Simplify the radical expression.
start root start-fraction 63 x superscript 15 baseline y superscript 9 baseline over 7 x y superscript 11 baseline end-fraction end root
A. Start Fraction 8 lower x superscript 7 baseline lower y superscript 4 baseline Start Root lower x lower y End Root over Start Root 7 lower x lower y superscript 11 baseline End Fraction
B. Start Fraction 3 lower x superscript 7 baseline over y End Fraction
C. Start Fraction 9 lower x superscript 7 baseline over lower y End Fraction
D. 9 lower x superscript 7 baseline lower y
A. Start Fraction 8 lower x superscript 7 baseline lower y superscript 4 baseline Start Root lower x lower y End Root over Start Root 7 lower x lower y superscript 11 baseline End Fraction
Simplify the radical expression.
Square root 5 plus 6 times square root 5
A. 5 times square root 5
B. 7 times square root 10
C. 7 times square root 5
D. 5 times square root 10
C. 7 times square root 5
Simplify the radical expression.
3 times square root 5 plus 6 times square root 45
A. 9 times square root 50
B. 21 times square root 10
C. 6 times square root 96
D. 21 times square root 5
B. 21 times square root 10
Simplify the radical expression.
The quantity 5 plus square root 3 times the quantity 5 minus square root 3
A. 16
B. 22
C. 25 plus 10 times square root 3
D. 16 plus 10 times square root 3
A. 16
What is the domain of the function?
y equals Start Root 4 x plus 8 End Root
A. x greater-than-or-equal-to negative 2
B. x less-than-or-equal-to negative 2
C. x greater than or equal to 2
D. x less than or equal to 2
A. x greater-than-or-equal-to negative 2
Simplify the radical expression by rationalizing the denominator.
start fraction start root 8 end root over start root 6 x end root end fraction
A. start fraction 2 start root 3 x end root over 3x end fraction
B. start fraction 2 start root 2 x end root over x end fraction
C. start fraction start root 6 x end root over 3x end fraction
D. start fraction 4 start root 3x end root over 3x end fraction
B. start fraction 2 start root 2 x end root over x end fraction
Find the mean, median, and mode of the data set. Round to the nearest tenth.
7, 5, 4, 2, 1, 1, 2, 3, 5, 4, 5
A. mean = 3.5 median = 4 mode = 5
B. mean = 3.25 median = 4 mode = 5
C. mean = 3.5 median = 5 mode = 4
D. mean = 3.25 median = 5 mode = 4
A. mean = 3.5 median = 4 mode = 5.
Make a box-and-whisker plot of the data.
29, 21, 17, 10, 15, 27, 22, 30
A. A box-and-whisker plot with median plotted at 21.5, first quartile plotted at 15, third quartile plotted at 29, minimum plotted at 10, and maximum plotted at 30.
B. A box-and-whisker plot with median plotted at 22, first quartile plotted at 17, third quartile plotted at 29, minimum plotted at 10, and maximum plotted at 30.
C. A box-and-whisker plot with median plotted at 21, first quartile plotted at 15, third quartile plotted at 28, minimum plotted at 10, and maximum plotted at 30.
D. A box-and-whisker plot with median plotted at 21.5, first quartile plotted at 16, third quartile plotted at 28, minimum plotted at 10, and maximum plotted at 30.
C. A box-and-whisker plot with median plotted at 21, first quartile plotted at 15, third quartile plotted at 28, minimum plotted at 10, and maximum plotted at 30.
The data below gives the number of speeding tickets given per day at a certain location on a highway over a two-week period.
1, 3, 7, 6, 12, 6, 5, 2, 0, 8, 4, 8, 10, 1
Which frequency table represents the data?
A.
Speeding Tickets Frequency
0 –3 5
4 –7 5
8 – 11 3
12 – 15 1
B.
Speeding Tickets Frequency
0 –3 4
4 –7 6
8 – 11 3
12 – 15 1
C.
Speeding Tickets Frequency
0 –3 5
4 –7 5
8 – 11 2
12 – 15 2
D.
Speeding Tickets Frequency
0 –3 6
4 –7 4
8 – 11 2
12 – 15 2
B.
Speeding Tickets | Frequency
--- | ---
0-3 | 4
4-7 | 6
8-11 | 3
12-15 | 1
The data below show the number of games won by a baseball team in each of the last 15 seasons.
20, 15, 10, 7, 2, 12, 12, 22, 16, 13, 8, 8, 14, 17, 23
Which histogram represents this data?
A. A histogram has a first interval of 1 to 5 with a frequency of 1. The second interval of 6 to 10 has a frequency of 4. The third interval of 11 to 15 has a frequency of 5. The fourth interval of 16 to 20 has a frequency of 2. The fifth interval of 21 to 25 has a frequency of 2.It is divided into five partitions. The first is labeled 1 dash 5. The second is labeled 6 dash 10. The third is labeled 11 dash 15. The fourth is labeled 16 dash 20. The fifth is labeled 21 dash 25. The vertical axis is numbered from 0 to 6 with a step size of 1. Five rectangles or bars are shown. The rectangle spanning the 1 dash 5 partition has a height of 1. The rectangle spanning the 6 dash 10 partition has a height of 4. The rectangle spanning the 11 dash 15 partition has a height of 5. The rectangle spanning the 16 dash 20 partition has a height of 2. The rectangle spanning the 21 dash 25 partition has a height of 2.
B. A histogram has a first interval of 1 to 5 with a frequency of 1. The second interval of 6 to 10 has a frequency of 4. The third interval of 11 to 15 has a frequency of 5. The fourth interval of 16 to 20 has a frequency of 3. The fifth interval of 21 to 25 has a frequency of 2.It is divided into five partitions. The first is labeled 1 dash 5. The second is labeled 6 dash 10. The third is labeled 11 dash 15. The fourth is labeled 16 dash 20. The fifth is labeled 21 dash 25. The vertical axis is numbered from 0 to 6 with a step size of 1. Five rectangles or bars are shown. The rectangle spanning the 1 dash 5 partition has a height of 1. The rectangle spanning the 6 dash 10 partition has a height of 4. The rectangle spanning the 11 dash 15 partition has a height of 5. The rectangle spanning the 16 dash 20 partition has a height of 2. The rectangle spanning the 21 dash 25 partition has a height of 2.
C. A histogram has a first interval of 1 to 5 with a frequency of 1. The second interval of 6 to 10 has a frequency of 5. The third interval of 11 to 15 has a frequency of 4. The fourth interval of 16 to 20 has a frequency of 3. The fifth interval of 21 to 25 has a frequency of 1.It is divided into five partitions. The first is labeled 1 dash 5. The second is labeled 6 dash 10. The third is labeled 11 dash 15. The fourth is labeled 16 dash 20. The fifth is labeled 21 dash 25. The vertical axis is numbered from 0 to 6 with a step size of 1. Five rectangles or bars are shown. The rectangle spanning the 1 dash 5 partition has a height of 1. The rectangle spanning the 6 dash 10 partition has a height of 5. The rectangle spanning the 11 dash 15 partition has a height of 4. The rectangle spanning the 16 dash 20 partition has a height of 3. The rectangle spanning the 21 dash 25 partition has a height of 1.
D. A histogram has a first interval of 1 to 5 with a frequency of 1. The second interval of 6 to 10 has a frequency of 6. The third interval of 11 to 15 has a frequency of 4. The fourth interval of 16 to 20 has a frequency of 3. The fifth interval of 21 to 25 has a frequency of 1.
B. A histogram has a first interval of 1 to 5 with a frequency of 1. The second interval of 6 to 10 has a frequency of 4. The third interval of 11 to 15 has a frequency of 5. The fourth interval of 16 to 20 has a frequency of 3. The fifth interval of 21 to 25 has a frequency of 2.
It is divided into five partitions. The first is labeled 1 dash 5. The second is labeled 6 dash 10. The third is labeled 11 dash 15. The fourth is labeled 16 dash 20. The fifth is labeled 21 dash 25. The vertical axis is numbered from 0 to 6 with a step size of 1. Five rectangles or bars are shown. The rectangle spanning the 1 dash 5 partition has a height of 1. The rectangle spanning the 6 dash 10 partition has a height of 4. The rectangle spanning the 11 dash 15 partition has a height of 5. The rectangle spanning the 16 dash 20 partition has a height of 2. The rectangle spanning the 21 dash 25 partition has a height of 2.
Is the histogram uniform, symmetric, or skewed?
A histogram with 5 bars is shown. The graph has a scale of 0 to 10 in increments of one.
The first bar has a height of 10.
The second bar has a height of 8.
The third bar has a height of 3.
The fourth bar has a height of 2.
The fifth bar has a height of 1.
A. uniform
B. symmetric
C. skewed
C. skewed.
The table shows the number of hours that a group of friends spent in their first week training to run a marathon. In the second week, they each add five hours to their training times. What are the mean, median, mode, and range of times for the second week?
Runner Hours
Jeff 9
Mark 5
Karen 5
Costas 5
Brett 7
Nikki 6
Jack 7
A.
mean = 10
median = 11
mode = 11.3
range = 4
B.
mean = 11
median = 11.3
mode = 10
range = 0.3
C.
mean = 11.3
median = 11
mode = 10
range = 4
D.
mean = 11.3
median = 11
mode = 10
range = 0.3
C.
To find the mean, median, and mode of the second week, we add 5 to each of the hours:
Runner | First Week | Second Week
--- | --- | ---
Jeff | 9 | 14
Mark | 5 | 10
Karen | 5 | 10
Costas | 5 | 10
Brett | 7 | 12
Nikki | 6 | 11
Jack | 7 | 12
Now we can find:
- Mean: (14 + 10 + 10 + 10 + 12 + 11 + 12) / 7 = 11.3
- Median: 11
- Mode: 10
- Range: 12 - 10 = 2
So the answer is:
mean = 11.3
median = 11
mode = 10
range = 2
What are the minimum, first quartile, median, third quartile, and maximum of the data set?
60, 50, 130, 200, 180, 150, 100, 140
A.
minimum = 50
first quartile = 80
median = 135
third quartile = 165
maximum = 200
B.
minimum = 50
first quartile = 107.5
median = 150
third quartile = 182.5
maximum = 200
C.
minimum = 50
first quartile = 80
median = 135
third quartile = 182.5
maximum = 200
D.
minimum = 50
first quartile = 65
median = 150
third quartile = 165
maximum = 200
B.
To find the minimum, first quartile, median, third quartile, and maximum, we first need to put the data in order:
50, 60, 100, 130, 140, 150, 180, 200
Now we can find:
- Minimum: 50
- First quartile: median of {50, 60, 100, 130} = (60 + 100) / 2 = 80
- Median: median of {140, 150} = (140 + 150) / 2 = 145
- Third quartile: median of {180, 200} = (180 + 200) / 2 = 190
- Maximum: 200
So the answer is:
minimum = 50
first quartile = 80
median = 145
third quartile = 190
maximum = 200
Simplify the radical expression.
square root 50.
A. 5 times square root 2.
B. 2 times square root 5.
C. 5 times square root 10.
D. 5
C. 5 times square root 2.
Simplify the radical expression.
Square root 56 times x squared
A. 28x
B. 2 times x times square root 14.
C. 2 times x times square root 7.
D. 2 times square root 14 times x squared
B. 2 times x times square root 14.
Simplify the radical expression.
Square root 490 times y to the fifth power times w to the sixth power
A. 245 times y squared times w cubed
B. 7 times y squared times w cubed times square root 10 times y
C. 7 times y squared times w cubed times square root 10 times y times w
D. 7 times square root 10 times y to the fifth power times w to the sixth power