City A and City B had two different temperatures on a particular day. On that day, four times the temperature of City A was 7° C more than three times the temperature of City B. The temperature of City A minus three times the temperature of City B was −5° C. The following system of equations models this scenario:

4x = 7 + 3y
x − 3y = −5

What was the temperature of City A and City B on that day?

The Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 for 0 ≤ x ≤ 0.9 is approximately 0.000129.

To find the Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0, we need to find the maximum value of the fifth derivative of [tex]e^x[/tex] on the interval [0, 0.9].

Since the nth derivative of [tex]e^x[/tex] is [tex]e^x[/tex] for all n, the fifth derivative is also [tex]e^x[/tex]. To find the maximum value of[tex]e^x[/tex]on the interval [0, 0.9].

We evaluate [tex]e^x[/tex] at the endpoints and at the critical point x = 0.45, which is the midpoint of the interval:

[tex]e^0[/tex] = 1

[tex]e^0.9[/tex]≈ 2.4596

[tex]e^0.45[/tex] ≈ 1.5684

The maximum value of [tex]e^x[/tex] on the interval [0, 0.9] is approximately 2.4596.

The Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 is given by:

E₄(x) ≤ (M/5!)[tex]|x-0|^5[/tex]

where M is the maximum value of the fifth derivative of [tex]e^x[/tex] on the interval [0, 0.9].

So, we have:

E₄(x) ≤ (2.4596/5!) [tex]|x|^5[/tex] for 0 ≤ x ≤ 0.9

Substituting x = 0.9 into this inequality, we get:

E₄(0.9) ≤ (2.4596/5!)[tex](0.9)^5[/tex] ≈ 0.000129

Therefore, the Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 for 0 ≤ x ≤ 0.9 is approximately 0.000129.

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The probability of selecting an M&M that is not red is 11/15.To find the probability of selecting an M&M that is not red, we need to first find the total number of M&Ms in the bag,

It is the sum of the number of M&Ms of each color: 4 + 8 + 6 + 12 = 30.

Next, we need to find the number of M&Ms that are not red, which is the sum of the number of M&Ms of all other colors: 4 + 6 + 12 = 22.

Therefore, the probability of selecting an M&M that is not red is 22/30, which can be simplified by dividing both the numerator and the denominator by 2:

22/30 = 11/15

So the probability of selecting an M&M that is not red is 11/15.

In other words, there is an 11/15 chance that the selected M&M will be blue, orange, or green, and a 4/15 chance that it will be red.It is important to note that this assumes that each M&M is equally likely to be selected, and that the bag is well-mixed so that each M&M has an equal chance of being chosen.

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Answer:

The radius of the basketball is 20 cm.

Step-by-step explanation:

The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.

We are given that the volume of the basketball is 11488.2 cm, so we can set up the equation:

Simplifying, we get:

Dividing both sides by (4/3)π, we get:

Taking the cube root of both sides, we get:

Rounding to the nearest whole number, the radius of the basketball is 20 cm.

The value of x and y is 11 and 4 respectively

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also sometimes called inscribed quadrilateral.

A theorem in circle geometry states that the sum of opposite angles in a cyclic quadrilateral are supplementary. i.e they sum up to give 180.

10x + 16y+6 = 180

10x+16y = 174... eqn1

4+18y +10x-6 = 180

18y +10x = 182... eqn2

subtract equation 1 from 2

2y = 8

y = 8/2 = 4

Subtitle 4 for y in equation 1

10x+ 16(4)= 174

10x= 174-64

10x = 110

x= 110/10

x = 11

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To find the annual rate at which the car depreciated, we need to use the formula for exponential decay:

A(t) = P(1 - r)^t

where A(t) is the current value of the car after t years, P is the initial value of the car, and r is the annual rate of depreciation.

We know that P = $15,500 and A(t) = $8,400, so we can plug in these values to solve for r:

$8,400 = $15,500(1 - r)^t

Divide both sides by $15,500:

0.54 = (1 - r)^t

Take the logarithm of both sides:

log(0.54) = t*log(1 - r)

Solve for r:

log(0.54)/t = log(1 - r)

1 - r = 10^(log(0.54)/t)

r = 1 - 10^(log(0.54)/t)

Plugging in t = 7 (since the car has depreciated for 7 years), we get:

r = 1 - 10^(log(0.54)/7) ≈ 9.35%

Therefore, the car depreciated at an annual rate of approximately 9.35%.

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The test statistic for the hypothesis about a consumer activist decides to test the authenticity of the claim is t = 1.38.

In a hypothesis test, a test statistic—a random variable—is computed from sample data. To decide whether to reject the null hypothesis, you can utilise test statistics. Your results are compared to what would be anticipated under the null hypothesis by the test statistic. The p-value is computed using the test statistic.

A test statistic gauges how closely a sample of data agrees with the null hypothesis. Its observed value fluctuates arbitrarily from one random sample to another. When choosing whether to reject the null hypothesis, a test statistic includes information about the data that is important to consider. The null distribution is the sample distribution of the test statistic for the null hypothesis.

Sample size, n = 20

Sample mean, x = 14.8 pounds

Sample standard deviation, s = 2.6

The null hypothesis is,

[tex]H_o[/tex]: μ ≤ 14

The alternative hypothesis is,

[tex]H_a[/tex] : μ > 14

t-test statistic is defined as:

[tex]t = \frac{x - \mu}{\frac{s}{\sqrt{n} } }[/tex]

[tex]= \frac{14.8 - 14}{\frac{2.6}{\sqrt{20} } }[/tex]

= [tex]\frac{0.8}{0.581}[/tex]

= 1.377

t = 1.38.

Therefore, the test statistic for the hypothesis is 1.38.

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Complete question"

An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 14 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 20 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 14.8 pounds with a standard deviation of 2.6 pounds. The test statistic for this hypothesis would be Multiple Choice -1.38 1.38 1.70 -1.70 O O

Answer:

Step-by-step explanation:

To prove that lines a and b are parallel lines cut by transversal f, we need to show that the alternate interior angles are congruent. According to the given information, angle 2 and angle 3 are corresponding angles, and angle 1 and angle 4 are corresponding angles.

Therefore, the set of equations that is enough information to prove that lines a and b are parallel lines cut by transversal f is:

angle 2 = angle 3 (corresponding angles)

angle 1 = angle 4 (corresponding angles)

The math fact that 4 x 6 = 24 helps Matt remember that 6 x 4 = 24, and Sadie arrived at the answer 10 for 6 + 4 by incorrectly adding the numbers in reverse order.

Matt knows that 6 x 4 = 24. This helps him remember that 4 x 6 and 6 x 4 are both equal to 24.

The math fact that Matt can remember based on 4 x 6 = 24 is that multiplication is commutative. This means that the order of the numbers being multiplied doesn't affect the result. So, if 4 multiplied by 6 equals 24, it also implies that 6 multiplied by 4 would give the same result of 24.

Sadie arrived at the answer 10 for 6 + 4 by mistakenly swapping the order of the numbers and performing the addition incorrectly. The correct sum for 6 + 4 is indeed 10. Sadie's error demonstrates the importance of following the correct order of operations, where addition should be performed after ensuring the numbers are in the correct order.

As for Sadie's answer of 6 + 4 = 10, it is not directly related to the multiplication fact that Matt knows.

It is possible that Sadie used a different math fact or strategy to arrive at that answer.

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(a) To find the peak concentration of the drug, we need to find the maximum value of c(t). Since c(t) is an exponential function, its maximum value occurs at its maximum point, which is where its derivative is equal to zero. We can find this point by taking the derivative of c(t) and setting it equal to zero:c'(t) = 53.2e^{-0.26} - 13.832te^{-0.26} = 0Solving for t, we get t = 3.870 hours. Therefore, the peak concentration of the drug is c(3.870) = 109.2 ng/ml.(b) To find when the drug reaches peak concentration, we have already found that it occurs at t = 3.870 hours. Therefore, the drug reaches peak concentration 3.870 hours after it is administered.

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The peak concentration of the drug is approximately 42.83 ng/ml, and it occurs around 3.85 hours after the drug is administered.

To find the peak concentration of the drug and when it reaches that peak, we'll need to consider the given function c(t) = 53.2te^(-0.26t), where t is the time in hours.

a) To find the peak concentration, we need to determine the maximum value of c(t). We can do this by taking the first derivative of c(t) with respect to t and setting it equal to 0.

c'(t) = 53.2(-0.26)e^(-0.26t) + 53.2e^(-0.26t) = 0

Now, solve for t:

t ≈ 3.85 hours

b) Plug the value of t back into the c(t) function to find the peak concentration:

c(3.85) = 53.2(3.85)e^(-0.26(3.85)) ≈ 42.83 ng/ml

So, the peak concentration of the drug is approximately 42.83 ng/ml, and it occurs around 3.85 hours after the drug is administered.

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To add one number to each column of the table and make it show a function, we need the specific table or information about the columns to provide a precise answer.

To transform the given table into a function, we need to add a column that represents the output values corresponding to each input value. A function relates each input value to a unique output value.

Here is an example of how the table could be modified to represent a function:

Input (x) Output (y)

1             3

2               5

3             7

4            9

In this modified table, the output values (y) are obtained by adding 2 to each input value (x). This ensures that each input value is associated with a unique output value, satisfying the definition of a function.

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To find the effective interest rate that Hannah is being offered, we need to take into account the compounding period, which is daily in this case. The effective annual interest rate (EAR) can be calculated using the formula:

EAR = (1 + APR/n)^n - 1

where APR is the annual percentage rate, and n is the number of compounding periods per year.

For the first 30 days, Hannah is offered a 0% APR, so the EAR for this period is simply 0.

After 30 days, Hannah is offered a 12.22% APR compounded daily, which means that there are 365 compounding periods per year. Therefore, the EAR for this period can be calculated as follows:

EAR = (1 + 0.1222/365)^365 - 1

   ≈ 0.1267

So the effective interest rate that Hannah is being offered is approximately 12.67%.

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So the equivalent expression that matches one of the answer choices is option C, 100c/3d.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that can be evaluated to produce a value. An expression can represent a single number or a more complex calculation, and it can be written using symbols, variables, and/or numbers.

Here,

To simplify the given expression, we need to multiply the two binomials using the distributive property:

(10c6d - 5)(2c - 5d/4)

= 10c * 2c + 10c * (-5d/4) - 5 * 2c - 5 * (-5d/4)

= 20c² - 25cd + 10c + 25/4 d

None of the answer choices match this expression exactly, but we can simplify it further. Factoring out a common factor of 5 from the last two terms, we get:

20c² - 25cd + 10c + 25/4 d

= 5(4c² - 5cd + 2c + 5/4

20c/3 * 5d/4

= 100c/3d

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The scale factor from A to B is 5 / 4.

The value of t in the diagram is 5.6 cm.

Scale factor is the ratio between corresponding measurements of an object and a representation of that object.

Therefore, let's find the scale factor from the shape A to the shape B as follows:

5 / 4 = 15 / 12

Therefore, the scale factor is 5 / 4.

Hence, let's find the value of t in the diagram as follows:

Therefore, using the proportionality,

7 / t = 5 / 4

cross multiply

28 = 5t

divide both sides by 5

t = 28 / 5

t = 5.6 cm

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Using mathematical operations, each box of a dozen donuts should cost $3.40.

The basic mathematical operations used to determine the cost of a dozen donuts include multiplication and addition.

Firstly, the total cost of 12 donuts is computed by multiplication, while the total cost of the donuts per box (including the cost of the box) is obtained by addition.

1 dozen = 12 donuts

The cost unit of a donut = $0.27

The total cost of donuts = $3.24 ($0.27 x 12)

The cost per square foot of cardboard = $0.16

The total cost of a dozen donuts and the box = $3.40 ($3.24 + $0.16)

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The value of the tangent segment b is 20.15.

The secant-tangent power theorem, also known as the tangent-secant theorem, states that if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

It is expressed as:

( tangent segment )² = External part of the secant segment + Secant segment.

From the diagram:

Tangent segment = WX = b

External part of the secant segment = YX = 14

Secant segment = ZX = 15 + 14 = 29

Plug these values into the above formula and solve for b.

( tangent segment )² = External part of the secant segment + Secant segment.

b² = 14 × 29

b² = 406

b = √406

b = 20.15

Therefore, the value of b is 20.15.

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The answer is  (3.25, 2.75)

To find point B, we can use the fact that AB and BC form a 1:3 ratio. Let's start by finding the coordinates of point B.

First, we need to find the distance between A and C. We can use the distance formula for this:

[tex]d = \sqrt{ ((x2 - x1)^2 + (y2 - y1)^2)[/tex]

where  [tex](x1, y1) = (4, 2)[/tex]  and [tex](x2, y2) = (1, 5)[/tex]

[tex]d = \sqrt{((1 - 4)^2 + (5 - 2)^2)} = \sqrt{(9 + 9)} = \sqrt{(18)}[/tex]

Next, we need to find the distance between A and B, which we'll call x, and the distance between B and C, which we'll call 3x (since AB and BC are in a 1:3 ratio).

Using the distance formula for AB:

[tex]x = \sqrt{\\((x2 - x1)^2 + (y2 - y1)^2)[/tex]

where [tex](x1, y1) = (4, 2)[/tex] and [tex](x2, y2) = (Bx, By)[/tex]

[tex]x = \sqrt{((Bx - 4)^2 + (By - 2)^2)[/tex]

Using the distance formula for BC:

[tex]3x = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)[/tex]

where [tex](x1, y1) = (1, 5)[/tex] and [tex](x2, y2) = (Bx, By)[/tex]

[tex]3x = \sqrt{((Bx - 1)^2 + (By - 5)^2)[/tex]

Now we can set up an equation using the fact that AB and BC are in a 1:3 ratio:

[tex]x / 3x = 1 / 4[/tex]

Simplifying this equation, we get:

[tex]4x = 3(AB)[/tex]

[tex]4x = 3\sqrt{((Bx - 4)^2 + (By - 2)^2)[/tex]

And

[tex]9x = \sqrt{((Bx - 1)^2 + (By - 5)^2)[/tex]

Now we have two equations and two unknowns (Bx and By). We can solve for Bx in the first equation and substitute into the second equation:

[tex]Bx = (3\sqrt{((Bx - 4)^2 + (By - 2)^2))} / 4[/tex]

[tex]9x = \sqrt{((Bx - 1)^2 + (By - 5)^2)[/tex]

[tex]81((Bx - 4)^2 + (By - 2)^2) / 16 = (Bx - 1)^2 + (By - 5)^2[/tex]

Expanding the squares and simplifying, we get:

[tex]81Bx^2 - 648Bx + 1245 = 16Bx^2 - 32Bx + 266[/tex]

[tex]65Bx^2 - 616Bx + 979 = 0[/tex]

Using the quadratic formula, we get:

[tex]Bx = (616 ± \sqrt{(616^2 - 4(65)(979)))} / (2(65))[/tex]

[tex]Bx = (616 ± \sqrt{(223456))} / 130[/tex]

[tex]Bx = 3.25[/tex] or [tex]Bx = 10.2[/tex]

We can eliminate the solution Bx ≈ 10.2 because it is outside the segment AC. Therefore, the solution is:

B = (3.25, 2.75)

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Answer:is 230

Step-by-step explanation:

230 i hoped i helped

The length of BC rounded to 3 significant figures is 6.98.

Since ∠cab = 90°, we can use the Pythagorean Theorem to find the length of AB.

Let's call BC = x, then we have:

sin(65°) = AB/BC

AB = sin(65°) * BC

In right triangle ABC, we have:

AB^2 + BC^2 = AC^2

(sin(65°) * BC)^2 + BC^2 = 8.9^2

Solving for BC, we get:

BC = 8.9 / sqrt(sin^2(65°) + 1)

BC ≈ 6.98

Therefore, the length of BC rounded to 3 significant figures is 6.98.

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Answer:

  (C)  Neither

Step-by-step explanation:

You want to know if the function values in the table represent an even function, and odd function, or neither.

An Even function is symmetrical about the y-axis:

  f(-x) = f(x)

An Odd function is symmetrical about the origin:

  f(-x) = -f(x)

The attached graph of the given points shows the function has no symmetry at all.

The table represents neither an even nor odd function.

Answer:

Neither

Step-by-step explanation:

In an even function, f(x) = f(-x).

Look at x = 2 and x = -2.

f(2) = -4; f(-2) = 2

Since f(2) ≠ f(-2), the function is not even.

In an odd function, f(x) = -f(-x).

Look at f(2) and f(-2).

f(2) = -4; f(-2) = 2

Since f(2) ≠ -f(-2), the function is not odd.

Answer: C  Neither

The triangle has two sides with equal lengths (AB and AC) and one side with a different length (BC). This makes it an isosceles triangle.

Triangle ABC has vertices A(0,0), B(0,3), and C(3,0).

To determine the type of triangle, we can find the lengths of the sides using the distance formula:

AB = sqrt((0-0)^2 + (3-0)^2) = sqrt(0 + 9) = 3

BC = sqrt((3-0)^2 + (0-3)^2) = sqrt(9 + 9) = sqrt(18) = 3√2

AC = sqrt((3-0)^2 + (0-0)^2) = sqrt(9 + 0) = 3

The triangle has two sides with equal lengths (AB and AC) and one side with a different length (BC). This makes it an isosceles triangle.

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From the calculation, you are 100 m away from the plateau.

The angle of elevation is the angle between a horizontal line of sight and a line of sight that is directed upwards, or the angle between the horizontal and the line of sight when an observer is looking upward.

We know that;

Angle of elevation = 35°

Height of the Plateau = 70 m

Thus;

Tan 35 =70/x

x = Your distance from the plateau.

x = 70/Tan 35

x = 100m

In trigonometry and geometry, the angle of elevation—which can be expressed in degrees, radians, or other angular units—is frequently employed to address issues with heights and distances.

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Candace is flipping the coin 5 times.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.

The theoretical probability of flipping tails on any single flip of a fair coin is 1/2, since there are two equally likely outcomes (heads or tails) on each flip.

If Candace is flipping the coin a certain number of times and the theoretical probability of flipping tails on all flips is 1/32, we can set up the equation:

[tex](1/2)^n[/tex] = 1/32

where n is the number of times Candace is flipping the coin.

We can simplify this equation by taking the logarithm of both sides:

[tex]log((1/2)^n) = log(1/32)[/tex]

Using the property of logarithms that [tex]log(a^b) = b*log(a)[/tex], we can rewrite the left-hand side as:

n*log(1/2) = log(1/32)

We can simplify the logarithms using the fact that log(1/a) = -log(a), so:

n*(-log(2)) = -log(32)

Dividing both sides by -log(2), we get:

n = -log(32) / log(2)

Using a calculator, we find:

n ≈ 5

Therefore, Candace is flipping the coin 5 times.

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Mariah cycles a distance of 8.6 miles, which is more than 8 miles, hence more than 2/3 of the cycling portion of the triathlon.

A triathlon is  described as an endurance multisport race consisting of swimming, cycling, and running over various distances.

The coordinates are given as follows:

Suppose that we have two points,  and . The distance between them is given by:

distance = √(x2 - x1)² + (y2-y1)²

We substitute in the equation

Hence the distance between her house and the library is:

D = 8.6 miles.

She cycles a distance of 8.6 miles, which is more than 8 miles, hence more than 2/3 of the cycling portion of the triathlon.

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Herbert will earn $63,417 for his tenth year of work which is calculated using compound interest formula.

After graduating from college, Herbert decided to join a new company. He agreed to a salary which will increase by 4.5% each year. This means that every year, Herbert's salary will increase by 4.5% of his previous year's salary. For example, if his salary in the first year is $50,000, his salary in the second year will be $52,250, and so on.

To find out Herbert's salary for his tenth year of work, we need to use compound interest formula. The formula is:

A = P(1 + r)ⁿ

Where:
A = Final amount (salary in the tenth year)
P = Initial amount (salary in the first year)
r = Annual interest rate (4.5%)
n = Number of years (10)

Substituting the values in the formula, we get:

A = $50,000(1 + 0.045)¹⁰
A = $63,417

Therefore, Herbert will earn $63,417 for his tenth year of work. It is important to note that the increase in salary is a result of compound interest, which means that the salary growth rate accelerates over time. This is a good incentive for Herbert to stay with the company and work hard.

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Answer:

2*Ab    Or AC

Step-by-step explanation:

No detail in question

We can start by integrating both sides of the differential equation to obtain:

∫f '(x) dx = ∫([tex]5x^2 - x^2/5[/tex]) dx

f(x) = (5/3)[tex]x^3[/tex] - (1/15) [tex]x^5[/tex] + C

where C is the constant of integration.

To find the value of C, we can use the initial condition f(1) = 0:

f(1) = (5/3)[tex](1)^3[/tex] - (1/15) [tex](1)^5[/tex] + C = 0

Simplifying this equation gives:

C = (1/15) - (5/3)

C = -2/9

Therefore, the solution to the initial value problem f '(x) = 5[tex]x^2[/tex] − [tex]x^2[/tex]/5 , f(1) = 0 is:

f(x) = (5/3) [tex]x^3[/tex] - (1/15) [tex]x^5[/tex] - (2/9)

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The inequalities for which the ordered pair (-1,-9) is a solution are a and b

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

The inequality expression y> -5/4x-3 and the list of options

To determine the ordered pairs of the inequality expression, we set x = -1 and then calculate the value of y

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

y > -5/4(-1) -3

Evauate

y > -1.75 -- this is false because -9 < -1.75

For the list of options, we have

Graph (a) True

Graph (b) True

Hence, the inequalities for which the ordered pair (-1,-9) is a solution are a and b

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Approximate amount of dough that is remaining. Is  (length - 2r)(width - 3r) - 6πr^2.

Without the size of the original sheet of dough or the size of the circles cut from it, it's not possible to give an exact expression. However, assuming that each circle has the same radius of 'r' and the original sheet of dough was a rectangle, we can write an expression in factored form for the remaining area of the dough:

Remaining area of dough = (Area of original rectangle) - 6(Area of circle)

= (length x width) - 6(πr^2)

= (length - 2r)(width - 3r) - 6πr^2

Whether there is enough dough for another circle would depend on the size of the circles and the original sheet of dough.

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