Two similar solids have a scale factor of 5:3.
What is the ratio of their volumes expressed in lowest terms?
Answers
The ratio of the volumes of the two similar solids that have a scale factor of 5:3 is: 125:27.
How to Determine The Ratio of the Volume of Similar Solids?If two solids that are similar to each other, have volumes A and B respectively, and have a scale factor of a:b, thus, the ratio of their volumes would be expressed as:
Volume of solid A/Volume of solid B = a³/b³
or
Volume of solid A : Volume of solid B = a³ : b³
Thus, the given similar solids have a scale factor of 5:3, therefore, the ratio of their volumes would be expressed as shown below:
5³ : 3³
125 : 27
Thus, the ratio of the volumes of the two similar solids that have a scale factor of 5:3 is: 125:27.
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Related Questions
What is the solution to 7x2 –2x ≤ 5?A. x is less than or equal to five sevenths or x ≥ 1B. x is greater than or equal to five sevenths or x < 1C. negative five sevenths is less than or equal to x is less than or equal to 1D. negative 1 is greater than x is greater than five sevenths
Answers
C. negative five-sevenths is less than or equal to x is less than or equal to 1
1) Let's solve this inequality and then consider the options:
\(\begin{gathered} 7x^2-2x\le \:5 \\ \\ 7x^2-2x-5\le \:5-5 \\ \\ 7x^2-2x-5\le\:0\:\:\:Factor\:this: \\ \\ \left(7x^2+5x\right)+\left(-7x-5\right)\leq0 \\ \\ x\left(7x+5\right)-\left(7x+5\right)\leq0 \\ \\ \left(7x+5\right)\left(x-1\right)\leq0 \\ \\ x=-\frac{5}{7}\quad \mathrm{or}\quad \:-\frac{5}{7}Thus, as we can see the only possible answer is C, since that presents the restraints we have found algebraically.find the period of y = 2 sin 0-3
Answers
Answer:
2π
Step-by-step explanation:
Given :-
y = 2 sinθ - 3And we need to find out the period of it . Now using the form ,
\(:\implies\) y = a sin ( bx - c ) + d
On comparing we have ,
a = 2b = 1c = 0d = -3We can find the period using formula ,
\(:\implies\) Period = 2π/ |b|
\(:\implies\) Period = 2π/|1|
\(:\implies\) Period = 2π
Hence the period is 2π .
David throws a ball up in the air. The graph below shows the height of the ball hh in feet after tt seconds. What is the ball’s greatest height?
HELP ASAP!
Answers
The greatest height is 9 feet.
What is projectile?
A projectile is any object thrown into space upon which the only acting force is gravity.
As, from the graph we can see that
The highest point the ball reaches shown by the coordinates (0.75, 9)
As, the maximum height is shown by y- axis(vertical axis).
Hence, the greatest height is 9 feet.
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Consider a component that fails according to the Exponential distribution with rate 2. Failures can be of three severities 1, 2, and 3, and the failure of severity i occurs with probability Oli. The repair time for failure of severity i is exponentially distributed with rate ui. Failures of severity 1 are show stoppers, that is, the system fails completely when a failure of severity 1 occurs. On the other hand, failures of severities 2 and 3 do not completely knock out the system, and it continues to operate in a degraded mode.
a) Draw a state transition diagram that represents the failure and repair processes of the component.
b) Derive an expression for the system to be completely available.
c) Derive an expression for the system to be operating in a degraded mode.
Answers
Answer:
attached below
Step-by-step explanation:
a) Diagram of state transition representing failure and repair process of component
attached below
b) expression for the system to be completely available
attached below
c) Expression for system to be operating in a degraded mode
attached below
Help as quick as possible
Answers
The top number goes first then the second number goes second
Find sin theta, sec theta, and tan theta, where theta is the angle shown in the figure. Give exact values, not decimal approximations.
Answers
Based on the definition of sin, sec and tan of an angle, you have:
\(\begin{gathered} sin\theta=\frac{opposite}{hypotenuse} \\ sec\theta=\frac{1}{cos\theta}=\frac{hypotenuse}{adjacent} \\ tan\theta=\frac{opposite}{adjacent} \end{gathered}\)the opposite side length can be calculated by using the Pythagorean theorem:
\(\begin{gathered} h^2=c_1^2+c_2^2 \\ c_1^2=h^2-c_2^2 \\ c_1=\sqrt[\placeholder{⬚}]{11^2-8^2} \\ c_1\approx7.55 \end{gathered}\)then, by replacing the values of the lengths of hypotenuse, opposite and adjacent sides, you obtain;
\(\begin{gathered} sin\theta=\frac{7.55}{11}=0.68 \\ sec\theta=\frac{11}{8}=1.37 \\ tan\theta=\frac{7.55}{8}=1.37 \end{gathered}\)Please help I’m stuck on this question
Answers
Answer:
B. circumcenter
Step-by-step explanation:
you have to draw in the perpendicular lines inside the triangle to find the circumcenter as shown in the picture.
The perimeter of a triangle is 37 inches. The second side is 3 times as long as the first
side. The third side is 2 inches longer than the second side. Find the length of each
side. Show your work.
help asap
Answers
Answer:
5 in, 15 in, 17 in
Step-by-step explanation:
Let x = the first side
the second side = 3x
the third side = 3x + 2
The perimeter = x + 3x + (3x + 2) = 7x + 2 = 37
7x = 37 - 2 = 35
x = 35/7 = 5 inches
3x = 3*5 = 15 inches
3x + 2 = 17 inches
f(x)=10x-15 g(x)=2x-3 Find: (f/g)(x)
Answers
The function operation (f/g)(x) in the functions f(x) = 10x-15 and g(x) =2x-3 is 5.
What is the function operation (f/g)(x) in the given function?A function is simply a relationship that maps one input to one output.
Given that;
f( x ) = 10x - 15g( x ) = 2x - 3( f / g )( x ) = ?First, we replace the function designators in f/g with the actual functions.
(f / g )(x) = f(x) / g(x)
(f / g )(x) = ( 10x - 15 ) / ( 2x - 3 )
Now, factor out 5 from 10x and -15
(f / g )(x) = 5( 2x - 3 ) / ( 2x - 3 )
Cancel the common factor of 2x - 3
(f / g )(x) = 5( 1 ) / ( 1 )
(f / g )(x) = 5 / 1
(f / g )(x) = 5
Therefore, the function operation (f/g)(x) equals 5.
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can somebody help answer this one for me its very difficult for me :[
Answers
Answer:
Step-by-step explanation:
This is a proof. You need to use theorems and definitions to get to your answer. You cannot make any assumptions without a definition for it. You can you use the information that you have proven from previous statements.
m<1 = m<2 Given
QP = QR Given
m<3 = m<4 Vertical Angles
m<1 + m<3 + m<P = 180 Triangle Sum Theorem
m<P = 180 - m<1 - m<3 Subtraction
m<P = 180 - m<2 - m<3 Substitution
m<2 + m<4 + m<R = 180 Triangle Sum Theorem
m<R = 180 - m<2 - m<4 Subtraction
m<R = 180 - m<2 - m<3 Substitution
m<P = m<R Transitive
m<Q = m<Q Reflexive
ΔQTP ≅ ΔQTR ASA
We proved that the triangles are congruent by proving an angle, a side and another angle are the same.
<Q and <Q same
QR and QP same, this was give
<R = <P same through proof
Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run?
A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by.
Select all that apply.
You know the difference in the distances the boys ran, so this is a subtraction problem.
You are finding the total distance the boys ran, so this is an addition problem.
Dean ran part of the distance Sam ran, so this is a multiplication problem.
The correct equation is s + 2.3 = 6.8.
The correct equation is s – 2.3 = 6.8.
The correct equation is 2.3s = 6.8.
Answers
Answer:
A,E
Step-by-step explanation:
Operation: Minus
To find how far Sam ran, we need to subtract 2.3 from Dean's distance of 6.8 km.
6.8 km - 2.3 km = 4.5 km
Therefore, Sam ran 4.5 km, since Dean ran 2.3 km fewer than Sam.
Answer:
a and e
Step-by-step explanation:
got it right on homework
A lumberyard charges $ 1 per cut to trim boards. Bob buys a 12-ft board and wants it out into twelve 1-ft pieces. How much will he be charged for the cutting? The correct answer is $11.
Answers
Answer:11
Step-by-step explanation:
There are 11 cuts to make 12 pieces on 1ft each
Length of the model airplane is 87 ft, the scale is 2 inches = 15 ft. What is the length of the model
Answers
By using proportions, the length of the model airplane is 11.6 inches.
What are proportions?
Proportions refer to the relationship between the size of an object or feature on a map and its actual size on the ground. A map that uses proper proportions will accurately represent the relative sizes and distances of objects or features, making it easier for users to navigate and understand the map.
To find the length of the model airplane, we need to use the scale factor provided.
The scale is 2 inches = 15 ft, which means that for every 2 inches on the model, it represents 15 feet in the actual airplane.
We can set up a proportion to solve for the length of the model:
2 inches / 15 ft = x inches / 87 ft
2 inches * 87 ft = 15 ft * x inches
174 inches = 15 ft * x inches
x inches = 174 inches / 15
x inches = 11.6 inches
Therefore, the length of the model airplane is 11.6 inches.
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could someone help me with this and show work?
Answers
The volume of the shape is 490cm³
What is volume of prisms?A prism is a solid shape that is bound on all its sides by plane faces. prism is named after the shape of these bases.
The base of this prism is rectangular. The volume of a prism is expressed as;
V = base area × height
base area = 7 × 10 = 70cm²
height = 7cm
the volume of the shape = 70× 7 = 490cm²
therefore the volume of the shape is 490cm³.
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Point of intersections=
Answers
answer is attached too
What is the range of the function y=3√√x+8 1x
Answers
Answer:
The range of the function is: -∞≤y≤∞.
Consider the provided function.
The range of the function is the set of all values which a function can produce or the set of y values which a function can produce after substitute the possible values of x.
The range of a cubic root function is all real numbers.
Now consider the provided function.
The above function can be written as:
Taking cube on both sides.
The graph of the function is shown in figure 1:
For any value of x we can find different value of y.
Here, the cube root function can process negative values. Since, the function can produce any values, the range of the given function is -∞≤y≤∞ .
Therefore, the range of the function is: -∞≤y≤∞ (A).
Three grade seven classes were raising money for a
charity. Class A raised $647.53. Class B raised $80.91
more than Class A. Class C raised
as much money
as Class B. How much did the three classes raise in total?
Answers
Answer:
Class A raised $647.53. Since class B raised $80.91 more than class A, then class B raised $728.44. If class B Raised as much money as class C, we multiply $728.44 by 2, and then add $647.53, we get our final answer of $2,104.41
Step-by-step explanation:
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Which of the following is a factor of 24x^6 - 1029y^3?
Answers
The factors of (24x⁶ - 1029y³) are 3, (2x² - 7x), (4x⁴ +14x²y+49y²)
Factors of Polynomials:When a polynomial is factored, its prime factorization is used to break it down into the product of two or more other polynomials. Polynomials may be easily simplified with the use of factoring.
When a polynomial is factored, its factors are expressed as the polynomial's product. Finding the zeros of the polynomial expression or the values of the variables in the supplied expression are both made possible by factoring polynomials.
Here we have
24x⁶ - 1029y³
Take 3 as common
=> 3(8x⁶ - 343y³)
As we know 8 = 2³ and 343 = 7³
=> 3[(2x²)³ - (7y)³]
From the algebraic identities
a³-b³ = (a-b)(a²+ab+b²)Take a = 2x² , b = 7y and apply above formula
=> 3[(2x² - 7x)((2x²)²+(2x²)(7y)+(7y)²)]
=> 3 [ (2x² - 7x) (4x⁴ +14x²y+49y²)]
Therefore,
(24x⁶ - 1029y³) = 3 (2x² - 7x) (4x⁴ +14x²y+49y²)
Therefore,
The factors of (24x⁶ - 1029y³) are 3, (2x² - 7x), (4x⁴ +14x²y+49y²)
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simplify: (2x^2y^3)3 x (4xy)2
Answers
Answer: 48yx^1+2y^3
Step-by-step explanation:
Multiply by applying the commutative and/or associative property (3/10) (-3.2) (-100)
Answers
Multiplying (3/10) (-3.2) (-100) by applying the commutative property of multiplication and/or associative property of multiplication, will give us:
\(\mathbf{(3/10)(-3.2) (-100) = 96}\)
Recall:
Based on the Commutative Property of multiplication, if you move or swap a number you want during multiplication, the result remains the same irrespective of the swap you made. i.e. (2)(3)(4) = 24; (2)(4)(3) = 24The Associative Property is similar to the Commutative Property. Here, it holds that: 2 x (3 x 4) = 24; 3 x (2 x 4) = 24We can apply the Commutative Property or Associative Property to multiply (3/10) (-3.2) (-100).
Thus:
Applying the Commutative Property and the Associative Property, let's multiply:\((3/10) (-3.2) (-100) = 3/10 \times (-3.2 \times -100)\\\\(3/10) (-3.2) (-100) = 3/10 \times 320\\\\(3/10) (-3.2) (-100) = 3 \times 32\\\\(3/10) (-3.2) (-100) = 96\)
Therefore, Multiplying (3/10) (-3.2) (-100) by applying the commutative property of multiplication and/or associative property of multiplication, will give us:
\(\mathbf{(3/10)(-3.2) (-100) = 96}\)
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Mathematics question ok
Answers
Answer:
3
Step-by-step explanation:
to find the volume of a rectangular prism, Volume = length x height x width
Volume is 45 units (given)
length is 5 units (given)
45 = 5 x w x l
45 / 5 = w x l
9 = w x l
only 3 x 3 = 9 works with these numbers
45 = 5 x 3 x 3
helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
Correct answer is B
Answer:
B.
Step-by-step explanation:
comment if u need explanation :))
20 points!!!! helppp
Answers
Answer:
51°
Step-by-step explanation:
The line is supplementary meaning that it equals 180°. Since you already know the degrees of two of the three angles, you will add the angles you know. 95+34=129 Sine supplementary lines equal 180°, you will subtract the 129° you already know, resulting in an answer of the remaining 51°.
Answer:
51
Step-by-step explanation:
josslyn placed $4,400 in a savings account which earns 3.2% interest, compounded annually. How much will she have in the account after 12 years? Round your answer to the nearest dollar. Do NOT round until you have calculated the final answer.
Answers
Answer:80
Step-by-step explanation:
Answer:6421
Step-by-step explanation:
P=4400
r=3.2%
n=1
t=12
f=4400 * (1+3.2/100/1)^12
3x + 18y = 1 what is the slope intercept form?
Answers
Answer:y=-1/6*x-1/18
Step-by-step explanation:answer = y=-1/6*x-1/18
18y=1-3x
y=1/18-3/18x
y=-1/6*x-1/18
solve the equation and give the verified answer 9 Y - 5 (2 Y - 3) is equals to 1 - 2 y
Answers
Answer:
y= -14
Step-by-step explanation:
First, distribute to get 9y-10y+15=1-2y
Then, combine like terms: -y+15=1-2y
Then, bring the 2y over and the 15 over: y= -14
Hope this helped!
hellooooooooooooooooooooooooooooooooooo
Answers
Answer:
Step-by-step explanation:
Hi
Imagine that you have the opportunity to purchase a large piece of land for $100,000, after taking out a loan. You have decided to take out a loan for $135,000 in order to cover the cost of the land purchase and building your park. You have hired a financial adviser to help you explore different loan options and decide which one is best for you. Below you will see the different loan options. You will need to calculate the total cost of each loan with interest. Once you have do this you and your group members will need to decide which of the loan options is best for you and why.
Option #1 – charges 5% simple interest per year; this is a short-term loan for only 5-years.
Option #2 – charges 7% simple interest per year; this is a short-term loan for only 3-years.
Option #3 – charges 3.2% simple interest per year; there is no time limit on this loan (as a group determine how long you think it will take you to make enough money to be able to pay back the loan with interest)
Option #4 - charges 10% simple interest per year; only lasts 10 months
Option #5 - charges 12% simple interest per year; only lasts 6 months
Written Response
You will be meeting with your financial adviser in two days. Write out which loan option your group is choosing to use and why. You really want to impress her with how much thought you have put into this decision so be as detailed as possible.
Answers
what is this
Step-by-step explanation:
Option #1 – charges 5% simple interest per year; this is a short-term loan for only 5-years.
Option #2 – charges 7% simple interest per year; this is a short-term loan for only 3-years.
Option #3 – charges 3.2% simple interest per year; there is no time limit on this loan (as a group determine how long you think it will take you to make enough money to be able to pay back the loan with interest)
Option #4 - charges 10% simple interest per year; only lasts 10 months
Option what is this
Answer:
Its option one
Step-by-step explanation:
Because 135,000/5=27000 then x5=135,000
Parallel Structure:Question 6
Which sentence uses parallel
structure correctly:
Select one:
Eggs, flour, and turning the oven to 350 degrees are needed for
baking the pie.
Eggs, flour, and having turned the oven to 350 degrees will be
needed to bake the pie.
Eggs, flour, and sugar are needed to bake the pie crust.
Eggs, flour, and turning the oven to 350 degrees are needed to
bake the pie crust.
Answers
parallel structure is used correctly in :
Eggs, flour, and sugar are needed to bake the pie crust.
In grammar, parallelism, also referred to as parallel structure or parallel construction, is the distribution of identical phrases or clauses with the same grammatical structure within one or more sentences.
The use of parallel structure is more of a stylistic option than a strict rule because it aids in the patterning of sentence elements.
The use of parallelism has an impact on reading and may facilitate text processing.
The rhythm and grammatical balance of a sentence are both guaranteed by using parallel construction.
However, if this structure is not used when creating a sentence with two or more pieces of information, the sentence will have a disruption in rhythm or grammatical imbalance.
Therefore, the correct answer is:
Eggs, flour, and sugar are needed to bake the pie crust.
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The length of a rectangular field is represented by the expression 14x-3x^2+2y . The width of the field is represented by the expression 5x-7x^2+7y . How much greater is the length of the field than the width?
Answers
The length of the field is greater than the width by the expression \((14x - 3x^2 + 2y) - (5x - 7x^2 + 7y).\)
1. The length of the field is represented by the expression \(14x - 3x^2 + 2y.\)
2. The width of the field is represented by the expression \(5x - 7x^2 + 7y\).
3. To find the difference between the length and width, we subtract the width from the length: (\(14x - 3x^2 + 2y) - (5x - 7x^2 + 7y\)).
4. Simplifying the expression, we remove the parentheses: \(14x - 3x^2 + 2y - 5x + 7x^2 - 7y.\)
5. Combining like terms, we group the \(x^2\) terms together and the x terms together: \(-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.\)
6. Simplifying further, we add the coefficients of like terms:\((7x^2 - 3x^2) + (14x - 5x) + (2y - 7y).\)
7. The simplified expression becomes: \(4x^2 + 9x - 5y.\)
8. Therefore, the length of the field is greater than the width by the expression \(4x^2 + 9x - 5y.\)
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