By evaluating ∭ (x + y + z) dV, the final answer is 342.
What is the change of variables method?
In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better-understood problem.
We can evaluate the triple integral by using the change of variables method. We can set u = x, v = y, and w = z, and find the corresponding bounds for each variable in terms of the original bounds.
Then, we have
∭ (x + y + z) dV = ∭ (u + v + w) det(J) du dv dw,
where J is the Jacobian matrix of the transformation and det(J) is its determinant.
We know that 0 <= x <= 3, 0 <= y <= 3, and 0 <= z <= 9 - x^2 - y^2. Therefore, we have:
u = x, 0 <= u <= 3
v = y, 0 <= v <= 3
w = z, 0 <= w <= 9 - u^2 - v^2
The determinant of the Jacobian matrix is 1, so we can simplify the integral to:
∭ (u + v + w) du dv dw = ∫(0,3) ∫(0,3) ∫(0,9-u^2-v^2) (u+v+w) dw dv du
= ∫(0,3) ∫(0,3) (u+v)(w) + (1/3)(w^3) dv du
Hence, By solving this iteratively we get the final answer as 342.
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Which of the following represents a sum from the expression given?
3(14x^2+9x)-22
Answer:
Your answer is 42x^2+27x-22
Step-by-step explanation:
Hope this helps :)
question a factory manager selected a random sample of parts produced on an old assembly line and a random sample of parts produced on a new assembly line. the difference between the sample proportion of defective parts made on the old assembly line and the sample proportion of defective parts made on the new assembly line (old minus new) was 0.006. under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being the proportion of defective parts made on the old assembly line is greater than that of the new assembly line. the pp-value of the test was 0.018.
Two methods can be used to administer the test.
A different theoryAbsent HypothesisThe justification for each of them is given below.What is hypothesis?Writing down the hypothesis throughout the proposal phase is required. Instead of a hypothesis that develops as a result of looking at the data, this will help to keep the research effort concentrated on the main goal and establish a firmer foundation for evaluating the study's outcomes. For these questions, answer option C is the best choice.Another possibility is that there are more faulty parts produced on the old assembly line than on the new assembly line.The value of the p is equal to 0.018, which is equivalent to 0.06 under the null hypothesis that the proportion of defective components produced on the old assembly line is equal to that produced on the new assembly line.Therefore, We infer that the solution to these questions is option C. The likelihood of noticing a difference of 0.006 is 0.018 if there is no difference in the proportions of all defective parts produced on the two assembly lines.
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Eddy's plum weighs 3.042 ounces. Desta's plum weighs 3.24 ounces. Whose plum weighs more? How can you tell?
Answer:desta's plum
Step-by-step explanation:
Desta's plum weighs 0.198 ounces more than Eddy’s plum.
Given that, Eddy’s plum weighs 3.042 ounces Desta's plum weighs 3.24 ounces.
We need to find whose plum weighs more.
How to subtract decimal numbers?
Subtracting decimals is similar to the usual subtraction of whole numbers. We just need to place the decimal numbers, one below the other, according to their place values along with the decimal point. In some cases the two given numbers are different. If needed, we change the given decimal fractions to like decimal fractions to make the subtraction easier. Two decimals are called decimal fractions if they have an equal number of decimal places.
Now, the weight of Desta's plum-the weight of Eddy’s plum=3.24-3.042
=0.198 ounce
Hence, Desta's plum weighs 0.198 ounces more than Eddy’s plum.
what is the slope through the line of (6, 3) and (5, -1)
Answer:
slope is 4
Step-by-step explanation:
2. Evan runs a t-shirt business. He sells shirts for $10. After selling 10 shirts, Evan has $70. Assume x represents the number of shirts sold, and y represents the profit, use this information to fill in the blanks in the statement: How much money did Evan have before he sold any shirts?
A) -$30
B) $30
C) $100
D) $0
Answer:
D
Step-by-step explanation:
The statement says that Evan sells shirts for $10 and after selling 10 shirts, he has $70. We know that the profit is the revenue (the amount of money earned) minus the costs. In this case, the revenue is the amount of money Evan earns from selling shirts and the costs are the amount of money Evan has spent on producing and buying the shirts. We can use this information to set up the equation y = 10x - c where y is the profit, x is the number of shirts sold, and c is the costs.
Given that Evan has $70 after selling 10 shirts, we can substitute 10 for x and 70 for y into the equation to get:
70 = 10(10) - c
Solving for c we get:
c = -30
This means that the costs were $30. To find out how much money Evan had before he sold any shirts we need to subtract the costs from the initial amount. Evan had $0 before he sold any shirts, so the answer is D) $0.
A random sample of 100 adults aged 18 years or older were given a list of ice cream flavors and were asked to list which flavors they liked. The responses are given below. Chocolate 45 Strawberry 42 Vanilla 23 Mocha 19 Which of the following graphs would be most appropriate for visually displaying the results? Pie Chart Frequency Bar Graph Relative Frequency Bar Graph
The most appropriate graph to visualize the information is a PIE CHART. The frequency bar graph makes an independent bar of each fruit each, while it is ideal, it is not easy to identify the total or percentage of each.
Both charts could be used to make a display of the information given.
The frequency bar graph makes an independent bar of each fruit each, while it is ideal, it is not easy to identify the total or percentage of each.
The pie chart could be used to represent a whole of the 100 fruits as a single circle and divides the circle into parts based on the number of fruit belonging to each type including their respective percentages.
Also, since the number of fruits/types are just 5, using a pie chart gives a more accurate and readable visual representation of the information.
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A poll of 1,000 randomly selected registered voters was taken and 680 responded that they favor candidate X for mayor (p 1 = 0.6800). Just before the election, another poll of 900 registered voters was taken and 598 individuals responded that they favor candidate X (p 2 = 0.6644). A 90% two-proportion z confidence interval for the true difference between p 1 and p 2was found to be (-0.0199, 0.0510). What is the meaning of the interval in the context of the problem?
a)There has been no change in support for the candidate.
b)There has been a substantial drop in support for the candidate.
c)There has been a substantial gain in support for the candidate.
d)It is probable for the candidate to get most of the votes because the confidence interval includes zero.
e)It is not probable for the candidate to get most of the votes because support has dropped below 50%.
The meaning of the interval is "there has been no change in support for the candidate". Thus, option (a) is correct.
The 90% two-proportion z-confidence interval (-0.0199, 0.0510) represents the likely range of the genuine difference between the two polls in support of candidate X.
Because the interval comprises 0, the difference in support between the two polls is unlikely to be statistically significant. In other words, there is no compelling evidence that there has been a significant shift in support for the candidate.
Options b), c), d), and e) imply a substantial change in support for the candidate, either positive or negative.
Thus, option (a) is correct.
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Over the last 50 years the average cost of a car has increased by a total of 1,126%. If the average cost of a car today is 30.031, how much was the average cost 50 years ago.
The amount of average cost 50 years ago will be $2,667.05.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Over the last 50 years, the average cost of a car has increased by a total of 1,126%. If the average cost of a car today is 30,031. Then the amount of average cost 50 years ago will be given as,
⇒ $30,031 / 1,126%
⇒ $30,031 / 11.26
⇒ $2,667.05
The amount of average cost 50 years ago will be $2,667.05.
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identify whether each of the following variables is a nominal, ordinal, discrete, or continuous variable.
variables is a nominal, ordinal, discrete, or continuous variable.Nominal: Labels/categories. Ordinal: Order/ranking. Discrete: Whole numbers. Continuous: Any value in range
Nominal variable: A nominal variable is a type of variable that is used to name, label, or categorize particular attributes that are being measured. It is often used in survey research to represent different categories or groups.
Ordinal variable: An ordinal variable is a type of variable that is used to represent a specific order or ranking of values. It is frequently used when measuring psychological or social characteristics, such as job satisfaction or political opinions.
Discrete variable: A discrete variable is a type of variable that can only take on certain values, such as whole numbers. It is often used to count the number of specific events or occurrences within a given time period.
Continuous variable: A continuous variable is a type of variable that can take on any value within a given range. It is typically used to measure quantity or amount, such as the height or weight of an individual.
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2x² + 1 = 5x
A.
X =
B. X=
C.
X =
D. X =
-1+√39
5-√17
4
-1-√39
5+√√17
4
Answer: x= (5+√17)/(4) AND x=(5-√17)/(4)
Step-by-step explanation:
You subtract 5x to put it on the other side, so it's 2x^2-5x+1 and then use the quadratic formula. Hope this helps.
approximately where does the particle achieve its greatest possible acceleration on the interval 0 to b?
The greatest positive acceleration occurs at the midpoint of the interval, when the particle is changing velocity most rapidly.
What is velocity?
Velocity is a measure of the rate of change of an object's position over a period of time. It is a vector quantity, which means it has both magnitude (or size) and direction. Velocity is usually expressed in terms of distance traveled per unit of time, such as meters per second (m/s). Velocity can be determined by dividing the distance traveled by the time taken. For example, if an object travels 20 meters in 5 seconds, its velocity would be 4 m/s. Velocity can also be calculated by taking the derivative of the object's position with respect to time.
The particle will achieve its greatest positive acceleration at the midpoint of the interval, at t = b/2.
This is because the acceleration is greatest when the velocity is changing most rapidly.
At the beginning of the interval, the particle has zero velocity, so it has no acceleration.
At the end of the interval, the particle has reached its maximum velocity, and the rate of change of velocity is zero, so it has no acceleration. Therefore, the greatest positive acceleration occurs at the midpoint of the interval, when the particle is changing velocity most rapidly.
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At a restaurant, hot chocolate can be purchased in two different cup sizes. A 12-ounce cup costs $3.60 and a 16-ounce cup costs $4.80.
Is the linear relationship between cup size and cost also proportional? Why or why not?
Yes, the constant of proportionality is 0.3.
Yes, there is no constant of proportionality.
No, the constant of proportionality is 0.3.
No, there is no constant of proportionality.
The relationship between the cup size and the cost is proportional and the constant of proportionality is 0.3.
How to solve proportional relationship?At a restaurant, hot chocolate can be purchased in two different cup sizes. A 12-ounce cup costs $3.60 and a 16-ounce cup costs $4.80.
Let's find if the relationships of the variables are proportional.
proportional relationship are relationships between two variables where their ratios are equivalent.
Therefore, proportional relationship is rep[resented as follows:
y = kx
where
k = constant of proportionalityHence,
3.6 = 12k
k = 3.6 / 12
k = 0.3
4.80 = 16k
k = 4.8 / 16
k = 0.3
Therefore, the constant of proportionality is 0.3
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Answer:
The relationship between the cup size and the cost is proportional and the constant of proportionality is 0.3.
Step-by-step explanation:
Write the equation for a parabola with a focus at (9, 0) and a directrix at y = -4.
y =
The equation for a parabola with a focus at (9, 0) and a directrix at y = -4 is y = (x - 9)^2 - 4.
What is parabola?Parabola is a type of curve that is symmetrical around a line called the directrix. It is an important conic section and is described by a quadratic equation.
This equation is derived from the equation for a parabola in standard form, which is y = a(x - h)^2 + k.
To find the equation for the parabola, we need to determine the values of a, h, and k. The focus of the parabola is (9, 0), so h = 9. The directrix of the parabola is y = -4, so k = -4. The value of a can be determined by the distance between the focus and the directrix, which is 4. So a = 1/4.
Putting these values together, we get y = (x - 9)^2 - 4.
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3xsquared minus 5 equals negative 5x minus 3
Answer:
x = 1/3 and x = -2
Step-by-step explanation:
3x² - 5 = -5x - 3
turn this into a quadratic equation by adding -5x and -3 to the other side
3x² + 5x - 2 = 0
factor:
(3x-1)(x+2) = 0
3x-1 = 0
x = 1/3 AND
x+2 = 0
x = -2
The solutions of the quadratic equation:
3x² - 5 = -5x - 3
are:
x = 1/3
x = -2
How to solve the quadratic equation?Here we want to solve this quadratic equation:
3x² - 5 = -5x - 3
We can move all the terms to the left side to get:
3x² - 5 + 5x + 3 = 0
3x² +5x - 2 = 0
The solutions are given by the quadratic formula:
[tex]x = \frac{-5 \pm \sqrt{5^2 - 4*3*(-2)} }{2*3} \\\\x = \frac{-5 \pm7 }{6}[/tex]
Then the two solutions are:
x = (-5 + 7)/6 = 1/3
x = (-5 - 7)/6 = -2
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The cost of a school banquet is $70 plus 13 for each person attending? Write an expression that models the problem
Answer: Cost = $70 + ($13)(n)
Step-by-step explanation: As we can see that the cost of the banquet is 70$ and for each person attending there will be a 13$ extra so as to model this problem, let's from an expression. The expression that models the problem can be written as -
Cost = $70 + ($13)(n)
In this expression 'n' will be the number of people attending the banquet at that time.
In this expression the 'x' will be the number of people attending the banquet. 'y' will be the cost of the banquet. y-intercept will be 70$, which is actually the cost of the banquet and the slope will be 13$ which is the cost for each person that will be attending.
mr. starnes and his wife have 6 grandchildren: connor, declan, lucas, piper, sedona, and zayne. they have 2 extra tickets to a holiday show, and will randomly select which 2 grandkids get to see the show with them.
The probability of each combination occurring is 1/15.
Let G be the set of grandchildren, G={Connor, Declan, Lucas, Piper, Sedona, Zayne}.
We can use the formula of nP2 to calculate the possible outcomes of the two grandkids being selected, where n is the number of elements in the set G or 6:
6P2 = 6!/(4!2!) = (6 x 5)/2 = 15
Therefore, there are 15 possible combinations in which the two tickets to the holiday show could go to. These 15 combinations are:
Combination 1: Connor and Declan
Combination 2: Connor and Lucas
Combination 3: Connor and Piper
Combination 4: Connor and Sedona
Combination 5: Connor and Zayne
Combination 6: Declan and Lucas
Combination 7: Declan and Piper
Combination 8: Declan and Sedona
Combination 9: Declan and Zayne
Combination 10: Lucas and Piper
Combination 11: Lucas and Sedona
Combination 12: Lucas and Zayne
Combination 13: Piper and Sedona
Combination 14: Piper and Zayne
Combination 15: Sedona and Zayne
The probability of each combination occurring is 1/15.
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A random survey of autos parked in the student lot and the staff lot at a large university classified the brands by county of origin, as seen in the accompanying table. Are there differences in the national origins of cars driven by students and staff?
Yes there is difference in the national origins of cars driven by students and staff, and that is 31 cars.
Following is the table showing the data of the survey of auto parked in the student lot and the staff lot, classified the brands by the country of origin. we can see that total number of car of all the given countries, driven by the students is 195. And the total number of car of all the given countries, driven by the staff is 164.
So the difference is 195 - 164 = 31 cars.
--The given question is incomplete, the complete question is
"A random survey of autos parked in the student lot and the staff lot at a large university classified the brands by country of origin, as seen in the accompanying table. Are there any difference in the national origins of cars driven by students and staff?
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how do you find the value of f(-5) for the function
f(x)=3x^2-2x+5
Answer: 90
Step-by-step explanation:
f(x) = 3x^2-2x+5
f(-5) = 3 x (-5)^2 - 2(-5) + 5
f(-5) = 3 x (-5)^2 - 2(-5) + 5
f(-5) = (3x25) +10 + 5
f(-5) = 75 + 15
f(-5) = 90
To find the value of f(-5) for the given function , we just need to put the value of x ( which is -5) in the given function. Let's do it!
[tex] \purple{\frak{\implies f(x) = 3x^2-2x+5}} \\ [/tex]
[tex] \sf \implies f(-5) = 3 \times (-5)^2 - 2(-5) + 5 \\ [/tex]
[tex] \sf \implies f(-5) = 3 \times (-5)^2 - 2(-5) + 5 \\ [/tex]
[tex] \sf \implies f(-5) = (3\times 25) +10 + 5 \\ [/tex]
[tex] \sf \implies f(-5) = 75 + 10+5\\ [/tex]
[tex] \purple{\frak{ \implies f(-5) = 90} }\\ [/tex]
Henceforth, the value of the function is 90.From the observation deck of a skyscraper, Morgan measures a 67∘ angle of depression to a ship in the harbor below. If the observation deck is 955 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
405.37
Step-by-step explanation:
tan(67) = 955/ X
(tan(67) )(X), (955) (X)
X tan(67) = 955
X tan(67)/ tan(67) = 955/ tan(67)
X= 405.37
The function is defined below. Find all values of that are NOT in the domain of g. g(x)=x^2+13+40 / x^2-9
Answer:
g(x)=x-2/x^2-9
If there is more than one value, separate them with commas.
Step-by-step explanation:
The variables x and y are proportional.Use the vaules to find the constant aof proportonality.Then write the equation that relates x and y. When y = 20, x=12.
PLEASE HELP
The equation that relates x and y is: x = 3y/ 5
What is direct proportion?A direct proportion is a variation in which two given variables are related to one another in such a way that as the value of one increases, the values of the other also increases.
Thus, given that x and y are proportional, we have;
x [tex]\alpha[/tex] y
x = ky
But x = 12, and y = 20. Then;
12 = k*20
k = 12/ 20
= 3/5
So that,
substituting the value of k, to have
x = 3/5 * y
= 3y/ 5
x = 3y/ 5
Therefore, the equation that relates x and y is: x = 3y/ 5
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Find the surface area of the soild.
Answer:
288
Solution
(8x5)x4=160
(8x8)x2=64
160+64=288
if TU=10 and UV=10, , what is TV
Answer:
TV = 20
Step-by-step explanation:
TV is given by the formula
TV =TU + UV
From the question
TU = 10
AND
UV = 10
Therefore
TV= 10 + 10
TV = 20.
Andys total bill for lunch is 20 dollars the cot of the drink is 15 % of the total bill and the rest is the cost of the food .what percent of the total bill did Andys food cost ?what was the cost of the food?
Answer:
The answer would be [tex]x[/tex]=17 because the food cost 85% of Andy's bill, that is, $17.
Step-by-step explanation:
Since 15% of the $20 bill Andy paid was for drink, it means that (100−15)% of the same amount will be for food. Hence, the food came to 85% of the bill.The amount (x) Andy paid for food therefore is:
[tex]x[/tex]= 20 x 85/100
[tex]x[/tex]= 1 x 85/5
[tex]x[/tex] = 85/5
[tex]x[/tex] = 17
So, the answer would be 17$.
what is the slope through the line of (-8, 11) and (-1, -5)
Answer:
-2.29
Step-by-step explanation:
Slope is Y - Y/X - X
- 5 - 11/ - 1 - (- 8)
-16/-1+8
-16/7
-2.29
The number of assaults in a city is depicted in two different graphs below.
Step 1 of 2: How many times as many assaults were there actually in Year 5 compared to Year 1? Round your answer to 2 decimal places.
1) There were 1.26 times as many assaults in Year 5 compared to Year 1
2) Graph B best represents the data.
What is Graph?
A graph is a structure that resembles a set of items in discrete mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
Given that;
The data is most accurately depicted in bar graph B.
It allows for the following data observations:
In year 1, there were 235 assaults.
Year 1 saw 265 assaults, Year 2 saw 250 attacks, Year 1 saw 280 assaults, Year 1 saw 295 assaults, and Year 2 saw 260 assaults.
1)In the first year, there were 235 assaults, and by the fifth year, there were 295 assaults.
ratio = year5/year1 = 295/235 =1.26
Hence , there were 1.26 times as many assaults in Year 5 compared to Year 1
2) The total number of data points falls between 200 and 300.
Therefore, graph A, whose output value ranges from 0 to 300, is not truly necessary.
Graph B, on the other hand, uses the right range and has a step size of 10, which is also fairly accurate.
Therefore, Graph B best depicts the data.
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Compute the expression shown below.
3
(3.0 × 10-3) ³
Submit your answer in scientific notation.
The result of the given expression in the scientific notation is 2.7 × 10⁻⁸.
What is the scientific notation answer?
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10⁸.
To compute the expression (3.0 × 10⁻³)³, we can use the following steps.
Multiply 3.0 × 10⁻³ by itself three times.
The expression (3.0 × 10⁻³)³ can be calculated as follows:
(3.0 × 10⁻³)³ = (3.0)³ × (10⁻³)³ = 27 × 10⁻⁹
So the answer in scientific notation is 2.7 × 10⁻⁸.
Therefore, the answer in scientific notation is 2.7 × 10⁻⁸.
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If f(x) is an exponential function where f(3.5)=10 and f(9.5)=30, then find the value of f(12), to the nearest hundredth
The equation for an exponential function is f(x) = [tex](ab)^{x}[/tex], where a and b are constants, and the value of f(12) is 1144.14.
What is an exponential function?An exponential function is one that raises the independent variable to a power. It is typically stated as f(x) = [tex]b^{x}[/tex], where b is the base and x is the exponent. Several real-world phenomena, such as population expansion, radioactive decay, and compound interest, are modelled using exponential functions.
The equation for an exponential function is f(x) = [tex](ab)^{x}[/tex], where a and b are constants.
Since we know that f(3.5) = 10 and f(9.5) = 30, we can solve for a and b.
We first need to solve for b. We can use the equation: b = f(x) / f(x-1)
So, b = 30 / 10 = 3
Now, we can solve for a. We can use the equation: a = f(x) / [tex]b^{x}[/tex]
So, a = 10 / [tex](3)^{3.5}[/tex] = 0.093
Now, we can plug in the values for a and b and x = 12 into our equation to find f(12).
f(12) = 0.093 * [tex]3^{12}[/tex] = 1144.14
Therefore, the value of f(12), to the nearest hundredth, is 1144.14.
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Dean measured a picnic area near the river and made a scale drawing. The picnic area is 9 inches wide in the drawing. The actual picnic area is 81 yards wide. What is the scale of the drawing?
Answer:
1 inch = 9 yards
Step-by-step explanation:
suppose you want to make a visualization that shows how many students bought certain quantities of candy from the vending machine during the month of september. of the choices below, which chart would best convey this information to the person looking at the graph?
In the given situation the best way for the viewer to comprehend this information is through the graph's histogram.
What is the Histogram?The distribution of numerical data is roughly depicted by a histogram.
Karl Pearson was the person who first coined the phrase.
The first stage in creating a histogram is to "bin" (or "bucket") the range of values, divide it into a series of intervals, and then count the number of values that fall into each interval.
The bins are often defined as a series of discrete intervals that don't overlap.
The bins (intervals) must be close together and frequently, though not always, have the same size.
The graph's histogram would help the viewer understand this information the best.
Therefore, in the given situation the best way for the viewer to comprehend this information is through the graph's histogram.
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Correct question:
Suppose you want to make a visualization that shows how many students bought certain quantities of candy from the vending machine during the month of September. What chart would best convey this information to the person looking at the graph?
