Aleks and Melanie used a protractor to measure the angle below. Aleks thinks the angle measures 50° but Melanie says it is actually 130°. Their teacher confirms that Melanie has the correct answer. What mistake did Aleks make while measuring the angle?

Each portion of Grace weighs 1/8 pound.

It gauges how much gravity is pulling on a body.

If Robert has 3/4 pound of Grace and he wants to divide it into six equal portions, we can find the weight of each portion by dividing 3/4 by 6:

(3/4) / 6 = (3/4) * (1/6) = 1/8

So each portion of Grace weighs 1/8 pound.

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The function may still be continuous.

The lack of differentiability only implies that the function is not smooth at that point.

Here are three scenarios in which the derivative of a function may not exist, along with a sketch of each situation:

Corner: A function may not be differentiable at a corner, where the graph abruptly changes direction.

At a corner, the left and right-hand limits of the derivative do not match. Here is a sketch of the situation:

                   /

                  /

                 /

                /

               /

---------------/----------------

Cusp: A function may not be differentiable at a cusp, where the graph has a sharp point.

At a cusp, the left and right-hand limits of the derivative approach different values. Here is a sketch of the situation:

           /

          /

         /

        /

       /

------/--------

      \

       \

        \

         \

          \

Vertical tangent: A function may not be differentiable at a vertical tangent, where the graph has a vertical line tangent to the curve.

At a vertical tangent, the derivative is either infinite or undefined. Here is a sketch of the situation:

     |

     |

------|-------

     |

     |

Note that in all three of these situations, the function may still be continuous.

The lack of differentiability only implies that the function is not smooth at that point.

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The width of a small paving stone is 0.62 m or 62 cm

Length of path = 4 sides of a large paving stone = 3.72 m

Width of large paving stone: 3.72 m ÷ 4 = 0.93 m

Width of small paving stone: 1.55 m − 0.93 m = 0.62 m

or: Length of path = 6 sides of a small paving stone = 3.72 m

Width of small paving stone: 3.72 m ÷ 6 = 0.62 m

or: Let the width of the small paving stone be x and the width

of the large paving stone be y.

Then in cm: x + y = 155 cm,

and 2x + 3y = 372 cm

We can see from the diagram that y = 372 cm – 2 × (x + y)

so y = 372 cm − 2 × 155 cm = 372 cm – 310 cm = 62 cm

Therefore, the width of a small paving stone is 0.62 m or 62 cm.

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Steve paid $10 more than Cole for gas, regardless of the actual prices of gas at the two gas stations.

To answer this question, we need to know the prices of gas at both gas stations. Let's assume that Cole bought 10 gallons of gas at the gas station with the lowest price, and that the price difference between the two gas stations is $x per gallon.

If we denote the price per gallon of gas at the gas station where Cole bought gas as "c", then the total amount Cole paid for gas is:

10c

If we denote the price per gallon of gas at the gas station where Steve bought gas as "s", then the total amount Steve paid for gas is:

10s

The difference between the two amounts is:

10s - 10c

But we know that Steve bought gas at the gas station with the highest price, so we can assume that s = c + x.

Substituting this expression for s into the equation above, we get:

10s - 10c = 10(c + x) - 10c = 10x

So Steve paid $10 more than Cole for gas, regardless of the actual prices of gas at the two gas stations.

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Answer: The answer to your question is the square root of 65

There are 120 possible orders in which the five Smith children can be served one at a time.

If we assume that each child is served one at a time, then the first child can be served in 5 ways, the second child can be served in 4 ways (since one child has already been served), the third child can be served in 3 ways, the fourth child can be served in 2 ways, and the fifth child can be served in 1 way.

Therefore, the total number of orders in which the children can be served one at a time is:

5 x 4 x 3 x 2 x 1 = 120

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The probability that a randomly chosen student is a male who enjoys reading P(male and enjoys reading) ≈ 0.261

To calculate the probability that a randomly chosen student is a male who enjoys reading, you need the number of males who enjoy reading divided by the total number of students.

The probability that a randomly chosen student is a male who enjoys reading can be found by dividing the number of males who enjoy reading by the total number of students.

From the table, we see that there are 30 males who enjoy reading and a total of 115 students. Therefore, the probability is:

P(male and enjoys reading) = 30/115

Rounding to the nearest thousandth, we get:

Therefore, The probability that a randomly chosen student is a male who enjoys reading P(male and enjoys reading) ≈ 0.261

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The volume of the cone with a height and radius both of 7 units is 359.24 cubic units.

In Mathematics and Geometry, the volume of a cone can be determined by using this formula:

V = 1/3 × πr²h

Where:

By substituting the given parameters into the formula for the volume of a cone, we have the following;

Volume of cone, V = 1/3 × 3.142 × 7² × 7

Volume of cone, V = 1/3 × 3.142 × 49 × 7

Volume of cone, V = 359.24 cubic units.

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Answer:

343/3

Proof of answer is in the image, please give brainliest

The equivalent expressions are,

A. [tex]-30 + 40d - 10c[/tex],

B. [tex]-6 + 8d - 2c[/tex]

D. [tex]6 - 8d + 2c[/tex].

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, [tex]2x+3[/tex]

The given expression.

[tex]\implies -25(15 - 20d + 5c)[/tex]

[tex]\implies -125(3 - 4d + c)[/tex]

So, the given expression can be converted into

[tex]k(3 - 4d + c)[/tex]

The equivalent expressions are:

A. [tex]-30 + 40d - 10c[/tex],

B. [tex]-6 + 8d - 2c[/tex]

D. [tex]6 - 8d + 2c[/tex].

A. [tex]-30 + 40d - 10c[/tex]

[tex]\implies -30 + 40d - 10c[/tex]

[tex]\implies -10(3 - 4d + c)[/tex]

B. [tex]-6 + 8d - 2c[/tex]

[tex]\implies -6 + 8d - 2c[/tex]

[tex]\implies -2(3 - 4d + c)[/tex]

D. [tex]6 - 8d + 2c[/tex]

[tex]\implies6 - 8d + 2c[/tex]

[tex]\implies2(3 - 4d + c)[/tex]

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2.25 liters of solution in all is there in the test tubes. So, the correct option is 2.25 l.

The total volume of solution in the 15 test tubes can be calculated by multiplying the volume of one test tube by the number of test tubes:

Total volume = 15 test tubes × 150 milliliters/test tube

Total volume = 2,250 milliliters

However, the question asks for the answer in liters, so we need to convert milliliters to liters by dividing by 1,000:

Total volume = 2,250 milliliters ÷ 1,000

Total volume = 2.25 liters

Therefore, there are 2.25 liters of solution in all the test tubes.

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Answer:

Step-by-step explanation:

A. Sales Budget:

To prepare the sales budget, we need to multiply the unit sales by the sales price per unit for each month. The sales budget for July, August, September, and the total quarter is as follows:

Jones Corporation Sales Budget

Month Unit Sales Sales price Total sales dollars

July 20,000 $180 $3,600,000

August 35,000 $180 $6,300,000

Sept 25,000 $180 $4,500,000

Total 80,000 $180 $14,400,000

B. Production Budget:

To prepare the production budget, we need to calculate the number of units to be produced each month to meet the sales demand and maintain the desired ending inventory level. The production budget for July, August, September, and the total quarter is as follows:

Jones Corporation Production Budget

Month Unit Sales Add: Desired Ending Inventory Total Units Needed Less: Beginning Inventory Units to be Produced

July 20,000 4,000 24,000 - 24,000

August 35,000 5,000 40,250 20,000 20,250

Sept 25,000 7,000 28,750 15,250 13,500

Total 80,000 16,000 93,000 35,250 57,750

Note: The desired ending inventory for finished goods for each month is calculated as 20% of the unit sales for the next month. For materials, the desired ending inventory for September is given as 25,200 pounds.

Therefore, we can calculate the total materials needed for September and subtract the desired ending inventory to find the materials to be purchased for September.

The production budget takes into account the inventory levels for both finished goods and materials.

We can now calculate the total direct materials needed, direct labor hours needed, and total manufacturing overhead costs for the quarter.

C. Direct Materials Budget:

To prepare the direct materials budget, we need to calculate the total materials needed for production and deduct the beginning inventory and desired ending inventory levels to determine the materials to be purchased each month.

The direct materials budget for July, August, September, and the total quarter is as follows:

Jones Corporation Direct Materials Budget

Month Units to be Produced Materials required per unit Total Materials Needed Add: Desired Ending Inventory Total Materials Required Less: Beginning Inventory Materials to be Purchased

July 24,000 3 72,000 - 72,000 20,700 51,300

August 20,250 3 60,750 7,500 68,250 51,300 16,950

Sept 13,500 3 40,500 25,200 65,700 36,300 29,400

Total      

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Tina received $12.30 for recycling her cans last week.

To find how much money Tina got for her cans last week, we need to find the total number of cans she collected and then multiply that by 0.05 (since she gets 5 cents per can).

On Wednesday and Thursday, Tina collected 37 cans each day, for a total of 2 x 37 = 74 cans.

On Tuesday, Friday, Saturday, and Sunday, she collected 43 cans each day, for a total of 4 x 43 = 172 cans.

The total number of cans collected is 74 + 172 = 246 cans.

To find the total amount of money Tina received, we multiply 246 by 0.05, which gives us:

246 x 0.05 = $12.30

Therefore, Tina received $12.30 for recycling her cans last week.

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The fraction of the cookies do they still need to made after Cameron and Lindsey made 80 cookies is 1/2.

Fractions are referred to as the components of a whole in mathematics. A single thing or a collection of objects might be the entire. When we cut a slice of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Roman. "Fractus" means "broken" in Latin.

The fraction was expressed verbally in earlier times. It was afterwards presented in numerical form. A piece or sector of any quantity is another name for the fraction.

Total cookies to be made is 160

Out of which Cameron made 2/5 of the cookies so,

2/5 x 160 = 64 cookies are made by Cameron

Lindsey made 16 cookies

So total cookies that still need to be made is,

= 160 - (64 + 16) = 80

The fraction of cookies still need to made is 80/160 = 1/2 .

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A graph of the function p(x) and the function p(x + 2) is shown below.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided above, we can determine the value of a as follows:

f(x) = a(x - h)² + k

0 = a(-3 - 0)² + 4

0 = 9a + 4

a = -4/9

Therefore, the required quadratic function is given by:

f(x) = a(x - h)² + k

p(x) = y = -4/9(x - 0)² + 4

p(x + 2) = -4/9(x + 2)² + 4

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Missing information:

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

The total revenue over the two days is GH¢305.

We can represent the number of items sold and the cost for each item in matrices as follows:

[tex]\begin{equation}A = \begin{bmatrix} 3 & 4 & 1 \ 4 & 2 & 3 \end{bmatrix}, \quad B = \begin{bmatrix} 10 \ 15 \ 20 \end{bmatrix}\end{equation}[/tex]

Here, matrix A represents the number of items sold on each day, and matrix B represents the cost per item. To find the total revenue, we need to multiply the two matrices and then take the sum of all the elements in the resulting matrix:

[tex]\begin{equation}A \cdot B = \begin{bmatrix} 3 & 4 & 1 \ 4 & 2 & 3 \end{bmatrix} \cdot \begin{bmatrix} 10 \ 15 \ 20 \end{bmatrix} = \begin{bmatrix} 95 \ 140 \end{bmatrix}\end{equation}[/tex]

Therefore, the total revenue over the two days is GH¢(95 + 140) = GH¢305.

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In linear equation, The sides of the triangle on the drawing should be 6 inches, 8 inches, and 9 inches.

What in mathematics is a linear equation?

An algebraic equation B. y=mx+b (where m is the slope and b is the y-intercept) containing simple constants and first-order (linear) components, such as the following, is called a linear equation.

                           The above is sometimes called a "linear equation in two variables" where x and y are variables. Equations in which the variable is power 1 are called linear equations. axe+b = 0 is a one-variable example where a and b are real numbers and x is a variable. 

A triangle with sides 12 feet, 16 feet, and 18 feet on a drawing where 1 inch = 2 feet.

Then, 1 feet of original triangle = 1/2 inch on drawing.

Now, the sides of the triangle on the drawing are

12 feet = 1/2 * 12 = 6 in

12 feet = 1/2 * 16 = 8 in

12 feet = 1/2 * 18 = 9 in

Hence, the sides of the triangle on the drawing should be 6 inches, 8 inches, and 9 inches..

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The type of bankruptcy that typically affects a person's credit score for seven years is Chapter 7 bankruptcy.

Chapter 7 bankruptcy involves the liquidation of assets to pay off debts, and it remains on a person's credit report for up to seven years from the filing date. This can have a significant negative impact on a person's credit score and their ability to obtain credit in the future.

Chapter 9 bankruptcy is specifically designed for municipalities such as cities, towns, and counties, and it does not apply to individuals or affect personal credit scores.

Chapter 11 bankruptcy is primarily used by businesses to reorganize their debts and continue operating. While it can affect a business owner's personal credit if they have personal liability for the business debts, it does not have a specific time frame for how long it remains on a credit report. The impact on an individual's credit score can vary depending on the circumstances and how the bankruptcy is structured.

Hence the answer is Chapter 7.

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Answer:

Chapter 13

Step-by-step explanation:

it’s not on there but that’s the answer

The null hypothesis (H0) for this situation would be that there is no difference in the proportion of male and female students with an overall GPA of 3.5 or higher.

The alternative hypothesis (Ha) would be that there is a difference in the proportion of male and female students with an overall GPA of 3.5 or higher.

Formally, we can write the hypotheses as:

H0: p_male = p_female (where p_male represents the proportion of male students with an overall GPA of 3.5 or higher, and p_female represents the proportion of female students with an overall GPA of 3.5 or higher)

Ha: p_male ≠ p_female

The president of the university can test these hypotheses using a hypothesis test for the difference in proportions. She can calculate the test statistic using the sample proportions and sample sizes for male and female students, and then compare it to the appropriate critical value or p-value based on the desired level of significance.

If the test results provide strong evidence against the null hypothesis, she can reject it and conclude that there is a statistically significant difference in the proportion of male and female students with an overall GPA of 3.5 or higher. If the test results do not provide enough evidence to reject the null hypothesis, she can fail to reject it and conclude that there is not enough evidence to suggest a difference in grades between males and females.

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(a) Discount amount is $6. (b) Maturity value is $2,200. (c) Current yield is 0.27%.

Here, we have,

A discount is a reduction in the regular selling price of a good or service, either in terms of money or as a percentage.

A product may, for instance, be discounted by $10 from its list price or by 10% from its list price. A sales discount is a lower price that a company offers on a good or service.

Find out how to add discounts to invoices. A sales discount, usually referred to simply as a "discount," offers clients of a business a lower price on one or more of the goods or services being provided.

(a) Discount amount

= Maturity (face) value - Purchase price

=$2,200 - $2,194

=$6

(b) Maturity value

=Face value

=$2,200

(c) Current yield

=Discount amount / Purchase price

=$6 / $2,194

=0.0027, or 0.27%

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From the given data set, the mean absolute deviation is 10.72

To determine the mean absolute deviation of the data set, we need to find the mean first.

mean = (0 + 1 + 3 + 10 + 12 + 12 + 15 + 17 + 18 + 22 + 66) / 11

mean = 16

Now, let's calculate the mean absolute deviation

|0 - 16| = 16

|1 - 16| = 15

|3 - 16| = 13

|10 - 16| = 6

|12 - 16| = 4

|12 - 16| = 4

|15 - 16| = 1

|17 - 16| = 1

|18 - 16| = 2

|22 - 16| = 6

|66 - 16| = 50

MAD = (16 + 15 + 13 + 6 + 4 + 4 + 1 + 1 + 2 + 6 + 50) / 11

MAD = 10.72

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You would have to receive an approximately 8.696% increase in pay to regain your original salary after an 8% decrease.

To find the percentage increase in pay needed to regain your original salary after an 8% decrease, follow these steps:

1. Assume your original salary is 100%. After an 8% decrease, your salary becomes 100% - 8% = 92%.

2. Calculate the difference between your original salary (100%) and your current salary (92%). The difference is 100% - 92% = 8%.

3. To find the percentage increase needed to regain your original salary, divide the difference (8%) by your current salary (92%): 8% / 92% = 0.08696.

4. Multiply the result by 100 to convert it to a percentage: 0.08696 (100) = 8.696%.

So, you would have to receive an approximately 8.696% increase in pay to regain your original salary after an 8% decrease.

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Answer:

There is an outlier at 28.

The tumor was approximately 1.47 grams six months before the first measurement. It would not have been detected by the instrument at that time.

Let M(t) be the mass of the tumor at time t (in months) since the first measurement. Since the rate of growth is proportional to the size of the tumor, we have the differential equation dM/dt = kM, where k is the proportionality constant. The general solution to this differential equation is M(t) = Me^(kt), where M is the initial mass of the tumor.

Using the given data, we have M(0) = 4.0 and M(4) = 6.76. Substituting these values into the equation M(t) = Me^(kt), we get the system of equations M = 4.0 and 6.76 = Me^(4k). Solving for M and k, we get M = 4.0 and k = ln(6.76/4.0)/4 ≈ 0.153. Thus, the equation for the mass of the tumor is M(t) = 4.0e^(0.153t).

To find the mass of the tumor six months before the first measurement (i.e., when t = -6), we plug in t = -6 into the equation M(t) = 4.0e^(0.153t) to get M(-6) ≈ 1.47 grams.

Finally, we check whether the tumor would have been detected at that time. Since the mass of the tumor was less than 1 gram at that time, the instrument would not have detected it.

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To generate a recursive rule for the sequence 13, 15, 23, 55, 183, we need to identify the pattern in the sequence.

Looking at the differences between each term, we can see that:

15 - 13 = 2

23 - 15 = 8

55 - 23 = 32

183 - 55 = 128

So the differences are increasing by a factor of 4 each time.

Using this pattern, we can create a recursive rule:

a(1) = 13

a(n) = a(n-1) + 4^(n-2)

So for example,

a(2) = a(1) + 4^(2-2) = 13 + 1 = 14

a(3) = a(2) + 4^(3-2) = 14 + 4 = 18

a(4) = a(3) + 4^(4-2) = 18 + 16 = 34

a(5) = a(4) + 4^(5-2) = 34 + 64 = 98

a(6) = a(5) + 4^(6-2) = 98 + 256 = 354

And so on.

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The critical points are (t, y) = (t, 0) and (t, -4c/5).

To find the partial derivatives, we need to differentiate f(t, y) with respect to each variable separately.

f1(t, y) = ∂f/∂t = 0 (since there is no t term in the function)

fy(t, y) = ∂f/∂y = -12cy^3 + 15y^4

fz(t, y) = ∂^2f/∂t∂z = 0 (since there is no z term in the function)

fy(t, y) = ∂^2f/∂y∂z = 0 (since there is no z term in the function)

So, 2. - f1(,y) fy(x, y) = = frz(, y) = fry(x, y) = 0 - 12cy^3 + 15y^4 = 0  (since f1(,y) and frz(, y) and fry(x, y) are all 0)

Therefore, -12cy^3 + 15y^4 = 0

Factor out y^3:

y^3(-12c + 15y) = 0

This gives us two solutions: y = 0 or -4c/5.

So, the critical points are (t, y) = (t, 0) and (t, -4c/5).

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Round the answer to the nearest mile: She is 398 miles from her starting position.

To solve this problem, we'll use the Law of Cosines.

Here are the steps to find the distance from the starting position:

1. Convert the given time to hours: 1 hour 45 minutes = 1.75 hours 2 hours 15 minutes = 2.25 hours

2. Calculate the distance traveled in each direction:

Distance1 = Speed × Time1 = 235 mi/h × 1.75 h = 411.25 miles

Distance2 = Speed × Time2 = 235 mi/h × 2.25 h = 528.75 miles

3. Use the Law of Cosines to find the distance between the starting position and her final position:

Distance = √(Distance1² + Distance2² - 2 × Distance1 × Distance2 × cos(35°))

4. Plug in the values and solve for the distance:

Distance = √(411.25² + 528.75² - 2 × 411.25 × 528.75 × cos(35°))

Distance ≈ 397.69 miles

5. Round the answer to the nearest mile: She is 398 miles from her starting position.

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The radius of convergence R is 1/4 and the interval of convergence is (-6.25, -5.75) for the power series

∑((-4[tex])^n[/tex]) * (-(x + 6[tex])^n[/tex]) / sqrt(n)
To find the radius of convergence (R) and interval of convergence for the power series ∑((-4[tex])^n[/tex]) * (-(x + 6[tex])^n[/tex]) / sqrt(n)

where n starts from 1 to infinity,

We can use the Ratio Test.
Step 1: Apply the Ratio Test
We want to find the limit as n approaches infinity of the absolute value of the (n+1)th term divided by the nth term:
lim (n→∞) |((-4[tex])^{(n+1)[/tex] * (-(x + 6)^(n+1)) / sqrt(n+1)) / ([tex](-4)^n[/tex] * (-(x + 6[tex])^n[/tex]) / sqrt(n))|
Step 2: Simplify the expression
The limit simplifies to:
lim (n→∞) |((-4)(x + 6))/sqrt((n+1)/n)|
Step 3: Find when the limit is less than 1
For the series to converge, the limit must be less than 1:
|(-4)(x + 6)| / sqrt((n+1)/n) < 1
As n approaches infinity, (n+1)/n approaches 1, so the expression simplifies to:
|-4(x + 6)| < 1
Step 4: Determine the radius of convergence (R)
Divide both sides by 4:
|-(x + 6)| < 1/4
The radius of convergence, R, is 1/4.
Step 5: Determine the interval of convergence
To find the interval of convergence, solve for x:
-1/4 < (x + 6) < 1/4
-1/4 - 6 < x < 1/4 - 6
-6.25 < x < -5.75
Thus, the interval of convergence is (-6.25, -5.75).
In summary, the radius of convergence R is 1/4 and the interval of convergence is (-6.25, -5.75).

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Answer:

Step-by-step explanation:

5^2 + x^2 = 8^2

25 + x^2 = 64

x = 6.2

Answer:

Let's start by drawing a diagram of the cornfield with the plowed strip around it:

markdown

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_____________________________

|                             |

|                             |

|                             |

|                             |

|        _____________________|__

|       |                       |

|       |                       |

|       |                       |

|       |                       |

|_______|_______________________|

The plowed strip has a uniform width, which we'll call w. We want to find w such that half of the cornfield is plowed.

The total area of the cornfield is:

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12 km x 9 km = 108 km^2

If we plow a strip of width w around the cornfield, the new dimensions of the cornfield will be:

scss

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(12 + 2w) km x (9 + 2w) km

The area of the plowed strip is the difference between the area of the new cornfield and the area of the original cornfield:

scss

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(12 + 2w)(9 + 2w) - 12(9) = 108 + 42w + 4w^2

We want half of the cornfield to be plowed, so we set the area of the plowed strip equal to half the area of the original cornfield:

scss

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108 + 42w + 4w^2 = (1/2)(108)

Simplifying, we get:

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4w^2 + 42w - 54 = 0

We can solve this quadratic equation using the quadratic formula:

css

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w = (-b ± sqrt(b^2 - 4ac)) / 2a

Where a = 4, b = 42, and c = -54. Substituting these values, we get:

scss

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w = (-42 ± sqrt(42^2 - 4(4)(-54))) / 8

arduino

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w = (-42 ± sqrt(1936)) / 8

makefile

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w = (-42 ± 44) / 8

So we have two possible solutions:

makefile

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w = 1/2 km (discarded since it does not satisfy the given condition)

or

makefile

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w = 11/2 km

Therefore, the width of the plowed strip is 11/2 km = 5.5 km if half of the cornfield is plowed.

To know more about plowed refer here

https://brainly.com/question/2852405#

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Answer: 15 feet

Step-by-step explanation: