Answer: 1

Prompt: Compute 8^7 mod 7.


Answer: 3

Prompt: Compute 9^8 mod 13.


Answer: 5

Prompt: Compute 6^6 mod 11.


Answer: 9

Prompt: Compute 8^5 mod 17.


Answer: 2

Prompt: Compute 3^8 mod 7.


Answer: 16

Prompt: Compute 4^6 mod 17.


Answer: 9

Prompt: Compute 9^6 mod 11.


Answer: 6

Prompt: Compute 7^7 mod 11.


Answer: 3

Prompt: Compute 7^8 mod 13.


Answer: 4

Prompt: Compute 7^6 mod 11.


Answer: 4

Prompt: Compute 7^4 mod 17.


Answer: 5

Prompt: Compute 3^5 mod 17.


Answer: 1

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [4, 3, 2, 1], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=2.5; MAD=1.0.


Answer: 1.375

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [5, 7, 10, 7], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=7.25; MAD=1.375.


Answer: 2.25

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [4, 3, 6, 10], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=5.75; MAD=2.25.


Answer: 2.875

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [12, 6, 4, 3], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=6.25; MAD=2.875.


Answer: 0.375

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [8, 9, 8, 8], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=8.25; MAD=0.375.


Answer: 2.5

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [5, 8, 1, 2], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=4.0; MAD=2.5.


Answer: 1.5

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [7, 9, 8, 4], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=7.0; MAD=1.5.


Answer: 2.75

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [4, 10, 6, 1], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=5.25; MAD=2.75.


Answer: 3

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [1, 5, 8, 10], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=6.0; MAD=3.0.


Answer: 2.25

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [11, 11, 8, 5], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=8.75; MAD=2.25.


Answer: 3.25

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [9, 1, 2, 7], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=4.75; MAD=3.25.


Answer: 2.75

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [3, 5, 12, 6], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=6.5; MAD=2.75.


Answer: 2.125

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [7, 6, 1, 7], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=5.25; MAD=2.125.


Answer: 3.5

Population-style /n not /n-1
Deviation from the mean

Compute mean
Average absolute deviations

Prompt: For the sample [1, 10, 9, 4], what is the mean absolute deviation from the arithmetic mean?

Solution: mean=6.0; MAD=3.5.


Answer: 7

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (0,3) and (-1,-4) as a simplified rational (or integer)?


Answer: 0

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (1,3) and (2,3) as a simplified rational (or integer)?


Answer: 0

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (-1,4) and (5,4) as a simplified rational (or integer)?


Answer: 4

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (-4,-3) and (-3,1) as a simplified rational (or integer)?


Answer: 0

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (0,0) and (3,0) as a simplified rational (or integer)?


Answer: 5/7

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (-3,-2) and (4,3) as a simplified rational (or integer)?


Answer: 4/3

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (1,3) and (-5,-5) as a simplified rational (or integer)?


Answer: 3/11

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (-5,-3) and (6,0) as a simplified rational (or integer)?


Answer: -6

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (2,3) and (3,-3) as a simplified rational (or integer)?


Answer: 3/7

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (4,3) and (-3,0) as a simplified rational (or integer)?


Answer: -1/7

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (4,0) and (-3,1) as a simplified rational (or integer)?


Answer: 2/5

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (4,6) and (-1,4) as a simplified rational (or integer)?


Answer: 0

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (0,3) and (3,3) as a simplified rational (or integer)?


Answer: -7/2

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (2,6) and (4,-1) as a simplified rational (or integer)?


Answer: -5/2

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (2,-5) and (0,0) as a simplified rational (or integer)?


Answer: -2

Simplified fraction
Two distinct x-coordinates

Prompt: What is the slope of the line through (5,-4) and (1,4) as a simplified rational (or integer)?


Answer: -3/2

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=2x^2 + (6)x + (5).


Answer: -2

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=1x^2 + (4)x + (2).


Answer: -3/2

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=2x^2 + (6)x + (4).


Answer: -3

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=1x^2 + (6)x + (-5).


Answer: 1

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=2x^2 + (-4)x + (3).


Answer: 1

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=2x^2 + (-4)x + (5).


Answer: 3

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=1x^2 + (-6)x + (4).


Answer: 2

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=1x^2 + (-4)x + (-5).


Answer: 1/2

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=2x^2 + (-2)x + (1).


Answer: -1

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=1x^2 + (2)x + (-2).


Answer: -1

Prompt: Complete the square (or use -b/2a) to find the x-coordinate of the vertex of y=2x^2 + (4)x + (4).


Answer: 90

Prompt: In the expansion of (1 + 3x)^5, what is the coefficient of x^2?


Answer: 5103

Prompt: In the expansion of (1 + 3x)^7, what is the coefficient of x^5?


Answer: 135

Prompt: In the expansion of (1 + 3x)^6, what is the coefficient of x^2?


Answer: 1512

Prompt: In the expansion of (1 + 3x)^8, what is the coefficient of x^3?


Answer: 1458

Prompt: In the expansion of (1 + 3x)^6, what is the coefficient of x^5?


Answer: 448

Prompt: In the expansion of (1 + 2x)^8, what is the coefficient of x^3?


Answer: 160

Prompt: In the expansion of (1 + 2x)^6, what is the coefficient of x^3?


Answer: 945

Prompt: In the expansion of (1 + 3x)^7, what is the coefficient of x^3?


Answer: 18

Prompt: In the expansion of (1 + 3x)^6, what is the coefficient of x^1?


Answer: 280

Prompt: In the expansion of (1 + 2x)^7, what is the coefficient of x^3?


Answer: 54

Prompt: In the expansion of (1 + 3x)^4, what is the coefficient of x^2?


Answer: 7

Prompt: Simplify log_5(a^5 · a^2) to an integer.


Answer: 8

Prompt: Simplify log_3(a^4 · a^4) to an integer.


Answer: 5

Prompt: Simplify log_5(a^3 · a^2) to an integer.


Answer: 5

Prompt: Simplify log_3(a^3 · a^2) to an integer.


Answer: 8

Prompt: Simplify log_2(a^5 · a^3) to an integer.


Answer: 6

Prompt: Simplify log_10(a^2 · a^4) to an integer.


Answer: 6

Prompt: Simplify log_3(a^2 · a^4) to an integer.


Answer: 9

Prompt: Simplify log_3(a^5 · a^4) to an integer.


Answer: 9

Prompt: Simplify log_10(a^5 · a^4) to an integer.


Answer: 7

Prompt: Simplify log_3(a^4 · a^3) to an integer.


Answer: 4

Prompt: Simplify log_5(a^2 · a^2) to an integer.


Answer: 4

Prompt: Simplify log_3(a^2 · a^2) to an integer.


Answer: 5

Prompt: Simplify log_10(a^3 · a^2) to an integer.


Answer: 1

Prompt: On the unit circle, what is the x-coordinate of the point at 0 degrees from the positive x-axis (standard position)?


Answer: 0

Prompt: On the unit circle, what is the x-coordinate of the point at 90 degrees from the positive x-axis (standard position)?


Answer: -1

Prompt: On the unit circle, what is the x-coordinate of the point at 180 degrees from the positive x-axis (standard position)?


Answer: 0

Prompt: On the unit circle, what is the x-coordinate of the point at 270 degrees from the positive x-axis (standard position)?


Answer: 1

Prompt: On the unit circle, what is the x-coordinate of the point at 360 degrees from the positive x-axis (standard position)?