Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.72 with a standard deviation of $0.10. Using Chebyshev's Theorem, what is theminimum percentage of stores that sell a gallon of milk for between $3.42 and $4.02? Round your answer to one decimal place.
Answers
Solution
We know that the mean= 3.72$ and the sd= 0.10$
and using the Chebysev theorem we want to know whick percentage of stores will be between 3.42$ and $4.02
We can calculate the distance between the limits and the mean:
3.72 - 3.42= 0.3
k=0.3/0.1= 3
4.02-3.72= 0.3
k= 0.3/0.1 = 3
Then we are between 3 deviations from the mean
So then we can calculate the percentage required with this formula:
\(1-\frac{1}{k^2}=1-\frac{1}{3^2}=1-\frac{1}{9}=\frac{8}{9}\cdot100=88.9\)So then we expect at least 88.9%
Related Questions
Eliana loves music, especially 80's punk rock. Eliana looked at the number of songs in her itunes account and she has 6 less than 4 times her best friend. Eliana's classmate David has 3 more than double her best friend. When talking to her Social Studies teacher, Eliana found out social study teacher has 7 more than two times the number of songs in his library than Eliana. Define a variable, then write and solve an equation. If the total number of songs is 382, how many songs does Eliana, her best friend, David and her social study teacher have?
Answers
Answer
Step by step explantion:
bsf= 26
Eliana:98
SS teacher=203
David=55
Step-by-step explanation:
m= music
bsf: m
eliana:4m-6
David:2m+3
SS teacher: 2(4m-6)+7
m+4m-6+2m+3+8m-12+7
382=15m-7
7+ +7
389=15m
/15m /15m
m=26
multiply 26 to each one of them
Graph. Find an ordered pair and where they intersect.y=-1/4x+2y=1/2x-1
Answers
We need to solve the following equation system:
\(\begin{gathered} y=-\frac{1}{4}x+2 \\ y=\frac{1}{2}x-1 \end{gathered}\)We can do this by graphing both equations and find the point where they intersect. To graph them, we need two points that belong to each equation.
For equation 1, we have:
\(y=-\frac{1}{4}\cdot0+2=2\)Which means our first point is (0, 2).
\(\begin{gathered} 0=-\frac{1}{4}\cdot x+2 \\ -\frac{1}{4}\cdot x=-2 \\ x=-2\cdot(-4) \\ x=8 \end{gathered}\)The second point is (8,0).
For equation 2, we have:
\(y=\frac{1}{2}\cdot0-1=-1\)So the first point is (0, -1).
\(\begin{gathered} 0=\frac{1}{2}\cdot x-1 \\ \frac{1}{2}\cdot x=1 \\ x=2 \end{gathered}\)So the second point is (2, 0).
Now we can graph both equations.
We need to find the point at which they intersect each other. We can see that they intersect right above x = 4, if we look at the y-axis, the height is approximately y=1. So the point of intersection is (4, 1).
does anyone know this?!
the answers are
a- 0.12
b- 0.32
c-0.20
d.0.08
Answers
Answer:
a
Step-by-step explanation:
find the positive suare root of the following number 57.27
Answers
The positive square root of 57.27 is approximately 7.5726, with further decimal places available through iterative approximation methods.
To find the positive square root of the number 57.27, we can use a calculator or mathematical operations.
Taking the square root of a number involves finding a value that, when multiplied by itself, gives the original number. In this case, we want to find the value that, when squared, equals 57.27.
Using a calculator, we can find the square root of 57.27 as approximately 7.5726. However, it's important to note that this is an approximation and may not be completely accurate due to rounding errors.
If we want to find a more precise answer manually, we can use iterative approximation methods. One such method is the Newton-Raphson method, which involves repeatedly refining an initial guess.
Starting with an initial guess of, let's say, 7, we can use the formula:
x(n+1) = (x(n) + (57.27/x(n)))/2,
where x(n) is the current approximation and x(n+1) is the next approximation. Iterating this formula a few times will converge to a more accurate value.
After a few iterations, we find that the positive square root of 57.27 is approximately 7.572615. This value can be further refined by performing more iterations or using more advanced numerical methods.
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1. Two runne
race.
(Miles)
Y
(Minutes)
2
RUNNER
4
18.5 37 55.5
8
RUNNER 2:
y = 9.5x
x = number of miles
y = number of minutes
Which runner is traveling at a
greater speed?
Explain your reasoning.
Answers
Runner 2 is traveling at a greater speed than Runner 1.
To determine which runner is traveling at a greater speed, we need to compare the rates at which they cover the distance. The speed of a runner can be calculated by dividing the distance traveled by the time taken.
Let's compare the speeds of Runner 1 and Runner 2:
Runner 1:
Distance: 2 miles
Time: 18.5 minutes
Speed = Distance / Time = 2 / 18.5 ≈ 0.108 mph/min
Runner 2:
The equation given is y = 9.5x, where x represents the number of miles and y represents the number of minutes.
This equation implies that Runner 2 takes 9.5 minutes to cover each mile.
From the equation, we can see that Runner 2's speed is constant at 9.5 minutes per mile.
Comparing the speeds, we can conclude that Runner 2 is traveling at a greater speed than Runner 1. Runner 2 maintains a constant speed of 9.5 minutes per mile, while Runner 1's speed varies depending on the distance covered. Therefore, Runner 2 has a higher rate of covering the distance, indicating that they are traveling at a greater speed.
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What is the midpoint of segment EF? E(-8,1) and F(1,1
Answers
Answer:
The answer is
\(( - \frac{7}{2} \: , \: 1) \\ \)Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
\(M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )\\\)
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
E(-8,1) and F(1,1)
The midpoint is
\(M = ( \frac{ - 8 + 1}{2} \: , \: \frac{1 + 1}{2} ) \\ = ( - \frac{7}{2} \: , \: \frac{2}{2} )\)
We have the final answer as
\(( - \frac{7}{2} \: , \: 1) \\ \)
Hope this helps you
Step-by-step explanation:
Hey there!
The given points are; (-8,1) and F (1,1). Let M(x,y) be the midpoints.
Now,
Using midpoint formulae.
\((x,y) = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )\)
Put all values.
\((x,y) =( \frac{ - 8 + 1}{2} , \frac{1 + 1}{2} )\)
Simplify it to get answer.
\((x,y) = ( \frac{ - 7}{2} , \frac{2}{2}) \)
\((x,y) = (\frac{ - 7}{2} ,1)\)
Therefore the slope is M(-7/2,1).
Hope it helps...
A plane from Waco to Dallas travels 85 miles. It took the plane 30 minutes to complete the trip. What is the plane’s average speed to the nearest hundredths of a m/hr
Answers
Answer
the plane will travel 170 miles per hour because you double the amount it already went because you had to double the minutes. so the answer is 170
Step-by-step explanation:
The plane traveled 85 miles in 30 minutes.
1 hour is 60 minutes.
30 minutes x 2 = 60 minutes ( 1 hour)
85 miles x 2 = 170 miles in one hour
The speed is 170 miles per hour
Help please help I need help to this assignment I need an 80
Answers
Answer:
A) 15/52
Step-by-step explanation:
Good luck with your assignment
Answer:
A
Step-by-step explanation:
15/52
Good Luck!!!!!
The machinery in a cereal plant fills 350 g boxes of cereal. The specifications for the machinery permit for a certain amount of fill tolerance. It is found that the weights of filled cereal boxes are normally distributed with a mean of 350 g and a standard deviation of 4 g. What is the probability that a box of cereal is under filled by 5 g or more?
Answers
There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.
First, we can standardize the problem by using the z-score formula:
z = (x - μ) / σ
Where:
x = the weight value we want to find the probability for (345 g in this case)
μ = the mean weight (350 g)
σ = the standard deviation (4 g)
Substituting the values into the formula:
z = (345 - 350) / 4 = -1.25
Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.
The probability of obtaining a z-score less than -1.25 is approximately 0.1056.
However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.
The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.
Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
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The 3-rd term of the arithmetic progression is equal to 1. The 10-th term of it is three times as much as
the 6-th term. Find the first term and the common difference. (Hint: Use the formula for the n-th term
of the progression and write what is given in the problem using this formula.)
Answers
Answer:
First term: 3
Common difference: -1
Step-by-step explanation:
3rd term: 1
6th term: x
10th term: 3x
Formula for the nth term using the common difference d and the first term a1:
an = a1 + (n - 1)d
Third term: a3 = a1 + (3 - 1)d = a1 + 2d = 1
6th term: a6 = a1 + (6 - 1)d = a1 + 5d = x
10th term: a10 = a1 + (10 - 1)d = a1 + 9d = 3x
a1 + 2d = 1 Eq. 1
a1 + 5d = x Eq. 2
a1 + 9d = 3x Eq. 3
Eq. 2 - Eq. 1
3d = x - 1
Eq. 3 - Eq. 2
4d = 2x
x = 2d
3d = x - 1
Substitute 2d for x.
3d = 2d - 1
d = -1
a1 + 2d = 1
a1 + 2(-1) = 1
a1 = 3
Check:
Here are the first 10 terms:
3, 2, 1, 0, -1, -2, -3, -4, -5, -6
The third term is 1. Correct
The tenth term (-6) is 3 times the 6th term (-2). Correct
Answer:
First term: 3
Common difference: -1
PLEEASE HELP ME IM RUNNING LATE
If mC = 49 , find the values of x and y.
Answers
Answer:
m∠y=41
m∠x=90
Step-by-step explanation:
It is an isosceles triangle, so m∠B=49 too
49+49=98
180-98=82
82÷2=41
m∠y=41
41+49=90
180-90=90
m∠x=90
The cost price of 10 bananas is equal to selling price of 12 bananas find the loss percentage?
Answers
Given that the cost price of 10 bananas is equal to selling price of 12 bananas, you need to find the Loss Percentage.
Therefore, you need to use the following formula to find the Loss Percentage:
\(\text{ }Loss\text{ \%}=\frac{Cost\text{ }Price-Selling\text{ }Price}{Cost\text{ }Price}\cdot100\)In this case, the cost price of 1 bananas is:
\(Cost\text{ }Price=\frac{1}{10}\)And the selling price of 1 bananas is:
\(Selling\text{ }Price=\frac{1}{12}\)Then, you can substitute values into the formula:
\(\text{ }Loss\text{ \%}=\frac{\frac{1}{10}-\frac{1}{12}}{\frac{1}{10}}\cdot100\)In order to subtract the fractions in the numerator, you can use this formula:
\(\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}\)\(\text{ }Loss\text{ \%}=\frac{\frac{(1)(12)-(1)(10)}{10\cdot12}}{\frac{1}{10}}\cdot100\)\(\text{ }Loss\text{ \%}=\frac{\frac{12-10}{120}}{\frac{1}{10}}\cdot100\)\(\text{ }Loss\text{ \%}=\frac{\frac{2}{120}}{\frac{1}{10}}\cdot100\)\(\text{ }Loss\text{ \%}=\frac{\frac{1}{60}}{\frac{1}{10}}\cdot100\)\(\text{ }Loss\text{ \%}=\frac{10}{60}\cdot100\)\(\text{ }Loss\text{ \%}\approx16.67\text{\%}\)Hence, the answer is (approximately):
\(16.67\text{\%}\)ACD is a triangle and B is a point on AC. AB = 8cm and BC is 6cm. Angle BCD = 48° and angle BDC = 50°. (a) Find the length of BD. (b) Find the length of AD. (c) Find the area of triangle ABD. (This is all one question)
Answers
Answer:
5.8206 cm10.528 cm23.056 cm^2Step-by-step explanation:
(a) The Law of Sines can be used to find BD.
BD/sin(48°) = BD/sin(50°)
BD = (6 cm)(sin(48°)/sin(60°)) ≈ 5.82064 cm
__
(b) We can use the Law of Cosines to find AD.
AD^2 = AB^2 +BD^2 -2·AB·BD·cos(98°) . . . . . angle ABD = 48°+50°
AD^2 ≈ 110.841
AD ≈ √110.841 ≈ 10.5281 . . . cm
__
(c) The area of ∆ABD can be found using the formula ...
A = ab·sin(θ)/2 . . . . . where a=AB, b=BD, θ = 98°
A = (8 cm)(5.82064 cm)sin(98°)/2 ≈ 23.0560 cm^2
_____
Angle ABD is the external angle of ∆BCD that is the sum of the remote interior angles BCD and BDC. Hence ∠ABD = 48° +50° = 98°.
please help me with this thank you
Answers
(9) The slope of a line perpendicular to the line, f(x) = 0.75x + 6 is - 4/3.
(10) The slope of a line parallel to this line, y = 10 -8x is -8.
What is the slope of a line perpendicular to the line?The slope of a line perpendicular to the line is the negative reciprocal of the slope of the line equation.
Question 9.
f(x) = 0.75x + 6
where;
0.75 is the slope of the line6 is the interceptThe slope of a line perpendicular to this line = -1/0.75 = -100/75 = -4/3
Question 10.
For the equation of another line, y = 10 - 8x
The slope of a line parallel to this line is equal to the slope of this line and it is calculated as follows;
y = 10 - 8x
where;
-8 is the slope10 is the y interceptslope of a line parallel to the line = -8
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GEOMETRY 100 POINTS
Find the length of BC
Answers
Answer:
x = 16
Step-by-step explanation:
Opposite sides are equal in a parallelogram
AD = BC
5x - 12 = 3x + 20
5x - 3x = 20 + 12
2x = 32
x = 32/2
x = 16
Consumer Price Index, 1970-2002
Year
1970
1975
1980
1985
1990
1995
2002
Source: World Almanac 2003
CPI
116.3
161.2
248.8
322.2
391.4
456.5
535.8
Describe how the CPI is related to the year.
As the year increases, the CPI decreases and then increases.
As the year increases, the CPI increases and then decreases.
As the year increases, the CPI decreases.
d. As the year increases, the CPI increases.
C.
a.
b.
Answers
The computation of the increased in salary is $500.
Here, we have,
Explanation:
Data provided in the question
Salary for the first year = $50,000
CPI increase during the year = 4%
Overstated inflation = 1% i.e. 5%
The computation of the increased in salary is shown below:
= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year
= $50,000 × 5% - $50,000 × 4%
= $2,500 - $2,000
= $500
Hence, The computation of the increased in salary is $500.
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complete question:
Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.
Find the quotient of z₁ by z2. Express your answer in
trigonometric
form.
² - 3 (0 (4) + (*))
Z₁ cos
+/sin
Z₂
²2 = 7 (cos(377)+
COS
8
O A. 7 (cos (577) + i sin (5/77))
8
B.
21(cos(577)+isin (577))
8
OC. 21 cos
21(cos(-7)+ i sin(-77))
O D. 7 (cos(-7) + + sin(-7))
i
+/sin
37T
8
Answers
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.
Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.
We have:
z₁ = 7(cos(577°) + i sin(577°))
Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.
From the given information, we have:
z₂ = 21(cos(-7°) + i sin(-77°))
To find the quotient, we divide z₁ by z₂:
z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]
Substituting the given values, we have:
z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]
= (7/21) * [cos(584°) + i sin(584°)]
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.
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Brian set his compass equal to the radius of circle C and drew two circles centered at points A and B on circle C. He labeled the points of intersection of the two circles as shown.
Two circles are drawn by having another circle in the center. The center circle has points A, M, N, B, P, Q, and C. At C the two circles intersect, and at P the center circle and the top circle intersect.
To complete his construction, Brian only needs to use his straightedge to draw some chords of circle C.
Which figures could Brian be constructing?
equilateral triangle MNQ inscribed in circle C
equilateral triangle ANP inscribed in circle C
regular hexagon AMNBPQ inscribed in circle C
square MNPQ inscribed in circle C
square ANBQ inscribed in circle C
Answers
The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:
Equilateral triangle MNQ inscribed in circle C
Regular hexagon AMNBPQ inscribed in circle C
Brian is constructing figures inscribed in circle C.
Equilateral triangle MNQ inscribed in circle C:
This option is possible since the points M, N, and Q are labeled and they lie on circle C.
Equilateral triangle ANP inscribed in circle C:
This option is not possible. The points A and P are labeled, but the third vertex of the equilateral triangle is not specified.
Regular hexagon AMNBPQ inscribed in circle C:
This option is possible since the points A, M, N, B, P, and Q are labeled and they lie on circle C.
Square MNPQ inscribed in circle C:
This option is not possible based on the given information. The label points do not form a square.
Square ANBQ inscribed in circle C:
This option is not possible . The points A, N, B, and Q are labeled, but they do not form a square.
The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:
Equilateral triangle MNQ inscribed in circle C
Regular hexagon AMNBPQ inscribed in circle C
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I’m so done with math bro
Answers
What is 237 out of 10 in mixed number form
Answers
Answer: 23 7/10
Step-by-step explanation:
Your starting salary at a company is 70000 dollars, and you get a raise of 6000 dollars each year. Let t represent the number of years since you joined the company.
a) Express the percentage rate of change of your salary as a function of time.
Answers
Answer:
Step-by-step explanation:
70000 + t600
A researcher sends out a survey questionnaire to 200,000 people living in California, asking them to report how satisfied they are with their local political representatives. Of the 30,000 people who respond, 40% report being satisfied. Would it be appropriate to conclude that approximately 40% of the entire population of California is satisfied? Group of answer choices yes, as long as the 200,000 people were randomly sampled from the larger population of Californians Yes, regardless of sampling technique Probably not, people who respond to the survey may be different than people who do not respond to the survey
Answers
Answer:
I would say the last one.
Step-by-step explanation:
Political views are often reflected on every aspect of life, including whether or not the respond to a survey.
Last season Emily soccer team how to win loss ratio of 9 to 12 and Grant soccer team how to win loss ratio of 10 to 15 who’s team has a higher ratio of wins to losses use complete sentences to explain your reasoning
Answers
The Emily soccer team has the higher ratio of wins to losses.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b.
Given that,
Ratio of win to loss of Emily soccer team = 9 : 12
Ratio of win to loss of Grant soccer team = 10 : 15
9 : 12 = 9 / 12 = (9 × 5) / (12 × 5) = 45 / 60
10 : 15 = 10 / 15 = (10 × 4) / (15 × 4) = 40 / 60
If 60 games are losses, then 45 games are wins for Emily soccer team.
If 60 games are losses, then 40 games are wins for Grant soccer team.
Higher ratio is for Emily soccer team.
Hence higher ratio of wins to losses is for Emily soccer team.
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a student spends 18 out of 35 of his pocket money on transport and fruit what is the fraction left?
Answers
To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.
The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.
Therefore, the fraction of pocket money left can be written as 17/35.
A bicycle wheel has diameter 66 cm. Find how many turns the wheel makes when the bicycle travels 400 metres.
Answers
The number of turns the wheel makes is 1.93 ≈ 2.
What is Turns?
This is referred to as a cycle. It is a unit of plane angle measurement that is equivalent to 2π radians, 360 degrees, or 400 gradians.
formular for calculating Turns:
Turns = Lenght
Circumference
Circumference of a circle, C= πD
Where,
Diameter=D
π =22/7
Calculating Circumference;
C= 22 * 66
7
=207.4
From the question:
D= 66cm
L =400m
Calculating Turns:
Turns = Lenght
Circumference
= 400m
207.4
Turns =1.93
Turns =1.93≈ 2
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What is the remainder of 525 divided by 28? as a whole number
Answers
Answer:
R = 21
Step-by-step explanation:
525 ÷ 28 = 18 R 21
28 × 18 = 504
525 - 504 = 21
Therefore, the remainder is 21.
Hope this helps! :)
The remainder of 525 divided by 28 is 21
First step
Division
525 ÷ 28
= 18
Second step multiply 28 by 18
28 × 18
= 504
Now let determine remainder of 525 divided by 28
Remainder=525 - 504
Remainder= 21
Inconclusion remainder of 525 divided by 28 is 21
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Let A be a 7×5 matrix with rank equal to 4 and let b be a vector in R8. The four fundamental sub- spaces associated with A are R(A), N(AT ), R(AT ), and N (A).
Answers
The value of R(A) = 4, N(AT ) = 3, R(AT ) = 4, and N (A) = 3.
Given that
Dimension of matrix = 7×5
Rank of matrix = 4
The range space of A,
Which is a subspace of R, is known as R(A).
It is made up of all conceivable linear combinations of A's columns.
The dimension of R(A) = rank of A,
Which is 4 in this case.
The null space of the transpose of A,
Which is also a subspace of R, is designated as N(AT).
All potential answers to the equation ATx = 0,
Where x is a R column vector, are included in it.
N(AT) has a dimension = nullity of A,
which in this case is 3 in this example.
The range space of the transposition of A, is designated as R(AT).
The rows of A are arranged in all conceivable linear configurations.
The rank of A = 4
Thus it equal to dimension of R(AT).
N(A) is the null space of A.
Axe = 0, where x is a column vector in R, are included in it.
The nullity of AT, which is three, is likewise equivalent to the dimension of N(A).
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Which of the following is the equation of the function f(x) graphed above? A. ƒ(x) = x(x − 2)²(x − 1)(x + 1) B. f(x) = (x - 2) (x − 1)(x + 1) c. f(x)= x(x - 2)²(x − 1)(x + 1) + 1)² D. f(x) = (x - 2)²(x - 1)(x - 1)^ E
Answers
Which expression is equivalent to "9 more than the quotient of x and 5
Answers
The required expression is (x / 5) + 9
Given that we have to build an equation for the statement "9 more than the quotient of x and 5,
So,
This expression represents the quotient of x divided by 5, and then adding 9 to the result.
Therefore,
"9 more than the quotient of x and 5" can be written mathematically as:
(x / 5) + 9
Hence the required expression is (x / 5) + 9
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A movie theater has a seating capacity of 367. The theater charges $5.00 for children, $7.00 for
students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket
sales was $2660 on a sold out night, how many children, students, and adults attended?
Answers
Based on the given equation condition, the number of children is 182, the number of students is 94 and the number of adults is 91 respectively.
What is an equation?
A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation. The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.
Let c represent the number of children, s represent the number of students and a represents the number of adults. Then,
According to the question,
or, c+s+a = 367 ....................(i)
or, a=c/2 .................. (ii)
or, 5c+7s+12a = 2660 ................ (iii)
Multiply equation (i) with 5, then
7c+7s+7a = 7(367)= 2569......... (iv)
subtract (iv) from (iii), we get
-2c +5a = 2660-2569 = 91
From (ii), -2c +5(c/2) = 91
or, 0.5c = 91
or, c = 182
Then, a = 182/2 = 91
And, s = 367-c-a = 367-182-91 = 94
Hence, the number of children is 182, the number of students is 94 and the number of adults is 91 respectively.
To learn more about an equation
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