the circle below has center O, and its radius is 5 ft. Given that m AOB = 70, Find the area of the shaded region and the length of the arc ADB

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here is real answer :>

Sixty percent of 800 students in a business statistics class are female. if you want to make probability estimates of the sample proportion of female students without applying the finite population correction factor, 368 is the minimal sample size of the random sample should be used

The appropriate sample size for probability estimates of the sample proportion of female students in the business statistics class is determined by the margin of error (m) and the level of confidence (Z).

The formula for sample size calculation is as follows:

N = [tex](Z^2\times p \times q) / m^2[/tex]

where

N is the sample size

Z is the z-score that corresponds to the level of confidence

p is the estimated proportion of female students

q is 1 - p (proportion of male students)m is the margin of error.

Since we don't have any margin of error, we can assume it to be a standard value of 5%. And a z-score of 1.96 is appropriate for a 95% level of confidence.

As a result, the sample size for estimating the sample proportion of female students in the business statistics class is given by

N = [tex](1.96^2\times0.60\times0.40) / (0.05^2)[/tex]

N = 368 students

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The ratio of SINA and COSA = 48/50 and 14/50

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

According to our question,

sina = perpendicular\ hypotenuse

= 48/50

cosa= base\ perpendicular

=

14/50

Hence, The ratio of SINA and COSA = 48/50 and 14/50

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1. It will take about 8 years for the tithe to double in value if invested at 7.75% APR compounded monthly.

2. An annual interest rate of 4.84% compounded semi-annually would be required for $22,500 to accumulate to $50,000 in 14 years.

3 A principal of $26,512.18 invested in a GIC at 4% APR compounded quarterly would return $40,000 in 9 years.

a. Using the TVM Solver function in Excel, we can input the following information:

Present value (PV): -$35,000 (since it's an outgoing cash flow)

Future value (FV): $70,000 (since we want the tithe to double in value)

Interest rate per period (Rate): 7.75%/12 (since the APR is compounded monthly)

Number of periods (Nper): unknown (what we're solving for)

Payment (Pmt): 0 (since there are no recurring payments)

Solving for Nper, we get 96.16 months, or approximately 8 years.

Therefore, it will take about 8 years for the tithe to double in value if invested at 7.75% APR compounded monthly.

b. Present value (PV): -$22,500 (since it's an outgoing cash flow)

Future value (FV): $50,000

Interest rate per period (Rate): unknown (what we're solving for)

Number of periods (Nper): 14*2=28 (since the interest is compounded semi-annually, we need to double the number of years)

Payment (Pmt): 0

Solving for Rate, we get 4.84% APR.

Therefore, an annual interest rate of 4.84% compounded semi-annually would be required for $22,500 to accumulate to $50,000 in 14 years.

c. Using the TVM Solver function in Excel, we can input the following information:

Present value (PV): unknown (what we're solving for)

Future value (FV): $40,000

Interest rate per period (Rate): 4%/4 (since the APR is compounded quarterly)

Number of periods (Nper): 9*4=36 (since the interest is compounded quarterly, we need to multiply the number of years by 4)

Payment (Pmt): 0

Solving for PV, we get $26,512.18.

Therefore, a principal of $26,512.18 invested in a GIC at 4% APR compounded quarterly would return $40,000 in 9 years.

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Answer: $ 46.50

First divided 31 by 2

Which equals...

15.50

Then add 15.50 to 31.

46.50

The answer is $46.50

Total longer distance is [tex]3\frac{2}{21} miles[/tex], that kiki run during the second week of track practice than the first week of track practice.

We have, a runner Kiki and she runs on track for practice. In first week,

Distance runs by Kiki on track practic = [tex]4 \frac{3}{7} miles[/tex]

which is a mixed fraction so, simplify it into simple fraction that is 25/7 miles. In second week,

Distance runs by Kiki on track practice = [tex]6 \frac{2}{3} miles[/tex]

After simplification, it is equals to 20/3 miles. We have to calculate the longer distance that kiki run during the second week of track practice than the first week of track practice. Let the distance run during second week be longer by 'x miles' from distance run during first week. The required distance can be calculated by difference between the distance that kiki run during the second week of track practice and the first week of track practice. So, [tex]x = \frac{20}{3} - \frac{25}{7 }[/tex].

taking least common multiple of (3,7)= 21

=> [tex] x = \frac{20× 7 - 3× 25}{21} [/tex]

[tex] =>x = \frac{ 140 - 75}{21} = \frac{65}{21 }[/tex].

Hence, required distance value is

[tex]3\frac{2}{21} [/tex].

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Answer:

\

Step-by-step explanation:

Given expression: 3x+9

Take 3 outside from the expression, we get,

= 3(x+3), which is called the equivalent expresion

The correct option for the given graph is option 1 and option 3. The equation matches the intersection point (1,1).

For option 1: intersection point (1,1)

substitute the values of x & y in the given equation.

1 = 3 (1) - 2

1 = 1

LHS = RHS

For option 2: point (1,1)

substitute the values of x & y in the given equation.

1 = 2 (1) + 3

1 = 5

LHS ≠ RHS

For option 3: point (1,1)

substitute the values of x & y in the given equation.

1 = -2 (1) + 3

1 = 1

LHS = RHS

For option 4: point (1,1)

substitute the values of x & y in the given equation.

1 = - [tex]\frac{1}{2}[/tex] (1) + 3

1 = [tex]\frac{5}{2}[/tex]

LHS ≠ RHS

For option 5: point (1,1)

substitute the values of x & y in the given equation.

1 = - [tex]\frac{1}{3}[/tex] (1) + 3

1 = [tex]\frac{8}{9}[/tex]

LHS ≠ RHS

Therefore, correct option for the given graph is option 1 and option 3.

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Answer:

Step-by-step explanation:

One potential drawback of using a histogram is that it can be sensitive to the choice of bin width or bin size. If the bin size is too small, the histogram may appear too noisy or have too many empty bins, which can obscure patterns in the data. If the bin size is too large, important features of the distribution may be lost or smoothed out. Additionally, histograms do not always show the actual values of the data points, but rather a summary of the data. This means that some details about the data may be lost, such as the exact values of outliers or individual data points.

Since the value of a is less than 0, the graph of the parabola would be opening downwards. Because of this we can rule out option C. In a quadratic equation, c represents the y-intercept, and, in this case c is negative, meaning the y-intercept is less than 0. Only option B has a downward-opening curve and a y-intercept less than 0, so it is the answer.

Answer: p= 2+c

Step-by-step explanation:

Using coordinate geometry,

The problem provides two pieces of information about Hannah's jogging routine: she started with 3 41 miles and added 1/21 miles every week. We can use this information to create a linear equation that represents the number of miles Hannah jogged as a function of the number of weeks she has been jogging.

To create this equation, we first identify the starting value, which is 3 41 miles. This is also the y-intercept of the line. Next, we determine the slope of the line, which is the rate at which the number of miles increases each week. The slope is equal to the change in y (miles) divided by the change in x (weeks), which in this case is (1/21 - 3/41)/1 = -2/1 = -2. Therefore, the slope of the line is -2.

Putting these two pieces of information together, we get the equation y = -2x + 3 41, where y is the number of miles jogging and x is the number of weeks of jogging. This is a linear equation in slope-intercept form, where the slope is -2 and the y-intercept is 3 41.

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In response to the stated question, we may state that As a result, the Pythagorean theorem angle of depression from the helicopter to Landing Pad B is around 16.7 degrees.

The Pythagorean theorem is a fundamental mathematical principle that describes the connection between the sides of a right triangle. It asserts that the sum of the squares of the other two sides' lengths equals the square of the hypotenuse's length (the side opposite the right angle). The mathematical theorem is as follows: c2 = a2 + b2 Where "c" denotes the hypotenuse length and "a" and "b" indicate the lengths of the other two sides, known as the legs.  

We can calculate the angle of depression from the helicopter to Landing Pad B using trigonometry.

Let we make a diagram:

            B

              /|

             / |

            /  |  8 miles

        14 /   |

          /θ  |

         /    |

        /     |

       /______|______ A

             20 miles

Using trigonometry, we can deduce:

tan(θ) = opposite / adjacent

The opposing side in this example is 14 - 8 = 6 miles (since the helicopter is 14 miles from Landing Pad A and 8 miles from Landing Pad B, and the pads are 20 miles apart). The distance between the two sides is 20 miles (the distance between the landing pads).

tan(θ) = 6 / 20

tan(θ) = 0.3

θ = arctan(0.3)

θ ≈ 16.7 degrees

As a result, the angle of depression from the helicopter to Landing Pad B is around 16.7 degrees.

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The magnitude of the force P is 464.77 N.

STEP BY STEP EXPLANATION:

Step 1: Break down each force into components.
F = 320 N at 30°
Fx = F * cos(30°) = 320 * cos(30°) = 277.13 N (horizontal)
Fy = F * sin(30°) = 320 * sin(30°) = 160 N (vertical)

120 N is in the horizontal direction (assume positive x-direction):
Fx2 = 120 N

80 N is in the vertical direction (assume positive y-direction):
Fy2 = 80 N

Step 2: Sum up the components.
Total horizontal force (Fxtotal) = Fx + Fx2

= 277.13 + 120 = 397.13 N

Total vertical force (Fytotal) = Fy + Fy2

= 160 + 80 = 240 N

Step 3: Find the magnitude of the resultant force.
            Resultant force (R) = sqrt(Fxtotal^2 + Fytotal^2)

= sqrt(397.13^2 + 240^2) = 464.77 N

Step 4: Determine the magnitude of the force P.
Since the resultant of the four forces should act on the rim of the plate, it means that the force P should be equal in magnitude and opposite in direction to the resultant force R.

The magnitude of the force P is 464.77 N.

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The percentage of scores greater than 34 is 0.5398 or 53.98%.

Given that the mean of scores (μ) = 35 and the standard deviation (σ) = 10. We need to find the percentage of scores greater than 34. Since the scores are normally distributed, we can standardize the variable by using the z-score formula.

z = (x - μ) / σ

Here, x = 34, μ = 35 and σ = 10z = (34 - 35) / 10z = -0.1

We need to find the area to the right of the z-score line on the standard normal distribution table. The standard normal distribution table provides the probabilities corresponding to the z-scores, i.e. the area under the curve to the right or left of the z-score line on the distribution table. The area to the right of the z-score line represents the percentage of scores that are greater than the given value. Using the standard normal distribution table, the area to the right of the z-score line -0.1 is 0.5398.

The percentage of scores greater than 34 is 0.5398 or 53.98%.

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The fence ought to be cut into 12 pieces, every one of length 28 m, to make three squares, each with a side length of 28 m. This will limit the total area encased by the fence.

To limit the total area encased by the fence, the three squares ought to have equivalent areas. Let x be the length of each side of the squares. Then the perimeter of each square is 4x, and the total length of the fence is 3(4x) = 12x. Since the total length of the fence is given to be 336 m, we have:

12x = 336

Addressing for x, we get:

x = 28

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There are a total of 48 soccer games in the season.

Since there are 3 soccer games in a month, there will be 12 games in a season (3 games/month x 4 months). Since 8 games are played at night and assuming that all games are played either during the day or at night, we can calculate the number of games played during the day as:

Number of day games = Total number of games - Number of night games

= 12 games/month x 4 months - 8 night games/month x 4 months

= 48 games - 32 games

= 16 games

Therefore, the total number of games in the season is:

Total number of games = Number of day games + Number of night games

= 16 games + 32 games

= 48 games

So, there are 48 soccer games in the season.


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The coordinates of the vertices for the image if the preimage is translated 4 units down are A′(-4, -1), B′(0, 1), C′(-2, -4).

What is meant by preimage?

In geometry, a preimage is the original figure or shape before any transformation is applied. It is the initial configuration of the object that is being transformed. For example, if we have a square and we rotate it by 90 degrees, the original square is the preimage and the resulting figure after the rotation is the image.

To translate the preimage 4 units down, we need to subtract 4 from the y-coordinates of all vertices. Therefore, the coordinates of the image vertices are:

A′(-4, 3-4) = (-4, -1)

B′(0, 5-4) = (0, 1)

C′(-2, 0-4) = (-2, -4)

Therefore, the vertices of the image triangle are A′(-4, -1), B′(0, 1), and C′(-2, -4).

So, the correct option is: A′(-4, -1), B′(0, 1), C′(-2, -4).

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The trigonometric expression cosAcotA = 8x/(4x² - 1)

A trigonometric expression is an expression that contains trigonometric ratios.

Given that for any acute angle A if sin A = 2x-1/2x+1, we desire to find the value of cos A cot A?

So, we proceed as follows

cosAcotA = cosA × cosA/sinA  (since cotA = cosA/sinA)

= cos²A/sinA

Now using the trigonometric identity

sin²A + cos²A = 1

⇒ cos²A = 1 - sin²A

So, substituting this into the equation, we have that

cosAcotA = cos²A/sinA

=  (1 - sin²A)/sinA

= 1/sinA - sin²A/sinA

= 1/sinA - sinA

Substituting the value of sinA into the equation, we have

= 1/(2x - 1)/(2x + 1) - (2x - 1)/(2x + 1)

= (2x + 1)/(2x - 1) - (2x - 1)/(2x + 1)

Taking the L.C.M, (2x - 1)(2x + 1), we have

= [(2x + 1)² - (2x - 1)²]/[(2x - 1)(2x+ 1)]

=  [(2x + 1)² - (2x - 1)²]/[(2x)² - 1²)]

=  [(2x + 1 + 2x - 1)(2x + 1 - (2x - 1)]/(2x)² - 1²)

=  [(2x + 1 + 2x - 1)(2x + 1 - 2x + 1)]/4x² - 1)

=  [(4x)(2)]/4x² - 1)

= 8x/(4x² - 1)

So, cosAcotA = 8x/(4x² - 1)

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Ten chairs are arranged in a circle. The number of subsets of this set of chairs that contain at least three adjacent chairs is 310.

The given that 10 chairs arranged in a circle.

            Now we have to find the number of subsets of this set of chairs that contain at least three adjacent chairs.

           To solve this, we can use the concept of permutations and combinations. The first step is to consider the number of ways in which three chairs can be selected and arranged in a subset that is adjacent to each other.

           This can be done in 10 different ways, as there are 10 chairs in total and we can select any one of them as the starting point.

           The next step is to consider the number of ways in which we can add additional chairs to this subset. For example, we can add a fourth chair to the subset in two different ways: either to the left of the first chair or to the right of the third chair.

            Similarly, we can add a fifth chair to the subset in four different ways, a sixth chair in six different ways, and so on. Using this logic, we can create the following table:

                    Length of subset number of ways to select the subset number of ways to add chairs

           Total number of subsets31 (adjacent)

                                = 10  ---43 (adjacent) 10*2

                                =20---55 (adjacent)10*4

                                =40---67 (adjacent)10*6

                                =60---79 (adjacent)10*8

                               =80---810 (adjacent)10*10

                               =100---

              As we can see from the table, the total number of subsets that contain at least three adjacent chairs is given by:

           Total number of subsets = 10 + 20 + 40 + 60 + 80 + 100

                                                     = 310

       Therefore, the number of subsets of this set of chairs that contain at least three adjacent chairs is 310.

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The prompt on fractions is given as follows:

1 ) (1/2) ÷ 4 = 1/8
2) ( 1/5) ÷ 2 = 1/10

3) (1/3) ÷ 5 = 1/15

4) (1/4) ÷ 4 = 1/16
5) The solution to the puzzle for (1/2) ÷ 3 is given below.

The calculations are given as follows;

1 )

= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]

= 1/8

2) (1/5) ÷ 2

= (1/5) x (1/2)

= 1/10

3)

(1/3) ÷ 5

= (1/3) x (1/5)

= 1/15

4) (1/4) ÷ 4

= (1/4) x (1/4)

= 1/16

5) Mary had 1/2 of a pie that she wanted to share with 3 of her friends. She decided to divide it equally among them. Each friend got 1/6 of the pie. To check, Mary multiplied 1/6 by 3 and got 1/2. This shows that (1/2)/3 equals 1/6, since dividing by 3 is the same as multiplying by its reciprocal, 1/3.


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Bending moment curve equation below point A will be:

M = 15x - 3x² for 0 ≤ x ≤ b

Determination of shear and bending moment curves.

For the beam and loading shown, we can do the following:

Equation of shear curve (above point A):V = RA - w.x

For x = a,V = RA - w.a

For x = b,V = RA - w.b

Since the loading is symmetric, RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15 - 6a for a ≤ x ≤ b

Equation of shear curve (below point A):

V = RA - w.x

For x = 0,V = RA - w.0RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15k for 0 ≤ x ≤ a

The shear curve equation becomes;

V = 15k for 0 ≤ x ≤ a

V = 15 - 6a for a ≤ x ≤ b

Equation of bending moment curve (above point A):

M = RAx - ½w.x²For 0 ≤ x ≤ a,

M = 15x - ½(6x²) = 15x - 3x²For a ≤ x ≤ b,

M = 15x - 6a(x - a) - ½(6x²)= 15x - 6ax + 6a² - 3x²

The bending moment curve equation above point A becomes:

M = 15x - 3x² for 0 ≤ x ≤ a

M = 15x - 6ax + 6a² - 3x² for a ≤ x ≤ b

Equation of bending moment curve (below point A):

M = RAx - ½w.x²For 0 ≤ x ≤ b,

M = 15x - ½(6x²) = 15x - 3x²

The bending moment curve equation below point A becomes;

M = 15x - 3x² for 0 ≤ x ≤ b

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The subtraction property of equality is used for the justification of step 2 in the solution.

The subtraction property of equality states that subtracting the same number from both sides of an equation does not affect the equality.

Therefore, Justify the property used for step 2 in the equality.

1 / 2 r + 1 / 2  = - 2 / 7 r + 6 / 7  - 5

Step 1 : 1 / 2 r + 1 / 2  = - 2 / 7 r - 29 / 7

Step 2: 1 / 2 r = - 2 / 7 r - 65 / 14

We had to subtract 1 / 2 from both sides of the equation to arrive at step 2. Therefore, the subtraction property of equality is the justification for step 2 in the solution.

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From the given information provided, the expression that need to determine the total amount is Total cost = $2.85/gallon x g gallons + $3.15/can x c cans.

The expression that can be used to determine the total amount Joe spent on gasoline and oil is:

Total cost = Cost of gasoline + Cost of oil

We can represent the cost of gasoline as:

Cost of gasoline = price per gallon x number of gallons

Substituting the given values, we get:

Cost of gasoline = $2.85/gallon x g gallons

Similarly, we can represent the cost of oil as:

Cost of oil = price per can x number of cans

Substituting the given values, we get:

Cost of oil = $3.15/can x c cans

Putting it all together, we get:

Total cost = $2.85/gallon x g gallons + $3.15/can x c cans

Expression that can be used to determine the total amount Joe spent on gasoline and oil is:

Total cost = $2.85/gallon x g gallons + $3.15/can x c cans

Question - Joe bought g  gallons of gasoline for $2.85 per gallon and c  cans of oil for  $3.15 per can. What expression can be used to determine the total amount Joe spent on gasoline and oil?

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The vertical axis of the graph represents profit, so the x-intercepts represent prices in the produce 0 profit. The maximum value of the graph is the maximum profit that can be obtained for anyprice

The higher or largest number of the chart is the maximum reach

B) We read the value of f(1) from the graph to be about 120, so the average rate of change is about:

(f(4) -f(1))/(4 -1) = (270 -120)/(3) = 50

The average rate of the change from x = 1 to x = 4 is about 50.* This means profit will increase on average $50 for each $1 increase in price in what interval.

If we take the peak profit to be $270 we can write f(x) as:

f(x) 16.875x(x-8)

Then f(1) = 118.15 and average rate of change is 50.625.

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The probability of getting at least one 2 given that the sum of the numbers is 7 is 2/6 or 1/3.

To find the probability that the number 2 has appeared at least once given that the sum of the numbers is 7, we need to use the concept of conditional probability.

Let's consider the possible outcomes when two dice are rolled. The total number of outcomes is 36, as each die has six possible outcomes.

Out of these 36 outcomes, there are six outcomes in which the sum of the numbers appearing on the upper faces is 7. These outcomes are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).

Out of these six outcomes, there are two outcomes in which the number 2 appears at least once: (1,6) and (2,5).

We can use the formula for conditional probability to verify our answer:

P(2 appears at least once | sum is 7) = P(2 appears at least once and sum is 7) / P(sum is 7)

P(2 appears at least once and sum is 7) = 2/36 = 1/18 (as there are two outcomes with a sum of 7 that have a 2 in them)

P(sum is 7) = 6/36 = 1/6

So, P(2 appears at least once | sum is 7) = (1/18) / (1/6) = 1/3, which is consistent with our previous answer.

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Answer:

432

Step-by-step explanation:

go 16x27 and that is your answer

Answer:

The area of the figureo will be 432

BECAUSE :-

You have to multiply 16 × 27 = 432

Hope Its Help You !!

The two consecutive positive integers are 5 and 6.

Let the two consecutive positive integers be x and x + 1. We are given that the product of these integers is 3 less than three times their sum. This can be expressed as:
[tex]x(x + 1) = 3(x + x + 1) - 3[/tex]
Now we can solve for x:
[tex]x^2 + x = 6x + 3 - 3[/tex]
[tex]x^2 + x = 6x[/tex]
[tex]x^2 - 5x = 0[/tex]
Factoring the left side of the equation, we get:
[tex]x(x - 5) = 0[/tex]
From this equation, x can be 0 or 5.

However, since the question asks for positive integers, we can't use x = 0. Therefore, x = 5.

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The subtraction of the polynomials (3.1x + 2.8z) - (4.3x - 1.2z) is -1.2x + 4x

A polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.

(3.1x + 2.8z) - (4.3x - 1.2z)

open parenthesis

3.1x + 2.8z - 4.3x + 1.2z

combine like terms

3.1x - 4.3x + 2.8z + 1.2z

-1.2x + 4x

Ultimately, -1.2x + 4x is the results of the subtraction of the polynomial.

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Answer:

d = 3.75

e = 8/3

Step-by-step explanation:

8/6 = 5/d = e/2

4/3 = 5/d

4d = 3 × 5

d = 3.75

4/3 = e/2

3e = 4 × 2

e = 8/3