Write a recursive formula for an,the nth term of the sequence 3,-12,48,-192

To find the equation of the tangent line, we need to find the derivative of both x and y with respect to t and evaluate them at t = 1 to get the slope of the tangent line. The equation of the line tangent to the curve at the point determined by t = 1 is y = (5/4)(x - 3) + 2.

dx/dt = 2t + 2

dy/dt = 3t^2 + 2t

At t = 1, dx/dt = 4 and dy/dt = 5

So the slope of the tangent line is m = dy/dx = (dy/dt)/(dx/dt) = 5/4

Now we need to find the point on the curve where t = 1.

x = t^2 + 2t = 1^2 + 2(1) = 3

y = t^3 + t^2 = 1^3 + 1^2 = 2

Therefore, the point on the curve where t = 1 is (3, 2)

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - 2 = (5/4)(x - 3)

Simplifying:

y = (5/4)x - (7/2)

So the equation of the line tangent to the curve at the point determined by t = 1 is y = (5/4)x - (7/2).

A curve is described by the parametric equations x = t^2 + 2t and y = t^3 + t^2. An equation of the line tangent to the curve at the point determined by t = 1 is given by the formula y = m(x - x1) + y1, where m is the slope, and (x1, y1) is the point of tangency.

First, find the point of tangency (x1, y1) by plugging t = 1 into the parametric equations:
x1 = (1)^2 + 2(1) = 3
y1 = (1)^3 + (1)^2 = 2

Next, find the derivatives of x and y with respect to t:
dx/dt = 2t + 2
dy/dt = 3t^2 + 2t

Now, find the slope m by dividing dy/dt by dx/dt at t = 1:
m = (dy/dt) / (dx/dt) = (3(1)^2 + 2(1)) / (2(1) + 2) = (5/4)

Finally, plug the slope m and point (x1, y1) into the equation of the tangent line:
y = (5/4)(x - 3) + 2

So, the equation of the line tangent to the curve at the point determined by t = 1 is y = (5/4)(x - 3) + 2.

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The probability that the point chosen is inside the right triangle outlined is approximately 0.3, or 8.33%, rounded to 2 decimal places.

To find the chance that a factor chosen in the ordinary polygon is likewise in the proper triangle mentioned, we need to examine the areas of the two shapes. The location of the everyday polygon may be determined using the formulation:

Area of everyday polygon = (variety of facets × period of 1 side × apothem)/2

The region of the right triangle can be found using the system:

Area of proper triangle = (base × top)/2

The probability is then given by way of the ratio of the 2 areas:

Probability = Area of proper triangle / Area of normal polygon

However, to apply this formulation, we need to recognize some values that aren't given within the query, inclusive of the range of facets, the duration of one facet, the apothem, and the base and peak of the triangle. Without those values, we can't calculate the exact opportunity. We can most effectively estimate it by looking at the discernment and making a few assumptions.

One possible way to estimate the chance is to anticipate that the everyday polygon is a hexagon (has six aspects) and that the right triangle is 1/2 of one among its facets. Then we will approximate the length of one facet as 1 unit and the apothem as 0.866 units (the use of trigonometry). The base and height of the triangle would then be zero. 5 units and 0.866 units respectively.

Using those values, we are able to estimate the areas as follows:

Area of regular polygon ≈ (6 × 1 × 0.866)/2 ≈ 2.598 devices² Area of right triangle ≈ (0.5 × 0.866)/2 ≈ 0.2165 devices²

Probability ≈ 0.2165 / 2.598 ≈ 0.0.33

Therefore, the opportunity is approximately 0.3, or 8.33%, rounded to 2 decimal places.

Note: This is best an estimate primarily based on a few assumptions and approximations. The actual possibility might also vary depending on the actual values of the parameters worried.

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Answer:

x = -2 and y = 2.5

Step-by-step explanation:

using elimination method:

y = 0.25x + 3                 call this equation '1'

x = -4y + 8

bring 4y on its own

4y = -x + 8                       call this equation '2'

multiply '1' by 4:

4y = x + 12                      call this equation '3'

add '2' and '3'

8y = (-x + x) + 20

8y = 20

y = 20/8 = 2.5.

go back to '1'

we have y = 0.25x + 3

              2.5 = 0.25x + 3

 subtract 3 from both sides

2.5 - 3 = 0.25x

-0.5 = 0.25x

multiply both sides by 4

-2 = x

x = -2

now put both y =2.5 and x = -2 into '2' to see if all is fine

4y = -x + 8

4(2.5) = -(-2) + 8

10 = +2 + 8

10 = 10

so x = -2 and y = 2.5

The function y = 14(1.49)ˣ is categorized as growth with 49% percentage increase

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

y = 14(1.49)ˣ

An exponential function is represented as

y = abˣ

If b > 1, then it is a growth function

Otherwise, it a decay function

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

y = 14(1.49)ˣ is a growth function because 1.49 is greater than 1

The percentage increase is then calculated as

percentage increase = 1.49 - 1

percentage increase = 0.49

Express as percentage

percentage increase = 49%

Hence, the percentage increase is 49%

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If a flag pole that is 15 feet tall casts a shadow that is 22 feet long. at the same time of day, the shadow of a nearby tree is 52.3 feet long then the tree is 35.5 feet tall

To determine the height of the tree, we need to use ratios and proportions. We know that the flagpole is 15 feet tall and casts a shadow of 22 feet. Using these values, we can create a proportion:
15/22 = x/52.3
To solve for x, we can cross-multiply:
15 x 52.3 = 22 x
x = (15 x 52.3)/22
x = 35.5
Therefore, the tree is 35.5 feet tall.
In mathematics, proportions are often used to compare two quantities. In this case, we used the ratio of the height of the flagpole to the length of its shadow to create a proportion and find the height of the nearby tree. It's important to note that this calculation assumes that both the flagpole and tree are standing vertically and that the angle of the sun's rays is constant. Understanding and using proportions is a valuable skill in many areas of math and science, including geometry, physics, and engineering. By using ratios and proportions, we can compare different quantities and make calculations that help us better understand the world around us.

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According to the U.S. Census Bureau, in 2010, by the age of 40, approximately 85% of individuals had ever been married.

This statistic is based on data from the American Community Survey, which is conducted by the U.S. Census Bureau. The survey includes questions about marital status and provides information on the percentage of individuals who have ever been married by various ages. The statistic that 85% of individuals had ever been married by the age of 40 suggests that marriage is still a common life experience in the United States. However, it's important to note that this statistic may be influenced by a variety of factors, including changes in societal attitudes towards marriage, cultural and religious practices, and economic factors. Additionally, it's important to consider that this statistic may not be representative of all populations or demographic groups, as marriage rates can vary significantly based on factors such as race, ethnicity, and income.

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The solution is: 3.7%, is the probability that the next customer will be a woman who requests a convertible.

Here, we have,

given that,

At a car rental office, 63% of the customers are men and 37% are women.

If 25% of people request a compact car, 37% request a full-sized, 10% request a convertible,16% request an SUV, and 12% request a luxury car

As per given

P(woman)= 37%

P(convertible) = 10%

So combined probability is:

P = 37%*10%

  = 37%*0.1

  = 3.7%

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complete question:

At a car rental office, 63% of the customers are men and 37% are women. If 25% of people request a compact car, 37% request a full-sized, 10% request a convertible,16% request an SUV, and 12% request a luxury car, what is the probability that the next customer will be a woman who requests a convertible?

Answer:

Answer: 1/7 as a decimal is 0.143

1-7-as-a-decimal

Let us understand the division method to write 1/7 as a decimal.

Explanation:

To convert any fraction to its decimal form, we just need to divide the numerator by the denominator.

Here, the fraction is 1/7 which means we need to divide 1 by 7 (1 ÷ 7)

This gives the answer as 0.14285714... which can be rounded off and written as 0.143. So, 1/7 as a decimal is 0.143

Irrespective of the methods used, the answer to 1/7 as a decimal will always remain the same.

Answer:

[tex] {2}^{ \frac{2}{7} } \times {2}^{ \frac{2}{7} } = {2}^{ \frac{2}{7} + \frac{2}{7} } [/tex]

[tex] {2}^{ \frac{2}{7} } \times {2}^{ \frac{2}{7} } = {2}^{ \frac{4}{7} } [/tex]

The value of the length of the hypotenuse is,

⇒ c = √85

Since, Three vertices and three angles totaling 180 degrees make up a triangle, a three-sided polygon with three sides.

And, Two rays (half-lines) that share a terminal make up an angle. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.

We have to given that;

In triangle ,

Perpendicular side = 9 mm

Base = 2 mm

Since, We know that;

The Pythagorean theorem states that the square of the hypotenuse of a right triangle equals the sum of the squares of its two opposite sides.

Hence, By Pythagoras theorem we get;

⇒ Hypotenuse² = Perpendicular² + Base²

⇒ c² = 9² + 2²

⇒ c² = 81 + 4

⇒ c = √85

Thus, The length of the hypotenuse is,

⇒ c = √85

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The distance between the Woozy Wheel and the Roller Rail is 13 units.

To determine the distance between the Woozy Wheel and the Roller Rail, we can use the distance formula in the coordinate plane.

The coordinates of the Woozy Wheel are (-14, 1), and the coordinates of the Roller Rail are (-2, -4).

Using the distance formula, the distance (d) between two points (x₁, y₁) and (x₂, y₂) is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates of the Woozy Wheel and the Roller Rail into the formula:

d = √((-2 - (-14))² + (-4 - 1)²)

= √(12² + (-5)²)

= √(144 + 25)

= √169

= 13

Therefore, the distance between the Woozy Wheel and the Roller Rail is 13 units.

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The probability of choosing 3 men and 1 woman at random for a 4 person committee can be calculated using the combination formula.

We want to choose 3 men from a pool of 10 men, which can be done in 10 choose 3 ways. We also want to choose 1 woman from a pool of 6 women, which can be done in 6 choose 1 ways. The total number of ways to choose a 4 person committee from a pool of 16 people is 16 choose 4. Therefore, the probability of choosing 3 men and 1 woman at random for a 4 person committee is:

(10 choose 3) * (6 choose 1) / (16 choose 4) = 120 * 6 / 1820 = 0.3956

So, the probability of choosing 3 men and 1 woman at random for a 4 person committee is approximately 0.3956 or 39.56%. This means that if we randomly choose a 4 person committee from a pool of 10 men and 6 women, there is a 39.56% chance that the committee will consist of 3 men and 1 woman.

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The probability that the first grape candy chosen from the bag will be, at least, the third candy chosen overall is 0.5608.

To solve this problem, we need to use the probability formula:
P(at least third grape candy) = P(first candy is not grape) x P(second candy is not grape) x P(third candy is grape) + P(first candy is not grape) x P(second candy is grape) x P(third candy is grape) + P(first candy is grape) x P(second candy is not grape) x P(third candy is grape) + P(first candy is grape) x P(second candy is grape) x P(third candy is grape)

From the given information, we know that the probability of choosing a grape candy from the bag is 26%. Therefore, the probability of choosing a non-grape candy is 74%.

Using this information, we can substitute the values into the formula:

P(at least third grape candy) = 0.74 x 0.74 x 0.26 + 0.74 x 0.26 x 0.26 + 0.26 x 0.74 x 0.26 + 0.26 x 0.26 x 0.26

Simplifying this expression, we get:

P(at least third grape candy) = 0.4524 + 0.0508 + 0.0508 + 0.0068

P(at least third grape candy) = 0.5608

Therefore, the probability that the first grape candy chosen from the bag will be, at least, the third candy chosen overall is 0.5608.

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The equation of the circle in standard form is (x - 5)² + (y + 4)² = 36

The center of the circle is the midpoint of the diameter.

Using the midpoint formula, we can find the center as follows:

x-coordinate of center = (x-coordinate of endpoint 1 + x-coordinate of endpoint 2)/2

= (-1 + 11)/2

= 5

y-coordinate of center = (y-coordinate of endpoint 1 + y-coordinate of endpoint 2)/2

= (-4 - 4)/2

= -4

So the center of the circle is (5, -4) and the radius is half the length of the diameter:

radius = distance between endpoints of diameter/2

= √(11 - (-1))² + (-4 - (-4))²]/2

= 6

Therefore, the equation of the circle in standard form is (x - 5)² + (y + 4)² = 36

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Answer:

Step-by-step explanation:

You want the values of the variables x and y, and the measure of angle Q in the given figure when ∆QPR ≅ ∆SPR.

The triangles are congruent by the ASA postulate when the angles at P are congruent and the angles at R are congruent.

  (2x +1)° = (x +18)°

  x = 17 . . . . . . . . . . . divide by °, subtract x+1

  (x +18)° = (17 +18)° = 35° . . . . the measures of the angles at P

  (8y -4)° = (4y +28)°

  4y = 32 . . . . . . . . . . . divide by °, add 4-4y

  y = 8 . . . . . . . . . divide by 4

  (4y +28)° = (32 +28)° = 60° . . . . . . the measures of the angles at R

The sum of angles in ∆QPR is 180°, so ...

  Q +35° +60° = 180°

  Q = 85° . . . . . . . . . . . subtract 95°

For x = 17 and y = 8, the triangles are congruent. m∠Q = 85°.

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Mindy's pay depends on the number of boots she produced. According to the given pay scale, we can break down her pay as follows:

For the first 50 boots, Mindy earns $1.65 per boot. So, for the first 50 boots, her pay is 50 * $1.65 = $82.50.

For the next 100 boots (51-150), Mindy earns $3.30 per boot. So, for these 100 boots, her pay is 100 * $3.30 = $330.

For the next 50 boots (151-200), Mindy earns $4.95 per boot. So, for these 50 boots, her pay is 50 * $4.95 = $247.50.

In total, Mindy has produced 200 boots so far, and her pay for these boots is $82.50 + $330 + $247.50 = $660.

Now, for the remaining 192 - 200 = -8 boots (less than 200), Mindy earns $6.00 per boot. Since she hasn't produced any additional boots beyond 200, we don't need to consider this part.

Therefore, Mindy's pay for producing 192 boots is $660 (according to the breakdown above).

So, the correct answer is E. None of these.

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Let's visualize the parallelogram-shaped land with sides of 240m and 160m. We know that the distance between the 240m sides is 40m. Let's denote this distance as "d".

To find the distance between the 160m sides, we can use the concept of similar triangles. The triangles formed by the sides of the parallelogram are similar. In the smaller triangle, the base is 160m, and the corresponding side in the larger triangle is 240m. Similarly, the height of the smaller triangle is "d", and the corresponding side in the larger triangle is 40m. Using the property of similar triangles, we can set up the following proportion:

160m / 240m = d / 40m

Simplifying the proportion, we get:

2/3 = d / 40m

Cross-multiplying, we have:

d = (2/3) * 40m

Calculating the value, we find:

d = 26.67m

Therefore, the distance between the 160m sides of the parallelogram-shaped land is approximately 26.67m.

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The calculated elements in the set B is {4, 5, 6}

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

The above means that

U = {1, 2, 3, 4, 5, 6}

The numbers greater than 3 in the above set are

Elements = 4, 5 and 6

This means that the elements in the set B is {4, 5, 6}

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Rounding to two decimal places, the relative frequency of male students who are chemistry majors is approximately 0.23.Therefore, the answer is 0.23.

To find the relative frequency of male students who are chemistry majors, we need to divide the number of male chemistry majors by the total number of male students in the sample.

According to the contingency table, there are 35 male chemistry majors.

To calculate the relative frequency, we divide the number of male chemistry majors by the total number of male students:

Relative Frequency = Number of Male Chemistry Majors / Total Number of Male Students

Relative Frequency = 35 / (35 + 34 + 38 + 42)

Relative Frequency ≈ 35 / 149

Relative Frequency ≈ 0.2349.

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A. From the stem and leaf plot below, there are about 28,000 cars manufactured before 2000.

B. lower quartile (Q1) is between the 7th and 8th values (1995+1997)/2 = 1996. Upper quartile is  the 23rd and 24th values (2009 + 2010) = 2009.5.

C. The number of cars in the city that were manufactured between 1996 and 2009.5 is 37100.

D. To determine the number of car manufactured in 1996 and 2009.5, first determined the relevant proportions from the sample data. Then, multiply the proportion by the total number of cars in the city to estimate the number of cars manufactured before between 1996 and 2007.5,

A. To find the number of cars manufactured at the given period, we find the number of cars sampled that were created before 2000. From the stem-and-leaf plot, we can see that there are 12 cars manufactured before 2000.

Proportion of cars = 12/30 = 0.4.

Using the proportion, we find the number of cars manufactured before 2000.

70,000 × 0.4.

=28,000

B The  lower quartile (Q1) is the 25th percentile, and the upper quartile (Q3) is the 75th percentile.

= 0.25×(n+1)              

= 0.25×(30+1)

= 7.75 Therefore the lower quartile is between 7th and 8th values.

Q1 = (1995+1997)/2 = 1996.

0.75×(n+1)

= 0.75×(30+1)

= 23.25  Therefore the upper quartile is between 23rd and 24th values.

(2009+2010)/2 = 2009.5

C. There are 16 cars manufactured between 1996 and 2009.5

16/30 = 0.53

= 70,000×0.53

= 37100

The answer provided is based on the stem and leaf plot below

3. Brittney randomly selected 30 cars in a parking lot and determined each car's year of manufacture. She made this stem- and-leaf plot to show the results.

CARS IN PARKING LOT-YEAR OF MANUFACTURE

197 | 1

198 | 26

199 | 345577899

200 | 12455677899

201 | 0011222

Key: 197 |1 = 1971

A There are about 70,000 cars in the city where Brittney lives. According to Brittney's data, about how many of the cars in her city were manufactured before the year 2000?

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The value of x is 35 degree.

We know,

The angle sum property of a quadrilateral states that the sum of the interior angles of any quadrilateral is always equal to 360 degrees.

In other words, if you add up the measures of all the interior angles of a quadrilateral, the total will always be 360 degrees.

So, applying angle sum property in Trapezium

145 + 110 + 70 + x = 360

325 + x = 360

x = 360 - 325

x = 35 degree

Thus, the value of x is 35 degree.

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Answer:

[tex]\pi 5[/tex]

Step-by-step explanation:

Use the formula [tex]C=\pi d[/tex].

[tex]C=\pi 5[/tex]

So your answer is [tex]\pi 5[/tex].

The sample size should be selected as 100 in order to be 99% confident that the sample mean differs from the population mean by ±0.5 km (or within a range of 0.5 km).

To determine the sample size needed to estimate the distance students travel to school with a 99% confidence level and a margin of error of ±0.5 km, we can use the formula for sample size calculation:

n = (Z * σ / E)^2

where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (in this case, 99% confidence level, which corresponds to Z = 2.576)

σ = population standard deviation

E = margin of error

Plugging in the given values:

n = (2.576 * 2.25 / 0.5)^2

Calculating this equation gives us the required sample size:

n ≈ 99.98

Since we cannot have a fractional sample size, we round up to the nearest whole number.

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8 cups = 64cm

From the catalog, we know that a stack of 2 cups is 16 cm tall, and a stack of 4 cups is 20 cm tall.

To find the height of a stack of 8 cups, we can use proportionality.

Let x be the height, in cm, of a stack of 8 cups. Then, we can set up the following proportion:

2 cups / 16 cm = 8 cups / x cm

Cross-multiplying, we get:

2 cups * x cm = 16 cm * 8 cups

Simplifying, we get:

2x = 128

x = 64 cm

Therefore, the height of a stack of 8 cups is 64 cm.

The coordinates of the point B of vector is B ( -5 , -3 )

Given data ,

To find the coordinates of the terminal point B, we can start with the initial point of vector AB and add its components.

Initial point of AB: (-9, 8)

x-component of AB: 4

y-component of AB: -11

To find the coordinates of the terminal point B, we add the x-component and y-component to the corresponding coordinates of the initial point.

x-coordinate of B = x-coordinate of initial point + x-component of AB

x = -9 + 4

x = -5

y-coordinate of B = y-coordinate of initial point + y-component of AB

y = 8 + (-11)

y = -3

Hence , the coordinates of the terminal point B are (-5, -3)

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The slope of the line above include the following: 1/5.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (3 - 0)/(7 + 8)

Slope (m) = (3)/(15)

Slope (m) = 1/5.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 1/5.

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It takes 7 hours to travel 385 miles at a constant speed.

To solve this problem, we need to use the direct variation formula, which states that distance traveled is directly proportional to time spent driving. This means that if we double the time spent driving, the distance traveled will also double.

Using this formula, we can set up a proportion to find the answer. We know that the car travels 330 miles in 6 hours, so we can write:

330/6 = 385/x

Where x is the time it takes to travel 385 miles.

To solve for x, we can cross-multiply and simplify:

330x = 2310

x = 7


It's important to note that this problem assumes that the car maintains a constant speed throughout the entire trip. If the car speeds up or slows down at any point, the distance traveled and time spent driving will not follow a direct variation relationship.

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The radius of the circle is 13.

To find the radius of the circle with the center at the origin and passing through the point (-12, 5), we can use the distance formula.

The distance formula between two points (x1, y1) and (x2, y2) is given by:

Distance = √[(x2 - x1)² + (y2 - y1)²]

In this case, the center of the circle is at the origin (0, 0), and the given point is (-12, 5). Plugging these values into the distance formula, we get:

Distance = √[(-12 - 0)² + (5 - 0)²]

= √[(-12)² + 5²]

= √[144 + 25]

= √169

= 13

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Finally, we need to subtract one-half the original number, which is $\frac{x}{2}$. So the final expression is:$$\frac{x+100}{2} - \frac{x}{2} = 50$$

1. Let's call the original number x.
2. Double the number: 2x
3. Add 200: 2x + 200
4. Divide the answer by 4: (2x + 200) / 4
5. Subtract one-half the original number: ((2x + 200) / 4) - (x / 2)

Now let's simplify the expression:

((2x + 200) / 4) - (x / 2)

= (2x/4 + 200/4) - (x / 2)

= (x/2 + 50) - (x / 2)

= x/2 - x/2 + 50

= 0 + 50

So, the value of the result is 50.

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