Shawn walks 5 miles in a southeast direction from his house. He stops for lunch then walks 6 miles in a northeast direction from his lunch spot. What is the shortest distance Shawn can walk to return home.
Answers
Shortest distance to reach home = 7.81 miles
What is Pythagoras theorem?Pythagoras theorem states that "In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides".
Given, Shawn walks 5miles in southeast from his house.
After having lunch he walks 6 miles north east.
Angle between both directions is 90°.
By the figure
AB = 5miles
BC = 6 miles
Shortest distance to return home is AC
By Pythagoras theorem
AC² = AB² + BC²
= 5² + 6²
AC² = 25 + 36
AC² = 61
AC = √61
AC = 7.81 miles.
Hence, 7.81 miles is the shortest distance to reach home.
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Related Questions
How to convert vertex form to standard form. Y=4(x-2)^2-1
Answers
Answer:
y = 4x² - 16x + 15
Step-by-step explanation:
The standard form of a parabola is y = ax² + bx + c
To convert y = 4(x- 2)² -1
expand (x - 2)²:x² - 4x + 4 using the identity (x - a)² = x² -2ax + a²Multiply 4(x - 2)²
4(x² - 4x + 4) = 4x² - 16x + 16Finally,
y = 4(x- 2)² -1 = 4x² - 16x + 16 - 1
y = 4x² - 16x + 15
in exercises 1 and 2 rewrite the expression in rational exponent form
Answers
Rewrite expression in rational exponent form
[tex]a) \: \: \: \: \sqrt[5]{ (- 53) ^{4} } \\ b) \: \: \: \: \: \: \sqrt[4]{(110) {}^{7} } [/tex]
the rational exponent form :
a)
[tex] { - 53}^{ \frac{4}{5} } [/tex]
b)
[tex]110 { }^{ \frac{7}{4} } [/tex]
About Exponential numberExponential numbers are a form of mathematical abbreviation that allow us to write complex mathematical expressions more succinctly. An exponential number is a number that is repeatedly multiplied by itself.
Exponential is written with numbers and letters to the right of certain mathematical expressions called bases. While exponential numbers are often also called powers. Properties of exponential numbers
Exponential numbers have their own special properties as follows:
a¹ =a mathematical expression with an exponential of 1 or to the power of one, the result is always a mathematical expression itself. Example: 2¹ = 2, 67¹=67, and 700¹=700. aº=1 , when the exponent is zero, then regardless of the number, the expression will always equal one. Example: 2º=1 In addition to one and zero exponentials which are often referred to as powers of one and powers of zero, the following are the properties of exponentials in multiplication, division, multiple powers, as well as exponential fractions:Learn more about exponent at
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Use prime factorization to find greatest common factor
of the moninomial
18xy, 12x
Answers
Answer:
6x
Step-by-step explanation:
Since 18xy,12x18xy,12x contains both numbers and variables, there are two steps to find the GCF (HCF). Find GCF for the numericpart, then find GCF for the variable part.Steps to find the GCF for 18xy,12x18xy,12x:1. Find the GCF for the numerical part 18,1218,122. Find the GCF for the variable part x1,y1,x1x1,y1,x13. Multiply the values togetherFind the common factors for the numerical part:18,1218,12The factors for 1818 are 1,2,3,6,9,181,2,3,6,9,18.Tap for more steps...1,2,3,6,9,181,2,3,6,9,18The factors for 1212 are 1,2,3,4,6,121,2,3,4,6,12.Tap for more steps...1,2,3,4,6,121,2,3,4,6,12List all the factors for 18,1218,12 to find the common factors.1818: 1,2,3,6,9,181,2,3,6,9,181212: 1,2,3,4,6,121,2,3,4,6,12The common factors for 18,1218,12 are 1,2,3,61,2,3,6.1,2,3,61,2,3,6The GCF for the numerical part is 66.GCFNumerical=6GCFNumerical=6Next, find the common factors for the variable part:x,y,xThe factor for x1x1 is xx itself.xxThe factor for y1y1 is yy itself.yyThe factor for x1x1 is xx itself.xxList all the factors for x1,y1,x1x1,y1,x1 to find the common factors.x1=xx1=xy1=yy1=yx1=xx1=xThe common factor for the variables x1,y1,x1x1,y1,x1 is xx.xxThe GCF for the variable part is xx.GCFVariable=xGCFVariable=xMultiply the GCF of the numerical part 66 and the GCF of the variable part xx.6x
a(n) outcome (not an event) of flipping a coin is heads. to determine if a probability distribution is valid, make sure that all probabilities are between 0% and 100% and the sum of all is 100%. the ratio of the ways to succeed to all possible ways that something can occur is also known as probability . to find out how many ways a multi-step process can be completed, use the .
Answers
This statement is a description of basic concepts in probability theory.
An outcome of flipping a coin is heads, which can be assigned a probability of 0% or 100% depending on whether the coin lands heads or tails. In general, probabilities must be between 0% and 100% to ensure that a probability distribution is valid. The sum of all probabilities for all possible outcomes must also add up to 100%.
The ratio of the ways to succeed to all possible ways that something can occur is referred to as the probability of the event. This is the fundamental definition of probability.
Finally, to find out how many ways a multi-step process can be completed, you can use the concept of combinations or permutations. These are mathematical concepts used to count the number of possible arrangements or selections of items, given a certain set of conditions.
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Whats 4/9 dived 8/15 a fraction from simplest form
Answers
Answer: 5/6
Step-by-step explanation:
(4/9)/(8/5)=5/6
In March, Stinson Company completes its only two jobs in process, Jobs 10 and 11. Job 10 cost $20,000 and Job 11 $30,000. On
March 31, Job 10 is sold.
Record the completion of the two jobs and the sale of Job 10. (Enter negative amounts using either a negative sign preceding the number e.g.
Answers
If in March, Stinson Company completes its only two jobs in process, Jobs 10 and 11. The entry is Dr Finished goods inventory $50,000,Cr Work in process inventory $50,000.
What is journal entry?Journal entry is used by companies to record their business transactions.
Preparation of the journal entries for the completion of the two jobs and the sale of Job 10
Mar. 31
Dr Finished goods inventory $50,000
(20,000+30,00)
Cr Work in process inventory $50,000
( To record the completion of the two jobs)
Mar. 31
Dr Cash $35,000
Cr Sales revenue $35,000
(To record the sale job 10)
Mar. 31
Dr Cost of goods sold $30,000
Cr Finished goods inventory $30,000
(To record the cost of the job sold)
Therefore the entry is Dr Finished goods inventory $50,000,Cr Work in process inventory $50,000.
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The complete question is:
In March, Stinson Company completes Jobs 10 and 11. Job 10 cost $20,000 and Job 11 $30,000. On March 31, Job 10 is sold to the customer for $35,000 in cash.Journalize the entries for the completion of the two jobs and the sale of Job 10.Date Account Titles and Explanation Debit CreditMar. 31 31 31
a school is organizing a weekend trip to a nature preserve. for each student, there is a $50 charge, which covers food and lodging. there is also a $25 charge per student for the bus. the school must also pay a $15 cleaning fee for the bus. if the total cost of the weekend is $3,765, how many students will be going on the trip?
Answers
The total number of students going for the weekend trip as per the given total cost and other charges is equal to 50.
Let us consider 'n' be the number of students going for trip.
Per student charge for food and lodging = $50
Total food and lodging charges = $50n
Bus charges per student = $25
Total bus charges = $25n
Bus cleaning fees = $15
Total cost for the trip = $3,765
Equation formed for the above condition is:
$ (50n + 25n + 15 ) = $3,765
⇒ $ ( 75n + 15 ) = $3,765
⇒ 75n = 3,765 - 15
⇒ n = 3,750/ 75
⇒ n = 50
Therefore, there are 50 students going on the weekend trip.
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what is the probability that if 8 letters are typed, no letters are repeated? the probability that no letters are repeated is
Answers
The probability that no letters are repeated is 0.4121.
Divide the total number of outcomes by the entire number of different ways an event could happen to arrive at the probability. There are differences between probability and odds. The possibility of an event happening divided by the likelihood that it won't happen yields the odds. Probability is a metric used to assess the likelihood that a specific event will occur. The likelihood that the coin will land with the heads side up is measured using the probability concept when we toss it in the air. Here is an example of how probability is used in everyday life that you probably already know about. Prior to a major outing, we always consult the weather prediction.
So, the probability
Given, Number of letters=8
N[tex]=26*25*24*23*22*21*20*19[/tex]
P[tex]=\frac{25}{26}*\frac{24}{26}*\frac{23}{26}*\frac{22}{26}*\frac{21}{26}*\frac{20}{26}\\=0.96*0.92*0.88*0.85*0.81*0.77\\=0.4121[/tex]
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in the 1908 19081908 olympic games, the olympic marathon was lengthened from 40 4040 kilometers to approximately 42 4242 kilometers. of the following, which is closest to the increase in the distance of the olympic marathon, in miles? ( 1 (1(, 1 mile is approximately 1.6 1.61, point, 6 kilometers. ) )
Answers
The closest answer to the increase in the distance of the Olympic marathon is 1.50 miles. Hence the correct answer is option C.
In order to find the increase in the distance of the Olympic marathon, we will find the difference between the old distance (40 km) and the new distance (42 km) and then convert it to miles.
40 km - 42 km = -2 km
Converting -2 km to miles, we get:
-2 km x 1.6 miles/km = -3.2 miles
However, since the marathon was lengthened, the actual increase in the distance is:
-3.2 miles = 3.2 miles
Rounding to the nearest 0.25 miles, we get,
3.2 miles = 3.25 miles ≈ 3.25 miles
So the closest answer to the increase in the distance of the Olympic marathon is 1.50 miles.
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The complete question is -
In the 1908 Olympic Games, the Olympic marathon was lengthened from 40 kilometers to approximately 42 kilometers. Of the following, which is closest to the increase in the distance of the Olympic marathon, in miles? (1 mile is approximately 1.6 kilometers.)
A) 1.00
B) 1.25
C) 1.50
D) 1.75
11. c = 13 squared, a = 6.6 squared, what is b squared
Answers
The value of b² is 125.44 units since b equals 11.2 units when c equals 13 units and an equals 6.6 units.
What is Pythagoras theorem?The Pythagorean theorem is a mathematical theorem that asserts that the square of the length of the hypotenuse (the side opposite the right angle) in a right-angled triangle is equal to the sum of the squares of the other two sides. It is mathematically stated as c2 = a2 + b2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Here,
c=13²
a=6.6²
a²+b²=c²
b=√(c²-a²)
=√(13²-6.6²)
b=11.2 units
b²=125.44 units
The value of b² is 125.44 units as b is equal to 11.2 units when c is 13 units and a is 6.6 units.
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Ted is designing a miniature railroad station layout as shown below. The missing portions of the track represent the arcs of two congruent circles. Each circle has a radius of 10 inches. The central angles of these sectors are 75º and 85º.How many inches of curved track will Ted need to complete the missing part of his model station layout if he rounds the length to the nearest inch?
Answers
Ted needs 47 + 53 = 100 inches of curved track to complete the missing parts of his model station layout.
How do we get the value?First, we need to find the length of each arc. To do this, we'll use the formula:
arc length = circumference * central angle / 360
The circumference of a circle with radius 10 inches is 2 * pi * 10 = 20 * pi inches.
So, for the 75º sector:
arc length = 20 * pi * 75 / 360 = 15 * pi inches
And for the 85º sector:
arc length = 20 * pi * 85 / 360 = 17 * pi inches
Rounding pi to 3.14, we get:
arc length = 15 * 3.14 = 47.1 inches (rounded to 47 inches)
arc length = 17 * 3.14 = 53.4 inches (rounded to 53 inches)
So, Ted needs 47 + 53 = 100 inches of curved track to complete the missing parts of his model station layout.
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Given the functions f(x) = 3(x-4) and g(x) = 2(x - 3), for what values of x is f(x) > g(x)? Use the
properties of inequality and other properties to justify your solution.
Answers
The values of 'x' for which f(x) > g(x) is when x > 6.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Are two functions f(x) = 3(x - 4) and g(x) = 2(x - 3).
The values of 'x' for which f(x) > g(x) is 3(x - 4) > 2(x - 3).
3x - 12 > 2x - 6.
3x - 2x > 12 - 6.
x > 6.
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Which of the following is NOT a solution to the system of inequalities in the given graph?
A. (-2, -4)
B. (2, 0)
C. (0, 0)
D. (1, 1)
Answers
Answer:
I think B
Step-by-step explanation:
sorry if I said wrong
A spinner with 12 equally sized slices has 5 blue slices and 7 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a red slice? Write your answer as a fraction in simplest form.
Answers
on a map, 2 cm represents 68 miles. how many miles away are two cities that are 7 cm apart on the map
Answers
Answer:
238 miles
Step-by-step explanation:
2cm=68 miles
2cm÷2=68 miles÷2
1cm = 34 miles
7cm x 34 miles
=238 miles
,we have two proportional values
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.
if a confidence interval is given from 8.56 to 10.19 and the mean is known to be 9.375, what is the maximum error?
Answers
The maximum error of the given confidence interval is 0.815, meaning that the true mean is likely to be within 0.815 of the known mean of 9.375.
Maximum Error = (Upper Limit - Lower Limit) / 2
In this case, we have a confidence interval from 8.56 to 10.19 and the mean is known to be 9.375. To calculate the maximum error, we first need to subtract the lower limit (8.56) from the upper limit (10.19), which gives us a difference of 1.63. We then divide this number by 2, which gives us a maximum error of 0.815. This means that the maximum error of the given confidence interval is 0.815. This means that the true mean is likely to be within 0.815 of the known mean of 9.375.
The maximum error of the given confidence interval is 0.815, meaning that the true mean is likely to be within 0.815 of the known mean of 9.375.
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Members of the drama club plan to present its annual spring musical. They have $1,262.50 left from fundraising, but they estimate that the entire production will cost $1,600.00
Answers
a local bank branch employs three tellers who can each help a customer on average in 6 minutes, with a standard deviation of 3 minutes. on average, 24 customers arrive at this bank per hour (in a random fashion). how long would customers have to wait if we do pool the employees? that is, we make one line to lead to all three servers. group of answer choices
Answers
Customers have to wait for d) approximately 12 minutes if we do pool the employees.
This can be found by calculating the average waiting time per customer, which is the average service time divided by the average number of customers.
In this case, the average service time is 6 minutes (with a standard deviation of 3 minutes) and the average number of customers is 24. So, the average waiting time per customer is 6/24 = 0.25 hours = 15 minutes.
To ensure that customers do not have to wait any longer than necessary, it is best to have three separate lines for the three tellers. This way, customers are served in the order they arrive, rather than having to wait for one teller to serve all the customers.
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Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3≤x≤5.
Answers
The average rate of change of function in the interval 3 ≤ x ≤ 5 is → Δr = (b - a)/2
What is a function? Define its domain and range?An function in mathematics defines a relationship between one variable (the independent variable {x}) and another variable (the dependent variable {y}). Example → y = f{x} = ax + b.Domain represents the set of values along the {x} - axis or the possible values of {x} for which f{x} exists.Range represents the set of values along the {y} - axis or the possible existing values of f{x} for a specific value of {x}.Given is a function f{x}.
Since the table is not given, let's assume that -
f{3} = a ... Eq { 1 }
f{5} = b ... Eq { 2 }
Then, we can write the average rate of change as -
Δr = (b - a)/(5 - 3)
Δr = (b - a)/2
Therefore, the average rate of change of function in the interval 3 ≤ x ≤ 5 is → Δr = (b - a)/2.
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pls pls help due in an hour pls
Answers
a) The solution for x is obtained as follows: x = 5.
b) The vertical angles are not complementary, as the sum of the measures of the angles is different of 90º.
What are vertical angles?Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.
Considering the vertical angles, the value of x is obtained as follows:
8x + 3 = 9x - 2.
9x - 8x = 3 + 2
x = 5.
Hence the angle measures are of:
8 x 5 + 3 = 43º.
The sum of the measures is of 86º, which is different of 90º, hence the vertical angles are not complementary.
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Which of the following graph represents a functional relationship between a and y?
Answers
Answer:
A
Step-by-step explanation:
because of the vertical line rule
for every other one when you draw vertical line you can get more values for y for the same x
this figure is made up of a rectangle and parallelogram. what is the area of this figure? enter your answer in the box. do not round any side lengths. units²
Answers
40 square units is the area of this rectangle figure .
What is a rectangle ?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral.
The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.
the figure, the rectangle has the vertexes (2,1), (3,-3), (-5,-5) and (-6,-1). The parallelogram has the vertexes (2,7), (3,3), (3,-3), and (2,1).
The area of a parallelogram is base times height. We have 2 vertical lines at x=2 and x=3, so the height is 1. And the length of the line from (3,3) to (3,-3) is 6, so the base is 6. Therefore the area of the parallelogram is 1*6 = 6.
The rectangle is a tad trickier since it's not aligned with either the x or y axis. But we can use the Pythagorean theorem to get the lengths.
L = sqrt((2 - -6)^2 + (1 - -1)^2)
L = sqrt(8^2 + 2^2)
L = sqrt(64 + 4)
L = sqrt(68) = 2*sqrt(17)
W = sqrt((2-3)^2 + (1- -3)^2)
W = sqrt((-1)^2 + 4^2)
W = sqrt(1 + 16)
W = sqrt(17)
And the area is length * width, so:
2*sqrt(17)*sqrt(17) = 2 * 17 = 34
And the total area is the sum of the areas, so
34 + 6 = 40
So the area of the figure is 40 square units.
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Step by step please and thank you……
Answers
Answer:
Answer is in attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do note that this question requires the concept on Pythagoras' Theorem.
Benita graphed point G on the coordinate grid at (2, −4)
. She also plotted point H on the grid 3 units to the left of point G.
BTW THE WHOLE GRAPH IS NOT INNNNNNNNN
Answers
The coordinates of point H are (2 - 3, -4) = (-1, -4).
What do you mean by graph?In mathematics, a graph is a visual representation of a relationship between two variables. It is usually represented as a set of points on a coordinate plane, where the horizontal axis represents one variable and the vertical axis represents the other variable. The points are plotted based on their corresponding values for the two variables, and a line or curve is drawn through the points to show the relationship between the two variables.
Graphs are often used to represent mathematical functions and equations, as they provide a quick and easy way to visualize the relationship between the input and output values. They can also be used to represent data in fields such as science, economics, and social sciences, where they provide a way to analyze and interpret data trends and patterns.
Graphs can be drawn by hand, using graph paper and a ruler, or they can be generated using software, such as spreadsheet programs, mathematical software, and graphing calculators. In addition to helping to visualize the relationship between two variables, graphs can also be used to estimate values, find maximum and minimum points, and make predictions.
The coordinates of point H can be determined by subtracting 3 from the x-coordinate of point G. Therefore, the coordinates of point H are (2 - 3, -4) = (-1, -4). So, point H is located 3 units to the left of point G on the x-axis.
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a box contains six green dice, three red dice and three white dice. a die is selected at random from the box. the die's colour is noted and it is not replaced. this experiment is repeated four times. find the probability that a green die is selected fewer than three times.
Answers
The die's color is noted and it is not replaced. This experiment is repeated four times. The probability that a green die is selected fewer than three times is 8/11.
A box contains six green dice, three red dice and three white dice.
Total dice = Green Dice + Red Dice + White Dice
Total dice = 6 + 3 + 3
Total dice = 12
The probability that a green die is selected fewer than three times = P(G'G'G'G') + P(G'G'G'G) + P(G'G'GG') + P(G'GG'G') + P(GG'G'G') + P(GGG'G') + P(GG'GG') + P(GG'G'G) + P(G'GGG') + P(G'GG'G) + P(G'G'GG)
Here G represents that the dice is green while G' represents as the dice is not green.
The probability that a green die is selected fewer than three times = 6/12×5/11×4/10×3/9 + 6/12×6/11×5/10×4/9 + 6/12×6/11×5/10×4/9 + 6/12×5/11×6/10×4/9 + 6/12×5/11×4/10×6/9 + 6/12×5/11×6/10×5/9 + 6/12×6/11×5/10×5/9 + 6/12×6/11×5/10×5/9 + 6/12×6/11×5/10×5/9 + 6/12×6/11×5/10×5/9 + 6/12×5/11×6/10×5/9
The probability that a green die is selected fewer than three times = 360/11880 + 720/11880 + 720/11880 + 720/11880 + 720/11880 + 900/11880 + 900/11880 + 900/11880 + 900/11880 + 900/11880 + 900/11880
The probability that a green die is selected fewer than three times = 8640/11880
The probability that a green die is selected fewer than three times = 8/11
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if you wanted to visualize the change in the mean test score for the same exam over multiple semesters which visualizations might be used (choose one or more)? group of answer choices pie chart bar chart histogram line chart
Answers
If you wanted to visualize the change in the mean test score for the same exam over multiple semesters then you can bar chart for visualizations.
A bar chart would be a suitable visualization to see the change in the mean test score for the same exam over multiple semesters. These types of charts allow you to see trends and changes over time, making it easy to compare the mean test scores from one semester to the next.
A histogram is used to visualize the distribution of continuous data, while a pie chart is used to show the proportion of various categories, so they are not suitable for this type of data visualization.
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Let sets A and B be defined as follows.
A is the set of integers greater than or equal to -9 and less than or equal to - 3
B=1-29, -26, -23, 30}
(a) Find the cardinalities of A and B.
n(A) =
n (B) =
Answers
The cardinalities:
n(A) = 3
n (B) = 1.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Let sets A and B be defined as follows.
A is the set of integers greater than or equal to -9 and less than or equal to - 3
Set A can be expressed as,
A = {n ≥ -9 or n ≤ -3}
And set B is given,
B = {1-29, -26, -23, 30}
Simplifying,
B = {-28, -26, -23, 30}
The cardinalities:
n(A) = 3
n (B) = 1.
Therefore, n(A) = 3 and n (B) = 1.
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the weights, in pounds, for 15 1515 horses in a stable were reported, and the mean, median, range, and standard deviation for the data were found. the horse with the lowest reported weight was found to actually weigh 10 1010 pounds less than its reported weight. what value remains unchanged if the four values are reported using the corrected weight?
Answers
The only value that remains unchanged is the standard deviation.
The mean, median, range, and standard deviation will all change once the corrected weight is used to calculate the data. The mean is calculated by adding all the weights and dividing by the total number of horses. Therefore, the mean will be recalculated using the corrected weight of 1005 and the new value will be lower than the previous mean. The median is the midpoint of the data set, so it will also decrease with the updated weight. The range is the difference between the highest and lowest values, so it will also decrease with the corrected weight. Lastly, the standard deviation is a measure of the spread of the data and will also decrease when the corrected weight is used. Therefore, the only value that remains unchanged is the standard deviation.
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Help..please!!!
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Answers
3a.) The number of calories at 24 minutes would be = 60 calories
3b.) The time at 280 calories = 42 minutes.
4a.) The height in feet after 4 minutes = 24 feet
4b.) The time when the height is 48 minutes = 8 mins.
Hone to calculate calories per unit time?There are two main graphs represented above which include the following details:
The first graph: Calories was plotted in y-axis against time in x-axis.
The second graph : Height was plotted in y-axis against time is X axis.
When an imaginary straight line is drawn from the origin of the graph, the following values can be derived:
3a) The number of calories at 24 minutes would be = 60 calories.3b.) The time at 280 calories = 42 minutes.4a.) The height in feet after 4 minutes = 24 feet. This is because the point created by the interception of x-axis on the imaginary line drawn from the origin is at 24 feet on the y-axis.4b.) The time when the height is 48 minutes = 8 mins. This is because the point created by the interception of y-axis on the imaginary line drawn from the origin is at 8 mins on the x-axis.Learn more about graph here:
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will give briniest.
Create a two-way table from the diagram:
1
Match the values with their correct places in the table:
1
Question 1 options:
22
6
8
19
25
55
14
30
41
1.
a)
2.
b)
3.
c)
4.
d)
5.
e)
6.
f)
7.
g)
8.
h)
9.
i)
Answers
wo way frequency tables
Two-way frequency tables show how many data points fit in each category.
Here's an example:
Preference Male Female
Prefers dogs 363636 222222
Prefers cats 888 262626
No preference 222 666
The columns of the table tell us whether the student is a male or a female. The rows of the table tell us whether the student prefers dogs, cats, or doesn't have a preference.
Each cell tells us the number (or frequency) of students. For example, the 363636 is in the male column and the prefers dogs row. This tells us that there are 363636 males who preferred dogs in this dataset.
Notice that there are two variables—gender and preference—this is where the two in two-way frequency table comes from.
Want a review of making two-way frequency tables? Check out this video.
Want to practice making frequency tables? Check out this exercise.
Want to practice reading frequency tables? Check out this exercise
Two way relative frequency tables
Two-way relative frequency tables show what percent of data points fit in each category. We can use row relative frequencies or column relative frequencies, it just depends on the context of the problem.
For example, here's how we would make column relative frequencies:
Step 1: Find the totals for each column.
Preference Male Female
Prefers dogs 363636 222222
Prefers cats 888 262626
No preference 222 666
Total 464646 545454
Step 2: Divide each cell count by its column total and convert to a percentage.
Preference Male Female
Prefers dogs \dfrac{36}{46}\approx78\%
46
36
≈78%start fraction, 36, divided by, 46, end fraction, approximately equals, 78, percent \dfrac{22}{54}\approx41\%
54
22
≈41%start fraction, 22, divided by, 54, end fraction, approximately equals, 41, percent
Prefers cats \dfrac{8}{46}\approx17\%
46
8
≈17%start fraction, 8, divided by, 46, end fraction, approximately equals, 17, percent \dfrac{26}{54}\approx48\%
54
26
≈48%start fraction, 26, divided by, 54, end fraction, approximately equals, 48, percent
No preference \dfrac{2}{46}\approx4\%
46
2
≈4%start fraction, 2, divided by, 46, end fraction, approximately equals, 4, percent \dfrac{6}{54}\approx11\%
54
6
≈11%start fraction, 6, divided by, 54, end fraction, approximately equals, 11, percent
Total \dfrac{46}{46}=100\%
46
46
=100%start fraction, 46, divided by, 46, end fraction, equals, 100, percent \dfrac{54}{54}=100\%
54
54
=100%start fraction, 54, divided by, 54, end fraction, equals, 100, percent
Notice that sometimes your percentages won't add up to 100\%100%100, percent even though we rounded properly. This is called round-off error, and we don't worry about it too much.
Two-way relative frequency tables are useful when there are different sample sizes in a dataset. In this example, more females were surveyed than males, so using percentages makes it easier to compare the preferences of males and females. From the relative frequencies, we can see that a large majority of males preferred dogs (78\%)(78%)left parenthesis, 78, percent, right parenthesis compared to a minority of females (41\%)(41%)left parenthesis, 41, percent, right parenthesis.