Answer:
246 Square Feet
Step-by-step explanation:
The cubes are of side length 1ft , 2ft, 3ft , 4ft, and 5ft in that order.
If the side of each smaller cube is completely touching the side of the adjacent larger cube.
In the first and last cubes, 5 sides out of 6 are visible, so we use the formula [tex]5l^2[/tex] for their surface area.In the 2nd, 3rd and 4th cubes, only 4 sides out of 6 are visible, so we use the formula [tex]4l^2[/tex] for their surface area.Surface Area of the Solid [tex]= 5(l_1)^2+4(l_2)^2+4(l_3)^2+4(l_4)^2+5(l_5)^2, where \: l_1,l_2,l_3,l_4,l_5[/tex]
are the length of the cubes in that order
Surface Area of the Solid
[tex]= 5(1)^2+4(2)^2+4(3)^2+4(4)^2+5(5^2)\\=5+16+36+64+125\\=246 \:Square\: feet[/tex]
A pound of chocolate costs 6 dollars. Diane buys P pounds. Write an equation to represent the total cost c that Diane pays.
Answer:
[tex]C=6P[/tex]
Step-by-step explanation:
Because the cost (c) depends on the pounds (p), we have to multiple the weight by 6, because it is $6 per pound.
Answer:
Step-by-step explanation:
prob c
Theo bought 8 packs of pencils for $4 each and 3 packs of
erasers that were on sale for $2 off their regular price of $5
each. Which keys could be entered into the calculator to
determine the total amount he spent?
O C8*4+385
C8*4+3*3
C8*4+3-2*
C8*4+3* 2-
Answer:
8*4+3*3
Step-by-step explanation:
It can't be the last answer because he buys three packs of erasers for three dollars each. It can't be the third answer because you have to multiply to get the price. It can't be the first answer because it's three of the numbers given put together. So it has to be 8*4+3*3
Final answer:
The total amount Theo spent can be calculated on a calculator with the input: 8 × 4 + 3 × 3, which represents the cost of pencils plus the discounted cost of erasers.
Explanation:
To determine the total amount Theo spent, you need to calculate both the cost of the pencils and the cost of the erasers, taking into account the sale on erasers.
For pencils, Theo bought 8 packs at $4 each. For erasers, he bought 3 packs at a $2 discount from their regular price of $5 each, meaning each pack of erasers cost $5 - $2 = $3 per pack on sale.
The correct calculation on the calculator for the total amount spent would be the cost of pencils plus the cost of erasers: 8 packs × $4 per pack for pencils, plus 3 packs × $3 per pack for erasers on sale.
This can be entered into the calculator as 8 × 4 + 3 × 3.
in half an hour josh ran 3/4 a mile. how many miles would Josh run in 1 hour?
Answer:
1 1/2
Step-by-step explanation:
Btw you have gacha??? me too
-x+6is the same as -(x-6) how do I know? Pls help
HELP PLS
What is the approximate distance from Denver to Chicago? Use proportional relationships to solve the problem. Show your work.
Answer:
About 1000 miles
Step-by-step explanation:
What is 0.¯42 expressed as a fraction in simplest form?
Answer:
Part B (solution): For 0.42... (with the two repeating forever), we need to break up the decimal into the part that does not repeat and the part that repeats.
For the part that does not repeat, pretend that the repeating part is not there (so you have 0.4). Then think about place value. The non-repeating part of this decimal (0.4) is 4 tenths, so write that as a fraction: 4/10.
For the part that repeats, pretend the part that does not repeat is not there (so you have 0.2....). Use the rule of 9s, which tells you to put the repeating part (2) over a nine for every place value that is repeating. In this case there is only one repeating place value (again, 2), so we have 2/9. However, since we skipped a place value (the 4 in our given problem), we need to multiply that place value (in this case 1/10) by 2/9, which is 2/90. Finally, we need to add that to 4/10. Make sure your answer is simplified. Click HERE for help on Question 1.
Part C (solution): For 0.42... (with the four AND two repeating forever), use the rule of 9s. The rule of 9s tells you to put the repeating part (42) over a nine for every place value that is repeating. In this case there is two repeating place values, so we have 42/99. Make sure your answer is simplified. Click HERE for help on Question 1.
Parts A-C (work shown): Please make sure you include all of your work. Click HERE for help on Question 1.
Question 2
Part A (explanation): Please explain what this student did wrong. What was his error? It might be helpful to estimate √75 the way you know how. That should help you see what this student did wrong. Click HERE for help on Question 2.
Part B (solution): Estimate the value of √75 to the nearest tenth. 75 is between the perfect squares 64 and 81. So √75 is between 8 and 9. The distance from 64 to 75 is 11. The distance from 64 to 81 is 17. The ratio is 11/17, or about .647. So, √75 is about .647 bigger than 8. Click HERE for help on Question 2.
Question 3
Part A - (work for π): Approximate the value of π to the nearest tenth. Click HERE for help on Question 3.
Part A - (work for √3): Approximate the value of √3 to the nearest tenth. 3 is between the perfect squares 1 and 4. So √3 is between 1 and 2. The distance from 1 to 3 is 2. The distance from 1 to 4 is 3. The ratio is 2/3, or about .7. So, √3 is about .7 bigger than 1. Click HERE for help on Question 3.
Part A - (work for √5): Approximate the value of √5 to the nearest tenth. 5 is between the perfect squares 4 and 9. So √5 is between 2 and 3. The distance from 4 to 5 is 1. The distance from 4 to 9 is 5. The ratio is 1/5, or .2. So, √5 is about .2 bigger than 2. Click HERE for help on Question 3.
Part A - (work for 2√5): Approximate the value of 2√5 to the nearest tenth. 5 is between the perfect squares 4 and 9. So √5 is between 2 and 3. The distance from 4 to 5 is 1. The distance from 4 to 9 is 5. The ratio is 1/5, or .2. So, √5 is about .2 bigger than 2. Now multiply that value by 2. Click HERE for help on Question 3.
The fraction representation of 0.¯42 in simplest form is 14/33.
To express the repeating decimal 0.¯42 as a fraction in simplest form, we can use a mathematical technique.
Let's represent the repeating decimal as x = 0.¯42.
To remove the decimal part, we can multiply both sides of the equation by 100 (to move the decimal point two places to the right):
100x = 42.¯42.
Next, we subtract the original equation from the one multiplied by 100 to eliminate the repeating part:
100x - x = 42.¯42 - 0.¯42.
Simplifying both sides gives:
99x = 42.
Now, we can divide both sides of the equation by 99 to isolate x:
x = 42 / 99.
To simplify the fraction 42/99, we can find the greatest common divisor (GCD) of 42 and 99 and divide both the numerator and the denominator by it.
The GCD of 42 and 99 is 3:
42 = 3 x 14,
99 = 3 x 33.
Dividing both sides by 3 gives:
42 / 99 = (3 x 14) / (3 x 33) = 14 / 33.
Therefore, the fraction representation of 0.¯42 in simplest form is 14/33.
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how many lines of symmetry does a star have?
Answer:
I believe it is 5 lines
Step-by-step explanation:
Answer:
5 (If it is a 5 pointed star)
Step-by-step explanation:
Just count
The ratio of petunias to geraniums in the greenhouse was 15 to 2. The combined numbernof petunias and geraniums was 1020.
ILL GIVE YOU BRAINLIEST!! How many geraniums were in the greenhouse?
A. 30
B. 510
C. 68
D. 2040
E. 120
Answer:
E. 120
Step-by-step explanation:
Let's say the number of total flowers is (15+2)x
That means the number of geraniums is 2x.
That also means that 1020 = 17x, which makes x = 60
Because 2x = geraniums and x = 60, the number of geraniums is 120
3 packets of French fries, 2 cheeseburgers, and one drink cost $10.95. 1 packet of French fries, 2 cheeseburgers, and 3 drinks cost $11.25. Find the price of 1 packet of French fries, 1 cheeseburger, and one drink?
Answer:
The price of 1 packet of French fries, 1 cheeseburger, and one drink cost $5.55
Step-by-step explanation:
Let
x ----> the price of 1 packet of French fries
y ---> the price of 1 cheeseburger
z ---> the price of one drink
we know that
[tex]3x+2y+z=10.95[/tex] ----> equation A
[tex]x+2y+3z=11.25[/tex] ---> equation B
Adds equation A and equation B
[tex]3x+2y+z=10.95\\x+2y+3z=11.25\\------------\\3x+x+2y+2y+z+3z=10.95+11.25\\4x+4y+4z=22.2[/tex]
Divide both sides of the equation by 4
[tex]x+y+z=5.55[/tex] ----> equation C
The equation C means ----> The price of 1 packet of French fries, 1 cheeseburger, and one drink cost $5.55
Find the area of XYZ by following these steps
1. Press Continue to circumscribe a rectangle around the triangle
Answer:48
Step-by-step explanation:did the questions
The area of the given rectangle is 48 square units.
What is Area?The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area. The area of a plane figure is the space enclosed by its boundary. The number of unit squares that cover the surface of a closed form is the figure's area.
We have the graph from which we can write
width of rectangle = 8 unit
Length of rectangle= 6 unit
So, the area of rectangle
= lw
= 8 x 6
= 48 unit²
Thus, the area of the given rectangle is 48 square units.
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"Your question is incomplete, probably the complete question/missing part is:"
Find the area of AXYZ by following these steps.
1. Press Continue to circumscribe a rectangle around the triangle
2. Find the area of the rectangle. Area = 48 units²
3. Find the area of A1. Area = units²
The table lists the number of male and female students at Lakeside High school.
What is the probability of selecting a female student?
A) 161/324
B) 1
C) 161/163
D) 1/2
Answer:
C) 161/163
Step-by-step explanation:
First, you add up all the students for both genders.
Female- 193+ 214 +197+ 201 = 805
Male- 216+ 207+ 198 + 194 = 815
That gives you a fraction on 805/815 which you simplify to 161/163
So your answer would be C, 161/163 :)
Answer:
A. [tex]\frac{161}{324}[/tex]
Step-by-step explanation:
I got it right on my quiz!!
Vera ordered a soup, salad, and sandwich to share with her friends. The probabilities of each item being ready first are as follows:P(Soup ready first)=
5
1
start text, P, left parenthesis, S, o, u, p, space, r, e, a, d, y, space, f, i, r, s, t, end text, right parenthesis, equals, start fraction, 1, divided by, 5, end fraction
P(Salad ready first)=0.45\text{P(Salad ready first}) = 0.45
P(Salad ready first)=0.45
start text, P, left parenthesis, S, a, l, a, d, space, r, e, a, d, y, space, f, i, r, s, t, end text, right parenthesis, equals, 0, point, 45
P(Sandwich ready first)=35%\text{P(Sandwich ready first}) = 35\%
P(Sandwich ready first)=35%
start text, P, left parenthesis, S, a, n, d, w, i, c, h, space, r, e, a, d, y, space, f, i, r, s, t, end text, right parenthesis, equals, 35, percent
Put the following events in order from least to most likely.
Salad ready first\text{Salad ready first
its
Soup ready first
Sandwich ready first
Salad ready first
Answer:
Soup ready first
Sandwich ready first
Salad ready first
Step-by-step explanation:
By accident, 6 burned out bulbs have additionally been mixed in with 26 good ones. Ken is replacing
old bulbs in his house. If he selects two bulbs at random from the box of 32, what is the probability
they both work?
The probability of randomly selecting two good bulbs is equal to 0.665.
How to find the probability?
So, we have a set of 32 bulbs, such that 26 are good and 6 are burned.
The probability of randomly selecting one good bulb is equal to the quotient between the number of good bulbs and the total number of bulbs.
It gives:
P = 26/32
Now, for the next bulb, the probability is computed in the same way, but now there are 25 good bulbs and 31 in total, so the probability is:
P' = 25/31
The joint probability is given by the product between the two individual probabilities:
p = (26/32)*(25/31) = 0.655
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The value of the digit 5 in 24,513 is how many times the value of the 5 in 357?
There are 4 jacks and 13 clubs in a standard, 52-card deck of playing cards. What is the probability that a card picked at random from a standard deck of playing cards is a club or a jack?
Answer:
16/52, or 4/13.
Step-by-step explanation:
First, since we know that the question is asking for the probability of a club or a jack, we know that we have to add the two probabilities. The first probability is that of picking a club, which is 13/52. The probability of picking a jack (be sure not to overlap; don't double count the jack of clubs) is 3/52. Adding these two gives us 13/52+3/52=16/52, which simplifies to 4/13.
Help me Select the correct answer from each drop-down menu.
The Sawyer and Ruiz families each bought a laptop computer at the same time.
The resale values, in dollars, of the laptops are modeled by the given functions, where x is the nu
laptop.
Sawyer Family's Laptop
Ruiz Family's Laptop
g(x)
640
480
A(x) = 620(0.85)*
360
The answer is in the picture below just did the test!
The correct answer of Resale value is :
The Ruiz family's laptop has the greater initial resale value.
The Ruiz family's laptop will have a higher resale value than the Sawyer family's laptop after 4 years.
The resale value of the Sawyer family's laptop decreases at a faster average rate than the resale value of the Ruiz family's laptop.
Based on the table, the Ruiz family's laptop has the greater initial resale value. They bought it for $640, while the Sawyer family bought their laptop for $620.
To compare the resale values of the two laptops after 4 years, we can evaluate the functions g(4) and A(4).
[tex]g(4) = 640 \times0.85^4 = 360.78[/tex]
[tex]A(4) = 620 \times 0.85^4 = 343.65[/tex]
Therefore, the Ruiz family's laptop will have a higher resale value than the Sawyer family's laptop after 4 years.
To compare the average rates of decrease of the resale values of the two laptops, we can calculate the following:
Average rate of decrease of the Ruiz family's laptop: (640 - 360.78) / 4 = 70.63
Average rate of decrease of the Sawyer family's laptop: (620 - 343.65) / 4 = 68.35
Conclusion:
The Ruiz family's laptop has the greater initial resale value.
The Ruiz family's laptop will have a higher resale value than the Sawyer family's laptop after 4 years.
The resale value of the Sawyer family's laptop decreases at a faster average rate than the resale value of the Ruiz family's laptop.
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A teacher needs to find out how many seventh-grade students will be going on a field trip. Which best describes the population that the teacher should survey?
A) the parents of all the students in the school
B) the parents of the seventh-grade students
C) each teacher in the school
D) each student in the school
Answer:
B
Step-by-step explanation:
The parents of the seventh-grade students, best describe the population that the teacher should survey. Option B is correct.
What is a survey?A survey in human subjects research is a set of questions designed to elicit specific information from a specific group of people.
As mentioned in the question, the teacher needs to find out how many seventh-grade students will be going on a field trip. For this teacher must ask to the students of seventh grade as well as survey the parents of the seventh-grade students.
Thus, the parents of the seventh-grade students, best describe the population that the teacher should survey. Option B is correct.
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Suppose a fair 6-sided die is tossed five times. What is the probability that we see at least one three in the five tosses?
a. 0.5981
b.0.8300
C. 0.1667
d. 0.4019
Answer:
C. 0.1667
Step-by-step explanation:
1/6 +0/6 + -1/6
The closest answer is C. 0.1667
Based on 2nd throw of dice shows zero then 0.1667 of the answer is shown on the 3rd throw in decimal form of -1/6
Solve the following:
5,138 ÷ 302
Answer:
17.0132
Step-by-step explanation:
What is 5(x+20) = 7x+30?
Answer: 35
Step-by-step explanation:
Simplifying
5(x + 20) = 7x + 30
Reorder the terms:
5(20 + x) = 7x + 30
(20 * 5 + x * 5) = 7x + 30
(100 + 5x) = 7x + 30
Reorder the terms:
100 + 5x = 30 + 7x
Solving
100 + 5x = 30 + 7x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-7x' to each side of the equation.
100 + 5x + -7x = 30 + 7x + -7x
Combine like terms: 5x + -7x = -2x
100 + -2x = 30 + 7x + -7x
Combine like terms: 7x + -7x = 0
100 + -2x = 30 + 0
100 + -2x = 30
Add '-100' to each side of the equation.
100 + -100 + -2x = 30 + -100
Combine like terms: 100 + -100 = 0
0 + -2x = 30 + -100
-2x = 30 + -100
Combine like terms: 30 + -100 = -70
-2x = -70
Divide each side by '-2'.
x = 35
Simplifying
x = 35
Answer:
[tex]x=35[/tex]
Step-by-step explanation:
Step 1: Distribute
[tex]5(x + 20) = 7x + 30[/tex]
[tex](5 * x) + (5 * 20) = 7x + 30[/tex]
[tex]5x + 100 = 7x + 30[/tex]
Step 2: Subtract 5x from both sides
[tex]5x + 100 - 5x = 7x + 30 - 5x[/tex]
[tex]100 = 2x + 30[/tex]
Step 3: Subtract 30 from both sides
[tex]100 - 30 = 2x + 30 - 30[/tex]
[tex]70 = 2x[/tex]
Step 4: Divide both sides by 2
[tex]70 / 2 = 2x / 2[/tex]
[tex]35 = x[/tex]
Answer: [tex]x = 35[/tex]
x^2-5x-36/x-2 ÷(x^2-18x+81)
what is the mean? 0.8, 1, 2.7, 2.8, 3.1, 13.3
Answer:
3.95
Step-by-step explanation:
the mean is
all numbers added up divided by how many numbers
.8+1+2.7+2.8+3.1+13.3=23.7
there are 6 numbers
23.7/6=
3.95
Answer: 3.95
Step-by-step explanation:
Got to add all them up 0.8+1+2.7+2.8+3.1+13.3=23.7 then divide that by 6 cuz that's how many numbers there are then it gives you 3.95
An international cake competition attracted 50 bakers from around the world. The graph below shows the relationship between the amount of sugar in the cakes (in grams per 100 grams of cake) and the scores the cakes received.
What is the best description of this relationship?
Choose 1 answer:
A
Positive linear association
B
Negative linear association
C
Nonlinear association
D
No association
Positive linear association shows the relationship between the amount of sugar in the cakes (in grams per 100 grams of cake) and the scores the cakes received.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given,
An international cake competition attracted 50 bakers from around the world.
We have to tell relationship between the amount of sugar in the cakes (in grams per 100 grams of cake) and the scores the cakes received.
Scores were highest for cakes that had between 15 and 25 grams of sugar per 100 grams of cake.
Positive linear association shows the relationship between the amount of sugar in the cakes (in grams per 100 grams of cake) and the scores the cakes received.
Hence Positive linear association shows the relationship between the amount of sugar in the cakes (in grams per 100 grams of cake) and the scores the cakes received.
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how does total revenue differ from marginal revenue
NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, in terms of time is given by h=−4.9t2+244t+269.
how high is the rocket after 9 seconds
how high was the rocket when it initially launched
Answer: The height of the rocket after 9 seconds is 2068.1 meters.
The height of the rocket when it initially launched is 269 meters.
Step-by-step explanation:
Given, NASA launches a rocket at [tex]t=0[/tex] seconds.
Its height, in meters above sea-level, in terms of time is given by [tex]h=-4.9t^2+244t+269.[/tex]
To find, the height of the rocket after 9 seconds put t=9, we get
[tex]h=-4.9(9)^2+244(9)+269\\\\=-4.9(81)+2196+269\\\\=-396.9+2465\\\\=2068.1[/tex]
Hence, the height of the rocket after 9 seconds is 2068.1 meters.
To find, the height of the rocket when it initially launched put t=0, we get
[tex]h=-4.9(0)^2+244(0)+269\\\\=0+0+269\\\\=269[/tex]
Hence, the height of the rocket when it initially launched is 269 meters.
Lauren mowed 3 lawns in 15 hours. What was her rate of mowing in hours per lawn?Lauren mowed 3 lawns in 15 hours. What was her rate of mowing in hours per lawn?
Answer:
5 hours per lawn
Step-by-step explanation:
15 hours divided by 3 lawns brings you to 5 hours per lawn.
The rate at which Lauren mows lawns is 5 hours per lawn, which means on average, it takes her 5 hours to mow one lawn.
Explanation:The question is asking us to find out how long, on average, it takes Lauren to mow one lawn given that she can mow 3 lawns in 15 hours. This is a classic problem of rate, specifically a rate of work. The formula we use for rate is simply: Rate = Total Work / Total Time. Here, the total work would be the 3 lawns that she mowed, and the total time would be the 15 hours. So, we divide 15 (total hours) by 3 (total lawns) to get the rate of mowing:
Rate = 15 / 3 = 5 hours per lawn.
This means that, on average, it takes Lauren 5 hours to mow a single lawn.
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Select the possible dimensions of a rectangular prism with volume of 72 cubic meters . HInt: V = B x h (Area of base times the height) points A. 2 m x 6 m x 7 m B.3 m x 4 m x 6 m C.3 m x 8 m x 4 m D.9 m x 8 m x 1 m E.12 m x 2 m x 3 m (more than one posible answer)
Final answer:
The possible dimensions for a rectangular prism with a volume of 72 cubic meters are options B (3 m x 4 m x 6 m), D (9 m x 8 m x 1 m), and E (12 m x 2 m x 3 m), as their product of dimensions equals 72 cubic meters.
Explanation:
The question presents a schoolwork problem related to finding the possible dimensions of a rectangular prism with a given volume. According to the formula for volume, V = B x h, where V stands for volume, B is the area of the base, and h is the height. For a prism to have a volume of 72 cubic meters, the product of its dimensions (length x width x height) must equal 72.
For option A (2 m x 6 m x 7 m), the volume is 2 x 6 x 7 = 84 cubic meters, which is not equal to 72.
For option B (3 m x 4 m x 6 m), the volume is 3 x 4 x 6 = 72 cubic meters, which is correct.
For option C (3 m x 8 m x 4 m), the volume is 3 x 8 x 4 = 96 cubic meters, which is not equal to 72.
For option D (9 m x 8 m x 1 m), the volume is 9 x 8 x 1 = 72 cubic meters, which is also correct.
For option E (12 m x 2 m x 3 m), the volume is 12 x 2 x 3 = 72 cubic meters, which is another correct possibility.
Therefore, the possible dimensions for the rectangular prism with a volume of 72 cubic meters are represented by options B, D, and E.
Which interval shows the greatest number of students?
Based on the histogram, an interval that shows the greatest number of students is: A. 0 - 1.99.
What is a histogram?In Mathematics and Statistics, a histogram refers to a type of graph that is used for the graphical representation of a data set into user-specified ranges, especially through the use of rectangular bars.
Based on the information provided in the histogram, a frequency table can be that models the data set can be completed as follows;
Class interval (hours) Number of students
0 - 1.99 7
2 - 3.99 6
4 - 5.99 3
6 - 7.99 4
8 - 9.99 1
By critically observing the frequency table above, we can logically deduce that the class interval with the highest frequency is 0 - 1.99 with a value of 7.
In conclusion, 7 students study between 0 and 2 hours per week.
Complete Question:
A survey of sixth-grader students recorded how many hours students studied each week. The histogram below displays the collected information.
Which interval shows the greatest number of students?
0 - 1.99
2 - 3.99
4 - 5.99
6 - 7.99
Area of rectangle with a length of 3 2/3m and a height of 1 1/4m.
Answer:
4.5834m^2
Step-by-step explanation:
You do (length)*(width) which is (3 3/2m)*(1 1/4m) = 4.5834m^2 This is rounded because it was 4.5833333333 repeating.
Answer: the answer is 4 7/12m
Step-by-step explanation: Multiply both 3 2/3 and 1 1/4 to get 4 7/12. i know it isn't an explanation.
how to compare box plots.
Box plots, or box-and-whisker plots, show data distribution through five main points: minimum, Q1, median, Q3, and maximum. A wider box indicates greater variability within the middle 50% of the data. To compare box plots, assess the spreads, medians, and potential outliers.
Explanation:A box plot, also known as a box-and-whisker plot, is a graphical representation of a data set that shows the distribution through five main data points: minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value.
To construct a box plot, you typically start with a number line that has been properly scaled. Using a ruler for this purpose ensures accuracy.
The box in a box plot represents the middle 50 percent of the data, spanning from Q1 to Q3.
The 'whiskers' of the plot stretch from the box to the minimum and maximum values, indicating the entire range of the dataset.
Comparing the spread of the middle 50 percent of the data involves looking at the width of the box: a wider box suggests a greater spread, meaning the data is more varied within the interquartile range (IQR).
If you are using a graphing calculator, you can enter the data into a list and then select the box plot function to graphically display the data.
When comparing two or more box plots, look for differences in their central values (medians), spreads (IQRs), and potential outliers (which lie beyond 1.5 times the IQR from the quartiles).