The Question is in the picture

Answer:

Step-by-step explanation:

y = x³ - 27x

(i). Domain: x ∈ ( - ∞ , ∞ )

(ii). f'(x) = 3x² - 27 ; f''(x) = 6x

(iii). 3x² - 27 = 0 ⇔ x² - 9 = 0 ⇒ [tex]x_{12}[/tex] = ± 3

If [tex]x_{1}[/tex] = - 3 , then [tex]y_{1}[/tex] = 54

If [tex]x_{2}[/tex] = 3 , then [tex]y_{1}[/tex] = - 54

Points are ( - 3 , 54 ) and ( 3 , - 54 )

(iv). ( - ∞ , - 3 ) ∪ ( - 3 , 3 ) ∪ ( 3 , ∞ )

increasing ----> decreasing -----> increasing

(v). x = - 3 is the maxima, the local maximum value is 54, f(-3) = 54

x = 3 is the minima, the local minimum value is ( - 54 ), f(3) = - 54

(vi). Concave up if f''(x) > 0 ; The interval is ( - ∞ , 0 )

Concave down if f''(x) < 0 ; The interval is ( 0 , ∞ )

(vii). Point of inflection is ( 0 , 0 )

f''(x) = 0

6x = 0

x = 0

Answer:

To determine when each company is projected to break even, Jami needs to find the point where the Cost and Revenue equations intersect. This point will represent the month when the business is projected to break even, as the Cost and Revenue will be equal.

Using the given equations, we can set the Cost equation equal to the Revenue equation for each business:

Blysis: -13124.3190x + 3586 = -6941915384x + 21954

Solving for x, we get x = 0.00057 months.

Since this value is extremely small, we can assume that Blysis is already profitable.

Appster: -13124.3190x + 3586 = -6941915384x + 21954

Solving for x, we get x = 0.00057 months.

Since this value is extremely small, we can assume that Appster is already profitable.

Enrich: -3586x - 21954 = -6941915384x + 13174

Solving for x, we get x = 0.0035 months.

Since this value is also very small, we can assume that Enrich is already profitable.

Green Team: 178420.64421x - 68419 = -4289115387x + 13174

Solving for x, we get x = 0.0009 months.

Since this value is extremely small, we can assume that Green Team is already profitable.

Southwest Fusion: -13124.3190x + 4289115387x = 13174

Solving for x, we get x = 35.23 months.

This value indicates that Southwest Fusion is projected to break even in approximately 35 months.

Zoo to You: -13124.3190x + 54209539 = -10381x

Solving for x, we get x = 4.05 months.

This value indicates that Zoo to You is projected to break even in approximately 4 months.

Based on these projections, Jami should recommend Blysis, Appster, Enrich, and Green Team to the investor, as they are already profitable or expected to break even within the next 24 months. Southwest Fusion and Zoo to You may not be as attractive for investment, as they are projected to take longer to become profitable.

Step-by-step explanation:

The area of the shaded sector is 575π/9 square units.

The area of the unshaded sector is 325π/9 square units

The value of the angle subtended by the unshaded sector is 130⁰ the value of the angle subtended by the shaded sector is 230⁰.

To find the area of a sector with radius 10 units and angle 230⁰, we can again use the same formula:

Area of sector = (angle/360) x πr^2

Substituting the values given in the formula, we get:

Area of sector = (230/360) x π(10)²

= (23/36) x 100π

= 575π/9 square units

To find the area of a sector with radius 10 units and angle 130⁰, we can use the formula:

Area of sector = (angle/360) x πr^2

Substituting the values given in the formula, we get:

Area of sector = (130/360) x π(10)^2

= (13/36) x 100π

= 325π/9 square units

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The function f(x) = (x-2)(x+4) is a quadratic function that can be written in standard form as f(x) = x^2 + 2x - 8.

To graph this function, we can start by finding the vertex, which is located at x = -b/2a = -2/2 = -1, and then plotting a few additional points to determine the shape of the parabola.

To find the y-coordinate of the vertex, we plug x = -1 into the equation and get f(-1) = (-1)^2 + 2(-1) - 8 = -7. So the vertex is at (-1, -7).

We can also find the x-intercepts by setting f(x) = 0 and solving for x:

(x-2)(x+4) = 0

x-2 = 0 or x+4 = 0

x = 2 or x = -4

So the x-intercepts are at (2, 0) and (-4, 0).

To find the y-intercept, we set x = 0 and get f(0) = (0-2)(0+4) = -8. So the y-intercept is at (0, -8).

Now we can plot these points and sketch the parabola:

```

|

|

|

| *

|

|

------+------------> x

|

|

|

|

|

|

```

The domain of the function is all real numbers, since there are no restrictions on the values that x can take.

To find the range of the function, we can look at the vertex and see that the lowest point on the parabola is at y = -7. Since the parabola opens upward, the range extends from -7 to infinity:

Range: [-7, ∞)

This Took me a long long time

a. The numeric values of the function are given as follows:

b. The function rule is given as follows: y = 2x - 8.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

From the table, when x = 0, y = -8, hence the intercept b is given as follows:

b = -8.

Considering points (0, -8) and (10, 12), when x increases by 10, y increases by 20, hence the slope m is given as follows:

m = 20/10

m = 2.

Hence the function is given as follows:

y = 2x - 8.

To complete the table, the numeric values are given as follows:

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Answer

3390

Step-by-step explanation:

rasheed still owes six months of rent because thats the lease that they signed so 565 times six is 3390. hope this helps.

The equivalent choices are (A) sqrt 3 and (F) sqrt 5. We can simplify the given quotient by rationalizing the denominator.

To do this, we multiply both the numerator and denominator by the conjugate of the denominator, which is sqrt 15. This gives us:

sqrt 75 / sqrt 15 = (sqrt 75 / sqrt 15) * (sqrt 15 / sqrt 15) = sqrt (75 * 15) / 15 = sqrt 1125 / 15

Now we can simplify the numerator by factoring out perfect squares. We have:

sqrt 1125 = sqrt (225 * 5) = sqrt 225 * sqrt 5 = 15 * sqrt 5

Substituting this back into our expression, we get:

sqrt 75 / sqrt 15 = (15 * sqrt 5) / 15 = sqrt 5

Therefore, the equivalent choices are (A) sqrt 3 and (F) sqrt 5. Choice (B) 5 is not equivalent because it does not have a square root, while (C) sqrt 15 / sqrt 3 and (D) sqrt 25 / sqrt 5 are not equivalent because they are not in simplest form. Choice (E) 15/3 is equivalent to 5 but not to the given expression sqrt 75 / sqrt 15.

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12 + 7 - 3 - 2

There are many ways to use mathematical symbols to make 3, 7, 12, and 2 equal 15. Here are a few examples:

3 + 7 + 2 + 3 = 15

(Add the first three numbers together, then add one of the 3's to get 15)

12 - 7 - 3 + 13 = 15

(Subtract 7 and 3 from 12 to get 2, then add 13)

2(7 + 3) - 12 = 15

(Add 7 and 3 together, multiply by 2, then subtract 12)

7(2) + 3 + 3 - 4 = 15

(Multiply 7 by 2, add 3 and the other 3, then subtract 4)

These are just a few examples - there are many other ways to use mathematical symbols to make these numbers equal 15!

The x-intercepts of the given expression which is a rational function is calculated to be 0 and the y-intercepts are ±√25.

The given expression is a rational function and can be written as the quotient of two polynomials.

The numerator of the rational expression is -x⁷ and the denominator is x²−25. The numerator is a degree 7 polynomial and the denominator is a degree 2 polynomial.

To find the x-intercepts, we need to set the numerator equal to zero and solve for x.

-x⁷ = 0

x⁷ = 0

x = 0

To find the y-intercepts, we need to set the denominator equal to zero and solve for x.

x²−25 = 0

x² = 25

x = ± √25

Therefore, the x-intercepts of the given expression are 0 and the y-intercepts are ± √25.

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Question :

Find the intercepts of the given function.

y = (-x⁷)/(x²−25)

3x² - 2x + 15x - 10 can be factored by grouping as:

3x² - 2x + 15x - 10

= (3x - 2)(x + 5)

Explanation:

Group the first two terms and the last two terms together:

(3x² - 2x) + (15x - 10)

Factor out the GCF from each group:

3x(x - (2/3)) + 5(3x - 2)

Now we have a common factor of (3x - 2):

(3x - 2)(x + 5)

Step-by-step explanation:

3x² - 2x + 15x - 10

=x(3x-2)+5(3x-2)

=(x+5)(3x-2)

(a) for every integer z, we can find integers x and y such that f(x, y) = z, and thus f(x, y) is onto.

(b) f(x, y) = |x| - |y| is not onto.

(a) To show that the function f(x, y) = 2x - 4y is onto, we need to show that for every integer z, there exists integers x and y such that f(x, y) = z.

Let z be an arbitrary integer. Then we need to find integers x and y such that 2x - 4y = z. We can rewrite this equation as x = (z + 4y)/2.

Now, if z is even, then we can choose any even number for y and solve for x using the above equation. Conversely, if z is odd, we can choose any odd number for y and solve for x.

Therefore, for every integer z, we can find integers x and y such that f(x, y) = z, and thus f(x, y) is onto.

(b) To show that the function f(x, y) = |x| - |y| is not onto, we need to find an integer z such that there does not exist integers x and y such that f(x, y) = z.

Let z = -1. Then we need to find integers x and y such that |x| - |y| = -1. However, the absolute value of any integer is non-negative, so |x| and |y| are both non-negative.

Therefore, |x| - |y| is non-negative, and it is impossible for f(x, y) to equal -1.

Hence, there does not exist integers x and y such that f(x, y) = -1, and thus f(x, y) is not onto.

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The edges where this rectangle could be added in order to complete the net are edges A, H, E and D.

The net shape of a rectangular pyramid is a two-dimensional representation of the three-dimensional shape that can be cut out and folded to create the actual pyramid. It consists of a rectangular base and four triangular faces that meet at a single point or vertex.

To create the net shape of a rectangular pyramid, start with a rectangular base and draw four lines from each of the four corners of the base to a single point above the center of the rectangle. These lines should be equal in length and form four congruent triangles.

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Answer:

the university should charge $13.50 per ticket to maximize revenue, and 85,000 people will attend at that price.

Step-by-step explanation:

To find the price per ticket that maximizes revenue, we need to find the price that maximizes the product of the number of tickets sold and the revenue per ticket. Revenue per ticket is equal to the ticket price plus the average concession spending per person, or $27 + $3 = $30.

Let x be the number of $3 decreases in ticket price, so the ticket price can be expressed as $27 - $3x. The number of people attending can be expressed as 40,000 + 10,000x.

Therefore, the revenue can be expressed as:

Revenue = (Ticket price) x (Number of tickets sold) x (Concession spending per person)

Revenue = ($27 - $3x) x (40,000 + 10,000x) x $3.00

Expanding this expression, we get:

Revenue = $81,000,000 + $270,000,000x - $30,000,000x^2

To maximize revenue, we need to find the value of x that maximizes this quadratic function. We can do this by finding the vertex of the parabola, which is located at:

x = -b / 2a

where a = -30,000,000, b = 270,000,000, and c = 81,000,000

x = -270,000,000 / 2(-30,000,000)

x = 4.5

Since x represents the number of $3 decreases in ticket price, we can find the optimal ticket price by subtracting 3 times x from the original price of $27:

Optimal ticket price = $27 - $3(4.5) = $13.50

The optimal number of people attending can be found by substituting x = 4.5 into the expression for the number of people attending:

Number of people attending = 40,000 + 10,000(4.5) = 85,000

Answer:

d

Step-by-step explanation:

1 kg has 1000 g

Then 2,5 kg has 2,5 × 1000 = 2500 g

You can also make a proportion:

1 kg - 1000 g

2,5 kg - x g

Use the property of the proportion to find x (cross-multiply):

x = 2,5 × 1000 / 1 = 2500 g

The random variable X represents the number of Californians in the sample of 6 who have been to Disneyland. X is a binomial random variable because each person in the sample can be classified as either having been to Disneyland or not, which is a binary outcome.The probability of success (having been to Disneyland) is constant at 0.41 for each person in the sample.  the probability that exactly 3 Californians in the sample of 6 have been to Disneyland is 0.274 or approximately 27.4%. The mean of X is 2.46.  The standard deviation of X is 1.27. The probability that the number of Californians in the sample who have been to Disneyland is within one standard deviation of the mean is 0.767 or approximately 76.7%.

a) The random variable X represents the number of Californians in the sample of 6 who have been to Disneyland.

b) X is a binomial random variable because the following conditions are met:

Each person in the sample can be classified as either having been to Disneyland or not, which is a binary outcome.

The probability of success (having been to Disneyland) is constant at 0.41 for each person in the sample.

The individuals in the sample are independent of each other.

c) To find the probability that exactly 3 people in the sample have been to Disneyland, we can use the binomial probability formula:

P(X = 3) = (6 choose 3) * (0.41)^3 * (1-0.41)^3 = 0.274

Therefore, the probability that exactly 3 Californians in the sample of 6 have been to Disneyland is 0.274 or approximately 27.4%.

d) The mean of X is given by the formula:

mean(X) = n * p = 6 * 0.41 = 2.46

Therefore, the mean of X is 2.46.

e) The standard deviation of X is given by the formula:

stddev(X) = sqrt(n * p * (1-p)) = sqrt(6 * 0.41 * (1-0.41)) = 1.27

Therefore, the standard deviation of X is 1.27.

f) To find the probability that the number of Californians in the sample who have been to Disneyland is within one standard deviation of the mean, we can use the normal approximation to the binomial distribution.

First, we need to find the z-scores corresponding to X = 1 and X = 4:

z1 = (1 - 2.46) / 1.27 = -1.17

z4 = (4 - 2.46) / 1.27 = 1.22

Then, we can use the standard normal distribution table to find the probabilities corresponding to these z-scores:

P(X ≤ 1) = P(Z ≤ -1.17) = 0.121

P(X ≤ 4) = P(Z ≤ 1.22) = 0.888

Finally, we can subtract these probabilities to find the probability that X is within one standard deviation of the mean:

P(1 < X < 4) = P(X ≤ 4) - P(X ≤ 1) = 0.888 - 0.121 = 0.767

Therefore, the probability that the number of Californians in the sample who have been to Disneyland is within one standard deviation of the mean is 0.767 or approximately 76.7%.

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The mean number of elective classes offered at different middle schools is given as follows:

8.25 elective classes per school.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The data-set in this problem is given as follows:

Hence the sum of the observations is given as follows:

2 x 7 + 3 x 8 + 2 x 9 + 1 x 10 = 66.

The number of observations is given as follows:

2 + 3 + 2 + 1 = 8 schools.

Hence the mean number is given as follows:

66/8 = 8.25 elective classes per school.

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Answer:

i  think it would be 24 times 6 althought since this is a college question its probably a lot more complex but ill just give it a shot and say its 168.

Step-by-step explanation:

i think its 168 because it woud be 6 more layers of that 24 cube layer so thatd be 6 times 24 which is 144 and then plus the other 24 thats already there it would be 168.

Answer:

144

Step-by-step explanation:

Area= L*W*H

(4*6)*6

24*6=144

(1) The graph that shows the solution of the inequality 7 ≤ n + 5 is the graph of option A.

(2) Eduardo wrote at least 34 pages before today.

(3)  The farmer needs to plant at least 8 rows of seeds to harvest at least 52 bushels of tomatoes.

The solution to the inequality 7 ≤ n + 5 is as follows:

7 ≤ n + 5

collect similar terms together

7 - 5 ≤ n

2 ≤ n

So we can interpret the result of this inequality as, n is greater than and equal to 2. Hence option A is the correct answer.

2. Let p be the number of pages Eduardo wrote before today. Then, the inequality that represents the situation is:

p + 16 > 50

To solve for p, first subtract 16 from both sides of the inequality:

p + 16 - 16 > 50 - 16

p > 34

Therefore, Eduardo wrote at least 34 pages before today.

3. Let r be the number of rows of seeds the farmer needs to plant. Then, the equation that represents the situation is:

6.5r ≥ 52

divide both sides of the equation by 6.5:

r ≥ 8

Therefore, the farmer needs to plant at least 8 rows of seeds to harvest at least 52 bushels of tomatoes.

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Answer:

x ≈ 30,37

y ≈ 29,00

Step-by-step explanation:

Use trigonometry:

[tex] \sin(38°) = \frac{9}{x} [/tex]

Now, use the property of the proportion to find x:

[tex]x = \frac{9}{ \sin(38°) } ≈30.37[/tex]

Do the same thing to find y:

[tex] \tan(38°) = \frac{9}{y} [/tex]

[tex]y = \frac{9}{ \tan(38°) } ≈29.00[/tex]

Answer:

52800 cm^3

Step-by-step explanation:

Given:

Rectangular prism

h = 6 cm (height)

l = 11 m = 1100 cm (length)

w = 8 cm (width)

[tex]v =a(base) \times h[/tex]

[tex]a(base) = l \times w = 1100 \times 8 = 8800 \: {cm}^{2} [/tex]

[tex]v = 8800 \times 6 = 52800 \: {cm}^{3} [/tex]

Thus, the current movie theater seats are 21.05 % of a theater seat from 30 years ago.

The change between a final value and even an initial value, presented as a percentage of the starting value, is the percent increase over two values. Subtract the starting value from the ending value to get the percent increase.

Next, divide the difference by the starting amount. In order to convert this value to a percentage, multiply it by 100%. The difference in percentage between the two numbers will be shown in the final result.

Given data:

width of current movie theatre seat = 23 inches.

width of 30 years ago movie theatre seat = 19 inches.

Let x be the percentage increase:

19 + x%19 = 23

1 + x% = 23/19

x/100 = 23/19 - 1

x/100 = 4/19

x = 400/19

x = 21.05 %

Thus, the current movie theater seats are 21.05 % of a theater seat from 30 years ago.

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Answer:12

Step-by-step explanation: 48/4

Answer:

see below.

Step-by-step explanation:

Use Trigonometric Expansion.

Verify the following identity:

[tex]cos(x)^2(tan(x)^2+1)=1[/tex]

Write tangent as [tex]\frac{sine}{cosine}[/tex]

[tex]cos(x)^2(\frac{sin(x)}{cos(x)} ^2+1)=1[/tex]

[tex]cos(x)^2(\frac{sin(x)}{cos(x)} ^2+1)=cos(x)^2(\frac{sin(x)^2}{cos(x)^2+1} )[/tex]

[tex](cos(x)^2(\frac{sin(x)^2}{cos(x)^2} +1))=1[/tex]

Put sin(x)^2/cos(x)^2 +1 over the common denominator cos(x)^2 : sin(x)^2/cos(x)^2+1 = cos(x)^2+sin(x)^2 /cos (x)^2:

cos(x)^2(cos(x)^2+sin(x)^2/cos(x)^2)=1

Cancel cos(x)^2 from the numerator to the denominator.

cos(x)^2(cos(x)^sin(x)^2)/cos(x)^2=cos(x)^2(cos(x)^2+sin(x)^2)/cos(x)^2=cos(x)+sin(x)^2:

(cos(x)^2+sin(x)^2=1

Substitute cos(x)^2 + sin (x)^2 = 1:

1 =1

With an eye level of 35 feet above the water, you can see approximately 7.24 miles to the horizon.

Multiplication is a mathematical operation that involves combining two or more numbers to find their total or product. It is often denoted by the symbol "×" or "*", and the result of multiplication is called the product. For example, multiplying 3 and 4 gives a product of 12, written as 3 × 4 = 12.

To find out how far you can see when your eye level is 35 feet above the water, we can use the given formula:

d = √(3h/2)

Plugging in h = 35, we get:

d = √(3 * 35/2)

d = √(105/2)

d = √52.5

d ≈ 7.24

So, when your eye level is 35 feet above the water, you can see approximately 7.24 miles to the horizon. Keep in mind that this is an approximation and actual visibility may vary due to factors such as atmospheric conditions and the height of objects obstructing the view.

Therefore, With an eye level of 35 feet above the water, you can see approximately 7.24 miles to the horizon.

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Answer:

Since the vertex is (0, -4), we know that the equation of the parabola will have the form:

y = a(x - 0)^2 - 4

where "a" is the coefficient that determines whether the parabola opens up or down.

To find the value of "a", we can use the fact that the parabola passes through the point (10, 1):

1 = a(10 - 0)^2 - 4

1 + 4 = 100a

5 = 100a

a = 1/20

Substituting this value of "a" into the equation for the vertex form, we get:

y = (1/20)x^2 - 4

So the equation of the parabola in vertex form is y = (1/20)x^2 - 4, with vertex (0, -4) and passing through (10, 1).

Step-by-step explanation:

Answer:D) A peak is a bar that is higher than the other bars around it is true.Step-by-step explanation:A histogram is an approximate representation of numerical data distribution.When multiple data points on a number line are close to the same value (or a neighbourhood of values), a cluster arises.A peak is a bar that stands taller than the bars around it. A single peak or plateau is formed when two or more adjacent bars are the same height but are taller than the bordering bars. A gap is a class or classes with frequency 0 on one side but non-zero on the other.

Step-by-step explanation:

Explanation:

I'll use x in place of 'a'

I'll also use y in place of b.

The equation 5a+b = 7 turns into 5x+y = 7

Solve for y to get

5x+y = 7

y = -5x+7

This is in slope-intercept form y = mx+b

The negative reciprocal of the slope is 1/5. Flip the fraction and flip the sign. So if -5 is the original slope, then 1/5 is the perpendicular slope.

Of the answer choices, only choice C has a slope of 1/5. Think of b = (1/5)a-2 as y = (1/5)x - 2

Therefore, choice C is the answer.

The equation of a line that is perpendicular to '5a+b = 7' is 'b = (1/5)a + c'. Therefore, the correct option among given choices is 'b = (1/5)a - 2' (option C).

To start with, the given line's equation, 5a + b = 7, can be converted to slope-intercept form (b = mx + c), where m represents the slope of line, and 'c' is the y-intercept.

Converting the equation, 5a + b = 7, we get b = -5a + 7. This tells us the slope of our original line is -5.

Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. So, the line perpendicular to the one with a slope of -5 would have a slope of 1/5. Therefore, the equation of a line perpendicular to '5a+b = 7' would be in the form 'b = (1/5)a + c'.

Thus, the correct answer is option C : b = (1/5)a - 2.

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Hence the sum of rational expressions is [tex]\frac{9x^2-5x+2}{7x^2-14x}[/tex] option  D is correct.

You must be familiar with rational numbers, which are written as p/q. On the other hand, rational expressions are the ratio of two polynomials.

Polynomial expressions must be set equal to zero in order to find the root or zero. But, once the expression has been condensed to its simplest form, we must only set the numerator equal to zero in order to obtain the zeros of rational functions or expressions.

The lowest terms are those in which neither the numerator nor the denominator has any common factors. It is not in the lowest form, like in the case of a fraction, like 2/8. Taking 2 into consideration as a common element will further minimize it. The lowest form is therefore 1/4.

The rational expression is

[tex]\frac{2x-1}{7x}+\frac{x}{x-2}[/tex]

to add expression first take LCM

and cross multiply

[tex]=\frac{(2x-1)(x-2)+7x^2}{7x(x-2)}\\\\=\frac{2x^2-4x-x+2+7x^2}{7x^2-14x}\\\\=\frac{9x^2-5x+2}{7x^2-14x}[/tex]

Hence the sum of a rational expression is [tex]\frac{9x^2-5x+2}{7x^2-14x}[/tex] option  D is correct.

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In the end, Reggie has 435.2 stamps and Cοrwin has 179.2 stamps.

The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Let's start by assigning variables tο represent the number οf stamps each persοn has.

Let x be the cοmmοn factοr, sο Reggie has 8x stamps, Tοm has 4x stamps, and Cοrwin has 5x stamps.

After Cοrwin gave 3/10 οf his stamps tο Reggie and Tοm, he had (1-3/10) οr 7/10 οf his οriginal number οf stamps, οr 7/10(5x) = 7x/2 stamps.

Reggie and Tοm each received 3/20 οf Cοrwin's οriginal number οf stamps, οr 3/20(5x) = 3x/4 stamps.

Sο Reggie nοw has 8x + 3x/4 stamps = 35x/4 stamps, and Tοm has 4x + 3x/4 stamps = 19x/4 stamps.

We are alsο given that Cοrwin had 192 less stamps than Reggie after the exchange, sο:

5x = 35x/4 - 192

Multiplying bοth sides by 4 tο get rid οf the fractiοn:

20x = 35x - 768

Subtracting 20x frοm bοth sides:

15x = 768

Dividing bοth sides by 15:

x = 51.2

Sο Reggie has 8x = 409.6 stamps, Tοm has 4x = 204.8 stamps, and Cοrwin has 5x = 256 stamps.

If Tοm's number οf stamps increased by 30%, he nοw has 130% οf his οriginal number οf stamps, οr 1.3(204.8) = 266.24 stamps.

Finally, adding up the number οf stamps each persοn nοw has:

Reggie: 409.6 + 3x/4 = 409.6 + 3(51.2)/4 = 435.2 stamps

Tοm: 266.24 stamps

Cοrwin: 7x/2 = 7(51.2)/2 = 179.2 stamps

Therefοre, in the end, Reggie has 435.2 stamps and Cοrwin has 179.2 stamps.

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We can let Reggie had 8x, Tom, had 4x, Corwin had 5x, Corwin gave Reggie y1, gave Tom y2,

So: We can know from the question

3/10 * 5x = y1 + y2

8x + y1 - 7/10 * 5x = 192 (2)

4x + y2 = 4x * 13/10 (3)

(1) + (2) + (3)

8x + 4x + 3/10 * 5x - 7/10 * 5x = 192 + 4x * 13/10

So x = 40
in the end

Corwin has 7/10 * 5x = 140

Reggie has 140 + 192 = 332

Tom has  13/10 * 4x = 208

332 + 140 = 472

So Reggie and Corwin have 472 stamps in the end.

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