a rancher who wishes to fence off a rectangular area finds that the fencing in the east-west direction will require extra reinforcement due to strong prevailing winds. because of this, the cost of fencing in the east-west direction will be $12 per (linear) yard, as opposed to a cost of $8 per yard for fencing in the north-south direction. find the dimensions of the largest possible rectangular area that can be fenced for $4800.

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Answer:

Below

Step-by-step explanation:

● (p+q) ×2 -(5-5)

● 2(p+q) - 0

● 2(p+q)

Replace p and q with 1

● 2 (1+1)

● 2 × 2

● 4

Suppose that today the exchange rate between the u.s. dollar and the chinese yuan is $1 =.12 yuan. if next week the exchange rate is $1 = .20 yuan, it is clear that yuan has depreciated relative to dollar.

What is meant by the exchange rate?

Last week: $1 = 0.12 yuan

Therefore, for exchange of $1, 0.12 yuan will be given

Today: $1 = 0.2

Therefore, for exchange of $1, 0.2 yuan will be given.

So, yuan will be given for same amount of $. Thus yuan has depreciated.

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Answer:

22 blueberry pies and 19 apple pies.

Step-by-step explanation:

This can be solved using a system of equations. Your equation for amount of pies sold is x + y = 41, with x representing apple pies and y representing blueberry pies, and 41 being the total amount of pies sold. The other equation is for the amount of dollars earned from selling the pies, which is:

12x + 14y = 536     $12 per apple pie, $14 per blueberry pie, and a total of $536.

Let's first solve for x. The new equation would be x = 41 - y. Now, we plug this equation into the second equation.

12(41 - y) + 14y = 536    Here we substituted x for the equation we made.

429 - 12y +14y = 536

-12y +14y = 44   Here we moved the 429 to the other side by subtracting it from the left and right.

2y = 44

y = 22. Now we know that there was a total of 22 blueberry pies sold. Now we plug 22 pies back into the very first equation to find x, the amount of apple pies.

x + 22 = 41

x = 19. Now we know there was a total of 19 apple pies sold.

Hope this helps!

Answer:

The value of the mean, median, and mode will be 22.4, 22, and 26. Then the correct option is A.

What are statistics?

Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.

The data set is given below.

18, 19, 20, 21, 23, 26, 26, 26

Then the mean will be

Then the median will be

Then the mode is given as

26

Step-by-step explanation:

The particular solution to the following system is x(t) = C₁\(e^{5t}\) + C₂\(e^{t}\) + (5/2) \(e^{t}\)/D

x' = 3x + 2y + 3\(e^{t}\)

y' = 2x + 3y - 2\(e^{t}\)

The first equation can be written as

(D-3)x - 2y = 3\(e^{t}\)

The second equation can be written as

-2x + (D-3)y = - 2\(e^{t}\)

(D-3)²x - 4x = (D-3)3\(e^{t}\) - 4\(e^{t}\)

(D²+9-6D-4)x = 3\(e^{t}\) - 9\(e^{t}\) - 4\(e^{t}\)

(D²-6D+5)x = - 10\(e^{t}\)

Auxiliary Equation

m²-6m+5=0

(m-5)(m-1)=0

CF = C₁\(e^{5t}\) + C₂\(e^{t}\)

Particular Integral

PI = -10\(e^{t}\)/(D²-6D+5)

= -10\(e^{t}\)/(D-5)(D-1)

= (5/2) \(e^{t}\)/D

x(t) = C₁\(e^{5t}\) + C₂\(e^{t}\) + (5/2) \(e^{t}\)/D

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Answer: C

Step-by-step explanation:

Step-by-step explanation:

Hey there!

The given equation is;

y = 3x - 2

Make table for"X" and "y"

x = 0 1 2

x = -2 1 4

Now;

The coordinates are; (0,-2) , (1,1), (2,4).

After that plot them on graph.

Hope it helps...

Answer:

8x and 6(2x)

Step-by-step explanation:

this is because when you calculate the area you multiply the length to the high

Answer:

12x and 6(2x)

Step-by-step explanation:

Area = LW

Area = (2x)(6)

Area = 12x

(a). The curl of F is given by curl F = (4e^7z) i - 4 j - 4x^3 k.

(b). The work done by the vector field F along the closed curve of the circle is zero.

To find the curl of the vector field

\(F = (42 + 4x^4) i + (4y + 62 + 6sin(y)) j + (4x + 6y + 4e^{7z})\)k, we'll compute the curl as follows:

(a) Curl F:

The curl of a vector field F = P i + Q j + R k is given by the following determinant:

curl F = (∂R/∂y - ∂Q/∂z) i + (∂P/∂z - ∂R/∂x) j + (∂Q/∂x - ∂P/∂y) k

Let's compute the partial derivatives:

∂P/∂x = \(16x^3\)

∂Q/∂y = 4

∂R/∂z = \(4e^{7z\)

∂Q/∂z = 0 (as there is no z term in Q)

∂R/∂x = 4

∂P/∂y = 0 (as there is no y term in P)

Now, we can calculate the components of the curl:

curl F =\((4e^{7z} - 0) i + (0 - 4) j + (0 - 4x^3) k\)

   = \((4e^{7z}) i - 4 j - 4x^3 k\)

(b) Regarding the line integral ∮ F · dr, where r is the circle

\((x - 3)^2 + (y - 5)^2 = 25\) :

Since the curl of F is zero (curl F = 0), it implies that F is a conservative vector field. This means that the line integral ∮ F · dr around any closed curve will be zero.

For the circle given by \((x - 3)^2 + (y - 5)^2 = 25\), it is a closed curve. Therefore, we can conclude that the line integral ∮ F · dr around this circle is zero.

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The given statement "For any integers a and b, if ab is even, then a is even or b is even." is true. This is because if the product of two integers is even, at least one of them must be even because the product of two odd numbers is always odd. Therefore, either a or b must be even.

Assume that a and b are integers such that a is odd and b is odd. We want to show that if ab is even, then our assumption is false.

If a is odd, then we can write a as 2k+1 for some integer k. Similarly, if b is odd, we can write b as 2m+1 for some integer m.

Then, ab can be written as:

ab = (2k+1)(2m+1) = 4km + 2k + 2m + 1 = 2(2km + k + m) + 1

Since 2km + k + m is an integer, we can see that ab is odd, which contradicts our assumption that ab is even.

Therefore, by contrapositive, we can conclude that for any integers a and b, if ab is even, then a is even or b is even.

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The quarterly operating profit margin of TMG Ltd over the past six years is provided in Table 4.1, indicating the financial performance of the business during that period.

In order to assess the impact of the intervention strategy introduced by the current CEO three years ago, the board of directors (BOD) of TMG Ltd has contracted a researcher to analyze the data and determine if there have been significant improvements in the business outcomes. The quarterly operating profit margin serves as the unit of analysis for this evaluation.

Table 4.1 allows the researcher to examine the trend and fluctuations in the quarterly operating profit margin over the six-year period. By analyzing the data, the researcher can identify any noticeable changes in the financial performance of TMG Ltd, particularly after the implementation of the intervention strategy. The BOD is interested in understanding whether the strategy has resulted in improved profitability and overall financial health of the company.

The researcher will likely perform statistical analysis, such as calculating averages, trends, and identifying any significant variations, to draw conclusions about the effectiveness of the intervention strategy. By comparing the quarterly operating profit margin before and after the strategy's implementation, the researcher can assess whether the new CEO's efforts have had a positive impact on the company's financial performance.

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The number of rotations taken by Diana when practising her pitching is 20

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

Number of pitches per rotation = 20

Total number of pitches = 400

The above parameters mean that:

The number of rotations = Total number of pitches/Number of pitches per rotation

Substitute the known values in the above equation, so, we have the following representation

The number of rotations = 400/20

Evaluate

The number of rotations = 20

Hence, the rotations is 20

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Answer:

Find the negative reciprocal of the slope of the original line and use the point-slope formula y−y1=m(x−x1) to find the line perpendicular to y=3x−5. y=−13x−2

Step-by-step explanation:

The approximate length of RS is 10 units.

We have the information from the question:

Length of the RX is = 6 units

Length of the XW is = 8 units

We have to find the length of RS.

Now, According to the question:

We use the formula, for finding the length of RS

\(RS=\sqrt{RX^2+XW^2}\)

Plug all the values in above formula, we get:

\(RS =\sqrt{6^2+8^} \\\\\)

\(RS=\sqrt{36+64}\)

\(RS=\sqrt{100}\)

RS = 10 units.

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Answer:

C) 1

Step-by-step explanation:

Absolute value means that the number will become positive.

For A, 15 will stay as 15.

For B, 5 will stay as 5.

For C, 1 will stay as 1.

For D, -25 will become 25.

So 1 is the smallest number out of the 4 options.

Answer:

Answered

Step-by-step explanation:

Answer:

well you did the law of inverse on 6x you proved it by putting the one above it and switched the minus with a plus and divided 24 by 6

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

When their aggregate is 132 and the third number is 4 times the second and the second is 6 more than the first, the numbers are 17, 23, and 92.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

Let x, y, z be the number.

x+y+z=132

z=4y

z=4(x+6)

z=4x+24

y=x+6

x+x+6+4x+24=132

6x+30=132

6x=102

x=17

y=x+6

y=23

z=4y

z=92

The numbers will be 17, 23 and 92 when their  sum is 132 and third number is 4 times the second and second is 6 more than the first.

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The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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m = 37.5

b = 43.8

mowing = m

babysitting = b

in all 81.3

Answer:

384 cm^3

Step-by-step explanation:

the volume formula:

     V = a*b*c,

where a - length, b - width, c - height

so, the volume of the solid is V = 4*8*12 = 384 cm^3

The volume of the solid, if the length is 4 centimeters, the width is 8 centimeters, and the height is 12 centimeters is 384 cm³.

To find the volume of the solid, we need to multiply the length, width, and height together. So, the volume of the solid is:

V = l x w x h
V = 4 cm x 8 cm x 12 cm
V = 384 cm³

Therefore, the volume of the solid is 384 cubic centimeters (cm³).

To find the volume of a solid with given dimensions, you can use the formula for the volume of a rectangular prism, which is Volume = Length × Width × Height. In this case, the length is 4 centimeters, the width is 8 centimeters, and the height is 12 centimeters.

Now, let's plug these values into the formula:

Volume = (4 cm) × (8 cm) × (12 cm)

By multiplying these numbers together, you'll get the volume of the solid:

Volume = 384 cubic centimeters (cm³)

So, the volume of the solid with the given dimensions is 384 cm³.

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Given,

The equations are,

The graph of the equation is,

The red line of the graph shows the equation of Alfred.

The green line of the graph shows the equations of Batgirl.

The blue line of the graph shows the equations of Robin.

Hence, the graph of the equation is obtained.

From the given mean and standard deviation the closest minimum annual profit, for a store that had a reward party is equal to $102,300.

As given in the question,

Given distribution of annual profit :

Approximately normal with mean μ = $66,000

Standard deviation σ = $22,000

Profits in the top 5 percent

Apply z-score formula :

z = ( x - μ) / σ

Top 5% mean 95% and more.

Using normal distribution table,

z -score corresponding to 95% or 0.95 is equal to 1.65.

Substitute all value in the formula we get,

1.65 = ( x - 66,000 ) / 22,000

⇒ x - 66,000 = 1.65 × 22,000

⇒ x = 36,300 + 66,000

⇒ x = 102,300

Therefore, from the given mean and standard deviation the closest minimum annual profit, for a store that had a reward party is equal to $102,300.

The complete question is :

The distribution of annual profit at a chain of stores was approximately normal with mean μ = $66,000, standard deviation σ = $22,000. The stores with profits in the top 5 percent each had a reward party for the employees to celebrate.

What is closest to the minimum annual profit for a store that had a reward party?

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The value of angle ∠ABD=144° and ∠DBC=36°.

An endless figure without width is a straight line. It consists of an infinite number of points connected at both ends. It doesn't have any curves at all. It can be straight, angled, or vertical. We use a sleeping straight line or a standing straight line when explaining geometry to preschoolers.

\(ABC\) is a straight line,

Hence,

∠ABD+∠DBC=180°

(4x+8)+(x+2)=180°

5x+10=180°

5x=170°

x=34°

Hence,

∠ABD=4*34+8

∠ABD=144°

∠DBC=36°

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The probability that the 2 marbles taken from the bag are the same color is 25/49.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of red marbles = 3

Number of blue marbles = 4

Total marbles = 7

Now,

The probability of taking two blue marbles consecutively with replacement.

= 4/7 x 4/7

= 16/49

The probability of taking two red marbles consecutively with replacement.

= 3/7 x 3/7

= 9/49

Since the two marbles of the same color can be blue or red.

The probability that the 2 marbles taken from the bag are the same color.

= 16/49 + 9/49

= 25/49

Thus,

The probability that the 2 marbles taken are the same color is 25/49.

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Answer:

A: 19

Two negatives make a positive, so the answer is just 19.

The number of liters of paint needed will be A divided by 8.

We have,

To calculate the amount of paint needed, we need to consider the coverage rate of the paint, which is given as 1 liter of paint covering 8 square meters.

This means that 1 liter of paint is sufficient to cover an area of 8 square meters.

To determine the total amount of paint needed for a specific area, we divide the total area (in square meters) by the coverage rate (8 square meters per liter).

This calculation gives us the number of liters required to cover the entire area.

For example,

Let's say we have a wall with an area of 32 square meters.

To calculate the amount of paint needed, we divide 32 by 8:

Number of liters needed

= 32 / 8

= 4

So, in this case, we would need 4 liters of paint to cover the entire 32 square meters of the wall.

This approach can be applied to any given area to calculate the required amount of paint based on the given coverage rate.

Thus,

The number of liters of paint needed will be A divided by 8.

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