the two samples.

H₁: There is a significant difference between the means of the two samples.

Step 2: Set the significance level (α):

In this case, the significance level is given as 95%, which corresponds to α = 0.05.

Step 3: Calculate the test statistic:

The test statistic for the independent samples t-test is given by:

t = (x₁ - x₂) / sqrt((s₁²/n₁) + (s₂²/n₂))

Where:

x₁ and x₂ are the sample means,

s₁ and s₂ are the sample standard deviations,

n₁ and n₂ are the sample sizes.

In this case, x₁ = 60, x₂ = 59, n₁ = 100, n₂ = 200, and σ = 50.

Step 4: Determine the critical value:

Since the significance level is 0.05 and the test is a two-tailed test, we divide the significance level by 2 to find the critical value. Using the t-distribution table or a statistical software, we find that the critical value for a two-tailed test with α = 0.05 is approximately 1.96.

Step 5: Compare the test statistic with the critical value:

If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Let's calculate the test statistic:

t = (60 - 59) / sqrt((50²/100) + (50²/200))

Using a calculator or software, the test statistic is calculated as:

t ≈ 0.1407

Since the absolute value of the test statistic (0.1407) is less than the critical value (1.96), we fail to reject the null hypothesis.

Therefore, based on the given data, there is no significant difference between the means of the two samples at the 95% level.

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For 2 sec the snowboarder in the air.

We have,

The height (in feet) of a snowboarder above the bottom of the half-pipe can be modeled by h=-16t²+24t + 16.4

So, 3.2 = -16t² + 24t + 16.4

-16t² + 24t + 12.4 = 0

Now, solving the above quadratic equation we get

t = -0.40650, 1.90650

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ANSWER: the amount an individual earns after subtracting all expenses, taxes and costs.

Answer:

yes (answer in the comments) U^U

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

who knows why it gets asked lol but why is this question in mathematics anyway

Answer:

It's 4!

Step-by-step explanation: It's as a j o k e or just so people get fre e poi nts without getting their question d ele ted!

Answer:

J and N.

Step-by-step explanation:

Non-collinear means that they do not lie on the same line. J and N because they do not lie on the same line. You could also have L and N.

Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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The value of the given and completed expression in this problem is

-1

Combined operations are defined as a set of operations applied to the same problem, for example addition, subtraction, multiplication, are frequently used in arithmetic polynomials.

In this case we have an arithmetic polynomial.

We complete the expression as follows:

1 + 2 - 3 + 4 - 5

We group the positive terms on one side and negative terms on the other:

The value of the expression (1 + 2 - 3 + 4 - 5) is -1

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Answer:

Step-by-step explanation:

dont know sorry I am in 6 grade

By using the method of trigonometry,

(1)sin B=P/H=AD/AB=12/13

(2)sec B=H/B=AB/BD=13/5

(3)cot B=B/P=BD/AD=5/12

(4)cos C=B/H=CD/AC=16/20=4/5

(5)cosec C=H/P=AC/AD=20/12=5/3

(6)tan C =P/B=AD/DC=12/16=3/4

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are the trigonometric functions (sometimes known as the circle functions) that make up trigonometry. The unit circle is the most straight forward way to define the trigonometric functions. Let theta represent an angle that is calculated along a circle's arc counterclockwise from the x-axis.

Given that,

\(AD^{2}= AB^{2}- BD^{2}= 13^{2}- 5^{2}= 169-25= 144\)

=>AD=12cm

(1)sin B=P/H=AD/AB=12/13

(2)sec B=H/B=AB/BD=13/5

(3)cot B=B/P=BD/AD=5/12

\(AC^{2}= AD^{2}+ DC^{2}= 12^{2}+ 16^{2}= 144+ 256= 400\)

=>AC=20cm

(4)cos C=B/H=CD/AC=16/20=4/5

(5)cosec C=H/P=AC/AD=20/12=5/3

(6)tan C =P/B=AD/DC=12/16=3/4

note: P=perpendicular

B=base

H=hypotenuse

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it will take k × x × w weeks to build x miles of highway with w workers, where k is the constant of proportionality.

Let's say it takes "t" weeks to build "m" miles of highway with "w" workers. Based on the given information, we can write the following proportion:

t weeks / m miles = k × w workers

Where "k" is the constant of proportionality.

Now, if we want to find how long it will take workers to build "x" miles of highway, we set up the proportion as follows:

t weeks / x miles = k × w workers

To solve for "t," we can cross-multiply and then divide:

t weeks = (k × w workers × x miles) / 1

t weeks = (k × x × w) / 1

t weeks = k × x × w

Therefore, it will take k × x × w weeks to build x miles of highway with w workers, where k is the constant of proportionality.

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The vector equation of the line passing through the point (8, 0, -3) and parallel to the line x = 4 - 4t, y = -1 + 3t, z = 6 + 6t is r = (8, 0, -3) + t(-4, 3, 6), and the parametric equations for the line are x = 8 - 4t, y = 3t, z = -3 + 6t.

To determine the vector equation and parametric equations for the line passing through the point (8, 0, -3) and parallel to the line x = 4 - 4t, y = -1 + 3t, z = 6 + 6t, we can use the direction vector of the line.

The direction vector of the line x = 4 - 4t, y = -1 + 3t, z = 6 + 6t is (-4, 3, 6). Since the line we seek is parallel to this line, it will have the same direction vector.

The vector equation of the line can be written as:

r = (8, 0, -3) + t(-4, 3, 6)

The parametric equations for the line are:

x = 8 - 4t

y = 3t

z = -3 + 6t

Here, t is the parameter that determines different points on the line. By varying t, we can generate various points on the line parallel to the given line and passing through the point (8, 0, -3).

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The approximate enthalpy change, δhrxn, for the combustion of methane is approximately -1283.79 kJ/mol.

To calculate the approximate enthalpy change, δhrxn, for the combustion of methane, we can use Hess's Law and the enthalpies of formation.

The balanced equation for the combustion of methane is:

CH4 + 2O2 → CO2 + 2H2O

To calculate the enthalpy change, we need to find the difference between the sum of the enthalpies of formation of the products and the sum of the enthalpies of formation of the reactants.

The enthalpy of formation for methane (CH4) is -74.81 kJ/mol. The enthalpy of formation for carbon dioxide (CO2) is -393.5 kJ/mol, and the enthalpy of formation for water (H2O) is -285.8 kJ/mol.

Using these values, we can calculate the enthalpy change:

ΔHrxn = (2 * -393.5 kJ/mol) + (2 * -285.8 kJ/mol) - (-74.81 kJ/mol)

     = -787 kJ/mol - 571.6 kJ/mol + 74.81 kJ/mol

     = -1283.79 kJ/mol

Therefore, the approximate enthalpy change, δhrxn, for the combustion of methane is approximately -1283.79 kJ/mol.Please note that the values used for enthalpies of formation are approximate and may vary slightly depending on the source. Additionally, this calculation assumes standard conditions.

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Answer:

2

Step-by-step explanation:

4x^3 + 2 = 34

4x^3 = 32

x^3 = 8

x=2

The solution to the system of differential equations is x(t) = -\(3e^{(31t)\) and z(t) = -\(3e^{(31t\)).

To solve the given system of differential equations, we'll begin by finding the eigenvalues and eigenvectors of the coefficient matrix.

The coefficient matrix is A = [[-22, 54], [-9, 23]]. To find the eigenvalues λ, we solve the characteristic equation det(A - λI) = 0, where I is the identity matrix.

det(A - λI) = [[-22 - λ, 54], [-9, 23 - λ]]

=> (-22 - λ)(23 - λ) - (54)(-9) = 0

=> λ^2 - λ(23 + 22) + (22)(23) - (54)(-9) = 0

=> λ^2 - 45λ + 162 = 0

Solving this quadratic equation, we find the eigenvalues:

λ = (-(-45) ± √((-45)^2 - 4(1)(162))) / (2(1))

λ = (45 ± √(2025 - 648)) / 2

λ = (45 ± √1377) / 2

The eigenvalues are λ₁ = (45 + √1377) / 2 and λ₂ = (45 - √1377) / 2.

Next, we'll find the corresponding eigenvectors. For each eigenvalue, we solve the equation (A - λI)v = 0, where v is the eigenvector.

For λ₁ = (45 + √1377) / 2:

(A - λ₁I)v₁ = 0

=> [[-22 - (45 + √1377) / 2, 54], [-9, 23 - (45 + √1377) / 2]]v₁ = 0

Solving this system of equations, we find the eigenvector v₁.

Similarly, for λ₂ = (45 - √1377) / 2, we solve (A - λ₂I)v₂ = 0 to find the eigenvector v₂.

The general solution of the system is x(t) = c₁e(λ₁t)v₁ + c₂e(λ₂t)v₂, where c₁ and c₂ are constants.

Using the initial condition x(0) = -3, we can substitute t = 0 into the general solution and solve for the constants c₁ and c₂.

Finally, substituting the values of c₁ and c₂ into the general solution, we obtain the particular solution for x(t).

Since z(t) = x(t), the solution for z(t) is the same as x(t).

Therefore, the solution to the system of differential equations is x(t) = \(-3e^{(31t)\) and z(t) = -\(3e^{(31t)\).

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The graph passes through the point (0, 2), which is the y-intercept, and it increases rapidly as x increases, since the base is 3. As such, the graph of the given function is exponential with a base of 3 and a coefficient of 2.

The given function is f(x)=2(3)x, which can be written as f(x)=2(3)x . In this function, the base is 3, and the coefficient is 2. To graph this function, we can use a table of values to plot the points and connect them with a smooth curve.

First, we will choose a few values for x and find their corresponding values for y using the function. Let's choose x values of -1, 0, and 1, and find the corresponding y values. We get:

f(-1)=2(3)-1=2/3
f(0)=2(3)0=2
f(1)=2(3)1=6

Therefore, the table of values for the given function f(x) is as follows:

x f(x)
-1 2/3
0 2
1 6

Now, we can plot these points on a graph with the x values on the horizontal axis and the y values on the vertical axis. The points are (-1, 2/3), (0, 2), and (1, 6). We can then connect these points with a smooth curve to get the graph of f(x)=2(3)x as shown in option A.

The graph passes through the point (0, 2), which is the y-intercept, and it increases rapidly as x increases, since the base is 3. As such, the graph of the given function is exponential with a base of 3 and a coefficient of 2.

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