The ratio of 2 days to 80 hours and 5 days to 80 hours is 1 day : 40 hours and 1 day : 16 hours respectively.
How to calculate ratio?2, 5 days : 80 hours
So,
2 days : 80 hours
= 2/80
= 1/40
= 1 day : 40 hours
Also,
5 days : 80 hours
= 5/80
= 1/16
= 1 day : 16 hours
Hence, the ratio of days to hours is given by 1 day : 40 hours and 1 day : 16 hours respectively.
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8068/31 as a mixed number
the easiest way is to divide, 8068÷31, since it's a big problem, you should use a calculator! When you do, you should get 260.258065, but once you round all the decimals you just get 260, your remainder should be 8. Use 8 as your numerator and 260 as your mixed number! And your finished, and that's why the answer is 260 8/31.
The Humber Room advertises two types of entrée, meat and fish. It is known that 70% of all customers order meat, and 30% order fish. All customers are individually asked after their meals if they were satisfied with them. This survey shows that 80% of those who ordered meat and 95% of those who ordered fish were satisfied. Draw a probability tree for this problem to answer the question.
If M represents the event of ordering meat, F is the event of ordering fish, + is the event of being satisfied, and − is the event of not being satisfied, then answer the following questions:
(a) Determine the following probabilities based on the probability tree:
P(M)
P(F)
--------- Determine the conditional probabilities
(iii) P (+ M)
(iv) P (- M)
(v) P (+F)
(vi) P(-F)
(b) Write down the results of calculating the joint probabilities below:
P (M and +)
P (M and -)
P (F and +)
P (F and -)
(c) If a randomly selected customer was satisfied with his/her meal, what is the probability that the customer ordered fish?
Can someone please explain how to resolve this ?
The probability of ordering meat is 0.7 and the probability of ordering fish is 0.3.
P(+ | M) = 0.8 and P(- | M) = 0.2,
P(+ | F) = 0.95 and P(- | F) = 0.05.
P(M and +) = 0.56 and P(M and -) = 0.14,
P(F and +) = 0.285 and P(F and -) = 0.015.
C: the probability that the customer ordered fish is 0.3.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.
Given The Humber, Room advertises two types of entrée, meat and fish,
70% of all customers order meat, and 30% order fish,
M represents the event of ordering meat, F is the event of ordering fish,
probability of M and F,
p(M) = 70% = 0.7
p(F) = 30% = 0.3
and 80% of those who ordered meat and 95% of those who ordered fish were satisfied,
+ is the event of being satisfied, and − is the event of not being satisfied,
probability of satisfied customers with meat,
p(+) = 80% = 0.8
not satisfied with meat,
p(-) = 1 - 0.8 = 0.2
probability of satisfied customers with fish,
p(+) = 95% = 0.95
not satisfied with fish,
p(-) = 1 - 0.95 = 0.05
B: calculating the joint probabilities,
P (M and +) = P(M ∩ +) = p(M)*p(+)
P (M and +) = 0.7*0.8
P (M and +) = 0.56
P (M and -) = P(M ∩ -) = p(M)*p(-)
P (M and -) = 0.7*0.2 = 0.14
P (F and +) = P(F ∩ +) = p(F)*p(+)
P (F and +) = 0.3*0.95
P (F and +) = 0.285
P (F and -) = P(F ∩ -) = p(F)*p(-)
P (F and -) = 0.3*0.05
P (F and -) = 0.015
C: Determine the conditional probabilities,
P (+ | M) = P(M ∩ +)/p(M)
substitute the values
P (+ | M) = 0.56/0.7
P (+ | M) = 0.8
P (- | M) = P(M ∩ -) /p(M)
P (- | M) = 0.14/0.7
P (- | M) = 0.2
P (+ | F) = P(F ∩ +)/p(F)
substitute the values
P (+ | F) = 0.285/0.3
P (+ | F) = 0.95
P(- | F) = P(F ∩ -)/p(F)
P(- | F) = 0.015/0.3
P(- | F) = 0.05
D: If a randomly selected customer was satisfied with his/her meal, what is the probability that the customer ordered fish,
to find P (F | +) = P(F ∩ +)/p(+)
substitute the values
P(F | +) = 0.285/0.95
P (F | +) = 0.3
Hence the probabilities are as followed.
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help help help
pleas3e
Answer: 3
Step-by-step explanation:
Brady is making snack bags with 18 juice boxes and 27 cookies. He wants each bag to have the same number of juice boxes and the same number of cookies. (a) What is the maximum number of snack bags he could make? (b) How many juice boxes and (c) how many cookies could he put in each bag?
(a) The maximum number of snack bags he could make,
= 18 snack bags.
(b) 18 juice boxes.
(c) 18 cookies in each bag.
What is greatest common factor?The greatest number that can divide the numbers in equal parts.
It is called as greatest common factor.
Given:
Brady is making snack bags with 18 juice boxes and 27 cookies.
He wants each bag to have the same number of juice boxes and the same number of cookies.
(a) The maximum number of snack bags he could make,
= GCF(18, 27)
= 18 snack bags.
(b) 18 juice boxes.
(c) 18 cookies in each bag.
Therefore, all the required values are given above.
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A gas station sells regular gas for $2.15 per gallon and premium gas for $2.90 a gallon. At the end of a business day 300 gallons of gas had been sold, and receipts totaled $690. How many gallons of each type of gas had been sold?
Answer: Let's call the number of gallons of regular gas sold "x". Then, the number of gallons of premium gas sold would be 300 - x.
The total revenue from regular gas would be 2.15 * x dollars. The total revenue from premium gas would be 2.90 * (300 - x) dollars.
We know that the total receipts for the day were $690, so we can set up the following equation:
2.15x + 2.90(300 - x) = 690
Expanding the second term, we get:
2.15x + 870 - 2.90x = 690
Combining like terms, we get:
0.25x = -180
Dividing both sides by 0.25, we get:
x = 720
So, 720 gallons of regular gas and 300 - 720 = -420 gallons of premium gas were sold. However, since it is not possible to sell a negative number of gallons of gas, this solution is not valid.
If we try another value of x that is less than 300, we will find a valid solution. Let's try x = 200:
2.15 * 200 + 2.90 * (300 - 200) = 690
Expanding and simplifying, we get:
430 + 90 = 520
So, 200 gallons of regular gas and 300 - 200 = 100 gallons of premium gas were sold.
Step-by-step explanation:
calculate the measure of x
Answer:
Step-by-step explanation:
Wow, that is a lot. You got to give me a brainliest ! Lol
1) 9²+12²=x², x=15
2)10²+24²=x², x=26
3)3²+7²=x², x=7.6
4)6²+x²=10², x=8
5)x²+6²=24², x=23.2
6)1²+1²=x², x=1.4
7)x²+8²=21², x=19.4
8)x²+24²=30², x=18
9)5²+9²=x², x=10.3
The base of a rectangular box measures 3 feet by 6 feet. What is the height in feet of the box if the volume is 72 cubic feet
Answer:
12 ft
Step-by-step explanation:
To find the height of a rectangular box with a base measuring 3 feet by 6 feet and a volume of 72 cubic feet, we need to use the formula for the volume of a rectangular prism:
Volume = Length x Width x Height
We are given the volume of the box and the length and width, so we can substitute the values and solve for the height:
72 = 3 x 6 x Height
72 / (3 x 6) = Height
12 = Height
So, the height of the box is 12 feet.
IF U ANSWER CORRECTLY UNDER 5 MINS U GET 100 PI0NTS!!
what is the amplified the sinusoidal function? enter your answer in the box.
Answer: 4
Step-by-step explanation: i took the test
16. AQRS is an equilateral triangle. If QR is seventeen more than twice x, RS is 19 less than six times x,
and QS is one less than four times x, find x and the measure of each side.
Topic 4: Congruent Triangles
18. Write three valid congruency statements given the triangles below.
P
17. In AJKL, if JK = JL, m/J = 23x - 4, m/K = 4x - 1, and m/L = 9x - 31, find x and the
measure of each angle.
¥
Q
R
S
|||
T
U
19. If AKPLAACM, complete each part.
a) KL =
d)
The value of x is 9 ,
The measure of each side of the equilateral i.e QR , RS , QS is 35
What is a Triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.
Given as :
Triangle QRS is an equilateral triangle
The side of the triangles are, QR , RS, QS
Now, According to the question
QR = 2 x + 17
RS = 6 x - 19
QS = 4 x - 1
If the Triangle is equilateral, then all sides are equal
So , QR = RS = QS
Or, 2 x + 17 = 6 x - 19 = 4 x - 1
Now, 2 x + 17 = 6 x - 19
So, 17 + 19 = 6 x - 2 x
Or, 36 = 4 x
x =
I.e x = 9
So, the measure of side QR = 2 x + 17 = 2 × 9 + 17
Or, the measure of side QR = 35
The measure of side RS = 6 x - 19 = 6 × 9 - 19
Or, The measure of side RS = 35
The measure of side QS = 4 x - 1 = 4 × 9 - 1
Or , The measure of side QS = 35
Hence the value of x is 9,
And the measure of each side of the equilateral i.e QR , RS, QS is 35 . Answer
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Lisa's living room has new carpet of 8 meters wide and 10.5 meters long. They want to put carpet in the basement that is twice as long as the living room and a fourth wider. They also wanted to put tile in the bathroom that has an area of 10 square feet. The bedroom is currently being completed with carpet. If the bedroom is 6 meters shorter in length than the living room, and is 34 the width of the living room, what is the bedroom's area in meters squared?
The bedroom's area in meters squared is 55.1693 m².
Solving for the bedroom's area in meters squared:finding the area of the basement:
The length of the basement is 2 * 10.5 m = 21 m
The width of the basement is 8 m / 4 = 2 m
The area of the basement is 21 m * 2 m = 42 m²
Next, let's find the equivalent area of the 10 square feet tile in meters:
1 square foot = 0.092903 m²
10 square feet = 10 * 0.092903 m^2 = 0.92903 m²
finding the area of the bedroom:
The length of the bedroom is 10.5 m - 6 m = 4.5 m
The width of the bedroom is 8 m * 34 = 2.72 m
The area of the bedroom is 4.5 m * 2.72 m = 12.24 m²
So the total area covered with carpet and tile is:
12.24 m² + 42 m² + 0.92903 m²
= 55.1693 m²
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Kevin has half of his investments in stock paying an 11% dividend and the other half in a stock paying 14% interest. If his total annual interest is $480, how much does he have invested?
Kevin has $3840 invested in stocks in total.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Annual interest in first investment - 11%
Annual interest in other investment - 14%
Total interest annually - $480
Let us assume, x is the investment in each stock
or, total investment = 2x
then, making an equation for the total interest
0.11x+.14x=480
Multiplying everything by 100
11x+14x=48000
25x=48000
Divide both sides by 25
x=1920
then, by total investment = 2x
2×(1920) = 3840
Hence, Kevin has $3840 invested in stocks in total.
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The functions f(x) and g(x) are shown on the graph. f(x) = x2 What is g(x)?  A. g(x) = 3x^2  B. g(x) = (1/3x)^2  C. g(x) = (x + 3)^2  D. g(x) = (x – 3)^2 (2,12)
The function g(x) is equal to g(x) = 3x².
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is functions f(x) and g(x) are shown on the graph and f(x) = x².
The function g(x) is equivalent to 3 times function f(x) for every value of {x}. So, we can write - g(x) = 3x²
Therefore, the function g(x) is equal to g(x) = 3x².
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Find an angle θ that is coterminal with an angle measuring −490∘, where 0∘≤θ<360∘. Do not include the degree symbol in your answer. For example, if your answer is 20∘, you would enter 20.
Answer: [tex]230[/tex]
Step-by-step explanation:
To find coterminal angles, add/subtract integer multiples of [tex]360^{\circ}[/tex].
[tex]-490^{\circ}+360^{\circ}=-130^{\circ}\\\\-130^{\circ}+360^{\circ}=230^{\circ}[/tex]
An angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘ is 130∘.
To find an angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘, we can use the concept of coterminal angles.
Coterminal angles are angles that have the same initial and terminal sides when drawn in standard position. To find a positive coterminal angle with a negative angle, we can add 360 degrees to the negative angle until we get an angle within the desired range (0∘ to 360∘).
Let's find the positive coterminal angle:
θ = -490∘ + 360∘
θ = -130∘
So, an angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘ is 130∘.
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Which of these currencies is used is Switzerland?
A) The pound sterling
B) The yuan
C) The franc
D) The yen
Answer:
C is the answer.
Step-by-step explanation:
Switzerland uses the currency called Switzerland Franc.
PLEASE MARK ME BRAINLIEST.
Determine whether the sequence is an arithmetic sequence, a geometric sequence, or neitherIf it is either arithmetic or geometric, give the next term in the sequence 1,4,25,125,625,...
Therefore , the solution of the given problem of arithmetic mean comes out to be the given sequence is geometric sequence..
Definition of arithmetic mean.The arithmetic average, also referred to as the group's means, is obtained by adding up all the values in a list and multiplying that amount by the total number of list items. Math also has a similar trend of progression. The following equation shows that the median of the actual figures 5, 8, and 9 is 3, while the mean of the actual figures 5, 7, and 9 is 4, and the number 21 multiplied by three (there are now multiple three numbers) equals 7.
Here,
Given :
Sequence = 1, 4,25,125,625
Thus,
from the sequence we can see it is an geometric sequence not an arithmetic sequence.
r = 5/1 = 5
=> 1 ,5 ,5(5) , 5(5)² , 5(5)³
So,
it is an geometric sequence.
Therefore , the solution of the given problem of arithmetic mean comes out to be the given sequence is geometric sequence..
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a small business owner is applying for a small business loan and has been approved for a $50,000 loan with a 6.15% annual interest. the first loan is a simple interest rate, the second loan compounds interest quarterly, and the third loan compounds interest continuously. the small business owner plans to pay off the loan in three years and 7 months. Determine the total value of the loan with the quarterly compounded interest.
Answer: The total value of the loan with quarterly compounded interest is $60,109.34.
Step-by-step explanation:
To calculate the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A = final amount (loan + interest)
P = principal (the original amount of the loan)
r = annual interest rate as a decimal
n = number of times the interest is compounded in a year
t = time in years
For the loan with quarterly compounded interest, the number of times the interest is compounded in a year is 4 (since interest is compounded quarterly), and the time is 3 years and 7 months, which we can convert to years as 3.5833.
Substituting the values into the formula, we get:
A = $50,000 * (1 + 0.0615/4)^(4 * 3.5833)
A = $50,000 * (1.015375)^(15.7532)
A = $50,000 * 1.22186888
A = $60,109.34
Therefore, To calculate the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A = final amount (loan + interest)
P = principal (the original amount of the loan)
r = annual interest rate as a decimal
n = number of times the interest is compounded in a year
t = time in years
For the loan with quarterly compounded interest, the number of times the interest is compounded in a year is 4 (since interest is compounded quarterly), and the time is 3 years and 7 months, which we can convert to years as 3.5833.
Substituting the values into the formula, we get:
A = $50,000 * (1 + 0.0615/4)^(4 * 3.5833)
A = $50,000 * (1.015375)^(15.7532)
A = $50,000 * 1.22186888
A = $60,109.34
Therefore, the total value of the loan with the quarterly compounded interest would be $60,109.34.
Which of these numbers in NOT divisible by 3?
300
321
241
8,910
Answer:
Step-by-step explanation:
241 is divisible by 3
D. 49. Mike will fill jars with water for an experiment. Each jar holds cup. Mike has 18 cups of water. How many jars can Mike fill with water? A 3 B 6 C
On solving the provided question we can say that by fraction, Mike can fill 18 X 1/3 = 6 cups with water
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
Each jar holds 1/3 cup.
Mike has 18 cups of water
by fraction, Mike can fill 18 X 1/3 = 6 cups with water
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The correct question is -
Mike will fill jars with water for an experiment. Each jar holds 1/3 cup. Mike has 18 cups of water. How many jars can Mike fill with water?
help me algebra value functions and graphs
The definition of the absolute value function for this problem is given as follows:
y = |x - 4| - 2.
What is the absolute value function?The absolute value function of vertex at coordinates (h,k) is defined as follows:
y = a|x - h| + k.
From the graph, the coordinates of the vertex are given as follows:
(4,-2).
Hence the equation is given as follows:
y = a|x - 4| - 2.
When x changes by one, y also changes by one, hence the coefficient a is given as follows:
a = 1.
Thus the function is defined as follows:
y = |x - 4| - 2.
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How do i solve this question
The graph of the equation can be seen on the image at the end, and when she uses 17 cups of flour, she will use 76.5 cups of honey.
How to find the relation between flour and honey?We assume that the relation is linear.
Remember that a general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the linear equation passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we have the two pairs:
(27, 6)
(45, 10)
First, you can graph these two points and connect them with a line, that will be the graph of our equation.
The slope is:
a = (10 - 6)/(45 - 27)
a = 4/18
a = 2/9
y = (2/9)*x + b
To find the value of b we can replace the values of the point (27, 6)
6 = (2/9)*27 + b
6 = 2*3 + b
6 = 6 + b
0 = b
So the equation is just:
y = (2/9)*x
And for 17 cups of flour, she will use:
17 = (2/9)*x
(9/2)*17 = x
76.5 = x
She needs to use 76.5 cups of honey.
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Let f be a differentiable function with f(−4) = −2, ƒ'(−4) = 6,
f(-5) = −4, and f'(-5) = 1. Let the function g(x) = ƒ(2x + 3). Write the
equation of the line tangent to the graph of g at the point where x = −4.
Therefore , the solution of the given problem of function comes out to be g(x) = ƒ(2x + 3) = f'(-5) = 1.
What is function ?Mathematics includes the study of numbers, various variations, the natural reality, architecture, and both actual and hypothetical locations. A function is a visual representation of the relationship variable between the number of inputs and the corresponding outputs for each. Simply explained, a function is a collection of inputs that, whenever combined, result in a different output by each input. Every function is assigned a city, county, or scope, sometimes known as a domain. The letter f is frequently used to denote functions (x).
Here,
Given :
=> f(−4) = −2
=> ƒ'(−4) = 6
=> f(-5) = −4
=> f'(-5) = 1
To find :
=> g(x) = ƒ(2x + 3)
=> g(4) = f(2(-4) + 3)
=> g(4) = f(-5)
=> f(-5) = -4
=> f'(-5) = 1
Therefore , the solution of the given problem of function comes out to be g(x) = ƒ(2x + 3) = f'(-5) = 1.
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A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters is t seconds after the hit is given by the quadratic function h(t) = −4.9t2 + 34.3t + 1.
How could we calculate how long it takes the baseball to reach its maximum height? How could we calculate the maximum height obtained by the baseball?
61.025 meters is the maximum height obtained by the baseball
What is a function?A relation is a function if it has only One y-value for each x-value.
The length of time and the maximum height can be found by finding the vertex of the parabola.
h(t) = -4.9t² + 34.3t + 1
x = -b/2a
t = -34.3/-9.8
t=3.5
Now plug in t value in the function
h(3.5)= -4.9(3.5)² + 34.3(3.5)+ 1
=-4.9(12.25)+120.05+1
=-60.025+120.05+1
=61.025 meters
Hence, 61.025 meters is the maximum height obtained by the baseball
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what makes an image not to scale
Answer:
It isn't measured, but it gives you a ruff representation of what the subject looks like.
Step-by-step explanation:
Please help. Thank you to anyone that can
The required volume of figure 1 is given as 55 ft³, and the volume of all the figures is evaluated by following the same procedure.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
Volume = 1/3 area of base × height - - - - -(1)
(1)
Area of base = area of triangle = 1/2 × base × height
Area of base = 1/2 × 5 * 6 = 15
Put this value in equation 1
Volume = 1 /3 ×15 × 11
Volume = 55 ft³
Similarly, the volume of each figure can be evaluated.
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If the graph of the function f(x) =e to the X power shift is it in six units to the right, what is the equation of the new graph?
Answer:
The equation for the new graph is e^(x -6)
Simplify (23+16) . Write the sum in the simplest form.
The simplification of (23+16) is 39
What is addition?Addition is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined.
For example of there are 20 mangoes. 50 cashews and 80 oranges in a store. The total number of fruits the store can be obtained by adding the number of oranges, mangoes and cashew.
This means that 80+20+50 = 150 fruits
Similarly to get the value of( 23+16) , we add the two numbers together
23+16 = 39
therefore the value of 23+16 = 39
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Complete the sentence the below. If the point (4,−1) is a point on the graph of f, then f( __ )=____.
If the point (4, -1) is a point on the graph of f, then f(4) = -1.
How to complete the given sentenceFrom the question, we have the following parameters that can be used in our computation:
Point (4,−1) is a point on the graph of f
The expression "f(4)" represents the output value of the function f, when 4 is plugged into it as the input.
If the point (4, -1) is on the graph of f, it means that for the input value of 4, the output value of the function is -1.
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Find a positive and a negative coterminal angle for each given angle.
A positive and a negative coterminal angle for each given angle is
A. 13π/4 and -3π/4.
B. 97π/36 and -47π/36.
What is the coterminal angle?
Coterminal angles are those with a common terminal side that are in standard position (angles with the starting side on the positive x-axis). Coterminal angles are the angles that have the same initial side and share the terminal sides.
Here, we have
A. 5π/4
We have to find the coterminal angle.
5π/4 + 2π = 13π/4
5π/4 - 2π = -3π/4
Hence, a positive and a negative coterminal angle for each given angle is 13π/4 and -3π/4.
B. 25π/36
We have to find the coterminal angle.
25π/36 + 2π = 97π/36
25π/36 - 2π = -47π/36
Hence, a positive and a negative coterminal angle for each given angle is 97π/36 and -47π/36.
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Question is attached to image
The probability that Deborah's first flight was delayed can be found to be 0. 85.
How to find the probability ?To find the probability that Deborah's first flight from Boston to Denver was delayed, use the following formula :
= 1 - probability that the flight takes off on time
Probability that the flight takes off on time = 0. 15 .
The probability that Deborah's first flight from Boston to Denver was delayed is therefore :
= 1 - 0. 15
= 0. 85
In conclusion, there is an 85 % probability that the first flight was delayed.
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how many to fill these here buckets
Answer:
Each bucket will be [tex]\dfrac{1}{2}[/tex] full
Step-by-step explanation:
First add up all the different fractions to find out how many buckets of water are in all 3 buckets combined.
Adding up the fractions we get the expression:
[tex]\dfrac{5}{12} + \dfrac{3}{4} + \dfrac{1}{3}[/tex]
To add these fractions first find the LCM(least common multiple of the denominators, 12, 4 and 3
This is the smallest number divisible by all 3 numbers without a remainder
There are several strategies for finding the LCM but here we can see that 12 is evenly divisible by12, 4 and 3
We convert each of the fractions to have the same denominator as the LCM of 12 and adjust the numerator accordingly
Multiply each of the fractions by the LCM
12 x 5/12 = 5
12 x 3/4 = 9
12 x 1/3 = 4
These will become the numerators in the addition with the common denominator of 12
[tex]\dfrac{5}{12} + \dfrac{3}{4} + \dfrac{1}{3}\\\\= \dfrac{5 + 9 + 4}{12}\\\\= \dfrac{18}{12}\\\\[/tex]
This is how many buckets it will take to hold the water from all three buckets
Divide numerator and denominator by 6 to reduce to lowest fraction
[tex]\dfrac{18 \div 6}{12\div6} = \dfrac{3}{2}[/tex]
This is 1 1/2 buckets. If this amount of water is to be evenly divided among 3 buckets then the amount of water in each bucket
[tex]\dfrac{3}{2} \div 3\\\\= \dfrac{3}{2} \times \dfrac{1}{3}\\\\= \dfrac{1}{2}[/tex]
So each bucket will be half full