[solved] These Cylinders are similar. Find the volume of the smaller cylinder. Round to the nearest tenth. (the answer is 84.9 cm^3)
![[solved] These Cylinders Are Similar. Find The Volume Of The Smaller Cylinder. Round To The Nearest Tenth.](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/BinY0ETFt8U3C4H4YXiasPpXw2H0DvaK.png)
Answers
Answer:
84.9 cm³
Step-by-step explanation:
Height of the bigger Cylinder = 5 cm
Volume of the bigger Cylinder = 393 cm³
Height of the smaller cylinder = 3 cm
Volume of the smaller cylinder = x cm³
Since they are similar, therefore: the cube of their ratio would equal the ratio of their volume.
Thus:
\( (\frac{5}{3})^3 = \frac{393}{x} \)
\( \frac{125}{27} = \frac{393}{x} \)
Cross multiply
\( 125*x = 393*27 \)
\( 125x = 10,611 \)
Divide both sides by 125
\( \frac{125x}{125} = \frac{10,611}{125} \)
\( x = 84.888 \)
Volume of the smaller cylinder = 84.9 cm³ (to nearest tenth?
Related Questions
What is the value of x in the triangle?
A.
B.
C.
D.
Answers
Answer:
The base angles of an isosceles triangle are the angles formed by the base and one leg of the triangle. The base angles theorem converse states if two angles in a triangle are congruent, then the sides opposite those angles are also congruent.Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.\(x = \sqrt{ {7}^{2} + {7}^{2} } \\ x= \sqrt{49 + 49} \\ x = \sqrt{98} \\ x= \sqrt{49 \times 2} \\ \boxed{x= 7 \sqrt{2} }\)
What is the value of x in the triangle?
A. 7
B. 14
✓C. 7√2
D. 7√2/2
C. is the right answer.A bag contains 3 gold marbles, 8 silver marbles, and 30 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
What is your expected value if you play this game?
Answers
Answer: To calculate the expected value, we need to multiply each possible outcome by its probability and then add up the results.
The probability of selecting a gold marble is 3/41, the probability of selecting a silver marble is 8/41, and the probability of selecting a black marble is 30/41.
The winnings/losses associated with each outcome are $3 for gold, $2 for silver, and -$1 for black.
Step-by-step explanation:
Therefore, the expected value can be calculated as follows:
(3/41) x $3 + (8/41) x $2 + (30/41) x (-$1)
= $0.073
The expected value is $0.073, which means that on average, you can expect to win $0.073 per game if you play this game many times.
Therefore, if you play this game, you can expect to win a small amount of money on average, but it is not a guaranteed win.
References:
Grinstead, C.M. and Snell, J.L. (2006). Introduction to Probability. American Mathematical Society.
"Expected Value," Investopedia, accessed May 14, 2023, https://www.investopedia.com/terms/e/expectedvalue.asp.
There are 12 pieces of pie left over in the cafeteria. If 6 pieces are apple and 6 are cherry, what fraction of the remaining pieces are apple? Simplify your answer as much as you can.
Answers
Answer:
1/2
Step-by-step explanation:
r=7/8cosθ+2sinθ
Which of the following gives the Cartesian form of the equation above?
Select the correct answer below:
x2+y2=7/10
y=−1/4x+7/8
y=−4x+7/2
8x2+2y2=7
Answers
Answer: 8x^2 + 2y^2 = 7
Step-by-step explanation:
The equation R = 7/8cosθ + 2sinθ can be rewritten in terms of x and y using the conversions x = Rcosθ and y = Rsinθ.
Substituting R = 7/8cosθ + 2sinθ into these equations, we get:
x = (7/8)cosθ cosθ + 2sinθ cosθ
y = (7/8)cosθ sinθ + 2sinθ sinθ
Simplifying these expressions using trigonometric identities, we get:
x = (7/8)cos^2θ + (4/8)sin2θ
y = (7/8)sinθ cosθ + (4/8)sin2θ
Multiplying both sides of the x equation by 8/7 and simplifying, we obtain:
8x^2 + 2y^2 = 7cos^2θ + 8sin^2θ
Using the identity cos^2θ + sin^2θ = 1, we get:
8x^2 + 2y^2 = 7(1)
Therefore, the Cartesian form of the equation is 8x^2 + 2y^2 = 7.
Answer:y=−4x+7/2
Step-by-step explanation:
Multiply each side of the equation by 8cosθ+2sinθ to get 8rcosθ+2rsinθ=7. Using the relationships x=rcosθ and y=rsinθ, the equation becomes 8x+2y=7. Solving this equation for y shows that y=−4x+7/2.
Solve : 4/3x + 3 < 23/3
Answers
Answer: This we help u
x<7/2<3 1/2
Find the area of the parallelogram in square meters
Answers
Answer: 27
Step-by-step explanation:
9*3
Please help
See the picture
I’m giving brainlest
Answers
Answer:
y = 3/5x+1
Step-by-step explanation:
m = 3/5
b = 1
Consider the given statement: Not all rooms at the hotel have a bed.
For each statement below, decide whether it is a negation of the given statement.
A.) No room at the hotel has a bed YES/NO
B.) Some rooms at the hotel have a bed YES/NO
C.) Some rooms at the hotel do not have a bed YES/NO
D.) All rooms at the hotel have a bed YES/NO
Answers
Answer:
The negation is the OPPOSITE of whatever is said, so in this case, the opposite of "Not all rooms at the hotel have a bed." would be D "All rooms at the hotel have a bed" and A "No room at the hotel has a bed"
The correct answers are A and D
Let me know if this helps!
Answer:
a. no because it states that no rooms have a bed when it states not all rooms at the hotel have a bed
b. yes because while its true some rooms dont have a bed other rooms will
c. yes again some rooms do have a bed and some dont
d. no because we have already established that only some rooms have beds not all
hope this helps
Step-by-step explanation:
Which measurement is a good estimate for the area of a circle if the radius is 4 meters?
Answers
The rule of the area of the circle of radius r is
\(A=\pi r^2\)Since the radius of the circle is 4 meters, then
\(r=4\)Substitute the value of r in the rule above by 4
Use pi = 3.14
\(\begin{gathered} A=3.14(4)^2 \\ A=3.14(16) \\ A=50.24\text{ m}^2 \end{gathered}\)Then the area of the circle is about 50 square meters
The answer is the last choice
The two dot plots below show the number of the miles run by 14 students at the beginning and end of the school year. complete the comparison of the medians for the two dot plots. If necessary, round to the nearest tenth.
The median at the start of the year was _____ miles, and the median at the end of the year was _____ miles. Please answer, it’s a quiz!
Answers
Answer:
Start of the year: 77 End of the year: 87
Step-by-step explanation:
1 dot equals the number represented below, so I multiplied up to the answers for both! (Hope you pass ur test :D)
Use substitution to solve the system x=2y-5 and -2x+5y=11
Answers
Answer:
(-3, 1)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations by substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
x = 2y - 5
-2x + 5y = 11
Step 2: Solve for y
Substitution
Substitute in x: -2(2y - 5) + 5y = 11Distribute -2: -4y + 10 + 5y = 11Combine like terms: y + 10 = 11Isolate y: y = 1Step 3: Solve for x
Define original equation: x = 2y - 5Substitute in y: x = 2(1) - 5Multiply: x = 2 - 5Subtract: x = -3HELP AS SOON AS POSSIBLE
Answers
The coordinates of polygon A'B'C'D' after the rotation of 180º are given as follows:
A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).
What are the rotation rules?The five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x).90° counterclockwise rotation: (x,y) -> (-y,x).180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y).270° clockwise rotation: (x,y) -> (-y,x).270° counterclockwise rotation: (x,y) -> (y,-x).The original coordinates for this problem are given as follows:
A(0,0), B(5,2), C(5,-5), D(0,-3).
Exchanging the sign of each of the coordinates, the coordinates after the rotation are given as follows:
A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).
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a survey was conducted with a large group of teenagers from 6 different states and it asked them for their favourite sport out of a large list of sports. the study aims to look at whether a teenager's state of residence is associated with their sporting preferences. assume that p is the proportion of teenagers who selected the sport most preferred in their state of residence, such that p1 is that for state 1, p2 is that for state 2 and so on. select from the following all statements that are true as well as the hypothesis that corresponds to this study:
Answers
H0: There is no link between state and preferred sport.
H1: There is a connection between state and preferred sport.
Given,
The question to be answered is whether the factor "state" and the factor "sporting choice" are related.
Therefore, the focus of the study is on "association" and whether or not state-to-state variations in athletic preference distributions exist. The most appropriate test in this instance is the test for association.
Unless there is evidence to the contrary, two things are assumed to not be related. Since the null hypothesis is assumed to be true, the following two hypotheses are the proper pair:
H0: There is no connection between a person's state and their preferred sport.
H1: The choice for sports and state are related.
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Find the measure of 44.
{
44
158°
K
*4 = [?]
![Find the measure of 44.{44158K*4 = [?]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/91ZM8GeQmfk7MKtFN66VhJO8lKxVKo9v.png)
Answers
<4=22°
Answer:
<4+158=180 co interior angle
<4=180-158=22°
Answer:
solution given:
<4+<158°=180°[co- interior angle]
<4=180°-<158°=22°
<4=22° is your answer
I need help I haven’t been here a week and I don’t understand my homework
Solve either
Answers
Answer: you need to add
Step-by-step explanation: I would ask your teacher to help you understand the lesson.
Graph the solution set.
3x - y < 9
2x + y 26
-20
Graph Lay
Answers
The solutions of x² - 2x - 4 = -3x + 9 are x = -4.14 and x = 3.14,
which is the x-coordinate of the intersection points of the graphs of y = x² - 2x - 4 and y = -3x + 9
What is quadratic equation?"It is a polynomial equation with degree two."
"The general form of quadratic equation is , where a, b, c are real numbers with a ≠ 0."
here, we have,
For given question,
We have been given an quadratic equation x² - 2x - 4 = -3x + 9
We simplify above quadratic equation.
=> x² - 2x - 4 = -3x + 9
solving we get,
=> x = -4.14 and x = 3.14
Consider the graphs for y = x² - 2x - 4 and y = -3x + 9 as shown below.
Therefore, the solutions of x² - 2x - 4 = -3x + 9 are x = -4.14 and x = 3.14,
which is the x-coordinates of the intersection points of the graphs of y = x² - 2x - 4 and y = -3x + 9
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1/4 of the total bird population in your town is 200 birds. How many birds are there in your town?
Answers
Answer:
800
Step-by-step explanation:
what is the slope of the line?
Answers
Answer:
-1
Step-by-step explanation:
the slope of the line is given by the equation m=(y2-y1)/(x2-x1)
here the line passes with the coordinate (-2,0),(0,-2)
m=(-2-0)/(0-(-2))
= -2/2
= -1
On the following composite figure, the longer edge length is 14 millimeters. The shorter edge length is 8 millimeters. The width of the figure, at its longest point, is 11.3 millimeters. Find the area of the figure. Explain or show how you got your answer. Note: Lines that look parallel are parallel, and angles that look like right angles are right angles.
Answers
The area of the given composite figure with a side length of 14mm and an edge length of 8mm is 158.2 mm².
What is a composite figure?
A two-dimensional figure built up of fundamental two-dimensional shapes like triangles, rectangles, circles, semicircles, etc. is known as a composite shape or composite figure. A variety of forms that we encounter every day are composite figures that can be created from two or more fundamental figures.
The figure is given below.
From the figure, we can see that the sides of a triangle at the top and bottom are the same.
So the triangle cut from the bottom is placed at the top of the figure.
When the cut triangle is placed back at the bottom, we get a rectangle of length 14 mm and breadth 11.3 mm, as given below.
So the area of the given composite figure is the same as the area of the rectangle.
The area of the rectangle = length * breadth = 14 * 11.3 = 158.2 mm²
Therefore the area of the given composite figure is 158.2 mm².
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Please solve this
∫ (log(1 + x ^ 2))/((x + 1) ^ 2) dx
Answers
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
We have,
To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.
Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:
∫ (log(1 + (u-1)²) / u²) du.
Expanding the numerator, we have:
∫ (log(1 + u² - 2u + 1) / u²) du
= ∫ (log(u² - 2u + 2) / u²) du.
Now, let's split the logarithm using the properties of logarithms:
∫ (log(u² - 2u + 2) - log(u²)) / u² du
= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.
We can simplify the second integral:
∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.
Using the power rule for integration, we can integrate both terms:
∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.
Now, let's focus on the second integral:
∫ (log(u) / u³) du.
This integral does not have a simple closed-form solution in terms of elementary functions.
It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).
Therefore,
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
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A right rectangular prism has a height of 12 in. And the area of its base is 18sq. In. What is the volume of the prism?
Answers
Answer:
Step-by-step explanation:
Volume = 12 × 18 = 216 in³
What is the solution to the equation squareroot 4t+5=3
Answers
Answer:
Step-by-step explanation:
√(4t+5) = 3
4t + 5 = 9
4t = 4
t = 1
Answer:
Step-by-step explanation:
Remark
This is a bit ambiguous. I'm going to take it to mean
√(4t + 5) = 3
Solution
√(4t + 5) = 3 Square both sides.
(√(4t + 5) )^2 = 3 ^2 If you square something and a √ is involved, sometimes squaring something will get rid of the√ sign. That's what happens here.
4t + 5 = 9 Subtract 5 from both sides.
4t + 5 - 5 = 9-5 Combine
4t = 4 Divide by 4
4t/4 = 4/4
t = 1
An aquarium of height 1.5 feet is to have a volume of 12ft^3. Let x denote the length of the base and y the width.
a) Express y as a function of x.
b) Express the total number S of square feet of glass needed as a function of x.
Answers
The aquarium has six rectangular faces, four of which are identical (two sides and two ends), and two of which are identical to each other but different from the others (top and bottom).
What is the needed as a function?a) We can use the formula for the volume of a rectangular prism, which is given by V = lwh, where l is the length, w is the width, and h is the height. In this case, we have \(V = 12 ft^3 and h = 1.5 ft\) . We want to express y as a function of x, so we need to eliminate w from the equation.
We can rearrange the equation for the volume to get \(w = V/(lh)\) , and substitute in h \(= 1.5 ft\) :
\(w = V/(1.5lx)\)
Now we can substitute y for w to get:
\(y = V/(1.5lx)\)
b) To find the total surface area, we need to find the area of each face and add them up.
The area of one of the identical sides or ends is lw, so the total area of these four faces is:
\(4lw = 4xy\)
The area of the top and bottom faces is lx, so the total area of these two faces is:
\(2lx\)
Therefore, the total surface area S is given by:
\(S = 4xy + 2lx\)
We can express y in terms of x using the equation from part a):
\(y = V/(1.5lx)\)
Substituting this into the expression for S, we get:
\(S = 4x(V/(1.5lx)) + 2lx\)
Simplifying, we get:
\(S = (8/3)V/x + 2lx\)
So the total surface area S is a function of x, and we can use this equation to find the value of S for any given value of x.
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There is a line whose slope is 2 and whose slope is 2 and whose y- intercept is 8. What is its equation in slope-intercept form?
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Suppose you are an operation manager for a plant that manufactures batteries Give an example of how you use descriptive statistics and alo inferential statics to better managerial decisions
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As an operations manager for a plant that manufactures batteries, I can use both descriptive statistics and inferential statistics to make better managerial decisions
Descriptive statistics help me to summarize and describe the data collected from the manufacturing process.
For instance, I can use measures such as mean, median, mode, range, and standard deviation to summarize the data on the production output of batteries over a specific period.
Inferential statistics allow me to draw conclusions and make predictions based on the data collected from a sample of batteries produced.
For example, I can use inferential statistics to determine the probability of the battery meeting the required specifications. I can also use inferential statistics to make predictions about future production output, based on the historical data.
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write an equation of the line in slope-intercept form where slope equals 1/4 and y-intercept equals 0, - 5
Answers
Answer:
\(y=\frac{1}{4}x-5\)
Step-by-step explanation:
Write an equation of the line in slope-intercept form where slope equals 1/4 and y-intercept equals 0, - 5
Slope-intercept form: y = mx + b
m = slope
b = y-intercept (when x = 0)
Ex:
y = 5x + 2
m = 5b = (0, 2)For our problem:
\(y=\frac{1}{4}x-5\)
m = \(\frac{1}{4}\)b = (0, -5)Hope this helps!
What is the value of y in the equation 4 + y = −3? (1 point) a 7 b 1 c −1 d −7
Answers
Answer:
-7
Step-by-step explanation:
please help because I don't know
Answers
Answer:
is that an exponent?
Step-by-step explanation:
The cost of 5 metres of cloth is 210. Tabulate the cost of 2, 4, 10 and 13 metres of cloth of the same type.
Answers
Answer:
2 meters: $84
4 meters: $168
10 meters: $420
13 meters: $546
Step-by-step explanation:
$210 / 5 meters = $42 / meter
2 meters: 2 * 42 = $84
4 meters: 4 * 42 = $168
10 meters: 10 * 42 = $420
13 meters: 13 * 42 = $546
hope this helps! <3
Is this right? Pls help
Answers
Answer:
A
Step-by-step explanation:
DE is the shortest side because it's is opposite to the smallest angle (<F)
180 - 60 = 3X +2X + 5,
X = 23
<F = 2*(23) +5 = 51