Answers
Answer:348
Step-by-step explanation:
For composite prisms, where the bases are a composite shape, the area of the bases is the sum of the areas of the parts it is made of. The volume of the composite prism is then given by multiplying the whole base area by the height of the prism.In math, volume is the amount of space in a certain 3D object. For instance, a fish tank has 3 feet in length, 1 foot in width and two feet in height. To find the volume, you multiply length times width times height, which is 3x1x2, which equals six. So the volume of the fish tank is 6 cubic feet.
Answer:
\( 1,205.8\: {ft}^{3} \)
Step-by-step explanation:
Given object is made up of cylindrical and conical parts.
Fir cylindrical part:
r = 16/2 = 8 ft
h = 4 ft
For conical part:
r = 16/2 = 8 ft
h = 6 ft
Volume of the object = Volume of cylinderical part + Volume of the conical part
\( = \pi {r}^{2} h + \frac{1}{3} \pi {r}^{2} h \\ \\ =\pi \times {8}^{2} \times 4 + \frac{1}{3} \times \pi \times {8}^{2} \times 6 \\ \\ = 64\pi \times 4 + \frac{1}{ \cancel3} \times 64\pi \times \cancel6 \\ \\ = 64\pi(4 + 2) \\ \\ = 64\pi \times 6 \\ \\ = 384\pi \\ \\ = 384 \times 3.14 \\ \\ = 1,205.8 \: {ft}^{3} \)
Related Questions
Your job is as an administrative assistant for factory operations for a company producing Whatchamacallits. Your boss hands you the information that the factory produces 4 Whatchas in the first hour, 8 total after hour 2, 12 total after 3 hours and 16 after 4 hours. You are tasked to produce an equation that models the number of Whatchas produced given the hours worked, and to find the predicted number of Whatchas produced if the factory can run for 50 hours uninterrupted.
Find an explicit formula for the nth term of the sequence 4,8,12,16... and use the equation to find the 50th term in the sequence. Show your reasoning for the equation.
Answers
Answer:
200
Step-by-step explanation:
\(a_n}\) = a + (n-1)d
\(a_{50}\) = 4 + (50 -1)4
\(a_{50}\) = 4 + 49(4)
\(a_{50}\) = 4 + 196
\(a_{50}\) = 200
a = the initial value.
n = the term
d = the common difference
Helping in the name of Jesus.
A rectangular prism is filled exactly with 605 cubes. Each cube has edge length 1/5 cm.
What is the volume of the rectangular prism?
Answers
The volume of the rectangular prism is 4.84 cm cube.
How to find the volume of the rectangular prism?A rectangular prism is filled exactly with 605 cubes. Each cube has edge
length 1 / 5 cm. Therefore, the volume of the rectangular prism can be
calculated as follows:
volume of each cube = l³
volume of each cube = (1 / 5)³
volume of each cube = 1 / 125 cm³
Therefore,
volume of the rectangular prism = 605 × 1 / 125
volume of the rectangular prism = 605 / 125
volume of the rectangular prism = 4.84 cm³
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The Pyramid of Khafre measured 143.5
meters high. The Pyramid of Menkaure
measured 65.5 meters high. Write and
solve an equation to find d, the difference
in the lengths of the two pyramids.
Answers
Answer:
143.5 - 65.5 = d
d = 143.5 - 65.5
0.5 - 0.5 = 0
143 - 65 = 72
Find the average of the list of numbers.
- 13, – 25, – 24, – 14
Answers
Answer:
-19
Step-by-step explanation:
-13-25-24-14
= -76/4
= -19
For the question of total area of the cuboid is 200cm^.
I understand where we divide 150 by 4.
But why do I need to multiply by 5, when there are 6 faces.
Answers
You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.
When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.
A cuboid has six faces, but each face has a pair that is identical in size and shape.
Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.
To find the surface area of a cuboid, you can add up the areas of all its faces.
However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:
(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.
By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.
Essentially, you are considering one face from each pair and then summing their areas.
Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.
When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.
Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.
Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.
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Choose the correct answer below.
A. The numerator of the expression simplifies to for all x, so the limits are equal.
B. The limits and equal the same number when evaluated using direct substitution.
C. Since whenever x, it follows that the two expressions evaluate to the same number as x approaches .
D. Since each limit approaches , it follows that the limits are equal.
Answers
Answer:
B. The limits Lim x-->7 (x²-9x+14)/x-7 and lim x--> 7 (x-2) equals the same number when evaluated using direct substitution. The limit of both functions is 5
Step-by-step explanation:
Find the complete question in the attachment.
Given the limit of the functions
Lim x-->7 (x²-9x+14)/x-7
To solve this, we will need to factorize the quadratic function at the numerator first.
x²-9x+14
= x²-2x-7x+14
= x(x-2)-7(x-2)
= (x-7)(x-2)
The expression therefore becomes:
= lim x-->7 (x-7)(x-2)/x-7
= lim x-->7 (x-2)
Now substitute the value of x into the simplified function
lim x-->7 (x-2) = 7-2
lim x-->7 (x-2) = 5
Hence Lim x-->7 (x²-9x+14)/x-7 = 5
From the calculation above, it can be seen that Lim x-->7 (x²-9x+14)/x-7 = lim x--> 7 (x-2) = 5
Hence the correct answer based on the explanation above is B.
The limits Lim x-->7 (x²-9x+14)/x-7 and lim x--> 7 (x-2) equals the same number when evaluated using direct substitution.
The mean of Fred’s grades on five tests was 75.2. The grades on the first 4 of these tests were 87, 84, 88, and 45. Find the grade on his fifth test.
Answers
304+x/5=75.2
Answer:
72
Step-by-step explanation:
mean x number of total test scores -> 75.2 x 5=376
sum of the four test scores given -> 304
difference of the two numbers -> 376- 304= 72
the missing test score, therefore the answer is 72.
A bucket contains 72 red, 48 blue, 48 green, and 48 yellow crayons. The art teacher also has 120 pieces of drawing paper. What is the largest number of identical kits the art teacher can make with all of the crayons and all of the paper?
Answers
The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.
To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.
The GCD represents the largest number that can divide all the quantities without leaving a remainder.
The GCD of the quantities of crayons can be found by considering the prime factorization:
72 = 2³ × 3²
48 = 2⁴ × 3
48 = 2⁴ × 3
48 = 2⁴ × 3
The GCD of the crayons is 2³ × 3 , which is 24.
Now, we need to find the GCD of the quantity of drawing paper:
120 = 2³ × 3 × 5
The GCD of the drawing paper is also 2³ × 3 , which is 24.
Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.
Each kit would contain an equal distribution of crayons and drawing paper.
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Brenda and her family ate dinner at Mi Hacienda. The cost for dinner was $25.50 and they had excellent service. They wanted to leave a 20% tip. How much money did they leave for a tip?
I need the percent and the whole please answer quickly first answer gets brainliest
Answers
Answer:
$5.1 tip
Step-by-step explanation:
2a^2 - 4b - 4a (b - a) = ?
a=4 b=7
Answers
trains on two different routes at the same train station. Train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes
Answers
When the train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes, the time when they will stop at same time is 18 minutes.
How to illustrate the information?From the information, the train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes.
Therefore, the time when will they stop at same time will be the lowest common multiple for 9 and 6. This is 18. Therefore, 18 minutes is the appropriate answer.
Therefore, the the time when they will stop at same time is 18 minutes.
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Trains on two different routes at the same train station. Train on one route stop there every 9 minutes and trains on the other route stop there every 6 minutes. When will they stop at same time?
algebra 1 slope intercept form: write an equation
Answers
Ok, so
A line passes through the points (20,-14) and (4,-14). We are asked to find the equation of this line.
First, we're going to find the slope of the line.
For this, remember that:
Given two points (x1,y1) and (x2,y2), the slope (m) between them can be found using the equation:
\(m=\frac{y_2-y_1}{x_2-x_1}_{}\)If we replace our values, we notice that:
\(\begin{gathered} x_1=20 \\ x_2=4 \\ y_1=-14 \\ y_2=-14 \end{gathered}\)And replacing in the equation:
\(m=\frac{-14-(-14)}{4-20}=\frac{0}{-16}=0\)The slope of our line is 0.
Now, given the slope "m" and one point (x1,y1), the equation in slope-intercept form can be found using the formula:
\(y=y_1+m(x-x_1)\)Replacing (x1,y1) as (4,-14) and m=0:
\(\begin{gathered} y=-14+0(x-4) \\ y=-14 \end{gathered}\)Therefore, the equation of the line is y=-14
A water company charges $20 for service and $2.75 for every thousand gallons of water used in month. Construct a linear model to represent the water bill; how much would you be charged if you used 14-thousand gallons of water this month?
Answers
Answer:
$58.50
Step-by-step explanation:
2.75 per 1000
2.75 x 14 = 38.5
$38.50 + $20 =$58.50
A phone receives signals from a transmitter that is 13km west and 21km south of it. what is the bearing from the phone to the transmitter? give your answer to the nearest degree
Answers
The bearing from the phone to the transmitter is approximately 31 degrees to the east of the north direction.
To determine the bearing from the phone to the transmitter, we can use trigonometry.
The bearing is typically measured clockwise from the north direction.
Given that the transmitter is 13 km west and 21 km south of the phone, we can form a right triangle with the phone as the vertex angle.
The side opposite to the vertex angle represents the north-south direction, and the side adjacent to the vertex angle represents the east-west direction.
Using the tangent function, we can calculate the angle:
tangent(angle) = (opposite side) / (adjacent side)
tangent(angle) = 21 km / 13 km
Taking the inverse tangent (arctan) of both sides, we find:
angle = arctan(21 km / 13 km)
Evaluating this using a calculator, we find the angle to be approximately 58.57 degrees.
However, since the bearing is measured clockwise from the north, we need to subtract this angle from 90 degrees (which represents the north direction) to obtain the bearing:
bearing = 90 degrees - 58.57 degrees
Calculating this, we find the bearing to be approximately 31.43 degrees.
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please help asap 50 points The sail of a boat is in the shape of a right triangle, as shown below:
The sail of a boat is a right triangle with an acute angle equal to 35 degrees and the side of the sail which is the hypotenuse
Which expression shows the height, in meters, of the sail? (6 points)
Select one:
a. 8 divided by cosec 35 degrees
b. 8 sin 35°
c. 8 sec 35°
d. 8 divided by sec 35 degrees
Answers
Answer:
d. 8 divided by sec 35 degrees
Step-by-step explanation:
Answer:
D is right
Step-by-step explanation:
A quiz consists of six multiple choice questions. Each question has four choices. A student who forgot to study guesses randomly on every question. What is the probability that the student answers at most four questions correctly?
Answers
Answer:
0.9945 = 99.45% probability that the student answers at most four questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student answers correctly, or he/she does not. The probability of the student answering a question correctly is independent of any other question. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
A quiz consists of six multiple choice questions.
This means that \(n = 6\)
Each question has four choices. Student guesses randomly.
This means that \(p = \frac{1}{4}\)
What is the probability that the student answers at most four questions correctly?
This is:
\(P(X \leq 4) = 1 - P(X > 4)\)
In which
\(P(X > 4) = P(X = 5) + P(X = 6)\). So
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 5) = C_{6,5}.(0.25)^{5}.(0.75)^{1} = 0.0053\)
\(P(X = 6) = C_{6,6}.(0.25)^{6}.(0.75)^{0} = 0.0002\)
\(P(X > 4) = P(X = 5) + P(X = 6) = 0.0053 + 0.0002 = 0.0055\)
\(P(X \leq 4) = 1 - P(X > 4) = 1 - 0.0055 = 0.9945\)
0.9945 = 99.45% probability that the student answers at most four questions correctly
[3x (4.6÷2)] +14.1 =
Answers
Answer:
21
Step-by-step explanation:
PEMDAS : Parenthesis, Exponent, Multiplication/Division, Addition/Subtraction.
First, we want to deal with the parenthesis within the parenthesis.
(4.6/2) = 2.3
Rewrite it into the equation.
[3 * 2.3] + 14.1 = ?
Now, do the work in the parenthesis again.
[6.9] + 14.1 = ?
There isn't anymore parenthesis, exponents, or multiplication/division, so we move onto addition now and add both terms.
6.9 + 14.1 = 21
? = 21
The answer is 21.
ONLY ANWSER IF YOU KNOW OR GET REPORT KID
Answers
Please help me i need help.
Answers
Answer:
5x+7 > 17 matches with 3.
1+3x > -5 matches with 2.
2x+1 < 3 matches with 1.
5-3x > 11 matches with 4.
Step-by-step explanation:
22.8 when rounded to the nearest tenth
Answers
Answer:
23
Step-by-step explanation:
The surface area of a sphere is 900pi cubic cm. What is the length of its diameter.
Answers
The length of the diameter of the sphere is 30 cm.
The surface area of a sphere is given by the formula:
\(A = 4\pi r^2\)
where A is the surface area and r is the radius of the sphere.
We are given that the surface area of the sphere is 900π cubic cm. Therefore:
\(A = 4\pi r^2 = 900\pi\)
Dividing both sides by 4π, we get:
\(r^2 = 225\)
Taking the square root of both sides, we get:
r = 15
The diameter of the sphere is twice the radius, so:
d = 2r = 30
Therefore, the length of the diameter of the sphere is 30 cm.
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help pleaseeeeeeeeeeeeeeeeee
Answers
20N pushing against another 20N pushing cancels each other out, subsequently balancing the forces.
need help with this ASAP
!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The fence in dead center is about 399 feet from the third base.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side, is equals to the sum of the squares of the lengths of the other two sides.
Hence the equation for the theorem is given as follows:
c² = a² + b².
In which:
c > a and c > b is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.For the triangle in this problem, we have that:
The sides are d ft and 90 ft.The hypotenuse is of 409 ft.Hence the distance is obtained as follows:
d² + 90² = 409²
\(d = \sqrt{409^2 - 90^2}\)
d = 399 ft.
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Bennett Griffin and Chula Garza organized Cole Valley Book Store as a corporation; each contributed $71,500 cash to start the business and received 5,600 shares of common stock. The store completed its first year of operations on December 31, current year. On that date, the following financial items for the year were determined: December 31, current year, cash on hand and in the bank, $69,250; December 31, current year, amounts due from customers from sales of books, $43,500; unused portion of store and office equipment, $72,500; December 31, current year, amounts owed to publishers for books purchased, $12,400; one-year note payable to a local bank for $3,200. No dividends were declared or paid to the stockholders during the year.
Required:
Complete the following balance sheet as of the end of the current year. Some information has been given below.
What was the amount of net income for the year? (Hint: Use the retained earnings equation [Beginning Retained Earnings + Net Income − Dividends = Ending Retained Earnings] to solve for net income.)
Answers
he net income for the year is $16,550.
Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)
Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500
Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800
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As the CAPS document outlines, the Content Specification and Content Clarification for Patterns, Functions, and Algebra shows sequenced mathematics content topics and a content area spread. In the Intermediate Phase, select one topic and report on the topic sequence and content area spread. Your report should demonstrate mathematics concepts and procedures’ hierarchical and logical progression.
Answers
Answer:
Step-by-step explanation:
In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."
The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:
Introduction to Variables and Expressions:
Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.
Solving One-Step Equations:
Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.
Solving Two-Step Equations:
Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.
Writing and Graphing Linear Equations:
Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.
Systems of Linear Equations:
Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.
Word Problems and Applications:
Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.
The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.
By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.
help me out really fast pleaseee
Answers
Distributive because he changed the fractions to the way it would go.
5. What is the degree of the following polynomial?
3x³ +9x²-x-10
A.) 4
B.) 5
C.) 3
D.) 6
Answers
Answer:
C
Step-by-step explanation:
the degree of a polynomial is the value of the largest exponent of the variable within the expression.
3x³ + 9x² - x - 10
the term 3x³ has the largest exponent in the expression
the polynomial is therefore of degree 3
How can I factor the following expression by grouping:
a) 4x^3 - 2x^2 + 8x - 4
Answers
The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping
How to factor the expression by groupingFrom the question, we have the following parameters that can be used in our computation:
4x³ - 2x² + 8x - 4
Group the expression in 2's
So, we have
(4x³ - 2x²) + (8x - 4)
Factorize each group
2x²(2x - 1) + 4(2x - 1)
So, we have
(2x² + 4)(2x - 1)
Hence, the factored expression is (2x² + 4)(2x - 1)
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Please help I am struggling bad with this question thank you all
Answers
b = speed of the boat in still water
c = speed of the current
when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.
Now, the boat goes Upstream 48 miles, so Downstream must be travelling the same 48 miles back.
\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&48&b-c&3\\ Downstream&48&b+c&2 \end{array}\hspace{5em} \begin{cases} 48=(b-c)(3)\\\\ 48=(b+c)(2) \end{cases} \\\\[-0.35em] ~\dotfill\)
\(\stackrel{\textit{using the 1st equation}}{48=(b-c)3}\implies \cfrac{48}{3}=b-c\implies 16=b-c\implies \boxed{16+c=b} \\\\\\ \stackrel{\textit{using the 2nd equation}}{48=(b+c)2}\implies \cfrac{48}{2}=b+c\implies 24=b+c\implies \stackrel{\textit{substituting}}{24=(16+c)+c} \\\\\\ 24=16+2c\implies 8=2c\implies \cfrac{8}{4}=c\implies \boxed{2=c}~\hfill~\stackrel{ 16~~ + ~~2 }{\boxed{b=18}}\)
Graph that line with slope -1 passing through the point (-2,4)
Answers
Answer:
To graph the line with slope -1 passing through the point (-2,4), we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)where m is the slope of the line, and (x1, y1) is the given point on the line. Substituting the given values, we get:
y - 4 = -1(x - (-2))Simplifying this equation, we get:
y - 4 = -x - 2y = -x + 2Now we can graph this line by plotting the given point (-2,4), and then using the slope of -1 to find one or more additional points on the line. We can do this by starting at the given point and then moving one unit down (since the slope is negative) and one unit to the right (since the slope is -1). This gives us the point (-1,3). We can then connect these two points to graph the line.
GRAPHICAL REPRESENTATION:|
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