1) Find the volume and surface area of the composite figure below 2) Find the surface area of the composite figure below
Answers
So the volume of the composite figure is 586.67 cubic units and the surface area is 552.8372 square units.
To find the volume and surface area of a composite figure, we need to break it down into simpler shapes and then add up their volumes and surface areas.
Let's take a look at the composite figure below:
This figure is made up of a rectangular prism and a pyramid. We can find the volume of the rectangular prism by multiplying its length, width, and height:
Volume of rectangular prism = length x width x height
Volume of rectangular prism = 10 x 8 x 6
Volume of rectangular prism = 480 cubic units
To find the volume of the pyramid, we need to first find its base area and height. The base of the pyramid is a rectangle with length 10 and width 8, so its base area is:
Base area of pyramid = length x width
Base area of pyramid = 10 x 8
Base area of pyramid = 80 square units
The height of the pyramid is 4, so we can now find its volume:
Volume of pyramid = (1/3) x base area x height
Volume of pyramid = (1/3) x 80 x 4
Volume of pyramid = 106.67 cubic units
Now we can add up the volumes of the rectangular prism and pyramid to get the total volume of the composite figure:
Total volume = volume of rectangular prism + volume of pyramid
Total volume = 480 + 106.67
Total volume = 586.67 cubic units
To find the surface area of the composite figure, we need to find the areas of each face and then add them up. The rectangular prism has six faces, each with an area of length x width:
Area of rectangular prism = 2lw + 2lh + 2wh
Area of rectangular prism = 2(10 x 8) + 2(10 x 6) + 2(8 x 6)
Area of rectangular prism = 396 square units
The pyramid has four faces: one rectangular base and three triangular faces. The area of the rectangular base is the same as the base area we found earlier:
Area of rectangular base = 80 square units
The area of each triangular face can be found using the formula (1/2)bh, where b is the base of the triangle and h is its height. The height of each triangular face is the slant height of the pyramid, which we can find using the Pythagorean theorem:
Slant height of pyramid = sqrt((4^2) + (5^2))
Slant height of pyramid = 6.4031 units
The base of each triangular face is a side of the rectangular base, which has length 8 and width 10. So we can find the area of each triangular face as:
Area of triangular face = (1/2)bh
Area of triangular face = (1/2)(8)(6.4031)
Area of triangular face = 25.6124 square units
Now we can add up the areas of all the faces to get the total surface area of the composite figure:
Total surface area = area of rectangular prism + area of pyramid
Total surface area = 396 + 80 + 3(25.6124)
Total surface area = 552.8372 square units
To know more about pyramid visit:-
https://brainly.com/question/17615619
#SPJ11
Related Questions
The formula to convert a temperature in degrees Fahrenheit (°F) to degrees Celsius (°C) is C = 5/9(F - 32). a. Solve the formula for F. Justify each step. b. Make a table that shows the conversion to Fahrenheit for each temperature: 0°C, 20°C, 32°C, and 41°C. c. Use your table to graph the temperature in degrees Fahrenheit as a function of the temperature in degrees Celsius. Is this a linear function?
Answers
a) F = (9/5)*C + 32
b)
0°C = 32°F 20°C = 68°F32°C = 89.6°F41°C = 105.8°Fc) The graph can be seen below, it is a linear function.
How to solve the formula for F?We have the formula:
C = (5/9)*(F - 32)
To solve it for F, we need to isolate the F in the formula:
F = (9/5)*C + 32
b) Now we want to convert some temperatures.
If C = 0° celcius, then:
F = (9/5)*0 + 32 = 32
This means that: 0°C = 32°F
if C = 20° Celcius, then:
F = (9/5)*20 + 32 = 68
then 20°C = 68°F
if C = 32°C then:
F = (9/5)*32 + 32 = 89.6°
So 32°C = 89.6°F
Finally, if C = 41°C then:
F = (9/5)*41 + 32 = 105.8
Then 41°C = 105.8°F
c) Here the function is:
F = (9/5)*C + 32
This clearly is a linear function, and the graph can be seen in the image below.
If you want to learn more about linear functions:
https://brainly.com/question/4025726
#SPJ1
in a normal distribution, what percent of test takers will score between two (2) and three (3) standard deviations below the mean?
Answers
In a normal distribution, approximately 2.28% of test takers will score between two (2) and three (3) standard deviations below the mean.
A normal distribution, also known as a Gaussian distribution or bell curve, is a probability distribution that describes how frequently different values occur in a dataset. The mean, or average, of the distribution is located at the center of the curve, and the standard deviation is a measure of how spread out the values are. In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations. Therefore, if a test taker scores between two and three standard deviations below the mean, they are in the tail end of the distribution and are in the bottom 2.28% of test takers.
Learn more about standard deviation here
https://brainly.com/question/13905583
#SPJ4
Difficult for me but should be easy for some big brain out there
Answers
Answer:
I would say the last one
Step-by-step explanation:
Answer:
42/45
Step-by-step explanation:
A 355ml can of juice is leaking at a rate of 5ml per hour.A 325 ml drink is leaking at a rate of 2ml per hour.how long will it take for both cans to have the same amount of liquid?
Answers
Answer:
I think its 355 - 5x = 5x => x = 35.5 minutes
Step-by-step explanation:
hope this helps
Determine if the sequence is arithmetic 28,26,24,22,...
Answers
Answer: yes it is
Step-by-step explanation:
Common difference -2
y=-x+9; (-9, ),(1, ),(5, )
Answers
Answer: (-9,18) , (1,8) and (5,4)
Step-by-step explanation:
If the x coordinate is -9 then plot it into the equation and solve for y.
y = -1(-9) + 0
y = 9 + 9
y = 18
Same for the second one plot in the value of x and solve for y
y= -1(1) + 9
y = -1 + 9
y = 8
Again same for the last one
y = -1(5) + 9
y = -5 + 9
y = 4
the volume of a cylinder is 980 pi cubic inches. the height of the cylinder is 20 inches. what is the radius of the cylinder?
Answers
The radius of the cylinder is 7 inches.
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
\(\[ V = \pi r^2 h \]\)
where V is the volume, r is the radius, and h is the height.
In this case, we are given that the volume of the cylinder is 980π cubic inches and the height is 20 inches. Plugging in these values into the formula, we get:
\(\[ 980\pi = \pi r^2 \cdot 20 \]\)
Simplifying the equation, we can divide both sides by π:
\(\[ 980 = 20r^2 \]\)
Dividing both sides by 20 gives us:
\(\[ 49 = r^2 \]\)
To solve for r, we take the square root of both sides:
\(\[ r = \sqrt{49} = 7 \]\)
Therefore, the radius of the cylinder is 7 inches.
To know more about radius refer here:
https://brainly.com/question/13449316
#SPJ11
Find the surface area of the figure
Answers
Answer:
36 in over 2
Step-by-step explanation:
Hello, i would love help since math is my worst subject ;
Answers
Answer:
4,5,6
Step-by-step explanation:
(x)+(x+1)+(x+2)= 15
3x + 3 = 15
3x = 12
x = 4
Answer:
Three consecutive numbers are: 4, 5, 6,
Step-by-step explanation:
Let three consecutive numbers be x , (x +1) , (x +2 )
x + x + 1 +x + 2 = 15
3x + 3 = 15
3x = 15 - 3
3x = 12
x = 12/3
x = 4
Three consecutive numbers are: 4, 5, 6,
Which expression is equivalent to (16 x Superscript 8 Baseline y Superscript negative 12 Baseline) Superscript one-half?.
Answers
To solve the problem we must know the Basic Rules of Exponentiation.
Basic Rules of Exponentiation\(x^ax^b = x^{(a+b)}\)\(\dfrac{x^a}{x^b} = x^{(a-b)}\)\((a^a)^b =x^{(a\times b)}\)\((xy)^a = x^ay^a\)\(x^{\frac{3}{4}} = \sqrt[4]{x^3}= (\sqrt[3]{x})^4\)The solution of the expression is \(\dfrac{4x^4}{y^6}\).
ExplanationGiven to us
\((16x^8y^{12})^{\frac{1}{2}}\)Solution
We know that 16 can be reduced to \(2^4\),
\(=(2^4x^8y^{12})^{\frac{1}{2}}\)
Using identity \((xy)^a = x^ay^a\),
\(=(2^4)^{\frac{1}{2}}(x^8)^{\frac{1}{2}}(y^{12})^{\frac{1}{2}}\)
Using identity \((a^a)^b =x^{(a\times b)}\),
\(=(2^{4\times \frac{1}{2}})\ (x^{8\times\frac{1}{2}})\ (y^{12\times{\frac{1}{2}}})\)
Solving further
\(=2^2x^4y^{-6}\)
Using identity \(\dfrac{x^a}{x^b} = x^{(a-b)}\),
\(=\dfrac{2^2x^4}{y^6}\)
\(=\dfrac{4x^4}{y^6}\)
Hence, the solution of the expression is \(\dfrac{4x^4}{y^6}\).
Learn more about Exponentiation:
https://brainly.com/question/2193820
Answer: C: 4x^4/y^6
Step-by-step explanation:
please help it is due by 11:59
Answers
Answer:
5
Step-by-step explanation:
30+20+50
50=50
The answer is 1) 5
Question Progress
2/4 Marks
Homework Progress
17/23 Marks
The diagram shows the position of a ship (S) and a marine base (B).
The scale of the diagram is 1 cm represents 10km.
a) Work out the real distance between
the ship and the base.
N
*B
b) Measure the bearing of B from S.
S*
A fishing boat F is 20 km from S on a bearing of 095°.
c) Mark the position of the fishing boat F with a cross (V).
Answers
Answer:
a) 35km
b) 070 degrees
Step-by-step explanation:
To get full marks look at what I did for question (c)
You have to use a protractor on letter s and make sure the 0 on the protractor is facing the letter (N). Now check where 90 degrees is and draw a line straight by using the ruler then use the compass as u can see in the photo, where (x) point is on the end of the compass is your answer {make sure the compass is 2cm which means its 20km. Also make sure to align the compass on the line you drawn}
Thank you
a characteristic, usually a numerical value, which describes a sample is called a _______. a. parameter b. statistic C. constant d. variable
Answers
Answer: B. statistic
Step-by-step explanation: A characteristic, usually a numerical value, which describes a sample, is called a statistic.
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?
Answers
Answer:
The answer is B
B) x>3
Who drove the fastest? Select the correct answer.
A Kevin drove 426 miles in 7 hours.
B Shanna drove 508 miles in 8 hours.
C Hector drove 220 miles in 5 hours.
D Harlan drove 363 miles in 6 hours.
Answers
Answer:
A
Step-by-step explanation:
:)
which graph represents a function
Answers
4. what is the slope in the regression equation, and how should this number be interpreted in the context of hurricane wind speed and central pressure?
Answers
The slope in the regression equation is the coefficient that represents the change in the response variable (in this case, hurricane wind speed) for every one-unit increase in the predictor variable (central pressure).
In the context of hurricane wind speed and central pressure, the slope represents the strength of the relationship between these two variables. A higher slope value indicates a stronger relationship between central pressure and wind speed, meaning that changes in central pressure have a larger impact on wind speed. Therefore, the slope is an important factor to consider when predicting or analyzing hurricane intensity.
In the context of hurricane wind speed and central pressure, the slope in the regression equation represents the relationship between the two variables. It shows how much the wind speed changes with respect to a change in central pressure.
To interpret the slope in this context, follow these steps:
1. Obtain the regression equation for the data on hurricane wind speed and central pressure. This equation will be in the form of y = mx + b, where y is the wind speed, x is the central pressure, m is the slope, and b is the y-intercept.
2. Identify the slope (m) in the equation. The slope represents the change in wind speed for every unit change in central pressure.
3. Interpret the slope value: If the slope is positive, it means that as central pressure increases, wind speed also increases. If the slope is negative, it indicates that as central pressure increases, wind speed decreases. The magnitude of the slope shows the strength of this relationship.
In conclusion, the slope in the regression equation between hurricane wind speed and central pressure helps us understand how the wind speed changes with respect to changes in central pressure, allowing for better prediction and analysis of hurricane behavior.
Learn more about Regression:
brainly.com/question/29753986
#SPJ11
The base is an equilateral triangle with an area of 6 square inches. the height of the pyramid is 15 inches. The height of the pyramid is 15 inches. what is the volume?
Answers
Answer:
V = 30 in³
Step-by-step explanation:
the volume (V) of a pyramid is calculated as
V = \(\frac{1}{3}\) × B × h ( B is the area of the base and h the height ) , then
V = \(\frac{1}{3}\) × 6 × 15 = 2 × 15 = 30 in³
Answer:
The volume of the pyramid is 30 inches cube.
How to find the volume of a pyramid?The base of the pyramid is an equilateral triangle with an area of 6 inches². The height of the pyramid is 15 inches.
Therefore, the volume of the pyramid can be calculated as follows:
volume of the pyramid = 1 / 3 BH
where
B = base area
H = height of the pyramid
Therefore,
B = 6 inches²
H = 15 inches
Hence,
volume of the pyramid = 1 / 3 × 6 × 15
volume of the pyramid = 1 / 3 × 90
Therefore,
volume of the pyramid = 30 inches³
learn more on volume here: brainly.com/question/19381679
#SPJ1
Step-by-step explanation:
write 2+3n=4n in a sentence for the equation
Answers
The given equation can be written in the form of the expression "The sum of two and three times a number is equal to four times the number".
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be broken into expressions and then can be written in form of phrases such as,
2 + 3n → Sum of two and three times a number4n → Four times the numberHence, The given equation can be written in the form of the expression "The sum of two and three times a number is equal to four times the number".
Learn more about Equation here:
https://brainly.com/question/14686792
#SPJ2
The side length of an equilateral triangle is 6x - 12. Write an expression for the perimeter of the triangle in simplest form.
Answers
Answer:
18x - 36
Step-by-step explanation:
In an equilateral triangle the 3 sides are congruent, then
perimeter = 6x - 12 + 6x - 12 + 6x - 12 ← collect like terms
= 18x - 36
The required expression would be 18x - 36 for the perimeter of the triangle in simplest form.
What is the perimeter of a triangle?The perimeter of a triangle is defined as the addition of the lengths of the triangle's three sides.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
As we know in an equilateral triangle the 3 sides are congruent.
The perimeter of the triangle = 6x - 12 + 6x - 12 + 6x - 12
Combine the likewise terms and we get
The perimeter of the triangle = 18x - 36
Therefore, the required expression would be 18x - 36 for the perimeter of the triangle in simplest form.
Learn more about the perimeter of a triangle here:
brainly.com/question/24388271
#SPJ6
there are six balls in a box if we select three balls what is the probability of having one white ball
Answers
The probability of having one white ball is 1/20 or approximately 0.05.
To find the probability of selecting one white ball out of three balls, you need to know the number of white balls in the box and the total number of balls in the box. You also need to know whether the balls are being selected randomly or not.
Assuming that there is only one white ball in the box and the rest are some other color, and that the balls are being selected randomly.
The probability of selecting one white ball out of three would be:
Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)
Since there is only one white ball, there is only one way to select one white ball out of three. The total number of ways to select three balls out of six is 6 choose 3, which is equal to 20.
Therefore, the probability of selecting one white ball out of three would be
Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)
Probability = 1/20
Probability = approximately 0.05.
Learn more about probability, here https://brainly.com/question/11234923
#SPJ4
Find the equation of the line through the points (-2, -8) and (3, 2). Enter your answer in slope-intercept form y = mx + b.
Answers
The equation of the line passing through the points (-2, -8) and (3, 2) is y = 2x - 4 in slope-intercept form.
To find the equation of the line passing through the points (-2, -8) and (3, 2), we can use the point-slope form of the equation, which is given by: y - y₁ = m(x - x₁). Where (x₁, y₁) are the coordinates of one of the points, and m is the slope of the line. First, let's calculate the slope (m) using the formula: m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) = (-2, -8) and (x₂, y₂) = (3, 2): m = (2 - (-8)) / (3 - (-2)) = 10 / 5 = 2.
Now that we have the slope, we can choose one of the points, let's use (-2, -8), and substitute the values into the point-slope form: y - (-8) = 2(x - (-2)), y + 8 = 2(x + 2), y + 8 = 2x + 4, y = 2x + 4 - 8, y = 2x - 4. Therefore, the equation of the line passing through the points (-2, -8) and (3, 2) is y = 2x - 4 in slope-intercept form.
To learn more about slope-intercept click here: brainly.com/question/30216543
#SPJ11
if a number is added to the numerator of (11)/(35) and twice the number is added to the denominator of (11)/(35), the resulting is equivalent to (1)/(3). find the number
Answers
For the statement to happen, the number should be 2.
An algebraic expression is is defined as the combination of numbers and variables in solving a particular mathematical question. Variable, usually letters, are used to denote the unknown quantity.
Let x = number
Based on the information given, add the number to the numerator of 11/35 and add twice the number to the denominator of 11/35, and the result should be equal to 1/3.
Hence, (11 + x) / (35 + 2x) = 1/3.
Simplify and solve for the value of x.
3(11 + x) = (35 + 2x)
33 + 3x = 35 + 2x
3x - 2x = 35 - 33
x = 2
number = 2
Learn more about algebraic expression here: https://brainly.com/question/3927786
#SPJ4
The monthly rent on a two bedroom apartment is $1,643. The monthly rent per square foot is $2.12. What is the total square footage of the apartment?
Answers
A two-bedroom apartment has a $1,643 rent each month and $2.12 is paid monthly in rent per square foot. The overall area of the apartment is 775 square footage.
Let's assume that the total square footage of the apartment be X
Given that:
The monthly rent of the apartment = $1,643
The monthly rent per square foot of the apartment = $2.12
Therefore, we can say that,
X = $1,643 / $2.12
Calculating the above equation, we get:
X = 775 square footage
Therefore, the apartment's total square footage is 775.
Read more related questions at
https://brainly.com/question/31345322
Melissa walks 3 miles to the house of a friend and returns home on a bike. She averages 4 miles per hour faster when cycling than when walking, and the total time for both trips is two hours. Find her walking speed (HINT: Write an expression that represents the time it takes for Melissa to walk to her friends house, and then write an expression for the time it takes to cycle back. The sum of these expressions is equal to the total time of the trip.)
Answers
Answer:
walking speed is 2 m/s
Step-by-step explanation:
given data
distance between Melissa and friend = 3 mile
total time of the trip = 2 hour
solution
we consider here
walking speed = s₁
bike speed = s₂
so s₂ = s₁ + 4 .................1
and
time is express as
time = distance ÷ speed .................2
so time for Melissa to friend reach = 3 ÷ s₁
and time for return from her friend = 3 ÷ s₂
so put this value in equation 2 we get
time = 3 ÷ s₁ + 3 ÷ s₂
2 = \(\frac{3}{s_1} + \frac{3}{s_1 + 4}\)
solve it and we will get
s₁² + s₁ - 6 = 0
s₁ = 2 m/s
so walking speed is 2 m/s
4 2/9 x 12 7/8 i need answer
Answers
54 13/36 hope this helps
Can you help me with this i will give you a branliest
Answers
A family bought a total of 16 adult and child tickets to a magic show. Adult tickets are $10.50 each andchild tickets are $7.50 each. The family paid a total of $141.How many of adult tickets, x, and child tickets, y, did they buy?(Only enter the numerical answer.)adult ticketschild tickets
Answers
number of adult ticket = x
number of child ticket = y
Total number of ticket = 16
\(undefined\)At a carnival it costs $34.92 for 12 tickets. Write an equation that can be used to express the relationship between the total cost (t) and the number of tickets(n) you buy.
Answers
The equation that can be used to express the relationship between total cost and tickets is t = $2.91n.
What is the total cost?The first step is to determine the cost of one ticket. The cost of one ticket can be determined by dividing the total cost of the ticket by the total number of tickets. Division is the operation that is used to determine the quotient of two or more numbers.
Cost of one ticket = $34.92 / 12 = $2.91
The equation that can be used to determine the total cost would have this form:
Total cost = cost per ticket x number of tickets
t = $2.91 x n
t = $2.91n
To learn more about total cost, please check: https://brainly.com/question/25717996
#SPJ1
for manual cutting operations, the travel angle should be a push angle of ____.
Answers
The ideal travel angle for manual cutting operations is a push angle of 30-45 degrees.
Explanation: When performing manual cutting operations, it is important to consider the travel angle, which refers to the direction in which the cutting tool moves in relation to the workpiece. The recommended travel angle for most cutting operations is a push angle of 30-45 degrees. This means that the cutting tool should be positioned at an angle, pushing forward against the workpiece as it cuts. This angle allows for optimal cutting efficiency and control.
A push angle within this range ensures that the cutting force is distributed evenly, minimizing the risk of tool slippage or workpiece damage. It also helps to maintain good visibility of the cutting path, reducing the chances of errors or accidents. Additionally, the push angle allows the operator to exert sufficient downward pressure on the cutting tool, aiding in effective material removal. Overall, a push angle of 30-45 degrees is considered the most effective for achieving accurate and efficient manual cutting operations.
To learn more about angle click here, brainly.com/question/30147425
#SPJ11