Evaluate the following.
Write an exponential function of the form y = ab^x that has the given points
(−1,6 3/4), (2, 1-4)

The height of the pistol after 10 seconds is 783 feet.

We can use the method of finite differences to find the degree of the polynomial function that models the data. The first differences are:

3, 18, 37, 56, 72

The second differences are:

15, 19, 19, 16

Since the second differences are constant, we know that the function that models the data is a quadratic function of the form:

h(t) = at² + bt + c

where a, b, and c are constants to be determined.

To find a, we can use the fact that the coefficient of t² in the quadratic function is equal to half of the second difference. Thus, we have:

a = 1/2(15) = 7.5

To find b, we can use the fact that the coefficient of t in the quadratic function is equal to the first difference minus twice the coefficient of t². Thus, we have:

b = 18 - 2(7.5) = 3

To find c, we can use the fact that the constant term in the quadratic function is equal to the value of h(0). Thus, we have:

c = h(0) = 3

Therefore, the equation that models the data is:

h(t) = 7.5t² + 3t + 3

To find the height of the pistol after 10 seconds, we can substitute t = 10 into the equation:

h(10) = 7.5(10)² + 3(10) + 3

h(10) = 750 + 30 + 3

h(10) = 783

Thus, the height of the pistol after 10 seconds is 783 feet.

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If the right-hand-side for the Labor Time constraint decreases to 400, the dual value (shadow price) will become a more negative number, such as -8.

This is because the constraint is tighter, and the reduced availability of labor time will make the resource more valuable in the cost minimization problem. The new allowable increase in the right-hand-side will be smaller and the allowable decrease will be larger, reflecting the increased importance of meeting the resource constraint. This is because the decrease in resource availability means that the value of an additional unit of that resource has increased, leading to a higher cost of not having enough of it.

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the average speed of the plane in still air is s + 30.

Let's call the average speed of the plane in still air "s" (in miles per hour).

We can use the formula:

time = distance / speed

to find the time it takes the plane to travel from Salt Lake City to Oakland with the wind and against the wind.

With the wind:

time with wind = [tex]600 / (s + 30)[/tex]

Against the wind:

time against wind =[tex]600 / (s - 30)[/tex]

time against wind > time with wind

So we can set up an inequality:

[tex]600 / (s - 30) > 600 / (s + 30)[/tex]

Multiplying both sides by [tex](s - 30)(s + 30)[/tex], we get:

[tex]600(s + 30) > 600(s - 30)[/tex]

Expanding and simplifying, we get:

[tex]600s + 18000 > 600s - 18000[/tex]

Subtracting 600s from both sides, we get:

[tex]18000 > -18000[/tex]

This inequality is true for all values of s. In other words, there are no restrictions on the value of s that would make the return trip take longer than the trip with the wind.

Therefore, we can use the average of the two speeds (with and against the wind) to find the average speed of the plane in still air:

Average speed = [tex]2s(s + 30) / (s + 30 + s - 30)[/tex]

Simplifying, we get:

Average speed = [tex]2s(s + 30) / (2s)[/tex]

Canceling the common factor of 2s, we get:

Average speed = s + 30

We know that the distance from Salt Lake City to Oakland is 600 miles, and we can use the formula:

time = distance / speed

to find the time it takes the plane to travel this distance:

time = [tex]600 / (s + 30)[/tex]

We also know that the return trip (against the wind) takes longer, so we can set up another equation:

time return trip =[tex]600 / (s - 30)[/tex]

We can use these two equations to solve for s:

[tex]600 / (s + 30) = 600 / (s - 30)[/tex]

Cross-multiplying, we get:

[tex]600(s - 30) = 600(s + 30)[/tex]

Expanding and simplifying, we get:

[tex]600s - 18000 = 600s + 18000[/tex]

Subtracting 600s from both sides, we get:

[tex]-18000 = 18000[/tex]

This is not a valid equation, so there must be no solution.

However, we can still find the average speed of the plane in still air by using the equation we derived earlier:

Average speed = s + 30

So the average speed of the plane in still air is s + 30. We don't have a specific value for s, but we can say that the average speed is equal to the speed with the wind plus 30 (which is the speed of the wind).

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From the dot plot we can count a total of 15 dots, which means that there were 15 observations of the number of hours the students in the band practiced their instruments during the week represented by the dot plot.

The distribution of a dataset is shown using a particular type of graph called a dot plot.

It is also referred to as a scatterplot, dot graph, and dot chart.

Each data point in a dot plot is represented by a dot that is positioned above a number line.

Each dot on the number line represents the frequency or count of the corresponding value, and the number line itself represents the range of values in the dataset.

To determine the number of observations used for the dot plot, we need to count the number of dots on the plot.

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The expression to set the initial value of the 'day' variable to match the first day of the calendar month is:
day = 1
This simple expression assigns the initial value of 1 to the 'day' variable, representing the first day of any calendar month.

As the days progress, you can update the 'day' variable accordingly to represent the current day of the month.

The initial value of the 'day' variable to match the first day of the calendar month, using terms such as expression, initial value, variable, and calendar month.
Expression:

An expression is a combination of variables, constants, and operators that represent a particular value or calculation.

In this case, we want an expression that sets the 'day' variable to the first day of the calendar month.
Initial Value:

The initial value is the starting value assigned to a variable.

The 'day' variable, we need to set its initial value to 1, as the first day of any calendar month is always represented by the number 1.
Variable:

A variable is a symbolic name that represents a value that can change.

In this context, the 'day' variable will represent the days in a calendar month, and we need to set its initial value to match the first day of the month.
Calendar Month:

A calendar month is a period of time that starts on the first day of a month and ends on the last day of the same month. Examples include January, February, March, etc.

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Answer:pl z give me brainliest the crown next to the stars when two people answer :) have a good day ;)

Step-by-step explanation:

hope this helped

The measure of angle FDE is 68.5°

the correct answer is an option (d)

Consider the following figure.

We know that whenever two chords cut across a circle, the resulting angle is equivalent to half of the sum of the measurements of the arc the angle intersects and that which the angle vertical to the first angle intercepts.

Here, chords BE and FC cuts across the circle forming ∠FDE.

According to above statement, the measure of ∠FDE would be equal to the sum of the measurements of the arc BC and FE

⇒ m∠FDE = 1/2( Arc BC + Arc FE)

⇒ m∠FDE = 1/2 (61° + 76°)

⇒ m∠FDE = 137/2

⇒ m∠FDE = 68.5°

Therefore, the correct answer is an option (d)

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Answer:

The measure of angle FDE is 68.5° (D)

Step-by-step explanation:

I TOOK THE TEST

The correct solution for the given equation is x = 17.

The distributive property is a mathematical property that relates multiplication and addition or subtraction. It states that multiplying a number by a sum (or difference) is equivalent to multiplying the number by each term of the sum (or difference) and then adding (or subtracting) the results.

Joe's error is due to not using the order of operations correctly. In step 2, he did not use parentheses to isolate the x term before dividing by 2. Instead, he divided both 3 and x by 2, resulting in x/2 = 7.

To fix Joe's mistake, we need to apply the distributive property by adding parentheses around the numerator of the left-hand side of the equation, like this:

(3 + x)/2 = 10

Then we can multiply both sides by 2 to eliminate the fraction:

3 + x = 20

Finally, we can solve for x by subtracting 3 from both sides:

x = 17

Therefore, the correct solution is x = 17.

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2(4/3) represents the shaded area in the diagram as two rectangles of equal size, each with a length of 4 units and a width of 2/3 units.

4 * 2/3 represents the shaded area in the diagram as a rectangle with a length of 4 units and a width of 2/3 units.

4 * 2 * 1/3 represents the shaded area in the diagram as a rectangle with a length of 4 units, a width of 2 units, and a smaller rectangle with a length of 1 unit and a width of 1/3 units.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

a. The diagram shows 3/5 by dividing the whole rectangle into 5 equal parts horizontally and shading 3 of those parts. This means that the shaded portion represents 3 out of 5 equal parts.

b. The diagram shows 3 * 1/5 by shading one-fifth of the rectangle, and then repeating this process three times. This means that the shaded portion represents three times one-fifth of the whole.

c. The value of 3/5 is equivalent to 0.6 or 60%. This means that if we divide a whole into 5 equal parts, and take 3 of those parts, we have 60% of the whole.

a. The expression 2(4/3) represents the shaded parts of the diagram by first finding the area of one shaded rectangle, which is 4/3. Then, we multiply this area by 2 because there are two shaded rectangles in the diagram. Therefore, 2(4/3) gives us the total shaded area.

b. The expression 4 * 2/3 represents the shaded parts of the diagram by multiplying the width of the shaded rectangle (2 units) by its height (2/3 units), and then multiplying that by the number of shaded rectangles (4). Therefore, 4 * 2/3 gives us the total shaded area.

c. The expression 4 * 2 * 1/3 represents the shaded parts of the diagram by multiplying the length of the shaded rectangle (4 units) by its width (2 units) by its height (1/3 units), and then multiplying that by the number of shaded rectangles (4). Therefore, 4 * 2 * 1/3 gives us the total shaded area.

Hence, 2(4/3) represents the shaded area in the diagram as two rectangles of equal size, each with a length of 4 units and a width of 2/3 units.

4 * 2/3 represents the shaded area in the diagram as a rectangle with a length of 4 units and a width of 2/3 units.

4 * 2 * 1/3 represents the shaded area in the diagram as a rectangle with a length of 4 units, a width of 2 units, and a smaller rectangle with a length of 1 unit and a width of 1/3 units.

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The null hypothesis for this test is that the 2 groups will not differ in terms of their suggested sentences.

The null hypothesis is a statement that there is no difference between the two populations or variables being tested.

It can be thought of as the "default" position, which assumes that any observed difference is due to chance.

The null hypothesis is usually written in a way that it can be tested and rejected or not rejected through statistical analysis.

The null hypothesis for this test is that the two groups will not differ in terms of their suggested sentences.

This means that any difference between the groups in their suggested sentences is due to chance and not a difference in the population or variables being tested.

This hypothesis can be tested and rejected or not rejected through statistical analysis.

If the two groups do differ in their suggested sentences then the null hypothesis will be rejected and it will be concluded that the difference is not due to chance but rather due to a difference in the population or variables being tested.

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The solutions to the equation sin(πx/3) = 0 in the interval -5 < x < 5 are x = -3, 0, and 3.

What is Trigonometric equation?

A trigonometric equation is an equation that involves trigonometric functions such as sine, cosine, tangent, or their inverses. Trigonometric equations arise in a variety of mathematical and scientific contexts, from solving geometric problems involving angles and triangles to modeling periodic phenomena in physics, engineering, and other fields.

Solving a trigonometric equation typically involves finding the values of the unknown variable that satisfy the equation within a certain interval. For example, the equation sin(x) = 0 has infinitely many solutions, but if we restrict the interval to [0, 2π], then the solutions are x = 0, π, 2π, which correspond to the x-intercepts of the sine function in that interval.

Here the equation sin(πx/3) = 0 has solutions whenever πx/3 is an integer multiple of π, since the sine function is zero at these values. Thus, we need to find all integers n such that πx/3 = nπ, or equivalently x = 3n for some integer n.

Since -5 < x < 5, we need to find all integers n such that -5 < 3n < 5. Dividing all sides by 3, we get -5/3 < n < 5/3. The only integers in this range are -1, 0, and 1. Therefore, the solutions to the equation sin(πx/3) = 0 in the interval -5 < x < 5 are x = -3, 0, and 3.

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The total number of monotonous positive integers either a strictly increasing or a strictly decreasing sequence is equal to 90.

Let us consider the cases of monotonous numbers with increasing digits and monotonous numbers with decreasing digits separately.

For a monotonous number with increasing digits, we can start with any digit from 1 to 9, and for each subsequent digit.

Choose any number from the set of remaining digits.

For example, if we start with 1, we have 8 choices for the second digit, 7 choices for the third digit, and so on.

Until we have only one choice left for the last digit.

There are a total of 9 + 8 + 7 + ... + 1 = 45 monotonous numbers with increasing digits.

For a monotonous number with decreasing digits, we can start with any digit from 9 to 1, and for each subsequent digit.

Choose any number from the set of remaining digits that is smaller than the previous digit.

For example, if we start with 9, we have only one choice for the second digit 8, one choice for the third digit 7, and so on.

Until we have only one choice left for the last digit.

There are a total of 9 + 8 + 7 + ... + 1 = 45 monotonous numbers with decreasing digits.

The number 0 cannot be the first digit of a monotonous number with increasing digits, because it is not a positive integer.

No need to consider this case separately.

Therefore, the total number of monotonous positive integers is 45 + 45 = 90.

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In the hexagon,

a) side length = 11.56 unit , radius = 11.56 unit.

b) Area = 346.8 square unit.

What is area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Here the given hexagon apothem a= 10 units.

We know that central angle = 360° and number of sides n=6

Then apothem bisect the angle. Then, [tex]\theta = \frac{360}{12}=30\textdegree[/tex]

Now using cosine ratio then cos30° = [tex]\frac{a}{radius} = \frac{10}{radius}[/tex]

=> radius = [tex]\frac{10}{cos30\textdegree}[/tex] = 11.56 unit.

Now using sine ratio then,

=> sin30° = [tex]\frac{\frac{s}{2}}{radius}[/tex]

=> s = sin 30°× 2radius  = 11.56  unit

Now using area formula then,

Area A = [tex]\frac{1}{2}aP[/tex]

=> A = [tex]\frac{1}{2}\times10\times6\times11.56[/tex]

=> A = 346.8 square unit.

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The radius of the circle with the given chord length is: radius = 7.25

The Radius of a Circle based on the Chord and Arc Height helps us to computes the radius based on the chord length (L) and height (h).

The formula for the radius of a circle based on the length of a chord and the height is:

r = (L²/8h) + (h/2)

where:

r is the radius of a circle

L is the length of the chord.  This is the straight line length connecting any two points on a circle.

h is the height above the chord.  This is the greatest distance from a point on the circle and the chord line.

We are given:

L = 5 + 5 = 10

h = 2

Thus:

r = (10²/8(2)) + (2/2)

r = 6.25 + 1

r = 7.25

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The upper control limit for the x-bar chart for the temperature of champagne bottles is 52.243 degrees Fahrenheit for standard deviation.

To find the upper control limit for an x-bar chart, we use the formula:

Upper Control Limit = X-bar + A2 * (standard deviation / [tex]\sqrt{(sample size)}[/tex])

Where X-bar is the average temperature across all bottles (52 degrees Fahrenheit), A2 is a constant factor based on the sample size (for a sample size of 9, A2 is 0.729), and the standard deviation is 0.9 degrees Fahrenheit.

Plugging in these values, we get:

Upper Control Limit = 52 + 0.729 * (0.9 / [tex]\sqrt{9}[/tex])
Upper Control Limit = 52 + 0.243
Upper Control Limit = 52.243 degrees Fahrenheit

Therefore, the upper control limit for the x-bar chart for the temperature of champagne bottles is 52.243 degrees Fahrenheit. This means that if any sample of 9 bottles has an average temperature above this limit, it may indicate a problem with the process that needs to be addressed.

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The upper control limit (UCL) for the X-bar chart is 52.9 degrees Fahrenheit.

We will use the following terms to find the upper control limit (UCL) for an X-bar chart:
Average temperature (µ) = 52 degrees Fahrenheit
Standard deviation (σ) = 0.9 degrees Fahrenheit.

Sample size (n) = 9 bottles
Number of days (m) = 105 days.

To find the UCL, we first need to find the standard error (SE) using the formula:
SE = σ / √n
Substitute the given values into the formula:
SE = 0.9 / √9 = 0.9 / 3 = 0.3 degrees Fahrenheit
Now we'll use the control chart formula to find the UCL, which is:
UCL = µ + 3 * SE
Substitute the values:
UCL = 52 + 3 * 0.3 = 52 + 0.9 = 52.9 degrees Fahrenheit.

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David's ratio of 1:2 is correct if we are considering the ratio of boys to girls. Al's ratio of 1:1 is correct if we are considering the ratio of boys to the total number of students in the class.

A ratio is a comparison of two quantities that have the same unit of measure. It is a way of expressing the relative sizes of two or more values, often as a fraction or with a colon between the values. Ratios are used in many areas of mathematics and science, as well as in everyday life. They can be used to compare measurements such as distance, speed, and weight, as well as to express probabilities and percentages. Ratios can also be used to simplify complex problems and make them easier to understand.

Here,

David says the ratio of boys to girls in Mr. Huff's class is 1:2. This means that there is one boy for every two girls. If there are 15 girls in the class, then there must be 30 boys (since 2 x 15 = 30). So the total number of students in the class is 15 + 30 = 45.

Al says the ratio of boys to girls in Mr. Huff's class is 1:1. This means that there is one boy for every one girl. If there are 15 girls in the class, then there must be 15 boys as well. So the total number of students in the class is 15 + 15 = 30.

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After completing the given statements, we have:

8.703 dekagrams = 0.08703 kilograms

100.3 meters = 10.03 hectometers

909.9 liters = 90,990 centiliters

To convert between units of measurement, we need to use conversion factors that relate the two units. These conversion factors can be derived from the definition of the units and the relationships between them.

In the first statement, we are asked to convert 8.703 dekagrams to kilograms. To do this, we use the conversion factor that 1 kilogram is equal to 1000 grams and 1 dekagram is equal to 10 grams. Thus, we have:

8.703 dekagrams = 8.703 * (10 grams/1 dekagram) * (1 kilogram/1000 grams) = 0.08703 kilograms

Therefore, 8.703 dekagrams is equivalent to 0.08703 kilograms.

In the second statement, we are asked to determine what value of 100.3, when multiplied by a conversion factor, equals 10.03 hectometers. To do this, we need to use the conversion factor that 1 hectometer is equal to 100 meters. Thus, we have:

100.3 * (100 meters/1 hectometer) = 10030 meters = 10.03 hectometers

Therefore, the value of 100.3 that, when multiplied by the conversion factor, equals 10.03 hectometers is 100.3 meters.

In the third statement, we are asked to convert 909.9 to centiliters. To do this, we use the conversion factor that 1 liter is equal to 100 centiliters. Thus, we have:

909.9 liters = 909.9 * (100 centiliters/1 liter) = 90,990 centiliters

Therefore, 909.9 liters is equivalent to 90,990 centiliters.

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Complete question is:

Complete the statements.

8.703 dekagrams =_____    kilograms

100.3   _____= 10.03 hectometers

909.9  _____= 90,990 centiliters

Answer:

x > - 4

Step-by-step explanation:

- x - 2.2 < 1.8 ( add 2.2 to both sides )

- x < 4

multiply both sides by - 1, reversing the symbol as a result of multiplying by a negative quantity

x > - 4

From the plot we deduce that

x intercept = 0

y intercept = 0

Domain = all real numbers

Range = all real numbers

Transformations

The transformation for the function

y = 2(x - 8)^1/3 + 4

Shows a movement from the parent function y = x^1/3

(x - 8)^1/3  represents translation 8 units to the right

(x - 8)^1/3 + 4  represents translation 4 units upwards

2(x - 8)^1/3 + 4  represents vertical stretch by a factor of 2

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The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

The equation would be:

C is the total cost and m is the miles driven.

We know that:
Charge of the truck: $35

Charge per mile: $2.50

Then, form the equation as follows:

C = 35 + 2.50m

Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

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In the given problem, there are two values of k that make the equation an identity: k = -x + √(x² + 2) and k = -x - √(x² + 2).

To make the equation x² + 2x = (x + k)² - 1 an identity, we need to find the value of k that makes both sides of the equation equal for all values of x.

First, we can expand the right-hand side of the equation using the square of a binomial formula:

(x + k)² - 1 = x² + 2xk + k² - 1

Now we can set this expression equal to the left-hand side of the equation and simplify:

x² + 2xk + k² - 1 = x² + 2x

Subtracting x² and 2x from both sides, we get:

2xk + k² - 1 = 0

Adding 1 to both sides, we get:

2xk + k² = 1

Now we can solve for k by using the quadratic formula:

k = (-2x ± √(4x² + 8))/2

Simplifying the expression under the square root:

k = (-2x ± 2√(x² + 2))/2

k = -x ± √(x² + 2)

So, there are two values of k that make the equation an identity:

k = -x + √(x² + 2)

and

k = -x - √(x² + 2)

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Answer:

Step-by-step explanation:

the correct form of g multiplied by 67 is 67g

Step-by-step explanation:

y will equal 0 when the frog hits on the ground after being in the air:

0 = -16t^2 + 10 t + 0.3

 Use quadratic formula with   a = -16       b = 10       c = 0.3

     to find t = .65 seconds

The answer to this question is  Scatter plot

Answer: Yes

Step-by-step explanation: SSS criteria

Answer:

Image

Step-by-step explanation:

the measure of the exterior angle ECD is 140 degrees.

Answer:

110°

Step-by-step explanation:

The sum of the angles in a triangle is equal to 180°

So, 2x°+3x°+(3x+4)°=180°

8x°+4°=180°

8x°=180°- 4°

8x°=176°

x°=22°

The exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle.

So, the exterior angle is 2x°+3x°=5x°

As we got x°=22°, then 5x°=5×22°=110°

Positive integers less than 100 that are neither multiples of 2 nor multiples of 3 are 33. Option (d)

To solve this problem, we can use the principle of inclusion-exclusion.

There are a total of 99 positive integers less than 100 (from 1 to 99, inclusive).

We want to count the number of integers that are not multiples of 2 or 3.

The number of integers that are multiples of 2 is 49 (from 2 to 98, inclusive, with a common difference of 2).

The number of integers that are multiples of 3 is 33 (from 3 to 99, inclusive, with a common difference of 3).

However, we have double-counted the integers that are multiples of both 2 and 3 (i.e., multiples of 6). There are 16 such integers (from 6 to 96, inclusive, with a common difference of 6).

Therefore, the number of integers that are not multiples of 2 or 3 is:

99 - (49 + 33 - 16) = 83

So there are 83 positive integers less than 100 that are neither multiples of 2 nor multiples of 3.

Therefore, the answer is (d) 33.

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The volume of the sphere with a radius of 7 feet is therefore 1436.8 cubic feet when expressed in terms of pi and rounded to the closest tenth (or about 1436.76 cubic feet).

The volume of such a three-dimensional object is the amount of space it takes up in algebra and geometry. It is a description of an object's capacity and, depending on the situation, may be stated in terms of cubic metres, cubic centimetres, litres, or gallons. A cube's volume, for instance, can be determined by adding up its length, width, and height. An equation for calculating a cube's volume is: V = l × w × h where V indicates for volume, l for length, w for width, and h for height.

given

The following equation determines a sphere's volume:

[tex]V = (4/3)\pi r^3[/tex]

where r denotes the sphere's radius.

If we substitute r = 7 feet, we obtain:

[tex]V = (4/3)\pi (7 feet)^3[/tex]

Using V, 1436.76 cubic feet (3.14159)

To the nearest tenth, we round and obtain:

1436.8 cubic feet equals V.

The volume of the sphere with a radius of 7 feet is therefore 1436.8 cubic feet when expressed in terms of pi and rounded to the closest tenth (or about 1436.76 cubic feet).

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