[tex]\textit{arc's length}\\\\ s = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{7\pi }{3}\\ r=3 \end{cases}\implies s=(3)(\frac{7\pi }{3})\implies s=7\pi \implies s\approx 21.99~in[/tex]
22. Represent Real-World Problems The railroad
tracks meet the road as shown. The town will
allow a parking lot at angle Jif the measure of
angle Jis greater than 38° Can a parking lot be
built at angle J? Why or why not?
If the town will permit a parking lot at angle J if the measure of angle Ji is greater than 38°, then yes, a parking lot can be erected at angle K.
what is angle ?In Euclidean geometry, an angle is a shape that is made up of two rays, known as the hood's sides, that meeting at a middle point known as the wall's apex. Two rays may combine to form an angle in the planes where they are positioned. When two planes collide, an angle is also created. They are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two photons or lines that share a termination. The origin of the English term "angle" is the Latin word "angulus," which meaning "horn." The vertex is the point where the two rays, sometimes known as two sides of the angle, converge.
given
Find the measure of angle K
we know that
m <K = m < green ------> by vertical angles
so
-----> by complementary angles
solve for m<K
m<K > 38
therefore
If the town will permit a parking lot at angle J if the measure of angle Ji is greater than 38°, then yes, a parking lot can be erected at angle K.
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the sumof the first two term of a g.p is 28 but the sum of the third and fourth term 252.find the second term of the g.p if the seventh term is 5103
S_ = a/(1 - r), where a denotes the first term and r denotes the common ratio, is the formula for calculating the sum of an infinite geometric progression.
What is Geometric Progression?If a series of phrases is called a geometric progression if each next term is created by multiplying each previous term by a fixed amount. (GP), while the common ratio refers to the constant value. As an illustration, a GP with the common ratio of 2 is 2, 4, 8, 16, 32, 64,...4 / 2 = 8 / 4 = 16 / 8 = 32 / 16 = 2.
Similarly,
A series of 1 through 5 and 1 through 16 is an example.1/2 / 1 = 1/4 / 1/2 = 1/8 / 1/4 = 1/16 / 1/8 = 1/2
The ratio is constant in the provided examples. Geometric Progressions are the name for such a series. G.P. is how it is shortened.When none of the terms in the sequence are zero, the constant r, often known as the common ratio, is used.A Sequence a1,a2,a3, ......,an,......... is a G.P, then ak + 1 / ak = r [k >1]The next step is to understand how to add GP when it has n words.To Learn more About geometric progression Refer To:
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How many 5 card hands are possible with a 52-card deck?
How many 5-card hands are possible with a 52-card deck?
Answer:
Only 10, there will still be 2 cards left though.
Step-by-step explanation:
You're welcome.
Which of the following represents a tragedy of the commons?
Plastic trash in the neighborhood park
Two hospitals for the town's residents
Leaves piled in a person's backyard
Plenty of food at a local market
Two hospitals for the town's residents represents a tragedy of the commons. Hence, option B is correct.
What is tragedy of the commons?The phrase "tragedy of the commons" describes a situation in which people who have access to a shared resource, also known as a common, act selfishly and ultimately deplete the resource. British author William Forster Lloyd initially conceived of this economic theory in 1833.
The Tragedy of the Commons, first proposed in 1968 by American ecologist Garret Hardin, is a scenario in which common environmental resources are overused, abused, and eventually exhausted, bringing risks to all parties concerned.
Thus, option B is correct.
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Suppose that a is inversely proportional to b. Let a1,a2 be two nonzero values of a such that {a1}/{a2}={2}/{3}. Let the corresponding b values be b1,b2. If b1,b2 are nonzero, find the value of {b1}/{b2}
If b1,b2 are nonzero, the value of {b1}/{b2} will be 3/2.
If a is inversely proportional to b. Let a1,a2 be two nonzero values of a such that {a1}/{a2}={2}/{3}. Let the corresponding b values be b1,b2. If b1,b2 are nonzero
a = k *1/b
2/3 =k * 1/b1 /k * 1/b2 [k = constant cancels out]
2/3 =1/b1 * b2
2/3 = b2/b1
b1 =3 and
b2 =2. Therefore:
b1/b2 =3/2.
Another way of looking at it, is this:
When a1 =2, b1=1/2
When a2 =3, b2=1/3
So, when a1/a2 = 2/3, then:
b1/b2 =(1/2) / (1/3) =(1/2) x (3/1)
=3/2
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Kamila makes a dot plot showing the heights of some sunflowers. She describes her dot plot
as follows: "The distribution is skewed right. There is an outlier."
Which dot plot matches Kamila's description?
6
Sunflower Height (ft)
Sunflower Height (ft)
...
5
Sunflower Height (ft)
Sunflower Height (ft)
1
O
Answer:
See attached photo.
"Choice D" The dot plot with the outlier at 4 feet and data points condensed on the right from 5.5-7 feet is the correct dot plot.
Step-by-step explanation:
ExplanationA dot plot is a statistical chart consisting of data points plotted on a simple scale, typically using filled-in circles.
A skew represents the direction in which the data points follow.
A negative skew indicates that the majority of the data points fall on the left side of the scale. Ex: "The height of the sunflowers in feet decreases when less sunlight is given."A positive skew indicates that the majority of the data points fall on the right side of the scale. Ex: "The height of the sunflowers in feet increases when more sunlight is given."An outlier is a data point that "stands out" from other data points.
Answer BreakdownChoices A and B are skewed left because their data points lie on the left side of the number line. These data points display a decrease in the sunflowers' height. So they are automatically eliminated. Choice C is skewed right, however, it contains no outliers. All the data points are condensed evenly to one side. This answer is incorrect. Choice D is the correct answer. The data points lie on the right side of the scale. There is also one outlier present at 4 feet, separating it from the rest of the data points.Please let me know if this helped!!!
Stephan and John are reading the same book. Stephan reads 7 pages a day and is on page 22. John reads 9 pages a day and is on page 10. How many days until Stephan and John are on the same page? What page will they be on?
The number of days until Stephen and John are on the same page would be 6 days
The page they would be on would be 64 pages
How to find the number of days ?Assuming that the number of days can be denoted as x, the equation for the number of pages that Stephen has read in total is:
= 22 + 7 x
The number of pages that John has read in total is:
= 10 + 9 x
To find the number of pages, equate these:
22 + 7 x = 10 + 9x
22 - 10 = 9x - 7 x
12 = 2 x
x = 12 / 2
x = 6 days
The page they would be on is:
= 10 + 9 x
= 10 + 9 ( 6 )
= 64 pages
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The total energy, E, in joules of a metal cylinder with an angular velocity of w radians per second
and a height of h meters above the ground is given by the equation above. The height and
angular velocity are independent. Which of the following expressions is the energy due to the
angular velocity?
The energy due to the angular velocity is given by the expression: [tex]E = 1/2 * I * w^2[/tex], where I is the moment of inertia of the cylinder.
Inertia: What is it?Everyone uses inertia, although few people are familiar with it. Additionally, it touches on every thing or person at some time. It is also a state of repose or inaction.
Inertia at rest: Until and unless an external force greater than the inertial force is applied to the object, the inertia (opposing force) existent inside the item keeps the object at rest. A body in motion maintains its motion until and until an outside force (such brakes, friction, etc.) is applied to it.
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Suppose that this is not a complete graph of a particular function.instead,the function also has a local maximum at x=-4 what might be true about the function
The right answer is B, i.e., option c. It might be a polynomial of sixth degree with a negative leading coefficient.
what is function ?The study of mathematics covers numbers and associated variations, formulas and associated tissues, shapes with their locations, and locations where they might be found. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a "function." A function is a relationship between inputs and results where each input produces a single, unique result. Each function is assigned a domain and a codomain, or scope. Typically, the symbol f is used to represent functions (x). input consists of an x. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
The function's negative leading coefficient
sixth-degree polynomial are determined by the local maximum,
which is x = -4. (x)
The right answer is B, i.e., option c. It might be a polynomial of sixth degree with a negative leading coefficient.
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Is side lengths 4 8 9 obtuse right or acute
The side lengths given as 4 8 9 shows that it is an obtuse Triangle.
How to illustrate the triangle?It should be noted that to determine whether the triangle is acute, right, or obtuse, add the squares of the two smaller sides, and compare the sum to the square of the largest side. Since this sum is greater, the triangle is acute
In a situation if the sum of the squares of the two shorter sides of a triangle is smaller than the square of the longest side, the triangle is obtuse
This will be:
4² + 8² < 9²
16 + 64 < 81
80 < 81
It is obtuse.
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Question 9 of 10
What is the product of the following numbers? Use a scientific calculator to
find the answer.
5.56 x 104 x 2.43 x 106
A. 2.23 x 10-2
OB. 1.97 x 10²1
C. 1.35 × 1020
OD. 1.35 x 10¹1
Gwen buys 3 identical pairs of shoes at store A. She pays $110.25 after the discount. What is the regular price of each pair?
The regular price of each pair of shoe is 36.75 dollars.
How to find the regular price of the pairs?Gwen buys 3 identical pairs of shoes at store A. She pays $110.25 after the discount.
The regular price of the each pair of shoe can be calculated as follows:
Therefore,
3 pairs of shoe = 110.25 dollars
1 pair of shoe = ?
cross multiply
Therefore,
regular price of a pair of shoe = 110.25 / 3
regular price of a pair of shoe = 36.75
Therefore, the regular price is 36.75 dollars.
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The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 68%, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
The likelihood of randomly selecting a chocolate chip cookie from the batch would be likely. That is option A
What is probability?Probability is defined as the possibility of an outcome of an event which may likely or unlikely occur.
The batch contains the following content:
chocolate chip,(68%)oatmeal raisin, and sugar cookiesThe chocolate chip makes up 68% of the batch and this shows a higher quantity than other content. Therefore, likelihood of randomly selecting a chocolate chip cookie from the batch would be likely.
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Felipe uploaded a funny viedo of his dog. The relationship between the elapsed time in days, d , since the viedo was first uploaded and the total number of views, v , that the viedo received is modeled by v=4^1.25d . Find the number of days it took Felipe's viedo to get 1024 views.
The number of days took to get the video of Felipe 1024 views is 4.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
The relationship between the elapsed time in days, d, since the video was uploaded and the total number of views, v, that the video received is modeled by the equation,
v = 4^(1.25d)
We have to find d when v = 1024
1024 = 4^(1.25d)
We have the rule for exponents aᵇⁿ = (aᵇ)ⁿ
1024 = [tex](4^{1.25} )^d[/tex]
1024 = (5.6569)^d
Taking logarithms on both sides,
㏒ (1024) = ㏒ [(5.6569)^d]
We have the exponent rule for logarithm, ㏒ (aᵇ) = b ㏒ (a)
㏒ (1024) = d ㏒ (5.6569)
d = ㏒ (1024) / ㏒ (5.6569)
d = 4
Hence it took 4 days to for Felipe's video to get 1024 views.
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The equation, A = 5,000(1 + 0.025t) represents the amount of money earned on a savings account with 2.5% annual simple interest. At the end of the investment period, the account balance is $5,875. How many years is the investment period? 1 year 4 years 7 years 9 years
The number of years in the investment period, given the account balance and the simple interest, is C. 7 years.
How to find the investment period ?To find the investment period, you can use the equation given on the account balance after a number of years, with " t " representing that number of years. And with simple interest,
With the formula being A = 5,000 x ( 1 + 0.025 t ), the investment period would be :
5, 875 = 5,000 x ( 1 + 0.025 t )
5, 875 = 5, 000 + 125 t
125 t = 5, 875 - 5, 000
125 t = 875
t = 875 / 125
t = 7 years
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Jason is married and has one child. He also takes care of his dad. What
is the highest number of allowances can he claim?
Jason can claim a total of 3 allowances.
Number of allowances to be claimed
The number of allowances that Jason can claim on his taxes depends on the number of dependents that he has and the deductions that he is eligible for.
As a married person with one child and taking care of his dad, Jason can claim the highest number of allowances which is three. He can claim one allowance for himself, one for his child and one for his dad. Therefore, Jason can claim a total of 3 allowances.
It's important to note that the number of allowances is based on personal financial situation and this should be confirmed through IRS guidelines or tax professional.
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A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory
Sunglacces Inventory
Number of Days Total Amount of Bungleccec
58
2
5
7
10
52
48
42
Which of the following graphs shows the relationship given in the table?
A graph which shows relationship between the number of days and total amount of sunglasses is shown in the image attached below.
How to construct and plot the data on a graph?In this scenario, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot while the total amount of sunglasses would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
here, we have,
From the scatter plot (see attachment) which models the relationship between the number of days and total amount of sunglasses, a linear equation for the line of best fit is given by:
y = -2x + 62
In conclusion, we can reasonably infer and logically deduce that the scatter plot indicates an inverse relationship between the number of days and total amount of sunglasses.
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After a 5% tax,a DVD costs $21.How much did it cost before the 5% tax was added?
Answer:
$20
Step-by-step explanation:
You want to know the pre-tax price if the price with 5% tax added is $21.
TaxThe added tax is 5% of the original amount (x), so the amount with tax added is ...
$21 = x + 0.05x = 1.05x
$21/1.05 = x = $20 . . . . . divide by the coefficient of x
The cost before tax was added was $20.
Step-by-step explanation:
Percentage left after the tax percentage is
100%-5%=95%
95% is equal to 95/100 = 0.95
therefore, the cost after tax divided by the percentage that is left after the tax percentage
costs after tax is 21 dollars which is
21/0.95 = 22.1dollars
Jennifer has 256 beads stella has 3 times more beads tiah had104
beads
The total number of beads will be 1128 beads.
How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.
In this case, Jennifer has 256 beads stella has 3 times more beads tiah had 104 beads.
The total number of beads will be:
= 256 + (256 × 3) + 104
= 256 + 768 + 104
= 1128
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Complete question
Jennifer has 256 beads stella has 3 times more beads tiah had 104 beads. What is the total number of beads?
Elena wants to make. scole drawing of her bedroom. Her
bedroom is a rectangle with length
decides on a scale of 1 to 50.
m and width 3 m. She
3.
Draw and label the dimensions of a scale drawing of Elena's
bedroom, using a scale of 1 to 50,
b. Elena's bedroom m door is 0.8 m wide. How wide should the
door be on the scale drawing? Explain how you know.
Elena's bed measures 4 cm by 3 cm on the scale drawing.
What are the actual measurements of her bed?
The scale drawing is thus 10 cm long and 6 cm wide, which corresponds to the actual dimensions of her bed.
what is rectangle ?A rectangle is a type of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral.4 sides, 4 corners, and 4 right angles make up the 2D shape of a rectangle. A rectangle's diagonal sides are equal in length, with one pair being longer than the other. A rectangle would be referred to as a square if all of its sides were the same size.
given
1 m equals 100 cm, to start.
Then
3 meters are equal to 300 centimeters, while 5 meters are equal to 500 centimeters.
If Elena wishes to sketch out her bedroom in scale (1 to 50), then
The scale drawing is thus 10 cm long and 6 cm wide.
The actual measurements of her bed are the scale drawing is thus 10 cm long and 6 cm wide.
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The number of CD's sold since April 8 at a music store can be
modeled by the function N(d) = 12d +35 and the price per
CD can be modeled by P(d) = 0.3d2 - d+5, where d is
the number of days since April 8.
of revenue
According to this model, what is the total amount of rev
generated by the store's CD sales on April 18?
The markup, expressed as a percentage of the cost, is the difference between the selling price and the product's cost.Markup on selling price is 27 %.
How do you calculate markup on selling price?The markup, expressed as a percentage of the cost, is the difference between the selling price and the product's cost.The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage.
Below, you'll find various possible formats for the markup formula or equation.
The selling price given as = $ 15
The cost per CD is = $ 11
The total profit = Selling price - Cost
Total profit per CD = $ 15 - $ 11
Total profit per CD = $ 4
The markup on selling price is calculated as - Total profit ÷ Selling price × 100
Markup on selling price = $ 4 ÷ $ 15 × 100 =26.6666 % or 27 %.
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-5v + 6 = 26 solve for v
Answer:v=-4
Step-by-step explanation:We move all terms to the left:
-5v+6-(26)=0
We add all the numbers together, and all the variables
-5v-20=0
We move all terms containing v to the left, all other terms to the right
-5v=20
v=20/-5
Find the number of six-digit numbers, where the sum of the digits is divisible by 8.
Answer:
12345
Step-by-step explanation:
j
Answer:
112500
Step-by-step explanation:
The price of a technology stock has risen to $9.62 today. Yesterday's price was $9.55. Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
0.73%
Step-by-step explanation:
First of all subtract the 2 values
9.62 − 9.55 = 0.07
then use this value and find the percentage from the original price which was 9.71 so 0.07/9.55 x 100
percentage increase is
0.73%
Drag figures and equations to the table to show the net and surface area.
The surface area of the figure is found by multiplying the area of each face together.
Drag figures and equationsThe table below shows the net and surface area of a three-dimensional figure:Net Area Surface Area
24 cm² 22 cm³
The net area of the figure is found by adding together the areas of each of the faces. In this case, there are two squares (2 cm x 3 cm) and one rectangle (3 cm x 1 cm).This gives us the equation 2(2 cm) (3 cm) +2(3 cm) (1 cm) + 2(2 cm) (1 cm), which works out to 24 cm².The surface area of the figure is found by multiplying the area of each face together. In this case, there are two squares (2 cm x 3 cm), one rectangle (3 cm x 1 cm), and one cube (3 cm x 1 cm).This gives us the equation 11 cm (2 cm) (3 cm) (3 cm) (1 cm) + (2 cm) (1 cm), which works out to 22 cm³.Net Area: 24 cm²
Surface Area: 22 cm³ + 11 cm = 33 cm³.
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Lily received 50 postcards. 16% of them were from Thailand. After he received ostcards from Thailand, the percentage of Thailand postcard increased to 30%. How many Thailand postcards did he receive?
Answer:
Step-by-step explanation:
Final answer: Lily received 10 postcards from Thailand.
Explanation: Number of postcards=50
Percentage of postcards from thailand= 16
Number of postcards from Thailand= 16/100*50= 8
Now, he received some postcards from Thailand. Let the number of postcards received from Thailand be x. Therefore,
Number of postcards=50+x
Number of postcards from Thailand= 8+x
We know that the percentage of postcards from Thailand now is 30.
Therefore,
30=(8+x/50+x)*100
0.3(50+x)=8+x
15+0.3x=8+x
0.7x=7
x=10
Therefore, he received 10 postcards from Thailand.
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Determine the domain and range of the function:
The domain of the function is x ∈ [ -3, -∞) and range is {-3, -2, 1}.
What is domain and range?The set of allowable inputs, or all the x-values in the (x, y) points decided by the relation, is known as the domain of a relation (and, by extension, a function). All the y-values in the (x, y) points determined by the relation make up the range of a relation (and, by extension, a function).
Graphs can be used as a second method to define the domain and range of functions. A graph's domain is the entire set of input values represented on the x-axis because the term "domain" refers to the set of potential input values. The possible output values are displayed on the y-axis and make up the range.
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A line has a slope angle of 63.5° and passes through the point (2, 3). What is the..
a) approximate slope of the line
b) equation of the line
a) The approximate slope of the line is; 2
b) The equation of the line is; y = 2x - 1
What is the equation of the line?The tangent of the angle formed by a straight line will give us the slope of the line.
a) Now, we are told that the slope angle is 63.5°. Thus;
Slope of given line = tan 63.5°
Slope = 2
b) The formula for equation of a line in point slope form is;
y - y₁ = m(x - x₁)
where m is slope
The line passes through the point (2, 3). Thus;
Equation of line is;
y - 3 = 2(x - 2)
y - 3 = 2x - 4
y = 2x - 1
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what are the stpes to answer 9 - 3 7/8
The subtraction is equal to the mixed number below:
9 - (3 + 7/8) = 5 + 1/8
How to solve the subtraction?Here we want to solve the expression below:
9 - (3 + 7/8)
So we have a whole number and a mixed number.
First we can subtract the two whole numbers so we get:
9 - (3 + 7/8) = (9 - 3) - 7/8
= 6 - 7/8
Now, to have a mixed number the fraction needs to be positive, so we can write:
6 - 7/8 = 5 + 1 - 7/8
5 + 1 - 7/8 = 5 + 1/8
That is the answer.
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3. Find the volume of the child's toy shown below. Use 3.14 for π Round all answers to 1 decimal place.
Volume of the top solid: ________
Volume of the bottom solid: _________
Volume of the entire toy: _________
The total volume of the toy is 497.4192cm³ with 340.3392 cm³ being the volume of the top solid and 157.08 cm³ being the volume of the bottom solid.
What is volume?Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas.
While capacity can be measured in virtually any other unit, such as liters, gallons, pounds, etc., volume is measured in cubic units.
So, the volume of the cone:
V = πr²h/3
Now, invert values:
V = π5²*13/3
V = 340.3392 cm³
The similar, volume of a cylinder:
πr²h
Now, insert values as follows:
πr²h
π5²2
V = 157.08 cm³
Total volume: 340.3392 cm³+157.08 cm³ = 497.4192cm³
Therefore, the total volume of the toy is 497.4192cm³ with 340.3392 cm³ being the volume of the top solid and 157.08 cm³ being the volume of the bottom solid.
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