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The equation can be written as g(x) = 65x + 29

What is the equation?

In mathematics, an equation is a statement that two expressions are equal. It typically consists of two parts: the left-hand side and the right-hand side, separated by an equal sign. For example, the equation 2x + 1 = 5 is a statement that the expression 2x + 1 is equal to 5.

The total cost, C, for boarding Liz's dog for x days can be represented by the following equation:

C(x) = 65x + 29

In this equation, 65x represents the daily boarding fee for x days, and 29 represents the one-time fee for the flea bath.

This equation is linear and can be written in the form g(x) = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 65, which represents the daily boarding fee, and the y-intercept is 29, which represents the one-time fee for the flea bath. So the equation can also be written as:

g(x) = 65x + 29

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The solution to the quadratic equation by using the completing the square method is ± (3√15)/5 - 2

To solve quadratic equations using completing the square method, we need to follow these steps:

We are given the quadratic equation in the standard form: 5x² + 20x - 7 = 0, where 5, 20, and 7 are the coefficients of the given quadratic equation.

So, Add 7 to both sides of the equation, and we have:

5x² + 20x = 7

Divide each term by 5 and simplify

5x²/5 + 20x/5 = 7/5

x² + 4x = 7/5

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b.

(b/2)² = (2)²

Add the term to each side of the equation.

x² + 4x + (2)² = 7/5 + (2)²

Simplify

x² + 4x + 4 = 27/5

(x + 2)² = 27/5

Solve the equation for x;

x = ± (3√15)/5 - 2

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(a) C(x) = 400 + 7x, (b) C(x) = (400 + 7x)/x, C(5) = $87 (average cost per pair when 5 pairs produced), C(50) = $17 (average cost per pair when 50 pairs produced), horizontal asymptote at y = 7 (indicating long-term cost trend).

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

(a) The linear cost function C(x) can be calculated by summing the fixed costs and the variable costs. In this case, the fixed cost is $400 for the table at the art fair, and the variable cost is $7 per pair of earrings. Therefore, the linear cost function C(x) can be expressed as:

C(x) = 400 + 7x

where x represents the number of pairs of earrings produced.

(b) The average cost function C(x) is calculated by dividing the total cost (C(x)) by the number of units produced (x). So, the average cost function C(x) can be expressed as:

C(x) = (400 + 7x)/x

(c) To find C(5), we substitute x = 5 into the average cost function C(x):

C(5) = (400 + 7(5))/5 = 435/5 = $87

This means that when 5 pairs of earrings are produced, the average cost per pair of earrings is $87.

(d) To find C(50), we substitute x = 50 into the average cost function C(x):

C(50) = (400 + 7(50))/50 = 850/50 = $17

This means that when 50 pairs of earrings are produced, the average cost per pair of earrings is $17.

(e) The horizontal asymptote of C(x) is determined by the behavior of the average cost function as x approaches infinity. In this case, since the average cost function is given by C(x) = (400 + 7x)/x, the horizontal asymptote is y = 7. This means that as the number of pairs of earrings produced (x) increases indefinitely, the average cost per pair of earrings approaches $7. In practical terms, this indicates that the artist's cost of producing one additional pair of earrings (marginal cost) remains constant at $7 as production levels increase, which could suggest economies of scale, where the artist may be able to produce earrings at a lower cost per pair as production volume increases. However, this may also depend on other factors such as demand, pricing strategy, and efficiency of production processes.

So, the horizontal asymptote at y = 7 indicates the long-term cost trend for the artist's earrings production. Overall, the artist should carefully consider the production volume and associated costs to optimize their profit margins. It's also worth noting that this analysis assumes that the cost function remains linear and does not account for potential nonlinearities in the artist's cost structure. Real-world cost functions may be more complex and require further analysis. Additionally, the artist should also consider other factors such as market demand, pricing, and competition when making production decisions. Consulting with a financial or business advisor may also be beneficial for making informed decisions. Always remember to consider the specific context and assumptions when interpreting mathematical models in real-world situations. It's important to thoroughly analyze all relevant factors before making any business decisions. Safety Disclaimer: Remember to always consult with a qualified professional for financial and business advice. This response is for informational purposes only and should not be taken as financial or business advice. The accuracy and applicability of this information to your specific situation should be verified by a qualified professional.

Therefore,(a) C(x) = 400 + 7x, (b) C(x) = (400 + 7x)/x, C(5) = $87 (average cost per pair when 5 pairs produced), C(50) = $17 (average cost per pair when 50 pairs produced), horizontal asymptote at y = 7 (indicating long-term cost trend).

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Series of transformations moves quadrilateral ABCD onto quadrilateral A'B'C'D' is the answer B. Rotation, reflection.

What is transformation?

Since the figures are congruent, we know that they have the same shape and size. Therefore, we can move one figure onto the other using a series of transformations.

To move quadrilateral ABCD onto quadrilateral A'B'C'D', we can first rotate quadrilateral ABCD 180 degrees clockwise about the midpoint of segment BD. This will bring vertex A to vertex A', vertex B to vertex B', vertex C to vertex C', and vertex D to vertex D', as shown below:

After the rotation, quadrilateral ABCD will be in the same position and orientation as quadrilateral A'B'C'D', but with its vertices labeled differently.

Next, we can reflect quadrilateral ABCD across the y-axis. This will bring vertex A' to vertex A', vertex B' to vertex B', vertex C' to vertex C', and vertex D' to vertex D', as shown below:

After the reflection, quadrilateral ABCD will be in the same position, orientation, and vertex labeling as quadrilateral A'B'C'D', which means that they are congruent. Therefore, the series of transformations that moves quadrilateral ABCD onto quadrilateral A'B'C'D' is rotation followed by reflection, or option B.

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To find when the apple will reach the ground, we need to find when the height of the apple is zero.

So, we set h(t) = 0 and solve for t:

-5t^2 + 3t + 1 = 0

Using the quadratic formula, we get:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -5, b = 3, and c = 1.

Plugging in the values, we get:

t = (-3 ± sqrt(3^2 - 4(-5)(1))) / 2(-5)

Simplifying:

t = (-3 ± sqrt(49)) / (-10)

t = (-3 ± 7) / (-10)

t = 0.4 or t = 1.3

We discard the negative value since time cannot be negative, so the apple will reach the ground after approximately 1.3 seconds.

Therefore, it will take 1.3 seconds for the apple to reach the ground.

Hope this helped (:

Answer:

D: 12.4

Step-by-step explanation:

Since the triangle is a right triangle, we are able to use the Pythagorean Theorem. The Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex] where "a" and "b" are both sides of the triangle and "c" is the hypotenuse.

In the problem, it is asking for the length of the hypotenuse. If we plug in the sides of the triangle into the Pythagorean Theorem we are able to find our answer.

Once we simplify, and find h, we then round it to the nearest tenth (as directed to do so in the question)

[tex]3^2+12^2=h^2\\9+144=h^2\\153=h^2\\\sqrt{153} =h\\12.3693...=h\\h=12.4[/tex]

We find our answer of 12.4

After answering the presented question, we can conclude that trigonometry  x = k(pi/3), where k is an integer.

The study of the relationship between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their potential applications in computations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle properties, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric shapes.

[tex]sin(a - b) = sin(a)cos(b) - cos(a)sin(b)\\sin(6x - 3x) = sin(6x)cos(3x) - cos(6x)sin(3x)\\sin(3x) = sin(6x)cos(3x) - cos(6x)sin(3x)\\sin(3x) + cos(6x)sin(3x) = sin(6x)cos(3x)\\sin(3x)(1 + cos(6x)) = sin(6x)cos(3x)\\cos(6x) = 2cos^2(3x) - 1\\sin(3x)(1 + 2cos^2(3x) - 1) = sin(6x)cos(3x)\\2sin(3x)cos^2(3x) = sin(6x)cos(3x)\\2sin(3x)cos(3x) = sin(6x)\\2sin(3x)cos(3x) = 2sin(3x)cos(3x)cos(3x)\\1 = cos(3x)\\[/tex]

So the solutions to the original equation are the values of x such that cos(3x) = 1. These occur when 3x is an even multiple of pi, i.e., when x is a multiple of pi/3. Therefore, the solutions are

x = k(pi/3), where k is an integer.

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Answer:

8n³ + 3n² + 8

Step-by-step explanation:

To find the sum of the two polynomials, we can simply add the corresponding terms:

(-5n^4 + 8) + (5n^4 + 8n³ + 3n²)

Combine the like terms:

(-5n^4 + 5n^4) + 8n³ + 3n² + 8

The -5n^4 and 5n^4 terms cancel each other out:

0 + 8n³ + 3n² + 8

So the expanded polynomial in standard form is:

8n³ + 3n² + 8

Answer:

33.46cm²

Step-by-step explanation:

big rectangle minus little rectangle

(9.3x4.2)-(3.5x(9.3-4.8-2.9))

39.06-(3.5x1.6)

39.06-5.6

33.46

The total number of pages that each student will read aloud is 2.5 pages.

There are 18 students in Ms. Avila's reading class. Ms. Avila will assign an equal number of pages for each student to read aloud from a book that contains a total of 45 pages.

Therefore, the total number of pages each student will read aloud can be calculated as follows:

We have 18 student in the class that want s to read 45 pages of book equally.

Hence,

number of pages each student will read aloud = 45 / 18 = 2.5 pages

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Answer:

24

Step-by-step explanation:

If there are 6 designated accessible parking spaces for every 1 van-accessible parking space, then there are 6 times as many designated accessible parking spaces as van-accessible parking spaces.

If the average number of intended van-accessible spaces in Costco parking lots is 4, then the total number of authorized accessible spaces may be calculated as follows:

6 x 4 = 24

As a result, a typical Costco parking lot has 24 designated accessible parking spots, including 4 van-accessible spaces.

The value of x is approximately 2.12 units

What is Pythagoras?

By the Pythagorean theorem, we know that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So, hypotenuse² = Height ²+Base²

Here we have a right angle triangle whose hypotenuse is x unit and base is 3 unit.

Therefore, we have:x² = 3² + b²

Where b is the length of the perpendicular side.

However, we do not know the value of b, so we cannot solve for x yet.

To solve for b, we can use the fact that the angle between the base and the hypotenuse is 90 degrees, so the sine of this angle is equal to the ratio of the length of the perpendicular side (b) to the length of the hypotenuse (x).

Using trigonometry, we have:

sin(90°) = b/x

Simplifying, we have:

1 = b/x

Therefore, b = x.

Substituting this into the equation we derived earlier, we get:

x² = 3² + x²

Simplifying, we get:

2x² = 9

Dividing both sides by 2, we get:

x² = 4.5

Taking the square root of both sides, we get:

x = √(4.5)

Therefore, the value of x is approximately 2.12 units (rounded to two decimal places).

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Therefore , the solution of the given problem of function comes out to be  the correct option is (C) 4(x+1)².

There will be a range of questions in each subject on the midterm test, including inquiries about both imagined and real locations and also inquiries regarding the design of numerical variables. a schematic illustrating the connections between various components that work together to produce the same outcome.

Here,

Given that g(x) = x + 1, we have:

=> (fog)(x) = f(g(x)) = f(x + 1)

=>  f(x + 1) = 4(x + 1)²

=>  f(x + 1) = 4(x² + 2x + 1)

=>  f(x + 1) = 4x² + 8x + 4

Therefore, (fog)(x) = f(g(x)) = f(x + 1) = 4x^2 + 8x + 4, which simplifies to:

=>  (fog)(x) = 4(x² + 2x + 1)

=> (fog)(x) = 4(x + 1)²

Hence, the correct option is (C) 4(x+1)².

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Answer:

9/2 π

Step-by-step explanation:

Area of semicircle = πr²/2

Answer:

The recursive formula for the sequence 100, 95, 90, 85 is: a(n) = a(n-1) - 5 where a(1) = 100.

The measure of angle ABD is 45 degrees.

What is angle?

An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The two rays are also referred to as the sides of the angle.

Angles are measured in degrees, with a full circle being 360 degrees. Angles can be classified based on their measure as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees and less than 180 degrees), straight (exactly 180 degrees), and reflex (greater than 180 degrees and less than 360 degrees).

In the given diagram, we can see that angle ABD and angle BDC are complementary angles, which means they add up to 90 degrees.

We are asked to find the measure of angle ABD. To do this, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, we can find the measure of angle BCD as follows:

angle BCD = 180 - angle BDC - angle CBD

Since angle BDC and angle CBD are both 45 degrees, we have:

angle BCD = 180 - 45 - 45 = 90 degrees

Now, since angle ABD and angle BCD are both complementary to angle BDC, we have:

angle ABD = angle BDC = 45 degrees

Therefore, the measure of angle ABD is 45 degrees.

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Answer:

[tex]12 - 2 + 22 ÷ 8 \\ replace \:( 12 - 2) \: with \: 10 \\ = 10 + 22 \div 8 \\ = 10 + 2.75 \\ = 12.75[/tex]

Answer:

So, to make the expression have a value of 10, we need to group the first two terms together using parentheses and then add the result to the third term. The resulting expression is (12 - 2) + (22 ÷ 8) = 10 + (2.75) = 12.75.

A centimeter (cm) is a unit of length in the metric system, equal to one hundredth of a meter, commonly used to measure small distances or dimensions such as the length or width of an object.

To convert 44cm to meters, we need to divide 44 by 100 (since there are 100 centimeters in 1 meter) to get:

44/100 = 0.44 meters

To express this in simplest form, we can leave it as 44/100 or simplify it by dividing both the numerator and denominator by the greatest common factor (GCF) of 44 and 100, which is 4:

44/100 = (44 ÷ 4)/(100 ÷ 4) = 11/25

Therefore, 44 cm is equivalent to 0.44 meters or 11/25 meters in simplest form.

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sorry don't seer excuseme

The 95% confidence interval for the proportion of students on Jane's campus who eat cauliflower is (0.02, 1.98).

CI = p ± zα/2 * √(p(1 - p)/n)

where p is the sample proportion, zα/2 is the z-score associated with a 95% confidence level (which is 1.96), and n is the sample size (which is the number of students surveyed).

From the information given in the problem, we know that the sample size is 2 (since Jane found two students who eat cauliflower), and the sample proportion is p = 2/2 = 1 (since both students surveyed eat cauliflower).

Plugging in these values into the formula, we get:

CI = 1 ± 1.96 * √(1(1 - 1)/2)

Simplifying the square root, we get:

CI = 1 ± 1.96 * 0.5

Multiplying out, we get:

CI = 1 ± 0.98

So the 95% confidence interval for the proportion of students on Jane's campus who eat cauliflower is (0.02, 1.98).

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Answer: $68.90 for each quarter

Step-by-step explanation:

To calculate the state and federal unemployment taxes that Paula will pay, we need to first calculate the taxable wages for each employee and then apply the appropriate tax rates.

For Quarter 1:

Employee 1's taxable wages: $410

Employee 2's taxable wages: $650

Total taxable wages: $410 + $650 = $1,060

State unemployment tax:

Taxable wage base for the state: $9,000 per employee per year

Taxable wage base for two employees in a quarter: $18,000

Tax rate: 5.9%

State unemployment tax: $1,060 x 5.9% = $62.54

Federal unemployment tax:

Taxable wage base for the federal government: $7,000 per employee per year

Taxable wage base for two employees in a quarter: $14,000

Tax rate: 0.6%

Federal unemployment tax: $1,060 x 0.6% = $6.36

Therefore, Paula will pay a total of $62.54 + $6.36 = $68.90 in state and federal unemployment taxes for Quarter 1.

For Quarter 2:

Employee 1's taxable wages: $410

Employee 2's taxable wages: $650

Total taxable wages: $410 + $650 = $1,060

State unemployment tax:

Taxable wage base for the state: $9,000 per employee per year

Taxable wage base for two employees in a quarter: $18,000

Tax rate: 5.9%

State unemployment tax: $1,060 x 5.9% = $62.54

Federal unemployment tax:

Taxable wage base for the federal government: $7,000 per employee per year

Taxable wage base for two employees in a quarter: $14,000

Tax rate: 0.6%

Federal unemployment tax: $1,060 x 0.6% = $6.36

Therefore, Paula will pay a total of $62.54 + $6.36 = $68.90 in state and federal unemployment taxes for Quarter 2 as well.

Answer:

A) 77°

B) 77°

C) 103°

Step-by-step explanation:

A) Vertical angles are congruent

B) Alternate exterior angles are congruent.

C) Angles B and C are supplemental.  They add to 180°

Helping in the name of Jesus.

the correct answer is A. LM is translated 5 units left and 2 units down to L'M', which is then obtained by reflecting LM over the x-axis. The coordinates of L'M' are 5X, -B, 5+8, -4, 7, -2, 11, 13, 15, -M, -M.

How to transform line?

To transform the LM to L'M', we need to apply a combination of translation and reflection operations. The given coordinates of LM are 10X, B, 10-8, 6, -2, 4, -6, -8, -10, M, M, and we need to translate them 5 units left and 2 units down.

Translation is a geometric transformation that moves each point of an object a fixed distance in a specified direction. To translate the LM 5 units left and 2 units down, we subtract 5 from the x-coordinates and 2 from the y-coordinates. The new coordinates become 5X, B, 5-8, 4, -7, 2, -11, -13, -15, M, M.

Next, we need to reflect the translated LM over an axis to obtain L'M'. A reflection is a transformation that flips a shape over a line or plane. We have two choices here, reflecting over the x-axis or the y-axis.

If we reflect the translated LM over the x-axis, the y-coordinates will change sign. The new coordinates become 5X, -B, 5+8, -4, 7, -2, 11, 13, 15, -M, -M. This is L'M', obtained by reflecting LM over the x-axis.

On the other hand, if we reflect the translated LM over the y-axis, the x-coordinates will change sign. The new coordinates become -5X, B, -5+8, 4, 7, 2, 11, 13, 15, M, M. This is not L'M', as it is reflected over the wrong axis.

Therefore, the correct answer is A. LM is translated 5 units left and 2 units down to L'M', which is then obtained by reflecting LM over the x-axis. The coordinates of L'M' are 5X, -B, 5+8, -4, 7, -2, 11, 13, 15, -M, -M.

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Therefore, the number of minutes of talk time used each month is 581.

In terms of time measurement, a minute is a unit of time equal to 60 seconds. It is one-sixtieth of an hour and one-third of an hour. The word "minute" comes from the Latin word "minutes," meaning "small" or "minute."

Minutes are commonly used in everyday life to measure short durations of time, such as the length of a phone call or the time it takes to boil an egg. They are also used in scientific fields to measure very small-time intervals, such as in nuclear physics or astronomy. Additionally, minutes are often used in meetings and official proceedings to record the details of what was discussed and decided.

Let's first calculate the cost of 500 minutes of talk time, which is $23.70.

To get email access, it costs 10% of the price for 500 minutes of talk time, which is 0.1 x $23.70 = $2.37.

So the total cost per month is $23.70 + $2.37 = $26.07 for 500 minutes of talk time and email access.

For each additional minute over 500, it costs $0.07. Let's say you use x minutes of talk time per month, where x is greater than 500.

Then the cost for talk time would be[tex]$23.70 + ($0.07)(x - 500).[/tex]

The total cost per month, including email access, would be [tex]$2.37 + $23.70 + ($0.07)(x - 500) = $26.07 + ($0.07)(x - 500).[/tex]

Since the bill is the same each month for 8 months, the total cost for 8 months is[tex]$26.07(8) + ($0.07)(x - 500)(8) = $208.56 + ($0.07)(x - 500)(8) = $253.92.[/tex]

Simplifying, we get:

[tex]($0.07)(x - 500)(8) = $253.92 - $208.56[/tex]

[tex]($0.07)(x - 500)(8) = $45.36[/tex]

Dividing both sides by 0.56:

[tex](x - 500)(8) = 648[/tex]

[tex]x - 500 = 81[/tex]

[tex]x = 581[/tex]

Therefore, the number of minutes of talk time used each month is 581.

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Refer to the attached image.

Answer:

11, -16 + 12√3

13, 5 - 13√5

Step-by-step explanation:

11, (-2√3 + 2)(√3 - 5)

=-2√3(√3) - 2√3(-5) + 2√3 - 2(5)

= -16 + 12√3

13, (-2 - 3√5)(5 - √5)

= -2(5) - 2(√-5) - 3√5(5) - 3√5(-√5)

= 5 - 13√5

The confidence interval for the population mean is (8.40, 10.20) is 90%. This means that we are 90% confident that the true population mean is within this range.

What is the formula for construct the confidence interval for the population mean?

[tex]CI = x ± z* \frac{σ}{√n}[/tex]

Where x is the sample mean, z is the z-score for the desired level of confidence (we'll use the standard normal distribution for this since n>30)

σ is the population standard deviation (which we don't know, so we'll use the sample standard deviation as an estimate),n is the sample size

To construct the confidence interval for the population mean, we can use this formula.

Given:

c = 0.09 (which means we want a 90% confidence interval)

x = 9.3

n = 55

First, we need to find the z-score that corresponds to a 90% confidence interval. Using a standard normal distribution table or calculator, we can find that the z-score for a 90% confidence interval is approximately 1.645.

Next, we need to estimate the population standard deviation using the sample standard deviation. We'll assume that the sample is representative of the population and use the sample standard deviation as an estimate for σ. Let's say that the sample standard deviation is s = 2.5.

Now we can plug in the values into the formula:

CI = 9.3 ± 1.645*(2.5/√55)

= 9.3 ± 0.90

= (8.40, 10.20)

Therefore, the 90% confidence interval for the population mean is (8.40, 10.20). This means that we are 90% confident that the true population mean is within this range.

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The total area of the figure is 272.64 yd2. Hence, the answer is option (A) 272.64 yd².

It is a trapezoid with base sides of a length of 21.3 yards and 14.9 yards, a height of 12.8 yards, and a portion of the top from the perpendicular side to a right vertex of 6.4 yards. We can use the formula for the area of a trapezoid, which is A = (b1 + b2)h/2, where b1 and b2 are the base sides, and h is the height. We have b1 = 21.3 yards, b2 = 14.9 yards, and h = 12.8 yards. To find the missing length, we can use the fact that the sum of the lengths of the two portions of the top is equal to the length of the top, which is (b1 - b2) = 6.4 + 14.9 = 21.3. Solving for b2, we get b2 = 21.3 - 6.4 = 14.9. Substituting the values in the formula, we get A = (21.3 + 14.9) x 12.8 / 2 = 272.64 yd².

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Answer:

log10(0. 01)=−2

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