a) Event and are such that P(X ) 0.6 and P(Y) 0.2 and
P[(X Y ) (X Y)] 0.45 . Find P(X Y ) . Hence, determine if and are
independent.
5 marks
b) Given that and are two events with the following probabilities :
7 1 5
( ) , ( ' ) ( )
8 12 16
P A P A B and P A B
Find
i. P(B)
3 marks
ii. P(A B')
3 marks

The price elasticity of demand when the price is $32 per orange is 2

To calculate the price elasticity of demand, we need to use the formula:

E = (%Δq / %Δp) x (p/q)

where E is the price elasticity of demand, %Δq is the percentage change in quantity demanded, %Δp is the percentage change in price, and p/q is the average price-quantity ratio.

Given that the weekly sales of Honolulu Red Oranges is given by q = 1040 - 20p, we can find the derivative of q with respect to p as follows:

dq/dp = -20

This tells us that for every $1 increase in price, the quantity demanded will decrease by 20 units.

At a price of $32 per orange, the quantity demanded is:

q = 1040 - 20(32) = 424

If the price were to increase to $33 per orange, the new quantity demanded would be:

q' = 1040 - 20(33) = 404

Using these values, we can calculate the percentage changes in price and quantity demanded as:

%Δp = [(33 - 32) / 32] x 100% = 3.125%

%Δq = [(404 - 424) / 424] x 100% = -4.72%

The average price-quantity ratio is:

(p+ p')/2q = [(32 + 33)/2]/424 = 0.015

Now we can calculate the price elasticity of demand as:

E = (%Δq / %Δp) x (p/q) = (-4.72 / 3.125) x 0.015 = -0.023

Since the price elasticity of demand is negative, we know that Honolulu Red Oranges have an inelastic demand at a price of $32 per orange. This means that a 1% increase in price will lead to a less than 1% decrease in quantity demanded.

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The forecast for Y3 is -3/8.

We can start by writing the MA(1) process as:

Yt = μ + θεt-1 + εt

where μ is the process mean, θ is the MA(1) coefficient, εt is the white noise error term with mean zero and variance σ^2.

From the given information, we know that the process mean is zero, so μ = 0.

The conditional least-squares estimate of θ given the first two observations can be obtained by minimizing the sum of squared errors:

S(θ) = (y1 - θε0)^2 + (y2 - μ - θε1)^2

where ε0 and ε1 are unobserved error terms and y1, y2 are the first two observations.

Substituting the given values, we get:

S(θ) = 1 + θ^2 + (1/4 - θ)^2

Taking the derivative of S(θ) with respect to θ and setting it to zero, we get:

dS(θ)/dθ = 2θ - 2(1/4 - θ) = 0

Solving for θ, we get:

θ = 3/8

Therefore, the conditional least-squares estimate of θ given the first two observations is 3/8.

To find the forecast for Y3, we can use the MA(1) model equation:

Y3 = μ + θε2 + ε3

where ε2 and ε3 are unobserved error terms. Substituting the estimated value of θ and the given value of Y2, we get:

Y3 = (3/8)(-1) + ε3 = -3/8 + ε3

Therefore, the forecast for Y3 is -3/8.

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The margin of error will decrease because the critical value will decrease.

According to Central Limit theorem the sampling distribution as;

Z= x`- u/ σ/√n

Z has in the limit a standard normal distribution,

x`= u ± zσ/√n

From the above;

x`- z∝(σ/√n) ≤ u ≤ x`+ z∝(σ/√n)

This formula is used for the confidence interval with normal population and unknown standard deviation.

But if the different values of Z∝ are used the results will be different.

If the CI of 99% or 95% or 90% is used the values of acceptance and rejection regions change and therefore the results will change.

The value of Z∝ for ,∝= 0.1 is ± 1.645

∝= 0.05 is ± 1.96

∝= 0.01 is ± 2.58

Let we get the calculated Z value equal 2.59 but we decrease the CI from 0.05 to 0.01 the acceptance region would become rejection region  and the level of confidence will change.

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The Q(Q) = {(a,b,c,√2a+b+c) | a,b,c ∈ Q} ∪ {(-a,b,c,-√2a+b+c) | a,b,c ∈ Q}, where Q is the  cubic.

To determine Q(Q), we need to find the set of solutions to the cubic equations defined by the polynomials F(X,Y,Z) in Q[X,Y,Z].

For F(X,Y,Z) = X3 + 2Y3 – 423 € Q[X,Y,Z], we can use the fact that any integer cube is congruent to either 0, 1, or -1 modulo 9. Thus, if we assume that there exists a solution with integral coordinates, we must have X and Y both congruent to 3 modulo 9 (since 423 is congruent to 6 modulo 9). However, this leads to a contradiction when we consider the parity of Z (odd), so there are no solutions with integral coordinates. Therefore, Q(Q) = {}.

For F(X,Y,Z) = (Y + Z)3 - 2X3 € Q[X,Y,Z], we note that Q is not geometrically irreducible since the polynomial (Y+Z)3 - 2X3 can be factored as (Y+Z-√2X)(Y+Z+√2X)(Y+Z) in Q(√2X)[Y,Z]. Thus, we need to study the Galois action on the irreducible components.

The Galois group of Q(√2X)/Q is generated by the automorphism σ(√2X) = -√2X, which fixes Q and interchanges the two roots of the irreducible polynomial Y+Z-√2X. Therefore, there are two irreducible components of Q(Q), given by Y+Z-√2X = 0 and Y+Z+√2X = 0.

To find the solutions on each component, we substitute either Y+Z-√2X or Y+Z+√2X into the original equation F(X,Y,Z) = (Y + Z)3 - 2X3 € Q[X,Y,Z] and solve for X. We obtain:

- For Y+Z-√2X = 0, we have X = (Y+Z)√2/∛2. Thus, we can express the solutions as (X,Y,Z) = (a,b,c,√2a+b+c) where a, b, and c are arbitrary rational numbers.
- For Y+Z+√2X = 0, we have X = -(Y+Z)√2/∛2. Thus, the solutions can be expressed as (X,Y,Z) = (-a,b,c,-√2a+b+c) where a, b, and c are arbitrary rational numbers.

Therefore, Q(Q) = {(a,b,c,√2a+b+c) | a,b,c ∈ Q} ∪ {(-a,b,c,-√2a+b+c) | a,b,c ∈ Q}.

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Note that the equation of the line perpendicular to the tangent to the curve y = x³ − 3x+1 is y = (-1/9)x + 7/3.

To find the  equation of the line perpendicular to the tangent of the curve at  the point (2, 3):


Get the slop of the tangent at that point.

To do this, we take  derivative of the function y = x³ - 3x + 1 and evaluating it at x = 2:

y' = 3x² - 3

y '(2) = 3 (2) ² -  3 = 9

So the slope of  (2, 3) =  9.

Since   the line we are looking for is  perpendicular to this tangent, its slope will be the  negative reciprocal of 9, which is -1/ 9.

Next,  use the point-slope form of a line to write the equation of the line

y - 3 = (-1/9) ( x - 2)

⇒ y = (-1/9)x  + 7/3

So the  equation of the lie perpendicular to the tangent to the curve at the point (2,3) is y = (-1/9)x + 7/3.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Find equation to the line perpendicular to the tangent to the curve y=x³−3x+1 , at the point (2,3)

.

To predict the value of y when x=10 is an example of Extrapolation. So, the correct answer is (b) extrapolation.

Extrapolation involves using a mathematical model, such as a line of best fit, to make predictions outside the range of the original data.

In this case, using the equation y = –3x + 21 to predict the value of y when x = 10 is an example of extrapolation because 10 is outside the range of the original x-values.

Using a line of best fit with the equation y = -3x+21 to predict the value of y when x = 10 is an example of extrapolation in statistics.

Extrapolation involves using a mathematical model, such as a line of best fit, to make predictions outside the range of the original data.

Ricardo's next step to construct the circumscribed circle for △XYZ would be to construct the perpendicular bisector of YZ

In this case, constructing the perpendicular bisector of YZ would give Ricardo the center of the circumscribed circle, which is equidistant from the three vertices of the triangle.

Complete Question:

Ricardo calculates a line of best fit for a data set with integer x-values 1 through 6. Complete the sentence with the correct word.

Using a line of best fit with the equation y = –3x + 21 to predict the value of y when x = 10 is an example of

a) correlation

b) extrapolation

c) causation

d) intrapolation

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Eastwood Enterprises offers horseback riding lessons and during the month of June, the company provided lessons on account totaling $5,100. By the end of the month, the company received on account $4,500 of this amount, meaning there is still $600 outstanding.

Eastwood Enterprises offered horseback riding lessons during the month of June, and the total value of lessons provided on account was $5,100. Here's a step-by-step explanation of the transactions:

1. Eastwood Enterprises provides horseback riding lessons worth $5,100 on account in June.
2. By the end of June, the company receives $4,500 on account from the customers who took lessons during that month.
3. In addition to the June payments, Eastwood also receives $500 on account from customers who took lessons in May.

To summarize, Eastwood Enterprises provided $5,100 worth of lessons on account in June, received $4,500 from those June lessons, and an additional $500 from customers who had taken lessons in May.

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A line which is perpendicular to vector HF include the following: line BC.

In Mathematics and Geometry, perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles).

In Mathematics and Geometry, a perpendicular bisector is a line that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

Based on the definition of perpendicular lines, we can reasonably infer and logically deduce that vector HF is perpendicular to line BC.

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To understand subtraction as an unknown-addend problem means to view subtraction as finding the missing number in an addition problem.

In the example given, subtracting 10-8 means finding the number that needs to be added to 8 to make 10. This is essentially an addition problem with an unknown addend.

To solve the problem, one needs to think about what number added to 8 will result in 10. This can be done by counting up from 8 until you reach 10, which is a difference of 2. Therefore, 10-8=2, and the missing number is 2.

In general, to subtract any two numbers using this method, you can start with the smaller number and count up until you reach the larger number. The difference between the two numbers is the missing addend. For example, to subtract 15-7, you would start with 7 and count up to 15, which is a difference of 8. So 15-7=8.

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Answer:[tex]\left(x-14\right)^{2}+\left(y-15\right)^{2}=92[/tex]

Step-by-step explanation:

Since the x value is 14 and the y value is 15, we know our H and K for this formula. In the formula, we state that the first part of the formula is equal to the radius squared. That would look something like this without the filled in values:

[tex]\left(x-h\right)^{2}+\left(y-k\right)^{2}=r^{2}[/tex]

The center point of the circle is found at (h, k)

I hope this helps :)

Celine will have taken 55 quizzes after attending 11 weeks of school.

In mathematics, an expression is a combination of numbers, variables, and operations that are grouped together to represent a mathematical relationship or quantity.

Celine took 45 quizzes in 9 weeks, so the unit rate is:

45 quizzes / 9 weeks = 5 quizzes per week

If Celine attends 11 weeks of school, we can use the unit rate to find how many total quizzes she will have taken:

Total quizzes = Unit rate × Number of weeks

Total quizzes = 5 quizzes per week × 11 weeks

Total quizzes = 55 quizzes

Therefore, Celine will have taken 55 quizzes after attending 11 weeks of school.

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The probability of selecting blue marble and green marble is 1/13.

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100%.

Probability = sample space/total outcome

total outcome = 13

The probability of picking blue in the first pick = 6/13

since there is no replacement, the total outcome for the second pick = 12

The probability of picking green in the second pick = 2/12 = 1/6

Therefore the probability of selecting blue and green marble = 6/13 × 1/6

= 1/13

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The probability that a student studied for exactly 5 hours is 0.17. (third option)

Probability calculates the chances that an event would happen. The probability the event occurs with certainty is 1 and the probability that the event would not occur with certainty is 0. The more likely the event is to happen, the closer the probability value would be to 1.

Probability that a student studied for exactly 5 hours = number of students that studied for 5 hours / total students surveyed

= 6 / 35 = 0.17

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1. Determine the equilibrium price and quantity: This is the point where the supply curve and the demand curve intersect.
2. This triangle represents the producers' surplus. To find its area, use the formula for the area of a triangle:

(base × height) / 2.

To find the producers' surplus, we need to first determine the equilibrium price at which the supply and demand curves intersect. At this price, the quantity supplied by producers will equal the quantity demanded by consumers.

Once we have the equilibrium price, we can then calculate the area between the supply curve and the equilibrium price. This represents the producers' surplus, which is the amount of profit they make on each unit sold above their cost of production.

Without knowing the specific supply and demand curves, it is not possible to provide an exact answer to this question. However, we can use the formula for producers' surplus to calculate an approximate answer:

Producers' Surplus = (Equilibrium Price - Minimum Supply Price) x Quantity Supplied

For example, if the equilibrium price is $5.50 and the minimum supply price is $3.00, and the quantity supplied is 100 units, the producers' surplus would be:

Producers' Surplus = ($5.50 - $3.00) x 100
Producers' Surplus = $2.50 x 100
Producers' Surplus = $250.00

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It took Lucy approximately 2 13/31 hours to bike the trail.

We can start by using the formula:

distance = rate × time

Let's begin by finding the distance of the bike trail. Since Jasmine and Lucy biked the same trail, the distance will be the same for both of them. Let d be the distance of the trail.

d = distance of the bike trail

We know that Jasmine finished the bike trail in 2.5 hours at an average rate of 9 3/10 miles per hour. So, we can write:

d = 9 3/10 × 2.5

Simplifying the right-hand side, we get:

d = 23 1/2

Therefore, the distance of the bike trail is 23 1/2 miles.

Now, we can use the formula to find the time it took Lucy to bike the trail. Let t be the time it took Lucy to bike the trail.

distance = rate × time

23 1/2 = 6 1/5 × t

To solve for t, we can divide both sides by 6 1/5:

t = 23 1/2 ÷ (6 1/5)

Converting the mixed numbers to improper fractions, we get:

t = 47/2 ÷ 31/5

To divide fractions, we can multiply by the reciprocal:

t = 47/2 × 5/31

Simplifying, we get:

t = 2 13/31

Therefore, it took Lucy approximately 2 13/31 hours to bike the trail.

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If the money supply doubles and the velocity of money is stable, the long-run impact on real GDP will depend on other factors that influence the economy's overall growth. In the short term, a sudden increase in the money supply may boost economic activity and output as businesses have more access to credit and consumers have more disposable income to spend.

However, in the long run, the economy's potential output is determined by its ability to produce goods and services efficiently, which is reflected in the level of real GDP.
If the money supply continues to grow faster than the economy's capacity to produce, it can lead to inflation, which can erode the purchasing power of money and reduce economic growth. Therefore, in the long run, the impact of a doubling of the money supply on real GDP will depend on whether it leads to sustainable economic growth or inflationary pressures.

Moreover, the relationship between money supply, velocity, and real GDP is complex and influenced by various factors, such as fiscal policy, monetary policy, technological progress, and demographic changes. Therefore, while a doubling of the money supply may lead to short-term growth, its long-term impact on real GDP depends on the broader economic context in which it occurs.
If the money supply doubles and the velocity of money remains stable, in the long run, the real GDP may not be significantly affected. Here's a step-by-step explanation of this scenario:

1. When the money supply doubles, there will be more money circulating in the economy. This increase may initially lead to higher demand for goods and services, causing prices to rise.

2. The velocity of money, which is the rate at which money is exchanged from one transaction to another, remains stable. This means that the overall pace of economic transactions doesn't change.

3. In the short run, the increased money supply may lead to a temporary boost in economic activity and possibly higher nominal GDP. However, this increase is primarily due to the inflation caused by the rise in prices, not necessarily an increase in the production of goods and services.

4. In the long run, the economy will adjust to the higher money supply, and the real GDP will return to its original level. This is because the long-run growth of the real GDP is determined by factors such as productivity, technological advancements, and the availability of resources, rather than changes in the money supply.

5. Eventually, the economy will reach a new equilibrium with higher prices, but the real GDP will remain unchanged in the long run. The increase in the money supply will only lead to higher inflation, not a sustainable increase in real economic output.

In summary, doubling the money supply while keeping the velocity of money stable may temporarily boost nominal GDP, but it won't result in a long-term increase in real GDP, as other factors determine its growth.

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The missing figures in the diagrams are:      88km                    616km²,   37.7km                      113.14km respectively

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.

                Radis          diameter            circumference            area

S/N           r                        2r                         2πr                           πr²

Applying the above formulae in each of the questions we have as follows:

1             3                  2*3=6             2*3.14*3=18.84        3.14*3*3=28.26       2        3.5                   7                 2*3.14*3.5=21.98    3.14*3.5*3.5=38.47      

3       7.5                 15               2*3.14*7.5=47.1ft      3.14*7.5*7.5=176.25

4       14km           28km         2*3.14*14=87.92km    3.14*14*14=615.44km²

5        5mi           10mi        2*3.14*5=31.4mi               3.14*5*5= 78.5mi²

6       2.5cm         5cm         2*3.14*2.5=15.7cm          3.14*2.5*2.5=19.63cm²

7      

14                     14*2 28             2*22/7*14                    22/7*14*14  

                                                     88km                    616km²

6                             12                2*22/7*6                     22/7*6*6

                                                    37.7km                      113.14km

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Answer:x= -9/2 which is -4.5

Step-by-step explanation:

8(x+5)=4

first divide by 8

(x+5)=4/8

simplify

(x+5)=1/2

subtract 5

x=1/2-5

change 5 to have a denominator of 2

5 x 2/2

=10/2

x= 1/2-10/2

=-9/2

The probability that the a point will fall on the red-shaded square to nearest hundredth is 0.56

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100% in decimal.

Probability = sample space / total outcome

sample space = area of shaded part

total outcome = area of the whole shape.

area of the shaded part = 3×3 = 9

area of the whole shape = 4×4 = 16

Therefore the probability that a point will fall in the shaded area = 9/16

= 0.56( nearest hundredth)

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Answer:

0.56

Step-by-step explanation:

just got it right

The amount of money in the account after 16 years is approximately $17,526.64.

Using the formula for continuous compounding, we have:

V = Pe[tex]^(rt)[/tex]

where V is the value of the account after t years, P is the principal initially invested, e is the base of the natural logarithm, r is the annual interest rate, and t is the time in years.

Substituting the given values, we get:

V = 8430e[tex]^(0.038*16)[/tex]

Simplifying this expression, we have:

V = 8430[tex]e^0.608[/tex]

Using a calculator, we get:

V ≈ $17,526.64

Therefore, the amount of money in the account after 16 years is approximately $17,526.64.

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The answer is option(b) greater than equal to the approximation given by Chebyshev's theorem.

To answer this, we need to use the empirical rule and compare it with the approximation given by Chebyshev's theorem.

The empirical rule states that approximately 68% of the data will be within one standard deviation, 95% within two standard deviations, and 99.74% within three standard deviations of the mean, given that the data has a bell-shaped distribution.

In this case, we're looking at 3 standard deviations from the mean. According to the empirical rule, approximately 99.74% of the data will be within 3 standard deviations. Now, we compare the approximation given by the empirical rule (99.74%) to the approximation given by Chebyshev's theorem (89%).

Since 99.74% (empirical rule) is greater than 89% (Chebyshev's theorem), the approximation given by the empirical rule is greater than equal to the approximation given by Chebyshev's theorem.

Your answer: B. greater than equal to the approximation given by Chebyshev's theorem.

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Answer:

a) a = 1 ; b = 2 ;c =-1

c) -1 + √2  ; -1 - √2

Step-by-step explanation:

        x² + 2x = 1

a)      x² + 2x - 1 = 0

Compare with ax² + bx + c = 0

a = 1 ; b = 2 and c = -1

b)  

      [tex]\boxed{x=\dfrac{-b \± \sqrt{b^2-4ac}}{2a}}[/tex]

           [tex]= \dfrac{-2 \± \sqrt{2^2-4*1*(-1)}}{2*1}\\\\\\\\C) \ =\dfrac{-2 \± \sqrt{4+4}}{2}\\\\=\dfrac{-2 \± \sqrt{8}}{2}\\\\=\dfrac{-2 \±2\sqrt{2}}{2}\\\\=\dfrac{2(-1 \± \sqrt{2})}{2}\\\\= -1 \± \sqrt{2}[/tex]

          x  = -1 + √2   or x = -1 -√2      

The probability that among 4 randomly selected motorists, the officer will find at least one motorist driving more than 5 miles per hour over the speed limit is 0.8704, rounded to the nearest ten-thousandth.

To solve this problem, we can use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

First, let's find the probability that none of the 4 randomly selected motorists will be driving more than 5 miles per hour over the speed limit.

Since the officer estimates that 40% of motorists will be driving more than 5 miles per hour over the speed limit, then the probability of a motorist not driving more than 5 miles per hour over the speed limit is 1 - 0.4 = 0.6.

The probability that none of the 4 motorists will be driving more than 5 miles per hour over the speed limit is therefore:

0.6 x 0.6 x 0.6 x 0.6 = 0.1296

Now we can use the complement rule to find the probability that at least one of the 4 motorists will be driving more than 5 miles per hour over the speed limit:

1 - 0.1296 = 0.8704

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The general solution of the differential equation is:

xy^2/2 + x^2y + (x^2/2)y - (x^2/4)y^2 + h(x) = C

where C is the constant of integration.

To solve this differential equation, we can use the method of exact differential equations.

First, we need to check if the equation is exact by verifying if the following condition is satisfied:

∂(y^2 + xy)/∂y = ∂(x^2)/∂x

Differentiating y^2 + xy with respect to y, we get:

∂(y^2 + xy)/∂y = 2y + x

Differentiating x^2 with respect to x, we get:

∂(x^2)/∂x = 2x

Since these two expressions are equal, the equation is exact.

To find the general solution, we need to find a function f(x,y) such that:

∂f/∂x = y^2 + xy

∂f/∂y = x^2

Integrating the first equation with respect to x, we get:

f(x,y) = xy^2/2 + x^2y + g(y)

where g(y) is a constant of integration that depends only on y.

Taking the partial derivative of f(x,y) with respect to y and equating it to x^2, we get:

∂f/∂y = x^2 = xy + 2xg'(y)

where g'(y) is the derivative of g(y) with respect to y.

Solving for g'(y), we get:

g'(y) = (x^2 - xy)/2x

Integrating both sides with respect to y, we get:

g(y) = (x^2/2)y - (x^2/4)y^2 + h(x)

where h(x) is a constant of integration that depends only on x.

Therefore, the general solution of the differential equation is:

xy^2/2 + x^2y + (x^2/2)y - (x^2/4)y^2 + h(x) = C

where C is the constant of integration.

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Answer:

Step-by-step explanation:

Answer:

13.5

Step-by-step explanation:

Find the gradient of a line perpendicular to the longest side of the triangle formed by A(-3,4),B(5,2) and C(0,-3)

The maximum number of coins that the oldest thief might get is 751.

Let's assume that there are seven thieves, numbered 1 through 7, and their ages are a1, a2, ..., a7 such that a1 is the age of the oldest thief.

If the oldest thief proposes that he gets all 1000 coins, then he will vote for his own proposal, and at most one other thief will vote for it (since they would receive nothing in this scenario). Therefore, the proposal would be rejected.

If the oldest thief proposes that he gets 999 coins and the remaining 1 coin is split among the other six thieves, then he will vote for his own proposal, and all the other thieves will vote for it as well (since they would receive a positive amount of coins in this scenario). Therefore, the proposal would be accepted, and the oldest thief would receive 999 coins.

If the oldest thief proposes that he gets 998 coins and the remaining 2 coins are split among the other six thieves, then he will vote for his own proposal, and at least two other thieves will vote for it (since they would receive a positive amount of coins in this scenario). Therefore, the proposal would be accepted, and the oldest thief would receive 998 coins.

Continuing in this manner, the oldest thief can propose that he receives n coins and the remaining 1000-n coins are split among the other six thieves, where n ranges from 999 to 502. For each value of n, the oldest thief will vote for his own proposal, and at least four other thieves will vote for it (since they would receive a positive amount of coins in this scenario). Therefore, the proposal would be accepted, and the oldest thief would receive n coins.

The maximum value of n for which the proposal would be accepted is when n=751, since in this case, the oldest thief would receive more than half of the coins (i.e., 751 coins), and therefore, at least four other thieves would vote for the proposal. Therefore, the maximum number of coins that the oldest thief might get is 751.

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Step-by-step explanation:

On Saturday, out of ( 370 + 433 + 465 = 1268)  ,   465 went to F&L

 465/1268   is the fraction that wen to F&L

      you might expect this fraction of 1500 to go there on Sunday

            1500  * 465/1268 =   550 people

The simplified expression is given by (x² - 3x - 3) / ((x + 3)(x - 2)(x - 4)).

To simplify this expression, we need to find a common denominator for the two fractions and then combine them. To do this, we need to factor the denominators of both fractions.

Let's start with the first fraction's denominator:

x² + x - 6

We need to find two numbers that multiply to -6 and add to +1. These numbers are +3 and -2. Therefore, we can write:

x² + x - 6 = (x + 3)(x - 2)

Now let's factor the second fraction's denominator:

x² - 6x + 8

We need to find two numbers that multiply to 8 and add to -6. These numbers are -2 and -4. Therefore, we can write:

x² - 6x + 8 = (x - 2)(x - 4)

Now we can rewrite the original expression with a common denominator:

(x(x - 2) - (1)(x + 3)) / ((x + 3)(x - 2)(x - 4))

Next, we can simplify the numerator:

(x² - 2x - x - 3) / ((x + 3)(x - 2)(x - 4))

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

Finally, we can't simplify this expression any further. Therefore, the simplified expression is:

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

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