if Grandson Sinko puts the forks in groups of 12, there will be no forks left over
Define least common multipleThe least common multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of each of the given integers. In other words, the LCM is the smallest number that is divisible by all the numbers in a given set.
the least common multiple of 4 and 6, is 12. So if Grandson Sinko puts the forks in groups of 12, there will be no forks left over.
To find the number of forks, we can use the fact that the number of forks is three more than a multiple of both 4 and 6. Let's call the number of forks x. Then we have:
x ≡ 3 (mod 4)
x ≡ 3 (mod 6)
Using the Chinese remainder theorem, we can combine these congruences to get:
x ≡ 3 (mod 12)
This means that the number of forks is three more than a multiple of 12. So we can write:
x = 12n + 3
where n is an integer. To find the value of n, we can plug in the values of x from the first two congruences:
x ≡ 3 (mod 4) => x = 4m + 3
x ≡ 3 (mod 6) => x = 6k + 3
Setting these two expressions for x equal to each other, we get:
4m + 3 = 6k + 3
Simplifying, we get:
2m = 3k
Since 2 and 3 are relatively prime, this means that m must be a multiple of 3 and k must be a multiple of 2. So we can write:
m = 3p
k = 2q
where p and q are integers. Plugging these into the expressions for x, we get:
x = 4m + 3 = 4(3p) + 3 = 12p + 3
x = 6k + 3 = 6(2q) + 3 = 12q + 3
Since x is the same in both expressions, we can set them equal to each other:
12p + 3 = 12q + 3
Simplifying, we get:
p = q
So we can write:
x = 12p + 3
where p is an integer. Therefore, if Grandson Sinko puts the forks in groups of 12, there will be no forks left over.
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Elaine is buying fabric for windows in her house. Each of her four windows is 35 inches wide and she needs to buy fabric equal to 2 1/2 times the width of the windows. How much fabric should she buy?
Elaine needs tο buy 350 inches οf fabric fοr her windοws.
What is fractiοn ?A fractiοn represents a part οf a number οr any number οf equal parts. There is a fractiοn, cοntaining numeratοr(upper value) and denοminatοr(lοwer value).
If each windοw is 35 inches wide, then the tοtal width οf fabric Elaine needs is:
Tοtal width = 4 windοws x 35 inches per windοw
Tοtal width = 140 inches
Fabric = 2 1/2 x Tοtal width
Tο simplify this, we can first cοnvert the mixed number tο an imprοper fractiοn: 2 1/2 = 5/2
Then, we can multiply this fractiοn by the tοtal width:
Fabric = 5/2 x Tοtal width
Substituting the value οf Tοtal width, we get:
Fabric = 5/2 x 140 inches
Fabric = 350 inches
Therefοre, Elaine needs tο buy 350 inches οf fabric fοr her windοws.
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What is the meaning of "cannot be all distinct"?
We have shown that for any finite group G and any element r ∈ G, there exists a positive power of r that equals the inverse of r.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.
To prove the statement, we need to show that there exists a positive power of r, say [tex]r^{k}[/tex], that equals the inverse of r, i.e., [tex]r^{k}[/tex], = [tex]r^{-1}[/tex].
Suppose all the powers of r are distinct, i.e., [tex]r^{n}[/tex]≠ [tex]r^{m}[/tex] for all n ≠ m in Z. Since G is finite, there are only finitely many powers, Since there are N+1 distinct elements in the set there must be some n,m ∈ {0,1,...,N} such that n < m and [tex]r^{n}[/tex] = [tex]r^{m}[/tex]
Without loss of generality, assume n < m. Then we have:
[tex]r^{n}[/tex] = [tex]r^{m}[/tex]
[tex]r^{m-n}[/tex]= 1
Let k = m - n > 0. Then we have:
[tex]r^{k}[/tex] = [tex]r^{m-n}[/tex]= 1
[tex]r^{-1}[/tex]= [tex]r^{(k-1)}[/tex]
Thus, [tex]r^{k}[/tex] = [tex]r^{(k-1)}[/tex], which is the desired result.
Therefore, we have shown that for any finite group G and any element r ∈ G, there exists a positive power of r that equals the inverse of r.
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At Layla's favorite restaurant, the price of supreme nachos is $13.50.After Layla adds a tip, the price of the item is $16.20. What is the percent of the tip?
Answer:After layla adds a tip, the price of the item is $16.20. The percent of the tip is 10 %
Step-by-step explanation:
What is a tip?
A tip is a gift or a sum of money placed or given for a service performed or anticipated, by extension, a form of gratuity. Even if the service is poor, it's recommended you leave at least 10 percent.
How to calculate a tip?
There are four ways of calculating a tip:
Method 1: Move over the decimal in the bill total and then double that number.
Method 2: Multiply the tax of the bill by two.
Method 3: Double the pretax bill and then move the decimal over one space.
Method 4: Determine 10% of the bill and add half
Which is the largest angle?
A4
OC
B
5
Cannot tell
OA
с
7
6
B
Find the Domain and Range.
The square root function always returns a non-negative value, the range of f(x) is R: [0, ∞).
What is domain?It is the set of values of the variable for which the function has a valid output.
According to question:To find the domain and range of the function f(x) = [tex]sqrt(x^2 - 49)[/tex], we need to consider the possible values of x that make the function well-defined and the corresponding values of f(x) that the function can take.
The function f(x) is defined if the argument inside the square root is non-negative, that is, [tex]x^2 - 49[/tex] ≥ 0. This inequality can be solved as:
(x - 7)(x + 7) ≥ 0
The solution to this inequality is x ≤ -7 or x ≥ 7, so the domain of the function is D: (-∞, -7] ∪ [7, ∞).
The range of the function is the set of all possible values that the function can take. Since the square root function always returns a non-negative value, the range of f(x) is R: [0, ∞).
Therefore, the correct answer is (B) D: (-∞, -7] ∪ [7, ∞), R: [0, ∞).
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Simplify: 5(y+2) +5(y-1)
Answer:
Step-by-step explanation:
To simplify 5(y+2) +5(y-1), we distribute the 5 to each term inside the parentheses, and then combine like terms as follows:
5(y+2) +5(y-1)
= 5y + 10 + 5y - 5 // Distribute the 5
= 10y + 5 // Combine like terms
Therefore, 5(y+2) +5(y-1) simplifies to 10y + 5.
The diagram shows the curve y = -x²-x+ 20.
(i) The curve cuts the x-axis at two points A and B, and the y-axis at the point C. Find the coordinates of A, B and C.
(ii) The point D(3, h) lies on the curve. Find the value of h.
Plotting the equation shows that the graph crosses the
y axis at A (-5, 0) and B (4, 0) and x axis at C (0, 20)The value of h is 8
How to find the value of hTo find the value of y when x is 3, we need to substitute 3 for x in the given equation -x^2 - x + 20:
y = -x^2 - x + 20 (substitute x = 3)
y = -(3)^2 - 3 + 20
y = -9 - 3 + 20
y = 8
Therefore, when x is 3, y is 8.
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How do u write a fraction for 6 and 10
The fraction for 6 and 10 is 6/10, which can be simplified to 3/5 by dividing both the numerator and denominator by their greatest common factor, which in this case is 2.
So 6/10 is equivalent to 3/5.
Blake collects stamps. He collected a total of 275 stamps. If 88% of the stamps he collected were foreign, how many other stamps did he collect?
If 88% of the stamps were foreign, then the remaining 12% must be domestic stamps.
To find out how many domestic stamps Blake collected, we can start by calculating what 12% of 275 is:
12% of 275 = 0.12 x 275 = 33
The remaining stamps are foreign stamps.
Therefore, Blake collected 33 domestic stamps.
I’m doing some homework and I completely forgot how to do perimeter since 5th. Just answer the first question so I can understand it againn :’)
Answer:
You can start by changing 12 3/4 into a decimal, which would be 12.75.
The formula for perimeter of a rectangle is (l + w) x 2, so you could write it like this:
(12.75 + 6.4) x 2
Then solve the question in the parenthesis...
19.15 x 2 = 38.30
Now, the question says to write the perimeter into simplest fraction form.
38.30 = 38 3/10.
So, there you have it!
38 3/10 meters
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Brian spent 20% of his savings on a bicycle and 15% of remainder on a book. What percentage of his savings did he have left?
Answer:65
Step-by-step explanation:
What is the meaning of "geometry tells us that following the symmetry about a straight line [tex]L[/tex] by the symmetry about a straight line [tex]{L}'[/tex] that intersects [tex]L[/tex] amounts to a rotation about the intersection by twice the angle from [tex]L[/tex] to [tex]{L}'[/tex]?
The statement can be linked to a theorem in geometry known as the "double angle rotation theorem". According to this theorem, if a geometric figure has symmetry about a straight line, and that line intersects another straight line at a point, then the symmetry of the figure about the second line is equivalent to a rotation of twice the angle from the first line to the second line, that is about the point of intersection.
What does the expression mean?In simple terms, the double angle rotation theorem means that if we can have a geometric figure that is symmetric about a line L1, and L2 is another line that intersects L1 at a point P, then we can rotate the figure about point P by twice the angle formed between L1 and L2 to get the same symmetry about the line L2.
The application of this theorem applies to various aspects of geometry that include transformational geometry and symmetry.
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A group of 10 students spent 813 minutes studying for an upcoming test. What prediction can you make about the time it will take 120 students to study for the test?
It will take them 1,626 minutes.
It will take them 6,775 minutes.
It will take them 7,963 minutes.
It will take them 9,756 minutes.
Answer:
It will take them 9756 minutes
Step-by-step explanation:
10 students take 813
How do you get from 10 to 120?
times 10 by 12
Now times 813 by 12
9756
I would really appreciate any help I can get. Thankyou!
The length of OI is 6.5 units. The solution has been obtained by using the Pythagoras theorem.
What is Pythagoras theorem?
Pythagoras' Theorem states that the square of a right-angled triangle's hypotenuse side is equal to the sum of the squares of its other two sides.
We are given a circle with two tangents drawn from a external point and the radius perpendicular to the tangent measures 3.9 units.
We know that the tangents when drawn from a external point are equal in length.
So,
IK = IJ = 5.2 units
Now, in triangle OJI, using the Pythagoras theorem, we get
⇒ [tex]OI^{2}[/tex] = [tex]OJ^{2}[/tex] + [tex]IJ^{2}[/tex]
⇒ [tex]OI^{2}[/tex] = [tex]3.9^{2}[/tex] + [tex]5.2^{2}[/tex]
⇒ [tex]OI^{2}[/tex] = 15.21 + 27.04
⇒ [tex]OI^{2}[/tex] = 42.25
⇒ OI = 6.5 units
Hence, the length of OI is 6.5 units.
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PLS HELP Triangle ABC
maps to triangle XYZ
by a rotation of 90∘
counterclockwise about the origin followed by a reflection across the line y=x.
In triangle ABC,
m∠A=45∘,
m∠B=55∘,
and m∠C=80∘.
What is the measure of ∠Y?
Enter your answer as the correct value, like this: 42
Based on the given information, the measure of angle Y is 30 degrees.
What is transformation?A transformation is a process or operation that changes the position, shape, or orientation of a geometric figure or an object in space.
There are several types of transformations, including:
Rotation: A transformation that rotates a figure around a fixed point, called the center of rotation, by a certain angle.
Reflection: A transformation that produces a mirror image of a figure across a line, called the line of reflection.
To start, let's first find the vertices of triangle XYZ after the given transformations:
Rotation of 90 degrees counterclockwise about the origin:
The rotation of point (x, y) by 90 degrees counterclockwise about the origin gives us the point (-y, x). So we can apply this transformation to each vertex of triangle ABC to get the vertices of triangle XYZ after rotation:
A = (cos(45), sin(45)) = (√2/2, √2/2) → A' = (-√2/2, √2/2)
B = (cos(55), sin(55)) → B' = (-sin(55), cos(55))
C = (cos(80), sin(80)) → C' = (-sin(80), cos(80))
Reflection across the line y=x:
To reflect a point (x, y) across the line y=x, we simply swap the x and y coordinates to get (y, x). So we can apply this transformation to each vertex of triangle XYZ to get the final vertices:
A'' = (√2/2, -√2/2)
B'' = (cos(55), -sin(55))
C'' = (cos(80), -sin(80))
Now we can use the law of cosines to find the measure of angle Y:
cos(Y) = [B''C''² + A''C''² - A''B''²] / [2 * B''C'' * A''C'']
= [cos(55)² + cos(80)² - (√2/2)²] / [2 * cos(55) * cos(80)]
≈ 0.866
So we have cos(Y) = 0.866, which means Y ≈ 30 degrees. Therefore, the measure of angle Y is approximately 30 degrees.
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Helpppppp
The fox population in a certain region has a continuous growth rate of 5 percent per year. It is estimated that the population in the year 2000 was 12500.
(a) Find a function that models the population t years after 2000 (t=0 for 2000).
Your answer is p(t)=-----------
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer)----------------
a. The function that models the fox population t years after 2000 is:
[tex]p(t) = 12500 * e^{(0.05t)[/tex]
b. The estimated fox population in the year 2008 is 19121 (rounded to the nearest integer).
What are Functions?Amοng the crucial kinds are: When there is a mapping fοr a range fοr each dοmain between twο sets, this is knοwn as an injective functiοn οr οne tο οne functiοn. When mοre than οne element is transferred frοm dοmain tο range, the functiοn is said tο be surjective οr tο be an οntο functiοn
(a) Since the fox population has a continuous growth rate of 5% per year, the population can be modeled using the exponential growth formula:
[tex]p(t) = p(0) * e^{(rt)[/tex]
where p(0) is the initial population, r is the continuous growth rate (expressed as a decimal), t is the time elapsed in years, and e is the mathematical constant e ≈ 2.71828.
Using the given information, we have:
p(0) = 12500 (the population in the year 2000)
r = 0.05 (the continuous growth rate)
Therefore, the function that models the fox population t years after 2000 is:
[tex]p(t) = 12500 * e^{(0.05t)[/tex]
(b) To estimate the fox population in the year 2008, we need to find the value of p(8) using the function from part (a):
[tex]p(8) = 12500 * e^{(0.05*8)} = 19121[/tex]
Therefore, the estimated fox population in the year 2008 is 19121 (rounded to the nearest integer).
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Find the value of x
Answer:
32°
Step-by-step explanation:
2x + 1 + x - 7 = 90
3x + 1 - 7 = 90
3x - 6 = 90
3x = 96
x = 32
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Answer:
[tex]\mathrm{x=32^o}[/tex]Step-by-step explanation:
Value of x:-
[tex]\mathrm{(2x+1)+(x-7)=90^o}[/tex]
[tex]\mathrm{2x+1+x-7=90}[/tex]
[tex]\mathrm{(2x+x)+(1-7)=90}[/tex]
** [tex]\mathrm{2x+x=\bf 3x}[/tex]
** [tex]\mathrm{1-7=\bf -6}[/tex]
[tex]\mathrm{3x-6=90}[/tex]
[tex]\mathrm{3x-6+6=90+6}[/tex]
[tex]\mathrm{3x=96}[/tex]
[tex]\mathrm{\cfrac{3x}{3}=\cfrac{96}{3}}[/tex]
[tex]\mathrm{x=32}[/tex]
Therefore, the value of x is 32°.
____________________
Hope this helps!
The cost of joining a gym includes an initial fee of $25 and then $2 per visit. Which linear equation represents the cost of visiting the gym x times?
The linear equation that represents the cost of visiting the gym x times is: y = 2x + 25
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.
The cost of joining a gym includes an initial fee of $25 and then $2 per visit. Let y be the total cost of visiting the gym x times.
To find the equation that represents this relationship, we need to determine the slope and the y-intercept.
The slope represents the rate of change of the cost with respect to the number of visits, which is the cost per visit. Since the cost per visit is $2, the slope is 2.
The y-intercept represents the initial cost of joining the gym, which is $25.
Therefore, the linear equation that represents the cost of visiting the gym x times is: y = 2x + 25
In this equation, x represents the number of visits to the gym, and y represents the total cost of those visits.
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How can we multiple 4/9and6/7
By dividing the numerator and denominator by their 3 greatest common factor, the resultant fraction is 8/21 .
what is fraction ?To express a portion of a whole or the division of a quantity, use a fraction. It consists of a horizontal or slant line separating the two integers that make up the numerator and denominator. The total quantity of components in the whole is represented by the denominator, while the numerator is the number of equal parts that are being taken into account. As an illustration, the numerator and denominator of the fraction 3/4 are 3 and 4, respectively. Parts of a set, chunks of a pie, and ratios between quantities can all be represented using fractions. Using particular guidelines and algorithms, they can be multiplied, divided, added, or subtracted. To make calculations and comparisons simpler, fractions can be changed to decimals or percentages.
given
We combine the numerators and denominators together to multiply two fractions. So:
(4/9) x (6/7) = (4 x 6) / (9 x 7) = 24/63
By dividing the numerator and denominator by their 3 greatest common factor, the resultant fraction can be made simpler:
24/63 = (3 x 8) / (3 x 21) = 8/21
Because of this, 4/9 x 6/7 Equals 8/21.
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Fill in the blanks. Then, choose the property of addition you used.
(a)
(b)
(c)
0 + 0 = 7
7 + 0 = 2 + 7
(5 + 7) + 5+ (7 + 3)
=
(Choose one)
(Choose one)
(Choose one)
Answer:
(a) 7
(b) 7
(c) 27
The property of addition used in all three equations is the associative property, which allows us to regroup the numbers being added without changing their sum.
1. You want to take out a $210,000 mortgage (home loan). The yearly interest rate
on the loan is 6%, and the loan is for 30 years. How much will your monthly
payment be? Answer= 1265.05
2. For the loan in problem #1, how much will you pay over the life of the loan? How
much interest will be paid over the life of the loan
So, for part b. I had got the answer 77 but it came back incorrect. I need help for this math problem.
This test is left-tailed and the test statistic is -1.53
What type of test is given?Since the alternative hypothesis is that less than 10% of treated subjects experienced headaches, and this is a lower bound, the test is left-tailed.
To find the test statistic, we first need to calculate the expected number of subjects who would experience headaches if the null hypothesis were true (i.e., if the true proportion were 10%). This is found by multiplying the total number of treated subjects by the hypothesized proportion:
Expected number of subjects with headaches = 0.10 * 288 = 28.8
We then use the formula for the z-score of a sample proportion:
z = (p - P) / √(P(1 - P) / n)
where p is the sample proportion (21/288), P is the hypothesized proportion (0.10), and n is the sample size (288).
Plugging in the values, we get:
z = (0.073 - 0.10) / √(0.10 * 0.90 / 288) = -1.53
Therefore, the test statistic is z = -1.53.
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Which of the following pairs show(s) triangles that are similar bu ΔΔΔΔΑ CA and C only CB only C A, B, and C B and C only
It be concluded that figure A and figure C are showing similar triangle but they are not congruent.
What is similar triangle?If two triangles are similar then they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are said to be similar figures.
Similarity of two triangles mean when two triangles satisfy the AAA property that is when three angles of one triangle is equivalent to angles with another triangle.
Here for the figure A and C they satisfy the AAA property.
Hence it be concluded that figure A and figure C are showing similar triangle but they are not congruent. The triangles have same shape but not in same size.
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Select one of the answer choices hurry asap
Help with math problems
The required solution of the given inequality is {m | 6 ≤ m < 9}.
What is inequality?In mathematics, inequality is a statement of an order relationship between two numbers or algebraic expressions that is greater than, greater than or equal to, less than, or less than or equal to.
According to question:
We can solve the inequality as follows:
3 + m ≥ 9 or 1 + 2m < 19
Subtracting 3 from both sides of the first inequality, we get:
m ≥ 6
Subtracting 1 from both sides of the second inequality and then dividing by 2, we get:
m < 9
Putting these two inequalities together, we get:
6 ≤ m < 9
This is the solution in interval notation. To write it in set-builder notation, we can use the following notation:
{m | 6 ≤ m < 9}
This means the set of all values of m such that m is greater than or equal to 6, and less than 9.
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HELP!!!
What is m∠EFG?
The measurement of angle EFG is 42.
The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. A circle can be divided into sectors by using the central angle. An excellent illustration of a central angle is a pizza slice. A pie chart is made up of several sectors and is useful for representing various amounts.
A straightforward illustration of a sector with a center angle of 180o is a protractor. The angle created by a circle's arc at its center is another way to describe the term "central angle."
We have a circle with center H and the central angle is 84 degrees
The central angle of the circle is double of circumference angle.
Then the measurement of angle EFG is 42.
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# 21 i
Find the area of the regular polygon. Round your answer to the nearest hundredth.
7.6
5.2
The area of the regular polygon and rounded to the nearest hundredth is 200 sq. units.
How to find the area of any polygon?
Area of Regular Polygon Formula = [tex]\frac{l^2n}{4tan\left(\frac{180}{n}\right)}[/tex] Square units
Length of side of the regular polygon is 5.2 and have n= 9 sides
Let's say, Area is A for the polygon,
[tex]A = \frac{(5.2)^2 \times 9}{4 tan\left(\frac{180}{9}\right)}\\\\A= 167.16\ sq.\ units\\A= 200\ sq.\ units\ (round-off\ to\ nearest\ hundred)[/tex]
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area is approximately 158.72 square centimeters
how to find the area of a regular octagon?To find the area of a regular octagon with a given side length and apothem, we can use the formula:
Area = (1/2) × Perimeter × Apothem
where Perimeter is the total length of all the sides of the octagon.
We are given that the side length of the octagon is 5.2 cm and the apothem is 7.6 cm.
To find the perimeter of the octagon, we can use the fact that the octagon is a regular polygon and has eight equal sides. Thus:
Perimeter = 8 × side length = 8 × 5.2 cm = 41.6 cm
Now we can substitute the values we have into the formula to get:
Area = (1/2) × Perimeter × Apothem
Area = (1/2) × 41.6 cm × 7.6 cm
Area = 158.72 cm²
Therefore, the area of the regular octagon with a side length of 5.2 cm and an apothem of 7.6 cm is approximately 158.72 square centimeters.
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In the figure above, what is the value of x ?
A) 45
B) 90
C) 100
D) 105
Answer:
D) 105
Step-by-step explanation:
All 4 side shape's interior angle add up to 360
360 - 45 = 315
315 / 3 = 105
I have a math ? and i dont know what it is
The terrarium has 594 cm³ volume of dirt.
What is volume?
Given the dimensions of the terrarium as h=12cm, l=22cm, and b=9cm, we can calculate the volume of the terrarium as follows:
Volume of terrarium = length x width x height
= 22 cm x 9 cm x 12 cm
= 2,376 cm³
Since the terrarium is filled 1/4 of the way with dirt, the volume of dirt is:
Volume of dirt = (1/4) x Volume of terrarium
= (1/4) x 2,376 cubic cm
= 594 cm³
Therefore, the terrarium has 594 cubic centimeters of dirt.
what is terrarium?
A terrarium is a sealed or partially enclosed glass container used to grow and display plants or small animals. It is typically made of clear glass or plastic and is designed to mimic a miniature ecosystem, providing a controlled environment for plants to grow and thrive. Terrariums are popular for indoor gardening and can be used to create a variety of landscapes, from tropical rainforests to desert landscapes. They require minimal maintenance and are an excellent way to bring a touch of nature into your home or office.
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Complete question is: A terrarium is filled 1/4 of the way with dirt. the terrarium have 594 cubic centimeters of dirt.
1. Name a minor arc.
2. Name a major arc.
3. Name a point of tangency.
4. Name a radius.
answer the 1,2,3,4 question in image
Answer: What is minor arc and major arc?
Image result for 1. Name a minor arc. 2. Name a major arc. 3. Name a point of tangency. 4. Name a radius.
Every pair of endpoints defines two arcs. An arc whose measure is less than 180 degrees is called a minor arc. An arc whose measure is greater than 180 degrees is called a major arc. An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two.
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