T = √(2023 2023) (2023 +2023) + (2023 x 2023) + (2023 - 2023).
To simplify the given expression, we can first evaluate each term inside the square root, and then add them up. Using basic algebraic operations, we get:
T = √(2023^2)(4046) + (2023^2) + 0
T = √(2023^2)(4046 + 1)
T = √(2023^2)(4047)
T = 2023√4047
Therefore, the simplified expression for T is 2023√4047.
Which research scenario would most likely be biased against non-voters? Select all that apply.
1. a convenience sample collected at a political rally used to determine candidate preferences
2. a volunteer sample collected at a political rally used to determine candidate preferences
3. a simple random sample of all non-voters used to determine why they don’t vote
4. a simple random sample of all eligible voters, some of whom didn’t have time to vote
5. a volunteer sample collected at large department store to determine who they voted for
The scenariο that wοuld mοst likely be biased against nοn-vοters is a vοlunteer sample cοllected at a pοlitical rally used tο determine candidate preferences
What is a biased expressiοn?A cοgnitive bias clοuds οur critical thinking and may result in the spread οf false infοrmatiοn that may be harmful tο οther peοple. Biases cause us tο avοid infοrmatiοn that might be uncοmfοrtable οr unwelcοme rather than lοοking intο the infοrmatiοn that might help us reach a mοre accurate cοnclusiοn.
A cοnvenience sample cοllected at a pοlitical rally used tο determine candidate preferences is nοt a biased sample. Since the nοn-vοters are nοt
A vοlunteer sample cοllected at a pοlitical rally was used tο determine candidate preferences. It prefers a particular member. This is a biased survey.
A simple randοm sample οf all nοn-vοters was used tο determine why they dοn’t vοte. It is biased. Because a grοup οf peοple decides nοt tο give a vοte.
A simple randοm sample οf all eligible vοters, sοme οf whοm didn’t have time tο vοte. It is a sample.
A vοlunteer sample was cοllected at a large department stοre tο determine whο they vοted fοr. It is a nοn-biased survery. The peοple dο nοt prefer a particular team.
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If sec(x) = -root2 and pi/2
Answer: x = π - π/4 = 3π/4
Step-by-step explanation:
If sec(x) = -√2 and x is in the second quadrant (between π/2 and π), we can use the identity:
sec^2(x) - 1 = tan^2(x)
to find the value of tan(x):
sec^2(x) - 1 = tan^2(x)
(-√2)^2 - 1 = tan^2(x)
2 - 1 = tan^2(x)
1 = tan^2(x)
Taking the square root of both sides, we get:
tan(x) = ±1
Since x is in the second quadrant, the angle that satisfies tan(x) = 1 is π/4. Therefore, we have:
x = π - π/4 = 3π/4
Note that the angle that satisfies tan(x) = -1 is in the fourth quadrant, so it is not relevant to this problem.
What conclusion can be determined by the dot plot
Dot plots are useful for visualizing the distribution of data and identifying patterns, trends, and outliers. They are often used in data analysis, quality control, and scientific research to help draw conclusions and make informed decisions based on data.
A dot plot is a graphical representation of statistics that presents character information factors through the use of dots. From a dot plot, possible decide several conclusions, depending on the data being displayed.
For instance, if the dot plot presents information on the height of a collection of people, you can still determine the range of heights inside the organization, the most common top, and any outliers (i.e., individuals with severe heights).
If the dot plot displays facts at the ratings of a collection of students on a test, you can still determine the range of rankings, the median score, and the distribution of rankings (i.e., whether or not the ratings are evenly distributed or clustered round sure values).
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What conclusion can be determined by the dot plot? Explain in detail about the dot plot.
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Please Show detailed algebraic work.
Using the equation C(x) = 120(0.88)ˣ, we found that after 19.27 hours, the amount of caffeine becomes 10mg.
What is meant by an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
Given,
The initial amount of caffeine in the beverage = 120 mg
The rate at which the caffeine decreases = 12% per hour w
We are asked to find the time taken for the caffeine amount to become 10mg.
Now let the initial amount be 100 per cent.
After one hour, the amount becomes (100-12) = 88% of 120 = 0.88 * 120
So after every one hour, there is 88% caffeine left.
Now after two hours,
the amount of caffeine = 88% of (0.88*120) = 0.88*0.88*120 = 120(0.88)²
So after x hours, we can write the equation as:
Amount of caffeine left C(x) = 120(0.88)ˣ
Now for 10mg to be left, the time taken is:
10 = 120(0.88)ˣ
1/12 = (0.88)ˣ
log (1/12) = x log(0.88)
-1.079 = x (-0.056)
x = 19.27 hours
Therefore using the equation C(x) = 120(0.88)ˣ, we found that after 19.27 hours, the amount of caffeine becomes 10mg.
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Work out 2 and 1/2 x 1 and 4/5
Give your answer as a mixed number in its simplest form
Answer:
[tex]4\frac{1}{2}[/tex]
Step-by-step explanation:
List 3 sides to a right triangle. explain how you can use three pythagorean theorem to know that your three sides will create a right triangle.
The 3 sides to a right triangle are:
Leg 1 (a)Leg 2 (b)Hypotenuse (c)State the pythagorean theorem?The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides (called the legs) is equal to the square of the length of the longest side (called the hypotenuse).
So, if we have three sides of a triangle and we want to know if it forms a right triangle, we can use the Pythagorean Theorem in the following three ways:
Check if a² + b² = c², where a and b are the lengths of the two legs and c is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.
Check if b² + c² = a², where b and c are the lengths of the two legs and a is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.
Check if a² + c² = b², where a and c are the lengths of the two legs and b is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.
If none of these equations are true, then the triangle is not a right triangle.
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Determine the power consumed by the resistor
The power consumed by resistor R3 is 0.79 watts.
What is power?The rate at which energy is transferred or converted is known as Power. It is a measure of how much work can be done in a given amount of time. Power is typically measured in watts and is a key factor in determining the efficiency of machines and systems.
To determine the power consumed by resistor R3, we need to first find the current flowing through it.
E₁ = I(R₁ + R₂ + R3 + R4)
I = E₁ / (R₁ + R₂ + R3 + R4)
= 30 / (152 + 202 + 252 + 102)
= 0.056 A
Now that we know the current flowing through R3, we can use Ohm's Law again to find the power consumed by it:
P = I²R3
= (0.056)² x 252
= 0.79 W
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Evaluate 1/3 · 5/6
GIVING 20 POINTS
xplain how you would calculate the area of a cross section of the dam without using calculus. use your explanation to calculate the area of the cross section. is the area you found exact? why or why not?
Cross-sectional area of the dam can be calculated without using calculus as explained below:
Step 1: Draw the cross-section of the dam on a graph paper and divide it into simple shapes like triangles, rectangles, and circles.
Step 2: Calculate the area of each shape separately using the appropriate formulae. For example, the area of a rectangle is length times width, area of a triangle is 1/2 times base times height and the area of a circle is pi times radius squared.
Step 3: Add the areas of all the shapes to find the total cross-sectional area of the dam. This gives an approximate value of the area since the actual shape of the cross-section is not perfectly regular.If we take a concrete example of a dam with a cross-section of a trapezoid,
we can calculate the cross-sectional area using the above steps:
Step 1: Draw the cross-section of the dam on a graph paper as shown below. The cross-section of the dam can be divided into a rectangle and a triangle.
Step 2: Calculate the area of the rectangle and the triangle separately using the formulae for the area of the rectangle and the triangle respectively.Area of the rectangle = base times height = 10 m times[tex]4 m = 40 m²[/tex]Area of the triangle = 1/2 times base times height = 6 m times 4 m = 12 m²
Step 3: Add the areas of the rectangle and the triangle to get the total cross-sectional area of the dam.Area of the cross-section = area of rectangle + area of triangle= [tex]40 m² + 12 m²= 52 m²[/tex]The area found using the above method is not exact since it is an approximation of the actual area of the cross-section of the dam. It can be more accurate by dividing the cross-section into smaller and simpler shapes and calculating their areas individually.
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I am an integer in quadrant to my exponent is less than -1 my y-coordinate is more than two my x-coordinate is greater than -3 the sum of the absolute values of my coordinates is five who am I
The integer that satisfies all of these conditions is -4.
Exponentiating -4 gives 16, which is less than -1.
The y-coordinate of -4 on the coordinate plane is above 2.
The x-coordinate of -4 on the coordinate plane is greater than -3.
And, the sum of the absolute values of the coordinates of -4 is 7, which is equal to five.
What is the result when the number 94 is decreased by 50%?
Step-by-step explanation:
94 - 50% * 94 =
94 - .50 * 94 =
94 - 47 = 47
Answer:
47
Step-by-step explanation:
50 × 94 ÷ 100 =
47,00 ÷ 100=
47
Harry, Jason and Sarah are taking the GMAT which is required by most applicants for admission to graduate schools of business. The three friends want to get admissions to three different business schools. Harry can get the admission if he gets a score above 650 in GMAT, Jason can get the admission if he gets above 630 and Sarah can get the admission if she gets above 670. Scores on the GMAT are roughly normally distributed with a mean of 550 and a standard deviation of 115. What is the probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another.
Probability that Harry, Jason, and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.0088 or approximately 0.9%.
The probability of Harry, Jason, and Sarah getting admission to their desired schools is the probability that Harry's score is above 650, Jason's score is above 630, and Sarah's score is above 670. The scores on the GMAT are roughly normally distributed with a mean of 550 and a standard deviation of 115.So, let's first standardize Harry's score:Z = (650 - 550) / 115 = 0.87Similarly, for Jason's score:Z = (630 - 550) / 115 = 0.70And for Sarah's score:Z = (670 - 550) / 115 = 1.04Now we need to find the probabilities of getting each of these Z-values. We can do that using the standard normal distribution table. The table gives the probability that a standard normal random variable is less than or equal to a certain Z-value.To find the probability that Harry's score is above 650, we need to find the probability that Z > 0.87. This can be found by subtracting the probability of Z ≤ 0.87 from 1:P(Z > 0.87) = 1 - P(Z ≤ 0.87) = 1 - 0.8078 = 0.1922Similarly, the probability that Jason's score is above 630 is:P(Z > 0.70) = 1 - P(Z ≤ 0.70) = 1 - 0.7580 = 0.2420And the probability that Sarah's score is above 670 is:P(Z > 1.04) = 1 - P(Z ≤ 1.04) = 1 - 0.8508 = 0.1492The probability that all three events occur (Harry's score is above 650, Jason's score is above 630, and Sarah's score is above 670) is the product of their probabilities:P(Harry, Jason, and Sarah) = P(Z > 0.87) × P(Z > 0.70) × P(Z > 1.04) = 0.1922 × 0.2420 × 0.1492 = 0.0088Therefore, the probability that Harry, Jason, and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.0088 or approximately 0.9%.
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What is the interest on a $1,000, 18-month loan, with a 10% simple interest rate?
Answer:
$150
Step-by-step explanation:
Interest = Principal x Rate x Time
where Principal is the amount borrowed, Rate is the interest rate, and Time is the duration of the loan.
In this case, the Principal is $1,000, the Rate is 10%, and the Time is 18 months (which we'll convert to a fraction of a year).
First, we need to convert 18 months to a fraction of a year. Since there are 12 months in a year, 18 months is equal to 18/12 = 1.5 years.
Using the formula:
Interest = Principal x Rate x Time
Interest = $1,000 x 0.10 x 1.5
Interest = $150
So the interest on the $1,000 loan with a 10% simple interest rate for 18 months is $150.
Answer:
The formula for simple interest is I = Prt, where I is the interest, P is the principal or amount borrowed, r is the interest rate, and t is the time in years.
In this case, P = $1,000, r = 10% or 0.10 as a decimal, and t = 1.5 years (since 18 months is equivalent to 1.5 years).
I = Prt
I = $1,000 * 0.10 * 1.5
I = $150
Therefore, the interest on the $1,000 loan with a 10% simple interest rate for 18 months is $150.
factorise fully
[tex]x {}^{2} + x[/tex]
[tex]15a {}^{2} + 19a - 8[/tex]
[tex]8x {}^{2} - 6xy - 9y {}^{2} [/tex]
[tex]a {}^{2} - ab - a + b[/tex]
Answer:
1 . x(x+1)
2.(3a-1)(5a+8)
3.(4x + 3y) ( 3x - 3y)
4.(a+b)
What is the length of DE? and What is the length of AD? and What is the length of EC?
Answer:
DE's length is 1/2 of BC's length, due to it being a mid segment (13)((You can tell it is a mid segment due to the congruency lines)). AD's length is 12, due to there being a midpoint. EC's length is 10, also due to the congruency lines.
A car dealer has 20 Toyota Camrys and 25 Honda Accords left on the parking lot. The dealer wants to arrange the cars in rows so that each row has the same number of vehicles and the same number of vehicles of each type. What is the greatest number of rows that can be formed?
There will be __ rows with __ Toyota Camrys and __Honda Accords in each row.
Use the data in the given table to fill in the missing coefficients. Round your answers to 3 decimal places. X y
2 8. 18
6. 5 12. 816
11 16. 768
15. 5 21. 222
20 26. 462
24. 5 31. 36
29 34. 584
y
=
x
+
The missing coefficients in the equation y = mx + b are m = 0.841 and b = 18.813. The final equation that fits the given data is y = 0.841x + 18.813
To find the missing coefficients in the equation y = mx + b, we need to use the given data in the table to determine the values of m and b.
We can start by using two of the data points to set up a system of equations:
Using (5, 23.018) and (6, 23.859):
m(5) + b = 23.018
m(6) + b = 23.859
Subtracting the first equation from the second equation gives:
m(6) - m(5) = 0.841
Simplifying this expression:
m = 0.841 / (6 - 5) = 0.841
Now we can substitute the value of m into one of the original equations to solve for b:
m(5) + b = 23.018
0.841(5) + b = 23.018
b = 23.018 - 4.205
b = 18.813
Therefore, the missing coefficients are:
m = 0.841
b = 18.813
The equation y = 0.841x + 18.813 fits the given data.
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The given question is incomplete, the complete question is:
Use the data in the given table to fill in the missing coefficients. Round your answers to 3 decimal places. X y 5 23.018 5.5 23.438 6 23.859 6.5 24.035 7 25.449 7.5 24.868 8 26.058 I Enter an integer or decimal number [more..] y = I+
The area of this circle is 72π m².
What is the area of a 45º sector of this circle?
Responses
8π m²
9π m²
12π m²
18π m²
The area of the sector is evaluated to be equal to 9π square meters
How to evaluate for the area of the sector.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.
For the area of circle 72π m²;
πr² = 72π m²
r² = 72 m²
hence the area of the sector is calculated as follows:
area of the sector = (45°/360°) × π × 72 m²
we simplify by multiplication and division
area of the sector = 1/8 × π × 72 m²
area of the sector = π × 9 m²
area of the sector = 9π m².
Therefore, the area of the sector is evaluated to be equal to 9π square meters
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5^x+1+5^x-1 simply using the law of exponents
Answer:
5^x+x
Step-by-step explanation:
5^x+1+5^x-1
First of all 1- 1 = 0
so we are here with 5^x +5^x
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
The answer you're looking for is x = 6, and the missing angle is 30º
Step-by-step explanation:
In order to find the answer we need to find out what the angle amount actually is. We can use the equation 180º = 110+ 40 + (8x-18).
Now there are two ways to solve this equation you could solve it by starting with the equation actually is or you can find out the missing angle using another equation.
First Method:
Using 180º = 110+ 40 + (8x-18), you first need to do is to combine like terms such as combining 110, 40, and -18, giving you 132.
Now you have 180 = 132 + 8x.
Then you will have to make sure that 8x is left by itself so do the opposite operation and to keep the equation balanced you do it on both sides giving you 48 = 8x. The only step left to do is to do the opposite operation on both sides which is dividing by 8, giving you 6 = x
Now with that, you replace x, with 6, and go from there.
(8x-18) = (8×6-18) = (48 - 18) = 30.
With that, we are finished with the equation.
However, the other method you could use, which is easier in my opinion, can be found below.
Second Method:
The first thing we do is find out immediately what the missing angle (m) is using the equation 180 = 110 + 40 + m.
You combine like terms 110 and 40, giving 150 and then get,
180 = 150 + m.
You then do the inverse of operations, which is subtracting 150 from both sides and you get 30 = m.
Now that we complete that we start with our other equation which is:
30 = 8x-18. You then do inverse of -18, which adds 18 to both sides giving: 48 = 8x.
Finally doing the inverse operation of multiplying is dividing 8 by both sides giving 6 = x as the correct answer.
what is the slope from (-4,6) to (2, 3/2)?
Answer:
1\2
Step-by-step explanation:
Find the value of Sin -¹ (tan 3.14/4)
a. 0
b. 3.14
c. 2
d. 3.14/2
Please select the best answer from the choices provided
Answer:
D.) 3.14/2
Step-by-step explanation:
What is the arc length of an arc with radius 18 inches and central angle 22°? Round to nearest hundredth or
leave in terms of π. Show your work.
As a result, the answer to the following question, As a result, the supplied radius arc's arc length is roughly 6.91 inches (rounded to nearest hundredth).
what is radius?In more modern use, the length of a sphere or sphere is equal to its radius in standard geometric, so it has several line segments from its centre to its circumference. The phrase is derived from the Latin word for radius, which also referred to the spokes of a waggon wheel. The radius of a circle is the distance between the centre and any point on its periphery. Often, "R" or "r" is used to signify it. A radius is a boundary line with one terminus in the centre and a second around the perimeter of a circle. Vide letter diameter equals radius The dimension of a circle is the segment that passes its centre and has extremities that are on the circle.
The formula for calculating the arc length of a circle is:
Arc length = radius x central angle in radians,
In order to use this formula, we must first convert the centre angle from degrees to radians. We are aware of the following:
2 radians Equals 360 degrees
360 degrees divided by 2 radians equals x degrees divided by y radians
(x degrees * 2 radians) / 360 degrees = y
y = (22 deg * 2 radians) / 360 deg = 0.38397 deg (rounded to five decimal places)
arc length Equals radius multiplied by Centre angle in radians
With r = 18 inches and = 0.38397 radians, we get:
arc length = 18 inches multiplied by 0.38397 equals 6.9115 inches (rounded to four decimal places)
As a result, the supplied arc's arc length is roughly 6.91 inches (rounded to nearest hundredth).
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What is this written as an algebraic expression? the sum of number and 9.
Answer:
The sum of a number and 9 can be written as:
x + 9
where "x" represents the number being referred to.
Alternatively, if we want to use a different variable, we can write it as:
n + 9
where "n" represents the number being referred to.
Hope this helped, if not I'm sorry! If you need more help, feel free to ask! :]
You are flipping two coins. Find the probability of flipping two tails.
A. 1/2
B. 1/24
C. 1/8
D. 1/4
Answer:
D. 1/4
Step-by-step explanation:
The probability of flipping a tail is 1/2. To find the probability of flipping two tails, multiply.
1/2 x 1/2 = 1/4
Answer: Here we will learn how to find the probability of tossing two coins.
Let us take the experiment of tossing two coins simultaneously:
When we toss two coins simultaneously then the possible of outcomes are: (two heads) or (one head and one tail) or (two tails) i.e., in short (H, H) or (H, T) or (T, T) respectively; where H is denoted for head and T is denoted for tail.
Therefore, total numbers of outcome are 22 = 4
The above explanation will help us to solve the problems on finding the probability of tossing two coins.
Step-by-step explanation:
THE ANSWER MUST BE AT LEAST 1/4 OR 1/8
IF THAT IS WRONG LET ME KNOW!
AND IF YOU NEED A TUTOR I AM OPEN FOR HELP JUST CONTACT ME IF YOU HAVE ANY QUESTIONS!
A hardware store charges a $40 rental fee and
$20 per day to rent a power washer. Which
equation correctly relates the total cost y to rent the
washer for x days? 8. F. 1-3
A. Y=20+40x. B. Y=40+20x
C. Y=40 -x/20.
D. Y=20 -x/ 40.
The equation correctly relates the total cost y to rent the washer for x days is option (B) Y = 40 + 20x
The rental fee of $40 is charged regardless of the number of days the power washer is rented. In addition to this fee, there is a daily charge of $20 per day.
Therefore, the total cost of renting the power washer for x days can be calculated by multiplying the daily charge by the number of days rented and adding the rental fee:
Total cost = (daily charge) x (number of days rented) + rental fee
Total cost = $20x + $40
This linear equation can be rearranged to the form:
Y = 40 + 20x
Therefore, the correct option is (B) Y = 40 + 20x
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I will give Brainliest! =D
Determine the rest of the side lengths, and describe your strategies!
Considering the figure, the missing lengths are
the topmost is 15the other length is 4What is similar triangles?In geometry, the phrase "similar triangles" refers to triangles whose respective sides are proportionate and whose corresponding angles are congruent.
Hence, if the triangle's corresponding angles are congruent, the side should be in proportion.
The proportions are as follows
say the side on top of 10 (in horizontal line) is y
y / (10 + 15 + 12.5) = 10 / (10 + 15)
y / 37.5 = 10 / 25
cross multiplying
25y = 37.5 * 10
25y = 375
y = 15
say the side below side 10 (in horizontal line) is x
x / 10 = 10 / (10 + 15)
x / 10 = 10 / 25
cross multiplying
25x = 100
x = 4
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What is equivalent to the answer in
8(2y+1/4)?
FYI the “1/4” is not divided it’s a fraction
Answer:
[tex]\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find an \underline{equivalent expression}.}[/tex]
[tex]\textsf{This expression is set up to allow us to use the \underline{Distributive Property}.}[/tex]
[tex]\Large\textsf{What is the Distributive Property?}[/tex]
[tex]\textsf{The \underline{Distributive Property} is a property that allows us to distribute.}[/tex]
[tex]\large\underline{\textsf{For this problem;}}[/tex]
[tex]\textsf{We can use the Distributive Property to distribute the 8 into values in the Parentheses.}[/tex]
[tex]\large\underline{\textsf{Distribute:}}[/tex]
[tex]\mathtt{8(2y+\frac{1}{4} )}[/tex]
[tex]\mathtt{(8 \times 2y) + (8 \times \frac{1}{4}) .}[/tex]
[tex]\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}[/tex]
Answer:
16y + 2
Step-by-step explanation:
Now we have to,
→ Find the equivalent expression.
The expression is,
→ 8(2y + (1/4))
Let's simplify the expression,
→ 8(2y + (1/4))
→ 8(2y) + 8(1/4)
→ 16y + (8/4)
→ 16y + 2
Hence, the answer is 16y + 2.
A school sports team contains 68 students. 33 do field events, 40 do track events, 23 do swimming, 14 do both field and track events. If 15 students do field events only and 10 do both swimming and track events, how many students do a) swimming knly b)track events only c) all three events?
Answer:
9, 20 and 4
Step-by-step explanation:
Swimming only 9
Track only 20
All 3 events
14 did track and field
10 did track and swimming
Those who sis all 14- 10 = 4
The answers are the students do a) swimming only = 9, b)track events only = 20 and c) all three events = 4
What is a Venn diagram?A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.
Given that, a school sports team contains 68 students. 33 do field events, 40 do track events, 23 go swimming, 14 do both field and track events. If 15 students do field events only and 10 do both swimming and track events,
Please refer to picture attached
Therefore,
15+a+c+d = 33.......1
b+c+d+e = 40.........2
a+b+d+f = 23..........3
c+d = 14...............4
a+d = 8.............5
b+d = 10.............6
Now, solving for variables,
From 1 and 4,
a = 4
Therefore, from 5,
d = 4
From 6,
b = 6
Put these in eq 3,
f = 9
c = 10
e = 20
Therefore,
Swimming only = 9
Track events = 20
All three = 4
Hence, the answers are the students do a) swimming only = 9, b)track events only = 20 and c) all three events = 4
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