On solving the provided question, we can say that w = 10 in; l = 2 in; volume of prism = WL = 10 X 2 = 20 in sq
what is prism?The definition of a prism in geometry is a polyhedron with an n-sided polygonal base, a second base that is a shifted copy of the first base, and n additional faces (necessarily all parallelograms), with two Connect the corresponding sides of the base. Translations of the base are all cross sections that are parallel to it. A prism is a two-sided, solid, three-dimensional object. It consists of equal cross-sections, flat sides, and identical bases. A prism has faces that are parallelograms or rectangles without bases. A prism is a homogenous, solid, transparent, refracting object enclosed by two planes that are obliquely angled to one another. Two triangular faces and three parallel rectangular faces make up a typical prism. They are constructed of either glass.
here,
w = 10 in
l = 2 in
volume of prism = WL = 10 X 2 = 20 in sq
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A toaster has 4 slots for bread. Once the toaster is warmed up, it takes 35 seconds to make 4 slices of toast, 70 seconds to make 8 slices, and 105 seconds to make 10 slices. Explain how to predict the time it takes to toast any number of slices of toast.
It will take the toaster about 175 seconds to make 20 slices.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
Given that The toaster takes 35 seconds to make 4 slices of toast.
It takes 70 seconds to make 8 slices of toast, It also takes 105 seconds to make 12 slices.
We are required to calculate how long it may probably take the toaster to make 20 slices.
To calculate the time it takes the toaster to make 1 slice:
4 slices ---------- 35 seconds
1 slice ----------- ? seconds
1/4 × 35 = 35/4 seconds
Now, if 1 slice will be made in 35/4 seconds,
20 slices will be made in:
1 slice --------- 35/4 seconds
20 slices ------ ? seconds
(20/1) × 35/4 = 175 seconds
Hence It will take the toaster about 175 seconds to make 20 slices.
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The coordinates of a triangle are: R(-4,4) S(-2,-2) T(2, 3) Brian determined A RST was a scalene triangle, but he wanted to the find the lengths of the three sides. Complete the table to determine the three side lengths of ARST. 37 38 140 141 length of RS length of ST length of TR
The length of the sides RS, ST and TR are √72, √41 and √37 in the scalene triangle RST.
The distance between any two points A(a,b) and B(c,d) in the plane is given by,
AB = √((c-a)²+(d-b)²)
Here, it is given that the points of the triangle are R(-4,4) S(-2,-2) T(2, 3).
The triangle is scalene so length of every side is different.
Now, Using the above formula,
RS = √((2+4)²+(-2-4)²)
RS = √(36+36)
RS = √72
ST = √((2+2)²+(3+2)²)
ST = √(16+25)
ST = √41
TR = √((2+4)²+(3-4)²)
TR = √(36+1)
TR = √37
So, Brian is correct, the triangle is a scalene triangle.
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A tank contains 60 kg of salt and 1000 L of water. A solution of a concentration 0. 03 kg of salt per liter enters a tank at the rate 9 L/min. The solution is mixed and drains from the tank at the same rate. A. ) What is the concentration of our solution in the tank initially?concentration = (kg/L)b. ) Find the amount of salt in the tank after 2. 5 hours. Amount = (kg)c. ) Find the concentration of salt in the solution in the tank as time approaches infinity. Concentration = (kg/L)
(a) The concentration of our solution in the tank initially is 0.060 kg/L. (b) the amount of salt in the tank after 2. 5 hours is 44.45 kg. (c) The concentration of salt in the solution in the tank as time approaches infinity is 0.030 kg/L.
How do you find the concentration of a salt solution?Divide the solute's gram weight by the total weight of the solution, then multiply the result by 100 to get the mass/mass percent of the solution. The amount of solute (measured in grams) per milliliter of solution is known as the mass/volume percent.
(A) Tank contains 60 kg of salt and 1000 L of water. So the concentration of solution in the tank initially = 60/1000 kg/l
The concentration of solution in the tank initially = 0.060 kg/L
(B) Let y(t) denote the amount of salt in the tank at any time t.
Rate In
A solution of concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min.
[tex]R_{i}[/tex] =(concentration of salt in inflow)(input rate of solution)
= (0.03kg/L)*(9L/min)
= 0.27kg/min
Rate Out
The solution is mixed and drains from the tank at the same rate.
Concentration, C(t) = Amount/Volume = y(t)/1000
[tex]R_{out}[/tex] =(concentration of salt in outflow)(output rate of solution)
= {y(t)/1000}kg/L*9L/min
= 0.009y(t) kg/min
Therefore, the differential equation for the amount of Salt in the Tank at any time t:
dy/dt = 0.27 - 0.009y(t)
So the amount of salt in the tank after 2. 5 hours (2.5*60 min = 150 min) is 44.45 kg.
(c) The concentration of salt in the solution in the tank as time approaches infinity
As t -> -∞, e^-∞ = 0
so, the concentration of salt in the solution in the tank as time approaches infinity is 0.030 kg/L.
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. A window is in the form of a rectangle surmounted by a semicir- cle. The rectangle is of clear glass, whereas the semicircle is of tinted glass that transmits only half as much light per unit area as clear glass does. The total perimeter is fixed. Find the proportions of the window that will admit the most light. Neglect the thick- ness of the frame.
The area of the window that lets in the most light will be the one that causes the window to transmit the most light overall.
To find the proportions of the window that will admit the lightest, we need to maximize the total area of the window while keeping the perimeter fixed. The total area of the window is the sum of the area of the rectangle and the area of the semicircle. The area of the rectangle is the product of its length and width, and the area of the semicircle is half the product of its radius and the area of a full circle with the same radius.
Since the perimeter is fixed, the length and width of the rectangle are also fixed. The radius of the semicircle can be found using the perimeter and the length and width of the rectangle.
Once we have the radius of the semicircle, we can find the area of the rectangle, the area of the semicircle, and the total area of the window. Since the semicircle is of tinted glass that transmits only half as much light per unit area as clear glass does, we will have to multiply the area of the semicircle by 0.5 to find the total amount of light transmitted by it.
Finally, we will have to compare the total amount of light transmitted by the window for different values of the length and width of the rectangle. The proportion of the window that admits the most light will be the one that results in the maximum total amount of light transmitted by the window.
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when journalizing an accounts payable account what account is credited
a. it depends on the transaction
b. accounts payable
c. cash
d. accounts receivable
Answer:
cash
Step-by-step explanation:
debit - account payable
credit - cash
Is 0 Infinity closed interval?
Thus, 0 itself is the sole position at which [0,∞] and (0,∞] are separated. Since it is in [0,∞] the set is closed. Given that it is not in (0,∞), the set is open interval.
A (real) interval in mathematics is a collection of real numbers that includes all real numbers that fall within any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1. The collection of numbers such that 0 x 1 and the collection of all real numbers are other examples of intervals.
the empty set, any singleton, the set of positive real numbers, the set of nonnegative real numbers, and (set of one element).
Because they are the most basic sets whose "length" (or "measure" or "size") is straightforward to define, real intervals are crucial in the theory of integration. The Borel measure and finally the Lebesgue measure result from extending the notion of measure to more intricate sets of real numbers.
Interval arithmetic is a broad numerical computing technique that automatically generates assured enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff. Intervals are at the centre of this technique.
Therefore, 0 itself is the sole place at which [0,∞] and (0,∞] have a boundary. Due to its location in [0,∞] the set is closed. Since it is not in (0,∞), the set is unclosed.
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Jamila deposits $800 in an account that earns yearly simple interest at a rate of 2.65%. How much money is in the account after 3 years and 9 months?
Answer:
$821.2
Step-by-step explanation:
cause 2.65 percentage of 800 dollars is 800/100=8*2.65=21.2dollars.+800 =$821.2
Makayla and Addison are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Makayla is 290 miles away from the stadium and Addison is 345 miles away from the stadium. Makayla is driving along the highway at a speed of 40 miles per hour and Addison is driving at speed of 51 miles per hour. Let MM represent Makayla's distance, in miles, away from the stadium tt hours after noon. Let AA represent Addison's distance, in miles, away from the stadium tt hours after noon. Write an equation for each situation, in terms of t,t, and determine the interval of hours, t,t, for which Makayla is closer to the stadium than Addison.
The linear functions for each situation are given as follows:
Makayla: 290 - 40x.Addision: 345 - 51x.Makayla is closer than Addision when:
x < 5.
How to define the linear functions?The linear functions in slope-intercept format for this problem are given as follows:
y = mx + b.
In which:
m is the slope, representing the velocity, as a negative as they are getting closer to the stadium with time.b is the intercept, representing the initial distance.Hence the functions are defined as follows:
Makayla: 290 - 40x.Addision: 345 - 51x.Makayla is closer when:
290 - 40x < 345 - 51x
11x < 55
x < 5.
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Need the answer plsss!
By solving, we see that the product of the polynomials 4 - a and a3 + 7a - 18 is a3 + 3a2 + 46a + 72.
what is polynomial ?The location on the y-axis where the slope of the line passes is known as the intersection point in mathematics. a point on a line or curve where the y-axis crosses. The equation for the straight line is given as Y = mx+c, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the line's slope (m) and y-intercept (b) are highlighted. The slope and y-intercept of an equation with the intercept form (y=mx+b) are m and b, respectively. There are several equations that can be rewritten to look like slope intercepts. The slope and y-intercept are both modified to 1 if y=x is rewritten as y=1x+0, for example.
given
(4 - a) * ( a3 + 7a - 18 )
= 4a3 + 28a - 72 - a4 + 7a2 + 18 a
= a3 + 3a2 + 46a + 72
By solving, we see that the product of the polynomials 4 - a and a3 + 7a - 18 is a3 + 3a2 + 46a + 72.
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How do you solve basic equations in algebra 1
Finn leaned a 100-foot ladder against the side of a building. The base
of the ladder is 14 feet from the base of the building. The top of the
ladder is 11 feet from the top of the building. How tall is the building?
Provide an answer accurate to the nearest tenth of a foot.
The height of the Building is 110.01 feet.
What is the Pythagorean theorem?The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' Theorem.
Given, Finn leaned a 100-foot ladder against the side of a building. The base of the ladder is 14 feet from the base of the building. The top of the ladder is 11 feet from the top of the building.
For the triangle made by ladder
hypotenuse = 100
base = 14
thus, from the Pythagorean theorem
hypotenuse² = base² + height²
100² = 14² + height²
height² = 10000 - 196
height = √9804
height = 99.01
total height of the wall = height of triangle + remaining height of the wall
Thus the total height of the wall = 99.01 + 11
the total height of the wall = 110.01
therefore, the building is 110.01 feet tall.
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Is Avogadro's number equal to one mole?
One mole consists of 6.02214076×10²³ units which is Avogadro's number. Thus one mole is known as Avogadro's number.
What is one mole?
A mole is 6.02214076×10²³ of any chemical unit, including atoms, molecules, ions, and others. Due to the large number of atoms, molecules, or other components that make up any substance, the mole is a useful measure to utilize. The mole was initially defined as the quantity of atoms contained in 12 grammes of carbon-12, but the General Conference on Weights and Measures declared in 2018 that the mole will only contain 6.02214076×10²³ of some chemical unit as of May 20, 2019.
In chemistry, a mole, sometimes spelled mol, is a common scientific measurement unit for significant amounts of very small objects like atoms, molecules, or other predetermined particles.
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GIVING BRAINLIEST AND 50 POINTS
Answer:
2x + 2
Step-by-step explanation:
Combine all the like terms:
-5x + 7x -12 + 14 = 2x + 2
Answer:
2x + 2
Step-by-step explanation:
(- 5x - 12) + (14 + 7x) ← remove parenthesis
= - 5x - 12 + 14 + 7x ← collect like terms
= (- 5x + 7x) + (- 12 + 14)
= 2x + 2
How many times smaller is 2.7 x 10^3 than 5.481 x 10^5?
Function: This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.
What is function?A function is a mathematical relation between two sets of values, usually between an input and an output. It can be thought of as a machine that takes a certain input and produces a certain output.
2.7 x 10^3 is about 0.049 times smaller than 5.481 x 10^5.
To determine this, we can divide the two numbers. 5.481 x 10^5 divided by 2.7 x 10^3 equals about 201.593.
This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.
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If b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2
Hence option (B) is a correct choice and rest all other options are incorrect
1/b^2 ∑ (-1)^k(t^2/b^2)^k
Step-by-step explanation:
Remember that the sum of infinite GP is given by the formula blow:
First term=a
Common ratio=r
S=a/1 - r
Wherever the common ratio r falls within the interval (-1,1)
When the given series is compared to the infinite sum:
First term=a
Common ratio=r
S= a/1-r = 1/b^2+t^2
Now given: |t| < |b|=0<t^2/b^2<1
S=1/B^2.1/1-(-T^2/B^2)
=A=1
R=-T^2/B^2
Writing the general form:
Hence option (B) is a correct choice.
What are real numbers simple definition?
Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category.
INCOMPLETE QUESTION: if b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2
A) 1/b^2 ∑(t^2/b^2)^k.
B) 1/b^2 ∑(-1)^K(t^2/b^2)^k.
C)B^2∑(T^2/B^2)^K
D)b^2∑(-1)(t^2/b^2)^k
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What is the value of 8 power 8?
Answer:16,777,216
Step-by-step explanation:
please help me with these 4 questions will mark branliest whoever gets all of it right
Answer:
1. The answer is 40 degrees
2. Adjacent angles are sometimes congruent.
3. UPR is vertical to TPQ
4. The answer is 132 Degrees
1. The ratio of peaches in a box is constant. The table below compares the number of peaches that are in the box.
boxes peaches
2 6
blank 9
5 blank
6 18
2. The ratio of strawberries in a box is
constant. the table below compares the number of strawberries that are in the boxes
boxes strawberries
2 blank
4 12
5 15
8 blank
please help
The table representing ratio of peaches in a box should be completed as follows;
Boxes Peaches
2 6
3 9
5 15
6 18
The table representing ratio of strawberries in a box should be completed as follows;
Boxes Strawberries
2 6
4 12
5 15
8 24
How to complete the tables?In order to have a proportional relationship and equivalent ratios that is constant, the variables x for boxes and y for peaches must have the same constant of proportionality. Next, we would determine the constant of proportionality (k) based on the given parameters:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 6/2 = 18/6
Constant of proportionality (k) = 3.
When y = 9 peaches, the value of x is given by;
x = y/k
x = 9/3
x = 3 boxes.
When x = 5 boxes, the value of y is given by;
y = kx
y = 3(5)
y = 15 peaches.
Question 2:Also, we would determine the constant of proportionality (k) based on the given parameters:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 12/4 = 15/5
Constant of proportionality (k) = 3.
When x = 2 boxes, the value of y is given by;
y = kx
y = 3(2)
y = 6 strawberries.
When x = 8 boxes, the value of y is given by;
y = kx
y = 3(8)
y = 24 strawberries.
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I'm need help asap! i dont get the question, i would appreciate it if somebody could help me( giving brainilest & 20 points)!!!
Look at picture below
Answer:
81/100 is the answer I believe if I'm wrong my bad
Answer:
81/100
Step-by-step explanation:
brainliest pls
Use the distributive property to simplify each expression.
-2(x - 2) + 5x
please help
Answer:
3x + 4
Step-by-step explanation:
Using the distributive property simply means that when there is a number in front of a pair of parentheses, every value inside the parentheses is multiplied by the co-efficient to expand the parentheses.
Here, the coefficient is -2, therefore we multiply both terms inside the parentheses (x and -2) by -2 to expand them:
-2(x - 2) + 5x
= (-2)(x) + (-2)(-2) + 5x
Now we simply evaluate and combine like terms to simplify:
= -2x +4 +5x
= 3x + 4
can somebody please help me solve this question:
you are going to climb the roof of your two-story house using a 15-foot ladder. If the safety directions say that you can put the ladder only 2 feet from the house, how far up will you be able to reach on your house?
thanks
Using Pythagoras theorem to solve the right angle triangle, the height of the building is 14.87 feet
What is Pythagoras TheoremPythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as an equation:
x² = y² + z²
where x is the hypothenuse and y, z are the legs of the right angle triangle.
To determine the height of the building in which the ladder will reach, we have to use Pythagoras theorem for that.
x² = y² + z²
15² = 2² + z²
z² = 15² - 2²
z² = 221
z = √221
z = 14.87 feet
The height is 14.87 feet
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Using the following equation, find the center and radius of the circle. You must show and explain all work and calculations to receive credit. Be sure to leave your answer in exact form.
x^2+y^2+8x-6y-15=0
The answers for Center of the circle is (-4,3) and radius is 2√10 units.
How to find the Center of the circle using Algebraic Expressions?(x - h)2 + (y - k)2 = r2 is the equation of the center of the circle. The radius (r) is specified as 5 units, while the center's (h, k) coordinates are (0, 0). (x - 0)2 + (y - 0)2 = 52 is the result of substituting the values of h, k, and r in the equation.
How to simplify Algebraic expressions?Finding the simplified term of the given expression is the goal of simplifying the algebraic statement. We must first understand how to join like terms, factor a number, and the order of operations before we can factorize or simplify the statement. When like words are combined, the constant terms are divided for the purpose of simplicity and the variables with the same degree are grouped together.
Examples of Algebraic Expressions
2x2+3xy+4x+7
Given,
[tex]x^2+y^2+8x-6y-15=0[/tex]
⇒ x².+8x+16–16+y²-6x+.9–9–15=.0
(x+4)²+(y-3)²-16–9–15=0
I.e. (x+4)²+(y-3)²=40
(x+4)²+(y-3)²={2√10}²
Hence center is (-4,3) and radius is 2√10 units.
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Anybody know the answer to this ?
On solving the provided question, we can say that - the data from graphs represents a curvilinear and straight graph.
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
Here,
in graphs,
as per data we can say that there two types
one is curvilinear and other is straight graph.
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Find whether x^n+y^h is disable by x-y(y not equal o)or not
What does 2 equivalents mean in chemistry?
An equivalent is the amount of a substance that reacts with an arbitrary amount of another substance in a given chemical reaction.
Arbitrary
It is a relative unit of measurement to show the ratio of amount of substance, intensity, or other quantities, to a predetermined reference measurement.
chemical reaction
chemical reaction is a process in which one or more substances, the reactants, are converted to one or more different substances, the products. Substances are either chemical elements or compounds.
Examples of chemical changes include baking soda and vinegar creating carbon dioxide, iron rusting, and wood burning.
There are five types of general chemical reactions: Combination or synthesis, decomposition, single displacement, double displacement, and combustion.
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Solve the system of equations.
y = 3x
y=x²-4
A. (-1, -3) and (4, 12)
O B. (-4, 12) and (1, -3)
C. (-1, 3) and (4, -12)
OD. (-4,-12) and (1, 3)
Answer:
A
Step-by-step explanation:
Se them equal to each other
3x = [tex]x^{2}[/tex] - 4
[tex]x^{2}[/tex] -3x -4 = 0
(x + 1) ( x -4)
x + 1 = 0
x = -1
y = 3x
y = 3(-1)
y = -3
(-1,-3)
x - 4 = 0
x = 4
y = 3x
y = 3(4)
y = 12
(4, 12)
Write a polynomial function in standard form
-6,0,0,2
Points D, B, and E are collinear. Find the value of a so that points A, B, and C
are collinear.
Answer:
Since A, O and B are collinear,
i.e.,
∠
A
O
B
=
180
∘
or,
∠
A
O
D
+
∠
D
O
C
+
∠
B
O
C
=
180
∘
(
x
−
10
)
∘
+
(
4
x
−
25
)
∘
+
(
x
+
5
)
∘
=
180
∘
Or,
x
+
4
x
+
x
−
10
∘
−
25
∘
+
5
∘
=
180
∘
Or,
6
x
−
30
∘
=
180
∘
Or,
6
x
=
180
∘
+
30
∘
=
210
∘
Or,
x
=
210
∘
6
=
35
∘
∠
B
O
C
=
x
+
5
∘
=
35
∘
+
5
∘
=
40
∘
Aisha has 50 chocolates she fills 3 boxes and has 2 left over How many chocolates does she have left? Write it as an equation
Aisha has 2 chocolates left. You can represent the problem as an equation as follows:
x = 3b + 2Where x is the total number of chocolates, b is the number of boxes filled and 2 is the remaining chocolates left.
Since we know that Aisha has 50 chocolates, we can substitute this value for x in the equation:
50 = 3b + 2
Solving for b, we find that b = 16. So, Aisha filled 16 boxes and had 2 chocolates left over. The equation is true, and Aisha has 2 chocolates left.
It's worth noting that this is a simple algebraic equation, we can use the same equation to find the number of chocolates given the number of boxes and remaining chocolates, or to find the number of boxes given the number of chocolates and remaining chocolates or to find the remaining chocolates given the number of boxes and the number of chocolates.
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Dollhouse furnishing comes in different sizes depending on the size of the dollhouse. Write a ratio of the size of the dollhouse item to the size of the larger item.
dollhouse sofa: 1 1/2 in. Long
real sofa: 6 ft long
The ratio of the size of the dollhouse item to the doll house is 14 : 9.
What are ratios?
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio.
A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as 1: 3 (for every one boy, there are three girls), which means that 14 of the population is made up of boys and 34 of the population is made up of girls.
The ratio is a mathematical expression that can be used to represent one item as a percentage of another.
First convert feet to inches
1 feet = 12 inches
12 x 6 = 72 inches
dollhouse item : doll house
112 : 72
14 : 9
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