Answers
The exact values of s in the interval [-2π, π) that satisfy the given condition cot²s = 1 are s = -3π/2, -π/2, π/2, and 3π/2.
The given trigonometric equation is cot²s=1 and the interval is [-2π, π).
The given equation can be rearranged as cot²s = 1, which can be written as cot s = ±1.
Using the inverse cotangent identity cot⁻¹(±1) = ±π/2, we can find the exact values of s in the interval [-2π, π) that satisfy the given condition:
s = ±π/2 + 2kπ, where k is an integer.
Therefore, the exact values of s in the interval [-2π, π) that satisfy the given condition cot²s = 1 are s = -3π/2, -π/2, π/2, and 3π/2.
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Related Questions
Jonna is sewing a front cover for a circular pillow. The pillow has a diameter of 15 inches. To sew the front cover, she must cut the fabric two inches wider than the pillow all the way around. What is the minimum area, in square inches, of the piece of fabric she will use?
Answers
Answer:
Step-by-step explanation:
To determine the minimum area of the piece of fabric Jonna needs, we need to calculate the diameter of the circle after adding 2 inches to the radius.
The radius of the pillow is half its diameter, which is 15/2 = 7.5 inches.
When Jonna adds 2 inches to the radius, the new radius becomes 7.5 + 2 = 9.5 inches.
The diameter of the circle with the new radius is 2 x 9.5 = 19 inches.
Therefore, Jonna needs to cut a circular piece of fabric with a diameter of 19 inches.
To calculate the minimum area of the fabric, we need to use the formula for the area of a circle:
Area = π x (radius)^2
The radius is 9.5 inches, so:
Area = π x (9.5)^2
Area = π x 90.25
Area ≈ 283.77 square inches
Therefore, Jonna needs a piece of fabric with a minimum area of approximately 283.77 square inches.
The table below shows information about the thickness of each of the books on a shelf. Work out an estimate for the mean book thickness. Give your answer as a decimal. Thickness, x (mm) 0< x≤2 2< x≤4 4< x≤6 Frequency 4 9 7
Answers
Answer:
3.2mm
Step-by-step explanation:
Answer:
3.2mm
Step-by-step explanation:
Malick is forming clay blocks in the shape of rectangular prisms.
Two faces of the blocks are squares.
First, find the missing length of the clay block. Then, find the volume.
Answers
The missing length is 4 in.
The volume of a rectangular prism is 32 in³.
We have,
Since the two faces of the blocks are squares.
The face that has the missing length can be considered as a square face.
i.e
The front and back faces are squares.
So,
The missing length is 4 in.
Now,
The volume of a rectangular prism.
= length x width x height
= 4 x 2 x 4
= 32 in³
Thus,
The missing length is 4 in.
The volume of a rectangular prism is 32 in³.
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Drag the tiles to the correct boxes to complete the pairs.
Match each system of linear equations with the correct number of solutions.
One solution
62
地址
3x - y
-
y =
Infinitely many solutions
-
= 4
2y = 8
-4x - 5
-4x + 1
-3x + y
2x
ee
4y
= 7
=
-8
Reset
Next
No solution.
Answers
In the given system of linear equations we get,
3x - y = 4, 6x - 2y = 8 has no solution.
y = -4x - 5, y = -4x + 1 has infinitely many solutions.
- 3x + y = 7, 2x - 4y = -8 has exactly one solution.
System of linear equations can have one solution or infinitely many solution or no solution based on their form.
If two lines are parallel to each other (that is, both linear equations have same slope) then the system of linear equations has no solutions.
A system of linear equation with infinitely many solutions has both the sides of equations equal.
When a system of linear equation has exactly one value of the variables which makes the equations satisfy is said to have one solution.
Here the system of linear equations are as,
3x - y = 4
6x - 2y = 8
The two equations of the system of linear equations are parallel to each other and hence has no solution.
y = -4x - 5
y = -4x + 1
The two equations of the system of linear equations has both the sides equal to each other and hence has infinitely many solutions.
- 3x + y = 7
2x - 4y = -8
The two equations of the system of linear equations has exactly one value of x and y which satisfies the conditions and hence has one solution.
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Please help me answer this question
Answers
The quadratic polynomial with integer as coefficients that has four real roots including these conjugates is a² + b² - 2ab - 20a - 20b + 88 ≥ 0
Here is how to derive the polynomialOne possible quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3, is:
(x - 5 - √3)(x - 5 + √3)(x - a)(x - b)
where a and b are the remaining two roots.
Expanding the first two factors using the difference of squares formula, we get:
(x - 5)² - 3
Expanding the last two factors, we get:
x² - (a + b)x + ab
Putting it all together, the quartic polynomial is:
a² + b² - 2ab - 20a - 20b + 88 ≥ 0
To ensure that a and b are also real, we can use the fact that the discriminant of a quadratic equation ax² + bx + c = 0 with real coefficients is b² - 4ac ≥ 0. Applying this to the quadratic factor in the above polynomial, we get:
(a + b)² - 4ab ≥ 0
Expanding and simplifying, we get:
a² + b² - 2ab - 20a - 20b + 88 ≥ 0
To simplify the problem, we can set a = b, since the polynomial is symmetric with respect to the roots. Then, the inequality becomes:
2a² - 40a + 88 ≥ 0
Dividing by 2 and factoring, we get:
(a - 10)² - 12 ≥ 0
This inequality is always true for real values of a, so we can choose any real value for a and set b = a to obtain a quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3.
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FOR 20 POINTS!!!
(Look at picture)
Answers
Answer:
Kenyon could make a total of 7 bouquets.
Step-by-step explanation:
To find the greatest number of bouquets we need to find GCF.
We need to find GCF for 21 and 28.
The factors of 21 are: 1,3,7, and 21.
The factors of 28 are: 1,2,4,7,14, and 28
1 and 7 are the common factors between 21 and 28.
From the factors, the greatest common factor is 7.
Val's whole-house central air conditioner uses 4,000 watts when running. Val runs the AC 7 hours per summer day. Electricity costs (10 cents)/(1 kilowatt-hour). How much does Val's AC cost to run for a summer month of 30 days?
Answers
The electricity cost for the Val's AC to run for a summer month of 30 days is $84.
Given that,
Val's whole-house central air conditioner uses 4,000 watts when running.
Val runs the AC 7 hours per summer day.
Electricity costs (10 cents)/(1 kilowatt-hour).
Total electricity used for the whole house = 4000 watts = 4 kilowatts
Number of hours that the AC runs = 7 hours
Cost of electricity = (10 cents)/(1 kilowatt-hour).
Cost of electricity for 4 kilowatts for 1 hour = 10 × 4 = 40 cents
Cost of electricity for 4 kilowatts for 7 hours = 40 × 7 = 280 cents
= $2.80
Cost of electricity for a summer month of 30 days = $2.80 × 30
= $84
Hence the total cost for the electricity is $84.
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The capacity of a swimming pool is given by C = l × w × , where l is the length, w is the width, d1 is the depth of the shallow end, and d2 is the depth of the deep end of the pool.
Select all the correct statements.
Answers
The correct statements about the capacity of swimming pool are (a) and (d)
The capacity of a swimming pool is given by C = l × w × (d₁ + d₂)/2
where l is the length,
w is the width,
d₁ is the depth of the shallow end,
and d₂ is the depth of the deep end of the pool.
If C = 9,216 ft, l = 48 ft, w = 24 ft, and d₂ = 12 ft, then d₁ would be,
9216 = 48 × 24 × (d₁ + 12)/2
d₁ + 12 = (9216 × 2) / (48 × 24)
d₁ + 12 = 16
d₁ = 4 ft
And formula for the depth of the shallow end would be,
d₁ = (2C/lw) - d₂
Therefore, the correct statements are (a) and (d)
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The complete question is:
The capacity of a swimming pool is given by C = l × w × (d1 + d2)/2, where l is the length, w is the width, d 1 is the depth of the shallow end, and d 2 is the depth of the deep end of the pool.
Select all the correct statements.
a) The depth of the shallow end is given by d1 = 2C/lw - d2.
b) If C = 9,216 ft, l = 48 ft, w = 24 ft, and d2 = 16 ft, then d1 = 4 ft.
c) The depth of the shallow end is given by 2C - d2/lw .
d) If C = 9,216 ft, l = 48 ft, w = 24 ft, and d2 = 12 ft, then d1 = 4 ft.
One number is 10 more than fifteen times another. Their sum is 42. Find the numbers.
Answers
From the problem, we know that:
- x = 15y + 10 (since "One number is 10 more than fifteen times another")
- x + y = 42 (since "Their sum is 42")
We can use substitution to solve for one of the variables. Substituting the first equation into the second equation, we get:
(15y + 10) + y = 42
Simplifying the left side, we get:
16y + 10 = 42
Subtracting 10 from both sides, we get:
16y = 32
Dividing both sides by 16, we get:
y = 2
Now that we know y, we can use the first equation to solve for x:
x = 15y + 10
x = 15(2) + 10
x = 40
Therefore, the two numbers are 2 and 40.
Answer:
40, 2
Step-by-step explanation:
x = number 1
y = number 2
x = 15y + 10
x + y = 42
we use the first in the second equation and get
15y + 10 + y = 42
16y = 32
y = 32/16 = 2
x + y = 42
x + 2 = 42
x = 40
The area of a large parking space is 162 square feet. If the width of the parking space is 9 feet, what is the length?
A 12 feet
B 14 feet
C 16 feet
D 18 feet
Answers
162 divided by 9 would equal 18.
For the polynomial 11x4 + 8x2 + x which represents how much Patrick won from Michael, find the degree of each term. Then find the degree of the polynomial.
Answers
The degree of the polynomial 11x⁴ + 8x² + x is 4, which is the highest degree among its terms. The degrees of the terms are 4, 2, and 1 for the first, second, and third terms, respectively.
The degree of a term in a polynomial is the exponent of its variable.
In the polynomial 11x⁴ + 8x² + x, the degree of the first term 11x⁴ is 4, the degree of the second term 8x² is 2, and the degree of the third term x is 1.
The degree of the polynomial is the highest degree among its terms. In this case, the highest degree is 4, which is the degree of the first term. Therefore, the degree of the polynomial is 4.
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1. Dave plays golf almost every day. The data set shown are his scores for his last 40 rounds of golf.
a. Construct a tally and frequency table for this data using class intervals 70-74, 75-79, 80-84, 85 - 89.
b. What percentage of Dave's scores were more than 84?
c. What percentage of Dave's scores were less than 75?
d. Copy and complete the following: More scores were in the interval..............than in any other interval.
Answers
More scores were in the interval 75-79 than any other interval
How to solvea. Class Interval Frequency
70-74 8
75-79 16
80-84 12
85-89 4
b. The % more than 84 = 4/40 x 100
=10%/
c. The % less than 75 = 8/40 x 100
= 20%
d. More scores were in the interval 75-79 than any other interval
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Determine if triangle RQP is similar to triangle YXW. If they are similar enter the scale factor from triangle YXW to triangle RQP
Answers
The triangles are similar, and the scale factor is given as follows: k = 0.8.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of the missing angle is given as follows:
x + 114 + 24 = 180
x + 138 = 180
x = 42º.
Which is equals to the measure on the second triangle, hence they are similar.
The scale factor is given as follows:
k = 16/20 = 36/45 = 0.8.
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Lisa is putting 11 colored light bulbs into a string of lights. There are 3 red light bulbs, 2 yellow light bulbs, and 6 pink light bulbs. How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?
Answers
We can see here that the distinct orders of light bulbs that are there if two light bulbs of the same color are considered identical is: 4,620.
How we arrived to the solution?We can see here that in order to find the solution, we use the permutation with repetition formula:
n! / (n1! × n2! x ... × nk!)
In order to adjust for overcounting, we divide by 3! because of the 3 red light bulbs we have. For the 2 yellow light bulbs, we divide with 2!. For the 6 pink light bulbs, we divide by 6!. This is because we are treating lights bulbs of the same color which are identical.
Therefore, the total number of distinct orders of bulbs will be:
11! / (3! × 2! × 6!) = 4,620
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on a 28 question test there are 2-point questions, 4-point, and 5- point questions. the test is worth a total of 100 points. there are twice as many 2 point questions as 5point questions on the test how many 2point questions are on the test
Answers
Answer:
Number of 2-point questions on the test as per given condition is equals to 8.
Total number of questions in a test = 28
Total points allotted for test = 100
Questions distribution as per points :
2-point questions, 4-point questions, and 5-point questions
'x' represents the 5-point questions
As per condition given,
Number of 2-point questions = 2x
Number of( 2-point + 4-point + 5-point ) questions = 28
⇒ 2x + 4-point questions + x = 28
⇒ 4-point questions = 28 - 3x
Substitute the value in the given condition of the equation we get,
2(2x)+4(28-3x)+5(x) = 100
4x+112-12x+5x=100
112-3x=100
x=4
A jet can fly (8 x 10^3) miles per hour. How far can it fly in a day?
Answers
The jet can fly a distance of 192,000 miles in a day, assuming it can maintain a speed of 8 x 10³ miles per hour for 24 hours.
There are 24 hours in a day, so the distance the jet can fly in a day is:
Distance = Speed x Time
where Time is the duration of the flight.
If we assume that the jet can fly continuously for 24 hours without refueling or stopping, then the time of the flight is 24 hours.
Therefore, we have:
Distance = Speed x Time
=8 x 10³ miles/hour x (24 hours)
= 192,000 miles
Therefore, the jet can fly a distance of 192,000 miles in a day, assuming it can maintain a speed of 8 x 10³ miles per hour for 24 hours.
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if there are 18 triangles in a polygon how many sides has the polygon
Answers
The number of sides of a polygon that has 18 triangles would be 20 sides.
How to find the number of sides ?To determine the number of sides in a polygon consisting of 18 triangles, we can calculate the sum of the interior angles. Each triangle has total interior angle sum of 180 degrees, and since there are 18 triangles, the sum of those angles would be 18 multiplied by 180, which comes to 3, 240 degrees.
Applying the given formula for calculating the interior angles of a polygon, we obtain that (n - 2) multiplied by 180 stands for the sum of all angles within it, with n being the number of sides.
Hence, rearranging the equation gives n :
n = (sum of interior angles ÷ 180) + 2
n = (3240 ÷ 180) + 2 = 20
There must be precisely 20 sides in that particular polygon.
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URGENT STATISTICS AND PROBABILITIES
Answers
Answer:
the expected point value is -1/5, so it is not advantageous to guess.
Step-by-step explanation:
1(1/5)+(-1/2)(4/5)
1/5-2/5
-1/5
List at least five combinations of nickels and dimes such that the number of nickels is double the number of dimes.
Answers
2 nickels and 1 dime
4 nickels and 2 dimes
6 nickels and 3 dimes
8 nickels and 4 dimes
10 nickels and 5 dimes
Let f(t) be the sales of a gaming product, in thousands of units, after t months.
Answers
The sales after 5 months is 36,000 units (since f(t) is given in thousands of units).
The given function f(t) represents the sales of a gaming product in thousands of units after t months. To find the sales after 5 months, we need to substitute t = 5 in the function f(t) and evaluate the expression. f(5) = 5(5) + 11
= 25 + 11
= 36
Therefore, the sales of the gaming product after 5 months is 36 thousand units. This means that the company has sold 36 thousand units of the gaming product within the first 5 months since the launch of the product. It also indicates that the sales are increasing by 5 thousand units every month.
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-- The given question is incomplete, the complete question is
"Let f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11. Find the sales after 5 months."
Find the 15th term of the geometric sequence 9, 18, 36, ...
Answers
Answer: 147,456
Step-by-step explanation: 9, 18, 36, 72, 144, 288, 576, 1,152, 2,304, 4,608, 9,216, 18,432, 36,864, 73,728, 147,456
Larry cut a ribbon into 8 equal pieces. If the ribbon was 26 m long, how many meters long was each piece?
Answers
As per the unitary method, each piece is 3.25 meters long by dividing the total length of the ribbon by the number of pieces.
Larry has cut a ribbon into 8 equal pieces. The total length of the ribbon is 26 m. We need to find out the length of each piece of the ribbon.
To do this, we can use the unitary method. We know that the ribbon is divided into 8 equal pieces, so each piece is 1/8th of the total length of the ribbon.
Therefore, we can find the length of each piece by dividing the total length of the ribbon by 8:
Length of each piece = Total length of ribbon / Number of pieces
Length of each piece = 26 m / 8
Length of each piece = 3.25 m
So, each piece of the ribbon is 3.25 meters long.
We used the unitary method by finding the value of one unit (1/8th of the ribbon) and then using it to calculate the value of other units (the length of each piece).
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find the following arc measures
Answers
The measure of the angles are;
<KL = 23 degrees
m<LON is 23 degrees
m<OM = 113 degrees
m<KNL = 23 degrees
m<NL = 157 degrees
How to determine the measures of the arcTo determine the measures of the arc, we need to note the following;
Angles on a straight line is equal to 180 degreesAngle at right angle is equal to 90 degreesFrom the information shown in the diagram, we have;
<KL +<KM = 90 degrees
Now, substitute the values
<KL + 67 = 90
collect like terms
<KL = 23 degrees
m<LON and <KL are corresponding angles
Then, m<LON is 23 degrees
m<OM = m<LON + 90 degrees
Substitute the values
m<OM = 113 degrees
m<KNL = 23 degrees
m<NL = 90 + <LM
Substitute the values
m<NL = 157 degrees
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Simplify. (5 x sqrt 2 - 1)^2
Answers
An article is sold for Rs.150 at a gain. Had it been sold for Rs.135 there would have been a loss equal to 50% of the original gain. Find the cost price of the article.
Answers
The cost price of the article, which is sold for Rs. 150 at a gain but if sold for Rs. 135 would have resulted in a loss equal to 50% of the original gain, is Rs. 127.50.
How the cost of the article is determined:The cost price is the difference between the selling price and the profit or gain.
The difference is determined by subtraction.
Selling price of the article = Rs. 150
Loss if sold at Rs. 135 = 50% of the original gain
Original gain = Rs. 15 (Rs. 150 - Rs. 135)
50% of the original gain = Rs. 7.50 (Rs. 15 x 50%)
Cost price of the article = Rs. 127.50 (Rs. 135 - Rs. 7.50)
Thus, the cost price is Rs. 127.50.
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Ferrese
2. (errencer feld acceed
rest
As and ove rect
The x-coordinate of 4s recex is 45
The x-ceerdinate of is rectex is
The coordinate os recex 45
he rease othe reser at
Answers
The true statements are
Its x-intercepts are (0,0) and (11,0)The x-coordinate of its vertex is 5.5How to find the true statementsTo find the true statements about the graph that represents y = -2x(x - 11), we need to analyze the equation and its properties.
x-intercepts by setting y = 0 and solving for x:
form the equation we have y = -2x(x - 11)
0 = -2x(x - 11)
0 = x(x - 11)
x = 0
x = 11
The x-intercepts are at (0,0) and (11,0).
Now let's find the vertex of the parabola. The vertex is located at the x-coordinate x = -b / 2a,
y = -2x^2 + 22x
given that
a = -2,
b = 22
x coordinate of the vertex is found by
= -22 / (2 * -2)
= 22 / 4
= 5.5
so we can say that the true statement is: The x-coordinate of its vertex is 5.5
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A virus takes 18 days to grow from 160 to 240. How many days will it take to
grow from 160 to 600? Round to the nearest whole number.
Answers
The virus will thus increase from 160 to 600 in around 10 days.
What is virus ?
A virus is a submicroscopic infectious agent that only reproduces inside of an organism's live cells.
We can resolve this issue using a proportion. Let x be the period of time needed for the virus to multiply from 160 to 600. Then: (240 - 160) / 18 = (600 - 160) / x
This equation may be written as
80/18 = 440/x.
Cross-multiplying:
80x = 18 * 440
80 divided by both sides yields x = 9.9
We obtain x = 10 by rounding to the next full value.
Therefore, The virus will thus increase from 160 to 600 in around 10 days.
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|x| = 9 Solve the equation. Check your solutions. Graph the solution(s) on a piece of paper.
Answers
The equation |x| = 9 has two solutions: x = 9 and x = -9. The shaded region includes all points to the left of -9 and all points to the right of 9.
The equation is given as follows:
|x| = 9
The equation |x| = 9 has two solutions: x = 9 and x = -9.
To check these solutions, we can substitute them back into the original equation and see if they satisfy it:
|x| = 9
|9| = 9 --> True
|-9| = 9 --> True
Therefore, the solutions x = 9 and x = -9 are both valid.
To graph the solution(s), we can draw a number line and mark the points x = 9 and x = -9 with closed circles (since the absolute value of x is equal to 9 at those points).
We can then shade the parts of the number line where the absolute value of x is greater than or equal to 9.
This includes all points to the right of 9 and all points to the left of -9.
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Answer
[tex]\large\textrm{There are two solutions: 9 and -9.}[/tex]
Further explanation
If we have the absolute value of x, that means x could be positive or negative.
This means that, in |x| = 9, x could be 9 or -9.
Checking
Plug the answers into the original equation.
You should get a true statement.
[tex]\rm{\mid 9\mid=9}[/tex]because the absolute value of 9 is 9 so that's a solution
[tex]\rm{\mid-9\mid=9}[/tex]the absolute value of -9 is also 9 so that's also a solution
therefore, the solutions are 9 and -9.
Graph the relationship with the greater rate of change on the coordinate grid.
• It takes Jason 2 hours to travel 180 miles to reach his destination.
.
Isaiah travels from Nashville to Atlanta. The equation below shows y as the number of miles traveled and x as the number of
hours he traveled.
y = 80x
SOMONE please tel me where to put the slope !!!‼️‼️
Answers
To graph the relationship between the two scenarios, we can plot the points on a coordinate grid. Jason's journey can be represented by the point (2, 180) and Isaiah's journey can be represented by the line y = 80x.
Since Isaiah's rate of change is greater than Jason's, we can see that the line y = 80x has a steeper slope than the line representing Jason's journey. Therefore, the graph of the relationship with the greater rate of change is the line y = 80x.
PLEASE HELP ( WILL GIVE BRAINLIEST)
Answers
Answer: Option C.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Given that the diameter of the container is 24 ft, the radius (r) would be half of that, which is 12 ft.
The depth of the container (h) is given as 4 ft.
Plugging in these values into the formula, we get:
V = π(12^2)(4)
V = 3.14(144)(4)
V = 1808.6 cubic feet (rounded to the nearest tenth)
So, the storage container can hold approximately 1808.6 cubic feet of wood, rounded to the nearest tenth.
Step-by-step explanation: