True or False?

All polygons are quadrilaterals.

Step-by-step explanation:

To calculate the amount of air used to fill a spherical balloon, we need to determine its volume. The volume of a sphere can be calculated using the formula:

Volume = (4/3) × π × radius³

Given that the radius of the balloon is 165 mm, we can substitute this value into the formula:

Volume = (4/3) × π × (165 mm)³

Now, let's calculate the volume of the balloon:

Volume = (4/3) × 3.14159 × (165 mm)³

Volume ≈ 4.18879 × (165 mm)³

Evaluating this expression will give us the volume of the balloon in cubic millimeters. However, to express it in a more practical unit, such as liters, we need to convert the volume from cubic millimeters to liters.

1 liter = 1000 cubic centimeters (cc)

1 cubic centimeter (cc) = 1 milliliter (ml)

1 milliliter (ml) = 1 cubic millimeter (mm³)

To convert the volume from cubic millimeters to liters, we divide the volume by 1000:

Volume (liters) = Volume (cubic millimeters) / 1000

So, let's calculate the volume of the balloon in liters:

Volume (liters) = (4.18879 × (165 mm)³) / 1000

Using a calculator to evaluate this expression, we find:

Volume (liters) ≈ 7.976 liters

Therefore, approximately 7.976 liters of air were used to fill the spherical balloon.

By comparing the result obtained in Part B (6N) with the result obtained in Part A, we can see that the conjecture holds true. The result of the process is indeed related to the original number (N) by multiplying it by 6.

Part A:

Based on the given process, the conjecture that relates the result of the process to the original number (represented as N) is as follows:

Start with the original number N.

Multiply N by 4.

Add 12 to the product.

Divide the sum by 2.

Subtract 6 from the quotient.

The result of this process is the final number obtained.

Part B:

To prove the conjecture using deductive reasoning, we will follow the steps given in Part A:

Start with the original number N.

Multiply N by 12.

Add 4 to the product.

Divide the sum by 2.

Subtract 2 from the quotient.

We will simplify the steps using algebraic notation:

Step 1: N

Step 2: 12N

Step 3: 12N + 4

Step 4: (12N + 4) / 2

Step 5: [(12N + 4) / 2] - 2

Now, let's simplify Step 5:

Step 5: (12N + 4) / 2 - 2

      = (12N + 4 - 2*2) / 2

      = (12N + 4 - 4) / 2

      = 12N / 2

      = 6N

Therefore, the result of this process is 6N.

We may verify that the supposition is correct by comparing the result from Part B (6N) with the result from Part A. By multiplying the outcome by 6, the process does in fact relate to the original number (N).

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The complete question is:

Multiply the number by 4. Add 12 to the product. Divide this sum by 2. Subtract 6 from the quotient. 1st number is 3 and the results 2nd number is 6 and the results 3rd number is 8 and the results 4th number is 12 and the results part A. Write a conjecture that relates the result of the process to the original number selected. Represent the original number as N. What is the result part b Represent the original number as N, use deductive reasoning to prove the conjecture in part (a) multiply the number by 12 and the results add 4 to the product and the results divide the sum by 2 subtract 2 from the quotient

(g∘f)(2) = 4.

To find (g∘f)(2), we need to substitute the value of f(x) into g(x) and evaluate the resulting expression at x = 2.

First, let's find f(2):

[tex]f(x) = -5 + 3[/tex]

[tex]f(2) = -5 + 3[/tex]

[tex]f(2) = -2[/tex]

Now, substitute f(2) into g(x):

[tex]g(x) = x^2[/tex]

[tex]g(f(2)) = (f(2))^2[/tex]

[tex]g(f(2)) = (-2)^2[/tex]

[tex]g(f(2)) = 4[/tex]

Therefore, (g∘f)(2) = 4.

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Answer:

the amount of metal required to make the can is 352.8π square centimeters.

Step-by-step explanation:

To calculate the amount of metal required to make the can, we need to find the surface area of the can.

The can consists of two circular ends (top and bottom) and a cylindrical body.

1. Surface Area of the Circular Ends:

The circular ends can be considered as two circles. The surface area of each circular end can be calculated using the formula for the area of a circle:

A_end = πr^2

Given the diameter of the can is 14 cm, the radius (r) is half the diameter, so r = 14 cm / 2 = 7 cm.

A_end = π * 7^2 = 49π cm^2 (for each circular end)

2. Surface Area of the Cylindrical Body:

The cylindrical body of the can can be represented as a rectangle that is rolled into a cylinder. The surface area of the cylindrical body can be calculated using the formula for the lateral surface area of a cylinder:

A_body = 2πrh

Given the height (h) of the can is 18.2 cm and the radius (r) is 7 cm, we can calculate the surface area of the cylindrical body:

A_body = 2π * 7 * 18.2 = 254.8π cm^2

3. Total Surface Area:

To calculate the total surface area of the can, we add the surface areas of the circular ends and the cylindrical body:

Total Surface Area = 2 * A_end + A_body

                 = 2 * 49π + 254.8π

                 = 98π + 254.8π

                 = 352.8π cm^2

Therefore, the amount of metal required to make the can is 352.8π square centimeters.

An x-y coordinate table is the appropriate table to use when graphing a piece of a function. This table helps you to determine the corresponding y-values for different x-values and plot the points on a graph.

To graph a piece of a function, you would typically use an x-y coordinate table, also known as a Cartesian coordinate system. This table consists of two columns: one for the x-values (also called the input values) and one for the corresponding y-values (also called the output values). Each row in the table represents a point on the graph.
To graph a piece of a function, you would need to identify the domain (the set of possible x-values) for that specific piece. Once you have the domain, you can choose values from that domain and calculate the corresponding y-values using the function.
For example, if you have a piece of a linear function, such as y = 2x + 3, you could create a table by choosing various x-values and calculating the corresponding y-values. Let's say we choose x-values of -2, 0, and 2. Plugging these values into the equation, we find the corresponding y-values: -1, 3, and 7.
So the table for this piece of the linear function would look like this:
x    |   y
--------------
-2  |  -1
0    |   3
2    |   7
Once you have the x-y coordinate table, you can plot the points on a graph and connect them to create the graph of the piece of the function.

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The ordered triple (p, q, r) that satisfies the given system of linear equations is (7, 2, 2).

To solve the given system of equations:

Start with the first equation: p - 2q = 3.

Multiply this equation by 2 to eliminate the coefficient of q: 2p - 4q = 6.

Next, we'll combine this equation with the second equation: q - 2r = -2.

Add the two equations together: (2p - 4q) + (q - 2r) = 6 + (-2).

Simplifying, we get: 2p - 3q - 2r = 4.

Now, let's consider the third equation: p + r = 9.

Rearrange this equation: p = 9 - r.

We can substitute this value for p in the equation we obtained in step 3:

2(9 - r) - 3q - 2r = 4.

Simplify the equation: 18 - 2r - 3q - 2r = 4.

Combining like terms, we have: -4r - 3q = -14.

We now have a system of two equations with two variables:

-4r - 3q = -14, (Equation 1)

q - 2r = -2. (Equation 2)

To solve this system, we can use various methods such as substitution or elimination. Here, we'll use the substitution method.

From Equation 2, we can solve for q:

q = 2r - 2.Substituting this value for q in Equation 1, we have:

-4r - 3(2r - 2) = -14.

Simplify and solve for r:

-4r - 6r + 6 = -14,

-10r = -20,

r = 2.

Now, substitute the value of r back into Equation 2 to solve for q:

q - 2(2) = -2,

q - 4 = -2,

q = 2.

Finally, substitute the values of q and r into Equation 3 to solve for p:

p + 2 = 9,

p = 7.

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The water source will provide 144 dal (or 1440 liters) more in 12 minutes compared to the initial 120 dal (or 1200 liters) in 10 minutes.

A water source provides 120 dal (decaliters) of water in 10 minutes. To determine how many additional liters it will provide in 12 minutes, we can convert the units and calculate the difference.

1 dal is equal to 10 liters. So, 120 dal is equal to 1200 liters.

In 10 minutes, the source provides 1200 liters of water.

To find out how many more liters it will provide in 12 minutes, we can set up a proportion:

10 minutes corresponds to 1200 liters

12 minutes corresponds to x liters

Using the proportion, we can cross-multiply:

10 * x = 12 * 1200

10x = 14400

x = 14400 / 10

x = 1440

Therefore, the water source will provide an additional 1440 liters in 12 minutes.

Converting back to decaliters, 1440 liters is equal to 144 dal.

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These are the four solutions for each given equation within the range of -360 degrees to 360 degrees.

To find the solutions for the given equations involving tangent (tan) functions, we need to solve for the angle (x) that satisfies each equation. Keep in mind that angles in trigonometry are typically measured in degrees.

tan(x) = 0.781:

To find the angle x that satisfies this equation, we can use the inverse tangent function (arctan or tan^(-1)). Taking the inverse tangent of both sides, we have:

x = arctan(0.781)

Using a calculator or a trigonometric table, we find that:

x ≈ 38.08 degrees

Since tangent is a periodic function with a period of 180 degrees, we can add or subtract multiples of 180 to find the other solutions:

x ≈ 38.08 degrees + 180n, where n is an integer

So, the four solutions for tan(x) = 0.781 are approximately:

x ≈ 38.08 degrees, 218.08 degrees, 398.08 degrees, -141.92 degrees

tan(x) = -1.036:

Similarly, using the inverse tangent function, we have:

x = arctan(-1.036)

Using a calculator or a trigonometric table, we find that:

x ≈ -45.14 degrees

Again, considering the periodicity of tangent, we can add or subtract multiples of 180 to find the other solutions:

x ≈ -45.14 degrees + 180n, where n is an integer

The four solutions for tan(x) = -1.036 are approximately:

x ≈ -45.14 degrees, 134.86 degrees, 314.86 degrees, 494.86 degrees

tan(x) = 2.145:

Using the inverse tangent function, we have:

x = arctan(2.145)

Using a calculator or a trigonometric table, we find that:

x ≈ 65.64 degrees

Considering the periodicity of tangent, we can add or subtract multiples of 180 to find the other solutions:

x ≈ 65.64 degrees + 180n, where n is an integer

The four solutions for tan(x) = 2.145 are approximately:

x ≈ 65.64 degrees, 245.64 degrees, 425.64 degrees, -114.36 degrees

These are the four solutions for each given equation within the range of -360 degrees to 360 degrees.

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The simplified form of 2i^68 is the value of 2^34.

To simplify 2i^68, we need to use the properties of imaginary numbers and the exponent rules. Here are the steps to simplify it:

Recall that i is defined as the square root of -1.

Since i^2 equals -1, we can rewrite the expression as (2i^2)^34.

Simplify the exponent by applying the rule that (a^m)^n equals a^(mn). In this case, we have (2i^2)^34 = 2^34 * (i^2)^34 = 2^34 * i^(234).

Simplify the terms. 2^34 is a large number, but we can still calculate it. i^(2*34) can be further simplified as i^68.

Determine the value of i^68 by noting that i follows a pattern: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1. The pattern repeats every four powers of i.

Since 68 is divisible by 4, i^68 equals 1.

Plug in the simplified values: 2^34 * i^(2*34) = 2^34 * i^68 = 2^34 * 1 = 2^34.

Calculate the value of 2^34 using a calculator or by applying exponent rules.

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Hello!

f(x) = x - 2

f(2) = 2 - 2 = 0

f(12) = 12 - 2 = 10

We reflect each vertex of triangle ABC across this line of reflection. After the reflection, A' will be (-2, 2), B' will be (-2, 4), and C' will be (-6, 2).

The reflected diagram will have triangle A'B'C' in the same orientation as triangle XYZ, with vertices A'(-2, 2), B'(-2, 4), and C'(-6, 2).

o place triangle ABC into the same orientation as triangle XYZ, we can perform a reflection across a line that preserves the shape and size of the triangles. In the given diagram, we can observe that the vertices of triangle ABC are labeled A(2, 1), B(4, 4), and C(6, 2), while the vertices of triangle XYZ are labeled X(5, 1), Y(7, 4), and Z(9, 2).

To find the line of reflection, we can draw a line that connects the midpoint of AB with the midpoint of XY. The midpoint of AB is ((2+4)/2, (1+4)/2) = (3, 2.5), and the midpoint of XY is ((5+7)/2, (1+4)/2) = (6, 2.5). Therefore, the line connecting these midpoints is a horizontal line with the equation y = 2.5.

Please note that the diagram provided is a rough representation, and the exact positions and orientations may vary based on the precise coordinates of the vertices.

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The range of the given sample data is 94 - 1 = 93.

To find the range of the given sample data, we need to calculate the difference between the maximum value and the minimum value in the data set.

The given sample data is: 4, 94, 37, 50, 46, 75, 5, 69, 1, 44, 35.

To find the range, we first need to determine the maximum and minimum values in the data set:

Maximum value: 94

Minimum value: 1

Now we can calculate the range by subtracting the minimum value from the maximum value:

Range = Maximum value - Minimum value

= 94 - 1

= 93

Therefore, the range of the given sample data is 93. The range represents the spread or the difference between the highest and lowest values in the data set.

The range tells us the extent of the variability in the data. In this case, the range of 93 indicates that the jersey numbers of the 11 randomly selected players from the football team have a relatively wide spread. The highest jersey number is 94, and the lowest jersey number is 1, with a difference of 93 between them.

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The volume of the larger can is approximately 3308.56 cubic inches.

To find the volume of the larger can, we can use the formula for the volume of a cylinder, which is given by V = πr²h, where V represents the volume, r represents the radius, and h represents the height.

Let's assume that the radius of the smaller can is r, and the height is h. According to the problem, the larger can has a radius and height that are both three times longer than the corresponding dimensions of the smaller can. Therefore, the radius of the larger can would be 3r, and the height would be 3h.

Given that the volume of the smaller can is 35.28 in³, we can substitute the values into the formula to solve for the volume of the larger can:

V_small = πr²h

35.28 = πr²h

To find the volume of the larger can, we need to calculate V_large = π(3r)²(3h):

V_large = π(3r)²(3h)

V_large = π(9r²)(3h)

V_large = 27πr²h

Since we know that 35.28 = πr²h from the volume of the smaller can, we can substitute this into the equation for the volume of the larger can:

V_large = 27πr²h

V_large = 27π(35.28)

V_large ≈ 3308.56 in³

Therefore, the volume of the larger can is approximately 3308.56 cubic inches.

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The probability that the student guesses all three compounds correctly is 1/1320.

To calculate the probability that the student guesses all three compounds correctly, we need to determine the number of favorable outcomes (correct guesses) and the total number of possible outcomes (all possible combinations).

Given that the student randomly chooses 3 compounds from a list of 12 possible compounds, the total number of possible outcomes is the number of ways to choose 3 compounds out of 12, which can be calculated using the combination formula:

Total number of possible outcomes = C(12, 3) = 12! / (3!(12-3)!) = 220

Now, let's consider the favorable outcomes, which are the cases where the student guesses all three compounds correctly. Since the student has no prior knowledge of the compounds, the probability of guessing each compound correctly is 1 out of 12.

For the first guess, there is a 1/12 probability of choosing the correct compound. Similarly, for the second guess, there is a 1/11 probability of choosing the correct compound (as one compound has already been chosen). Finally, for the third guess, there is a 1/10 probability of choosing the correct compound (as two compounds have already been chosen).

To find the probability of all three correct guesses, we multiply the probabilities of each independent event:

Probability of all three correct guesses = (1/12) * (1/11) * (1/10) = 1/1320

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The volume of the triangular prism that is given above would be = 6cm³. That is option B.

To calculate the volume of the triangular prism, the formula that should be used would be given below as follows;

Volume of triangle prism = ½×b×h×l

base length = 12 mm = 1.2cm

height = 2.5cm

length = 4cm

Volume = 1/2 × 1.2× 2.5× 4

= 6 cm³

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The percent increase in enrollment from 1980 to 2004 is 125%.

To calculate the percent increase in enrollment from 1980 to 2004, we can use the following formula:

Percent Increase = ((Final Value - Initial Value) / Initial Value) * 100

Given that the number of students in 1980 was 4,000 and the number of students in 2004 was 9,000, we can substitute these values into the formula:

Percent Increase = ((9,000 - 4,000) / 4,000) * 100

Simplifying the numerator:

Percent Increase = (5,000 / 4,000) * 100

Performing the division:

Percent Increase = 1.25 * 100

Calculating the final result:

Percent Increase = 125%

Therefore, the percent increase in enrollment from 1980 to 2004 is 125%.

This means that the number of students increased by 125% over the 24-year period. In other words, the enrollment more than doubled during this time frame.

It is important to note that the percent increase indicates the relative change in enrollment from the initial value. In this case, the enrollment increased by 125% compared to the enrollment in 1980.

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The function for the velocity is v(t) = 12t² – 12t – 72.

The velocity is zero at t = 3 and t = -2.

The function for the acceleration is a(t) = 24t – 12.

To find the velocity function v(t), we need to take the derivative of the position function s(t) with respect to time.

Given that s(t) = 4t³ – 6t² – 72t, we can differentiate it to obtain the velocity function v(t):

v(t) = s'(t) = d/dt (4t³ – 6t² – 72t)

To differentiate each term, we can apply the power rule of differentiation:

v(t) = 12t² – 12t – 72

Therefore, the function for the velocity is v(t) = 12t² – 12t – 72.

To find when the velocity equals zero, we set v(t) = 0 and solve for t:

12t² – 12t – 72 = 0

We can factor out a common factor of 12:

12(t² – t – 6) = 0

Now, we can solve the quadratic equation t² – t – 6 = 0 by factoring or using the quadratic formula:

(t – 3)(t + 2) = 0

This gives us two possible values for t when the velocity equals zero: t = 3 and t = -2.

Therefore, the velocity is zero at t = 3 and t = -2.

To find the function for acceleration a(t), we need to take the derivative of the velocity function v(t):

a(t) = v'(t) = d/dt (12t² – 12t – 72)

Differentiating each term:

a(t) = 24t – 12

Therefore, the function for the acceleration is a(t) = 24t – 12.

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The most appropriate reason for Christie making changes to her budget at the end of every month in terms of smart financial planning is B. She is reviewing her goals and aligning the budget to work toward them.Option B is correct.

Smart financial planning involves regularly evaluating and adjusting one's budget to ensure that it reflects their financial goals and current circumstances. By reviewing her goals, Christie can assess if her budget is still aligned with those goals and make any necessary changes to stay on track.

Life circumstances, such as changes in income, expenses, or financial priorities, may warrant adjustments to the budget. Christie recognizes that her needs may change over time, and by modifying her monthly budget, she can ensure that her financial resources are allocated appropriately to meet her evolving goals.

Regularly revisiting and modifying the budget allows Christie to adapt her financial plans, optimize her spending, and make informed decisions to achieve her financial objectives. Option B is correct.

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Using the commutative property of addition, we can write the expression (3+7^) + (8-6^) as (8-6^) + (3+7^).

The property that allows you to write the expression (3+7^) + (8-6^) as (8-6^) + (3+7^) is the commutative property of addition.

The commutative property of addition states that changing the order of the addends does not affect the sum. In other words, when adding two numbers, you can rearrange the order of the numbers without changing the result.

Applying this property to the given expression, we can rearrange the order of the two addition operations:

(3+7^) + (8-6^) = (8-6^) + (3+7^)

So, using the commutative property of addition, we can write the expression (3+7^) + (8-6^) as (8-6^) + (3+7^).

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The house will be worth approximately $1,258,884.83 in 8 years.

The correct answer is C: $1,258,884.

To find the worth of their house in 8 years, we need to substitute the value of t as 8 into the exponential equation:

y = 150,000(1.004)^(12t)

Plugging in t = 8:

y = 150,000(1.004)^(12*8)

Simplifying:

y = 150,000(1.004)^96

Using a calculator or a computer, we can evaluate the exponential expression:

y ≈ 1,258,884.83

Therefore, the house will be worth approximately $1,258,884.83 in 8 years.

The correct answer is C: $1,258,884.

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We can conclude that points, planes, lines, and other undefinable terms are important concepts in geometry. They are essential building blocks of geometric shapes and are used in mathematical calculations and problem-solving.

Geometry is a field of mathematics that deals with the study of shapes, sizes, relative positions, and properties of space. It involves understanding the properties of lines, points, planes, and other shapes in space. Undefinable terms are important concepts in geometry that are not defined or are difficult to define. Some statements that are true regarding undefinable terms in geometry are as follows: A point has no length or width.

A point is one of the fundamental concepts of geometry, and it is an essential building block of other geometric shapes. A point has no length or width; instead, it indicates a specific location in space. Points are represented as dots in geometry.A plane has one dimension, length. A plane is a flat, two-dimensional surface that extends infinitely in all directions. It has only one dimension, length.

A plane is a surface that has no thickness or depth, but it has an infinite number of points.A plane consists of an infinite set of lines. A plane is made up of an infinite number of lines that are parallel to each other. All of these lines extend in both directions, so they never meet. When a plane is intersected by a line, it creates a point where the two meet.

A line has a definite beginning and end. A line is a geometric object that extends infinitely in both directions. It has no width or thickness, but it has a definite beginning and end. A line is usually represented as a straight line that extends infinitely in both directions. A line is made up of an infinite number of points.

A line consists of an infinite set of points. A line is an infinite set of points that are aligned in a straight line. A line has no thickness or width, but it is infinitely long. The points on a line have no beginning or end, but they are considered to be in a specific order.

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The surface area of the rectangular prism is 108 cm².

To calculate the surface area of an object, you need to measure the areas of all of its faces and then add them up.

The formula for the surface area of a rectangular prism is SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

To calculate the surface area of a rectangular prism,

Measure the length, width, and height of the rectangular prism in centimeters.

Use the formula SA = 2lw + 2lh + 2wh to calculate the surface area. Plug in the values for l, w, and h, and perform the necessary calculations.

This will give you the surface area in square centimeters.

Round the answer to two decimal places to get the final answer.

The following example demonstrates how to calculate the surface area of a rectangular prism.

Example:

Calculate the surface area of a rectangular prism with a length of 6 cm, a width of 4 cm, and a height of 3 cm.

Measure the length, width, and height of the rectangular prism in centimeters.

l = 6 cmw = 4 cmh = 3 cm

Use the formula SA = 2lw + 2lh + 2wh

To calculate the surface area.

SA = 2lw + 2lh + 2whSA = 2(6 cm × 4 cm) + 2(6 cm × 3 cm) + 2(4 cm × 3 cm)SA

= 48 cm² + 36 cm² + 24 cm²

SA = 108 cm²

Round the answer to two decimal places to get the final answer.

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[tex]\tan(x )=\cfrac{\stackrel{opposite}{18}}{\underset{adjacent}{11}} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{18}{11} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{18}{11} \right)\implies x \approx 58.6^o[/tex]

Make sure your calculator is in Degree mode.

Answer:

x =  58.6°

Step-by-step explanation:

Because this is a right triangle, we're able to find the measure of angle x using one of the trigonometric ratios.  

When angle x is the reference angle, the side that is 18 units long is the opposite side and the side that is 11 units long is the adjacent side.

Thus, we can use the tangent ratio, which is given by:

tan (θ) = opposite / adjacent, where

Thus, we have tan (θ) = 18 / 11

In order to find angle measures we use inverse trigonometry:

tan^-1 (18 / 11) = x

58.57043439 = x

58.6 = x

Thus, the measure of angle x is about 58.6°

Answer: 1105 grams of protein

Step-by-step explanation:

If the athlete eats 65 grams of protein per day, we multiply that by 17 for the amount of days.

1105x65=1105

Answer:

12

Step-by-step explanation:

pitcher plant consumes one insect at a time so total number of pitcher plants used for insects consumption according to the given data set will be 12

S received $1050, J received $0, and the ratio of the money shared between S and J is 0:1. A received 23.33% of the total amount.

Step 1: Determine the amount A received.

We know that A received 1/2 of the total amount, which is $1050. Therefore, the total amount can be calculated by multiplying A's portion by 2: 1050 * 2 = $2100.

Step 2: Calculate the amount J received.

To find the amount J received, we need to subtract A's and S's amounts from the total.

From Step 1, we know that the total is $2100. S received the same amount as A, which is $1050.

Therefore, we subtract A's and S's amounts from the total: 2100 - 1050 - 1050 = $0.

Since J received the remainder, we see that J did not receive any amount from the initial sum of $4500.

Step 3: Calculate the amount S received.

To find the amount S received, we need to subtract S's amount from the total.

Again, from Step 1, we know that the total is $2100. S received the same amount as A, which is $1050.

Therefore, we subtract S's amount from the total: 2100 - 1050 = $1050.

Step 4: Calculate the ratio in which the money was shared between S and J.

Since J did not receive any amount, the ratio of the money shared between S and J is 0:1.

Step 5: Calculate the percentage of the total amount that A received.

To find the percentage, we divide A's amount by the total and multiply by 100: (1050/4500) * 100 = 23.33%.

Therefore, S received $1050, J received $0, and the ratio of the money shared between S and J is 0:1.

A received 23.33% of the total amount.

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Answer:

Annette should plan to spend 2.25 hours walking back.

Step-by-step explanation:

To solve this problem, we can use the formula:

Time = Distance / Speed

Let's assume the distance of the race is D miles.

Annette spends her time running the distance of the race, which takes:

Time running = D / 9 hours

She then walks back the same distance, which we need to find the time for:

Time walking = D / 3 hours

Since Annette has a total of 3 hours for her training, the sum of the running time and walking time should equal 3 hours:

D / 9 + D / 3 = 3

To simplify the equation, we can multiply all terms by 9 to eliminate the denominators:

D + 3D = 27

Combining like terms:

4D = 27

Dividing both sides of the equation by 4:

D = 6.75

So, the distance of the race is 6.75 miles.

To find the time Annette should spend walking back, we substitute the distance into the time-walking formula:

Time walking = D / 3 = 6.75 / 3 = 2.25 hours

Therefore, Annette should plan to spend 2.25 hours walking back.

The swimming pool can hold a volume of 3.456 cubic meters of water.

The volume of water that the swimming pool can hold can be calculated by multiplying the base area of the pool by its depth. In this case, the base area is given as 192 m² and the depth is 1.8 cm.

However, it is important to note that the depth should be converted to meters before performing the calculation.

To convert 1.8 cm to meters, we divide it by 100 (since there are 100 centimeters in a meter):

Depth = 1.8 cm ÷ 100 = 0.018 m

Now we can calculate the volume of water using the formula:

Volume = Base Area × Depth

Substituting the given values, we get:

Volume = 192 m² × 0.018 m = 3.456 m³

Therefore, the swimming pool can hold a volume of 3.456 cubic meters of water.

In the explanation, we use the formula for calculating the volume of a rectangular prism, which is given by multiplying the base area by the depth. We convert the depth from centimeters to meters and then substitute the given values into the formula to find the volume of water that the swimming pool can hold, which is 3.456 cubic meters.

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