Find an equation of the plane that passes through the given point and is perpendicular to the given vector or line.
Point (0, 9, 0) Perpendicular to
n = -2i ÷ 4k

Deloria is analyzing the relationships between relative frequencies of nuts.

She has found that the relative frequency of a specific type of nut is 15%, which is calculated by dividing the number of that nut (3) by the total number of nuts (30).

Deloria might be comparing this relative frequency to other types of nuts to determine their prevalence or importance in a given context.

To calculate the relative frequency, we can divide the number of occurrences of the specific nut (3) by the total number of nuts (30):

Relative frequency = (Number of occurrences of specific nut) / (Total number of nuts)

Relative frequency = 3 / 30 = 0.1 = 10%

Therefore, the relative frequency of the specific type of nut is 10%, not 15%. It seems there was an error in the initial statement.

By analyzing relative frequencies, Deloria can compare the prevalence or importance of different types of nuts in a given context.

By calculating and comparing the relative frequencies of different types of nuts, Deloria can gain insights into the distribution and significance of each nut type within the dataset or sample.

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The correct expression to represent the total number of miles Hayden biked is A. 5 × (3 + 3 + 2 1/4)

This is because each time Hayden rode his bike, he biked a 3-mile path, a 2-mile path, and a 2 1/4 -mile path. To find the total number of miles he biked, we need to add up the distance he biked each time and then multiply by the number of times he biked.

Using the distributive property of multiplication over addition, we can rewrite the expression as:

= 5 × (3 + 3 + 2 1/4)

Therefore, Hayden biked a total of 41 1/4 miles. The correct answer is A

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The solutions of the quadratic equation are:

x = - 3 ±√14

Here we want to solve the equation:

[tex]x^2 + 6x = 5[/tex]

We can rewrite that to standard form:

[tex]x^2 + 6x - 5 = 0[/tex]

Completing squares we will get:

[tex](x^2 + 2*3*x + 3^2 - 3^2) - 5 = 0[/tex]

[tex](x + 3)^2 = 5 + 9[/tex]

x = - 3 ±√14

These are the two solutions of the quadratic equation.

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Answer:

Step-by-step explanation:

The team drank a total of 7 x 8 = 56 juice boxes, and there were 29 remaining, so the team opened 56 - 29 = 27 juice boxes.

Since the team only opened a new box after finishing the previous one, the team opened 27 - 1 = 26 boxes of juice in total.

To explain this solution in more detail, we can use basic arithmetic. We know that the mom bought 7 boxes of juice, each containing 8 juice boxes,

so the total number of juice boxes is 7 x 8 = 56. After the team drank all the juice they wanted, there were 29 juice boxes remaining. This means that the team drank 56 - 29 = 27 juice boxes.

Since the team only opened a new box of juice after finishing the previous one, the number of boxes opened will be one less than the total number of juice boxes consumed.

Therefore, the team opened 27 - 1 = 26 boxes of juice in total. It is important to note that this assumes that the team opened all the boxes they consumed and did not drink any juice directly from the remaining boxes.

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The line intersects the plane at the point (-4, 15, -6).

The line (x, y, z) = (2, -3, 0) + k(-1, 3, -1) can be expressed parametrically as:

x = 2 - k

y = -3 + 3k

z = k

The plane [x, y, 2] = [4, -15, -8] + s[1, -3, 1] + t[2, 3, 1) can be expressed in scalar form as:

x + y - 2z = 14 + s - 2t

To find the intersection of the line and the plane, we can substitute the parametric equations of the line into the scalar equation of the plane:

(2 - k) + (-3 + 3k) - 2k = 14 + s - 2t

Simplifying this equation, we get:

-4k + 3 = 14 + s - 2t

We can also express the line and plane equations in vector form:

Line: r = (2, -3, 0) + k(-1, 3, -1) = (2-k, -3+3k, k)

Plane: r = (4, -15, -8) + s(1, -3, 1) + t(2, 3, 1) = (4+s+2t, -15-3s+3t, -8+s+t)

To find the intersection of the line and the plane, we need to find the values of k, s, and t that satisfy both equations simultaneously. We can do this by equating the vector forms of the line and plane and solving for k, s, and t:

2 - k = 4 + s + 2t

-3 + 3k = -15 - 3s + 3t

k = -8 - s - t

Substituting k into the first equation, we get:

2 + 8 + s + t = 4 + s + 2t

Simplifying this equation, we get:

t = 4

Substituting t = 4 and k = -8 - s - t into the second equation, we get:

-3 + 3(-8 - s - 4) = -15 - 3s + 3(4)

Simplifying this equation, we get:

s = -2

Substituting t = 4 and s = -2 into the first equation, we get:

k = 8 - s - t = 8 + 2 - 4 = 6

Therefore, the line intersects the plane at the point (x, y, z) = (2, -3, 0) + 6(-1, 3, -1) = (-4, 15, -6).

So the line intersects the plane at the point (-4, 15, -6).

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This requires an online learning algorithm that adapts to the changing costs of each expert and helps us make optimal choices

In this scenario, we can think of the slot machines as experts providing us with advice on which machine to play each day. The cost of taking advice from each expert, represented by cti, is the amount we lose by playing that particular machine.

To minimize our losses and regret, we want to choose the expert (i.e., slot machine) with the lowest cost each day. However, it's important to note that the cost of taking advice from each expert may change each day, so we need to constantly evaluate and adjust our choices.

To formalize this problem as an optimization task, we can use the concept of regret. Regret measures how much worse off we are by not knowing the best expert in advance. In other words, it's the difference between our cumulative losses if we always chose the best expert versus the losses we actually incur by following different experts each day.

To minimize our regret R, we need to choose the best expert as often as possible. One way to achieve this is by using an online learning algorithm that updates our choice based on the outcomes of each day's play. By continuously monitoring the performance of each slot machine, we can adjust our strategy and minimize our losses over time.

In summary, to minimize our losses while gambling at a casino, we need to treat each slot machine as an expert providing us with advice. We must choose the expert with the lowest cost each day and constantly update our strategy to minimize regret.

This requires an online learning algorithm that adapts to the changing costs of each expert and helps us make optimal choices.

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Answer: a) To find the speed of Train A, we need to divide the distance traveled by the time taken:

Speed = Distance / Time

Speed = 520.4 km / 4.8 h

Speed ≈ 108.42 km/h

Rounding to the nearest whole number, we get:

Train A is traveling at 108 km/h (approximately).

b) To find the speed of Train B, we need to divide the distance traveled by the time taken:

Speed = Distance / Time

Speed = 72.1 km / 0.8 h

Speed ≈ 90.13 km/h

Rounding to the nearest whole number, we get:

Train B is traveling at 90 km/h (approximately).

Step-by-step explanation:

The equation provided, "e3r + 6e2x + 7e et - 64 pestle da," is not an integral expression and does not have a variable of integration.

Additionally, the requested answer, "] +0," does not make sense in the context of the question. Please provide a complete and accurate question for me to assist you with. Hi! Based on your terms provided ("Integrals", "substitution", and "find"), I understand that you are looking to solve an integral using substitution. However, the integral you provided appears to have some typographical errors. Please provide the correct integral, and I'll be happy to help you solve it.

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The volume of the cylinder  V = πr²h. Therefore, we need to have more information about the cylinder's height in order to solve this problem.

To find the volume of the cylinder, we first need to know the height of the cylinder. However, the height is not given in the question. Therefore, we cannot determine the volume of the cylinder with the given information.

We can use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height.

Since r = 11 units and x = 15 units, we can find the diameter of the base of the cylinder by multiplying r by 2, which gives us 22 units. However, we still do not know the height of the cylinder.
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iStar Financial (STAR) has a lower PE ratio than Bank Rate (RATE), which suggests that it may be financially stronger

To determine which company is financially stronger using their PE ratios, we need to calculate the PE ratio for each company. PE ratio, or price-to-earnings ratio, is a financial metric used to measure the valuation of a company's stock. It is calculated by dividing the market price per share by the earnings per share.

For Bank Rate (RATE), the PE ratio can be calculated as:

PE ratio = market price per share / earnings per share

PE ratio = $13.95 / $2.71

PE ratio = 5.14

For iStar Financial (STAR), the PE ratio can be calculated as:

PE ratio = market price per share / earnings per share

PE ratio = $12.18 / $3.62

PE ratio = 3.37

A lower PE ratio indicates that a company's stock is relatively undervalued compared to its earnings. In this case, iStar Financial (STAR) has a lower PE ratio than Bank Rate (RATE), which suggests that it may be financially stronger.

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Answer:

250+25d= P

Step-by-step explanation:

How to say it aloud: "$250 plus 25 times miles ran is equal to total amount earned"

250 is a fixed amount that is apart of the equation. In order to get a correct total at the end, $250 must be added to 25d.

25d stands for $25 times the amount of miles ran, which according to the word problem is represented by d. The reason we multiply 25 times d is because Marcus is getting $25 for every mile he runs. At the end of his run, we need to multiply $25 by those miles.

The reason everything equals P is because according to the word problem, P is the amount of money earned.

I hope that makes sense.

If both belts are​ used, it will take 2.25 minutes to move the cans to the storage area

To solve this problem, we need to use the concept of rate of work. We know that the larger belt can move 200 pounds of aluminum in 3 minutes, which means its rate of work is 200/3 = 66.67 pounds per minute. Similarly, the smaller belt can move the same quantity of cans in 9 minutes, which means its rate of work is 200/9 = 22.22 pounds per minute.

When both belts are used together, their rates of work add up, so the total rate of work is 66.67 + 22.22 = 88.89 pounds per minute. We can use this rate of work to find how long it will take to move the cans to the storage area.

Let's assume that it takes x minutes to move the cans using both belts. Then, we can set up the following equation:

88.89x = 200

Solving for x, we get:

x = 2.25 minutes

Therefore, it will take 2.25 minutes to move the cans to the storage area using both belts.

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The range of x values between which a zero can be found is -9/4 < x < -4.

Since x + 4 and 4x + 9 are linear factors of the quadratic expression, the quadratic expression can be written as:

Q(x) = k(x + 4)(4x + 9)

where k is some constant.

To find the values of x for which Q(x) = 0, we can set each factor equal to zero and solve for x:

x + 4 = 0 --> x = -4

4x + 9 = 0 --> x = -9/4

Therefore, the zeros of Q(x) are x = -4 and x = -9/4.

To find the range of x values between which a zero can be found, we need to determine the sign of Q(x) in each of the three intervals:

1. x < -9/4

2. -9/4 < x < -4

3. x > -4

For x < -9/4, both x + 4 and 4x + 9 are negative, so Q(x) = k(negative)(negative) = k(positive), which is positive.

For x > -4, both x + 4 and 4x + 9 are positive, so Q(x) = k(positive)(positive) = k(positive), which is also positive.

For -9/4 < x < -4, x + 4 is positive and 4x + 9 is negative, so Q(x) = k(positive)(negative) = k(negative), which is negative.

Therefore, the range of x values between which a zero can be found is -9/4 < x < -4.

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Answer:

Obese

Step by Step Explanation:

looked it up :)

To find the total profit earned, we need to subtract the total cost from the revenue. Therefore, the profit function is:

P(q) = R(q) - C(q)
P(q) = 625q - q^2 - (50 + 6q)
P(q) = -q^2 + 619q - 50

To find the quantity which maximizes the profit, we need to take the derivative of the profit function and set it equal to zero:

P'(q) = -2q + 619
0 = -2q + 619
2q = 619
q = 309.5

Therefore, the quantity which maximizes the profit is 309.5. To find the total profit earned at this quantity, we plug it back into the profit function:

P(309.5) = -(309.5)^2 + 619(309.5) - 50
P(309.5) = $95,268.25

So the total profit earned at the quantity which maximizes the profit is $95,268.25.

To find the total profit function, you'll want to subtract the total cost function, C(q), from the revenue function, R(q). So the profit function, P(q), is given by:

P(q) = R(q) - C(q) = (625q - q^2) - (50 + 6q)

Now, simplify the profit function:

P(q) = 625q - q^2 - 50 - 6q = -q^2 + 619q - 50

To find the quantity which maximizes the profit, you can take the first derivative of the profit function with respect to q, set it equal to 0, and solve for q:

P'(q) = -2q + 619

Set P'(q) to 0 and solve for q:

0 = -2q + 619
2q = 619
q = 309.5

Since you can't have a fraction of an item, consider checking q = 309 and q = 310 to find the maximum profit. Evaluate P(q) at both points:

P(309) = -309^2 + 619(309) - 50
P(310) = -310^2 + 619(310) - 50

P(309) = 95441
P(310) = 95439

Thus, the quantity which maximizes the profit is 309 items.

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The area enclosed by the figure at the right is 2856 square meters.

To find the area enclosed by the figure at the right, we first need to find the area of the square and the two semicircles on each side. The square has sides of 40 meters, so its area is 40 x 40 = 1600 square meters. Each semicircle has a radius of 20 meters (half the side length of the square), so its area is 1/2 x pi x r^2 = 1/2 x 3.14 x 20^2 = 628 square meters. Since there are two semicircles on each side, the total area of all four semicircles is 2 x 628 = 1256 square meters.

To find the total area enclosed by the figure, we add the area of the square and the area of the four semicircles:

1600 + 1256 = 2856 square meters

Therefore, the area enclosed by the figure at the right is 2856 square meters.

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The problem involves finding the marginal cost of producing a certain number of DVD players, given the total cost function. Specifically, we are given the total cost function C(x) = 120 + 3x^2-3, where x is the number of DVD players produced, and we need to find the marginal cost when x = 3.

To find the marginal cost, we need to take the derivative of the total cost function with respect to x and evaluate it at x = 3. The marginal cost represents the cost of producing one additional unit of the product, and is an important concept in economics and business.

Understanding the relationship between marginal cost and production volume is crucial for optimizing production and pricing decisions for companies. Marginal cost analysis is used extensively in many fields, including manufacturing, finance, and marketing.

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Therefore, the expression 250 * [tex]2^h[/tex] gives the number of bacteria in the colony after h hours, assuming that the initial number of bacteria is 250.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. Expressions can also include parentheses, brackets, and other symbols to clarify the order of operations. Expressions can be evaluated to obtain a numerical result or can be simplified using mathematical rules and properties to make them easier to work with. In algebra, expressions are often used to represent relationships between variables and to solve equations and inequalities.

Here,

In the given expression 250*[tex]2^h[/tex], the constant 250 represents the initial number of bacteria in the colony.

Since the number of bacteria doubles every hour, if we start with 250 bacteria at the beginning, after one hour we will have 250 * 2 = 500 bacteria. After two hours, we will have 500 * 2 = 1000 bacteria, and so on.

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The cost of an adult ticket is $9 and the cost of a student/child ticket is $7. The solution was found by solving a system of two equations, where the variables x and y represent the costs of the two types of tickets.

Let's assign variables for the unknowns

x = cost of adult tickets

y = cost of student/child tickets

From the given information, we can create two equations

Equation 1 Friend, mom, and little sister paid a total of $23

x + 2y = 23

Equation 2 Another family paid $39 for two adults and three students

2x + 3y = 39

We now have two equations with two unknowns, which we can solve using substitution or elimination.

Here, using substitution

Solve for x in Equation 1

x = 23 - 2y

Substitute the value of x into Equation 2

2(23 - 2y) + 3y = 39

Simplify and solve for y

46 - 4y + 3y = 39

-y = -7

y = 7

Substitute the value of y into Equation 1 to solve for x

x + 2(7) = 23

x = 9

Therefore, the cost of adult tickets is $9 and the cost of student/child tickets is $7.

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The given expression, 14⁻³ · 14¹², written as a single, positive exponent is 14⁹

From the question, we are to write the given expression using a single, positive exponent

From the given information,

The given expression is

14⁻³ · 14¹²

This means

14⁻³ × 14¹²

To solve this, let us revise some of the laws of indices

Thus,

The expression

14⁻³ × 14¹²

can be written as

14⁻³ ⁺ ¹²

14⁹

Hence, the expression written as a single exponent is 14⁹

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The volume of the given cylinder is 84.78 cubic yards.

The first step to finding the volume of a cylinder is to use the formula V = πr^2h, where r is the radius of the cylinder (which is half of the diameter). So, to find the radius, we divide the diameter (which is 3 yards) by 2, giving us a radius of 1.5 yards. Then, we can plug in the values for radius (1.5), height (12), and π (3.14) into the formula to find the volume:

V = πr^2h
V = 3.14 x 1.5^2 x 12
V = 84.78 cubic yards

Therefore, the volume of the cylinder is 84.78 cubic yards.
Hi! To find the volume of a cylinder with a diameter of 3 yards and a height of 12 yards, the first step is to find the radius.

Step 1: Since the diameter is 3 yards, you can find the radius by dividing the diameter by 2. Radius = Diameter / 2. So, the radius is 1.5 yards.

Step 2: Now, you can find the volume of the cylinder using the formula: Volume = π × (radius^2) × height. In this case, Volume = π × (1.5^2) × 12.

Step 3: Calculate the volume: Volume = π × 2.25 × 12. Using the value of π as approximately 3.14, the volume becomes 3.14 × 2.25 × 12.

Step 4: Multiply the numbers: Volume ≈ 84.78 cubic yards.

So, the volume of the cylinder is approximately 84.78 cubic yards.

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Step-by-step explanation:

Let the other rational number be represented by "x". We know that the difference of the two rational numbers is 17/28, which can be written as:

x - (-9/14) = 17/28

Simplifying the left-hand side:

x + 9/14 = 17/28

Multiplying both sides by the least common multiple of 14 and 28, which is 28, we get:

28(x + 9/14) = 28(17/28)

Simplifying:

4(2x + 9) = 17

Expanding:

8x + 36 = 17

Subtracting 36 from both sides:

8x = -19

Dividing by 8:

x = -19/8

Therefore, the other rational number is -19/8.

Waterways Corporation's budget for Q1 2022 involves sales, inventory, materials, labor, overhead, expenses, and financing.

Waterways Corporation is preparing its budget for the first quarter of 2022. The company has gathered information from its managers to begin the budgeting process.

The company expects unit sales to be 112,000 in November 2021, 104,000 in December 2021, and 113,000 in January 2022. The company also expects to keep 10% of next month's unit sales in ending inventory. The company collects 85% of Accounts Receivable in the month of sale and 15% in the month after sale.

Raw materials cost 80 cents per pound, and two pounds of direct materials are required to produce each unit. The company likes to keep 5% of the materials needed for the next month in its ending inventory.

Labor requires 12 minutes per unit, paid at a rate of $9 per hour. The company has variable selling and administrative costs of $1.60 per unit, including advertising, insurance, salaries, and depreciation. The company also plans to make a $480,000 equipment purchase in February.

The company's cash balance on December 31, 2021, was $99,000, but the management wants to maintain a cash balance of at least $700,000 starting on January 31, 2022. The company pays dividends each month at the rate of $2.70 per share for 4,610 shares outstanding.

The company has an open line of credit with Romney's Bank with borrowing terms of $1,000 increments at 9% interest. The company borrows on the first day of the month and repays on the last day of the month.

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The crop sizes for first 4 years without using fertilisers are:

The size of the potato crop for each of the first four years is computed as follows:

For Year 1:

= 15 tonnes * 1

= 15 tonnes

For Year 2:

= 15 tonnes x 0.8

= 12 tonnes

For Year 3:

= 12 tonnes x 0.8

= 9.6 tonnes

For Year 4:

= 9.6 tonnes x 0.8

= 7.68 tonnes

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The expression for the surface area of the box is if w is A = x² + 2(xh) + 2(h²) the width of the box and h is the height. The dimensions of the box that minimize the surface area are approximately 11.68 cm by 11.68 cm by 6.19 cm.

The sketch of the box and the sketch of the net of the box is attached below. The box has a square base of side length x, and height h. The volume of the box is given as 500 cubic centimeters, therefore

x × x × h = 500

The surface area of the box can be found by summing the areas of each of the six faces. The top face is a square of side length x, so its area is x². The other five faces are all rectangles. The area of each of these rectangles is given by its length times its width. Therefore, the surface area of the box is

A = x² + 2(xh) + 2(h²)

To find the dimensions that minimize the surface area, we can use calculus. We can first solve the equation for x in terms of h

x² = 500/h

x = √(500/h)

Substituting this expression for x into the equation for the surface area, we get

A = 500/h + 2h×√(500/h) + 2h²

We can find the derivative of this expression with respect to h

dA/dh = -500/h² + sqrt(500/h) - 4h

Setting this derivative equal to zero and solving for h, we get

-500/h² + sqrt(500/h) - 4h = 0

Using a calculator or computer, we can find that this value is approximately 6.19. Substituting this value back into the equation for x, we get

x = √(500/6.19) ≈ 11.68

Therefore, the dimensions of the box that minimize the surface area are approximately 11.68 cm by 11.68 cm by 6.19 cm.

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Answer:

1 candy bar is $1.25

2 candy bars is $2.50

3 candy bars is $3.75

4 candy bars is $5

Equation:

y = 1.25x

y being the cost and x being number of candy bars

Answer:

5*5*3

5²*3

Step-by-step explanation:

Assuming that we have to find prime factorization of 75:

75 = 25 * 3

75 = 5*5*3

The probability of spinning an odd number , not flipping heads , then not spinning a 6 is 9/40

Multiply the three probabilities in order to get the compound probability:

Probability = favorable outcome / total number of outcome

Probability of getting an odd number

favorable outcome = 5

Total number of outcome = 10

P(odd number)= 5/10 = 1/2

Probability of not getting filling head  

Favorable outcome = 1

P( not flipping heads)= 1/2  

Probability of not getting a 6

favorable outcome = 9

P(not spinning a 6)= 9/10

= 1/2×1/2×9/10

= 9/40

The probability of spinning an odd number , not flipping heads , then not spinning a 6 is 9/40

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The sum of the heights of the two trees with given volumes and radius is equal to  9 cm (nearest whole number ).

Volumes of the cylindrical trunks of first tree = 904.78 cm³

and Volumes of the cylindrical trunks of first tree =113 cm³.

radius of the  first tree = 6cm

Radius of the second tree = 6cm

The formula for the volume of a cylinder is V = πr²h,

where r is the radius of the cylinder,

h is the height of the cylinder,

and π is the constant approximately value equal to 3.14.

For the first tree,

⇒904.78 = π(6)²h

⇒h = 904.78 / (π(6)²)

⇒h ≈ 8.004 cm

For the second tree, we have,

⇒113 = π(6)²h

⇒h = 113 / (π(6)²)

⇒h ≈ 0.9996 cm

This implies,

The sum of the heights of the two trees is equal to,

= 8.004 + 0.9996

= 9.003 cm

= 9 cm ( nearest whole number)

Hence, the sum of the heights of the two trees is approximately 9 cm nearest whole number.

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The given question is incomplete, I answer the question in general according to my knowledge:

The two trees trunk are in cylindrical shape. one with radius 6cm and volume 904.78 cm³ and  another one with radius 6cm and volume 113 cm³.

What is the sum of the heights of the two trees? Round your answer to the nearest whole number