In a sequence if Tn = 5n² - 4 What is the sum of the 5th and 7th terms?
a)121
b)244
c)365
d)367​

Answer:  the longest poster that could fit in the box is approximately 22.56 inches long.

Step-by-step explanation: Utilizing the Pythagorean theorem, able to calculate the corner to corner as takes after:

diagonal^2 = 11^2 + 18^2 + 8^2

diagonal^2 = 121 + 324 + 64

diagonal^2 = 509

inclining = sqrt(509)

corner to corner ≈ 22.56 inches

The equation of exponential function of following table is represented by the table below is y = A(Bˣ).

An exponential function is a mathematical function denoted by f(x) = eˣ (where the argument x is written as an exponent). Unless otherwise stated, the term usually refers to positive-valued functions of real variables, but can be extended to complex numbers and generalized to other mathematical objects such as matrices and Lie algebras. Although the exponential function arose from the notion of exponentiation (iterative multiplication), its modern definition (which has several equivalent characterizations) allows it to be extended exactly to any real argument, including irrational numbers. Its ubiquitous appearance in pure and applied mathematics has led mathematician Walter Rudin to believe that the exponential function is "the most important function in mathematics."

To find the equation of exponential form:

For case 1,

Exponential form: y = A(Bˣ)

y = 0.1, x = 0

[tex]0.1 = A(B^{0})[/tex]

0.1 = A(1)

A = 0.1

For case 2,

Exponential form: y = A(Bˣ)

y = 0.05, x = 1

[tex]0.05 = 0.1(B^{1})[/tex]

B = 0.5

For case 3,

y = 0.025, x = 2

[tex]A = 0.1(B^{2})[/tex]

[tex]0.025 = 0.1(0.5^{2})[/tex]

0.025 = 0.025

For case 4,

y = 0.0125, x = 3

0.0125 = 0.1(0.5³)

0.0125 = 0.1(0.125)

0.0125 = 0.0125

We calculated the value of A and B, and proved it in case 3 and case 4.

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The complete question is as follows:

Find the equation of the exponential function represented by the table below:

The margin of error for a survey with a sample size of 6400 and a 95% confidence level is approximately 1.6%.

Confidence level is a statistical concept that measures the degree of certainty or reliability associated with an estimate, such as the mean, proportion, or regression coefficient, derived from a sample of data.

The margin of error (ME) for a survey depends on several factors, including the size of the sample, the level of confidence desired, and the population size (if applicable). Assuming a 95% confidence level, a sample size of 6400, and no information about the population size, the formula for calculating the margin of error is:

ME = 1.96 × √[(p × q) / n]

where:

1.96 is the z-score associated with a 95% confidence level

p is the estimated proportion of the population that has the characteristic of interest (this is usually unknown and is typically replaced with 0.5 to get the maximum possible margin of error)

q is 1 - p

n is the sample size

Assuming a conservative estimate of p = 0.5, we have:

ME = 1.96 × √[(0.5 × 0.5) / 6400]

≈ 0.016 or 1.6%

Therefore, the margin of error for a survey with a sample size of 6400 and a 95% confidence level is approximately 1.6%. This means that if the survey were conducted multiple times using the same sample size and methodology, the results would likely differ by no more than 1.6% in either direction (plus or minus) from the true population value.

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Proof that cos²(x) + sin²(x) = 1 using the unit circle shows that this equation represents a circle with radius 1

The equation of the unit circle is given by:

x² + y² = 1

where x and y are the coordinates of any point on the circle. Let us assume that the point P on the circle makes an angle of x with the positive x-axis. Then, the coordinates of P are given by:

x = cos(x)

y = sin(x)

Substituting these values in the equation of the circlet:

cos²(x) + sin²(x) = 1

Therefore, we have shown that sin²(x) + cos²(x) = 1 using the unit circle.

Graphically, this equation represents a circle with radius 1 centered at the origin, and any point (cos(x), sin(x)) on the circle will satisfy this equation.

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The summary of the 3 rules on segments are written below.

The three rules on segments in circles are:

1. When two chords intersect inside a circle, they create four line segments.

The product of the lengths of the two segments of one chord is equal to the product of the lengths of the two segments of the other chord.

2. When two secants intersect outside a circle, they create four line segments.

The product of the length of the secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.

3. When one secant and one tangent intersect outside a circle, they create three line segments.

The product of the length of the secant segment and its external segment is equal to the square of the length of the tangent segment.

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Answer: To calculate the amount of money you will have in the account after 40 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount of money in the account after t years, P is the principal (the initial amount of money deposited), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $2000, r = 0.02 (since the interest rate is 2%), n = 12 (since the interest is compounded monthly), and t = 40. Plugging these values into the formula, we get:

A = 2000(1 + 0.02/12)^(12*40)

A = $5,837.85

So you will have $5,837.85 in the account after 40 years.

The solution to the system of equations is:

x = -19/5, y = 2, z = 1/10

4x + 6y - 2z = 2 (multiply first equation by 2)

x + 2y - 3z = -5 (third equation)

Add the two equations, we get:

5x + 8y = -3 (eliminated z)

-7x + 7y - 6z = -33 (multiplying second equation by 3 and subtracting from the first)

3x + y + 2z = 12 (second equation)

Add these two equations, we have:

-4x + 8y = -21 (eliminated z)

5x + 8y = -3

5x = -8y - 3

x = (-8y - 3)/5

Substituting this expression for x into the second equation, we get:

3((-8y - 3)/5) + y + 2z = 12

z = (39/10) - (19/10)y

Finally, substituting these expressions for x and z into any of the original equations (let's use the first one), we can solve for y:

2((-8y - 3)/5) + 3y - ((39/10) - (19/10)y) = 1

Simplifying and solving for y, we get:

y = 2

x = (-8(2) - 3)/5 = -19/5

z = (39/10) - (19/10)(2) = 1/10

In conclusion, the solution to the system of equations is:

x = -19/5, y = 2, z = 1/10

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The solution to the given system of linear equations is

x = 3, y = -1 and z = 2

From the question, we are to solve the given system of linear equations.

The given system of linear equations is

2x + 3y − z = 1

3x + y + 2z = 12

x + 2y − 3z = −5

Multiply the third equation by 2

x + 2y − 3z = −5 ) ×2

2x + 4y - 6z = -10

Subtract the first equation from the resulting equation

  2x + 4y - 6z = -10

- (2x + 3y − z = 1

----------------------------------------

y - 5z = -11     ---------- (1)

Now,

Multiply the third equation by 3

x + 2y − 3z = −5 ) ×3

3x + 6y -9z = -15

Subtract the second equation from the resulting equation

 3x + 6y -9z = -15

- (3x + y + 2z = 12

-----------------------------------------

5y - 11z = -27     ----------- (2)

Solve equations (1) and (2) simultaneously

y - 5z = -11         ------------ (1)

5y - 11z = -27     ------------ (2)

Multiply equation (1) by 5

y - 5z = -11  ) ×5

5y - 25z = -55

Subtract the resulting equation from equation (2)

  5y - 11z = -27

-( 5y - 25z = -55

-----------------------------

14z = 28

Divide both sides by 14

14z/14 = 28/14

z = 2

Substitute the value of z into equation (1)

y - 5z = -11

y - 5(2) = -11

y - 10 = -11

Add 10 to both sides of the equation

y - 10 + 10 = -11 + 10

y = -1

Substitute the value of y and z into the third equation

x + 2y − 3z = −5

x + 2(-1) − 3(2) = −5

x - 2 - 6 = -5

x - 8 = -5

Add 8 to both sides of the equation

x - 8 + 8 = -5 + 8

x = 3

Hence,

The solution is

x = 3, y = -1 and z = 2

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Answer: 3

Step-by-step explanation:

You would need to use the Pythagorean theorem to solve this equation. 6 is the hypotenuse and 3[tex]\sqrt{3}[/tex] is the longer leg.  

a^2+b^2=c^2

c= hypotenuse

6^2=3[tex]\sqrt{3}[/tex]^2 + a^2

36=27+a^2

36-27=9

[tex]\sqrt{9}[/tex] = 3

Keara has climbed up to 41 feet in the tree.

Rounding off a value to the nearest tenth means finding the closest multiple of 0.1 to the given value. To do this, you need to look at the digit in the hundredths place. If the digit is 5 or greater, you round the tenths place up by 1. If the digit is less than 5, you leave the tenths place unchanged. For example, to round the value 3.874 to the nearest tenth, you would look at the digit in the hundredths place, which is 7. Since 7 is greater than 5, you round up the tenths place to 8, and the rounded value is 3.9. Rounding to the nearest tenth is often used when working with measurements or values that require a certain level of precision.

According to the range finders, the distance from Keara to her friend is 55 feet and the angle of depression from Keara to her friend is 40°.

From this the following diagram can be drawn.

Now, we need to find the length of AB which will denote how high Keara climbed.

We can use the trigonometric sine function to find the length of AB,

Sin 40° = opposite side / hypotenuse = AB/ BC = AB/ 55

Hence AB = 55 × Sin 40° ≈ 40.981

That is she would have climbed approximately 41 feet.

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The solution of the system of equations given y = -6x + 5 and 4x - y = 5,  is (1, -1).

To solve this system of equations, we can use the substitution method. We can rearrange the first equation to solve for y in terms of x:

y = -6x + 5

Next, we can substitute this expression for y in the second equation:

4x - (-6x + 5) = 5

Simplifying this equation, we get:

4x + 6x - 5 = 5

Combining like terms, we get:

10x = 10

Dividing both sides by 10, we get:

x = 1

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Using the first equation, we get:

y = -6(1) + 5 = -1

Therefore, the solution of the system of equations is (1, -1). This means that the two equations intersect at the point (1, -1) on the coordinate plane, and this is the only point that satisfies both equations simultaneously.

In summary, to solve the system of equations y = -6x + 5 and 4x - y = 5, we used the substitution method to find that the solution is (1, -1).

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Answer:

5)

$332.19

6)

$16,857.36

7)

$248.91

Step-by-step explanation:

monthly premium = Base Rate * [tex]\frac{Monthly Payroll}{100}[/tex]

5)

given:

Base rate = $2.24
Monthly payroll = $14,830.00

unknown = monthly premium

 [tex]2.24 * \frac{14,830.00}{100}[/tex] = $332.192≈$332.19

6)

given:

Base rate = $19.89
Monthly payroll = $84,752.96

unknown = monthly premium

[tex]19.89 * \frac{84,752.96}{100}[/tex] = $16,857.364≈$16,857.36

7)

given:

Base rate = $2.90
Monthly payroll = $8,582.94

unknown = monthly premium

[tex]2.90 * \frac{8,582.94}{100}[/tex]=$248.90526≈$248.91

a) The break-even point for the division is: 4000 units

b) The level of sales for 10% profit is: 4681 units

The break-even point is defined as the point at which total cost and total revenue are equal, meaning there is no loss or gain for your small business. In other words, you've reached the level of production at which the costs of production equals the revenues for a product.

a) We are told that:

Selling price for income tax app = $8

Monthly fixed cost = $20000

Variable cost producing each app = $3

Thus:

8x = 3x + 20000

5x = 20000

x = 4000 units

b) 8x = 1.1(3x + 20000)

8x = 3.3x + 22000

4.7x = 22000

47x =220000

x = 4681 units

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Missing questions are:

(a) Find the break-even point for the division.

(x,y)=

(b) What should be the level of sales in order for the division to realize a 10% profit over the cost of making the income tax apps? (Round your answer up to the nearest whole number.)

Applying the intersecting secants theorem, the value of x is calculated as: x = 5.

According to the intersecting secants theorem, if two secant lines intersect outside of a circle, then the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.

Using the theorem, the equation below is created to find the value of x:

4(4 + 5) = (x - 2)(x - 2 + x + 4)

4(9) = (x - 2)(2x + 2)

36 = 2x² - 2x - 4

2x² - 2x - 4 - 36 = 0

2x² - 2x - 40 = 0

Factorize:

(x + 4)(x - 5) = 0

x = -4 or x = 5

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Answer:

Once a person has identified the ways they are wasting money, there are several steps they can take to stop wasting money and start saving it:

By taking these steps, a person can stop wasting money and start building a solid financial foundation for the future.

After answering the presented question, we may conclude that  As a percentage result, around 74.43 grammes of the drug will remain after 18 hours.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also used on occasion. However, it is commonly indicated using the percent symbol "%." The % amount has no dimensions. Percentages are just fractions with a denominator of 100. Place a percent sign (%) next to a number to indicate that it is a percentage. For example, if you answer 75 out of 100 questions properly on a test (75/100), you score a 75%. Divide the money by the total and multiply the result by 100 to calculate percentages. The percentage is derived by multiplying (value/total) by 100%.

A substance's radioactive decay rate is expressed as a percentage per unit time. This indicates that the amount of material left after each unit of time will be lowered by the set percentage.

We may use the exponential decay formula to this problem:

[tex]N(t) = N_0 * e^{(-kt)}[/tex]

where:

N₀  = starting drug quantity

N(t) = the amount of material that remains after time. t k = decay constant (related to decay rate)

t = the amount of time that has passed

To calculate the amount of material left after 18 hours, we must first determine the value of k. Using the rate of decay stated in the issue, we may accomplish the following:

[tex]3.75% = k * 1 hour\\k = 0.0375/hour\\N(18) = 150 * e^{(-0.0375*18)}\\N(18) = 74.43 grams \\[/tex]

As a result, around 74.43 grammes of the drug will remain after 18 hours.

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The quadratic equation written in vertex form is:

y = (x + 1)^2 - 9

A quadratic equation with a leading coefficient a and a vertex (h, k) can be written as:

y = a*(x - h)^2 + k

On the graph we can see that the vertex is at (-1, -9), then we have:

y = a*(x + 1)^2 - 9

Now we also can see that the y-intercept is y = -8, then evaluating in zero we should get:

-8 = a*(0 + 1)^2 - 9

-8 = a - 9

-8 + 9 = a = 1

The quadratic equation is:

y = (x + 1)^2 - 9

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The mass of the triangular region with density function ρ(x,y) = [tex]x^2 + y^2 is 136/375.[/tex]

A triangle is a three-sided polygon made up of three line segments that connect at three endpoints, called vertices. The study of triangles is an important part of geometry, and it has applications in various fields such as engineering, architecture, physics, and computer graphics.

The mass of a 2D region with variable density can be calculated using the double integral formula:

m = ∬R ρ(x,y) dA

where R is the region of integration, ρ(x,y) is the density function, and dA is the area element.

In this case, we have a triangular region with vertices (0, 0), (4, 0), and (0, 2), and the density function is ρ(x,y) = [tex]x^2 + y^2.[/tex]To set up the double integral, we need to determine the limits of integration for x and y.

Since the triangular region is bounded by the lines y = 0, y = 2, and x = (2/5)y, we can set up the integral as follows:

m = ∫0 ∫[tex]0^[/tex](2/5)y ([tex]x^2 + y^2)[/tex] dxdy

Integrating with respect to x first, we get:

m = ∫[tex]0^2 [(x^3/3) + xy^2]_0^(2/5[/tex])y dy

m = ∫[tex]0^2 [(8/375)y^5 + (4/15)y^3][/tex]dy

Evaluating the integral, we get:

m = [tex][(2/1875)y^6 + (2/5)y^4]_0^2[/tex]

m = (64/1875) + (16/5)

m = 136/375

Therefore, the mass of the triangular region with density function ρ(x,y) = [tex]x^2 + y^2 is 136/375.[/tex]

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The total number of 6 tickets will be earned when 54 points are earned.

Given that the total number of tickets earned for 9 points was earned = 1 ticket

the tickets earned when every 18 points are earned = 2 tickets

the tickets earned when every 27 points are earned = 3 tickets

Let's divide the points by tickets to find out how many points are earned for each ticket.

9/1 = 18/2 = 27/3 = 9

This shows for every ticket 9 points are earned. So, to find out the no. of tickets for 54 points, we can divide the 54 by 9.

no. of tickets earned for 54 points = 54/9 = 6 tickets.

From the above analysis, we can conclude that the 6 tickets are earned for 54 points.

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A square root function that is represented by the graph include the following: A. f(x) = √(4x + 8).

In Mathematics and Geometry, a square root function can be defined as a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

Therefore, the required square root function is given by;

f(x) = √(4x + 8)

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The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

you did not provide enough information to answer the question

Answer:

A. m∠X = 50°, AC = 3 cm

Step-by-step explanation:

If ABC is congruent to XYZ then the corresponding angle and sides are congruent so:

∠A = ∠X

∠B = ∠Y

∠C = ∠Z

and

AB = XY

BC = YZ

AC = XZ

Because we know m∠A is 50° and ∠A and ∠X are congruent then m∠X is also 50°

And because we know XZ is equal to 3 cm and XZ and AC are congruent  then AC is also 3 cm

The amount after 5 years with a principal of $5000 compounded quarterly at an interest rate of 2.25% annually is $5593.60 approximately.

Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment but also on any accumulated interest from previous periods. In other words, it's the interest earned on the principal amount plus any interest earned previously.

To calculate the amount after 5 years, we need to use the formula for compound interest:

A = P × {1 + r ÷ (n × 100)} ∧ (n × t)

where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $5000, r = 2.25% , n = 4 (since interest is compounded quarterly), and t = 5.

After applying these values, we get:

A = $5000 x (1 + 2.25/400) ⁴ ˣ ⁵

A = $5000 x (1.005625) ²⁰

A = $5000 x 1.1871955

A = $5593.60 (rounded off to 2 decimals)

Therefore, the amount after 5 years with a principal of $5000 compounded quarterly at an interest rate of 2.25% annually is $5593.60 approximately.

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Answer:

Volume = (1/2)(7)(24)(22) =

1,848 cubic meters

Surface area = 2(1/2)(7)(24) + 7(22) + 22(24) + 22(25) = 1,400 square meters

Dear Editor,


I am writing to express my concern about the issue of leakages in Zambia. The constant leakages of natural resources such as oil, gas and minerals have been a major setback to the country's economic growth and development.


It is disheartening to note that despite the country being rich in natural resources, the benefits of these resources have not been fully realized due to leakages. This has led to a loss of revenue that could have been used to improve the lives of citizens through investments in education, healthcare, and infrastructure.


Furthermore, leakages also have negative environmental impacts, which can affect the health and wellbeing of communities living in the vicinity of these resources.


As a concerned citizen, I urge the government to take decisive action to curb leakages and ensure that the country's natural resources are utilized for the benefit of all Zambians.


Sincerely, [Your Name]

Given:

[tex]\vec F_{1} =27 \ N[/tex]

[tex]\vec F_{2} =24 \ N[/tex]

[tex]\vec a_{1} = 9 \ m/s^2[/tex]

Find:

[tex]\vec a_{2} = ?? \ m/s^2[/tex]

We know that [tex]\vec F= m \vec a[/tex]. Use [tex]\vec F_{1}[/tex] and [tex]\vec a_{1}[/tex] to find mass, m.

[tex]\Longrightarrow \vec F_{1} = m \vec a_{1} \Longrightarrow 27= m(9) \Longrightarrow m= \frac{27}{9} \Longrightarrow m= \boxed{ 3 \ kg }[/tex]

We now know the mass of the moving object we can now find [tex]\vec a_{2}[/tex].

[tex]\Longrightarrow \vec F_{2} = m \vec a_{2} \Longrightarrow 24= (3) \vec a_{2} \Longrightarrow \vec a_{2}= \frac{24}{3} \Longrightarrow \vec a_{2}= \boxed{ 8 \ m/s^2 } \ \therefore \ Sol.[/tex]

Answer:

The mean of the numbers 5, 3, 6, x, 9, and 10 is given as 7.

To find the value of x, we can use the formula for the mean:

mean = (sum of all the numbers) / (number of numbers)

In this case, we have:

7 = (5 + 3 + 6 + x + 9 + 10) / 6

Multiplying both sides of the equation by 6, we get:

42 = 33 + x

Subtracting 33 from both sides of the equation, we get:

x = 9

Therefore, the value of x that makes the mean of 5, 3, 6, x, 9, and 10 equal to 7 is 9.

The average age of all the customers in the store, given the percentages that are parents and not, is 39.2 years.

To answer this question, we will use a weighted average formula. Since the percentage of parents and non-parents is given, we can use these percentages as weights.

Weighted Average Age = (Weight for Parents x Average Age of Parents) + (Weight for Non-Parents x Average Age of Non-Parents)

Parents:

Percentage (weight) = 60% = 0.60

Average age = 52 years

Non-Parents:

Percentage (weight) = 40% = 0.40

Average age = 20 years

Weighted Average Age = (0.60 x 52) + (0.40 x 20)

Weighted Average Age = 39.2 years

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The full question is:

At the store, 60% of the customers are parents and 40% of the customers are not. The average age of the parents is 52 years old. The average age of those not parents is 20 years old.

What is the average age of all the customers at the store?

Answer:

D. 263 degrees

Step-by-step explanation:

We know that central angles are congruent to the arcs they encompass or intercept. So, if the minor arc is 97 degrees, and the total measure of a circle's arcs are 360 degrees, then the major arc is 263 degrees.

Therefore, the answer is D.

The condensed form of the expression abc x abc x abc is (abc)^3

When we have the same base raised to different exponents that are being multiplied together, we can simplify or condense the expression by adding the exponents.

In this case, we have the same base "abc" being raised to the exponent of 1 three times, so we can write it as:

abc x abc x abc

To condense this expression, we add the exponents 1+1+1=3, and write it as:

(abc)^3

So, the condensed form of the expression "abc x abc x abc" is "(abc)^3".

This is an example of the exponent rule for multiplying powers with the same base.

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