For the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.
As given in the question,
Height of the right circular cone = 2.5 units
And radius of right circular cone = 7.5 units
Let r be the radius of the cylinder and h be the height of the cylinder.
Volume of a cylinder 'V' = π r² h
Cylinder is inscribed in right circular cone
From origin edge cylinder is inscribed at x distance in right circular cone.
r = 7.5 - x
h = (2.5 /7.5) x
= x/3
V = π ( 7.5 - x )² ( x / 3)
⇒ V = π ( x² -15x + 56.25 ) (x/3)
⇒ V = (π /3)( x³ - 15x² + 56.25x)
For maximum volume ,
dV/dx = 0
dV/dx = (π/3)( 3x² -30x + 56.25)
(π/3) ≠ 0
⇒ 3x² -30x + 56.25 = 0
⇒ 3 ( x² -10x + 18.75) = 0
3 ≠ 0
⇒ x² -10x + 18.75 = 0
x = [ - (-10) ± √ (-10)² -4(1)(18.75)]/2(1)
⇒ x = [ 10 ± √ 100 -75]/2
⇒ x= ( 10 ± 5 ) / 2
⇒ x = 7.5 or 2.5
As r = 7.5 -x
Hence x ≠ 7.5
r = 7.5 -2.5
= 5 units
h = x/3
= 2.5/3
= 0.8333 units
Therefore, for the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.
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A data set comparing a woman's shoe size to her height is represented by the table.
Shoe Size Height (inches)
7.5 63
9 72.5
11 70
7 62
9 69.5
10 72
12 72.5
13 73
13 70
What is the equation for the line of best fit for a woman's height, y, based on her shoe size, x?
Answer:
10 72
Step-by-step explanation:
Find the equation of the line passing through the given point and parallel to the given line.
(-1, 2), 2y = 6x + 13
The equation of the line passing through the given point and parallel to the given line (-1, 2), 2y = 6x + 13 will be y=3x+3.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that, the equation of the line passing through the given point and parallel to the given line.(-1, 2), 2y = 6x + 13
The slope of the given line is,
2y = 6x + 13
y=3x+13/2
m=3
The equation of the line passing through the (-1, 2) and slope equal to 3 is,
y-2=3(x+1)
y-2=3x+1
y=3x+3
Thus, the equation of the line passing through the given point and parallel to the given line (-1, 2), 2y = 6x + 13 will be y=3x+3.
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Make
x
the subject of the formula
3
a
x
=
m
+
n
Answer:
Below
Step-by-step explanation:
3ax = (m+n) divide both sides by 3 a
x = (m+n) / 3a that's it
thirty-six colonies grew in nutrient agar from 1.0 ml of undiluted sample in a standard plate count. how many cells were in the original sample? group of answer choices 72 per milliliter 36 per milliliter 4 per milliliter 18 per milliliter 9 per milliliter
By using the concept of dilution factor, it is obtained that the number of cells in the original sample is 36 per ml
What is dilution factor?
Suppose there is a solution. The volume of the solution present in the total volume is the dilution factor of the solution.
Here, the concept of dilution factor is important
Dilution factor = 1 [Undiluted solution]
Number of colonies = 36
Volume of the sample = 1 ml
Number of cells in the original sample = [tex]\frac{Number \ of \ colonies \times Dilution \ factor}{Volume\ of\ the \ solution}[/tex]
= [tex]\frac{36\times 1}{1}[/tex]
= 36 per ml
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A study found a strong positive correlation between the amount of soda consumed by children and aggressive behavior in those children.
In this discussion, you’ll work with your classmates to understand this statement and its implications.
In your first post, answer the following questions:
What does a “strong positive correlation” tell us about the relationship found in this study?
Does this correlation help us identify any causation between the variables in this scenario? Why or why not?
Regardless of your answer to #2 above, what do you think about the possibility of causation in this scenario? Explain your reasoning.
When you respond to
Answer: MARK ME BRAINLIEST I WORK HARD Soda consumption among children and teens is a health concern for a number of reasons. Drinking soda contributes to childhood weight issues, can lead to tooth decay,1 and can contribute to sleep problems. Some studies also suggest that kids who consume soda may have an increased risk for behavioral issues and mental health problems.
This article discusses the potential connection between soft drinks and behavioral problems, the limitations of this research, and other reasons to limit soft drink consumption in kids. It also covers some of the steps you can take if you are dealing with behavior issues and aggression in children.
Health Problems Associated Soft Drinks
Americans have some of the highest consumption rates of soda per capita worldwide.2 And many of those people consuming soda are very young children.
Over the years, there has been a big push to eliminate soft drinks from school vending machines and to educate parents about the risks associated with sugary drinks. Physicians and nutritionists have made it clear that soda provides children with empty calories and contributes to childhood obesity.
Dentists advise parents not to let children drink soda as well. Sugary drinks aren't good for children's teeth and may cause cavities.3
Most soft drinks also contain caffeine. Caffeine can cause headaches, upset stomach, jitteriness, and sleep problems. It’s also been associated with some behavioral problems and nervous system disorders in children.4
In children, it doesn’t take much caffeine to produce unwanted side effects. The American Academy of Pediatrics (AAP) discourages caffeine intake for kids of all ages.4
Recap
Soda and other sugary soft drinks pose a number of health risks including weight problems, dental cavities, headaches, and sleep problems.
Behavior Problems and Soft Drinks
If the health risks aren’t enough to dissuade parents from giving kids soda, the potential mental health concerns that might be associated with soft drink consumption might be a deterrent.
Research suggests that children who consume soda tend to have slightly higher scores on measures of aggression than do children who do not drink soda beverages. It's important to note, however, that the research only suggests that there is a correlation between soda consumption and aggressive behaviors; research has not proven a causal relationship, meaning that more research is needed to determine whether drinking soda causes this type of behavior.
In one 2013 study published in The Journal of Pediatrics found that aggression, withdrawal behavior, and attention problems are associated with soft drink consumption in young children.5
The researchers assessed 2,929 5-year-old children from 20 different U.S. cities. Even after adjusting for factors such as maternal depression, paternal incarceration, and domestic violence, soft drink consumption was still linked to aggressive behavior.
Children who drank four or more soft drinks per day were more than twice as likely to destroy other people's belongings, get into fights, and physically attack people.
However, it is important to note some flaws in the study that make it difficult to make assumptions about the potential impact of drinking soda. The study did not consider serving size, the type of soda, or what beverages specifically count as soft drinks.
While the study suggests there may be a correlation between drinking soda and behavioral aggression, it isn't enough to conclude that there is a causal connection.
One concerning point that this study indicates is that it is quite common for young children to consume soda. Forty-three percent of five years olds were reported to drink one serving of soda per day, while 4% reported drinking four servings per day.
Why Soda Might Affect Mental Health and Behavior
It’s unclear why soda consumption might be connected to aggressive behavior and other mental health issues. Soft drinks are highly processed, and there is not much research on how certain ingredients impact children. Some studies have linked aspartame to irritability6 and sodium benzoate to ADHD-related symptoms.7
Caffeine has also been linked to some behavior problems in children, so researchers suspect the caffeine content may play a role.
An underlying physical condition, such as low blood glucose levels, could also explain the link. Low blood glucose may cause children to crave soda while also causing them to become withdrawn or aggressive.8
However, further research is needed to understand how soda and mental health issues might be connected.
Recap
Soda may contain sugar, aspartame, sodium benzoate, and caffeine, and these ingredients may play a role in triggering negative side effects in kids.
MARK ME BRAINILEST I WORK SUPER HARD PLEASE!!! YOU ARE WELCOME FOR THE ANSER MARK ME BRAINIEST NOW THANKS. IF YOU NEED MORE ANSWER MORE QUESTION COME TO ME.
Step-by-step explanation:
*
10 The points A, B and C have coordinates A(2, 8), B(9, 7) and C(k, k-2).
a Given that AB = BC, show that a possible value of k is 4 and find the other possible value of k.
4, find the equation of the line that bisects angle ABC.
b For the case where k = 4， find the equation of the line that bisects angle ABC
By using distance formula the following results are obtained
a) Other value of k = 14
b) For k = 4, the equation of bisector of [tex]\angle ABC[/tex] is
[tex]y = \frac{1}{3}x + 4[/tex]
What is distance formula?
Distance formula is used to find the distance between two coordinates.
If the coordinates of one point be ([tex]x_1, y_1[/tex]) and coordinates of other point is ([tex]x_2, y_2[/tex]), then distance between the two points is
[tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]
The points A, B and C have coordinates A(2, 8), B(9, 7) and C(k, k-2).
Length of AB =
[tex]\sqrt{(9 - 2)^2 + (7 - 8)^2}\\\\\sqrt{49 +1}\\\\\sqrt{50}[/tex]
Length of BC =
[tex]\sqrt{(k - 9)^2 + (k - 2 - 7)^2}\\\\\sqrt{(k - 9)^2 + (k - 9)^2}\\\\\sqrt{2(k-9)^2}\\\\(k-9) \sqrt{2}[/tex]
By the problem,
[tex](k-9)\sqrt{2} = \sqrt{50}\\k - 9 = \sqrt\frac{50}{2}}\\k - 9 = \sqrt{25}\\k - 9 = \pm 5\\k - 9 = 5 \ or \ k - 9 = -5\\k = 5 + 9 \ or \ k = 9 -5\\k = 14 \ or \ k = 4[/tex]
The other value of k is 14
b) When k = 4
Coordinate of C = (4, 2)
Since AB =AC , the bisector of [tex]\angle ABC[/tex] passes through the midpoint of AC
Midpoint of AC =
[tex](\frac{2 + 4}{2} , \frac{8+2}{2})\\(3, 5)[/tex]
The line also passes through (9, 7)
Slope of the bisector of [tex]\angle ABC[/tex] = [tex]\frac{7 -5}{9 - 3}[/tex]
= [tex]\frac{1}{3}[/tex]
Equation of the bisector of [tex]\angle ABC[/tex]
[tex]y - 5 = \frac{1}{3}(x - 3)\\\\y - 5 = \frac{1}{3}x -1\\\\y = \frac{1}{3} x - 1 + 5\\\\y = \frac{1}{3} x + 4[/tex]
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/. Which equation represents the line that passes through the points (-8, 6) and (-11, -6)?
[A] (v-8)=-4(x+6)
[B] (v+6)= 4(x-8)
[C] (v-6)=-4(x+8)
[D] (v-6) = 4(x+8)
The equation (D) y - 6 = 4(x+8) represents the line passing through the points (-8, 6) and (-11, -6).
What is the point-slope form of a line?The point-slope form can be used to get the equation of a straight line that traverses a specified point and is inclined at a particular angle to the x-axis. A line exists if and only if each point on it fulfills the equation for the line. This suggests that a linear equation in two variables can represent a line.
The given points are
(x₁, y₁) = (-8, 6)
(x₂, y₂) = (-11, -6)
So, the slope is given by
m = (y₂- y₁)/ (x₂- x₁)
= (-6 -6)/ (-11 -(-8)
= -12/ -3
= 4
Put (x₁, y₁) = (-8, 6) in the equation (y - y₁) = m (x- x₁)
y - 6 = 4(x-(-8)
y - 6 = 4(x+8)
So, the correct option is (D).
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which of the following transducers can steer the sound beam electronically creating a parallelogram-shaped image?
Answer:
Step-by-step explanation:
u
Christa sells bracelets during the summer months, and she made this pictograph to represent her sales. A pictograph is entitled Bracelets Sold. It shows the summer months and pictures of bracelets. A key shows one bracelet equals 4 bracelets. June, 3 bracelets. July, 5 bracelets. August, 2 bracelets. How many bracelets did Christa sell in June?
Answer: 32 bracelets
First multiply each bracelet by 4 to get the correct amount:
3x4=12
4x5=20
Then, add the two.
12+20=32
Step-by-step explanation:
On a plane there were 6 airline
workers and 240 passengers.
If each worker looked after the same
number of passengers, how many
passengers did each worker look after?
Each worker looked 40 passengers
From the question, we have
On a plane there were 6 airline workers and 240 passengers.
each worker looked after the same number of passengers
number of passengers = 240/6
=40
Each worker looked 40 passengers
Divide:
Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.
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What term is used to describe an error that occurs when numbers are moved to the right or left in an amount column?.
The term used to describe an error that occurs when numbers are moved to the right or left in an amount column is "Slide".
Slide:
An accounting slide is a mistake that happens when the decimal point of a number is moved to the left or right of where it should be.
For instance, a bookkeeper would enter $1,200.50 in place of $12,005 in the revenue account or $250.75 in place of $2,507.50 in the monthly insurance expenses. In general, bookkeeping mistakes and accounting blunders lead to financial record misstatements.
"Slide" is the name for a mistake that happens when numbers are moved to the right or left in an amount column.
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10) Tell whether the slope of AB is parallel, perpendicular, or neither to the
slope of CD. A(-3, 2) and B(2, 4) C(4, 0) and D(6,-5)
AB slope is 2/5, CD slope is -5/2; Neither
AB slope is 2/5, CD slope is -5/2; Parallel
AB slope is 2/5, CD slope is -5/2: Perpendicular
AB slope is -5/2, CD slope is 2/5; Parallel
Answer:
its A
Step-by-step explanation:
-x+[tex]5-x=-3[/tex]
Answer:
x = 4
Step-by-step explanation:
-x + 5 - x = -3 Combine like terms
-2x + 5 = -3 Subtract 5 from both sides
-2x = -8 Divide both sides by -2
x = 4
Rita has $20,000 to invest for five years and she found an interest rate of
4%. How much money will she have at the end of five years if the interest
rate compounds monthly?
The amount of money Rita will get after 5 year with interest rate compounds monthly is $4,420.
Explain the term compound interest?The interest on either a deposit that is calculated using both the initial principle and the accrued interest from prior periods is known as compound interest. In other words, compounding is interest that is earned on interest. Different frequency patterns, such as daily, monthly, or yearly, are provided for compounding interest.The formula for the calculation of the compound interest is-
A = P(1 + r/100n)∧nt
In which,
A = amount after compounding
P = principal amount ( $20,000 )
n = number of time principal amount compounded in a year. ( 12 )
t = total time in years. (5 )
r = rate of interest (4%)
Put the value in eq.
A = 20,000(1 + 4/1200)∧5×12
A = 20,000×1.22
A = 24420
CI = A - P
CI = 24420 - 20000
CI = 4,420.
Thus, the amount of money Rita will get after 5 year with interest
rate compounds monthly is $4,420.
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g(n)=1+5(n−1)
Complete the recursive formula of g(n)=g(n−1)+ ?
The recursive formula which correctly represents the given formula; g ( n ) = g ( n − 1 ) + 5.
What is the recursive formula for the given arithmetic progression?It follows from the task content that the expression which represents the recursive formula.
By observation, the common difference, d of the arithmetic progression is; 5.
On this note, the recursive formula can be written as follows;
g ( n ) = g ( n − 1 ) + 5.
Consequently, the required recursive formula for the given arithmetic progression is; g ( n ) = g ( n − 1 ) + 5.
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Find the value of Z such that 0.11 of the area lies to the right of Z.
Round your answer to 2 decimal places.
The value of z is 1.23.
Given:
the value of Z such that 0.11 of the area lies to the right of Z.
0.11 = 11%
z score is calculated :
z = x - μ / σ
where μ=0 and σ=1
so z value is equal to 1.23.
More details in the image uploaded.
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a small group selected by the pollsters to represent the most important characteristics of an entire population are known as a
Answer:
SampleStep-by-step explanation:
The small group selected by pollsters to represent the entire population is called a “Sample”.7s+c/-3 use c=-9 and s=-5
Answer:
-32
Step-by-step explanation:
Given expression,
→ 7s + (c/-3)
Solving the given expression,
→ 7s + (c/-3)
→ 7(-5) + (-9/-3)
→ -35 + 3 = -32
Hence, the answer is -32.
Answer:
[tex]-32[/tex]
Step-by-step explanation:
[tex]When[/tex] [tex]c=-9, s=-5[/tex]
[tex]7s+\frac{c}{-3} = 7(-5) +\frac{-9}{-3}[/tex]
[tex]= -35+3\\\\=-32[/tex]
PLEASE ALOT OF POINTS I need an answer quick
Graph the line through (0, -4) with m = -3
Answer:
Step-by-step explanation:
hope it helps
Amira had 3 - of a bag of cat food. The food lasted 7 4 How much cat food did Amira's cats eat per week?
The cat ate 3/7 of a bag per week when the food lasted for 7/4 week.
According to the question,
We have the following information:
Amira had 3/4 of a bag of cat food. The food lasted 7/4 weeks.
Now, we can easily find how much food Amira's cat ate in one week by dividing the total number of bags of food by the number of weeks the food lasted.
So, we have the following expression:
3/4 of a bag = 7/4 weeks
1 week = 3/4 ÷ 7/4
1 week = 3/4 * 4/7 of a bag
1 week = 3/7 of a bag
Hence, the cat ate 3/7 of a bag per week when the food lasted for 7/4 week.
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What is the a equal to in the math problem below??
-6(a+8)
Answer: -6a-48
Step-by-step explanation:
-6(a+8)
distribute and you get
-6a-48
In isosceles triangle dac, ad is congruent to ac. Kiran knows that the base angles of an isosceles triangle are congruent. What additional information does kiran need to know in order to show that ab is a perpendicular bisector of segment cd?.
If DB and BC are congruent, then AB must be a perpendicular bisector. We conclude that AB is congruent to AB by the reflexive characteristic because DB and BC are congruent.
ADB is congruent to ACB according to the Side-Side-Side, or SSS, congruency rule because the sides AD, AB, and DB in triangle ADB are congruent to the equivalent sides AC, BC, and AB in triangle ACB.
As a result, CPCTC ABD = ABC according to the notion of congruency, where Congruent Parts of Congruent Triangles are Congruent.
Due to the fact that ABD and ABC are linear pair angles,
ABD + ABC = 180°,
ABD + ABD = 2, and ABD = 180°
by virtue of the substitution feature,
ABD = 180°/2 = 90°.
As AB is perpendicular to CD and AB is a perpendicular bisector of CD, ABD = 90° = ABC.
Therefore, the option; DB and BC are congruent is what Kiran needs to know in order to demonstrate that AB is a perpendicular bisector of segment CD.
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I need help please!!
the slope of the given point is m=−7/2
What is an angle that is supplementary to ∠ECF?
Please help!!!
Answer:
HCE or ECH
Explanation:
Supplementary is angle that add up to 180° (A line)
Answer: HCE
Step-by-step explanation:
A supplementary angle is an angle that when added to another angle, equals 180 degrees, or a straight line.
Angles HCE and ECF add up to 180 degrees.
Can someone please help
The angle 1 is 88 degree, 2 is 42 degree and the 3 is 113 degree.
We know that the sum of the angles of the triangle is 180, so in one triangle where the 3 angle is missing we can write as:
42 + 25 + ∠3 = 180
∠3 + 67 = 180 ,
∠3 = 113°
now in the triangle where 1 and 2 angles are missing, we can say that ∠2 = 42° because of transversely equal angles:
so, ∠ 2 = 42°
now again for a triangle,
∠1 + 42 + 50 = 180
∠1 + 92 = 180
∠1 = 88°
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5. suppose a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x
If a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1
The mean of the normal distribution = 4
Standard deviation of the normal distribution = 1.5
The value of x = 5.5
The z-score of the normal distribution = The mean of the normal distribution / Standard deviation of the normal distribution
Substitute the values in the equation
The z-score of the normal distribution = (5.5 - 4) / 1.5
Substract the terms
= 1.5 / 1.5
= 1
Hence, if a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1
The complete question is:
suppose a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x = 5.5
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Kaden drinks 1 3/4 glasses of milk each day. At this rate, how many days will it
take him to drink a total of 14 glasses?
Answer:
It will take 8 days
Step-by-step explanation:
Mixed numbers in equations
1 3/4 * d = 14
Change the mixed number to an improper fraction
1 3/4 = ( 4*1 + 3) /4 = 7/4
7/4 * d = 14
Multiply each side by 4/7
4/7 * 7/4 *d = 14 * 4/7
d = 8
It will take 8 days.
Laura received $10 from her aunt on her 8th birthday. On
her 9th birthday, her aunt gave her $20. For her 10th
birthday, her aunt gave her $40. How much do you think
Laura's aunt will give her on her 11th birthday? Justify your
answer (prove your answer is right or reasonable).
What is the shortest distance from the point (9, 1) to the line y = 2x + 3? Round to the
nearest tenth.
The shortest distance from the point (9, 1) to the line y = 2x + 3 is 10 units
The coordinates of the point = (9,1)
The equation of the line is
y = 2x + 3
Here the slope of the line is 2
The shortest distance between the point and the second line will be the perpendicular distance between the point and line
The perpendicular line slope will be -(1/m)
= -(1/2)
This perpendicular line will pass through the point (9, 1)
The point slope form is
y - 1 = -(1/2)(x - 9)
y - 1 = -(1/2x) + 9/2
y = -(1/2)x + 9/2 + 1
y = -(1/2)x + 11/2
Solve the equation
y = 2x + 3
y = -(1/2)x + 11/2
0 = (2 + 1/2)x -5/2
5/2 x = -5/2
x = -5/2 / 5/2
x = -1
Then
y = 2(-1) + 3
y = -2 + 3
y = 1
The distance between the point (9,1) and (-1, 1)
= [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(-1-9)^2+(1-1)^2}[/tex]
= [tex]\sqrt{100}[/tex]
= 10 units
Hence, the shortest distance from the point (9, 1) to the line y = 2x + 3 is 10 units
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There are 18 male students and 24 female students in a grade 10 math class. The math teacher
wants to divide the class into groups that will have equal amounts of girls in each
equal amounts of boys in each group. What is the greatest number of groups that the teacher can
make?
Answer:
the greatest number I guess is 2
Step-by-step explanation:
18÷2= 9male to the 2group
24÷2=12female to the 2group