If all 4 posts are painted, 44 square feet must be painted.
We know that the formula for the surface area of the cylinder is:
A = 2πrh + 2πr²
Here, the dimensions of the each cylindrical post:
the diameter d = 1 foot and the height is 3 feet high.
So, the radius r = 0.5 ft and height h = 3 ft
Let us assume that the surface area of one post be A₁
Using above formula of surface area of cylinder,
A₁ = 2πr(h + r)
A₁ = 2 × π × 0.5 × (3 + 0.5)
A₁ = 2 × 3.14 × 0.5 × (3.5)
A₁ = 10.99
A₁ ≈ 11 sq.ft.
So, the total surface area of 4 cylindrical posts would be,
A = 4 × A₁
A = 4 × 11
A = 44 sq.ft.
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Plsssss help and show work
The vertex form of quadratic equation is y = a(x - 0)² + 7 and the standard form of quadratic equation is y = 0x² + 7
What do you mean by Vertex form?The vertex form of a quadratic equation is an equation written in the form:
f(x) = a(x - h)² + k,
where (h, k) is the vertex of the parabola represented by the equation. The variable x represents the input value, f(x) represents the output value, a represents the coefficient of the x² term, h represents the x-coordinate of the vertex, and k represents the y-coordinate of the vertex. The vertex form of a quadratic equation is useful for easily identifying the location and shape of the parabola represented by the equation, especially if the parabolic function has a vertex that is not at (0,0).
The vertex form of a quadratic equation is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
To find the vertex form of this equation, we need to find the vertex first. To do this, we can average the x-values of the maximum and minimum points in the table, which gives us the x-coordinate of the vertex. In this case, the maximum and minimum points are (1, 7) and (-1, -9), so the x-coordinate of the vertex is (1 + -1)/2 = 0.
Next, we can find the y-coordinate of the vertex by evaluating f(0), which gives us 7.
So, the vertex of the parabola is (0, 7).
Using this information, we can write the vertex form of the equation:
y = a(x - 0)² + 7
To find the standard form of the equation, we need to expand the vertex form and simplify.
y = a(x² - 0x) + 7
y = ax² + 7
We can then find the value of a by using any one of the points in the table. Let's use the point (1, 7):
7 = a(1²) + 7
7 = a + 7
a = 0
So, the standard form of the equation is:
y = 0x² + 7
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A company manufactures computer memory chips as circular silicon wafers with a diameter of 10 inches. The wafers are cut into different sized sectors. Match each wafer's central angle to the area of that sector.
The area and the angle are matched as below.
Area Angle
25/8 π in² = 45°
25/18 π in² = 20°
25/36 π in² = 10°
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
Diameter = 10 in
Radius = 5 in
Area of the circle in sector = 360°
πr² = 360
π x 5² = 360
25π in² = 360° _____(1)
Now,
From (1),
25π in² = 360°
Divide both sides with 8.
25/8 π in² = 45°
From (1),
25π in² = 360°
Divide both sides with 18.
25/18 π in² = 20°
From (1),
25π in² = 360°
Divide both sides with 36.
25/36 π in² = 10°
Thus,
Area Angle
25/8 π in² = 45°
25/18 π in² = 20°
25/36 π in² = 10°
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A bookcase is to have 4 shelves including the top as pictured below.
The width is to be 10 feet less than 3 times the height. Find the width and the
height if the carpenter expects to use 30 feet of lumber to make it.
The scatter plot and line of best fit below shows the length of two peoples femur (the long leg bone in thigh) and their height in centimeters. Based on the line of best fit, what would be the predicted femur length for someone with a height of 218 cm.
The predicted femur length is 69 cm
How to determine the predicted femur lengthFrom the question, we have the following parameters that can be used in our computation:
The scatter plot
On the scatter plot, we have
x = the length of two peoples femur (the long leg bone in thigh)
y = height in centimeters
So, we have
Height = 218 cm
From the graph, we have
x = 69
Hence, the femur length is 69 cm
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8
Helen thinks of two numbers.
The Highest Common Factor (HCF) of her two numbers is 5
The Lowest Common Multiple (LCM) of her two numbers is a multiple of 12
Write down two possible numbers that Helen could be thinking of.
As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.
what is HCF ?The biggest integer that is able to divide two or more quantities is known as the highest common factor (HCF) or greatest common factor. Highest refers to the biggest or greatest number. The sharing a common meaning of two or more integers. Feature is an integer that can be used to divide a whole number (a divisor). Write each integer as the sum of one's main characteristics in step one. Step 3: The HCF of said given integers is the greatest number that can be found among the common factors.
given
1. It is assumed that when Helen thinks of two numbers, they have corresponding HCF and LCM values of 5 and 12.
2. The smallest common multiple shared by two numbers is referred to as the least common number.
LCM of 4 and 6 is 12, for instance.
3. The highest number that divides the two selected numbers, leaving a residue of 0, is referred to as the highest common factor.
HCF of 6 and 8 is 2, for instance.
4. Given that the LCM of Helen's two chosen numbers is 12, even multiples of 12 are the two numbers' common multiples. In light of this, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so forth.
5.The only numbers that may be divided by 5 are 60 and 120. All other numbers have HCF values other than 5. 60 and 120 have an HCF of 60, but not 5.
As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.
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A small country emits 92,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 5% per year for the next 15 years. In the first year of the agreement, the country will keep its emissions at 92,000 kilotons and the emissions will decrease 5% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 15 year period, to the nearest whole number?
Answer:
To calculate the total amount of carbon dioxide emitted over the course of 15 years, we can start with the initial amount of 92,000 kilotons and multiply by 0.95 (the reduction factor) each year.
Step-by-step explanation:
Year 1: 92,000 kilotons
Year 2: 92,000 * 0.95 = 87,400 kilotons
Year 3: 87,400 * 0.95 = 82,990 kilotons
and so on, until year 15.
To find the total amount of carbon dioxide emitted over the course of 15 years, we need to sum up the emissions for each year:
92,000 + 87,400 + 82,990 + ... + (92,000 * 0.95^14) = 92,000 * (1 + 0.95 + 0.95^2 + ... + 0.95^14)
This is a finite geometric series and can be calculated using the formula for the sum of a finite geometric series:
S = a * (1 - r^n) / (1 - r),
where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.
For this series, a = 92,000, r = 0.95, and n = 15. Plugging these values into the formula, we get:
S = 92,000 * (1 - 0.95^15) / (1 - 0.95)
S = 92,000 * (1 - 0.556774) / 0.05
S = 92,000 * 0.443226 / 0.05
S = 92,000 * 8.86452
S = 814,178.24 kilotons
Rounding to the nearest whole number, the country would emit 814,178 kilotons of carbon dioxide over the course of 15 years.
A. 829.6 mi³
B. 891.6 mi³
C. 437.8 mi³
D. 694.8 mi³
Answer:
b
Step-by-step explanation:
The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²
What is the greatest common factor between 18 and 30 and 54
Answer: 1, 2, 3, 6, 1
Step-by-step explanation:
When listing all the factors for 18, 30 ,54....
18 , 30 , 54 to find the common factors. The common factors for 18,30,54 18 , 30 , 54 are 1,2,3,6 1 , 2 , 3 , 6 . The GCF (HCF) of the numerical factors 1,2,3,6 1 , 2 , 3 , 6 is 6 .
( Hope this helps )
HELLP PLEASE!!!! I WILL MARK BRAINLIEST!!!
Answer:
No Solution.
Step-by-step explanation:
To solve for x in this equation, we need to simplify both sides of the equation and make them equal.
Starting with the left-hand side:
5 + x - 14 = x - 7
Adding 14 to both sides:
5 + x = x + 7
Subtracting x from both sides:
5 = 7
5 does not equal 7.
Therefore, the value of x is no solution.
Answer:
there is no solution for this, if you solve you will get 0=2 (This is also called a contradiction)
Step-by-step explanation:
5+x-14=x-7
5-14 = -9
-9+x=x-7
x-9=x-7
+9 +9
x=x+2
-x -x
0 = 2
the students in mr. juarez's homeroom collected more cans than students in ms. wade's homeroom. write an expression that represents how many more cans were collected.
The expression that can represent how many more cans were collected is 8n - 7 > 6n + 3, which is in fact an inequality.
An inequality in math is an algebraic expression that represents, well, inequality. It shows a relationship between two values or expression, which aren't equal to each other. It is used to compare two values/expression, showing if one is greater than, less than, or simply not equal to another. Thus, we would use a mathematical symbol of <, >, ≤, ≥, or ≠ to express an inequality.
Since students in Mr. Juarez's homeroom collected more cans than students in Ms. Wade's homeroom do, you can use the symbol > in your inequality. The number of cans collected in Mr. Juarez's homeroom is 8n − 7, while the number of cans collected in Ms. Wade's homeroom is 6n + 3. Therefore, your inequality would be 8n - 7 > 6n + 3.
This question is missing some parts, which are most probably these:
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a mean computed in such a way that each data value is given a weight reflecting its importance is referred to as a(
A mean computed in such a way that each data value is given a weight reflecting its importance is referred to as A weighted mean.
The weighted mean is defined as a type of mean that is calculated by multiplying the weight associated with a particular event or outcome and the associated with the quantitative outcome and then summarizing all the products together.
For each data point to contribute equally to the final mean, some data points contribute more weight than others.
The weighted mean is calculated by multiplying the weight with the quantitative outcome and adding all the products.
weighted average= The sum of variables/sum of all weights.
if the variables are denoted by x and their weights are denoted by y, then we have:
Weighted average = Σ(xy)/Σy
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Which interval notation represents the set of all number greater than or equal to 1
and less than 6?
Answer:
The interval notation for the set of all numbers greater than or equal to 1 and less than 6 is [1, 6).
Step-by-step explanation:
Find the value of each variable on the triangle
One side x one side y one side 13 and the measurement is 45 degrees
Value of variable x = 13/√2
Value of variable y = 13/√2
What is trigonometric ratio?Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
Given,
In the right triangle ABC
AC = 13
AB = x
BC = y
∠C = 45°
Sin 45° = AB/AC
1/√2 = x/13
x = 13/√2
AB = 13/√2
Tan 45° = AB/BC
1 = (13/√2)/y
y = 13/√2
BC = 13/√2
Hence, 13/√2 is the value of both variables x and y.
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(PLEASE HEEEEEEEEELP!!!!!)
I NEED TO KNOW
What does 1 + 1 equal?
(A) 11
(B) 1
(C) 16
(D) 1/8
I WILL MARK BRANLIEST
Value of expression 1 + 1 = 2
What is addition?Addition is the process of adding two or more items together. In math, addition is the method of calculating the sum of two or more numbers.
Given expression,
1 + 1
+ is sign of Addition, Adding the numbers,
1 + 1 = 2
Hence, 2 is the value of expression 1 + 1.
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If a regular octahedron has a surface area of 32 square inches what is the surface area of each face?
The surface area of each face is 4 square inches.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
A regular octahedron has a surface area of 32 square inches.
That means
all sides are equal.
The surface area of each face is,
= 32/8
= 4 square inches.
Therefore, the required area is 4 square inches.
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Which fraction of the whole circle is this sector?
Answer: 23/72
Step-by-step explanation:
180 degrees = half of circle
5 degrees = 1/72 of circle
5 degrees times 23 = 115 degrees
1/36*23 = 23/72
Answer:
23/72 of a circle
Step-by-step explanation:
4×sector=circle
90÷360=1/4
so,
115/360=23/72
Find the mean of these numbers:
2,6,9,56,63,68
Explanation:
First we add up those numbers
2+6+9+56+63+68 = 204
Then divide by 6 because there are 6 values in this list.
204/6 = 34
Answer:34
Step-by-step explanation:It's obtained by simply dividing the sum of all values in a data set by the number of values.
what are the measures of the angels in the right triangles formed by the two regular pentagons are
The measures of the angles in the right triangle formed by the two regular pentagons are 18 degrees and 72 degrees.
Right triangles and regular pentagonsThe interior angles of a regular pentagon measure 108 degrees each. Therefore, if we have two regular pentagons, the right triangle formed by the two pentagons will have two angles that are equal to 108 degrees each.
These two angles are the complement of each other, meaning they add up to 90 degrees. Therefore, one of the angles in the right triangle formed by the two pentagons is 72 degrees, and the other is 18 degrees.
So, the measures of the angles in the right triangle formed by the two regular pentagons are 18 degrees and 72 degrees.
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I need some help ! The options are 25,50,65,130
Answer:
XZ=65
Step-by-step explanation:
so half of the circle would be 180
we need XZ and we know that YW+WX+XZ= 180
we also know that WX and YZ are parallel
WX=50
YW=XZ
YW+XZ=2XZ
WX+2XZ=180
50+2XZ=180
2XZ=130
XZ=65
Answer:
25
Step-by-step explanation:
diameter YZ = 50
OZ = OX = 25
thus, mXZ= 25
Subtract and reduce to lowest terms: 3 1/4 - 1 1/8
A. 2 1/8
B. None
c. 2 0/4
d. 17/8
The correct answer is option A. 2 1/8 when reduced to the lowest terms.
To subtract 3 1/4 - 1 1/8, we need to convert the fractions to a common denominator. The common denominator for 3 1/4 and 1 1/8 is 8. To convert 3 1/4 to 8, we multiply both the numerator and denominator by 2, resulting in 6/8. To convert 1 1/8 to 8, we multiply both the numerator and denominator by 8, resulting in 8/8.
Now we have two fractions with a common denominator of 8. To subtract them, we subtract the numerators and keep the same denominator. We have 6/8 - 8/8, which is -2/8. To reduce this fraction to the lowest terms, we divide the numerator and denominator by the greatest common factor (GCF), which is 2. -2/8 divided by 2 is -1/4. Finally, we add -1/4 to 1 1/8 to get the answer 2 1/8.
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Bacteria can multiply at an alarming rate when each bacterium splits into two new cells, thus doubling. If a single bacterium is discovered at 9 a.m. and doubles every hour, how many bacteria will there be at the end of the day (midnight)? Write an equation and show the calculations that represent this situation.
The equation we get for the amount of bacteria with with time T
T(t)=15×2ⁿ where n is the number of hours.
What are exponents?Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.
Given here: A certain type of bacteria doubles every hour
Now number of hours between 9-12 pm
is 15 hours
if at 9 a.m the amount of bacteria is x then we have in 15 hours
at t=1 we have the number of bacteria was
T=2×15
=30
Similarly we have for t=15 we get
T=15×2¹⁵
Hence, The equation we get for the amount of bacteria with with time T
T(t)=15×2ⁿ where n is the number of hours.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The two sequences of transformations of ΔABC that exhibit the congruence between the two triangles include the following:
A. a rotation of 180° about the origin and a translation of 1 unit left.
E. a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit left.
What is a rotation?In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:
(x, y) → (-x, -y)
Point A = (-6, 2) → Point A' = (-(-6), -(2)) = (6, -2).
By translating the pre-image of triangle A'B'C' horizontally left by 1 unit, the coordinate A" of the image of triangle A'B'C' include the following:
(x, y) → (x - 1, y - 7)
Coordinate A' = (6, -2) → Coordinate A'' (6 - 1, -2) = (5, -2)
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what is the length of the line? the first quadrant of an x- y- coordinate plane. a line segment extends from two, eight to twelve, two.
The length of the line segment is approximately 12.04 units. This formula calculates the distance between two points, (x1, y1) and (x2, y2), on the line segment. The formula is as follows: d = √((x2 - x1)^2 + (y2 - y1)^2)
The length of a line segment in a two-dimensional x-y coordinate plane can be found using the distance formula. This formula calculates the distance between two points, (x1, y1) and (x2, y2), on the line segment. The formula is as follows:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the line segment extends from the point (2, 8) to the point (12, 2). By plugging these values into the formula, we find that:
d = √((12 - 2)^2 + (2 - 8)^2) = √(100 + 36) = √136 = 12.04
So, the length of the line segment is approximately 12.04 units. This formula is useful for finding the distance between any two points in a two-dimensional plane and can be used in various fields such as geometry, physics, and engineering. The formula is based on the Pythagorean theorem, which 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.
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Complete question:
What is the length of the line segment in the first quadrant of an x-y coordinate plane that extends from (2, 8) to (12, 2)?
Answer:
its D 136
Step-by-step explanation:
khan
or
Watch a video
Find the cosine of ∠U.
28
45
53
U
V
T
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
Cosine of ∠U is 28/53 in proper fraction, 28/53 in improper fraction, 0.52609 in whole number.
The cosine of an angle in a right triangle can be found using the ratio of the adjacent side to the hypotenuse. In this triangle, the adjacent side to ∠U is 28 and the hypotenuse is 53.
cos(∠U) = adjacent side ÷ hypotenuse = 28 ÷ 53 = 28/53
So, the cosine of ∠U is 28/53, written as a proper fraction.
Now let's convert cosine of ∠U is 28/53 in improper fraction:
The cosine of ∠U, which is 28/53, can be expressed as an improper fraction by dividing both the numerator and denominator by their greatest common factor.
gcd(28, 53) = 1, so the fraction cannot be further simplified.
Therefore, the cosine of ∠U, expressed as an improper fraction, is 28/53.
Now let's convert cosine of ∠U is 28/53 in whole number:
The cosine of ∠U, which is 28/53, can be expressed as a whole number by dividing the numerator by the denominator.
28 ÷ 53 = 0.526087
So, the cosine of ∠U expressed as a whole number is approximately 0.52609
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_____ The given question is not correct, so correct Question is:
Find the cosine of ∠U in Triangle UTV with side:
UV=28
VT=45
TU=53
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
A bobsled team is practicing runs on a track. Their first run takes 4.85 minutes. On each of the next two runs, the team’s time changes by −512% compared to the previous time.
A photo of a bobsled on a track is shown.
Question 1
Part A
What was the team’s time, rounded to the nearest hundredth of a minute on their final run?
Answer: The team's time on the final run can be found by successively multiplying their first time by (1 - 0.512) twice:
First run time: 4.85 minutes
Second run time: 4.85 * (1 - 0.512) = 2.37 minutes
Third run time: 2.37 * (1 - 0.512) = 1.15 minutes (rounded to the nearest hundredth)
So the team's time on their final run was 1.15 minutes.
Step-by-step explanation:
properties of equality
if you could figure out this it would be great but its a whole worksheet
Because of this, we apply a variety of equality characteristics, such as the multiplication, subtraction, and division properties.
what is inequality ?A relationship of two expresses or integers that is neither equal in mathematics is referred to as an inequality. Furthermore, inequity results from imbalance. In math and science, an inequalities establishes the connection between two ou alors elements. Egality and inequality are not the same. Use the not equal symbol most frequently when two quantities are not equal (). Values of any size can be examined using a variety of inequalities. By changing the two sides until only the variables are left, many straightforward inequalities can be solved. However, a number of factors support inequality: Both sides' 0 are split or added. Exchange the left and the right.
given
2(x- 9 ) = -10 ( given )
= 2x - 18 = -10 ( multiplication property )
= 2x = -10 + 18 ( subtraction property )
2x = 8 ( division property )
x = 4
Because of this, we apply a variety of equality characteristics, such as the multiplication, subtraction, and division properties.
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Please help! Need to turn it in soon
The required time duration is 0.13 s
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
[tex]h(t)=-5t^2 + v_{0}t+h_{0}[/tex]
Substitute given the values
2=-5t² + 15 t+0
=> 5t² -15t+2 =0
On solving this quadratic equation ,w e get
t= 0.13 s
The required time duration is 0.13 s
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In the diagram below, BE BC, m/A = 39° and m/EBC = 124°. Find m/FDC
∠AFB = 73° is the angles of a triangles .
What does a math angle mean?
An angle is made up of two rays (half-lines) that have a shared termination. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.
because the angles of a triangles add up to 180 degree
m∠A = 39° , m∠ADC = 107°
so ∠c = 180 - 107 - 39
= 34°
BE ≅ BC
∠C = ∠E = 34°
SO ∠EDF = 180 - 107 = 73°
So ∠DEF = 180 - 34 - 73 = 73°
Because m∠DFE and ∠AFB are vertical angle
so ∠DFE = ∠AFB
∠AFB = 73°
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Paula's Pizza Parlor uses the following ingredients to make pizza
Number of Pizzas
2
5
Sauce
18
Cheese
12
At this Rate how many sauce and cheese will paula use to make 5 pizzas?
To make 5 pizzas, Paula will use 45 sauce and 30 cheese.
What are multiplication and division?Multiplication is used to find the product of two or more numbers. Multiplication is also known as repeated addition.
The division is the opposite operation of multiplication. It is how one tries to determine how many times a number is contained into another.
Given,
Paula uses 18 sauce and 12 cheese to make two pizzas.
Ingredients needed to make one pizza = 18/2 sauce and 12/2 cheese
= 9 sauce and 6 cheese
Ingredients needed to make 5 pizzas = 9 × 5 sauce and 6× 5 cheese
= 45 sauce and 30 cheese
Hence, 45 sauce and 30 cheese is needed to make 5 pizzas.
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