Data Analysis - ACT Math
Card 0 of 1845
Set A contains the positive even integers less than 14. Set B contains the positive multiples of three less than 20. What is the intersection of the two sets?
Set A contains the positive even integers less than 14. Set B contains the positive multiples of three less than 20. What is the intersection of the two sets?
A = {2, 4, 6, 8, 10, 12}
B = {3, 6, 9, 12, 15, 18}
The intersection of a set means that the elements are in both sets: A∩B = {6, 12}
A = {2, 4, 6, 8, 10, 12}
B = {3, 6, 9, 12, 15, 18}
The intersection of a set means that the elements are in both sets: A∩B = {6, 12}
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What is the probability of choosing two consecutive red cards from a standard deck of cards, if replacement is not allowed?
What is the probability of choosing two consecutive red cards from a standard deck of cards, if replacement is not allowed?
Probability = what you want ÷ total number
A standard deck of playing cards has 52 cards, with 4 suits and 13 cards in each suit
Choosing two red cards = 26 * 25 = 650
Choosing two cards = 52 * 51 = 2652
So the probabiulity of choosing 2 red cards is 650/2652 = 25/102
If replacement is allowed, then the probability of choosing 2 red cards becomes 676/2704 = 1/4
Probability = what you want ÷ total number
A standard deck of playing cards has 52 cards, with 4 suits and 13 cards in each suit
Choosing two red cards = 26 * 25 = 650
Choosing two cards = 52 * 51 = 2652
So the probabiulity of choosing 2 red cards is 650/2652 = 25/102
If replacement is allowed, then the probability of choosing 2 red cards becomes 676/2704 = 1/4
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Susan got a job at a store folding the display clothes. If she folds shirts during her whole eight-hour shift, except for her thirty-minute lunch break, Susan can fold 180 shirts. How long does it take her to fold one shirt?
Susan got a job at a store folding the display clothes. If she folds shirts during her whole eight-hour shift, except for her thirty-minute lunch break, Susan can fold 180 shirts. How long does it take her to fold one shirt?
First you convert hours to minutes by multiplying 8 by 60, giving you 480 minutes. You then subtract her 30 minute lunch break, leaving you with 450 minutes. Then divide this by 180 shirts, giving you 2.5 minutes per shirt. Based on the available answer choices, you then multiply by 60 again to get the time in seconds, 150.
First you convert hours to minutes by multiplying 8 by 60, giving you 480 minutes. You then subtract her 30 minute lunch break, leaving you with 450 minutes. Then divide this by 180 shirts, giving you 2.5 minutes per shirt. Based on the available answer choices, you then multiply by 60 again to get the time in seconds, 150.
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History class has three major exams that make up Joe’s grade. If he scores an 88 on the first exam, an 86 on the second exam and a 96 on the third exam, what is his average grade on all three exams?
History class has three major exams that make up Joe’s grade. If he scores an 88 on the first exam, an 86 on the second exam and a 96 on the third exam, what is his average grade on all three exams?
Average or Mean = Sum of the Options / # of Options
Average = (88 + 86 + 96) / 3 = 270/3 = 90
Average or Mean = Sum of the Options / # of Options
Average = (88 + 86 + 96) / 3 = 270/3 = 90
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A bottle contains 7 yellow jelly beans, 8 blue jelly beans, 9 green jelly beans, and 14 purple jelly beans. If you select one jelly bean at random, what is the probability that it is neither purple nor yellow? Round to the nearest hundredth.
A bottle contains 7 yellow jelly beans, 8 blue jelly beans, 9 green jelly beans, and 14 purple jelly beans. If you select one jelly bean at random, what is the probability that it is neither purple nor yellow? Round to the nearest hundredth.
This is a probability question. There are 17 jelly beans that could be selected to satisfy the conditions of selecting a jelly bean that is neither purple or yellow. There are 38 total jelly beans. The proportion should be set up as 17/38 or 0.45, because this represents the probability that a jelly bean that is not purple or yellow will be selected.
This is a probability question. There are 17 jelly beans that could be selected to satisfy the conditions of selecting a jelly bean that is neither purple or yellow. There are 38 total jelly beans. The proportion should be set up as 17/38 or 0.45, because this represents the probability that a jelly bean that is not purple or yellow will be selected.
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The mean of five numbers is 40. The mean of the smallest two numbers is 25. What is the mean of the other three numbers?
The mean of five numbers is 40. The mean of the smallest two numbers is 25. What is the mean of the other three numbers?
The equation for the mean of a group of numbers is to find the sum of all of the numbers and then divide by how many numbers are in the group. This means that if we know the mean and how many numbers are in the group, we can find the sum of those numbers.
(sum of all five numbers) / 5 = 40 --> sum of all five numbers = 200
(sum of two smallest numbers) / 2 = 25 --> sum of two smallest numbers = 50
Subtracting the sum of the two smallest numbers from the sum of all five gives us the sum of the remaining three. We can then divide by three to find the mean of those three remaining numbers.
200 – 50 = 150
150 / 3 = 50
The equation for the mean of a group of numbers is to find the sum of all of the numbers and then divide by how many numbers are in the group. This means that if we know the mean and how many numbers are in the group, we can find the sum of those numbers.
(sum of all five numbers) / 5 = 40 --> sum of all five numbers = 200
(sum of two smallest numbers) / 2 = 25 --> sum of two smallest numbers = 50
Subtracting the sum of the two smallest numbers from the sum of all five gives us the sum of the remaining three. We can then divide by three to find the mean of those three remaining numbers.
200 – 50 = 150
150 / 3 = 50
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In a theatre there are 600 people. Out of this, 100 males have an average age of 50 and 500 females have an average age of 30. To the nearest whole year, what is the average age of the town’s entire population?
In a theatre there are 600 people. Out of this, 100 males have an average age of 50 and 500 females have an average age of 30. To the nearest whole year, what is the average age of the town’s entire population?
To find the average age, compute:
100 * 50 + 500 * 30= 5000+ 15000= 20000. Then divide by the total amount of people that are at the theatre: 20000/600= 33.3=33.
To find the average age, compute:
100 * 50 + 500 * 30= 5000+ 15000= 20000. Then divide by the total amount of people that are at the theatre: 20000/600= 33.3=33.
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LeBron James had played in 7 playoff games. He scored 31, 30, 55, 14, 29, 20, and 12 points in those games. What is his average for those 7 games?
LeBron James had played in 7 playoff games. He scored 31, 30, 55, 14, 29, 20, and 12 points in those games. What is his average for those 7 games?
To find the mean, you have to add all of the items and then divide by the number of items. Finding the sum (31+30+55+14+29+20+12)= 191 and then dividing by 7 would give a result of 27.3. \[Side Note: The Median is 29 and the range is 43.\]
To find the mean, you have to add all of the items and then divide by the number of items. Finding the sum (31+30+55+14+29+20+12)= 191 and then dividing by 7 would give a result of 27.3. \[Side Note: The Median is 29 and the range is 43.\]
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Angela scores 17, 19, 13, 24, and 14 points in the first five games of a seven-game basketball season. If the scoring leader in Angela’s league averages 18 points per game, how many points must Angela score in the final two games combined to end the season with the highest scoring average in the league AND have a higher scoring average than any other player?
Angela scores 17, 19, 13, 24, and 14 points in the first five games of a seven-game basketball season. If the scoring leader in Angela’s league averages 18 points per game, how many points must Angela score in the final two games combined to end the season with the highest scoring average in the league AND have a higher scoring average than any other player?
Since a given player’s scoring average can be determined by dividing the sum total of points scored by the number of games, we can determine the total points of the scoring leader by multiplying the average points per game by the total number of games. 18 x 7 = 126. Angela would have to score 1 more point than the current scoring leader. Angela’s current total is 87 points; therefore, she must score 40 (87 + 40 = 127) over the course of the final two games to have the highest average points per game in the league.
Since a given player’s scoring average can be determined by dividing the sum total of points scored by the number of games, we can determine the total points of the scoring leader by multiplying the average points per game by the total number of games. 18 x 7 = 126. Angela would have to score 1 more point than the current scoring leader. Angela’s current total is 87 points; therefore, she must score 40 (87 + 40 = 127) over the course of the final two games to have the highest average points per game in the league.
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What is the mean of the following set of numbers: 13, 15, 100, 54, 345, rounded to the nearest 1’s place?
What is the mean of the following set of numbers: 13, 15, 100, 54, 345, rounded to the nearest 1’s place?
mean = sum of all values divided by the number of values.
mean = sum of all values divided by the number of values.
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If the average of A, B, and C is 50, which of the following expressions represents the average of A, B, C, and D?
If the average of A, B, and C is 50, which of the following expressions represents the average of A, B, C, and D?
We take the average 50 and multiply it by 3 (the number of terms in the set) to get the total sum of the initial set. Then you take the total sum and add D and divide by the numbers of terms in the new set.
We take the average 50 and multiply it by 3 (the number of terms in the set) to get the total sum of the initial set. Then you take the total sum and add D and divide by the numbers of terms in the new set.
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Sixty high school seniors were polled to see if they were taking history and calculus. A total of 29 students said they were taking calculus, and a total of 50 students said they were taking history. What is the minimum number of students who take both history and calculus?
Sixty high school seniors were polled to see if they were taking history and calculus. A total of 29 students said they were taking calculus, and a total of 50 students said they were taking history. What is the minimum number of students who take both history and calculus?
We can draw a Venn diagram to see these two sets of students.
We need to find the overlap between these two sets. To find that, add up the total number of students who are taking history and the total number of students who are taking calculus.
Notice that we have more students this way than the total number who were polled. That is because the students who are taking history AND calculus have been double counted. Subtract the total number of students polled to find out how many students were counted twice.
We can draw a Venn diagram to see these two sets of students.
We need to find the overlap between these two sets. To find that, add up the total number of students who are taking history and the total number of students who are taking calculus.
Notice that we have more students this way than the total number who were polled. That is because the students who are taking history AND calculus have been double counted. Subtract the total number of students polled to find out how many students were counted twice.
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Given the Venn diagram below, which of the following does not belong to 
?
Given the Venn diagram below, which of the following does not belong to
The symbol 
stands for the union between two sets. Therefore, 
means the set of all numbers that are in either A or B. Looking at our choices, the only number that isn't in either A, B, or both is 23.
The symbol
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Forty students play soccer and/or basketball after school. Twenty-four students play soccer and twenty-nine play basketball. How many students play both soccer and basketball?
Forty students play soccer and/or basketball after school. Twenty-four students play soccer and twenty-nine play basketball. How many students play both soccer and basketball?
We can draw a Venn diagram of these students.
Drawn this way, there are more students on the Venn diagram than we have.
This is because some of the students play both sports and should be in the overlap on the Venn diagram. To find the number of students in the overlap, subtract the total number of students given from the number on the diagram.
This represents the number of students who were counted twice, or the number in the overlap.
We can redraw the correct Venn diagram with this number.
We can draw a Venn diagram of these students.
Drawn this way, there are more students on the Venn diagram than we have.
This is because some of the students play both sports and should be in the overlap on the Venn diagram. To find the number of students in the overlap, subtract the total number of students given from the number on the diagram.
This represents the number of students who were counted twice, or the number in the overlap.
We can redraw the correct Venn diagram with this number.
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Giving the Venn diagram above, what is the sum of the numbers in the set 
?
Giving the Venn diagram above, what is the sum of the numbers in the set
The notation 
stands for "A union C," which refers to everything that is in either set 
or set 
.
When we add the numbers together, we get:
The notation
When we add the numbers together, we get:
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Calculate the arithmetic mean of the following set of numbers: 54, 35, 50, 49, 54, 65, 82, 54, and 25.
Calculate the arithmetic mean of the following set of numbers: 54, 35, 50, 49, 54, 65, 82, 54, and 25.
To solve this question, you must know that the mean is the sum of the values divided by the number of values, in this case: 468/9=52. It is not 54, which is the median (the most commonly occurring number of the set).
To solve this question, you must know that the mean is the sum of the values divided by the number of values, in this case: 468/9=52. It is not 54, which is the median (the most commonly occurring number of the set).
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A group of high school juniors are taking Biology, Calculus, and Spanish as shown above. Which student is not in the set 
?
A group of high school juniors are taking Biology, Calculus, and Spanish as shown above. Which student is not in the set
The notation 
stands for "union," which refers to everything that is in either set. 
refers to the group of students taking either Calculus or Spanish (everyone on this diagram except those taking only Biology). From the diagram, Patrick and Ashley are the only students taking neither Calculus nor Spanish, so Patrick is the correct answer.
The notation
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In a class of senior high-school students, 
have pet cats, 
have pet dogs, 
have both cats and dogs, and 
have neither cats nor dogs. How many total students are in the class?
In a class of senior high-school students,
A Venn diagram can help us determine the total number of students in the class.
First, we must calculate the number of students who have ONLY cats or ONLY dogs. First, for cats, 15 students have cats, and 5 students have both cats and dogs.
Ten students have only cats.
For dogs, 12 students have dogs, and 5 students have both cats and dogs.
Seven students have only dogs.
Using this information, we can fill in the Venn diagram.
This diagram shows the 10 students with only cats, the 7 students with only dogs, the 5 students with both, and the 8 students with neither. Adding up the numbers will give us the total number of students.
A Venn diagram can help us determine the total number of students in the class.
First, we must calculate the number of students who have ONLY cats or ONLY dogs. First, for cats, 15 students have cats, and 5 students have both cats and dogs.
Ten students have only cats.
For dogs, 12 students have dogs, and 5 students have both cats and dogs.
Seven students have only dogs.
Using this information, we can fill in the Venn diagram.
This diagram shows the 10 students with only cats, the 7 students with only dogs, the 5 students with both, and the 8 students with neither. Adding up the numbers will give us the total number of students.
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In the venn diagram above, let the set 
and let 
, what is the set 
Use set notation to enumerate your answer.
In the venn diagram above, let the set
means the intersection of the sets 
and 
, the only things in the intersection are elementes that are in BOTH of the sets. Since there is nothing shared by the two sets (no elements are in both), the interesction is the emptyset, or: 
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In a venn diagram, let 
and let 
What is 
In a venn diagram, let
What is
is the union of the sets 
and 
which is the set that contains anything that is in either set. Thus, the total of 
is every element that is in one of the two sets, and so 
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