The rate exists water being poured into the cup when the water level is 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].
What is meant by chain rule?To determine the derivative of a composite function in differential calculus, apply the chain rule formula. If y = f(g(x)), then according to the chain rule, the instantaneous rates of change of the functions f and g with respect to x produce the instantaneous rate of change of f with respect to x.
A composition of functions, such as the composition of the functions f and g, f(g(x)), can be used to determine the derivative using the chain rule.
Let us set up the following variables:
R, Radius of conical cup (cm) = 30 cm
H, Height of the conical cup (cm) = 10 cm
Our aim is to find dV/dt when h = 9 and we are given dh/dt = 2
By similar triangles we have
r : h = R : H
r/h = 30/10
⇒ r = 3h
The volume of a cone is 1/3π r²h, So:
V = 1/3π r²h
simplifying the equation, we get
= 1/3π (3h²)h
= 1/3π 9h²h
= 3π h³
Differentiating wrt h we get:
dV/dh = 9π h²
Applying the chain rule we have:
dV/dt = (dV/dh)(dh/dt)
= 9π h² × 2
= 18π h²
If h = 9 then
[tex]$\left[\frac{d V}{d t}\right]_{h=9}=18 \pi\left(9^2\right)=1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].
Therefore, the rate exists water being poured into the cup when the water level 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].
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A certain statistic d is being used to estimate a population parameter D. The expected value of d is not equal to D. What property does d exhibit?
The sampling distribution of dis normal.
B
The sampling distribution of d is binomial.
с
The sampling distribution of dis uniform.
d is unbiased.
E
d is biased
Using the Central Limit Theorem for proportions, the correct option is:
E. The statistic is biased.
In plain English, what is the central limit theorem?
According to the central limit theorem, even if a population isn't normally distributed, you may still obtain sufficiently big samples from it and have the samples' means be distributed normally.
What is the central limit theorem and why is it significant?
Because of the Central Limit Theorem, we can confidently assume that the sampling distribution of the mean will be normally distributed in most situations.
Since a normal distribution is assumed, we can benefit from statistical methods, as we will see in the section after this one.
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Find the area of the polygon with the given vertices.
W(-1, 1)
-4
Z(-3,-2)
4
Ay
2
-4
2
X(4,1)
4 x
Y(2,-2)
The area of a polygon with the given vertices is calculated by adding the areas of the individual triangles that make up the polygon.
What is polygon?A polygon is a closed figure in a plane consisting of a set of straight line segments connected end-to-end. The sides of a polygon are all of equal length, and the angles between them are all of equal measure. Polygons are one of the most fundamental shapes in geometry. They include triangles, squares, rectangles, hexagons, and many more.
The area of triangle WXZ is calculated as (1/2) × |XW × ZY|,
where XW is the vector from W to X and ZY is the vector from Z to Y.
In this example,
XW = (3, -2) and ZY = (-2, -4).
Therefore, the area of triangle
WXZ is (1/2) ×|(3, -2) × (-2, -4)| = (1/2) × 14 = 7.
The area of triangle XYA is calculated similarly,
where XY = (2, 3) and YA = (-2, -4).
Therefore, the area of triangle
XYA is (1/2) ×|(2, 3) ×(-2, -4)| = (1/2)× (-14) = -7.
The area of the polygon is calculated by adding the areas of the individual triangles, which in this example is 7 + (-7) = 0. Therefore, the area of the polygon with the given vertices is 0.
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How is the number of Electoral College seats per state determined? A. by the number of party delegates assigned to the state B. by the total number of
Each state is given a specific amount of "votes" under the "Electoral College" system. The amount of "votes" each state receives is proportionate to its size.
What is the makeup of the Electoral College? There are 538 electors in all. The number of electors allotted to each state is equal to the sum of its two Senate seats plus the number of representatives in the House of Representatives.Three electoral votes are granted to the District of Columbia under the 23rd Amendment. According to the amount of each State's population as established by the Census, each State is given a certain number of electors equal to the sum of its U.S. Senators (which are always two) and U.S. Representatives.There are two steps involved in selecting each State's electors. The political parties in each State first select elector candidate slates before the general election. Second, during the general election, each State's voters choose its electors by voting ballots.To learn more about Electoral College refer to :
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1. Write the equation of the mirror line for the segment with endpoints (5, 4) and (-1, -1).
2. Find the reflection of the point A(3, -2) through the mirror line of y = 1/2x − 1.
The light blue askes for the word form, the green says g= -1, the yellow askes for possible solutions, the purple wants how you shade the number line.
Please help!!!!!!!!!!!!!!!!!!!!!
Answer: get yio colors straightv
Step-by-step explanation:
whats the answer? please help!
Answer:
Step-by-step explanation:
we konw the speed of burn is 1.25 inchs per hour. so, the left candle is
15-1.25t. the answer is L=15-1.25t
A distribution of exam scores has mean 60 and standard deviation 18. If each score is doubled, and then 5 is subtracted from that result, what will be the mean and standard deviation, respectively, of the new scores
If each score is doubled, and then 5 is subtracted from that result, then the mean and standard deviation will be 115 and 36 respectively.
What will be the mean and standard deviation?A huge group of test results has a mean of 60 and a standard deviation of 18. If each score is doubled and then 5 is deducted from the result, the mean and standard deviation are “ mean = 115; standard deviation = 36”. Mean = 2 x 60 -5 = 120 -5 = 115
2 x 18 = 36 standard deviation
The mean is the average and is calculated as the sum of all the results from the example divided by the total number of events.
The standard deviation (SD) is a statistic used to assess the degree of variation or dispersion in a set of data values.
A low standard deviation indicates that the information points slant toward being near the mean of the set, whereas an exclusive expectation deviation or a high standard deviation indicates that the information points tilt toward being near the mean of the set.
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what is 2/3(x+7)-18x+4/5 simplifyed
A hot air balloon is cruising at an altitude of 120 m above ground when it begins its descent the balloon descends at a rate of 4.5 m per minute explain how you would set up the equation to model when the balloon will reach an altitude of 75 m above ground then solve the equation and check your solution
The equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation.
The balloon will reach an altitude of 75 meters above the ground.
Now, 120-75 =45 meters
Let t be the time to descends 45 meters
So, 120 - 4.5t= 75
= -4.5 t = 75-120
= -4.5t = -45
= t = -45/(-4.5)
= t = 10 minutes
Hence, the equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.
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Question 2
In 2007 the US Census Bureau reported that 71.3% of American families owned their
homes. The city council is debating on whether to offer tax breaks to first time
homebuyers, but they only want to do so if there is strong evidence that the rate of
home ownership has increased since 2007 since it will cost the city money to do so.
a) What are the null and alternative hypothesis?
b) Describe a Type I error in context along with the consequence.
c) Describe a Type Il error in context along with the consequence.
d) Which is a more serious error in this context? Justify your answer
e) For each type of error, tell who would be harmed.
(These are questions to answer, not answer choices.)
The answer to all the questions is explained below with justifications.
What is hypothesis testing?In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test. The type of data used and the purpose of the study will determine the methodology the analyst uses.
a) The null hypothesis[tex](H_o)[/tex] is that 71.3% or more of American families owned their homes.
The alternative hypothesis[tex](H_1)[/tex]is less than 71.3% of American families owned their homes.
b) The type I error is the null hypothesis is true but we assumed it to be false that is 71.3% or more of American families owned their homes but the council did not provide tax breaks.
The type II error is the null hypothesis is false and we assumed it to be true
that is less than 71.3% of American families owned their homes and the council provides tax breaks.
c) The consequences of the type II error would be the council will provide tax breaks to more people and it would cost them a large amount of money.
d) Type II error is more serious in this context as the council has to lay off a large amount as compared to individual homeowners who already can afford to buy a house.
e) For type I error house owners will be harmed and for type II error counsel will be harmed.
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What is another word for undecidable?
Therefore , the solution of the given problem of algorithm comes out to be incomputable. is another word for undecidable.
Clarify algorithm.A calculation or problem-solving procedure is known as an computation or algorithm. Algorithms serve as a thorough set of instructions that direct hardware- or software-based routines through a sequence of planned actions step by step. In all areas of IT, algorithms are commonly employed.
Here,
If it is impossible to develop an algorithm that reliably returns a true or false result for each input value, the problem is said to be undecidable.
The category of inherently unknowable questions, a subtype of insoluble problems, only includes questions that ought to receive a yes-or-no response .
Thus ,incomputable. is another word for undecidable.
Therefore , the solution of the given problem of algorithm comes out to be incomputable. is another word for undecidable.
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Is 2 a positive number?
Answer:
the 2 positive of number is
Step-by-step explanation:
2_:3+23*3⅔+09=2465
3. Given: ACAN
m/ATN= (4x + 18)
Find: x so that AT is an altitude
N
Therefore , the solution of trigonometry function comes out to be tan x tan(4x+18)
What does trigonometry mean exactly?When it comes to trigonometry, the relationship between the rectangular line segment and The field is believed to have originated in the 1770s, most likely beginning in the third century through the fusion of astrophysics and mathematical sciences. Numerous mathematical equations and their possible uses in calculations are covered by precise mathematical techniques. The basis of trigonometry are the six basic trigonometric operations.
Here,
tan x tan 4x=1
cos 4X cos X - sin 4x sin x=0
cos 5x=0
5x=(n+1/2)π,n ∈ Z
x=(2n+1)/10 π,0 <x <π
π/10, 3π/10, 5π/10, 7π/10,9π/10 (5π/10 is not possible)
Thus, there are only four solutions.
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Can a polynomial have no real roots?
Odd degree polynomials can have no real roots.
A polynomial of even degree can have any number from 0 to n distinct real roots. A polynomial of odd degree can have any number from 1 to n distinct real roots.
polynomials
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
Real root
A real root is a solution to an equation which is also a real number.
Real number
Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.
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Help ASAP!!!!!!!!!!!!!!!!
The correct order of match is 1-a, 2-b, 3-d and 4-c.
What are conic sections?The term "conic" refers to a curve formed by the intersection of a right circular cone with a plane. In Euclidean geometry, it has distinctive features. The cone is split into two nappes, the upper nappe and the lower nappe, at its vertex.
A plane crosses the cone, and the resulting section is referred to as a conic section.
Given the equations,
the equation for parabola is given by
(y - b)² = 4p(x - a)
Vertex is (a,b)
equation 2 follows the same
x = -2(y - 4)² + 3
this is the equation for parabola.
Equation for ellipse is
(x − a)²/h² + (y − b)²/k² = 1
the equation x²/4 + (y - 8)²/144 = 1
(x/2)² + ((y - 8)/12)² = 1
the equation is same is equation for ellipse,
Equation for circle
(x - h)² + (y - k)² = r²
fourth equation
(x - 9)² + (y + 2)² = 7²
is same as equation of circle
Equation for hyperbola
(x − a)²/h² − (y − b)²/k² = 1
equation (x - 3)²/5 - (y + 4)²/25 = 1
is same as equation of hyperbola.
Hence the correct order is a, b, d, and c.
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I’m doing homework and this may be easy for others but I’m not that good at learning quickly. Take ur time it’s fine. Please help
the statement that "you walk at a constant rate" tells us that the relationship is indeed proportional, namely, there's a value in the input that's consistent or common yielding the output.
Check the picture below.
to get the equation of any straight line, we simply need two points off of it, for the distance "from school" table, let's use those two points in that table
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{0.5})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{1.5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1.5}-\stackrel{y1}{0.5}}}{\underset{\textit{\large run}} {\underset{x_2}{30}-\underset{x_1}{10}}}\implies \cfrac{1}{20}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0.5}=\stackrel{m}{\cfrac{1}{20}}(x-\stackrel{x_1}{10})\implies y-0.5=\cfrac{1}{20}x-\cfrac{1}{2} \\\\\\ y=\cfrac{1}{20}x-\cfrac{1}{2}+0.5\implies y=\cfrac{1}{20}x-\cfrac{1}{2}+\cfrac{1}{2}\implies \boxed{y=\cfrac{1}{20}x}[/tex]
Are polynomials closed under addition?
Polynomials form a system like to that of integers hence they are closed under the operations of addition and subtraction.
Exponents of polynomials are whole numbers.
Hence the resultant exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.
If an operation results in the production of another polynomial, the resulting polynomials will be closed.
The outcome of subtracting two polynomials is a polynomial. They are also closed under subtraction as a result.
The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and nominal means terms. This article will teach us about polynomial expressions, polynomial types, polynomial degrees, and polynomial properties.
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3. A sample of 10 networking sites for a specific month has a mean number of visits of 26.1 and a sample standard deviation of 4.2. Find a 99% confidence interval of the population mean.
The confidence interval is (22.68,29.52).
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.
n = 10
x = 26.1
s = 4.2
Two-sided confidence interval :
CI = [tex](x-\frac{z*s}{\sqrt{n}},x+\frac{z*s}{\sqrt{n} } )[/tex]
= [tex](26.1-\frac{2.576*4.2}{\sqrt{10}},26.1+\frac{2.576*4.2}{\sqrt{10}} )[/tex]
= (26.1−3.42,26.1+3.42)
= (22.68,29.52)
Hence, the confidence interval is (22.68,29.52).
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two families with four people in each family go to a movie theater. in how many ways can they be seated
According to probability, if both families want to sit together, they can be seated in a row a maximum of two times.
What seating configuration?The direction that each person is facing is crucial when arranging the people.
In order to determine how many ways they can be seated in a row if both families want to sit together, imagine that two families with four members each attend a movie theatre.
Given that the arrangement is important, we will apply the permutation rule. We'll divide the remaining four into two groups of four each.
There are two different ways to arrange the groups so they can sit together.
2! = 2 * 1
2! = 2ways
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How can these models be used to find the sum 2. 3 + 1. 94?
Enter your answers in the boxes.
The models show a total of 3 wholes,
tenths, and
hundredths. After regrouping 10 tenths into 1 whole, there are
wholes,
tenths, and
hundredths. Therefore, the sum of the numbers is
The sum of 2.3 and 1.94, that is 2.3 + 1.94 is 4 wholes, 2 tenths and 4 hundredths, which can be written in decimal form as 4.24.
Therefore the answer is 4.24.
The first number, 2.3, can be broken down into 2 wholes and 3 tenths.
The second number, 1.94, can be broken down into 1 whole, 9 tenths and 4 hundredths.
To add the two numbers together, we first add the wholes: 2 + 1 = 3.
Next, we add the tenths: 3 + 9 = 12
Since we cannot have more than 9 tenths in a whole, we must regroup 12 tenths as 1 whole and 2 tenths.
We add the regrouped tenths to the number of wholes: 3 + 1 = 4
After regrouping, we have 4 whole and 2 tenths.
Now we add the hundredths: 0 + 4 = 4
Thus the sum is 4 wholes, 2 tenths and 4 hundredths, which can be written in decimal form as 4.24.
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As part of an experiment to test different liquid fertilizers, a sprinkler has to be set to cover an area of 140 square yards in the shape of a sector of a circle of radius 50 yards. Through what angle should the sprinkler be set to rotate? If necessary, round the answer to two decimal places
The sprinkler should be set to rotate through the angle 6.42 degrees.
What is an angle?
Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.
r = 50 yards
Area, A = 140 square yards
Θ = angle
A= (Θ /360) πr²
140 = (Θ /360) * 3.14 * 50*50
Θ = (140*360)/(3.14*25*100) = 6.42 degrees
The sprinkler should be set to rotate through the angle 6.42 degrees.
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Knowing that 6 < x < 7 and 10 < y < 12, find the possible values of x+y,xy,y/x,y-x
16<x+y<19,60<xy<84,10/7<y/x<12/6,3<y-x<6
smallest with the smallest biggest with the biggest, biggest with smallest, smallest with biggest
Sidney would like to buy a winter coat with an original price of $44.60. Which coupon should she use?
How do you simplify 3 ratios?
To simplify 3 ratios, divide each part of the ratio with the same amount and keep diving numbers in the ratio until they are as small as possible but they remain as whole numbers.
To simplify or reduce a fraction, first, we need to find a common factor between the ratio numbers. When we have multiple ratio numbers, we must find a common factor between all of them.
The greatest factor between all the ratio numbers (greatest common factor) will be utilised to divide or reduce the ratios down to their lowest form.
For example reduce the ratio 350: 250: 125
The first step is to determine a common factor between all of the ratio numbers. In this example, we can see that all of the numbers end in either 5 or 0. This means that each number should have 5 as a factor.
If numbers are large and we are not sure of the greatest common factor between them all, we can reduce by a common factor and then reduce again.
Now divide each number by 5 and see what we get.
350/5: 225/5: 125/5
70: 45: 25
When we divide each one by 5 again, we can see that each number again ends in 5 or 0 which means that 5 is still a factor of each number.
Now divide each number by 5 again and get a final ratio of 14: 9: 5.
70/5: 45/5: 25/5
14: 9: 5
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Find the area of the right triangle below.
9m
4m
Area = 1/2*base*height = 1/2*9*4 = 18 sq.m
The length and breadth of the three rectangles are as given below:(a) 9 m and 6 m(b) 17 m and 3 m(c) 4 m and 14 mWhich one has the largest area and which one has the smallest?Solution:
We will be using the area of rectangle formula to calculate the areas of the three rectangles given.
(a) Length(l) = 9 m and Breadth(b) = 6 m
Area of rectangle = l × b
= 9 × 6
= 54 m2
(b) Length(l) = 17 m and Breadth(b) = 3 m
Area of rectangle = l × b
= 17 × 3
= 51 m2
(c) Length(l) = 4 m and Breadth(b) = 14 m
Area of rectangle = l × b
= 4 × 14
= 56 m2
Therefore, the area of the rectangle with the dimensions 4m and 14m having an area of 56 m2 that is (c) has the largest area whereas, the area of the rectangle with dimensions 17m and 3m having an area of 51 m2 that is (b) has the smallest area.
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BRAINLIEST IF YOU CAN HELP ME!
52. 0.5(cos 100deg + I sin 100 deg ) convert to trigonometric form
PAGE 347; 52, 58, 60
Answer:
the answer us on the attatched documet
Step-by-step explanation:
can u just give me the brainliest
Students who attend Anytown College pay either in-state or out-of-state tuition, depending on where they reside. The mean and standard deviation of the sum, S, of tuition for a randomly selected pair of in-state and out-of-state students are μS = $6,348. 75 and σS = $1,508. 48. How can these values be interpreted? Check all that apply. The average of the sums of both types of tuitions would be $6,348. 75 for many, many randomly selected pairs of students. Students who pay both types of tuition will pay $6,348. 75 per semester. For a pair of randomly selected in- and out-of-state students, the sum of their tuitions is $6,348. 75. For a pair of randomly selected in- and out-of-state students, the sum of their tuitions typically varies from the mean of $6,348. 75 by about $1,508. 48. Students who pay both in- and out-of-state tuition should expect their cost to vary by about $1,508. 48 per semester
The average tuition for two randomly chosen in-state and out-of-state students is around $1,508 less than the mean of $6,348.75.
Mean Deviation
The average deviation from the mean value of the provided data set is determined using the mean deviation, which is defined as a statistical metric.
Given
μS = $6,348.75
σS = $1508.48
The average sum of the tuition fees is $6348.75
As a result, it follows:
The standard deviation of the tuition for in-state students is measured as a difference from 6348.75.
The standard deviation for out-of-state students gauges how their tuition is different from 1508 in total.
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What are the factors of a term 5x?
The factors of 5x as calculated from the data given is found to be as 5, x and 1 .
On factorizing 5x we can write it as ,
5 x 1 x x .
Therefore the factors are 5 , 1 and x.
There are some integers which are positive and can divide a number completely leaving no remainders. Such integers are known as factors for a number. If we want to get a product by multiplying two numbers , we will have to multiply two factors. Each number is a multiplier of itself.
The prime factor is the factor of a given number that is also a prime number. Factors are numbers that are multiplied together to produce another number.
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How do you graph LN functions?
We will plot the graph for a LN function by keeping in mind that the domain must be greater than 0.
What is LN function?LN means natural logarithm. LN function denotes natural logarithm function. It has also another name, logarithm of base e.
It is expressed as
y = ㏑x that is the inverse of
the natural base exponential function
y = ex
How do we graph LN function?If we have a logarithm function, f(x) = y = ln x
while plotting with the above function, ln x can be found for only the positive value of x and there is no value of ln x for negative values.
The properties of the graph of the LN function are following.
The domain of the LN function is only the real numbers that means x > 0.
The ranges of the LN function are all real number.
The coordinate of x intercept of the LN function is (1, 0).
The graph of LN function will be such that it will never touch the Y axis although it always approaches to it.
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In a market urvey, 100 trader ell fruit. 40 ell apple, 46 orange, 50 mangoe, 14 apple and orange, 15 apple and mangoe and 10 ell all three fruit each of the 100 trader ell at leat one of the three fruit. (A) how many trader ell only one fruit. (B) how many trader ell only two fruit
A)There are 88 trader sell only one fruit.
B) There are 46 trader sell only two fruit.
Since there are three sets, use the formula
n (A∪O∪M) = n(A) + n(O) + n(M) - n(A∩O) -n(O∩M) - n(A∩M) + n(A∩O∩M)
A represents apple traders = 40
O represents orange traders = 46
M represents mangoes traders = 50
A∪O∪M = total traders = 100
A∩O = 14
O∩M = ?
A∩M = 15
A∩O∩M = 10
B) Substitute values into the formula
100 = 40 + 46 + 50 - 14 - 15 - O∩M + 10
100 = 146 - 29 - O∩M
100 = 117 - O∩M
Make O∩M subject of formula
O∩M = 100 -117
O∩M = 17 traders
Now,
n(A∩O) -n(O∩M) - n(A∩M)
= 14 + 17 + 15
= 46
Therefore, the number of traders that sells two fruits are 46.
A) oranges n(O)
= 46-(4+10+ x)
= 32
Again,
mangoes n(M).
= 50-(5+10+x)
= 35
Now,
apple n(A)
= 40-(4+10+5)
= 21
Now, adding all of them we get:
n(o) + n(M) + n(A) = 32 + 35 + 21
= 88
Therefore, 88 trader sells only two fruit
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