LOTS OF PTS AND BRAINLIEST TO CORRECT ANSWERS!
1) Solve for x. (Attachment Below in Pic 1)
2) Find EF. (Attachment Below in Pic 2)
3) Solve for x. (Attachment Below in Pic 3)
4) Find NM. (Attachment Below in Pic 4)

TYSM TO WHOEVER HELPS!

Answer:

$5500

Step-by-step explanation:

3500 + 0.05 * 40,000 = 5500

His gross salary in a month in which his sales amounted to $40,000 would be; 5500 dollars.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

It is given that man received a monthly salary of $3500 together with a commission of 5% on all sales over $5000 per month.

Let the x represents his gross salary in a month in which his sales amounted to $40,000.

Therefore,

x = 3500 + 0.05 (40,000)

x = 3500 + 2000

x = 5500

Hence,  his gross salary in a month in which his sales amounted to $40,000 would be; 5500 dollars.

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Answer:

7.25 inches

Step-by-step explanation:

formula for the area of a rectangle:

base × perpendicular height

inputting what we have:

8 × height = 58

divide both sides by 8

58/8=7.25

height=7.25 inches

The derivative dy/dx of the equation ysin(x^2) = xsin(y^2) is given by (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

In the given equation, y and x are both variables, and y is implicitly defined as a function of x. To find dy/dx, we differentiate each term using the chain rule and product rule as necessary.

Differentiating the left-hand side of the equation, we apply the product rule to ysin(x^2). The derivative of ysin(x^2) with respect to x is dy/dxsin(x^2) + ycos(x^2)*2x.

Differentiating the right-hand side of the equation, we apply the product rule to xsin(y^2). The derivative of xsin(y^2) with respect to x is sin(y^2) + x*cos(y^2)2ydy/dx.

Now we have two expression for the derivative of the left and right sides of the equation. To isolate dy/dx, we can rearrange the terms and solve for it.

Taking the derivative of ysin(x^2) = xsin(y^2) with respect to x using implicit differentiation yields:
dy/dxsin(x^2) + ycos(x^2)2x = sin(y^2) + xcos(y^2)2ydy/dx.

By rearranging the terms, we can solve for dy/dx:
dy/dx * (sin(x^2) - 2yxcos(y^2)) = sin(y^2) - y*cos(x^2)*2x.

Finally, we can obtain the value of dy/dx by dividing both sides by (sin(x^2) - 2yxcos(y^2)):
dy/dx = (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

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The surface area of the rectangular prism is 88 square inches.

Given that:

Length, L = 6 inches

Width, W = 2 inches

Height, H = 4 inches

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

SA = 2(6 x 2 + 2 x 4 + 4 x 6)

SA = 2 (12 + 8 + 24)

SA = 2 x 44

SA = 88 square inches

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(A) Usain Bolt's average speed in meters per second was approximately 10.36 m/s.

(B) Usain Bolt's average speed in miles per hour was approximately 23.35 mph.

(A) Average speed = Distance / Time

Average speed = 200 meters / 19.30 seconds

Average speed = 10.36 meters per second

Therefore, Usain Bolt's average speed in meters per second was approximately 10.36 m/s.

(B) 1 mile = 2580 feet

Converting the distance from meters to miles:

Distance in miles = Distance in meters / (1 meter / 3.28 feet) / (1 mile / 5280 feet)

Distance in miles = 200 meters / 3.28 / 5280 miles

Time in hours = Time in seconds / (60 seconds / 1 minute) / (60 minutes / 1 hour)

Time in hours = 19.30 seconds / 60 / 60 hours

Average speed = Distance in miles / Time in hours

Average speed = (200 meters / 3.28 / 5280 miles) / (19.30 seconds / 60 / 60 hours)

Average speed = 23.35 miles per hour

Therefore, Usain Bolt's average speed in miles per hour was approximately 23.35 mph.

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Answer:

Step-by-step explanation:

9/100 i believe as you would multiply 3/10 by 3/10 due to the fact the marble is being replaced so the probability of getting a red marble the second time will be more unlikely. If I'm right please thank me or give me brainly. Hope this helps :)

The probability of drawing two red marbles, if the first marble is replaced after it is drawn, is 9/100.

What is Probability?

It is a branch of mathematics that deals with the occurrence of a random event.

The probability of drawing a red marble on the first draw is 3/10, since there are 3 red marbles out of a total of 10 marbles.

Since the first marble is replaced before the second draw, the probability of drawing a red marble on the second draw is also 3/10.

To find the probability of drawing two red marbles in a row, we multiply the probabilities of the individual events, since they are independent:

P(drawing two red marbles) = P(red on first draw) × P(red on second draw)

P(drawing two red marbles) = (3/10) × (3/10)

= 9/100

Therefore, the probability of drawing two red marbles, if the first marble is replaced after it is drawn, is 9/100.

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Answer:

\( - \frac{5 + 5 \sqrt{3} }{2} \)

Option A is the correct option.

Solution,

Multiply and divide by its conjugate.

\( \frac{5}{1 - \sqrt{3} } \times \frac{1 + \sqrt{3} }{1 + \sqrt{3} } \\ = \frac{5(1 + \sqrt{3)} }{(1 - \sqrt{3} )(1 + \sqrt{3)} } \\ = \frac{5 + 5 \sqrt{3} }{ {(1)}^{2} - { (\sqrt{3}) }^{2} } \\ = \frac{5 + 5 \sqrt{3} }{1 - 3} \\ = \frac{5 + 5 \sqrt{3} }{ - 2} \\ = - \frac{5 + 5 \sqrt{3} }{2} \)

hope this helps...

Good luck on your assignment..

\(\begin{cases} g(x) = x + 8\\\\ h(x)=x-2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ h(-8)=(-8) - 2\implies h(-8) = -10 \\\\[-0.35em] ~\dotfill\\\\ g(~~h(-8)~~)\implies g(-10)=(-10) + 8\implies g(-10)=-2\)

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Step-by-step explanation:

Refer to the attachment ♪♪

Using the distance formula,  \(\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}\) to find the length of each sides, the longest side is about 6.71 units which is: d. AB

To find the longest side, we would apply the distance formula to find the length of each side.

Given:

Distance formula = \(\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}\)

Length of AB:

\(A(-2,1) = (x_1, y_1)\\\\B(4,4) = (x_2, y_2)\)

\(AB = \sqrt{(4 - 1)^2 + (4 - (-2))^2}\\\\AB = \sqrt{9 + 36}\\\\AB = \sqrt{45} \\\\AB = 6.71\)

Length of BC:

\(B(4,4) = (x_1, y_1)\\\\C(5,0) = (x_2, y_2)\)

\(BC= \sqrt{(0-4)^2 + (5-4)^2}\\\\BC = \sqrt{16 + 1}\\\\BC = \sqrt{17} \\\\BC =4.12\)

Length of CD:

\(C(5,0) = (x_1, y_1)\\\\ D(-1,-2) = (x_2, y_2)\)

\(CD = \sqrt{(-2 - 0)^2 + (-1 - 5)^2}\\\\CD = \sqrt{4 + 36}\\\\CD = \sqrt{40} \\\\CD =6.32\)

Length of DA:

\(D(-1,-2) = (x_1, y_1)\\\\ A(-2,1) = (x_2, y_2)\)

\(DA = \sqrt{(-2 - 1)^2 + (-1 - (-2))^2}\\\\DA= \sqrt{9 + 1}\\\\DA = \sqrt{10} \\\\DA = 3.16\)

Therefore, the using the distance formula,  \(\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}\) to find the length of each sides, the longest side is about 6.71 units which is: d. AB

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Answer:

Step-by-step explanation

Frist, the area = ab = 30 m^2 and the perimeter = 2(a + b) = 34 m or a + b = 17 m (2). Solving (1) and (2), a = 15 m and b = 2 m. Since it is a rectangle, the dimensions are (all in m) so the answer is: 15, 2, 15, 2.

Answer:

THe kitchen is 8 by 10

Step-by-step explanation:

x = width

y = length

Area = xy = 80 m²

Perimeter = 2x + 2y = 36 m

2x = 36 - 2y

x = 18 - y   substitute into equation 1

(18 - y)(y) = 80

-y² + 18y - 80 = 0    find roots of y by factoring

y² - 18y + 80 = 0

(y - 8)(y - 10) = 0

y = 8, 10

Since xy = 80, then:

x = 80/10 = 8, or, x = 80/8 = 10

Now you have your dimensions: 8 and 10

To check the answers:

8 x 10 = 80 m²

2(8) + 2 (10) = 36 m

Answers are correct!

The matrix of a quadratic form is always a symmetric matrix.A quadratic form is a mathematical expression that consists of variables raised to the power of two, multiplied by coefficients, and added together.

It can be represented in matrix form as Q(x) = x^T A x, where x is a vector of variables and A is the matrix of coefficients. The matrix A is known as the matrix of the quadratic form.

To show that the matrix of a quadratic form is symmetric, let's consider the expression Q(x) = x^T A x. Using the properties of matrix transpose, we can rewrite this expression as Q(x) = (x^T A^T) x. Since the transpose of a matrix A is denoted as A^T, we can see that A^T is the same as A, as A is already a matrix.

Therefore, we have Q(x) = x^T A x = x^T A^T x. This implies that the matrix of the quadratic form A is symmetric, as A^T = A. In other words, the elements of the matrix A are symmetric with respect to the main diagonal. This property holds true for any quadratic form, regardless of its coefficients or variables, making the matrix of a quadratic form symmetric.

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Answer:

y=2x-3

Step-by-step explanation:

Y-intercept can be read off the graph.

Slope can be determined using the formula:

y2-y1 divided by x2-x1 (Substitute co-ordinates)

Answer:

y=2x-3

Step-by-step explanation:

y=mx+b

Where m is the slope and b is the y intercept

Slope is rise over run, the line is up 2 over 1

And the point of the line where it meets the y axis is -3. so b is -3

Answer:

24

Step-by-step explanation:

The  probability that the number showing on die B will be greater than the number on die A is also 5/12 or approximately 0.417.

The outcomes of rolling two dice can be represented by a table of all possible combinations of numbers on the two dice. There are 36 possible outcomes in total, since each of the six faces of the first die can be paired with any of the six faces of the second die.

To find the probability that the number showing on die A will be greater than the number on die B, we can count the number of outcomes where this is true and divide by the total number of outcomes. There are 15 outcomes where the number on die A is greater than the number on die B, as shown in the table below:

| Die A | Die B |
|-------|-------|
|   2   |   1   |
|   3   |   1   |
|   4   |   1   |
|   3   |   2   |
|   4   |   2   |
|   5   |   1   |
|   5   |   2   |
|   4   |   3   |
|   5   |   3   |
|   6   |   1   |
|   6   |   2   |
|   5   |   4   |
|   6   |   3   |
|   6   |   4   |
|   6   |   5   |

Therefore, the probability that the number showing on die A will be greater than the number on die B is 15/36, which simplifies to 5/12 or approximately 0.417.

Similarly, we can count the number of outcomes where the number on die B is greater than the number on die A. There are also 15 such outcomes, as shown in the table above. Therefore, the probability that the number showing on die B will be greater than the number on die A is also 5/12 or approximately 0.417.

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Answer:

\(\frac{1331x-6\times \:121^x}{5\times \:121^x}\)

Step-by-step explanation:

\(\frac{11^2x\times \:11^1-6\times \:121^x}{5\times \:121^x}\)

\(\mathrm{Apply\:exponent\:rule}:\quad \:a^b\times \:a^c=a^{b+c}\)

\(11^2\times \:11^1=11^{2+1}\)

\(=\frac{11^{2+1}x-6\times \:121^x}{5\times \:121^x}\)

\(\mathrm{Add\:the\:numbers:}\:2+1=3\)

\(=\frac{11^3x-6\times \:121^x}{5\times \:121^x}\)

\(11^3=1331\)

\(=\frac{1331x-6\times \:121^x}{5\times \:121^x}\)

[RevyBreeze]

Answer:

1

Step-by-step explanation:

\( \dfrac{11^{2x} \times 11^1 - 6 \times 121^x}{5 \times 121^x} = \)

​\( = \dfrac{11 \times 11^{2x} - 6 \times 11^{2x}}{5 \times 11^{2x}} \)

​\( = \dfrac{5 \times 11^{2x}}{5 \times 11^{2x}} \)

​\( = 1 \)

The quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

To solve the quadratic equation 2a^2 = -6 + 8a, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0, where a, b, and c are coefficients.

Step 1: Move all the terms to one side of the equation to set it equal to zero:

2a^2 - 8a + 6 = 0

Step 2: The equation is now in standard quadratic form, so we can apply the quadratic formula to find the solutions for 'a':

a = (-b ± √(b^2 - 4ac))/(2a)

Comparing with our equation, we have:

a = (-(-8) ± √((-8)^2 - 4(2)(6)))/(2(2))

Simplifying further:

a = (8 ± √(64 - 48))/(4)

a = (8 ± √16)/(4)

a = (8 ± 4)/(4)

Now, we can calculate the two possible solutions:

a1 = (8 + 4)/(4) = 12/4 = 3

a2 = (8 - 4)/(4) = 4/4 = 1

Therefore, the quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

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Answer:

Acute

Step-by-step explanation:

It is not a right triangle. Because the biggest angle is less than , the other two angles are also, and the triangle is an (a) Acute triangle.

Explanation

Refer to the converse of the pythagorean theorem. That theorem converse has three cases.

The a,b,c refer to the side lengths. The c is the longest side.

In this case

a = 4, b = 5, c = 6

We find that \(a^2+b^2 = 4^2+5^2 = 16+25 = 41\)

And also \(c^2 = 6^2 = 36\)

Compare \(a^2+b^2 = 41\) and \(c^2 = 36\) to see that 41 is larger, so we'll go with the case \(a^2+b^2 > c^2\) to prove the triangle is acute.

You can use a tool like GeoGebra to confirm the answer is correct.

None of the options provided (e || O or None of these) accurately represent the equation of the cone z = √3\(x^{2}\) + 3\(y^{2}\) in spherical coordinates when expressed in the form p = 3.

The equation of a cone in spherical coordinates can be expressed as p = \(\sqrt{x^{2} + y^{2} + z^{2}}\), where p represents the radial distance from the origin to a point on the cone. In the given equation z = √3\(x^{2}\) + 3\(y^{2}\), we need to rewrite it in terms of p.

To convert the equation to spherical coordinates, we substitute x = p sin θ cos φ, y = p sin θ sin φ, and z = p cos θ, where θ represents the polar angle and φ represents the azimuthal angle.

Substituting these values into the equation z = √3\(x^{2}\) + 3\(y^{2}\), we get:

p cos θ = √3{(p sin θ cos φ)}^{2} + 3{(p sin θ sin φ)}^{2}

Simplifying the equation further:

p cos θ = √3\(p^2\) \(sin^2\) θ \(cos^2\)φ + 3\(p^2\)\(sin^2\) θ \(sin^2\) φ

Now, canceling out p from both sides of the equation, we have:

cos θ = √3 \(sin^{2}\) θ \(cos^{2}\) φ + 3 \(sin^2\) θ \(sin^2\) φ

Unfortunately, this equation cannot be reduced to the form p = 3. Therefore, the correct answer is "None of these" as none of the given options accurately represent the equation of the cone z = √3\(x^{2}\)+ 3\(y^{2}\) in spherical coordinates in the form p = 3.

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Answer:

I’m going to said A

Step-by-step explanation:

The required area under the whole probability density curve is given by option C. 1.

The area under the entire probability density curve is equal to,

As the probability density function (pdf) represents the probability of a continuous random variable.

And continuous random variable taking on a specific value within a certain range.

Since the total probability of all possible outcomes must be equal to 1.

This implies that the area under the entire probability density function (pdf) curve must also be equal to 1.

Therefore, the area under the entire probability density curve function is equal to option c. 1.

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The correct answer is C. $11,250.

To calculate the interest on a 90-day, 9% note for $50,000, we can use the simple interest formula:

Interest = Principal × Rate × Time

Given:

Principal (P) = $50,000

Rate (R) = 9% = 0.09 (decimal)

Time (T) = 90 days

Since the interest is calculated based on a 360-day year, we need to convert the time in days to a fraction of a year:

Time (T) = 90 days / 360 days = 0.25 (fraction of a year)

Now we can calculate the interest:

Interest = $50,000 × 0.09 × 0.25

Interest = $11,250

Rounded to the nearest dollar, the interest on the 90-day, 9% note for $50,000 is $11,250.

Therefore, the correct answer is C. $11,250.

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Answer:

Step-by-step explanation:

Kindly find a simple sketch of a baseball pitch, the circle with a dot inside represents the first base coach(don't mind my drawing please I will improve).      

So, from the diagram, we can see that the expression that describes the distance and the first base coach is

y=90+3

y=93

so the distance  between Roberto Clemente and the first base coach is 93ft                                  

For given triangles ABC and CDF, these are congruent by Angle Angle side theorem.

What is the definition of a triangle?

Triangles are polygons with three sides and three vertices in geometry. This figure is two-dimensional and has three straight sides. A triangle is a polygon with three sides. The sum of a triangle's three angles equals 180°. The triangle is contained inside a single plane. Triangles are categorised into three types based on their sides .

Based on its sides, a triangle is classified into three types:

Scalene Triangle - Each side is different in length.

Isosceles Triangle - A triangle with two sides that are equal in length and one side that is not.

Equilateral Triangle - A triangle with three equal-length sides.

Now,

As Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side in one triangle are congruent to two angles and a non-included side in another triangle, the triangles are congruent.

and here AB congruent CD and angle ABF = angle CDF and

Angle AFB= Angle CFD  (vertically opposite angles)

Hence,

           By AAS triangle ABC is congruent to triangle CDF.

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The slope of the tangent to the curve is -5/14.

Apply implicit differentiation and the product rule to the curve:

\(3y^{2} \frac{dy}{dx} x + y^{3} + 2y\frac{dy}{dx} x^{2} + y^{2}2x = 0\)

Do some rewriting

\(3xy^{2}\frac{dy}{dx} + 2x^{2}y\frac{dy}{dx} + y^{3} + 2xy^{2} = 0\)

Factor and move terms without a  \(\frac{dy}{dx}\)  factor to the right side

\(\frac{dy}{dx}(3xy^{2}+2x^{2}y) = -y^{3} - 2xy^{2}\)

Now divide both sides by  \(3xy^{2}+2x^{2}y\)  and factor where you can

\(\frac{dy}{dx} = \frac{-y^{2}(y+2x)}{yx(3y+2x)}\)

\(\frac{dy}{dx} = \frac{-y(y+2x)}{x(3y+2x)}\)

Now evaluate the given point \((2,1)\)

\(\frac{dy}{dx} = \frac{-1(1 + 2(2))}{2(3(1) + 2(2))} = \frac{-1(5)}{2(7)} = \frac{-5}{14}\)

Therefore, the slope of the tangent to the curve is -5/14.

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Answer:

The answer is 45150£

Step-by-step explanation:

Solution,

Given: Cost price of computer(C.P)= 43000£

Profit percent = 5%

Selling price (S.P) = ?

We know that,

Profit = Profit percent × C.P

= 5% × 43000£

= 5/100 × 430000£

= 2150£

S.P = Profit + C.P

= 2150£ + 43000£

= 45150£ Ans

The value of the selling price would be,

= £45150

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A trader bought a computer for 43000£ and sold it at a profit of 5%.

Hence, Cost price of computer(C.P)= 43000£

Profit percent = 5%

We know that,

Profit = Profit percent × C.P

        = 5% × 43000£

        = 5/100 × 430000£

        = 2150£

Hence, S.P = Profit + C.P

= 2150£ + 43000£

= 45150£

Thus., The value of the selling price would be,

= £45150

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By solving linear equation, it can be calculated that x = 60 , y = 70 is one possible solution of the linear equation.

Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by <, >, ≤, ≥

A one degree inequation is known as linear inequation.

Let the number of tacos sold be $x and the number of burrito sold be $y

He only has enough supplies to make 130 tacos or burritos.

x + y ≤ 130 ... (1)

He sells each taco for $4.25 and each burrito for $8.50.

Isaac must sell a minimum of $850 worth of tacos and burritos each day.

4.25x + 8.5y ≥ 850

x + 2y ≥ 200 ... (2)

The inequalities has been solved graphically as;

One possible solution is x = 60, y = 70

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The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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