The factors of the number 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100. If you add them up, you will get the total of 217
I fill the 42 l tank in my car and take a 360 km trip. if my car consumes gasoline at a rate of 8 l per 100 km, how much farther can i go before i run out of gasoline?
Using the principle of proportional relationship, you can go 165km farther after the trip of 360km with 42L gasoline in the tank.
Consumption rate =[tex]8L[/tex] for [tex]100 km[/tex]
So, per number of Km per Litre is
[tex]8L = 100km[/tex]
[tex]1 L = x[/tex]
so,
[tex]8x = 100[/tex]
[tex]x=8 \div 100\\[/tex]
[tex]x= 12.5[/tex] kilometer per Litre
Number of kilometers for [tex]42 L[/tex]
[tex]12.5 km = 1 L[/tex]
[tex]y=42L[/tex]
On, Cross multiplying
[tex]y = 12.5\times42[/tex]
[tex]y = 525 km[/tex]
The difference in the distance [tex]= 525 - 360 = 165 km[/tex]
Therefore, the gas can go for a further [tex]165 km[/tex]
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in a order pair (4,9) witch is the y-coordinate?
In order pair (4,9), 9 is the y- coordinate while 4 is the x-coordinate.
The coordinates are the pair of numbers that describe the position of some point in a plane using the horizontal x-axis and the vertical y-axis as the point of reference. The representation of this coordinate is usually done by (x,y) where x represents the point's reference with respect to the x-axis and y represents the point's reference with respect to the y-axis. There are four quadrants in the graph which are named quadrant 1, quadrant 2, quadrant 3, and quadrant 4. In quadrant 1 both the x and y-axis is positive, in quadrant 2 x-axis is negative and the y-axis is positive, in quadrant 3 both the x and y-axis are negative, and in quadrant 4 x-axis is positive while the y-axis is negative.
I hope this answer helps
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Answer:
9
Step-by-step explanation:
Remember that all points have the form, [tex](x,y)[/tex].
Soo in this problem,
[tex]\begin{cases}\text{4 is the x-coordinate}\\\text{9 is the y coordinate}\end{cases}[/tex]
Thus, The y-coordinate is 9!!
Which of the following describes the transionnation of g(x)=3(2) ^-x+2 from the parent iuciction f(x) =2^x?
O reflect across the x-axis, stretch the graph vertically by & factor of 3,shift 2 units up. O reflect across the y-axis, stretch the graph vertically by & factor of 2,shift 3 units up. O reflect across the x-axis, stretch the graph vertically by & factor of 2, shift 3 units up. O reflect across the y-axis, stretch the graph vertically by & factor of 3,shift 2 units up
The transformation of g(x) = 3(2)⁻ˣ+2 from the parent function f(x) = 2ˣ will be carried out by reflecting f(x) across the y-axis, then stretching the graph of f(x) vertically by a factor of 3 and then shifting 2 units up,
What is a transformation function?
A function that transforms one function or graph into another, typically a related function or graph, is called a transformation function.
How to convert the parent function into the transformation function?
The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.
Here, we have
Transformation Function - g(x) = 3(2)⁻ˣ+2
Parent Function - f(x) = 2ˣ
To convert the parent function into the transformation function, we will follow some steps:
Multiply 3 by the function f(x). Due to this the graph of f(x) shift vertically by 3 units. f(x) = 3(2ˣ )Now, replace x with -x. Due to this the graph of f(x) reflects the y-axis. f(x) = 3(2)⁻ˣAdd 2 to the function f(x). Due to this the graph of f(x) shift by two units. f(x) = 3(2)⁻ˣ+2 = g(x)Hence, the transformation of g(x) = 3(2)⁻ˣ+2 from the parent function f(x) = 2ˣ will be carried out by reflecting f(x) across the y-axis, then stretching the graph of f(x) vertically by a factor of 3 and then shifting 2 units up.
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Find x 96+2x+(x+12).
Answer:
bro u find it
Step-by-step explanation:
Find the measurement of V.
Answer:
60°
Step-by-step explanation:
As we can conclude from the equal measured side lengths, this is an equilateral triangle so all angles have equal measurement.
Since the sum of interior angles in a triangle is equal to 180 to find the measure of angle V we need to divide 180 by 3:
180 ÷ 3 = 60
Two cars start at the same point and simultaneously drive in opposite directions.
The speed of the first car is s miles per hour. The speed of the second car is 5
miles per hour less than the speed of the first car.
How far apart are the cars 1.5 hours after they start moving?
Answer:
3s - 7.5 milesStep-by-step explanation:
GivenThe speed of car1 is s,The speed of car2 is 5 less than s,Time is 1.5 hrs.SolutionDistance equation:
Distance = speed * timeIf cars move in opposite directions their speeds add up, then the distance between them after 1.5 hours is:
(s + s - 5)*1.5 = (2s - 5)*1.5 = 3s - 7.5Answer:
After 1.5 hr, they are 3s - 7.5 mi away.
Step-by-step explanation:
Forming the expression,
→ 1.5 × (s + s - 5)
Now the required solution will be,
→ 1.5 × (s + s - 5)
→ 1.5 × (2s - 5)
→ 1.5(2s - 5)
→ 3s - 7.5
Hence, answer is 3s - 7.5 miles.
if a password is to have 4 digits, each from 0 to 9, what is the probability that there will be no repeats on the digits?
The probability that there will be no repeats on the digits is 0.504.
What is meaning of probability?
The ratio of favorable outcomes with the total number of outcomes is known as probability of that event.
The number of digits of the password is 4.
The numbers from 0 to 9 is 10.
If the digit can repeat, then we can chose first digit in 10 ways, the second digit in 10, third digit in 10 ways and fourth digit in 10 ways.
The total number of ways is 10 × 10 × 10 × 10 =10000.
If the digit can't repeat, then we can chose first digit in 10 ways, the second digit in 9 (because we can't use first digit) , third digit in 8 ways (because we can't use first digit and second digit) and fourth digit in 7 ways(because we can't use first digit, second digit, and third digit).
The total number of ways is 10 × 9 × 8 × 7 =5040.
The favorable outcomes for this event is 5040.
The total number of outcomes is 10000.
The required probability is 5040/10000 = 0.504.
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0.1 times n equal's89.5
Which of the following sets is equal to {1, 2, 3, ...}?
The set which is equivalent and equal to the given set; {1, 2, 3, ...} is; Z+.
Which set is equivalent to the given set?It follows from the task content that the set which is equivalent to the given set; {1, 2, 3, ...} is to be determined.
Since the numbers in the set are all integers and which happen to be positive integers.
Hence, the best representation of a set which is equivalent to the given set as given in the task content is; Z+.
The set of positive integers is represented as Z+. It implies all the integers greater than 0.
Hence, the set which is equivalent to the given set; {1, 2, 3, ...} is; Z+.
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why do we use the pooled proportion when we calculate the standard error for the difference in proportions when performing a hypothesis test?
we use the pooled proportion when we calculate the standard error for the difference in proportions when performing a hypothesis test whne When the variances of both populations are the same
The standard error for the distinction within the proportions is calculated utilizing the population proportions but in cases where the population proportions are unknown, we utilize the test proportions to calculate the standard error. In the case of hypothesis testing, we are mindful of the population proportions whereas in evaluating the confidence interval for the distinction between the proportions we have no thought of the population proportions. So, the standard error for a hypothesis test of distinction in two proportions is distinctive from the standard error for a certain interval of the difference in two proportion.
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Write equivalent fractions for 11/12 and 5/6 using least common denominator.
Type the fractions using a slash ( / ) to separate the numerator and denominator.
11/12 =
5/6 =
This shows a diagram.
What is the value of x?
Step-by-step explanation:
[tex](3x + 2) + x = 180 \\ 3x + x = 180 - 2 \\ 4x = 178 \\ x = 44.5[/tex]
Answer:
x° = 44.5°
Step-by-step explanation:
x° and (3x + 2)° are supplementary angles, which means they add up to 180°.
Equation: x + 3x + 2 = 180
Step 1: Combine like terms.
[tex]\implies 4x + 2 = 180[/tex]
Step 2: Subtract 2 from both sides.
[tex]\implies 4x + 2 - 2 = 180 - 2[/tex]
[tex]\implies 4x = 178[/tex]
Step 3: Divide both sides by 4.
[tex]\implies \dfrac{4x}{4}=\dfrac{178}{4}[/tex]
[tex]\implies x = 44.5[/tex]
Step 4: Substitute 44.5 as the value of x in (3x + 2) to find its measure.
[tex]\implies 3(44.5)+2[/tex]
[tex]\implies 135.5[/tex]
Therefore, the measure of x° is 44.5°, and the measure of (3x + 2)° is 135.5°. Together, they add up to 180°.
Monty spends 2.5 hours playing basketball each
day. What is the total amount of time (in hours)
hat Monty spent playing basketball after 7
days?
Answer:
Your answer is 17.5 hours
Step-by-step explanation:
Simply multiply 2.5 and 7 to get your answer.
You have to multiply the number of hours by the number of days to get the correct product or answer.
How would you write the work to get the answer to the problem your neighbor pays you $20 every two hours you work you work for eight hours on saturday how much does your neighbor owe you
The neighbour us an amount of $160 for the work that we did for him.
As per the agreement the never will pay 20 dollars were every hour that we work.
We worked for a total of 8 hours on Saturday.
So, according to the unitary method,
Total amount of money owned by the neighbour = number of hours for which we work x the amount received for working per hour.
Total amount of money owned by the neighbour = 8 × 20
Total amount of money owned by the neighbour = 160 dollars.
The total amount of money owned by the neighbour to us is 160 dollars.
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a survey showed that a family of four spends an average of $215.60 per day while on vacation. suppose a sample of 64 families of four vacationing at niagara falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50. a. develop a 95% confidence interval estimate of the mean amount spent per day by a family of four visiting niagara falls. 9 pts. b. based on the confidence interval from part (a), does it appear that the population mean amount spent per day by families visiting niagara falls differs from the mean reported by the survey? explain. 1 pt.
The confidence interval is (233.8436; 271.0564).
What is a confidence interval?
The likelihood that a population parameter will fall between a set of values for a specific percentage of the time is referred to as the confidence interval. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
What is the margin of error?
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings.
We have,
Sample mean = 252.45
Sample standard deviation = 74.50
n = 64
α = 0.05
By applying the margin of error formula, we get
Margin of Error = tα/2 * s/√n
df = n - 1 = 64 - 1 = 63
t(α/2, df = 63) = 1.998
Margin of Error = 1.998 * 74.50/√64
Margin of Error = 18.6064
The confidence interval = 252.45 ± 18.6064
= (233.8436; 271.0564)
Hence, the confidence interval is (233.8436; 271.0564).
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Please provide, with your answer, the steps taken.
The value of the given expression is 9/2 when substituting the values of m = -3, n = 2, and p = -1 in the expression.
The value of the given expression is 10/3 when substituting the values of x = 3, y = 2, and z = 4 in the expression.
Given that m = -3, n = 2, and p = -1
The expression is given in the question
⇒ m(p -n)²/ 3p +m
Substitute the values of m = -3, n = 2, and p = -1 in the expression
⇒ -3(-1 -2)²/( 3(-1) +(-3))
⇒ -3(-3)²/(-3-3)
⇒ -3(9)/(-6)
⇒ 27/6
⇒ 9/2
Given that x = 3, y = 2, and z = 4
The expression is given in the question
⇒ (3z + 2x + y)/(4y - 2x + z)
Substitute the values of x = 3, y = 2, and z = 4 in the expression
⇒ (3×4 + 2×3 + 2)/(4×2 - 2×3 + 4)
⇒ (12 + 6 + 2)/(8 - 6 + 4)
⇒ 20/6
⇒ 10/3
Thus, the value of the given expression is 10/3 when substituting the values of x = 3, y = 2, and z = 4 in the expression.
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the augusta national golf club in augusta, georgia is an 18-hole course that consists of par-3 holes, par-4 holes, and par-5 holes. a golfer who shoots par has a total of 72 strokes for the entire course. there are two more par-4 holes than twice the number of par-5 holes, and the number of par-3 holes is equal to the number of par-5 holes. find the numbers of par-3, par-4, and par-5 holes on the course.
No. of par-3 holes be represented by = 5
No. of par-4 holes be represented by = 8
No. of par-5 holes are represented by = 5
Total number of courses in the club= 18 (given in the question)
Total shot taken by golfer=72 (given in the question)
Let par-3 holes be represented by t
Let par-4 holes be represented by f
Let par-5 holes be represented by v
forming equations:
f+2=2v
t=v
f + v + t = 18
f+2=2v
f=2v-2 -(i)
t=v -(ii)
f + t + v=18
putting values from (i) and (ii)
(2v-2) + v + v=18
2v-2+2v=18
4v=18+2
4v=20
v=20/4
v=5
Number of par-5 holes=5
from (i)
f=2v-2
putting value
f=2(5)-2
f=10-2
f=8
Number of par-4 holes=8
from (i)
t=v-
putting value
t=5
t=5
Number of par-3 holes=5
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HELPPPPPPPPPPPpp
Robert pays for his family to go to the arcade. He pays an entrance fee for his group and an additional amount per game that his family plays as shown in the graph. Use the graph to answer.
Find the slope and interpret its meaning.
Answer:
3/4,. it's means for every 4 games there's a $3 fee
Step-by-step explanation:
3/4
it's means for every 4 games there's a $3 fee
what is the difference between independent samples and related samples when dealing with two samples
The difference between an independent sample and a dependent sample is that the dependent sample for one set of items is paired measurement while measurements made on two samples are termed an independent sample.
In statistics, while considering two samples and conducting a hypothesis test, one should be aware of which type of test should be conducted based on samples whether they are dependent or independent. If the value of another sample is affected by any one sample then the samples are dependent. If no information can be deduced from the other sample using one sample then the samples are independent.
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Complete the equation so that it has no solution.
9(x – 4) – 5x =__x-30
For the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.
As given in the question,
Given equation is equal to :
9 ( x - 4) - 5x = _ x - 30
Simplify Left hand side of the given equation we get,
9 ( x - 4) -5x
= 9x - 36 - 5x
Collect the like terms we have,
9x - 5x - 36
= 4x - 36
Now compare left hand side and right hand side to get no solution of the equation,
4x -36 = _x -30
Blank should be filled by 4
Therefore, for the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.
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From the diagram below, choose the correct letter for each of the
following parts of a circle:
a) a major arc
b) a minor sector
c) a major segment
A
B
D
✓ Scroll down
E
From the diagram, A is the major arc
B is the minor sector
C is the major segment.
What do you mean by major arc, minor sector, and a major segment of a circle?
1. Major arc: A significant arc is one that is larger than 180 degrees in measure.
2. Minor sector: A circle's intercepted arc and two of its radii define a region known as a sector. The center angle is the intersection of the two radii. A minor sector is defined as having a center angle of less than 180°.
The major arc is A significant arc is one that is larger than 180 degrees in measure. So, A is the major arc. The minor sector is defined as having a center angle of less than 180°. So, B is the minor sector. And C has the maximum portion of length so C is a major segment.
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-
Find the equation of a line parallel to x - 4y = 36 that passes through the point
(-4,-5).
The equation of a line parallel to x - 4y = 36 is x - 4y = 16.
If the two lines are parallel then their slope must be equal. Two parallels lines have different intercepts but same slope. The slope intercept form of a line is y = mx + c. Where m is the slope and c is the intercept.
Now, writing the given equation in slope-intercept form,
x - 4y = 36
4y = x - 36
[tex]y=\frac{1}{4}x-9[/tex]
By comparing it with slope-intercept form, we get
[tex]m=\frac{1}{4}[/tex]
c = -9
Now, Finding the equation of line passing through (-4,-5) with slope as [tex]\frac{1}{4}[/tex],
[tex]m=\frac{y-y_1}{x-x_1} \\\\\frac{1}{4}=\frac{y-(-5)}{x-(-4)}\\\\ \frac{1}{4}=\frac{y+5}{x+4}\\x+4=4y+20\\x-4y=16[/tex]
The equation of parallel line is x - 4y = 16.
Hence, the equation of a line parallel to x - 4y = 36 is x - 4y = 16.
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change 4-1/2 to a improper fraction
Answer: 9/2
Step-by-step explanation: Hope this helps.
Jackson buys 60 books at £3 each.
He sells 35 of these at £8 each and
the remainder at £4 each. What
percentage profit does he make
(give the answer to the nearest
whole number).
Answer:
111%
Step-by-step explanation:
£3 × 60 = £180
(35 × £8) + ( 25 × £4) = £380
£380 ‐ £180 = £200
200/180 × 100% = 111% (nearest whole number)
A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed that: What is the probability that a designer does not prefer red? 1.00 0.77 0.73 0.23
The probability that a designer does not prefer red is 0.77.
Define the meaning of the term probability?Probability is synonymous with possibility. It is a mathematical branch that deals with both the occurrence of something like a random event. The value varies from 0 to one. Probability has just been introduced in mathematics to predict the likelihood of occurrences occurring.Probability (event) = favorable outcome / total outcome
Total primary color designers = 400.
The number of opinions for red = 92
The probability for designer prefer red = 92 /100
The probability for designer prefer red = 0.23
Then, the probability that a designer does not prefer red = 1 - 0.23
The probability that a designer does not prefer red = 0.77
Thus, the probability that a designer does not prefer red color = 0.77.
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The correct question along with table is attached-
a group of 1,000 randomly selected adults is classified into 4 smoking groups: nonsmoker, light smoker, moderate smoker, and heavy smoker. at the end of a ten-year period, the proportion in each group who developed lung cancer was determined. the null hypothesis is that all 4 groups will have the same incidence rate of lung cancer. the p-value is found to be smaller than the level of significance (i.e. smaller than .05). what is the most appropriate conclusion?
The null hypothesis is rejected thus there is a significant difference in the incidence of lung cancer in all four groups.
When the p-value is less than 0.05, the null hypothesis that there is no difference between the means is rejected, and we come to the conclusion that there is a significant difference. The existence of a significant difference cannot be inferred if the p-value is higher than 0.05.
The null hypothesis in the given scenario was that all four groups will have the same incidence rate of lung cancer which is rejected.
An assertion that there is no correlation between two population measures is referred to as a null hypothesis. To prepare the ground for additional experimentation or study that explains the position of interest, researchers reject or refute the null hypothesis.
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Given that x is a nonnegative number, a student conjectured that x+4
Which value of x is a counterexample to the student's conjecture?
Responses
A. x=−1/4
(x equals negative one fourth)
B. x=−4
C. x = 1
D. x = 4
The value of x that is a counterexample to the student's conjecture is (a) x = -1/4
How to determine the value of x?From the question, we have the following statement that can be used in our computation:
x = Non-negative number
Student's conjecture:
x + 4 < x²
Using the options, we have:
(a) x = -1/4
x + 4 < x²
-1/4 + 4 < (-1/4)²
3.75 < 1/16 -- false
(b) x = -4
x + 4 < x²
-4 + 4 < (-4)²
0 < 16 -- true
(c) x = 1
x + 4 < x²
1 + 4 < (1)²
5 < 1 -- false
This cannot be used because x is non-negative
(c) x = 4
x + 4 < x²
4 + 4 < (4)²
8 < 16 -- true
The false statements are the counterexamples
Hence, the value of x is (a) x = -1/4
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Complete question
Given that x is a nonnegative number, a student conjectured that x + 4 < x². Which value of x is a counterexample to the student's conjecture?
Responses
A. x=−1/4
B. x=−4
C. x = 1
D. x = 4
50 POINTS
Your parents have heard about your business and would like to invest in it to help you earn as much money this summer as possible. They decide to give you $100 towards your business. However, there's a catch. They want 10% of the money you make.
1. if you mowed 10 lawns while charging $15 a lawn, how much would you have to pay your parents?
2. if you needed to make $300 to buy a switch, how many lawns would you have to mow?(Hint: don't forget about how much you would have to pay your parents.)
3. With all cost taken into account, your start up money, the money your parents gave you and what you paid your parents, how much profit did you make after 20 lawns?
The profit made from the business that receives an initial $100 investment are as follows;
1. The amount received from the investment is $15
2. The number of lawns that should be mowed to buy the switch is 23 lawns
3. The profit made from the business considering the cost and the initial investment of the parents is $170
What is an investment?An investment is the money directed towards an asset purchase to increase the valuation of the business and products within a time period.
The amount invested = $100
The amount desired as return = 10% of the amount made from the business
1. The amount charged per lawn = $15
The number of lawn mowed = 10
The revenue of the business = 10 × $15 = $150
The amount paid as return on investment = 10% × $150 = $15
2. The amount required to buy the switch = $300
The number of lawns to be mowed, n, is therefore;
300 = 15 × n - 10% × 15 × n = 15·n - 1.5·n = 13.5·n
300 = 13.5·n
n = 300/13.5 ≈ 23 ( rounding up to the nearest whole number)
The number of lawns to be mowed is 23 lawns
3. The revenue from mowing 20 lawns is 20 × $15 = $300
The amount received by the investing parents = 10% × $300 = $30
The amount received from the parents investment = $100
The profit made after 20 lawns = $300 - $30 - $100 = $170
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William leaves work at 16:00. He drives 36 kilometres from work to home at an average speed of 48 km/h. What time does William arrive home?
answer using the 24 hour clock.
William will arrive home at 16:45, it will take 45 min to reach home.
Given, that William leaves work at 16:00
Distance from work to home is 36 kilometres
Also, he drives at an average speed of 48 km/hr
Now, using distance-speed relation to find the time
So, as we know Distance = Speed × Time
On putting the values of distance and speed, we get
36 km = 48 km/hr × Time
On dividing both the sides by 48, we get
36/48 = (48×Time)/48
36/48 = Time
Time = 0.75
Hence, he will take 0.75 hr to reach home.
0.75 hr ≈ 45 minutes
As, 1 hr = 60 minutes
0.75 hr = 0.75 × 60 = 45 minutes
So, William will arrive home at 16:45
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is the drink proportinal?
The proportional of price of the drink to the number of ounces is 0.2.
In the given question we have to find the proportional of price of the drink to the number of ounces.
As given from the table that;
Drink Size (oz) 12 16 20
Price (dollars) 2.40 3.20 4.00
If we find the proportional of price of the drink to the number of ounces. Then;
Price of the drink/Number of drink = 2.40/12 = 3.20/16 = 4.00/20
Price of the drink/Number of drink = 0.2 = 0.2 = 0.2
So we can see that the proportional of price of the drink to the number of ounces is 0.2.
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Answer:
Yes it is proportional.
