To find the quotient of 5/12 and 1 1/6, we need to convert 1 1/6 to an improper fraction.
1 1/6 = (6 * 1 + 1)/6 = 7/6
Now, we can divide 5/12 by 7/6:
(5/12) ÷ (7/6) = (5/12) * (6/7) = (5 * 6)/(12 * 7) = 30/84 = 5/14
Therefore, the quotient of 5/12 and 1 1/6 is 5/14, which is option A.
What is the quotient of 5/12 and 1 1/6?
A.
5/14
B.
35/72
C.
2 2/35
D.
2 4/5
22 answers
Mrs. Patel has two plants. The first plant has a height of 0.6 meter. The height of the second plant is 0.25 meter shorter.
What is the height of Mrs. Patel’s second plant?
A.
0.3 meter
B.
0.35 meter
C.
0.4 meter
D.
0.85 meter
What is the height of Mrs. Patel’s second plant?
A.
0.3 meter
B.
0.35 meter
C.
0.4 meter
D.
0.85 meter
The height of the second plant is 0.25 meter shorter than the height of the first plant, which is 0.6 meter. To find the height of the second plant, we need to subtract 0.25 meter from 0.6 meter.
0.6 meter - 0.25 meter = 0.35 meter
Therefore, the height of Mrs. Patel's second plant is 0.35 meter, which is option B.
0.6 meter - 0.25 meter = 0.35 meter
Therefore, the height of Mrs. Patel's second plant is 0.35 meter, which is option B.
The table shows the items Stevie bought from a garage sale and their prices.
What is the mean price of the items Stevie bought?
A.
36
B.
5
C.
21
D.
6
What is the mean price of the items Stevie bought?
A.
36
B.
5
C.
21
D.
6
In order to find the mean price of the items Stevie bought, we need to find the average of the prices listed in the table.
The total cost of the items can be found by adding up all the prices: 12 + 5 + 4 + 18 + 8 + 25 = 72
Since there are 6 items, we divide the total cost by 6 to find the mean price:
72/6 = 12
Therefore, the mean price of the items Stevie bought is 12, which is option A.
The total cost of the items can be found by adding up all the prices: 12 + 5 + 4 + 18 + 8 + 25 = 72
Since there are 6 items, we divide the total cost by 6 to find the mean price:
72/6 = 12
Therefore, the mean price of the items Stevie bought is 12, which is option A.
The numbers of participants in various library programs are shown below.
45, 34, 49, 63, 31, 30, 46, 53, 46, 51, 61, 33, 62, 40Which histogram represents the data correctly?
A.
The histogram has a bar between 30 and 40 is raised to 5, a bar between 40 and 50 is raised to 4, a bar between 50 and 60 is raised to 3, and a bar between 60 and 70 is raised to 2.
B.
The histogram has a bar between 30 and 40 is raised to 4, a bar between 40 and 50 is raised to 5, a bar between 50 and 60 is raised to 2, and a bar between 60 and 70 is raised to 3.
C.
The histogram has a bar between 30 and 40 is raised to 2, a bar between 40 and 50 is raised to 4, a bar between 50 and 60 is raised to 5, and a bar between 60 and 70 is raised to 3.
D.
The histogram has a bar between 30 and 40 is raised to 2, a bar between 40 and 50 is raised to 3, a bar between 50 and 60 is raised to 4, and a bar between 60 and 70 is raised to 5.
45, 34, 49, 63, 31, 30, 46, 53, 46, 51, 61, 33, 62, 40Which histogram represents the data correctly?
A.
The histogram has a bar between 30 and 40 is raised to 5, a bar between 40 and 50 is raised to 4, a bar between 50 and 60 is raised to 3, and a bar between 60 and 70 is raised to 2.
B.
The histogram has a bar between 30 and 40 is raised to 4, a bar between 40 and 50 is raised to 5, a bar between 50 and 60 is raised to 2, and a bar between 60 and 70 is raised to 3.
C.
The histogram has a bar between 30 and 40 is raised to 2, a bar between 40 and 50 is raised to 4, a bar between 50 and 60 is raised to 5, and a bar between 60 and 70 is raised to 3.
D.
The histogram has a bar between 30 and 40 is raised to 2, a bar between 40 and 50 is raised to 3, a bar between 50 and 60 is raised to 4, and a bar between 60 and 70 is raised to 5.
To accurately represent the given data in a histogram, we need to analyze the frequencies of each range.
The data given is: 45, 34, 49, 63, 31, 30, 46, 53, 46, 51, 61, 33, 62, 40
Looking at the ranges:
30-40: 2 participants
40-50: 4 participants
50-60: 5 participants
60-70: 3 participants
Based on this information, the correct histogram representation is option C, where the bar between 30 and 40 is raised to 2, the bar between 40 and 50 is raised to 4, the bar between 50 and 60 is raised to 5, and the bar between 60 and 70 is raised to 3.
The data given is: 45, 34, 49, 63, 31, 30, 46, 53, 46, 51, 61, 33, 62, 40
Looking at the ranges:
30-40: 2 participants
40-50: 4 participants
50-60: 5 participants
60-70: 3 participants
Based on this information, the correct histogram representation is option C, where the bar between 30 and 40 is raised to 2, the bar between 40 and 50 is raised to 4, the bar between 50 and 60 is raised to 5, and the bar between 60 and 70 is raised to 3.
Tia, Bill, Kay, and Marco counted the number of fireflies they saw each day for a week in the summer. They each put their numbers in order from least to greatest.
Tia: 9, 12, 15, 18, 21, 24, 27
Bill: 3, 6, 8, 18, 20, 21, 22
Kay: 14, 15, 16, 18, 24, 27, 32
Marco: 2, 6, 10, 14, 18, 22, 26
Whose data is skewed left?
A.
Tia's data
B.
Bill's data
C.
Kay's data
D.
Marco's data
Tia: 9, 12, 15, 18, 21, 24, 27
Bill: 3, 6, 8, 18, 20, 21, 22
Kay: 14, 15, 16, 18, 24, 27, 32
Marco: 2, 6, 10, 14, 18, 22, 26
Whose data is skewed left?
A.
Tia's data
B.
Bill's data
C.
Kay's data
D.
Marco's data
To determine whose data is skewed left, we need to analyze the distribution of the numbers.
Skewed left means that the data is asymmetrical and the tail (lower values) is longer on the left side.
Looking at the numbers provided:
Tia: 9, 12, 15, 18, 21, 24, 27
Bill: 3, 6, 8, 18, 20, 21, 22
Kay: 14, 15, 16, 18, 24, 27, 32
Marco: 2, 6, 10, 14, 18, 22, 26
Based on the numbers, we can see that Marco's data is skewed left. The majority of his numbers are on the lower end, with a longer tail towards the left side. Therefore, option D (Marco's data) is the correct answer.
Skewed left means that the data is asymmetrical and the tail (lower values) is longer on the left side.
Looking at the numbers provided:
Tia: 9, 12, 15, 18, 21, 24, 27
Bill: 3, 6, 8, 18, 20, 21, 22
Kay: 14, 15, 16, 18, 24, 27, 32
Marco: 2, 6, 10, 14, 18, 22, 26
Based on the numbers, we can see that Marco's data is skewed left. The majority of his numbers are on the lower end, with a longer tail towards the left side. Therefore, option D (Marco's data) is the correct answer.
Lindsey found the median and mean of the list of numbers below.
4, 6, 8, 8, 15
Which statement is true if Lindsey includes the number 23 in the list?
A.
The median would decrease.
B.
The median would increase.
C.
The mean would increase.
D.
The mean would decrease.
4, 6, 8, 8, 15
Which statement is true if Lindsey includes the number 23 in the list?
A.
The median would decrease.
B.
The median would increase.
C.
The mean would increase.
D.
The mean would decrease.
To determine how adding the number 23 to the list would affect the median and mean, we need to calculate the median and mean of the original list first.
The original list: 4, 6, 8, 8, 15
To find the median, we arrange the numbers in ascending order: 4, 6, 8, 8, 15. The median is the middle value, which in this case is 8.
To find the mean, we sum up all the numbers and divide by the total count: (4 + 6 + 8 + 8 + 15) / 5 = 41 / 5 = 8.2.
Now, if we include the number 23 in the list, the new list becomes: 4, 6, 8, 8, 15, 23.
The new median is still the middle value, and since there are now 6 numbers, the middle value is still 8. Therefore, the median would not change. Option A is incorrect.
To find the new mean, we sum up all the numbers (4 + 6 + 8 + 8 + 15 + 23) and divide by the new total count, which is 6: 64 / 6 = 10.6667.
Therefore, if Lindsey includes the number 23 in the list, the mean would increase. Option C is true, and option D is incorrect.
The original list: 4, 6, 8, 8, 15
To find the median, we arrange the numbers in ascending order: 4, 6, 8, 8, 15. The median is the middle value, which in this case is 8.
To find the mean, we sum up all the numbers and divide by the total count: (4 + 6 + 8 + 8 + 15) / 5 = 41 / 5 = 8.2.
Now, if we include the number 23 in the list, the new list becomes: 4, 6, 8, 8, 15, 23.
The new median is still the middle value, and since there are now 6 numbers, the middle value is still 8. Therefore, the median would not change. Option A is incorrect.
To find the new mean, we sum up all the numbers (4 + 6 + 8 + 8 + 15 + 23) and divide by the new total count, which is 6: 64 / 6 = 10.6667.
Therefore, if Lindsey includes the number 23 in the list, the mean would increase. Option C is true, and option D is incorrect.
Normal
Multiple Select Question
Sean counted the number of stuffed animals available for prizes in each of the booths at a county fair. The list shows the results.
2, 23, 27, 29, 30, 32, 32, 34, 35, 96
Select all the data values that are outliers.
A.
2
B.
27
C.
34
D.
96
Multiple Select Question
Sean counted the number of stuffed animals available for prizes in each of the booths at a county fair. The list shows the results.
2, 23, 27, 29, 30, 32, 32, 34, 35, 96
Select all the data values that are outliers.
A.
2
B.
27
C.
34
D.
96
To determine the outliers in the given dataset, we can use the interquartile range (IQR) method.
First, we need to calculate the first quartile (Q1) and the third quartile (Q3) of the dataset.
The dataset, arranged in ascending order, is: 2, 23, 27, 29, 30, 32, 32, 34, 35, 96
Q1 is the median of the lower half of the dataset. The lower half is: 2, 23, 27, 29, 30. Median of the lower half is (27+29)/2 = 28.
Q3 is the median of the upper half of the dataset. The upper half is: 32, 32, 34, 35, 96. Median of the upper half is (32+34)/2 = 33.
Next, we calculate the IQR:
IQR = Q3 - Q1
IQR = 33 - 28
IQR = 5
Now, to identify outliers, we consider any value below Q1 - 1.5*IQR or above Q3 + 1.5*IQR as an outlier.
Q1 - 1.5*IQR = 28 - 1.5*5 = 28 - 7.5 = 20.5
Q3 + 1.5*IQR = 33 + 1.5*5 = 33 + 7.5 = 40.5
Based on this calculation, the values 2 and 96 are below Q1 - 1.5*IQR and above Q3 + 1.5*IQR, respectively. Therefore, the outliers in the dataset are 2 and 96.
Thus, the correct answer is options A and D.
First, we need to calculate the first quartile (Q1) and the third quartile (Q3) of the dataset.
The dataset, arranged in ascending order, is: 2, 23, 27, 29, 30, 32, 32, 34, 35, 96
Q1 is the median of the lower half of the dataset. The lower half is: 2, 23, 27, 29, 30. Median of the lower half is (27+29)/2 = 28.
Q3 is the median of the upper half of the dataset. The upper half is: 32, 32, 34, 35, 96. Median of the upper half is (32+34)/2 = 33.
Next, we calculate the IQR:
IQR = Q3 - Q1
IQR = 33 - 28
IQR = 5
Now, to identify outliers, we consider any value below Q1 - 1.5*IQR or above Q3 + 1.5*IQR as an outlier.
Q1 - 1.5*IQR = 28 - 1.5*5 = 28 - 7.5 = 20.5
Q3 + 1.5*IQR = 33 + 1.5*5 = 33 + 7.5 = 40.5
Based on this calculation, the values 2 and 96 are below Q1 - 1.5*IQR and above Q3 + 1.5*IQR, respectively. Therefore, the outliers in the dataset are 2 and 96.
Thus, the correct answer is options A and D.
The dot plot below shows the number of hours that several sixth graders spent inside the school building in a day. Each X represents one student.
A dot plot showing hours from 0 to 8 in the increments of 1 has one X at 0, 2 X's at 7 and seven X's at 8.
Which of the following statements is true regarding this data? Select all that apply.
A.
The median better represents these data than the mean.
B.
The mean is affected by the one student who was absent from school.
C.
The distribution is skewed since most students were in the school building for 7 or 8 hours.
A dot plot showing hours from 0 to 8 in the increments of 1 has one X at 0, 2 X's at 7 and seven X's at 8.
Which of the following statements is true regarding this data? Select all that apply.
A.
The median better represents these data than the mean.
B.
The mean is affected by the one student who was absent from school.
C.
The distribution is skewed since most students were in the school building for 7 or 8 hours.
To analyze the given dot plot of the number of hours sixth graders spent inside the school building, we can make the following observations based on the plot:
- One X is at 0
- Two X's are at 7
- Seven X's are at 8
A. The median better represents these data than the mean:
Since the median is the middle value when the data is sorted, it would be unaffected by outliers, if any. In this case, the median would be 8 since it falls in the middle. This is true as most of the X's are at 7 or 8 hours, making the median of 8 a better representation of the overall data. So, option A is correct.
B. The mean is affected by the one student who was absent from school:
The mean is calculated by summing up all the values and dividing by the total count. In this case, since the absent student is not represented by an X, their value is not included in the calculation of the mean. Therefore, the mean is not affected by the absence of the student. Hence, option B is incorrect.
C. The distribution is skewed since most students were in the school building for 7 or 8 hours:
Skewness in the data implies that the distribution is not symmetric. In this case, since most students are in the school building for 7 or 8 hours, there is a clustering on the right side of the plot. This indicates a right skew or positive skew, which is true in this scenario. Therefore, option C is correct.
In conclusion, options A and C are true statements regarding the data represented in the dot plot.
- One X is at 0
- Two X's are at 7
- Seven X's are at 8
A. The median better represents these data than the mean:
Since the median is the middle value when the data is sorted, it would be unaffected by outliers, if any. In this case, the median would be 8 since it falls in the middle. This is true as most of the X's are at 7 or 8 hours, making the median of 8 a better representation of the overall data. So, option A is correct.
B. The mean is affected by the one student who was absent from school:
The mean is calculated by summing up all the values and dividing by the total count. In this case, since the absent student is not represented by an X, their value is not included in the calculation of the mean. Therefore, the mean is not affected by the absence of the student. Hence, option B is incorrect.
C. The distribution is skewed since most students were in the school building for 7 or 8 hours:
Skewness in the data implies that the distribution is not symmetric. In this case, since most students are in the school building for 7 or 8 hours, there is a clustering on the right side of the plot. This indicates a right skew or positive skew, which is true in this scenario. Therefore, option C is correct.
In conclusion, options A and C are true statements regarding the data represented in the dot plot.
Normal
Multiple Choice Question
The following measurements show the lengths of 5 grasshoppers in inches:
3.7, 2.5, 2.3, 1.2, and 3.4
What will happen if 2 more grasshoppers with measurements of 2.3 and 3.2 inches are added?
A.
the mean will increase
B.
the median will increase
C.
the mean will decrease
D.
the median will decrease
Multiple Choice Question
The following measurements show the lengths of 5 grasshoppers in inches:
3.7, 2.5, 2.3, 1.2, and 3.4
What will happen if 2 more grasshoppers with measurements of 2.3 and 3.2 inches are added?
A.
the mean will increase
B.
the median will increase
C.
the mean will decrease
D.
the median will decrease
To determine the impact of adding two more grasshoppers to the given measurements, we need to examine how it will affect the mean and median.
The original measurements are: 3.7, 2.5, 2.3, 1.2, 3.4.
Mean calculation:
To find the mean, we sum up all the measurements and divide by the total count. Original mean = (3.7 + 2.5 + 2.3 + 1.2 + 3.4) / 5 = 2.82.
Median calculation:
To find the median, we arrange the measurements in ascending order: 1.2, 2.3, 2.5, 3.4, 3.7. In this case, the median is the middle value, which is 2.5.
Now, let's add two more grasshoppers with measurements of 2.3 and 3.2 inches:
New measurements: 3.7, 2.5, 2.3, 1.2, 3.4, 2.3, 3.2.
Mean calculation:
New mean = (3.7 + 2.5 + 2.3 + 1.2 + 3.4 + 2.3 + 3.2) / 7 ≈ 2.71.
Median calculation:
New median remains the same because we added two measurements that are already present in the original set (2.3 and 3.2). Therefore, the median will not change and it will still be 2.5.
Based on these calculations, we can conclude that if two more grasshoppers with measurements of 2.3 and 3.2 inches are added, the mean will decrease (option C) but the median will remain the same (option D).
The original measurements are: 3.7, 2.5, 2.3, 1.2, 3.4.
Mean calculation:
To find the mean, we sum up all the measurements and divide by the total count. Original mean = (3.7 + 2.5 + 2.3 + 1.2 + 3.4) / 5 = 2.82.
Median calculation:
To find the median, we arrange the measurements in ascending order: 1.2, 2.3, 2.5, 3.4, 3.7. In this case, the median is the middle value, which is 2.5.
Now, let's add two more grasshoppers with measurements of 2.3 and 3.2 inches:
New measurements: 3.7, 2.5, 2.3, 1.2, 3.4, 2.3, 3.2.
Mean calculation:
New mean = (3.7 + 2.5 + 2.3 + 1.2 + 3.4 + 2.3 + 3.2) / 7 ≈ 2.71.
Median calculation:
New median remains the same because we added two measurements that are already present in the original set (2.3 and 3.2). Therefore, the median will not change and it will still be 2.5.
Based on these calculations, we can conclude that if two more grasshoppers with measurements of 2.3 and 3.2 inches are added, the mean will decrease (option C) but the median will remain the same (option D).
Byron wants to use the distributive property to rewrite the addition problem shown so that the numbers left in the parentheses have no common factor except 1.
(48 + 36)
Which is an equivalent expression that has numbers in the parentheses whose only common factor is 1?
A.
4(12 + 9)
B.
2(24 + 18)
C.
12(4 + 3)
D.
36(12 + 1)
(48 + 36)
Which is an equivalent expression that has numbers in the parentheses whose only common factor is 1?
A.
4(12 + 9)
B.
2(24 + 18)
C.
12(4 + 3)
D.
36(12 + 1)
To rewrite the addition problem (48 + 36) using the distributive property, we need to find an equivalent expression with numbers in the parentheses whose only common factor is 1.
Let's consider the options:
A. 4(12 + 9)
Both 12 and 9 have a common factor of 3, so this option does not satisfy the condition.
B. 2(24 + 18)
Both 24 and 18 have a common factor of 6, so this option does not satisfy the condition.
C. 12(4 + 3)
The numbers 4 and 3 have no common factors other than 1, so this option satisfies the condition.
D. 36(12 + 1)
The numbers 12 and 1 have a common factor of 1, so this option satisfies the condition.
Therefore, the equivalent expression that has numbers in the parentheses whose only common factor is 1 is option C.
Let's consider the options:
A. 4(12 + 9)
Both 12 and 9 have a common factor of 3, so this option does not satisfy the condition.
B. 2(24 + 18)
Both 24 and 18 have a common factor of 6, so this option does not satisfy the condition.
C. 12(4 + 3)
The numbers 4 and 3 have no common factors other than 1, so this option satisfies the condition.
D. 36(12 + 1)
The numbers 12 and 1 have a common factor of 1, so this option satisfies the condition.
Therefore, the equivalent expression that has numbers in the parentheses whose only common factor is 1 is option C.
Mr. Hon purchases a new car every 4 years. Ms. Jasper purchases a new car every 6 years. They both purchased new cars this year. When will they next both purchase new cars in the same year?
A.
in 2 years
B.
in 8 years
C.
in 12 years
D.
in 24 years
A.
in 2 years
B.
in 8 years
C.
in 12 years
D.
in 24 years
To determine when Mr. Hon and Ms. Jasper will next purchase new cars in the same year, we need to find the least common multiple (LCM) of 4 and 6.
The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, ...
The multiples of 6 are: 6, 12, 18, 24, 30, 36, ...
From the lists, we can see that the least common multiple (LCM) of 4 and 6 is 12.
Therefore, Mr. Hon and Ms. Jasper will next purchase new cars in the same year in 12 years.
Hence, the correct answer is option C.
The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, ...
The multiples of 6 are: 6, 12, 18, 24, 30, 36, ...
From the lists, we can see that the least common multiple (LCM) of 4 and 6 is 12.
Therefore, Mr. Hon and Ms. Jasper will next purchase new cars in the same year in 12 years.
Hence, the correct answer is option C.
ean counted the number of stuffed animals available for prizes in each of the booths at a county fair. The list shows the results.
2, 23, 27, 29, 30, 32, 32, 34, 35, 96
2, 23, 27, 29, 30, 32, 32, 34, 35, 96
6 answers