The general solution of an exact differential equation can also be found by solving the associated homogenous equation and adding the particular solution obtained from the original equation.
1. Identify the exact differential equation.
2. Find the integrating factor by multiplying the equation by an expression of the form e^(f(x)).
3. Multiply the integrating factor with the equation to make it exact.
4. Integrate both sides of the equation to obtain the general solution.
5. Check the solution by differentiating it to confirm that it satisfies the original equation.
6. Add the particular solution obtained from the original equation to the homogenous solution to get the general solution.
The general solution of an exact differential equation can be found by using an integrating factor. An integrating factor is a function of the independent variable which can be multiplied with the equation in order to make it exact. Once the equation has been made exact, it can be solved using the standard integration techniques. In addition, the general solution can be found by solving the associated homogenous equation and then adding the particular solution obtained from the original equation.
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the time t needed to paint a fence varies directly as the length L and inversely as the number of workers w if it takes 10 hours to paint 400 feet of fence with six workers how long it will take for 10 workers to paint 1000 ft fence
Using the direct and inverse variations, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.
What is proportionality constant?The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship. The Direct Variation and Inverse Variation types of proportions between the two provided values determine the proportionality constant's value.
Given that the time t needed to paint a fence varies directly as the length L and inversely as the number of workers w.
This is represented as follows:
t = k(l/p)
Where, k is the proportionality constant.
Given that, it takes 10 hours to paint 400 feet of fence with six workers.
Substitute the value of t = 10, l = 400 and w = 6 in the equation we have:
10 = k (400 / 6)
10 = k (66.66)
k = 10 / 66.66
k = 0.15
Now, for or 10 workers to paint 1000 ft fence, take l = 1000, w = 10, and k - 0.15:
t = (0.15) (1000 / 10
t = (0.15) (100)
t = 15
Hence, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.
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How do I find the median of this trapezoid?
The median of the trapezoids is given by QR = 23.5 and VW = 15.2
What is a trapezoid?The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
There are three types of trapezoids , and those are given below:
a) Isosceles Trapezoid
b) Scalene Trapezoid
c) Right Trapezoid
The area of the Trapezoid is given by
Area of Trapezoid = ( ( a + b ) h ) / 2
where , a = shorter base of trapezium
b = longer base of trapezium
h = height of trapezium
Given data ,
Let the first trapezoid be represented as A
Let the second trapezoid be represented as B
Now , the median of the trapezoid M = ( 1/2 ) ( sum of longer base and shorter base )
Substituting the values in the equation , we get
a)
The length of longer base = 35.6
The length of shorter base = 11.4
So , the median of A is QR = ( 1/2 ) ( 35.6 + 11.4 )
On simplifying the equation , we get
The median of trapezoid QR = ( 1/2 ) 47
The median of trapezoid QR = 23.5
b)
The length of longer base = 19.1
The length of shorter base = 11.3
So , the median of B is VW = ( 1/2 ) ( 19.1 + 11.3 )
On simplifying the equation , we get
The median of trapezoid VW = ( 1/2 ) 30.4
The median of trapezoid VW = 15.2
Hence , the median of trapezoid is solved
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A student is standing, with her arms outstretched, on a platform that is rotating at 1.6 rev/s. She pulls her arms in and the platform now rotates at 2.2 rev/s. Her original moment of inertia (I0) is 25 kg m2.
What is her final moment of inertia (If)?
The student's final moment of inertia is 18.18 kgm².
What is moment of inertia?The moment of inertia of an objecr is the property of an object which shows its ability to rotate.
How to find the final moment of inertia?Since a student is standing with her arms outstretched, on a platform that is rotating at 1.6 rev/s. She pulls her arms in and the platform now rotates at 2.2 rev/s. Her original moment of inertia (I0) is 25 kgm². To find the r final moment of inertia, we use the law of conservation of angular momentum.
What is the law of conservation of angular momentum?The law of conservation of angular momentum states that for any rotation, angular momnetum is constant.
So, Iω = constant where
I = moment of inertia and ω = angular speed.So, Iω = I'ω' where
I = initial moment of inertia of student = 25kgm²ω = initial angular speed of student = 1.6 rev/s I' = final moment of inertia of student ω' = final angular speed of student = 2.2 rev/sMaking I' subject of the formula, we have that
I' = Iω/ω'
So, substituting the values of the variables into the equation, we have that
I' = Iω/ω'
I' = 25 kgm² × 1.6 rev/s ÷ 2.2 rev/s
= 40 kgm²rev/s ÷ 2.2 rev/s
= 18.18 kgm²
So, the final moment of inertia is 18.18 kgm².
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PLEASE HELP 100 POINTS!!
A line has a slope of 0 and a y-intercept of –5/3. Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
the answer is 0= -5/3x + c
Answer: non
as a wordf 2 b geven
Need help please !!
Ian often takes his dog to the park. He estimates that 30% of the other dogs he sees are retrievers, 20% are terriers,and 20% are German shepherds. He designs a simulation.
Let 0,1, and 2 represent retrievers.
Let 3 and 4 represent terriers.
Let 5 and 6 represent German shepherds.
Let 7,8, and 9 represent other dogs.
The table shows the simulation results
The probability that at least one of the next five dogs he sees is a German shepherd is 0.75.
We have from the question.
0,1, and 2: retrievers
3 and 4: terriers
5 and 6: German shepherds
7,8 and 9: other dogs
In these results, 5 and 6 represent a german shepherd "at least one of the next five dogs he sees is a German shepherd." this means that at least one of the five numbers is 5 or 6.
There are a total of 20 results among them; 12 results include at least one 5 or 6.
∴P = 12/20 = 0.75
Hence, the correct option is B.
--The given question is incomplete; the complete question is
"Ian often takes his dog to the park. He estimates that 30% of the other dogs he sees are retrievers, 20% are terriers, and 20% are German shepherds. He designs a simulation. Let 0,1 and 2 represent retrievers. Let 3 and 4 represent terriers. Let 5 and 6 represent German shepherds. Let 7,8, and 9 represent other dogs. The table shows the simulation results. According to this simulation, what is the probability that at least one of the next five dogs he sees is a German shepherd?
A. 0.70
B. 0.75
C. 0.65
D. 0.60"--
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As part of a project about response bias, Ellery surveyed a random sample of 25 students from her school. One of the questions in the survey required students to state their GPA aloud. Based on the responses, Ellery said she was 90% confident that the interval from 3. 14 to 3. 52 captures the mean GPA for all students at her school.
Required:
a. Interpret the confidence level.
b. Explain what would happen to the length of the interval if the confidence level were increased to 99%.
c. How would a 90% confidence interval based on a sample of size 200 compare to the original 90% interval?
d. Describe one potential source of bias in Ellery's study that is not accounted for by the margin of error
It should be emphasized that this suggests that we are 90% certain that the mean GPA for all students at the institution is between 3.14 and 3.52
Sampling
If the confidence level were raised to 99%, something would happen to the interval's length, increasing it.
The difference between a 90% confidence interval based on a 200-person sample and the original 90% interval is that the latter is narrower.
Last but not least, having the students say their grades aloud could have introduced bias into Ellery's study, which is not taken into account by the margin of error. Some of them with lesser grades will start to lie as a result.
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The perimeter of an isosceles trapezoid is 40 ft. The bases of the trapezoid are 11 ft and 19 ft. Find the area of the trapezoid. Hint: Think characteristics of isosceles trapezoid
The area of an isosceles trapezoid is 45 square ft.
We have to evaluate the area of trapezoid.
The perimeter of an isosceles trapezoid is 40 ft.
The bases of the trapezoid are 11 ft and 19 ft.
The perimeter of an isosceles trapezoid = a + b + c + d
a, b, c and d all are sides of an isosceles trapezoid.
a + b + c + d = 40
According to question, c = d
11 + 19 + c + c = 40
30 + 2c = 40
Subtract 30 on both side, we get
2c = 10
Divide by 2 on both side, we get
c = 5 = d
The formula of area of an isosceles trapezoid is
A = [tex]\frac{1}{2}[/tex](a+b)h, where a and b are bases and h is the height.
We can see on the diagram that we can use Pythagorean theorem to find the height.
According to theorem;
[tex]c^2=a^2+b^2[/tex]
[tex](5)^2 = h^2+(4)^2[/tex]
25 = [tex]h^2[/tex] + 16
Subtract 16 on both side, we get
[tex]h^2[/tex] = 9
Taking square root on both side, we get
h = 3
The height of an isosceles trapezoid is 3 ft.
Now, the area of an isosceles trapezoid is
A = [tex]\frac{1}{2}[/tex](11+19)×3
A = [tex]\frac{1}{2}[/tex] × 30 × 3
A = 15 × 3
A = 45 square ft
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Dax is buying coffee for 5 people in his office. He also leaves a $2:00 tip for the batista.
If his total,with tip,is $18.25 how much is each cup of coffee, not including the tip?
Enter your answers as a decimal like this:42.53
The cost of each cup of coffee, not including the tip, is $3.25.
What is division?One type of operation in mathematics is division. We divide the phrases or numbers into the same number of components during this operation.
Given:
Dax is buying coffee for 5 people in his office.
He also leaves a $2.00 tip for the Batista.
If his total, with tip, is $18.25,
then the total bill of the coffee,
= $18.25 - $2.00 (not including the tip)
= $16.25
The cost of one coffee is,
= $16.25 / 5
= $3.25.
Therefore, $3.25 is the cost of one coffee.
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3. Find the area of the circle below.
Help the circle is 3
Answer:
28.26 [tex]in^{2}[/tex]
Step-by-step explanation:
a = [tex]\pi r^{2}[/tex]
a = 3.14([tex]3^{2}[/tex])
a = 3.14(9)
a = 28.26
URGENT!!
Which of the 3 graphs to the left best models the path
of a firework given it didn't explode?
Note: The path may be going in a different direction,
perhaps reflected or translated vertically or horizontally
while maintaining the same shape.
Linear
Quadratic
Exponential
Explain your thinking.
The path may be Quadratic in nature.
What is a graph?The path of a firework is modeled by a quadratic function. The firework ascends from point of launch with decreasing speed (negative acceleration due to gravity) until it reaches its maximum height and then starts dropping back to the ground at increasing speeds due to positive acceleration exerted by the force of gravity.
The flight path of the parabola can thus be modeled by height as a function of elapsed time
h = f(t) where f(t) is a quadratic equation in t with the general form being
a · t² +b · t + c
We can easily eliminate the linear model since that implies the firework will ascend at a constant speed forever
The exponential model indicates that at the moment of launch the speed of the firework is constant and then it suddenly accelerates. However, we know from observation that the firework has the highest speed at the moment of launch
Do not be confused by the shape of the graph - it seems to indicate the firework shoots down and up.
Note: The path may be going in a different direction, perhaps reflected or translated vertically or horizontally while maintaining the same shape.
Indeed the actual path of the firework is a reflection of the graph about the x-axis. so that it is a downward-facing parabola. The vertex of the parabola is the highest y-value which is the maximum height the firework would reach.
The height would be the y-axis and the time t the x-axis.
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a box contains 90 balls numbered from 1 to 90. if 8 balls are drawn with replacement, what is the probability that at least two of them have the same number?
The probability that at least two of the balls have the same number is 27.40%
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
Probability requested is equivalent to:
P(at least 2 have same number) = 1 - P(no 2 have the same number)
P(no 2 have same number) = No. of ways to succeed / No. of possible outcomes
No. of ways to succeed = 90P8
No. of possible outcomes = 90^8
No. of ways to succeed =
nPr = n! / (n-r)!
90P8 = 90! / (90-8)!
90P8 = 90! / (82)!
90P8 = 90*89*88*87*86*85*84*83*82! / [(82)!
90P8 = 90*89*88*87*86*85*84*83
90P8 = 3.13x10^15
P(no 2 have same number) = 3.13x10^15 / 90^8
P(no 2 have same number) = 0.73
P(at least 2 have same number) = 1 - P(no 2 have the same number)
P(at least 2 have same number) = 1 - 0.73
P(at least 2 have same number) = 0.2740 = 27.40%
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16 - x + x + 19 - x = 31
Answer:
X = 4
Step-by-step explanation:
We have to add like variables, so all the x variables will be added together. We get this:
-x + 35 = 31
Get x by itself.
-x = -4
Get rid of the negatives since what you do on one side you do to both sides.
x = 4
I hope this was able to help you out :D
16 (-x +x ) +19 + x = 31
16+19+x = 31
35+x = 31
x= -4
hey buddy i hope uh got an answer
to write and solve each inequality.
and
9. Seven more than the quotient of a number b
and 45 is greater than 5..
+15
45
5
Multimedia
E
45
An algebraic equation which represents this word description "Seven more than the quotient of a number b and 45 is greater than 5" is b > -90.
What is a quotient?In Mathematics, a quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.
In order to translate this word problem into algebraic equation, we would assign a variable to the unknown number and then translate the word problem into algebraic equation as follows:
Let the variable b represent the unknown number.
Translating the word problem into an algebraic equation, we have the following;
7 + b/45 > 5
By collecting like terms, we have the following:
b/45 > 5 - 7
b/45 > -2
By cross-multiplying, we have the following:
b > -2 × 45
b > -90
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Find the measure of the indicated angle.
Answer:
Step-by-step explanation:
Given: ∠A =75°, ∠B=60° and ∠C=x
To find: ∠C
Proof: In △ABC
∠A =75° (given)
∠B=60° (given)
∠A+∠B +∠C=180° (angle sum property of a triangle: states that the sum of interior angles of a triangle is 180°)
75°+60°+∠C=180°
∠C=180-75+60
∠C=180-135°
∠C=45°
Therefore is 45 degrees.
a smaller square of side length feet is cut out of a square board. what is the approximate area (shaded region) of the remaining board in square feet?
If a smaller square of side length 17 feet is cut out of a square board , then the approximate area of remaining board in square feet is x² - 289 square feet .
le the side length of the big square board be = "x" ft ;
the side length of smaller square is = 17 ft ;
So , the area of the smaller square is = (side length) × (side length)
= 17 × 17
= 289 ft² .
and , the area of the larger square is = (x) × (x) ;
= x² .
So , the approximate area of the remaining board is calculated as :
= x² - 289 ;
Therefore , area of remaining board is "x² - 289" .
The given question is incomplete , the complete question is
A smaller square of side length 17 feet is cut out of a square board. What is the approximate area of the remaining board in square feet ?
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how do i get my w2 from walgreens if i no longer work there
Send your request via email on the company mail, include your name, employee ID number, and the W2 you are asking for the particular year.
For more than a century, Walgreens has operated on the same set of values: Honesty, Trust, and Integrity with Our Customers, Our Shareholders, Our Suppliers, The Communities We Serve, and Among Ourselves.
Quality via dependable and consistent advice, goods, and services at all points of contact and through all channels.
kind, sensitive, and motivated to provide excellent service and a positive patient and customer experience in order to achieve healthy outcomes.
via service, knowledge, and the personal engagement of each member of the Walgreen team, a strong commitment to and presence in the community.
All products under the Walgreens brand come with a 100% satisfaction guarantee! Return the unused amount if you're not entirely happy, and we'll refund the entire purchase price.
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What will be the length of the south, west and north side of the scale drawing?
Answer:
See below
Step-by-step explanation:
North, 50
West, 28
South, 71
Answer: i got North, 50
West, 28
South, 71
but have a good day
Step-by-step explanation:
Find the equation of the line with y-intercept - 6 and slope - 6 over 7
It can be written as
y = -6/7x - 6/7 * x1 + y1
What is the slop?
The slope, also known as the gradient, is a measure of the steepness of a line. It tells us how much the y-coordinate of a point on the line changes as the x-coordinate changes. The slope is often represented by the letter "m" in the equation of a line. The slope is defined as the ratio of the rise (the change in y-coordinate) to the run (the change in x-coordinate) between two points on a line.
An equation of a line in slope-intercept form is:
y = mx + b
where:
m = slope of the line
x = variable of the line
y = variable of the line
b = y-intercept
Given the y-intercept is -6 and the slope is -6/7, we can substitute these values into the equation above:
y = -6/7x + -6
This equation of the line is in slope-intercept form, and it can be used to find the y-coordinate of any point on the line given the x-coordinate, or to find the x-coordinate of any point on the line given the y-coordinate.
You can also write it in point-slope form.
The point slope form is
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line.
So it can be written as
y = -6/7x - 6/7 * x1 + y1
Where the x1 and y1 are arbitrary value which lies on the line.
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Timmy buys four T-shirts costing t dollars. For buying four T-shirts he gets a 25% discount on each T-shirt. Write two expressions to represent the cost of the four T-shirts
Expression 1: 4t - (4t x 0.25) = 4t - (t) = 3t
Expression 2: 4 x (t - (t x 0.25)) = 4 x (t x 0.75) = 3t
where 't' is the cost of one T-shirt.
In expression 1, the original cost of the four T-shirts (4t) is multiplied by 25% (0.25) which is the given discount percent, and then subtracted from the original cost.
In expression 2, the original cost of one T-shirt (t) is multiplied by 25% (0.25) and subtracted from the original cost, and then the resulting cost (t x 0.75) is multiplied by four to represent the cost of four T-shirts.
Both expressions represent the cost of the four T-shirts after a 25% discount has been applied. they both yield the same result of 3t, which represents the final cost of the four T-shirts after the discount has been applied.
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4x(5x+3)
Find the product
Answer:
[tex]20x^{2} + 12x[/tex]
Step-by-step explanation:
We can expand this equation:
(4x * 5x) + (4x * 3)
= [tex]20x^{2} + 12x[/tex]
If simplified/factored further, we can take out the common variable, x, as well as 4, which is a common number shared between 20 and 12:
4x(5x + 3)
10. A warehouse has 2,100 tables packaged in boxes. They ship 25 tables daily. After how many days will there be fewer than 1,500 tables in the warehouse? Solve and graph the inequality.
The number of days that it will take for there to be fewer than 1,500 tables in the warehouse is given as follows:
More 24 days.
How to solve the inequality?The initial number of tables is given as follows:
2,100 tables.
They ship 25 tables daily, hence the function for the number of tables after n days is given as follows:
T(n) = 2100 - 25n.
There will be fewer than 1,500 tables after n days, for which;
T(n) < 1500
Hence:
2100 - 25n.< 1500
25n > 600
n > 600/25
n > 24.
Hence the time is more than 24 days.
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Popcorn sales at a Saturday afternoon matinee were 108% of the sales at the 8:00 showing of the movie. Calvin expressed 108% as 10.8. is Calvin correct? Explain.
Calvin representation of 108% as 10.8 is incorrect
How to determine if the statement is correctFrom the question, we have the following parameters that can be used in our computation:
Percentage increase = 108%
Express the percentage as a fraction
So, we have the following representation
Percentage increase = 108/100
Evaluate the quotient
This gives
Percentage increase = 1.08
Hence, the expression is 1.08 and Calvin is wrong
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need the answer asap ! thank you to anyone who helps !
Answer:
Step-by-step explanation:
D
What is the slope of the line shown in the graph?
Someone please help me :/
Answer: It's the third down. (-1/-2) - PLEASE TAKE THIS WITH A GRAIN OF SALT. I'm not very good at this type of math.
Step-by-step explanation:
Jayden bought 70 feet speaker wire for $18. 20 he needed 30 more feet if the unit price is the same how much will jayden Pay for an extra 30 feet of wire
For the extra 30 feet of wire Jayden have to pay an amount of $7.80 at a rate of $0.26 per feet.
In these type of problems, first we have to find out the unit price. First let's look at what data is available.
The length of wire Jayden bought = 70 feet
Amount Jayden paid for 70 feet = $ 18.20
Unit price or price of 1 feet of speaker wire = Amount paid / length bought.
Unit price = 18.20/ 70 = 0.26.
So he have to pay 26 cents for each foot of wire.
Now let's calculate the amount for 30 feet of wire = Unit price × 30 = 0.26×30 = 7.80.
So Jayden have to pay $7.80 for the extra 30 feet of wire.
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If you work 32 hours cleaning, how many hours do you need to work babysitting to get $420 for the week?
I just don't understand any of this because I'm dyslexic.
Answer:
HI = 9
Step-by-step explanation:
HJ = HI + IJ
2x + 10 = x + 9 + 1
2x - x = 10 - 10
∴ x = 0
∴ HI = x + 9
= 0 + 9
= 9
−n + (−3) + 3n + 5
please help its due tmrw
suppose you want to gamble in vegas. in a game, you win $x if the number is prime and lose $x/2 if composite. the number is uniformly randomly generated by a machine between 1 and 10 inclusive. will you play this game?
It is favorable to play this game.
This question requires a mathematical calculation of expected value to determine if the game is favorable or not.
The expected value is calculated as the sum of the product of each outcome and its corresponding probability.
The probability of winning $x for each prime number (2, 3, 5, 7) is 1/4, and the probability of losing $x/2 for each composite number (4, 6, 8, 9, 10) is 1/5.
Expected value = (1/4)*2x + (1/4)*3x + (1/4)*5x + (1/4)*7x - (1/5)*x/2 - (1/5)*x - (1/5)*x/2 - (1/5)*x - (1/5)*x/2
= (1/4)(2 + 3 + 5 + 7)x - (1/5)(x/2 + x + x/2 + x + x/2)
= (17/4)x - (5/2)x
= (17/4 - 5/2)x
= (3/4)x
Since the expected value is positive, it is favorable to play this game.
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What are given?Php 45.50 - cot of 1 kilo of mango Php 35.00 - cot of a pineapple Php 19.50 -change Php100.00-Amount given to the fruit vendor with olution
It is right to receive a change of 19.50 if Juan gave php 100.00 to the fruit vendor
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
Mango = 45.50Pineapple = 35.00Amount given = 100Calculating how many Juan spend we have:
Total cost = mango + pineapple
Total cost = 45.50 + 35.00
Total cost = 80.5
Calculating how much Juan should receive in change:
Change = Amount given - Total cost
Change = 100 - 80.5
Change = 19.5
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Correctly written question:
Juan bought a kilo of mango at 45.50 and pineapple at 35.00 is it right to receive a change of 19.50 if he gave php 100.00 to the fruit vendor?