1. (30 points) There are two coins in a box. For Coin1, the probability of a head is 1/4. For Coin2, the probability of a head is 3/4. (a) One coin is picked at random and is tossed three times. The observed tosses are HTH. Find the probability that Coin2 was picked. (b) As before a coin is picked at random, and is tossed n times. It is observed that m heads appear (m
Answers
The probability that we picked Coin2 given m heads and (n - m) tails is 2^(n-m-1) * 3^m / C(n, m).
a) One coin is picked at random and is tossed three times. The observed tosses are HTH.
The goal is to find the probability that Coin2 was picked. Given that there are two coins in the box with different probabilities of head:
Coin1 has a probability of head 1/4, and Coin2 has a probability of head 3/4.
The probability of getting HTH using
Coin1 is: P(HTH|Coin1) = P(H|Coin1) * P(T|Coin1) * P(H|Coin1)
= (1/4) * (3/4) * (1/4) = 3/64
Similarly, the probability of getting HTH using
Coin2 is: P(HTH|Coin2) = P(H|Coin2) * P(T|Coin2) * P(H|Coin2)
= (3/4) * (1/4) * (3/4) = 27/64
Therefore, the total probability of getting HTH is: P(HTH)
= P(Coin1) * P(HTH|Coin1) + P(Coin2) * P(HTH|Coin2)
Given that we picked a coin at random, both coins have equal probability of getting selected,
hence: P(Coin1) = P(Coin2) = 1/2
So, P(HTH) = (1/2) * (3/64) + (1/2) * (27/64)
= 15/64
The probability that we picked Coin2 is: P(Coin2|HTH)
= P(H|Coin2) * P(T|Coin2) * P(H|Coin2) * P(Coin2) / P(HTH) = (3/4) * (1/4) * (3/4) * (1/2) / (15/64)
= 9/15 = 3/5
Hence, the probability that we picked Coin2 given the observed tosses HTH is 3/5.
b) As before a coin is picked at random, and is tossed n times. It is observed that m heads appear (m < n).
Find the probability that Coin2 was picked.
In this case, the goal is to find the probability that we picked Coin2 given that we got m heads and (n - m) tails in n tosses of a randomly selected coin.
Using Bayes' Theorem, the probability is: P(Coin2|m heads, n - m tails)
= P(m heads, n - m tails|Coin2) * P(Coin2) / P(m heads, n - m tails)P(m heads, n - m tails|Coin2) is the probability of getting m heads and (n - m) tails in n tosses using Coin2:P(m heads, n - m tails|Coin2)
= C(n, m) * (3/4)^m * (1/4)^(n-m)
where C(n, m) is the number of ways of getting m heads in n tosses of the coin, which is given by C(n, m) = n! / (m! * (n - m)!).
P(Coin2) is the probability of picking Coin2, which is 1/2 (as we have two coins, each with equal probability of getting selected).
P(m heads, n - m tails) is the probability of getting m heads and (n - m) tails irrespective of the coin we picked.
This is the sum of the probabilities of getting m heads and (n - m) tails using both coins, i.e. :P(m heads, n - m tails)
= P(m heads, n - m tails|Coin1) * P(Coin1) + P(m heads, n - m tails|Coin2) * P(Coin2)
where P(m heads, n - m tails|Coin1) is the probability of getting m heads and (n - m) tails using Coin1,
which is: C(n, m) * (1/4)^m * (3/4)^(n-m)
and P(m heads, n - m tails|Coin2) is the probability of getting m heads and (n - m) tails using Coin2, which we already calculated above,
i.e.: C(n, m) * (3/4)^m * (1/4)^(n-m)
Therefore, P(m heads, n - m tails)
= C(n, m) * (1/4)^m * (3/4)^(n-m) * (1/2) + C(n, m) * (3/4)^m * (1/4)^(n-m) * (1/2) = C(n, m) * (1/2) * (1/4)^m * (3/4)^(n-m) * (1 + 1)
= C(n, m) * (1/2) * (1/4)^m * (3/4)^(n-m) * 2
= C(n, m) * (1/2) * (3/4)^n
Therefore, substituting these values in the Bayes' Theorem: P(Coin2|m heads, n - m tails)
= C(n, m) * (3/4)^m * (1/4)^(n-m) * (1/2) / (C(n, m) * (1/2) * (3/4)^n)
= 2^(n-m-1) * 3^m / C(n, m).
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Related Questions
A type of account that pays zero or low interest on the money deposited is a ____.
A. savings account
B. checking account
C. money market account
D. certificate of deposit
Answers
Answer:
Checking account
Step-by-step explanation:
Answer:
B. Checking Account
Step-by-step explanation:
3 more until I can move on from this section, if anyone has the answer it would be greatly appreciated
Answers
Answer: y= |x-1|+3
Step-by-step explanation:
again lol used desmos graphing it’s 3 high so that +3 at the end and -1 to bring it to the side i’m bad at explaining
Two friends, Liam and Jonathan, had just bought their first cars. The 27.6x represents the number of miles, y, that Liam can drive his car for every x gallons of gas. The table below represents the number of miles, y, that Jonathan can drive his car for every x gallons of gas.
Answers
Step-by-step explanation:
Seeing 27.6x means Liam can drive for 27.6 miles for one gallon
On the table we show Johnathons. The smallest is 5gallons for 108miles. But we want 1 gallon. Divide the 5 by 5, you get one
5/5 = 1.
Now we do the same for the miles
108/5= 21.6
Since Liam does 27.6, and Johnathon does 21.6, that means Liam can drive 6 more miles per gallon
A certain brand of coffee costs $5.99 for 12.4 ounces. What is the unit rate? please help asap
Answers
Answer:
.483≈ $.48 per ounce
Step-by-step explanation:
Unit rate will be cost/ounce
$5.99 ÷12.4 = .483
.483≈ $.48 per ounce
Someone please solve this rational exponent equation plss
Answers
Answer:
n=81
Step-by-step explanation:
We have the equation \(-4n^{-1/2} =-4/9\). To isolate the variable n, we must first divide each side by -4. This would give us \(n^{-1/2}\)=1/9. Now, we need to get rid of the exponent =-1/2. To do this, we must raise both sides of the equation by the reciprocal of -1/2, or -2. This gives us the equation \((n^{-1/2})^{-2}=1/9^{-2}\), or simplified, n=81. Hope this helps!
Brigid is picking strawberries at the Pick-Your-Own Farm. Her goal is to pick 5 bushels of strawberries. She has already picked 1
1
2
bushels, and she picks at a rate of
5
8
bushel per hour. The scenario is represented as
5
8
h + 1
1
2
= 5, where h is the number of hours she picks. How many more hours will it take Brigid to fill 5 bushels of strawberries?
2 and StartFraction 3 Over 16 EndFraction hours
2 and StartFraction 3 Over 16 EndFraction hours
5 and three-fifths hours
10 and two-fifths hours
Answers
Answer:
We can start by isolating the variable "h".
5 8 h + 1 1 2 = 5
Subtracting 11/2 from both sides:
5 8 h = 5 - 1 1 2
Simplifying:
5 8 h = 8 1 2
Dividing both sides by 5/8:
h = 8 1 2 ÷ 5 8
Converting the mixed number to an improper fraction:
h = (8 x 8 + 1) ÷ 5 8
h = 65/8
Now, we can convert this fraction to a mixed number:
h = 8 1/8
Brigid has already picked for 8 1/8 hours, so the amount of time needed to pick the remaining strawberries is:
5 - (1 1/2 + 5/8 x 8) = 5 - (3 5/8) = 1 3/8
Therefore, Brigid still needs to pick for 1 3/8 hours to fill 5 bushels of strawberries. The answer is 1 and 3/8 hours or 2 and 3/16 hours (if simplified).
Step-by-step explanation:
You hear that Peter the Anteater is walking around the student centre so you go and sit on a bench outside and wait to see him. On average, it will be 16 minutes before you see Peter the Anteater. Assume there is only 1 Peter walking around and let X be the waiting time until you see Peter the Anteater.Which distribution does X follow?A. X ~ Expo(1/16)B. X ~ Poisson(1/16)C. X ~ U(0,16)D. X ~ Normal(16,4)
Answers
The distribution that X follows in this scenario is A. X ~ Expo(1/16), which means that the waiting time until you see Peter the Anteater follows an exponential distribution with a rate parameter of 1/16.
This can be determined by considering the characteristics of an exponential distribution, which models the waiting time for an event to occur given a constant rate. In this case, the event is seeing Peter the Anteater, and the rate is the average time it takes for him to appear, which is given as 16 minutes.
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How can you use clues and resources to
determine and verify the meanings of words?
Answers
Answer:
Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using context clues, analyzing meaningful word parts, and consulting general and specialized reference material
Step-by-step explanation:
Christina's bird feeder holds 7/10 of a cup of birdseed. Christina is filling the bird feeder with a scoop that holds 1/10 of a cup. How many scoops of birdseed will Christina put into the feeder? Leave answer in simplest form
Answers
Answer:
7 scoops
Step-by-step explanation:
hope this helps
Find the 8th term of the arithmetic sequence x + 1 x+1, 8 x − 3 8x−3, 15 x − 7 ,
Answers
Answer: 50x - 27
Step-by-step explanation:
To find the 8th term of the arithmetic sequence, we need to first find the common difference between consecutive terms:
Common difference (d) = second term - first term
d = (8x - 3) - (x + 1)
d = 7x - 4
Now, we can use the formula to find the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the term number we want to find.
Plugging in the values, we get:
a8 = (x + 1) + (8 - 1)(7x - 4)
a8 = x + 1 + 7(7x - 4)
a8 = x + 1 + 49x - 28
a8 = 50x - 27
Therefore, the 8th term of the arithmetic sequence x + 1, 8x - 3, 15x - 7 is 50x - 27.
For the given sequence of 6 numbers and target value inputted for task \( 1 a \), find an arrangement of the 6 numbers that generates the biggest difference \( { }^{2} \) between the calculated result
Answers
By performing the desired calculation using each arrangement and squaring the difference between the result and the target value, you can determine the arrangement that yields the largest squared difference.
To find the arrangement of the 6 numbers that generates the biggest difference squared, you need to consider all possible permutations of the numbers. For each arrangement, perform the desired calculation using the given, such as addition, subtraction, multiplication, or any other specified operation.
Once you have the calculated result for each arrangement, calculate the squared difference between the result and the target value. This is done by subtracting the target value from the calculated result and then squaring the difference.
By comparing the squared differences obtained for each arrangement, you can identify the arrangement that yields the largest squared difference. This arrangement will have the maximum difference squared between the calculated result and the target value.
It's important to note that the specific calculation or operation to be performed is not mentioned in the question. Therefore, you need to specify the operation or provide more information to determine the exact steps for performing the calculation.
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In the diagram below of triangle MNOP, P is the midpoint of MO and Q is the midpoint of NO. If PQ=5x+62 and MN=6x-4, what is the measure of PQ
Answers
The measure of length PQ will be 22 units.
What is the mid-point theorem?A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.
Given:
PQ = 5x + 62, and MN = 6x-4
Now, using Mid- Point Theorem
PQ= 1/2 MN
-5x+ 62 = 1/2( 6x - 4)
-5x+ 62 = 3x - 2
-5x- 3x = -2 - 62
-8x = -64
x= 8
PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22
Hence, the measure of PQ is 22 units.
The missing image is attached below.
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Answer asappp plssss
Answers
Answer:
The answer should be B.
Step-by-step explanation:
Btw a school orchestra should usually contain only string instruments and whatnot. If it has woodwinds, brass instruments, and percussion, then that would be a band.
PLEASE ANSWER!!!
In 1987, 34.7 million households owned a dog, and 27.7 million
owned a cat. Since then, dog ownership has decreased by 0.025
million households per year, and cat ownership has increased by
0.375 million households
per year. How many years, y, will it
take for them to be equal?
Answers
Answer:
y=17.5
Step-by-step explanation:
y=# of years
34.7-0.025, you subtract since it has decreased.
27.7+0.375, you add since it increased.
Put them into equations:
34.7-0.025y=27.7+0.375y
*whatever you do to one side, you do to the other*
Solve the equation and get y=17.5
Answer:
17.5
Step-by-step explanation:
Your welcome From DanYeetzz
does the angle bisector at the vertex angle intersect the base at the base midpoint in an isosceles triangle
Answers
Answer:
Yes.
Step-by-step explanation:
Yes.
You can prove it using SAS and CPCTC.
Start with an isosceles triangle with a horizontal base and the vertex angle above.
Draw the angle bisector at the vertex angle and extend it down until it intersects the base of the isosceles triangle.
Now you have two smaller triangles, right and left sides of the original triangle.
We now prove the two smaller triangles are congruent. The two congruent sides of the main triangle are congruent corresponding sides of the two smaller triangles. The bisected angle becomes two congruent angles in the two smaller triangles. Finally, the angle bisector is congruent to itself and is a side of both smaller triangles. By SAS, the two smaller triangles are congruent. Then, the two segments in the base of the isosceles triangle are congruent by CPCTC. That makes the point of intersection of the angle bisector and the base of the isosceles triangle the midpoint of the base.
at a large airport, data were recorded for on emonth on how mayn baggage items were unloaded on each flight upon arrival as well as the time to deliver all the baggage items on the fligh tto the baggage claim area
Answers
The correct option is (B) The actual time required to deliver all the items to the baggage claim area based on the number of items unloaded will be very close to the time predicted by a least-squares model.
What is least-square model (regression line)?In order to find the line that is most suitable for a set of data, the least squares method is a type of mathematical regression analysis. It offers a visual representation of the relationship between both the data points.
Some characteristics of least square model are-
The correlation between a recognized independent variable but also an unknowable dependent variable is represented by each data point.By reducing the total of the offsets and residuals of spots from either the plotted curve, the least squares approach is a statistical technique for identifying the best estimate for a group of data points.In order to forecast the evolution of dependent variables, least squares is employed.The location of such line of best fit amongst some of the data points under study is explained generally by the least squares method.To know more about least square model/ regression line, here
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The complete question is-
At a large airport, data were recorded for one month on how many baggage items were unloaded from each flight upon arrival as well as the time required to deliver all the baggage items on the flight to the baggage claim area scatter plot of the two variables indicated a Strong; positive linear association between the variables_ Which of the following statements is a correct interpretation of the word ~strong in the description of the association?
(A) least-squares model predicts that the more baggage items that are unloaded from a flight; the greater the time required to deliver the items to the baggage claim area
(B) The actual time required to deliver all the items to the baggage claim area based on the number of items unloaded will be very close to the time predicted by a least-squares model .
(C) The time required to deliver an item to the baggage claim area is relatively constant; regardless of the number of baggage items unloaded from a flight,
(D) The variability in the time required to deliver all items to the baggage claim area is about the same for all flights, regardless of the number of items unloaded from flight
(E) The time required to unload baggage items from a flight is related to the time required to deliver the items to the baggage claim area.
Please help me find mBOC!
mZAOC = 96
mZBOC = 8x - 67
MZAOB = 9x - 75
Answers
\(\bf Step-by-step~explanation:\)
We are given that m∠AOC is 96º. One angle's expression is 8x - 67 and the other is 9x - 75. That means when we add both of these angles, they would equal to 96º.
\(\bf Step~1:\)
To solve for x: We set up our equation like this:
\(\bf(9x-75)+(8x-67)=96\)
Let's add the like terms together.
\(\bf9x+8x=17x\\-75-67=-142\)
\(\bf Step~2:\)
Our equation now:
\(\bf 17x-142=96\)
Now, we add 142 on both sides to get 17x on its own.
\(\bf17x-142(+142)=96(+142)\\17x=238\)
\(\bf Step~3:\)
Divide both sides by 17 to get our value for x.
\(\bf\frac{17x}{17} =x\\\\\frac{238}{17}= 14\\\\x=14\)
\(\bf Step~4:\)
Now that we have x's value, we plug it into the equation for m∠BOC.
\(\bf 8x-67\\8(14)-67\\112-67\\45\)
\(\large\boxed{\bf Our~final~answer: mBOC=45}\)
could use some help.
35−x=8
Two-Step Equations and Properties of Equality
Answers
Answer:x=27
Step-by-step explanation:
First rearrange the terms: x+35=8
Second subtract 35 from either side:
-x=-27
Third divide both sides of the equation by the same term:
-x/1=-27/1
Fifth simplify:
X=27
Hope this helps!
What is a parabola parent function?
Answers
The parent function of a parabola is y = x².
A function is said to be a parent function if it is expressed in the simplest form and satisfies the definition of a particular type of function.
The simplest function that satisfies the definition of a parabola is given by y = x². It is also called quadratic function.
Its graph passes through the origin (0,0) and lies in first and second quadrant.
One or more parabolas can be easily obtained by transforming the parent function of the parabola.
Therefore, the parent function of parabola is given by y = x².
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Maximum Marks: 5 Given the total cost function TC=100Q−Q 2
+0.3Q 3
Where Q= rate of output and TC= total cost, determine a) The marginal and average cost functions. (2 Marks) b) The rate of output that results in minimum average cost. ( 3 Marks)
Answers
a) To find the marginal cost, we need to find the derivative of the total cost function with respect to the rate of output (Q).
TC = 100Q - Q² + 0.3Q³
Marginal cost (MC) = dTC/dQ
= d/dQ(100Q - Q² + 0.3Q³)
= 100 - 2Q + 0.9Q²
To find the average cost, we need to divide the total cost by the rate of output (Q).
Average cost (AC) = TC/Q
= (100Q - Q² + 0.3Q³)/Q
= 100 - Q + 0.3Q²
b) To find the rate of output that results in minimum average cost, we need to find the derivative of the average cost function with respect to Q. Then, we set it equal to zero and solve for Q.
AC = 100 - Q + 0.3Q²
dAC/dQ = -1 + 0.6Q
= 0-1 + 0.6Q
= 00.6Q
= 1Q
= 1/0.6Q
≈ 1.67
Therefore, the rate of output that results in minimum average cost is approximately 1.67.
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A vet treats dogs (D), cats (C), birds (B), hamsters (H), and reptiles (R). A veterinary assistant randomly selects a patient’s file.
What is the sample space for this experiment?
Responses
S={D, B, H}
S equals left curly bracket D comma B comma H right curly bracket
S={D, C, B, H, R}
S equals left curly bracket D comma C comma B comma H comma R right curly bracket
S={C, B, H, R}
S equals C comma B comma H comma R right curly bracket
S={D}
Answers
Answer:
The sample space for the experiment of randomly selecting a patient's file from the given animals is:
S={D, C, B, H, R}
The sample space includes all the possible outcomes of the experiment, which in this case are the animal types that can be selected by the veterinary assistant. Since the assistant can randomly select a file for any of the five types of animals, the sample space consists of all the possible animal types, which are D (dogs), C (cats), B (birds), H (hamsters), and R (reptiles).
Step-by-step explanation:
is the sum of the integers x and y a prime number? (1)x is an even prime number. (2)y is a prime number between 10 and 20.
Answers
Based on the given information, we know that x must be 2 since it is the only even prime number. We also know that y must be either 11, 13, 17, or 19 since those are the only prime numbers between 10 and 20.
So, the sum of x and y can be 2 + 11 = 13, 2 + 13 = 15, 2 + 17 = 19, or 2 + 19 = 21.
Out of these four possible sums, only 13, 17, and 19 are prime numbers. Therefore, we can say that the sum of x and y may or may not be a prime number, depending on the specific values of x and y.
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Find the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) C a a = 4 b = 8 C = d = 0 = 30�
Answers
The missing values by solving the parallelogram are: a) 34.10; b) θ = 96.42° c) φ = 83.18°
What is a parallelogram?You should understand that a parallelogram is a flat shape with opposite sides parallel and equal in length.023 It is a quadrilateral with two pairs of parallel sides.
The missing side and angles of the parallelogram are given by:
a² = (c² + d²)/2 - b² = (42² + 38²)/2 - b² = 1163;
a = √1163 = 34.10;
b) By cosine law 42² = 21² + 34.10² - 2·21·34.10cosθ;
cosθ = (21² + 34.10² - 42²)/(2·21·34.10) = - 0.11185;
c) θ = 96.42°; φ = 180° - 96.42°
= 83.18°
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t the beginning of an experiment; scientist has 280 grams of radioactive goo. After 75 minutes; her sample has decayed to 17.5 grams What is the half-life ofthe goo in minutes? Preview Find formula for G(t). the amount of goo remaining at time t Previen How many grams of goo will remain after mnutes _ Previen You may enter the exact value Or round to decimal places
Answers
After 75 minutes, a sample of 280 grams of radioactive goo has decayed to 17.5 grams. The half-life of the radioactive is 18.75 minutes.
The problem can be solved using decay model. The formula of decay system is given by:
Nt = No . e^(-λ . t)
Where:
Nt = quantity at time t
No = initial quantity
λ = decay constant = ln(2) / T
T = half life
The above formula can be rearranged to:
T = t . ln(2) / [ln(No/Nt)]
Parameters given in th problem:
No = 280 grams
t = 75 minutes
Nt = 17.5 grams
Plug these parameters into the formula:
T = 75 . ln(2) / [ln(280/17.5)]
= 18.75 minutes
Hence, the half-life of the radioactive goo is 18.75 minutes.
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the family fine arts center charges $24 per adult and $12 per senior citizen for its performances. on a recent weekend evening when 483 people paid admission, the total receipts were $7548. how many who paid were senior citizens?
Answers
337 were senior citizens.
What is the system of equations?
A system of equations, also known as an equation system or a set of simultaneous equations, is a finite set of equations for which common solutions are sought.
Here, we
Let
x = the number of adult tickets sold
y = the number of senior tickets sold
483 people paid admission => a total of 483 tickets were sold and
x + y = 483
the total receipts were $7548
24x + 12y = 7548
by solving the system of equations
x + y = 483....(1)
24x + 12y = 7548....(2)
From equation (1), we get
x = 483-y....(3)
Now, we put the value of x in equation (2) and we get
24(483 - y) +12y = 7548
11592 - 24y + 12y = 7548
12y = 4044
y = 337
Now, we put the value of y in equation (1) and we get
x = 483 - 337
x = 146
Hence, 337 were senior citizens.
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-2 (2x + 5) SIMPLIFY
I get one answer but my calculator gives me another pls help!!
Answers
Answer:
−2⋅(2x+5)
Step-by-step explanation:
which number comes next in this series 5, 7, 11, 19, 35
Answers
Answer: 67
Step-by-step explanation:
We see a pattern where we multiply the number we added by previously by two.
For example, from 5 to 7, it is 2.
From 7 to 11, we add by 4.
From 11 to 19, we add by 8.
From 19 to 35, we add by 16.
This means the next number would be 32, adding 35 by 32 gives us 67,
passes through (10,2), perpendicular to y = 4x + 6
Answers
Step-by-step explanation:
When two lines are perpendicular, the product of their slope/gradient = -1. Another way of thinking of this is that they are negative-reciprocal of each other.
Let y = 4x + 6 be [a] & the perpendicular line [b]
since the slope of [a] = 4
then the slope (m) of [b] = - ¹/₄
Since we know the slope of [b], we can use the point-slope form (y - y₁) = m (x - x₁); where (x₁ , y₁) = (10 , 2) & m = - ¹/₄
∴ the equation of the perpendicular line : (y - 2) = - ¹/₄ (x - 10)
Needing some help Thanks!
Answers
Answer:
Correct answer is the second choice
Step-by-step explanation:
This is because Fredrick Douglas was aware of the inequalities and the large gap that many slaves suffered. With Fredrick Douglas suffering from these injustices similar to slaves during this time period, he maintained the sentiment that the United States at the time was a country that was greatly divided as there were many disparities present.
How can you represent and interpret data using a picture graph or a bar graph? Give an example and explain how you answer questions based on the graph.
Answers
Each bar's height corresponds to the value of the quantity it represents. For comparing numbers and data, bar graphs are excellent.
what is graph ?In mathematics, the word "graph" has (at least) two distinct meanings. The term "graph" in elementary mathematics refers to a diagram known as a function graph or "function graph." A graph is, in the language of mathematics, a set of points and lines that link a subset (potentially empty) of the points and lines. Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. Bar charts, line charts, histograms, and pie charts are the four types of fundamental statistical charts.
Each bar's height corresponds to the value of the quantity it represents. For comparing numbers and data, bar graphs are excellent. The x and y axes are the names of the vertical and horizontal axes in bar graphs, respectively. A bar graph can be used, for instance, to compare your classmates' heights.
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