Answers
The volume of the solid is 2160ft^3
Define the volume of cuboid?Volume of Cuboid is the multiplication of length breath and height.
We know that, Volume of Cuboid = l×b×h
put the given values from figure,
= 12×10×15
=1800ft^3
Volume of top = Area of triangle × length
= 1/2 × 4× 12× 15
=360ft^3
Total volume= 1800 + 360
= 2160ft^3
Therefore, the volume of the solid is 2160ft^3
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Cuboid: According to the question the volume of the solid is \(2160ft^3\).
What is cuboid?A cuboid is a three-dimensional geometric shape which is composed of six rectangular faces. It has 12 edges and 8 vertices. It is also referred to as a rectangular prism. The three dimensions of a cuboid are its length, width, and height. The cuboid is a versatile shape that can be used in many different ways and can be seen in everyday objects such as boxes, desks, and bookshelves. It is also a common shape for mathematically-based problems such as calculating the volume of a cuboid.
We know that, Volume of Cuboid = l×b×h
put the given values from figure,
= 12×10×15
=\(1800ft^3\)
Volume of top = Area of triangle × length
= 1/2 × 4× 12× 15
=\(360ft^3\)
Total volume= 1800 + 360
= \(2160ft^3\)
Therefore, the volume of the solid is \(2160ft^3\)
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Related Questions
find the length of side x using the Law of Cosines.
Answers
Answer:
The length of side x is 22.91
Step-by-step explanation:
As per law of cosine
\(X = \sqrt{a^2 + b^2- 2*a*bcos\gamma}\)
Where
\(gamma = 56\) degrees
a = 20
b = 27
Substituting the given values in above equation, we get -
\(X = \sqrt{20^2 + 27^2 - 2*20*27*cos 56} \\X = 22.91\)
Hence, the length of side x is 22.91
2-simplifica
1)x²-5x-16
x+2=
2)6an²-3b²n²
b4-4ab²+4a²=
3)4x²-4xy+y²
5y-10x
4)n+1-n³-n²
n³-n-2n²+2=
5)17x³y4z6
34x7y8z10=
6)12a²b³
60a³b5x6=
Answers
1. x² - 5x - 16 can be written as (x - 8)(x + 2).
2. 6an² - 3b²n² = n²(6a - 3b²).
3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².
4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).
5. 17x³y⁴z⁶ = (x²y²z³)².
6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.
Let's simplify the given expressions:
Simplifying x² - 5x - 16:
To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.
Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).
Simplifying 6an² - 3b²n²:
To simplify this expression, we can factor out the common term n² from both terms:
6an² - 3b²n² = n²(6a - 3b²).
Simplifying 4x² - 4xy + y²:
This expression represents a perfect square trinomial, which can be factored as (2x - y)².
Simplifying n + 1 - n³ - n²:
Rearranging the terms, we have -n³ - n² + n + 1.
Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).
Simplifying 17x³y⁴z⁶:
To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:
17x³y⁴z⁶ = (x²y²z³)².
Simplifying 12a²b³:
To simplify this expression, we can multiply the exponents of a and b with the given expression:
12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.
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write the expanded form of the expression
4(3x-5)
4 (3x-5)=
Answers
One technique to write numbers such that you can see the mathematical significance of each individual digit is in expanded form or expanded notation. So the expanded form of (3x-5)³ is 27x³-135x²+225x-125.
How do you write in a more detailed format?One technique to write numbers such that you can see the mathematical significance of each individual digit is in expanded form or expanded notation.
It is also possible to create a mathematical expression using integers that have been divided into distinct place values and decimal places.
5,000 + 300 + 20 + 5 = 5,325 is the expanded notation for the number.
Expanded form of the given expression.
1) We can expand the given term by the direct formula of the algebra
(A-B)³ = A³-B³-3AB(A-B)2)
We have (3x-5)³on comparing with the formula:
A = 3x
B = 5
(3x-5)³
(3x)³-5³-3×3x×5(3x-5)
27x³-125-45x(3x-5) 27x³-125-135x²+225x
So the expanded form of (3x-5)³ is 27x³-135x²+225x-125.
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Can someone pls help me with these!!!!
Answers
Answer:
I hope this helps, sorry for my hand writing
Plz help me! 25 POINTS!
Answers
Answer:
g(x) = 24(2^(x-1)) +16
Step-by-step explanation:
A function is stretched vertically by a factor of 'a' by multiplying by 'a'.
g(x) = 4·f(x) = 4(6(2^(x-1) +4)
g(x) = 24(2^(x-1)) +16
Find the missing angle.
86°
84•
?
36
Answers
Answer:
? = 64°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
The third angle in the triangle on the right is
third = 180° - (84 + 36)° = 180° - 120° = 60°
Thus the third angle in the triangle on the left is
third = 90° - 60° = 30° , then
? = 180° - (86 + 30)° = 180° - 116° = 64°
12²+ 9 - 4
a) 119
b)147
c)137
d)221
Answers
Answer:
it will be 147
Step-by-step explanation:
12x12=144
Hi There!!
Well, Some sort your answer suppose to be 149.
Because, \(12\) \(x\) \(12\) ≈ 144 ⁺ 9 ≈ 153 - 4 ≈ 149
But, I guess your answer is B). 137.....
Hope This Helps!!~
\(Itsbrazts\)
What numbers are 1.4 units from −3.2 on a number line? A number line ranging from negative four point eight to negative one point four, with intervals of point one. Select from the drop-down menus to correctly complete the statements. Choose... is 1.4 units from −3.2 on a number line. Choose... is 1.4 units from −3.2 on a number line.
Answers
Answer:
-4.6 is 1.4 units from −3.2 on a number line.
-1.8 is 1.4 units from −3.2 on a number line.
Step-by-step explanation:
Hope this helped! :D
The correct option is D which is -4.6 will be 1.4 units from −3.2 on a number line.
What is a number line?A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
Given that there are two numbers -3.2 and -4.6 on the line. The distance between the numbers will be calculated as below:-
-4.6 is 1.4 units from −3.2 on a number line. -1.8 is 1.4 units from −3.2 on a number line. The image of the number line is attached with the answer below.
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Including a 5% sales tax, Ms. LeBoeuf spent $18.90 on
school supplies. How much did the supplies cost before
the tax?
Answers
Answer:
$18
Step-by-step explanation:
Find the cost before tax by dividing the cost by 1.05
18.9/1.05
= 18
So, the cost of the supplies before tax was $18
63) Julia has 1/3 many stamps as Robert and also 2/3
as many stamps as
Erin. If Erin has 36 stamps, what is the total number of stamps that
the 3 children have?
Answers
Answer: The total number of stamps is 132.
Step-by-step explanation:
We know that Erin has 36 stamps.
Given that information, we can calculate how many stamps Julia has which is 2/3 as many stamps as Erin.
2/3 * 36 = 24
Julia has 24 stamps.
Julia also has 1/3 as many stamps as Robert.
24 = 1/3 * Robert
Robert = 72 stamps
Add the three numbers together to get your final answer
24 + 72 + 36 = 132
Two more than a certain membership is 15 less than twice the number
Answers
2+15=2x - x
17 = x
Dashboard
< Exit
Topics 1-8 Cumulative/Benchmark Assessment
00:00
Simplify the expression below:
3(7x) – 2(4 - x)
Answers
Answer:
23x - 8
Step-by-step explanation:
The simplified form of the expression 3(7x) – 2(4 - x) is: 23x-8.
Here, we have,
given that,
the expression is:
3(7x) – 2(4 - x)
now we have to simplify this expression.
so, we have,
3(7x) – 2(4 - x)
= 21x - 8 + 2x
adding the like terms we get,
=> 23x - 8
Hence, The simplified form of the expression 3(7x) – 2(4 - x) is: 23x-8.
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the bed of a dump truck has dimensions shown below.
Answers
Answer: 102,047
its wu 3993 and 3000
Step-by-step explanation: while 39,000
Please help me I will give brainly if correct
Answers
Answer:
D
Step-by-step explanation:
-3 * 2/5 = - 1/2
Also an odd # of negative signs means the answer is going to be negative. (Just a little hint) Hope this helps!! :)
point a is located at (-7, 1). the midpoint of the line segment ab is point (-3, 2). what are the coordinates of point b? question 3 options: (3, 1) (1, 3) (5, 11) (0, 4)
Answers
The coordinates of point b are (1,3)
What are coordinates?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).
(x1,y1) = (-7, 1)
Let point b has coordinates (x2,y2)
M (-3, 2)
mid point formula:
M= [ (x1+x2)/2, (y1+y2)/2 ]
(-3, 2) = [ (-7+x2)/2, (1+y2)/2 ]
=> -3= (-7+x2)/2 , 2 = (1+y2)/2
=> -6 = -7+x2 => 1+y2 = 4
=> x2= -6+7 = 1 => y2=4-1 =3
(x2,y2) = (1,3)
The coordinates of point b are (1,3)
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1. A hotdog manufacturer made 400 hotdogs between 9am and 11 am this morning. The machine that makes the
hotdogs is supposed to produce hotdogs so that their weight is approximately normally distributed with a
mean of 8 ounces and a standard deviation of 0.44 ounces. An employee randomly selects 6 of the hotdogs
and finds that the mean weight of the hotdogs is 7.7 ounces.
Identify the population, the parameter, the sample, and the statistic in this context.
(Show work if possible)
Population:
Parameter:
Sample:
Statistic:
Answers
Parameter: The mean weight of hotdogs produced by the machine, which is approximately normally distributed with a mean of 8 ounces and a standard deviation of 0.44 ounces.
Sample: The 6 hotdogs that were randomly selected by the employee.
Statistic: The sample mean weight of the 6 hotdogs, which is 7.7 ounces.
Lena must choose a number between 67 and 113 that is a multiple of 2,8 and 16 . Write all the numbers that she could choose.
Answers
All of these numbers are Multiples of 2, 8, and 16, and they are between 67 and 113.
A number between 67 and 113 that is a multiple of 2, 8, and 16, we need to find the least common multiple (LCM) of these three numbers.
The prime factorization of each number is:
2 = 2
8 = 2 × 2 × 2
16 = 2 × 2 × 2 × 2
The LCM is the product of the highest power of each prime factor that appears in any of the three numbers. In this case, the LCM is:
LCM(2, 8, 16) = 2 × 2 × 2 × 2 = 16
Therefore, Lena must choose a number that is a multiple of 16 between 67 and 113. To find all the numbers that she could choose, we need to list all the multiples of 16 between 67 and 113.
The smallest multiple of 16 that is greater than or equal to 67 is:
4 × 16 = 64
The largest multiple of 16 that is less than or equal to 113 is:
7 × 16 = 112
Therefore, Lena could choose any of the following numbers:
64, 80, 96, 112
All of these numbers are multiples of 2, 8, and 16, and they are between 67 and 113.
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Suppose that 23 inches of wire costs 92 cents. At the same rate, how much (in cents) will 19 inches of wire cost?
Answers
Answer:
76 cents
Step-by-step explanation:
23 inches = 92 cents
1 inches = 92 ÷ 23
= 4 cents
19 inches = 19 × 4
= 76
The quastion is on graph theory, matching.
Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B.
Consider taking |E| =aN, i.e., the total number of edges is proportional to the number of vertices. This is a relatively sparse number of edges, given the total number of edges that can exist between A and B.
6) Show that taking |E| = 3/N, the expected number of matchings goes to 0 as N › [infinity]. (5 points)
7) Show that taking |E| = 4.V, the expected number of matchings goes to infinity as N › [infinity]. (5 points)
Answers
The expected number of matchings goes to infinity as N › [infinity].
Matching in Graph Theory:A matching in Graph Theory is a set of edges of a graph where no two edges share a common vertex. In other words, a matching is a set of independent edges of a graph. A perfect matching in a Graph Theory is a matching of size equal to half the number of vertices in a graph.The expected number of matchings goes to 0 as N › [infinity]:The expected number of matchings goes to zero as N › [infinity] when |E| = 3/N. It is because 3/N is a relatively dense number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very small in comparison to the total number of matchings possible as N › [infinity].The expected number of matchings goes to infinity as N › [infinity]:The expected number of matchings goes to infinity as N › [infinity] when |E| = 4.V. It is because 4.V is a relatively large number of edges that are independent of the number of vertices that can exist between A and B. The expected number of matchings is thus very large in comparison to the total number of matchings possible as N › [infinity]. Hence the expected number of matchings goes to infinity as N › [infinity].
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Let the long-run profit function for a representative firm is given by π i
=p 2
−2p−399, where p is the price of computer. The inverse market demand for computer is given by p=39−0.009q, where q is unit of computers. Suppose technology for producing computers is identical for all firms and all firms face identical input prices. (a) Find the firm's output supply function. (b) Find the market-equilibrium price and the equilibrium number of firms. (c) Find the number of computers sold by each firm in the long run.
Answers
(a) The firm's output supply function is given by q = (p + 199) / 2.
(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.
(c) Each firm sells 70 computers in the long run.
To find the firm's output supply function, we need to maximize the firm's profit function, which is given by π = p^2 - 2p - 399. In the long run, firms will produce where marginal cost equals marginal revenue. Marginal revenue can be obtained by differentiating the inverse market demand function with respect to q, and marginal cost is equal to the derivative of the profit function with respect to q. Equating the two, we get:(39 - 0.009q) = (2q - 2) / q
Simplifying the equation, we find:
q = (p + 199) / 2
This represents the firm's output supply function.
To find the market-equilibrium price and the equilibrium number of firms, we need to find the intersection point of the market demand and supply. Substituting the output supply function into the inverse market demand function, we have:p = 39 - 0.009((p + 199) / 2)
Simplifying and solving for p, we get:
p ≈ $32.56
Substituting this price back into the output supply function, we find:
q = (32.56 + 199) / 2 ≈ 115.78
Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:
Number of firms = q / 70 ≈ 10
Since each firm sells 70 computers in the long run, and there are 10 firms, the total number of computers sold by each firm is:70 * 10 = 700
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How did you get -16 from -9-5-20?
Answers
Answer:
it would be -34
Step-by-step explanation:
Lane bought 12 pencils for
$0.39 each. What was the total cost of the
pencils before sales tax was added?
Answers
Answer:
$4.68
Step-by-step explanation:
if you do 0.39 x 12 you get 4.68
Answer:
$4.68
Step-by-step explanation:
12x0.39=$4.68
PLEASE HELP ME!!!!!!!!!!
Answers
Answer:
A.)
Step-by-step explanation:
Laura Bernett is 5 ft-4 inches tall: She stands 9 feet from streetlight and casts a 7-foot-long shadow How tall is the streetlight? Give your answer to the nearest hundredth. h feet
Answers
Let x be the enrollment of the school before the $10\%$ increase. We can represent the increase by multiplying $x$ by $1+10\% = 1+0.1 = 1.1$.
According to the problem statement, the new enrollment of the school is $506$, hence:$$1.1x = 506$$Solving for $x$:$$x = \frac{506}{1.1} \approx 460$$Therefore, the school's enrollment before the increase was approximately $460$.Given that Laura Bernett is 5 ft-4 inches tall. She stands 9 feet from the streetlight and casts a 7-foot-long shadow. To find how tall is the streetlight,
let us assume the height of the streetlight be h.Let the height of Laura Bernett be Lb = 5.33 ft (Converting 5 ft 4 inches to feet)From the similar triangles concept, the height of the streetlight can be found. We know that the length of the shadow, the distance from the person to the streetlight, and the height of the person are in proportion.h/Lb = (h + 7)/9Cross-multiplying the above equation, we get9h = 9Lb + 7hThus, we can obtain the value of h ash = 9Lb/2We know that the height of Laura Bernett is Lb = 5.33 ftTherefore, substituting this value in the above equation,h = 9 × 5.33/2= 24.0 feet (rounded off to the nearest hundredth)Therefore, the height of the streetlight is 24.0 feet.
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HELP ASAP
A picture is 7 inches wide and 9 inches long. A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long. What scale factor was used to enlarge the picture?
9/7
7/9
31.5/7
7/31.5
Answers
By simply taking the width after it was enlarged and dividing it by the width before it was enlarged we can find the scale factor that was used. In this case it would be 31.5 (width after)/ 7 (width before) which gives us a scale factor of 31.5/7. Simplifying would yield a scale factor of 4.5 times.
The Scale factor was used to enlarge the picture is 7/ 31.5.
What is Scale factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.
Given:
A picture is 7 inches wide and 9 inches long.
A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.
So, scale factor is
= Original dimension / Enlarged dimension
= 9/ 40.5
= 90/ 405
= 10/45
= 2/9
Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.
= 7/ 3.15
= 70/31.5
= 2/9
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Which of the following triangles have three sides of different lengths?
A. scalene triangle
B. acute triangle
C. right triangle
D. equilateral triangle
I will mark the brainiest if correct. Thank you.
Answers
Answer:
Sclaene triangle
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
The Lines are all different angles hence they are all different lengths
Can someone please help me with this problem?
Answers
Any help, I would highly appreciate it
Answers
Answer:
B
Step-by-step explanation:
We are given the equation:
\(\displaystyle x(b-c) = y+x\)
And that:
\(2b=3c=7\)
And we want to find the value of y / x.
To start, subtract x from both sides in the first equation:
\(x(b-c) -x = y\)
Divide both sides by x:
\(\displaystyle \frac{x(b-c)-x}{x}=\frac{y}{x}\)
Simplify:
\(\displaystyle (b-c)-1 = \frac{y}{x}\)
Next, in the second equation, divide everything by two:
\(\displaystyle b = \frac{3}{2} c = \frac{7}{2}\)
Substitute:
\(\displaystyle \left(\frac{3}{2} c - c \right) - 1= \frac{y}{x}\)
Simplify:
\(\displaystyle \frac{1}{2} c - 1 = \frac{y}{x}\)
From the modified second equation, we can multipy both sides by 1/3:
\(\displaystyle \frac{1}{2} c = \frac{7}{6}\)
Substitute:
\(\displaystyle \left(\frac{7}{6}\right) -1 = \frac{y}{x}\)
Subtract:
\(\displaystyle \frac{y}{x} = \frac{7}{6} - \frac{6}{6} = \frac{1}{6}\)
Therefore, our answer is B.
Pleaseeeeee help me with this!! And can you have answer in fraction form!?
Answers
Answer:
the answer is 24/5
.....
what involves asking questions and answering those questions using statistical and quantitative tools for explanatory and predictive analysis?
Answers
A process of analysing, purifying, manipulating, and modelling data in order to find relevant information, come to conclusions, and enhance decision-making is known as data analytics.
It entails posing queries and providing answers utilising quantitative and statistical methods for explanatory and prescriptive analysis. Descriptive, diagnostic, predictive, and prescriptive analytics are the four basic categories of data analysis.
Diagnostic analytics is used to determine the reason why something occurred, whereas descriptive analytics is used to report what has already occurred.
The use of predictive analytics, on the other hand, enables the prediction of likely future events. Last but not least, prescriptive analytics is employed to decide what steps should be taken in order to accomplish a particular result or goal in light of the knowledge gleaned from descriptive, diagnostic, and predictive analytics.
By using these different types of analytics, individuals will be able to gather and analyze data to better understand trends, identify problems, and make informed decisions.
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